51’. at AJ ABSTRACT THE MICROWAVE SPECTRA OF CYCLOPROPYL CARBOXALDEHYDE AND CYCLOPROPANECARBOXYLIC ACID FLUORIDE BY Hermann Nikolaus Volltrauer A short presentation of the theory of the rigid rotator is given. A description of the microwave spectrometer is presented together with a discussion of the factors influenc- ing observed line shapes. A scheme for absolute intensity measurements is presented with results for the J=0—1 transi- tion of OCS. Microwave spectra are analyzed for the ground states and three excited states of the torsion for cis- and trans- cyc10propyl carboxaldehyde. Three rotational constants were determined for all species except the excited states of the trans conformer for which only B and C could be obtained. Dipole moments for both ground state species were obtained as follows: oxygen cis to the ring; ”a = 2.019 D, ”b = 1.856 D, ”c = 0.0 D, u = 2.742 D; oxygen trans to the ring; ”a = 5.221 D, ”b = 0.0 D, “c = 0.495 D, u = 5.259 D. Spectra for the ground state and four excited states are assigned for cis-cycloprOpanecarboxylic acid fluoride and .m C8 :U as C51 .3. CL Hermann Nikolaus Volltrauer for the ground and two excited states for trans-cycloprOpane- carboxylic acid fluoride. Dipole moments for the ground states of both conformers of this compound were determined as follows: oxygen cis to the ring; ”a = 2.85 D, ”b = 1.65 D, ”c = 0 D, u = 5.28 D, oxygen trans to the ring; ”a = 5.44 D, “b 0.44 D, “‘c = 0.0 D, u = 5.47 D. A three parameter potential function for the internal rotation about the carbon-carbon bond was determined for both compounds by analysis of torsional excitation energies ob- tained from microwave relative intensities. For cyc10pr0pyl carboxaldehyde the potential function is (in cm‘l) V(a) = -40(1 - cos a) + 767 (1 — cos 2a) + 48 (1 - cos 5a) and for cycloprOpanecarboxylic acid fluoride it is V(a) = -265 (1 - cos a) + 900 (1 - cos 2a) + 172 (1 - cos 5a) Some circuits for use in a microwave Spectrometer used for teaching are presented. THE MICROWAVE SPECTRA OF CYCLOPROPYL CARBOXALDEHYDE AND CYCLOPROPANECARBOXYLIC ACID FLUORIDE BY Hermann Nikolaus Volltrauer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1970 hel ng ACKNOWLEDGEMENTS I wish to thank Professor R. H; Schwendeman for his help in all phases of this work. Financial aid from the National Science Foundation is gratefully acknowledged. ii IV TABLE OF CONTENTS Page I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . 1 II. THEORY. . . . . . . . . . . . . . . . . . . . . . . 5 III. INTENSITY.AND SHAPES 0F SPECTRAL LINES. . . . . . . 17 5.1 Introduction. . . . . . . . . . . . . . . 17 5.2 Intensity and Shapes of Spectral Lines. . . . .18 5.5 Modulation Broadening . . . . . . . . . . . . .19 5.4 Saturation. . . . . . . . . . . . . . . . . . 25 5.5 wall Collision Broadening . . . . . . . . . . 28 5.6 DOppler Broadening. . . . . . . . . . . . . 28 5.7 Other Factors Influencing Linewidths. . . . . 29 IV.-EXPERIMENTAL PROCEDURES . . . . . . . . . . . . . . 51 4.1 Introduction. . . . . . . . . . . . . . . . . 51 4.2 The Spectrometers . . . . . . . . . . . . . . 58 4.2a Absorption Cell . . . . . . . . . . . . 58 4.2b Other Microwave Components. . . . . . . 40 4.2c Electronic Components . . . . . . . . . 42 4.5 Frequency Measurement . . . . . . . . . . . . 46 4.4 Stark Effect. . . . . . . . . . . . . . . . . 49 4.5 Intensity Measurements. . . . . . . . . . . . 50 4.5a Temperature . . . . . . . . . . . . . . 50 4.5b~Relative-intensity Measurements . . . . 52 4.5c Absolute Intensity Measurement. . . . . 55 V} THE MICROWAVE SPECTRA . . . . . . . . . . . . . . . 59 5.1 Cyc10propyl Carboxaldehyde. . . . . . . . . . 60 5.1a Rotational Constants. . . . . . . . . . 60 5.1b Dipole Moments. . . . . . . . . . . . 70 5.1c The.AhOmalous Stark Effect of the 101-202 Transition of the trans Species 74 5.1d Relative Intensities and the Torsional Potential Function. . . . . . . . . . . 77 iii VI. VII. LIST APPE TABLE OF CONTENTS--continued 5.2 Cyclopropane Carboxylic Acid Fluoride 5.2a Spectra and Rotational Constants. 5.2b Dipole Moments. . . . . . . . . 5.2c Relative Intensities and the Torsional Potential Function. . . . . . . VI. DISCUSSION. . . . . . . . . . . . . . . . VII. A STUDENT SPECTROMETER. . . . . . . . . . LIST OF REFERENCES . . . . . . . . . . . . . . APPENDIX--EXPERIMENTAL RELATIVE-INTENSITY DATA iv Page 89 90 99 .108 115 127 150 TAB] II III IV VI VII VI I I IX. TABLE II. III. IV . VI. VII.- VIII. IX. LIST OF TABLES Coordinates for cis-cyclOprOpyl carboxaldehyde in the principal axis system. . . . . . . . . . Coordinates for trans-cyclOprOpyl carboxalde- hyde in the principal axis system . . . . . . . Observed and calculated (last three digits only) frequencies (MHz) for cis-cyclOprOpyl carboxal- dehyde. . . . . . . . . . . . . . . . . . . . . Rotational constants (MHz), moments of inertia (amu A2) and second moments (amu A2) for cis- cyclopropyl carboxaldehyde. . . . . . . . . . . Observed and calculated (last three digits only) frequencies (MHz) for trans—cycloPrOpyl car- boxaldehyde . . . . . . . . . . . . . . . . . . Rotational constants (MHz), moments of inertia (amu A2) and second moments (amu A?) for trans- cycloPrOpyl carboxaldehyde. . . . . . . . . . . Stark effect and dipole moment of'cis-cyclo- prOpyl carboxaldehyde . . . . . . . . . . . . . Stark effect and dipole moment of trans-cyclo- propyl carboxaldehyde . . . . . . . . . . . . . .Energy separation (cm-l) between successive torsional states for cis-cycloprOpyl carboxal— dehYde O O O O O O O O O O O O I O O O O O O O 0 Energy separation (cm-1) between successive torsional states for cis-cyclOprOpyl carboxal- dehyde; data obtained at the Hewlett-Packard Laboratories, Palo Alto, California . . . . . . Page 62 65 65 66 68 69 72 72 80 85 LIST TABII XII. XIII. XIV. XVI. 1VIII . XVIII . VII, LIST OF TABLES--continued TABLE ‘XI. XII. XIII. XIV. XVII. XVIII. .XIX. XXII. Page Energy separation (cm-l) between successive torsional states for trans-cyc10propyl carbox- aldehYde o o o o o o o o o o o o o o o o o ' o o 84 Energy separation'(cm’4) between successive torsional states for trans-cyclopropyl car- boxaldehyde; data obtained at the Hewlett- Packard Laboratories, Palo Alto, California . 86 Coordinates for cis-cyc10pr0panecarboxylic acid fluoride in the principal axis system. . 92 Coordinates for trans-cyclopropanecarboxylic acid fluoride in the principal axis system. . 95 Observed and calculated (last three digits only) frequencies (MHz) for cis-cyc10pr0pane- carboxylic acid fluoride. . . . . . . . . . . 94 Rotational constants (MHz), moments of iner- tia (amu A2) and second moments (amu A2) for cis-cyclopr0panecarboxylic acid fluoride. . . 95 Observed and calculated (last three digits only) frequencies (MHz) for trans-cyclo- pr0panecarboxylic acid fluoride . . . . . . . 97 Rotational constants (MHz), moments of inertia (amu A2) and second moments (amu A2) for trans-cyclopropanecarboxylic acid “ fluoride. . . . . . . . . . . . . . . . . . . 98 .Stark effect and dipole moment of cis—cyclo- propanecarboxylrc acid fluoride . . . . . . . 100 Stark effect and dipole moment of trans- cyc10pr0panecarboxylic acid fluoride. . . . . 100 Energy separation (cm-1) between successive torsional states for cis-cyclopropanecar¥ boxylic acid fluoride . . . . . . . . . . . . 102 .Energy separation (cm'l) between successive torsional states for cis-cyclOpropanecar- .boxylic acid fluoride; data obtained at the Hewlett-Packard Laboratories, Palo Alto, California. . . . . . . . . . . . . . . . . . 104 vi LI! TA] LIST OF TABLES--continued TABLE XXIII. HIV 0 Page Energy separation (cm-1) between successive torsional states fOr trans-cycloPropane carboxylic acid fluoride; data obtained at the Hewlett-Packard Laboratories, Palo Alto, California. . . . . . . . . . . . . . . . . . .104 .Potential constants (cm‘l) for cycloprOpyl carboxaldehyde, cycloprOpanecarboxylic acid fluoride and arcryloyl fluoride . . . . . . . 111 vii FIG] 11 LIST OF FIGURES FIGURE 1. Comparison between predicted and observed J = 0-1 transition of OCS at 150V Stark voltage. . . . . . . . . . . . . . . . . . . . 2. Cross-sections of sample cells . . . . . . . . 5. Crystal current versus microwave frequency for sample cells of various lengths. . . . . . . . 4. Block diagram of microwave spectrometer. . . . 5. Microwave frequency modulator. . . . . . . . . 6. Projection of cis-cyclopropyl carboxaldehyde in its plane of symmetry . . . . . . . . . . . 7. Projection of trans-cycloPrOpyl carboxaldehyde in.its plane of symmetry . . . . . . . . . . . 8. Observed and calculated Stark effect of the |M |= 1 component of the 101-202 transition of ftrans—cycloprOPyl carboxaldehyde . . . . . . . 9. Potential function and some energy levels for cycloPropyl carboxaldehyde . . . . . . . . . . 10. Projection of cis-cyc10pr0panecarboxylic acid fluoride in its plane of symmetry. . ... . . . 11. Projection of trans-cyclopr0panecarboxylic acid fluoride in its plane of symmetry . . . . 12. Potential function and some energy levels for cycloPrOpanecarboxylic acid fluoride . . . . . :15. Block diagram of student-spectrometer. . . . . 14.151612 tuned amplifier . . . . . . . . . . . . 15. Phase-sensitive detector and amplifier . . . . viii Page 24 54 55 59 55 61 61 78 88 91 91 106 116 118 119 LIST FIGU LIST OF FIGURES--continued FIGURE 16..15 kHz reference oscillator. 17. Power amplifier (modulator). 18. Modulator power supply . 19. 5 MHz oscillator . . ix Page .121 122 124 »124 rote fcrc 1615 the the: mean I. INTRODUCTION Microwave Spectroscopy and the study of potential barriers to internal rotation in molecules had their origins at about the same time in the middle 1950's. Before 1956 it was generally believed that rotation about carbon-carbon single bonds is free. Inconsistencies in thermodynamic data led Kemp and Pitzer (1) to the conclusion that this internal rotation is not free but is restricted by intramolecular forces. Coincidentally, the first microwave study was closely related to the internal rotation problem in that it involved the inversion Spectrum of ammonia (2). In addition to the thermodynamic method used by Kemp and Pitzer, many other means are available for obtaining the magnitudes of barriers to internal rotation including several spectrosc0pic methods (5). The purpose of this thesis is to describe the determin- ation of the potential functions for internal rotation in cyclopropyl carboxaldehyde and cyclopropanecarboxylic acid fluoride by microwave spectrosc0py. The information contained in the microwave Spectrum of a molecule of the type studied here is considerable, but so are the problems associated with extracting all but a small amount of it. The easily obtainable information includes rota transition frequencies and Stark shifts. From the transition frequencies moments of inertia, rotational constants, and ultimately structures can be determined if enough iso- tOpically substituted Species are studied. From the Stark shifts dipole moments can be calculated. Since the structure of a molecule in an excited vibrational state is similar to that in the ground state, the rotational constants in the two states are not very different. The changes in rotational constants are difficult to calculate theoretically, so that not much use is made of this accurate and potentially useful information.1 As a result of the small but observable dif— ference in the rotational constants, rotational Spectra are observed for many vibrational states. The intensities of rotational transitions in excited vibrational states relative to those of the ground state are almost entirely determined by the Boltzmann factors involving the energies of the vi- brational states compared to the ground state. Therefore, by measuring these relative intensities vibrational frequencies can be determined. Because the Boltzmann factor and hence the intensity is roughly halved for each 100 cm".L and the sensitivity of a Spectrometer is limited, not all vibrations can be studied. Furthermore, the number of excited states that can be observed for a given vibration is usually small, seldom greater than 7 or 8. 1However, see reference 4 for an application of this type. tec tai ine Spe The potential function governing the internal rotation (or torsion) about a single bond is often such that torsional energy spacings are more conveniently studied by microwave techniques than by infrared spectrosc0py. For molecules con- taining a methyl group (which has a very small moment of inertia) tunneling through the barrier often distorts the Spectrum in a way which is sensitive to the barrier height and makes possible its accurate determination (5). When heavier groups are involved in the internal rotation, tunnel- ing is usually not important and less accurate methods must be used to determine the potential function. If the compound can be transformed into two different stable isomers by an internal rotation about a Single bond, then at least three numbers are obtainable from the microwave Spectrum: the two torsional excitation energies and the energy separation of the ground states of the two isomers. These three pieces of data allow the characterization of a three-parameter poten- tial function. For the molecules studied here the potential functions chosen were of the form of a truncated Fourier cosine Series. Each of the molecules studied, cyclOpropyl carboxaldehyde and cycloprOpanecarboxylic acid fluoride, has two stable isomers, one with the oxygen atom cis and one with the oxygen atom trans to the cycloPropane ring. An electron diffraction study of cyc10propyl carboxaldehyde (6) indicated that it consists of a 55-45 mixture of the cis and trans species and that the height of the barrier separating the two was 1301' E (7) 0—01 (J '1 was in excess of 2.5 kcal/mole. Cis and trans species are more characteristic of what would be exPected for acrolein (7) than for a molecule with a carbon containing three single bonds attached to an aldehyde group. In the equilibrium configuration of acetaldehyde a methyl.C—H bond eclipses the C-0 bond (5). .Since eclipsed C-H and C-C bonds at opposite ends of a carbon-carbon single bond are not usually found for the stable conformation (6), a trans and gauche form might be eXpected for cyclOpropyl carboxaldehyde. The fact that cis and trans isomers are observed points to the Similarity of the cycloproPane ring and the vinyl group in this respect. The aim of this work was to obtain more accurate information concerning the potential function of cycloPrOpyl carboxalde- hyde and to extend the study to the related molecule, cyclo- propanecarboxylic acid fluoride. The following pages report the results of this investi- gation. A chapter is also devoted to the description of a "student spectrometer" which was partially built by this investigator (those circuits for which schematics are sup- plied) and which has been successfully used in an undergradu— ate physical chemistry laboratory during the past two years. Vne II. THEORY Since few real problems in quantum mechanics can be solved exactly, simplified models, which the systems under study are assumed to closely approximate, are commonly chosen as the basis for calculations. In the present case where the system consists of a molecule which can rotate in Space and which has among its vibrational modes one vibration (an internal rotation) of lower frequency than any other, the model of the molecule will be a structure of two rigid parts, the frame and the top, connected by a bond about which rotation can take place. A potential function governing this internal rotation is assumed to be of the form 3 V(a) = fi- 2 V1 (1 - cos i a) (2-1) i=1 Where a is the angular displacement from a configuration with a plane of symmetry. The potential function has been truncated after only three terms because only three pieces of data can be obtained from our eXperimentS. The effect of this truncation is discussed below. The two molecules studied can exist in cis and trans configurations and in each molecule a = 0 has been chosen to correSpond to the Species with the oxygen atom trans to the ring. whe t3; 3: axi A theoretical treatment of a problem of this type—- where the frame (the ring) has a plane of symmetry and the t0p is planar——has been presented by Quade (8). In this formulation a coordinate system is chosen in which the z axis is parallel to the bond about which rotation is taking place and the y axis is in the plane of symmetry. In a ‘ center of mass coordinate system with axes defined in this way the angle dependent moments and products of inertia are as follows:1 I = I + 21 cos a - I sin2 a xx oxx 1xx a I = I + I sin2 a YY OYY a I = I + 2 I cos a 22 022 1xx I = -I Sin a cos a — I Sin a xy a 1xx I = -I sin a (2-2) xz x I = -I - I cos a yz oyz x Ixa = -Ix Sin a Iya = Ix cos a Iza = -Ia - 211xx cos a I = I aa a In a coordinate system as Specified above but with the z axis coinciding with the bond about which rotation is taking place the terms on the right side of Equation (2-2) can be expressed as functions of the coordinates and masses of the atoms as follows: 1There is a sign error in reference 8 for Iyz' la‘z lei Ir; VII where M tions labeled F involve only the atoms of the frame, MP3 II II M8" 2 -2 _ 2 yi MB F 2 miyi and B i i T Zlmiyi. M M The summa- . A 1 those labeled T involve the atoms of the t0p only while the un;. labeled summations include both. The I's appearing on the left Side of Equation (2—2) define a moment of inertia tensor Then in terms of the angular transpose is w written as I I I xx xy xz xa I I I I I XY YY YZ Ya I I I I xz yz zz za Ixa Iya Iza Iaa) velocity vector whose (wk, my, wz, a) the kinetic energy can be T = w ° I ° w (2-5) Expressing the kinetic energy in terms of angular momenta gives _ , , _ _ 2 T - 2 H11 (Pi pi) (Pj pj) + up (2-4) wh mo th sea the the fe: tht em fOL In ine where the P1 are the components of the total angular momentum along the molecule-fixed x, y, z axes, the pi are the components of the internal angular momentum along the same axes, p is the momentum conjugate to a, and the ”i are the components of the matrix inverse to I. The torsional part of the kinetic energy will involve the terms with pi and the rotational part the terms with Pi' The interaction of the two will be contained in the cross-terms Pipj' An ef- fective reduced mass, “T' which is a complicated function of the angle a, can be used to express the purely torsional energy. By expanding “T in a trigonometric series and keep- ing only the first two terms the torsional Hamiltonian is found to be H = (u; +-u% cos a) p2 + V (a) (2-5) In this equation u; and u; can be written in terms of the inertial coefficients of Equations (2-2) and are 0: _ 2 _ 2 _ n.1, fi-(ony 1022 on2 IX)/D (2 6) i = _ LlT (ony lex onz Ix)/D = 2_ 2 _ 2 2 where D Ia(ony 1022 + Ix onz) ony (Ia + lex) _ 2 I022 Ix + 2 onz I1xx Ix Since both u; and u; are approximately known from the assumed geometry of the molecule, only three quantities, the potential constants, remain to be determined. Measurement of the torsional excitation energies of the two Species and th St USe Cis aha the energy separation of the two isomers in their ground states provides the three numbers needed to calculate the potential function. The torsional energies of the molecule are calculated by setting up and.ldiagonalizing the matrix of Equation (2-5) using exp(ima) as basis functions (m-O, 1.1,.1 2, . . . .). The non-zero elements of this matrix are (.m'HIm) =ugm2+§(vl+v2+vs) (ml uépcosap‘rvicosa! mi1)=g(mi1) “5+ 3;, (2-7) (m I V; cos i a I m i.i) = 31- i = 2 and 5 Diagonalization of a sufficiently large matrix of these elements will yield the necessary eigenvalues and eigenvectors. Relative probabilities for a having certain values can be used to determine whether a given eigenvalue belongs to the cis or trans Species. Since there is no noticeable distortion of the rotational Spectrum due to the torsion in any of the torsional states, the theory of the asymmetric rigid rotator can be used to analyze the spectra. A brief presentation of this theory will now be given (9). For each Species, cis or trans, an effective rigid rotator will be assumed. This assumption is justified by the fact that for most molecules calculations of the fre- quencies of transitions involving the lower energy levels na- By: in! m ON 3151 to tar 0f 10 based on the rigid-rotator approximation reproduce the experi— mental frequencies to the accuracy with which they are measured routinely. If xi, yi and 21 are the effective rigid-rotator coordi— nates of atom i with mass mi in a center of mass coordinate system, then the moments of inertia Iaa and products of inertia Iab are defined by 2 2 - I 2 m. (bi + Ci)’ (2 8) aa 1 Iab = ’5 mi ai bi’ where a, b and c stand for x, y and z in any order. The co- ordinate system chosen to calculate this inertia tensor (the matrix made up of the lab) can be rotated in such a way as to make the products of inertia zero. The diagonal elements obtained from this diagonalization of the matrix I are called the principal moments of inertia and are labeled Ia’ Ib and Ic in order of increasing size. In some calculations second moments, which involve dis- tances from a plane instead of an axis, are useful. In terms of the principal moments, the principal second moments are = _ = 2 Paa Q ( Ia + Ib + IC) >3 miai = — = 2 - Pbb i? ( Ia Ib + Ic) 2: mibi (2 9) = — = 2 Pcc §.( Ia + Ib Ic) E mici For each of the two molecules treated here the second moment involving coordinates measured from the plane of symmetry 11 includes contributions from two carbon atoms and four hydrogen atoms of the ring. Thus, this second moment should have nearly the same value for both Species of both molecules. The fact that this is the case is the strongest evidence that the plane of symmetry is present. The rotational Hamiltonian of a molecule can be written in terms of the rotational constants and is H=4—7r'2-(AP2+BP*2+CP2) (2—10) h a b c h In this equation A = 8W2 I etc. so that A 2 B 2 C. a The P's here are the components of the angular momentum along the three principal aXes and Should not be confused with the second moments above. The solution to the equation H‘V = EH’ can not be given in closed form for the above H if all three rotational constants are different and none is zero. Solu- tions are readily obtained if two rotational constants are the same. A molecule with two equal rotational constants is called a symmetric top, and is classified further as either a prolate or oblate symmetric top depending on whether B = C or B = A, respectively. Using the solutions of either the prolate or oblate top as basis functions a matrix can be set up and diagonalized to yield the energies of the asym- metric top (A # B #’C i 0). - From the commutation relations for angular momentum operators in a molecule-fixed axis system, 12 [P,P]=-iHP, x y z [ Py, Pz ] = —1h PX , (2-11) [PIP ]=-ifip , z x y matrix elements for Px’ Py and P2 and their squares can be calculated . In a basis in which P and P2 = P 2 + P 2 + P 2 are 2 x y z diagonal the matrix elements are (J,K| Pal J, K) =HZJ(J+1) (J, KI pzl J1..K) =HK (J,K|Px2|J,K)=(J,K|PyzlJ,K)=12r—' [J (J + 1) - K2] (2—12) (J. Kl Pyzl J. K12) =- (J, KI anl J, K12) = 2 3-2-- [[J(J+1)-K(Ki-1)] [J(J+1)- (Ki-.1.) (K:t:2)]}‘lr The matrix elements given here are the only non-zero elements for P 2, P 2, P 2. x y 2 For a symmetric top the energies are equal to the diagonal elements only since the sum of the off-diagonal elements is zero (for a prolate tOp a {-9 z, b “x, c 9y) . This gives for the energy of a prolate symmetric top E=hJ(J+1)B+h(A—B)K2 (2-15) The quantum numbers J and K serve to label the energy levels of the symmetric top. In the case of the asymmetric tOp J is still a good quantum number and is used to label the levels, 15 but since there is no direction in the molecule along which the projection of the total angular momentum is constant, K loses its significance except for near symmetric tops. The energy levels of an asymmetric tOp are usually labeled as JK_1',K+1 where K_1 is the K value which the top would have in the limit in which B -é>C (a prolate top) and K+1 is the K value which the tOp would have in the limit as B -+-A (an oblate top). Since the matrix for the energy is symmetric about both diagonals and has elements removed from the diagonal by two as the only off-diagonal elements, each submatrix correspond- ing to a given J can be factored into four smaller submatrices, two for even K and two for odd K. The transformation which factors the even and odd K matrices into two each is known as the Wang transformation. Its effect is to change from a basis involving functions such as [ ¢(J,K)] to functions like [2)(J,K) i w (J, -K)]. Transitions between various levels can be classified in a number of ways. If J increases by one, the transition is an R-branch transition. If J decreases by one, it is a P-branch transition, and no change in J occurs for Q-branch transitions. A further classification involves the component of the dipole moment responsible for the transition. An a-type transition, for instance, is one for which the dipole moment matrix element involving “a is non-zero. The quantum numbers of the energy levels involved in the transition CCDI int a m 0f 993 Spe 14 contain the information necessary to classify transitions in these ways. If the first subscript on J (corresponding to K_1, the limiting prolate tOp K) changes by an even integer between the two levels and the second subscript (K+1, the limiting oblate tOp K) by an odd integer, the transition is an a-type transition. The reverse is true for c-type transitions, while both subscripts change by odd integers for the b-type transitions. The most intense transi- tions are generally those involving changes in the K's of zero or one although larger changes are possible. Stark effect (10,11) When a rotating molecule is exposed to an electric field, an additional term must be added to the Hamiltonian to take into account the interaction of the field with the electric dipole moment of the molecule. .Since the degree of inter- action is a function of the magnitude of the dipole moment, a means of obtaining dipole moments is available. The result of this interaction, called the Stark effect, also makes possible the modulation technique of the Stark modulated spectrometer (12). The term added to the Hamiltonian is —-L ._L HE = - p. - E (2-14) where u is the dipole moment and E the electric field. If a molecule has an average non-zero component of the dipole moment in the direction of the field, the energy change due to the field is proportional to the product of the average w) ti Ia Io ab is Ni; 15 component and the first power of the field, and a first- order Stark effect occurs. If no such average component exists, the field will induce one and will then interact with it to give a (usually much smaller) second-order effect which is proportional to the square of the field. .In asym- metric-t0p molecules the second-order case always applies unless degeneracies are present, in which case deviations from the quadratic dependence on the field become important. The presence of a static electric field defines a di- rection in Space along which the angular momentum is quan— tized in units of fi'M, M ranging from -J to J. In the absence of the field M does not enter into the energy expression and was therefore omitted above. The energy corrections according to second-order perturba- tion theory are (‘91 JHE W1) (‘pj IHE I'Qi) 3' Bi ' Ej AEi = (2-15) In this eXpression the «Pi I HE I 4Q) are the dipole moment matrix elements multiplied by the field strength in the asymmetric rotor representation which diagonalized the energy matrix. The transformations necessary to bring the asymmetric rotor dipole moment matrix elements into this form are avail- able from the solutions of the energy problem. Because HE is proportional to the field and the dipole moment, AE will be pr0portional to their squares. Analysis of Equation (2-15) shows that it can be written as a sum of two terms, In the 16 AB. = (z 2 32 A.) + M2 (2 2 15:2 B.) (2-16) 1. k FLI< 1k k “1‘ 1k In this exPression the summations are over a, b and c, and the A1 and B1 are constants which are evaluated from the k k perturbation sums in Equation (2-15). 3.1 nine tion sion inte nal the must the iSc is m Cell atio the fOr ‘ The e III. INTENSITY AND SHAPES OF SPECTRAL LINES 5.1 Introduction The line shape and intensity of a transition is deter- mined if the absorption coefficient is known as a function of microwave frequency. Since this is exactly the informa- tion that the spectrometer is designed to provide, a discus- sion of the factors influencing the exPerimentally determined intensities and line shapes is apprOpriate. Before the sig- nal from the detection system can be interpreted, however, the relationship between it and the fractional absorption must be found. Two cases will be considered. For case 1 the crystal current is allowed to vary as the radiation level is changed, while for case 2 an additional microwave signal is mixed with the signal that has passed through the sample cell in such a way as to keep the crystal current constant. If E8 is the electric field due to the microwave radi- ation passing through the sample and Eb is the value of the field added to keep the crystal current fixed (Eb = 0 for case 1), then the crystal current IC can be approximated by _ B _ IC - k (ES + Eb) _ (5 1) The exponent B is equal to 2 for the ideal diode, but for 17 18 real diodes both k and B can depend on IC so that this expression is valid for small variations in Ic only. The change in crystal current due to absorption can be shown to be prOportional to APS PS-é for case 2 and approximately to P(2-1) s APs for case 1. P8 is the power level in the cell and APs is the power absorbed by the sample. .In either case the detected signal is proportional to the amount of radia- tion absorbed and line Shapes are therefore accurately reproduced. .This assumes that the power level is constant over the frequency region where appreciable absorption takes place. Use of the power dependence on the detected signal will be made in the discussion of saturation. 5.2 Intensity and Shapes of Spectral Lines Many factors contribute to linewidths and line Shapes and which of them dominates depends on the conditions chosen for the experiment. In moSt cases the interactions of mole— cules resulting from close approaches make the major contribu- tion. Because of the many different types of interactions possible (15), accurate quantitative calculations are diffi- cult in most cases, but a qualitative line shape which agrees well with experimentally determined Shapes is readily calcul- able. The result of such a calculation will be used here as a starting point to which corrections due to factors other than molecular collisions will be applied. The absorption coefficient 7 as a function of microwave frequency v assuming only collisions contribute to broadening is Her T i mat. t i 3101. 19 is (14) 8w2 2 2 1/2nt 5ckT Nf I ”ijl V (v-vo)a + (1/2nt)2 (5—2) Here c is the velocity of light, k is Boltzmann's constant, T is the absolute temperature, ”ij is the dipole moment matrix element, v0 is the frequency at the center of the line, t is the mean time between collisions and Nf is the number of molecules in the lower state. The value of IV-VOI for which 7 is one-half of its maximum value is equal to 1/2nt and is called the linewidth. Corrections to this line Shape or to the linewidth due to modulation, saturation, the DOppler effect, wall collisions and instrumental deficiencies will be discussed. 5.5 Modulation Broadening A wave train of frequency f; when periodically inter- rupted at a frequency f2 will have frequency components equal to the sum and difference of f1 and f2. A similar combina- tion of the microwave frequency and the modulation frequency can be observed under suitable conditions. .Calculations which follow the approach used in Townes and Schawlow (15) for Sine-wave modulation are in good agreement with measure- ments made here for the J z 0 - 1 transition of OCS using squaredwave modulation. Let the wave function for the molecule for the state i be $1; then whe wi ( ex; Sin the the 3%. . we: 20 ¢i = V10 exp ( -% f: Wi(t)dt), (5-3) where wio is the wavernction with no electric field, and Wi(t) is the instantaneous molecular energy which can be expressed as o ' A 2 Wi(t) - wi + wi E (t). Here W10 is the energy with no field, Awi is the change in 'Wi for unit field and E(t) is the square wave with frequency v0 which can be written as an infinite series a) . Em = E0 (4 + s 2 314:“ ggfiflmt) (23-4) n=o Since E2(t) = EOE(t) (a square wave squared is a square wave), the integral in equation (5-5) becomes 0 2 t _ 1 cos(2n+1)2wvgt Wi t + AWiEo [2' F7; 2 (2n+1)2 + constant] (5—5) If a transition can take place between states 1 and j, the intensity of the absorption will be pr0portional to the Square of the integral f * dn'= [ 2 v t + 2 Av E2[ §-- 1 2(’1 W1 ”ij ”P 7’1 ij 7’1 ij Fvo cos(2n+1)2WVQt _ Z (2n+1)2 ]] (5 6) where ”ij = f ¢i°*u¢i°dt, vij = Eigfll. and Avij = AW . AW . l "' l h 21 An exponential, eXp(i a cos b), can be eXpressed as an infinite series of Bessel functions (16) oo exp(i a cos b) = 2 ik Jk (a) eXp(ikb). (5—7) k=—a> *- With this substitution the integral f¢i uwjdm becomes . Av--E2 21ri.(v.. —J-9—9-)t oo ‘00 .k znv- ~22 ij e 13 2 F7 2 1 JkngoI2n¢1)2) n==0 k=-oo u e27ri [vok(2n+1)]t (5-8) If the sample is eXposed to radiation having one of the microwave frequencies appearing in this expression absorption will take place. For a frequency Vij+ égift-132+va where a) m = Z k(n,m)[2n+1] (5-9) n=0 the intensity of absorption will be proportional to °° 2Avi'E2 2 ( Z 1’ Jk(n,m) [ —_'J—?7rvo(2n+1) 1’ ' n—0 where the sum consists of as many terms as there are possible ways of getting a particular value of m. The k(n,m) are positive or negative integers (they are the k's in Equation (5-8)) and the form of Equation (5-9) is such that no ex- pression other than Equation (5-9) relating the dependence of the k's on n and m can be given. The frequencies obtained with negative m's correspond to zero Stark field transitions while positive m frequencies belong to the Stark component. 22 Since Jfk = Jfi , a symmetrical pattern of lines separated by multiples of the modulation frequency from a point equi- distant from the transition and its Stark component is expected. Because any value of m can be obtained infinitely many ways, calculations of the individual intensities would be impossible if it were not for the fact that Jk(Ar) is small for small Ar and large k and J0(Ar) is close to 1 for small Ar (17). For m=5, for example, the terms in three of the infinitely many sums are as follows: 1. k(l) = 1, k (nfii) = O 2. k(O) = 5. k (n#0) = 0 5. k(0) = -5, k (1) = 2, k (n7‘0 or 1) = 0 Thus a transition will appear as a series of 5 or 4 lines each separated from the next one by the modulation frequency and all moving in the direction of the Stark component as the square-wave amplitude is increased. .The intensity of these lines will start from zero, increase to a maximum at the transition frequency and then decrease to zero again. Since the positions of these lines change linearly with E3, two series of lines will appear if E3 has two values and more if E0 has more than two values. Because E0 is not constant (due to instrument difficulties) but is effectively a dis- tribution about some average value, the individual lines will broaden as the square wave is increased. Ultimately, the broadening is so severe that the individual lines can not be 25 resolved, leaving a single line with a half-width approximately equal to the modulation frequency. A comparison between experiment and the calculations outlined above is given in Figure 1 for the J= 0 - 1 transi- tion of OCS at 12162.976 MHz. The modulation frequency v0 is 0.1 MHZ and AVij is 2.6 x 10-5 MHz/(Egigfi. The effect of this kind of splitting on intensity measure- ment can be important. .The error in intensity due to the Splitting of the transition can be shown to be 2a/[(1+2a) (W2 + .01)] % for a pattern consisting of one center line with intensity 1 and two sidebands each with intensity a. For a = 0.4 and 2W, the width at half height, equal to 0.62 MHZ the error is 4%. For other patterns the error is less. To resolve these modulation sidebands, all other sources of line broadening must be minimized. This means Operating at a low temperature to reduce doppler and wall collision broadening, a low power level to avoid saturation broadening, and most importantly a low pressure to reduce collision broadening--usually the main source of broadening. The ap- proximate linewidth of the lines in Figure 1 is 50 kHz. Taking doppler and wall collision broadening into account, the linewidth due to molecular collisions is apparently 40 kHz assuming no saturation broadening. Using 6 MHz per millimeter as the pressure dependence<1f linewidth for the J = 0 - 1 transition of OCS (18) the pressure can be calcu- lated to be approximately 7 microns. 24 12165.00 MHz 12165.50 MHz Figure 1. Comparison between predicted and observed J % 0 - 1 transition of OCS at 150 V Stark voltage. Calculated intensities use a linewidth of 50 kHz. 25 5.4 Saturation (19) Absorption of microwave radiation by a sample is accom- panied by a net decrease in the population of the lower state involved in the transition. As a result of this saturation effect the amount of radiation absorbed is not proportional to the power level. Let n be the instantaneous difference in the pOpulations of two states involved in a transition and let a be the equilibrium difference when no radiation is present. The effect of radiation of the apprOpriate frequency is to de- crease n according to dn _ _ _ _ (EEIrad - - 21y - 2 I nk. (5 10) . . _.3; _ 8W2 2 1/2w1 . Here k 18 defined by k - n - 2ch u‘v (v—Vo)2 + (1/2wf)2 and I is the radiation intensity (quanta/(cm2 sec)). Collisions will tend to keep n near a; — i. _ - _ coll - - T (n a) (5 11) dn (at) where T is the mean time between collisions restoring equilibrium. In microwave Spectroscopy this T is usually assumed to be the same as the T appearing in the expression for 7 which is the mean time between collisions responsible fOr line broadening. .If the radiation is turned on at time t = 0 when n = a, then n 1 [ 1 + zine exp (- %~{21ke + 1 })1 (5-12) = a 21kt + 26 When the steady state value of n [in the presence of radi- ation] is substituted into the equation for y, the result is 8112 v2 U221 .______ , 2 _ 5ch a (v-vo)2 + 1/2wn' + égggl I (5-15) At v= v0 7 is proportional to 1/(I + const.). For the second of the two cases considered at the beginning of this chapter é.01' the signal is proportional to 7 I i . _ I _ Signal - C I + const. (5 14) This function has a maximum which can be shown to be propor- tional to a and independent of 13 Therefore the maximum sig- nal is a measure of the equilibrium population of either state since a is related to the population of the lower state by the relation a = n?- hv/kT (5-15) Equation (5-15) is derived assuming a Boltzmann distribution and hv/kT <3<1. This direct relationship between the popu- lation of a state and the signal obtained from the Spectrometer has been used by Harrington as the basis for an intensity measurement scheme (20). When the variation of power density in the waveguide is taken into account, the relation between 7 and I is more complicated, but the conclusion that the maximum signal obtainable is prOportional to n? is still valid. For the first of the two cases considered above, where the crystal current is allowed to change with the radiation 27 intensity, the signal is a Simple function of the power level only if the crystal current is prOportional to the power. In this case, neglecting the power-density variation in the waveguide, I 7 g I + const. (5-16) Since crystal current is not prOportional to power over a wide range, not much use of the saturation effect is made in this case. Instead, intensity measurements are made by measuring line height and linewidth and avoiding saturation. Under conditions of no saturation the product of line height and linewidth is also proportional to the population of the lower state and independent of T. Therefore, equivalent information can be obtained in this case and the case dis— cussed above. The signal intensity at the line center is a well-defined quantity, if saturation is negligible, Since it is independent of pressure over a wide pressure range. To relate the signal intensities of various transitions, however, linewidths must be taken into account. When square-wave modulation is used, the molecular absorption frequency switches between two values at a rate which is equal to the modulation frequency. If the frequency of the radiation is kept constant this-is equivalent,;as far I as absorption is concerned, tthurning the radiation on and off at the modulation rate. For a high modulation frequency the steady-state value of the population difference used to calculate the saturation effect might not be approached 28 sufficiently closely, making a correction necessary. The fractional error in the total absorption at the radiation level necessary to obtain a maximum Signal for case 2 dis- cussed above can be shown to be approximately f/(f + WAV) where f is the modulation frequency and Av is the half widthi1 For a halfdwidth of 0.2 MHz and a modulation frequency of 100 kHz the absorption error is 7.4%. The error in the detected signal can be obtained from the first Fourier com- ponent of the exponential exp(-2t/T) between t =_0 and t a 1/f. 5.5 Wal; Collision Broadening (22) In the expression for line shape, the linewidth Av is related to the mean time between collisions of molecules 1' by Av = 1/217‘T. If molecules with molecular weight M and at temperature T are confined in a waveguide where the smallest dimension S is much smaller than the next smallest dimension, then the mean time between collisions of the molecules with the two closest surfaces will beIJ5S/v'where v is the mean velocity 4 4JRT723M1 The resulting linewidth is v/2n9J5 which for OCS at 2000K and with S g 0.47 centimeters is 5 kHz. 5.6 DOppler Broadening (25) For molecules traveling with a velocity v relative to the direction of prOpagation of the radiation peak absorption 'c lThiS assumes Equation (5-12) to apply which is not strictly true. See reference 21. 29 will occur at a frequency v0 - v0 %- if the transition frequency is v0. Since the relative number of molecules with velocity v in any one direction is proportional to mv e" 2KT , absorption at v0 - vog-is proportional to this . _ m (V‘VQ (3)2 factor. The absorption at v is prOportional to e ZET’ v0 . This is a gaussian shaped curve whose intensity is one-half 2len m . giving a half-width of maximum for v = v0 + £9- of ¥?- -£%lfl- . For the J = 0 - 1 transition of OCS at 2000K. the Doppler linewidth (half-width) is 8 kHz. 5.7 Other Factors Influencing Linewidths Although in principle instrument deficiencies can be eliminated, they do occur in practice and their effect on measurements should be determined. A problem more troublesome with BWO'S than with klystrons is ripple in the power supply. If the tuning ratio of a microwave oscillator is 10 MHz per volt, then a 5 millivolt peak-to-peak ripple in the power supply will result in a .50 kHz frequency modulation. The increase in linewidth due to this ripple is not nearly this large since only the curva— ture in the line shape causes it to increase at all. The increase in linewidth for a 0.4 MHz wide line is only 1% while a similar decrease in intensity takes place. Another potential source of line distortion is the square- wave generator. Ideally the square wave has only two values, zero and some constant value E0. Real square waves always have a non-zero transition time, and their value during the 50 off period is v0 which is seldom zero. The non-zero transi- tion time together with the inhomogeneity of the electric field inside the sample cell (due to sample cell design) results in absorption taking place along the entire frequency range between the line and its Stark component. For a second- order Stark effect and a linear rise period, the major part of this absorption will take place near the zero field line and will cause it to be asymmetric. If the rise and fall time of the square wave is 0.5 microseconds at 100 kHz then more than 10%tof the absorption will occur between the line and its Stark component. The net effect on the signal obtained from the detection system (which is the first Fourier com- ponent of the absorption signal) is very small however, amounting to about 1% for the case discussed. The principal result of'a non-zero voltage during the off-period will be to shift the line if it consists of only one Stark component. More serious distortion results if more Stark components are present. In either case an error in the frequency measurement will occur. This error can sometimes be eliminated by performing a quantitative Stark effect measurement and using A as the transition frequency where A is obtained from a fit of the data to the equation v = A + (81) E2. Slopes, 81, must be determined for both positive and negative E since the effect of a non-zero off-voltage v0 is magnified when it is added to some other large voltage. IV. EXPERIMENTAL PROCEDURES 4.1 Introduction Before describing the Spectrometer and its Operation a short description of microwave behavior will be given (24,25). Electric and magnetic field distributions in a waveguide can be calculated with the aid of Maxwell's equations. Such calculations Show that in general infinitely many different modes of propagation are possible, the solutions in fact form- ing a complete set. Because waveguides are not made of perfect conductors, some radiation will be lost to the walls as heat. This attenuation depends on the size and composition of the waveguide, the mode of propagation, and the frequency. For a given size of waveguide there exists a frequency, the cutoff frequency, below which the attenuation is infinite so that no radiation can be transmitted. .Since this cutoff frequency is different for each mode, it is possible by the proper Choice of waveguide Size to allow only one mode to exist at a given frequency. Because all higher frequencies are also transmitted, this unique mode must necessarily be the one with the lowest cutoff frequency. This mode, the so-called TElo mode, has an electric field distribution whose component across the large 0 a o c XIT a c o dimenSion passes through one maXimum (a Sin ;-distribution, 51 52 with a the large dimension) and whose components in the other two directions are zero. .In a 0.400 inch x 0.900 inch wave? guide the cutoff frequency of the TElo mode is 6.5 GHz while for the next higher mode, the TEgo mode, it is 15 GHz. Any discontinuity in the waveguide will disturb the fields to some extent, resulting in the generation of higher modes and partial reflection of the radiation. If conditions are such that only one mode can be easily prOpagated, the higher modes will be attenuated and a decrease in transmitted power will be observed. If like obstacles occur at distances from each other equal to one-fourth the wavelength of the radiation (or odd multiples thereof) the reflections due to them will cancel because their phases will differ by 180°. Reflections will reinforce each other if they are caused by discontinuities at separations equal to one—half wavelength or multiples thereof. The reflected wave from the second obstacle when re-reflected from the first obstacle will also either reinforce or diminish the original radiation level depending on whether the separation of the two reflectors iS one-half or one-fourth wavelength. .For fixed obstacles, a change in frequency will alternately separate them by multiples of one- half the wavelength and multiples of one-fourth the wavelength. resulting in variations in transmitted power with changes in frequency. If discontinuities are far apart, the change in frequency required to fit an extra wavelength between them is relatively small so that more power fluctuations are expected 9'1 In In a! 55 for a given frequency interval than if the discontinuities are close together. There are a number of irregularities introduced into a waveguide to make it useful as an absorption cell and each can be expected to make some contribution to the reflection problem. First and of most importance is the septum and its teflon support. The septum is a strip of metal that passes through the length of the waveguide parallel to the larger dimension and equidistant from both sides. The teflon insu- lates the septum from the waveguide making it possible to apply an electric field to the sample. .Cross-sections of sample cells using two different methods for supporting the septum are illustrated in Figure 2. Plots of rectified crystal current (roughly proportional to transmitted power) versus frequency for absorption cells constructed in these two dif- ferent ways are given in Figure 5. The conventional design of Figure 2b is used for the first two cells of Figure 5 with lengths of 95 and 585 centimeters, while the design of Figure 2a1 is used for the third cell whose length is 122 centimeters. From the qualitative discussion of reflections given above, the shortest cell should have the fewest power dips. This assumes that these power fluctuations are due to reflections originating at the ends of the teflon strips and the septum. The design of Figure 2a is obviously superior to the con- ventional design. 1The design of the cell in Figure 2a was modeled after the sample cell of the Hewlett-Packard Spectrometer but see also reference 26. Pic 54 -—#- 0.062 m -—~w ‘ 0.051 * 0.062 I..___ J_I'1 ’ TI a - new design ‘ g—I -—s- 4 0.051 1.000 0.062 r ‘ l I ‘~—-0.500 -—*I b - conventional design Figure 2. Cross-sections of sample cells--dimensions in inches. 55 0.9W 95 cm — design of Figure 2b 008'- 78 5 0.9 4.) c o g 585 cm - design of Figure 2b 0 H 0.8~ m 4.) n >1 H U 122 cm - design of Figure 2a 0.8 L 1 9200 MHz 9500 Figure 5. Crystal current versus microwave frequency for sample cells of various lengths. In s». 56 Sharp dips in the power versus frequency curve are undesirable for a number of reasons. The obvious reason is that it is easiest to compare transitions if they are observed under the same conditions. .Secondly, because the frequency of microwave sources is voltage sensitive, some frequency modulation occurs due to the small amount of ripple and noise in the power supplies. This frequency modulation will have no effect on the rectified crystal current if there is no power variation with frequency. On the other hand, at microwave frequencies where power variations occur the frequency modula- tion will cause a power modulation which will be detected and displayed if it has any frequency component equal to the Stark modulation frequency. The resultant signal is prOportional to the lepe of the power versus frequency curve. This un— wanted frequency modulation has been observed in the spectrom- eters using backward wave oscillators as microwave sources, but to a large part has been eliminated by additional filter- ing of the power supply. The appearance of these derivatives suggested a method of absolute intensity measurement which is discussed in a later section. If the unwanted frequency modulation is of random nature (noise), only additional noise will appear at the output. An even more troublesome effect of the power dips is due to their origin, namely reflections. When part of‘the radia- tion is reflected several times in a sample cell, the absorp- tion due to the sample will increase. For this reason the 57 relative intensities of two transitions measured at different frequencies may be incorrect. Consistent ratios of intensi- ties should be obtained if the geometry of the sample cell does not change with time. However, the geometry may change if the cell is cooled with dry ice because the temperature cycling causes the septum and teflon to move, resulting in a change of the pattern of power dips. When the septum and teflon of the conventional design are initially placed in the waveguide, the teflon is stretched because of the tight fit necessary to prevent vibrations in the finished cell. Since one strip of teflon is firmly attached at one end of the wave- guide where contact with the septum is made, its Shrinkage upon cooling will draw the septum toward this end. The other strip of teflon shrinks in a more symmetrical manner. This relative motion of the two strips of teflon with respect to each other and to the septum is believed to be responsible for the changing appearance of the power versus frequency . curve. The geometry of the 122 centimeter cell is expected to be more stable than that of the other cells and since the power dips are farther apart and fewer in number, changes are not noticeable. Unfortunately, this sample cell was not available when most of the relative-intensity measurements were made. Other microwave components will usually not cause any additional difficulties if they are used over the frequency range for which they are intended. 58 4.2 The Spectrometers A simple absorption spectrometer might consist of a source of radiation, a sample cell, and a detector. Since the importance of gas phase microwave spectroscopy is in large part a result of its high resolving power, additional instrumentation is required for accurate frequency measure- ment. A further increase in the complexity of a Spectrometer results from the need to detect fractional absorptions of very small magnitude-—usually in the parts per million range. A block diagram of a spectrometer which satisfies both these demands is given in Figure 4. Two research spectrometers are available at Michigan .State University, one with backward wave oscillators “ and one with klystrons as the sources of radiation. 4.2a Absorption Ce;l_ Any one of four sample cells can be made part of either Spectrometer. Three cells, with lengths of 505, 500 and 585 centimeters, use the conventional septum support while the fourth is the 122 centimeter cell mentioned above. The ef- fective length (the length of the septum) of the Short cell is 118 centimeters while for the other three it is about 15 centimeters less than the cell length. Grooved flanges soldered to the ends of the cells allow other components which are also equipped with flanges to be attached. Each cell is made vacuum tight by clamping a Sheet of mica, 0.002 in. thick, between the cell and a short section of waveguide at each end. 9 5 .Hmumfiouuommm m>m3ouoflfi mo EmummHo onHm Hobomumn .e wusmwm k .J Hm>wwomu rt owomu Eoum m mmoom Hmume Hmwmwwsfim - IoHHHomo ucmunou o a _ Houomumo m>wufimcmm Houmumcmmd Immmsm madman m>m3 Hmonoumm 0o >m Iwnmovm Hmamoou Hamo mHmEmm _ . Hmcowuownfin Souumhax t. L _O _ O ._ - “3.9a __ m \V .(\ _ E f— Hm3om Eou mm muoumscmuua Gonumwak Ewummm Boson? 09 LHHIIII Hmumsm>m3 11... HoumH Iawumo ad z¢.ll «a Sm .IIII. um: a nomuumw nomuumo amnwaanmum mmoon Iodaflomo Hm>amomu mmoomoHHaUmo . Ile . .HO Oflmumm 9H. “mucooo 40 The grooved flange on the cell is fitted with a lightly greased O ring. As mentioned above, temperature cycling causes the septum to migrate toward one end of the cell. This is the reason for the 15-centimeter difference in length between cell and septum for the long cells. A small slit centered in the broad face of the waveguide and parallel to its length serves as inlet for the samples. A hollow metal block with a glass to metal seal on it is soldered over the slit completing the connection between the sample cell and a vacuum system. All the sample cells are placed in insulated troughs to allow cooling with dry ice. 4.2b Other Microwave Components The dimensions of microwave components are usually chosen to allow only the dominant TElo mode of prOpagation. Because the cutoff frequency for this mode and the one with the next higher cutoff frequency differ by only a factor of two a number of sets of components must be available to cover the frequency range from 8 to 40 GHz, the usual range for a general purpose microwave spectrometer. Because only one size of absorption cell is used, adapters in the form of gradually tapered waveguides are used to connect different Sized com- ponents. To adjust the radiation density in the sample cell, a fraction of that supplied by the source is absorbed by an attenuator inserted between the source and the cell. Attenuators are also used before any component that might be 41 damaged by too much radiation, to provide optimum radiation levels to mixers and harmonic generators, and to isolate components. Precision attenuators can be used to make in- sertion loss measurements and for calibrating other devices. If a quick measurement of the radiation frequency is desired, a cavity frequency meter or wavemeter is used. This consists of a cavity whose dimensions are such that it will absorb Significant amounts of radiation over a relatively small frequency region (1 to 5 MHz). By making the dimensions of the cavity continuously variable, this small frequency interval can be centered at any one of a wide range of fre- quencies. In the low frequency region of the spectrum wave- meter measurements can be made that are in error by less than 5 MHz. For more accurate measurements one of the frequency measuring methods discussed below must be used. All of the precise methods require a sample of microwave power for com- parison with a precisely known frequency. The sample is obtained by Splitting the radiation into two parts by means of a directional coupler. Directional couplers with a number of Splitting ratios are available--5, 10 and 20 db couplers sampling 50, 10 and 1% of the power, respectively, are usually sufficient. Detection of microwave radiation is accomplished by rectifying the microwave Signal by means of a silicon diode or crystal properly mounted in a short section of waveguide. Tunable detectors, ‘usable over only a few hundred Megahertz 42 without retuning, have given better results than untuned wide band detectors (in the lower frequency regions) although the latter are much more convenient to work with. Closely related to crystal detectors are crystal mixers and harmonic generators. Because of the non-linear response of silicon diodes, harmonics will be generated when a signal is applied to a crystal detector. When the diode is subjected to two or more signals at the same time, sums and differences of harmonics will also be generated. By means of various tuning arrangements the strength of one or another of these difference frequencies may he maximized and used for either frequency measurement or control. This process will be dis- cussed in more detail in a later section. Both backward wave oscillators (BWOS) and klystrons are used as microwave generators. The main advantage of the BWO is its complete voltage tunability. Because the voltage and frequency relationship is known and reproducible from day to day, programming is possible. A disadvantage is that BWOs are usually noisier than klystrons. This is at least in part due to the large Slope of the BWO frequency versus tuning voltage curve. 4.2c Electronic Compgpents Power supplies Two high-voltage power supplies connected in series-- a beam supply and a reflector supply--are required for Opera- tion of a klystron. In addition, a low voltage filament 45 supply and in some cases a grid supply are also needed. _Some frequency tuning can be obtained by changing the voltage Of the reflector (or beam) supply. To observe the microwave Spectrum of a molecule over a given frequency range, the frequency Of the klystron is continuously changed while the amplified signal from the detector is monitored on either an oscillOSCOpe or on a recorder. If an oscillosc0pe is used, the frequency change is produced by a repetitive volt- age ramp applied to the reflector. Recordings are obtained by mechanically changing the cavity Size and thereby the frequency of the klystron. At each position of the mechanical sweep there is an Optimum reflector voltage. If the reflector voltage is too far from this ideal value, power will be lost and no Spectrum obtained. For this reason reflector sweeps are usually restricted to approximately 50 MHz, and mechanical sweeps seldom go more than 1000 MHz.before readjustments have. tO be made. The Varian BWOS in use at MSU require only a helix supply, an anode supply and a filament supply for Operation. The construction of the BWO power supply is such that the helix voltage, which controls the frequency, may be varied at any rate from DC to several MHz by applying the apprOpriate signal to a ground-based input. By using a variable power supply as thetmain frequency determining voltage and a very low frequency Signal generator for sweeping, a convenient microwave source is obtained. Because the maximum 44 peak-to-peak voltage available from the function generator used at MSU is 50 volts, only about 5% of the range of the BWO can be covered at one time. Modulation Because of the rotational Stark effect the rotational frequencies of a molecule depend on the value of an applied electric field. If the microwave frequency in a spectrometer is equal to the transition frequency at zero electric field, then applying a field of sufficient strength will reduce the absorption to near zero. A high power, high-voltage square— wave generator can produce these two conditions alternately by charging and discharging the capacitor formed by the septum and the walls of the waveguide sample cell. The absorp- tion will be switched on and Off at the square-wave frequency. In the square-wave generator at MSU. provision has been made to allow arDC voltage of either polarity to be added to the square wave for convenience in making quantitative measurements of the Stark effect. Amplification For all but the strongest absorbing gases the fraction Of microwave radiation absorbed is only a few parts per million. A change in crystal current of this magnitude is not readily observable because randomly-varying noise is much larger than this under normal operating conditions. But, Since crystal noise has frequency components at all frequencies, the noise component over a particular frequency 45 region is small if the region is small. When square-wave modulation is employed, the crystal current will have a small AC component at the modulation frequency. A tuned amplifier can then be used to amplify only the wanted signal due to absorption by the sample plus the noise that lies within the bandwidth of the amplifier. .Since this remaining noise is prOportional to the bandwidth a small bandwidth is usually desirable, although a very small bandwidth will reduce the rate at which a given frequency range can be swept over. A phase-sensitive detector will allow both very small and also variable bandwidths to be used. The phase-sensitive detector as used here has two inputs, a reference signal Ob- tained from the square-wave generator and the absorption signal from the output of the tuned amplifier. These two signals are combined in such a way as to produce an output proportional to the cosine of their difference frequency (the phase relationships must be included) and to the magni- tude Of the smaller signal (the output from the tuned ampli- fier). The result is a pulsating Signal whose DC component is proportional to the magnitude of the change in crystal current due to absorption. Superimposed on the pulsating signal.is the noise that passed through the tuned amplifier. Because the noise has also been mixed with the Stark modula- tion frequency in the phase-sensitive detector, its spectrum now extends from zero to the bandwidth of the tuned ampli- fier. The DC output signal, which is prOportional to the 46 absorption, will have very low frequency components if the sweep Speed is kept low. Because most Of the noise is of higher frequency a resistor-capacitor (RC) filter is used to eliminate the high frequency noise components from the absorption signal. The extent of filtering is usually expressed as the RC product with units of seconds and is Often called the time constant. Typical values range from .1 to 5 seconds. A practical upper limit exists because the diode is not the only source of noise. Instabilities Of the microwave generators introduce very low frequency noise com- ponents which can not be filtered in this way. 4.5 Frequency Measurement Basically, frequency measurement involves electronic frequency multiplication of a stable measurable signal by a factor large enough to bring it to within about 20 MHz Of the microwave frequency. A microwave mixer may be used to generate this difference frequency which can then be detected and measured by an accurate radio receiver. At MSU a very stable quartz-crystal-controlled oscillatorl whose frequency (1 MHz) is periodically compared to the carrier frequency of Radio Station WWV is the standard to which other frequencies are compared. Two instruments use this 1 MHz Signal to generate a frequency high enough to be com- pared to the microwave frequency. In the first instrument2 J'Manson Laboratories RD-140A. 2Gertsch AM-1A VHF interpolator. 47 the frequency Of a 1 to 2 MHz variable frequency oscillator is added to the kth harmonic of'the 1 MHz signal giving com- plete frequency coverage between 20 and 40 MHz. This sum frequency is used to lock a variable frequency oscillator also covering the range 20 to 40 MHz. Both the 1 to 2 MHz and the 20 to 40 MHz oscillator are front panel tuned. The angular rates at which the two shafts must be rotated for the 20 to 40 MHz oscillator to remain locked to the sum of the other two frequencies are almost exactly prOportional. This makes frequency sweeping the oscillator over a 1 MHz range possible with a gear and pulley arrangement and a motor. This feature was used only when recordings were made with the klystron frequency stabilized. In the second instrur ment,l a variable high frequency (500-1000 MHz) oscillator is locked to the nth harmonic of the 20-40 MHz Signal using a 10 MHz difference frequency for control. This 500-1000 MHz signal is then impressed on a diode which is also exposed to the microwave radiation. Of all the difference frequencies generated by the diode from these two signals let the lowest frequency be F. Using the multiplication factors defined above the microwave frequency MF can be expressed as MF = m [n (k + f).i 10 ] i.F where f is the frequency of the 1-2 MHz oscillator and m is lGertsch FM-4A microwave frequency multiplier. m1 pa he S] 48 l is used for differ— an integer. ~A calibrated radio receiver ence frequency (F) measurements and the range of the receiver limits F to between 0.5 and 50.5 MHz. Typical limits on the other numbers are m = 8-80, n = 12-50 and k = 20-40. m, n, k and f are usually Obtained from a table which was generated by a computer. .Since f is variable, it is either measured with a counter or it is chosen to be Of the right frequency to give a stable identifiable Lissajous pattern when compared with a 1 MHz signal. In the higher region of the Spectrum the above method is not as easy to apply because the higher harmonics give weaker difference frequencies which are occasionally diffi- cult tO identify. These difficulties can be overcome by substituting an X-band microwave source for the 500-1000 MHz oscillator. In this case the multiplication factor required to reach 40 GHz is at most 5, and very strong difference signals are obtained. Since a counter is available that will measure frequencies below 18 GHz, it may be used to determine the frequency of the X-band source. Because microwave frequency changes as small as one part per million can produce a noticeable change in the Sig- nal from the detection system, instability problems at very Slow sweeps and with large time constants are not uneXpected. By locking the frequency of the microwave generator to some lCollins 51J4 or 5184. more above A ste £0114 diffe MHz) signa which great less Propc frequ refle erice exist its a the c COnst reSu] This 80me ments 49 more stable source, e.g., the 0.5—1 GHz oscillator discussed above, instabilities due to frequency drift can be reduced. A stabilizer which will accomplish this locking works as follows. A high-gain amplifier tuned to 60 MHz amplifies the difference frequency F (which is assumed to be very near 60 MHz) to the maximum output voltage of the amplifier. .This Signal is then passed through a frequency sensitive network which gives a:DC output of one polarity if the input is greater than 60 MHz and of Opposite polarity if the input is less than 60 MHz. The magnitude Of this error voltage is proportional to the difference between 60 MHz and the input frequency. The error signal is amplified and added to the reflector voltage with the correct phase to make the differ- ence frequency equal 60 MHz. A small difference will always exist because infinite amplification of the error signal before its application to the reflector would be necessary to reduce the difference to zero. Because the stabilizer keeps the difference frequency F constant at 60 MHz; a change in the 1-2 MHz frequency will result in a proportional change in the microwave frequency. This method of frequency Sweeping and measuring was used for some intensity measurements and some Stark effect measure- ments. 4.4 Stark Effect Determination of the Stark effect involves measuring the displacement of the transition--or its components if it is pos var div wit obt the P01. aVe: due Sta] Deb} mEas cart Stab 4.5 0f i‘ 50 is Split by the field--as a function of applied.DC voltage. To produce the applied DC voltage the output of a stable high voltage power supply was applied to two voltage dividers. One of these has a dividing ratio of 1000 to 1 and was used to monitor the voltage Of the supply, while the other has a variable ratio and an output which was applied to the Sample cell. The variable divider has six switchable positions and a one-turn potentiometer to provide continuous variation. By careful calibration of the variable voltage divider and frequent measurements Of the monitoring voltage, with readjustments when necessary, reproducible voltages were Obtained. To take into accounttflueimperfect zero basing of the square wave the DC voltage was added with both possible polarities and the resulting frequency displacements were averaged. The effective electric field in the sample cell due to the DC voltage was found by measuring the well-known Stark effect of the J = O - 1 transition of OCS (noes = 0.7152 Debye (27)). OscilloscOpe display was usually used for the frequency measurements although some of the values for cyclopropyl carboxaldehyde were obtained from recordings made with the stabilizer. 4.5 Intensity Measurements 4.5a Temperature The determination of temperature is important because of its appearance in the Boltzmann factor relating the ratio conta dire: the . the t of he the c the c PIOCe 0f in the f. With . duced ing t fille about Press measu had e to ca Sampl dilut ValueE 51 of the pOpulations Of two states to their energy difference. At temperatures above -20°C a thermometer was placed in contact with the sample cell and the temperature was read directly. Below -200C four thermocouples, which were attached to the side of the cell with epoxy resin, were used to Obtain the temperature. Because brass and OOpper are good conductors of heat, the temperatures were always higher at the ends of the cell than in the middle so that an average was used as the correct temperature. The development of a reproducible procedure for preparing the sample cell prior to each series of intensity measurements made temperature measurements after the first time unnecessary. This procedure was as follows. With the cell empty and at room temperature, sample was intro— duced and after a few minutes pumped out. The trough contain- ing the cell was then filled with dry ice and the cell again filled with sample at a relatively high pressure. After about one-half hour, the dry ice was replenished and the pressure reduced to the desired value. Relative intensity measurements were started after an additional 10-15 minutes had elapsed. About once every hour the dry ice, which tends to cake up, was broken up and the trough refilled. A fresh sample was introduced every 5 or 4 hours to counteract any dilution Of Sample due to leakage of air into the cell. Five temperature measurements resulted in the following values at the four locations: -69.1, -76.5, -79.0 and -76.20 C. The EVE! the t tions the c but i the p‘ Same. of 1i Satur As a . ginni: not a the t\ condi1 ables ture, all of there . PrESSu; little ferent the Qt Vents 52 The dry ice temperature used in all calculations is the average Of the four averages or 1980 K. 4.5b Relative-intensity Measurements (25) Intensity measurements are made at MSU by recording the two transitions which are to be compared keeping condi— tions as identical as possible. It is most important that the crystal current be the same for the two transitions, but it is also important that the filtering of the output of the phase-sensitive detector and the sweeping speed be the same. In order to reduce the linewidth, which makes overlap Of lines less of a problem, low pressures are usually used. Saturation effects are minimized by using low power levels. As a result of the microwave problems discussed at the be— ginning Of this chapter, reproducible intensity ratios are not always obtained. To reduce the error in these ratios the two lines of each pair are compared under many different conditions that Should all give the same result. The vari- ables available are Stark voltage, pressure, power, tempera- ture, time, and sample cell. For most ratio measurements all of these were varied and the results were averaged, unless there were good reasons for eliminating some results. Pressure, power, and Stark-voltage variations Should have little to do with the microwave problems. Therefore, if dif- ferent ratios are obtained by varying one of these, one or the other of the ratios can usually be eliminated. Measure- ments were made using the four sample cells described above wit SW£ the cox tur Pac W8); pha is are wit Vol rec det wit var SUr OCQ 55 with the BWO and its electronic sweep, with the klystron swept mechanically, and with the stabilized klystron. Some relative-intensity measurements were also made at the Hewlett-Packard microwave laboratory. .Two spectrometers covering the range from 18-40 GHz were used at room tempera- ture. Transition frequencies are measured with the Hewlett- Packard Spectrometer by changing the frequency of the micro- wave source (a phase-locked BWO) in small increments in the vicinity of a transition while monitoring the output Of the phase-sensitive detector. -The frequency of the peak output is then determined by interpolation. Intensity measurements are then made at this frequency by recording the transition with the Stark modulator on and with it Off. Peak signal voltages are determined from attenuator settings and the recorder readings. A correction for electronic pickup is determined, if necessary, by repeating the measurement process with the sample removed. Pressures and power levels were varied to reduce errors. For a variety of reasons the pres- sures used were generally higher than ideal, much overlapping occurred, and pressure-dependent intensity ratios resulted. 4.5c Absolute Intensity Measurement In making an absolute intensity measurement the quantity sought is the fractional change in power due to absorption. By artificially causing a known fractional change in power, a standard is developed to which transition intensities can be compared. 54 AS was mentioned earlier, a derivative of the power versus frequency curve is Obtained if the microwave frequency is swept while it is being modulated by a signal with some harmonic content equal to the Stark modulation frequency. If the microwave frequency variation due to the modulation is known, and if the lepe of the power versus microwave frequency curve is known, the resulting power variation can be calculated. This power variation causes a change in crystal current Similar to that caused by absorption by a sample. .Since all subsequent operations on this crystal current change are identical for both an absorption signal and the power modulation,‘a direct comparison is possible. To allow for the possibility that the detector is frequency sensitive a wavemeter is used to provide the power dip and to make power modulation possible at all frequencies. The microwave frequency is modulated by applying a square wave to a small resistor in series with the frequency determin- ing electrode of the microwave source. The square wave is supplied by the circuit of Figure 5. A signal from the Stark modulator is used to phase-lock a modified Wavetek Model 112 signal generator. The triangular wave output Of the signal generator is passed through a full wave bridge rectifier to give a triangular wave of twice the original frequency, but smaller amplitude. After passing through a transformer (for isolation), the signal is amplified and applied to the toggle input of a flip-flOp which divides its frequency by 55 .HoumHSOOE zoomsvmum O>m3onoflz. .m musmwm (A >Hmmsm Hmsom xwama Eoum . on , em 3 "ea 8 P on _ ((( w >0 f 23 . ooe onm , xflamn OB . mm: min MN 3 xmé xd cw Hmcmwn, foouuzmm >mn.d >n 56 two and gives a very symmetrical square wave. An emitter follower Operated from a.mercury battery is used to provide a relatively stable signal to a string of resistors from which the desired amplitude can be picked off. The flip— flOp can be made to remain in either one of its two states indefinitely, making accurate DC voltage measurements of the output possible. .If the microwave source is swept over a small portion Of the wavemeter dip by applying a triangular wave Of amplitude V3 to the power supply sweep input, the crystal current will vary nearly linearly with time provided the maximum slope of the wavemeter dip is swept over and V5 is small. Call the resulting crystal current change DIS. ‘ With the help Of a precision microwave attenuator the crystal current change due to a 0.1 db change in power can be deter- mined. Let this quantity be DIP. If Vh is the voltage across the 27 Ohm resistor, then the fractional change in power due tO this type Of modulation is Vm DIS 0.0250 VE—DIP- and this will cause an output Sm to be obtained from the de- tection system. If a transition at that same microwave frequency gives an output St under the same conditions, then the absorption due to the sample is a] = .230 5“ Vm DIS 57 TO Obtain the absorption coefficient 0( , d1 must be divided by the effective length i of the sample cell. The crystal current is measured as a voltage across a 50 Ohm load. A constant current source in series with a pre- cision resistor box is used to buck out part of the voltage across the 50 Ohms, making possible a more accurate measure- ment Of the slope. Two absolute intensity measurements were made using the J = 0 - 1 transition Of OCS. In each case the pressure was made as high as possible in order to allow reasonably high power levels to be used without noticeable saturation. In order to avoid overlap of the transition and its Stark com- ponent, as high a Stark voltage as possible was used to dis- place the component as far from the line as possible. A compromise must be made between the two requirements of high pressure and high Stark voltage because electrical dis- charges inside the sample cell become more likely as the pressure or Stark voltage is raised. The two measurements were made at a pressure of about 0.15 torr and at about 500 volts. The error due to overlap at these conditions amounts to less than two per-cent and was neglected. The two voltages vm and Vé were both indirectly measured with a digital voltmeter (DVM). vm was Obtained by applying a measured voltage to the precision voltage divider. The value of vm ranged from 8 microvolts to 1.55 millivolts but because Of pick-up problems the higher values were more 58 useful. Application of 1.55 millivolts to the helix of the BWO causes a frequency deviation Of approximately 4.2 kHz at 12160 MHz. The value of V8, which was usually in the range of 10-50 millivolts, was Obtained from the wiper Of a 10 turn potentiometer. The voltages of the two stable states Of a low frequency (cv0.1 Hz) square-wave signal applied to the potentiometer were measured with the DVM. The difference in the two voltages was then multiplied by the potentiometer ratio to Obtain Vs' After the voltage measurement, the fre- quency of the square wave was increased to the modulation frequency of 90 kHz. The two measurements, each of which represents an average of five to ten numbers, yielded the values 5.24 x 10'8 cm'1 and 5.55 x 10“ cm“1 for the absorption coefficient. For the sample cell used which had an effective length of 118 cm the peak-toepeak square wave at the detector amounts to about 6 microvolts for this strong transition. V. THE MICROWAVE SPECTRA The aim of this work was to extract the following information from the microwave spectrum of cyclOprOpyl carbox- aldehyde and cyclOprOpanecarboxylic acid fluoride. 1. Identification of the Species present in the vapor of each compound. 2. Rotational constants in the ground and excited torsional states of each species. 5. Dipole moments in the ground vibrational states of each Species. 4. Torsional potential constants from relative intensity measurements of transitions in the ground and excited torsional states of each species. All of these goals were realized so that it is possible to compare the results Obtained for the two compounds with each other and with data for similar compounds Obtained else- where. The theoretical and experimental techniques used to Obtain this informationwwere the subject of two previous sections, This section will present the data collected and the results calculated from these data. 59 60 5.1 CyclOprOpyl Carboxaldehyde 5.1a Rotational Constants The study of cyclopropyl carboxaldehyde (referred to as the aldehyde from here on) was begun by Dr. Schwendeman who calculated the approximate rotational constants from an as- sumed structure, made an initial assignment of transitions, and identified some transitions in excited torsional states (satellite lines). The initial assumption, based on the results Of an electron diffraction study (6) was that mole— cules would occur with the oxygen atom cis and trans to the cyclOprOpane ring. This assumption proved correct. The structure assumed for the cis conformer is shown in planar projection in Figure 6. The bond distances, bond angles, and coordinates in the principal inertial axis system for this structure are given in Table I. Similar information for the trans Species is presented in Figure 7 and Table II. From Figures 6 and 7 it is apparent that the plane of sym- metry of the cis species is the a-b inertial plane whereas for the trans species the plane of symmetry is the a-c.. inertial plane. Thus, a-type and b-type transitions are expected for the cis species and a-type and c-type transi- tions are eXpected for the trans Species. That these expec- tations were realized experimentally is partial evidence that the two Species identified are in fact cis and trans. .For the cis Species Of the aldehyde strong b-type Q-branch transitions were first assigned in the microwave 61 C2 Figure 6. Projection of cis-cyclopropyl carboxaldehyde in its plane of symmetry. C2 Figure 7. Projection Of trans-cycloprOpyl carboxaldehyde in its plane Of symmetry. 62 Table I. Coordinates for cis—cyclOpropyl carboxaldehyde in the principal axis system. M Atom a b c C; -0.40149 -0.71908 0.00000 C2 1.10151 -0.52717 0.00000 C3 —1.25210 0.29654 0.75750 C4 -1.25210 0.29654 -0.75750 0 1.62646 0.56292 0.00000 H1 -0.74815 -1.74194 0.00000 H2 1.59627 -1.48707 0.00000 H3 -0.70428 1.09788 1.25514 H4 —2.12224 -0.06178 1.25514 H5 -0.70428 ~1.09788 -1.25514 H5 -2.12324 -0.06178 -1.25514 aThe coordinates displayed here were calculated assuming the following structural parameters: < H3C3H4 = 116° r (CO). = 1.21 A (OCH; = 127° r (CH) = 1.08 A < cc0 = 125° r (CC) =1 .515A Tat) The str 65 Table II. Coordinates for trans-cyclOprOpyl carboxaldehyde ‘in the principal axis system.a Atom a b c C; —0.28407 0.00000 -0.45915 C2 0.98279 0.00000 0.57168 C3 -1.47566 0.75750 0.08999 C4 -1.47566 -0.75750 0.08999 0 2.09058 0.00000 -0.11549 H1 -0.14764 0.00000 -1.55050 H2 0.75511 0.00000 1.42290 H3 -1.55221 1.25514 1.04157 H4 -2.11888 1.25514 -0.62206 H5 -1.55221 -1.25514 1.04157 He -2.11888 -1.25514 -0.62206 aThe coordinates in this table were calculated assuming the structural parameters given in the footnote in Table I. 64 X-band region. .From the frequencies of these transitions two combinations of rotational constants (3-0 and 2A-B-C) could be deduced. The cis species assignment was completed by the identification of the a-type J= 1-2 transitions in the microwave P-band region. The identification of the J= 1-2 transitions was aided by the characteristic Stark effect of the 111-212 and 110-211 transitions. The I M I = 1 Stark components of these transitions are rapidly diSplaced toward each other when the Stark voltage is increased. The fre- quencies Of Observed transitions for the cis Species of the aldehyde are given in Table III and the derived rotational constants, moments of inertia and second moments are given in Table IV. The characteristic Stark effect of the J = 1-2 transi- tions was also responsible for the assignment of these transitions for the trans species. Because the trans alde— hyde is nearly a symmetric tOp (the B and C rotational con- stants are nearly equal and considerably smaller than the A rotational constant), the A dependence of low-J, a-type transitions is small. This makes it impossible to determine A accurately from these transitions. The c-type transitions, which have a strong A dependence, are less intense than the a-type transitions in this species by a factor of about 40. These transitions were not identified until a peculiar Stark effect of the I M I.= 1 component of the 1014202 transition was Observed, and analyzed. This Stark effect is very QT:£QTF“>C£&EL HDCCLCCKLDLIKWC HOW ANmzu mmflUflflflvwhm AXHCO mUflmflD WUHSU OMEN» UNUMHSUHQU 0C0 NU03HWWQO -HHH @NQME 65 .Nmz mo.o.H mum mwflocmsvmum om>ummnom Ame.ee m>.mmemm Amm.mnv ed.mmmmm mmoauoaeoe Asm.so me.moeem Asa.onv mo.mmmem oneness Ame.me mm.mmoom Aem.av Ne.emmma owedumeoa Am~.mo em.eo¢om Aom.sv me.mmmma smmumem Amm.mc oa.emeom Aeo.mo mm.mmmom ammueam Rom.¢e mm.mm>m Ame.mo m>.mmmm Amo.mv mm.>mmm Amo.mv sm.mmam m.m-oom Aa~.ee ma.eoem Aoe.mo me.mesm Ame.¢o me.emmm Aeo.mo mm.emmm vemumom Aoe.mo mm.e«am Amo.mo eo.meam 150.05 mo.0mam Adm.mo ma.memm n.¢u.oe “mo.ov ma.omem~ xom.mo.ma.mmmmm mmmuemm Amo.mo mo.emmmm Amm.mo mm.mmenm Aem.nv mm.mmmmm momnmom Aom.omo m>.mmanm Ams.mo om.memnm Amm.ev mm.eammm ”enumem Ame.mv ms.mmmme Amm.mo mm.mmnma Aes.se ee.emmma lam.sv a~.sm~mfi and- o Amm.mo om.memma Adm.mo me.mammfi “ma.me mo.ommmd mamufloa Aon.¢v mm.eesma Ame.mv m¢.~mmmd a.muoad Amm.oo me.omema Ame.mv m>.mm¢ma xem.mv nm.memma «amused m... II. > N > H > 0 H > COHuHmOmH—p .Ooanmonxonumu HumoumoHOMOImwo How Aumzv mmfiocmsvmum A>Hco muwmwo mounu unwav omumHouHmo 0cm mow>ummno .HHH manna T.‘ 66 Table IV. Rotational constants (MHz),a moments of inertia (amu A2) and second moments (amu A2) for cis- cyclopropyl carboxaldehyde. v = 0 v = 1 v = 2 V = 5 A 11417.29 11454.86 11485.56 11521.16 B 5994.18 5967.14 5950.26 5928.88 C 5849.92 5842.88 5856.80 5851.57 Ia 44.2641 44.1189 44.0010 45.8650 Ib 126.5281 127.5905 127.9549 . 128.6511 IC 151.2692 151.5097 151.7181 151.8979 Paa 106.7666 107.5906 107.8260 108.5520 Pbb 24.5026 24.1190 25.8921 25.5659 Pcc 19.7615 19.9998 20.1089 20.2991 aUncertainties are as follows: A, i 0.05 MHz: B, 1.0.05: CI 1 0005. 67 sensitive to the value of A and from it A could be calculated to sufficient accuracy to allow the identification of the weak c-type transitions. The Observed transitions for the trans aldehyde are given in Table V, and the derived rota- tional constants, moments Of inertia, and second moments are given in Table VI. After some searching, transitions in vibrationally excited states were found for both species. The Observed frequencies of assigned transitions are listed in Tables III and V. The intensities of these lines decrease by approximately a factor Of two between successive excited states indicating a vibra- tional energy separation of about 100 cm‘l. Presumably the only vibration in the aldehyde with that low an excitation energy is the torsion about the carbon-carbon bond. Additional evidence supporting this presumption is provided by the in- crease in the out-of-plane second moment with increasing v (the vibrational quantum number) Shown in Tables IV and VI. Such an increase is expected for an out-of-plane vibration. Satellites for both a- and b-type transitions were found for the cis species allowing accurate determination Of all three rotational constants for three excited states. From the a-type transitions of the trans aldehyde, however, only B and C could be calculated accurately for the excited states. Rotational constants in the ground state and in the excited states may be cOmpared in Tables IV and VI for the cis and trans conformers respectively. HON AME—Iv mmflUCmquvmuHmn AanCO mUfimflmU UQHSWrUW.m.m.vr UWU-0HBUH:NU mUCm. «unmoxwxfimomnao .3 QNQWE 68 .nmz mo.o.fl mum mowusmsqmum om>u0mnom sm.mmmfim Amm.sv mm.¢omam ammumme em.emmam xoa.ov sm.mkaam «mmunme em.smmam Amm.me Ho.mmaam momuvos «n.5mmon Amm.mo Ne.mmsom memu.de Asa.so mm.mmom osaoanoaooa Amm.mo mo.ammm mamumom Amo.mv ma.msmoa memumom Aom.mv mm.me>os sesusoe Amm.mv mm.mm~aa odwnoom Ame.ov ma.ommaa memumom Asm.mv om.maoma .Heusoe Aeo.fiv.¢o.aamma mflmumom Amm.oe «p.0sema momudoa Aem.mo em.meeme. lmo.ov mo.oaemd Amm.mo mm.mmm~e Amm.mv nu.mmmme Hemuoae Amd.eo m«.emmme Aem.me ¢N.msnmd Ame.mo me.msmma xem.ev «m.edmms «amused n u > N u > H n > u > SOwufinsmna .momsmoamxonumu HamOHmOHO>UImsmuu How ANmZV mwwucmskum Aaaco nuwmfio mmunu unmav ooumHSOHmu new mom>ummno .> wanna 69 Table VI. Rotational constants (MHz),a moments of inertia (amu A2) and second moments (amu A2) for trans- cyclOprOpyl carboxaldehyde. v = 0 v = 1 v = 2 v = 5 A 15885.40 B 5195.09 5207.74 5219.75 5251.18 C 5040.95 5046.02 5050.84 5055.52 Ia 51.8159 Ib 158.1727 157.5489 156.9622 156.4060 Ic 166.1902 165.9156 165.6514 165.4085 Paa 146.2745 Pbb 19.9157 P 11.8982 cc aUncertainties in rotational constants are as follows: A,.1 0.05 MHz: B, 1.0.05 MHz: C, 1.0.05 MHz. spé cor The not low wit cis tio: men‘ lea) (101') late Strt five for were t101 70 Examination of the rotational constants for the cis species in Table IV reveals that the change in rotational constants with vibrational quantum number is non—linear. The reason for this non—linear change for the cis species is not known. However, a reasonable explanation is that some low frequency, in-plane vibration (about 220 cm’l) interacts with the second and higher excited torsional states in the cis compound. The large differences between the cis and trans rota- tional constants and the small differences between the experi- mental and calculated rotatiOnal constants for both species leave no doubt that the constants have been assigned to the correct conformers. The good agreement between the calcu- lated and experimental constants indicates that the assumed structures are probably not far from correct. As many as five excited states were measured for some transitions, but, for the fourth and fifth excited states not enough lines were measured to Obtain a rigid-rotor fit to all three rota- tional constants. 5.1b Dipole Moments Further evidence for the existence of a plane of sym- metry in the two configurations Of the molecule is provided by the values Of the components Of the dipole moment. SlOpes of plots of the frequency versus the square of the electric field were determined for five Stark components in the cis species. The slopes were used to calculate the 71 three components of the dipole moment by a least squares procedure. As expected, the out-of-plane component (no) was zero within experimental error. The other two com- ponents were then re-calculated with ”c set equal to zero. Table VII contains the dipole moment components together with the experimental and calculated Slopes. Quadratic lepes from three Stark components were used to calculate the dipole moments for the trans conformer. .Stark effects of the I MI.= 1 components of the three J = 1-2 transitions were also measured. The results of these measure- ments are discussed in the next section while the three quadratic Slopes, both calculated and measured, are compared in Table VIII. Since voltages and frequencies are measured in the Stark effect, these are the sources of error. The uncertainties in the frequencies are a fixed percentage of the displacement because as the line is displaced from its zero field position it broadens and becomes more difficult to measure. This frequency error will be taken to be 0.5%. In addition to the error in the actual measurement of the voltage, which can be made very small, an additional error may be introduced due to the fact that the measured voltage is not necessarily the voltage applied to the sample cell. The difference is caused by the voltage drop across a conducting high-voltage diode used in the output section Of the square-wave generator. The effect of this additional voltage--call it Vor-can be 72 Table VII. Stark effect and dipole moment of cis-cyclOpropyl carboxaldehyde. 2 a,b 2 a TranSition (av/OE )obs- (Av/6E )calc. 0 -111 M = 0 56.46 56.50 111-212 M = 0 9.22 9.25 110-212 M = 0 18.01 17.87 101-202 M = 0 -10.02 -10.06 101-202 M = 1 42.25 42.23 ”a = 2.019 i.0.01 D ”b = 1.856.: 0.01 D ”c = 0.0 D u = 2.742 1.0.01 D a 2 Hz/(volt/cm) . “Ocs Uncertainty in observed Slopes is i.0.5%. Table VIII. = 0.7152 D prOpyl carboxaldehyde. Stark effect and dipole moment of trans—cyclo- . . 2 alb 2 a TranSition (Ov/OE )Obs. (OV/OE )calc. 101-202 M = 0 -74.21 -74.21 111-212 M = 0 52.75 52.55 110-211 M = 0 59.02 59.10 1:01:0me 5.221 1.0.01 D 0.0 0.495.: 0.01 D 5.259 2.0.01 D a 2 Hz/(volt/cm) . “OCS Uncertainty in Observed SlOpes is i.0.5%. = 0.7152 D 75 calculated for any particular case. If frequency measure- ments are made at five equally spaced voltages between 0.2 vm and Vh, the fractional error in the slepe due to V0 can be shown to be 2.81 Vo/Vm. The error in the intercept amounts to 1.08 Vo/Vm x slope. Since these errors change sign if the sign of vm is changed, they can be eliminated by using external voltages of both possible polarities. This has been done for the measurements reported here. In making this compensation it is important to average the Stark shifts for the same external voltages of different polarities rather than to calculate slopes for the two polarities obtained with arbitrary voltages and then average the slopes. However, V0 can be calculated if $10pes for the two polarities are calculated separately. From two determin— ations at different times of the sloPe of the J = 0—1 transition of OCS the values of 1.2 and 7.8 volts were obtained for V0. The difference is due to a change made in the square-wave generator between the times the two sloPes were measured. Even though the errors due to a finite Vo should cancel exactly, large errors seldom do; therefore, it would seem better to reduce or eliminate them. This could be done by means of an extra small low-voltage supply. It will be assumed that additional errors in the voltage measurement and in the calibration of the sample cell make any one sloPe uncertain by about one percent. Since a number of slopes are used in their calculation, the dipole 74 moments may be taken to be accurate to approximately0.5%. This corresponds to 0.01 Debye for the cis species and will also be used as the uncertainty for the dipole moment com- ponents for the trans conformer. 5.1c The Anomalous Stark Effect of the 101-202 Transition of the trans Species As was discussed in Chapter II the Stark effect in asymmetric t0ps is usually treated by second-order perturba- tion theory. When one or more of the energy differences appearing in the denominators of Equation (2-15) are very small, the requirements necessary for application of perturba- tion theory are no longer met and a direct calculation is required. This occurs regularily in near symmetric tOp mole- cules where the energy separation between the components of asymmetry doublets is small. .In the present case, an addi- tional level, the 202, is close in energy to the 111 and 110 levels and for I M '= 1 the 202 level has a perturbation connection to both the 111 and to the 110 level. The 202 level is not directly connected to the 111 level which is the level closest to it in energy. However, the 111 and 110 states are severely mixed by the perturbation, so that the 202 level is strongly affected by its proximity to the 111 level. When applying a Stark voltage the energies of the I M |= 1 components of the 111 and 202 levels change in such a way that they would coincide at about 525 volts if this mixing did not lead to an apparent perturbation connection between the 111 and 202 levels. This causes the peculiar It-..“ 75 behavior of the l M [= 1 Stark component of the 101-202 transition. The effect on the IM |= 1 Stark component of the transitions involving the other two levels (the.111-212 and 110-211 transitions) is not as pronounced as it is for the 101-202 transition at the lower voltages. The appear- ance of the peculiar Stark effect is as follows. As the Stark voltage is increased, the IM '= 1 Stark component of the 101-202 transition moves to higher frequency until at about 500 volts it reverses its direction and broadens out until it dissappears at about 517 volts. As the voltage is increased to 555 volts a Stark component appears again but at a higher frequency and this time moves to still higher frequency as the voltage is increased in a nearly normal fashion. ‘As mentioned before, the reason that this Stark effect was important was that at the time it was observed only two rotational constants (B and C) had been determined. The calculation of the effect consists of setting up the Stark effect matrix involving the three levels and diagonal- izing it. The matrix is uncoupled from the rest of the Stark effect matrix by means of a Van Vleck transformation. .The diagonal elements of the matrix are the energies of the three levels to which are added terms proportional to the square of the field which come from the uncoupling of the levels not included in the matrix. The energy of the 202 level (relative to the 111 level, whose energy is taken to be Zero at zero field) is very 76 nearly A-SB-ZC - 5/4 (B-C)2/(2A-B-C). By adjusting A until the calculated Stark effect agreed with the experimental one, the value of A could be determined. The components of the dipole moment needed for this calculation were obtained from the fit of the slopes of the lines showing a conventional Stark effect. The off-diagonal elements of the matrix con- sist of the direction-cosine matrix elements multiplied by the apprOpriate dipole moment component and the field strength. The direction-cosine matrix elements must be in the basis which diagonalizes the energies in the absence of the field. The transformation matrices needed to convert these matrix elements from the Wang basis to the assymetric rotor basis were obtained by means of the computer program EIGVALS (28). An additional small element directly connecting the 111 and 202 levels is due to levels not considered in the matrix and can be calculated using the Van Vleck perturbation theory. A simpler method of finding A was also used which required an exact calculation of only the asymmetry doublets and the usual second-order effect. By calculating the energies of the 111 and 202 levels at the voltage at which these energies are equal A can be determined. If this voltage is taken to be half-way between the value at which the Stark component dissappears in one place and the value at which it appears at another, the calculated value of A differs from the real value by approximately 0.25 MHz. 77 The matrix used for the complete calculation is 111 110 202 -0.05529 E2 0.86525 E ' 0.00595 22 0.86525 E 0.15414-0.05604 E2 0.05604 E 0.00595 E2 0.05604 E -0.21965 + 0.01088 32 The correct value of A has been used here. The energies are given in GHz and the voltages are in units of 500 volts. A comparison of experimental and calculated frequencies is given in Figure 8. The difference between calculated and observed frequency changes is greater than would be eXpected assuming reasonable voltage and frequency measurement errors. Part of the error can be due to the second-order correction terms. The 111 level changes energy by more than one percent at 525 volts. This would enter into the second-order terms because they are calculated at zero field. Some error is also caused by errors in the components of the dipole moment. 5.1d Relative Intensities and the Torsional Potential Function The numbers needed to calculate the three potential constants and the barrier to internal rotation are the energy separation of the first excited state from the ground state in both the cis and trans Species, hereafter called E51 and E:l, respectively, and the energy difference between the cis and trans conformers in the ground states, ESE. These energy differences are calculated from the ratio (r) of intensities 7B 15r- 10-— AV(MHz) Applied voltage 0 500 Figure 8. Observed and calculated Stark effect of the [M|= 1 component of the 101—202 transition of trans-cyclOprOpyl carboxaldehyde. 79 of like transitions in the two vibrational states using E = kT 1n r. 11 is assumed that the dipole moment components have the same value in the two states and that the linewidths of the transitions are equal. For comparison of intensities of cis lines to those of the trans species, the calculated intensities were used and the linewidths were measured. (When necessary, intensities are calculated for the different vibra- tional states of the same species to take into account the change of the rotational partion function and the frequency dependence on intensities. It was felt that fewer problems would be encountered if relative intensity measurements were made in X-band, because the Spectrum there is not as dense as it is at higher fre- quencies. Also, because the sample cell is made of X4band sized waveguide, the problems associated with reflections should be less than at higher frequencies. Another factor considered in choosing transitions for intensity measurements was the frequency separation of the transitions in successive vibrational states. For the cis aldehyde three Q-branch transitions (all in X-band) were used for the intensity measurements, with the results shown in Table IX. From the scatter of the individual numbers (given in the Appendix) from which these averages were computed some feeling for the quality of the averages can be obtained. In presenting these numbers, no distinction is made between the various Ei 1+1 (the energy separation between 80 Table IX. Energy separation (cm‘l) between successive torsional states for cis-cyCIOprOPyl carboxalde— hyde. Number of Transition Measurements Energy 303-312 19 .114.2 404*413 57 108.2 505'514 2 112.0 Average 110.5 A: 81 states i and i+1), that is, values of E01 are averaged to- gether with E12 numbers and any others that are measured. These were all assumed to be equal initially, but when theoretical calculations were performed this was found to be not likely. .Calculations based on the final potential func- tion show the E01 is about two percent less than E12. Since only the separation between the ground state and the first excited state (E01) is used to obtain the potential constants, the experimentally determined "E01" which has some E12 con- tributions and possibly others must be corrected. This cor- rection is possible if the ratios of the various Ei,i+1 are known. A calculation based on approximate potential constants will yield this information to sufficient accuracy. If EE?1 is the calculated Eij and 6?, is the E01 obtained by averag- ing all the E1 available, namely, no; values of E01, n12 ,i+1 values of E12, etc., then the corrected E01 is m calc calc calc n01 E01 + n12 E12 + ~- where N = 2 n1 In the present case, of the 58 measurements, j' 15 each are for E01 and E12, 9 are for E23 and 19 for E13/2. The E13/2 results from converting the square root of the ratio of the first excited state to the third excited state ihltensities to an energy difference. When the average of 11(3.5 cm'1 is adjusted in this manner, an energy difference 0f 112.6 :1: 4 cm"1 is obtained between the ground and first exczited states of the cis aldehyde. 82 Five additional transitions were measured with a Hewlett- Packard Spectrometer at the Hewlett-Packard Laboratory in Palo Alto, California. The measurements were made in the K-band region under various conditions of pressure and power. The numbers given in Table X are in order of decreasing pressure. The variation of the energy difference with pres- sure which was found for three of the transitions strongly suggests that these lines overlapped other extraneous transi- tions. The low pressures necessary to minimize the over- lapping were difficult to maintain because of a small leak in the Sample cell. Because the energies obtained from the remaining two transitions differed appreciably from the results obtained at MSU (a situation repeated to an even greater degree for the trans), they were not considered in the calculation of the potential constants. It should be added that the average frequency separation between the ground state and first excited state was over 500 MHz for these five transitions. In the case of the trans aldehyde the J = 1-2 transitions occurred in a region of the spectrum which was relatively free of other transitions. The frequency separation of ap— proximately 50 MHz between successive excited states made these transitions almost ideal for relative intensity measure- ments. The results given in Table XI support this statement. From the individual numbers (in the Appendix) there is seen to be considerably less scatter than was the case for the cis Species. Approximately 87% of the energies measured are 85 5.m> a.mm a.mm 000510505 0.00 5.50 0.50 5.005 .m0I050 0.555 0.555 0.055 0.055 0N0.50 0.555 0.055 0.505 0.00 0.00 0.50 305.3505 m.5N5 m.ON5 N.5m5 m.5m5 a.mad o.m55 0.0N5 n.0N5 wwwlbah ATIII wusmwmum 50304 whammwum um£m5m IIJV. c05u50cmue .MHSHOMHHMU .ouac 050m .mmwnoumnonmq pumxummluuma3wm 030 um UmSHMuQO mama. .mvwnmvameQHmu ammoumoHumo 1050 How mmumum Hmcoflmuou 0>Hmmmousm cmmBqu AHIEUV coflumnmmmm wmnmcm .X magma 84 Table XI. Energy separation (cmfl) between successive tor- sional states for trans-cyclOpropyl carboxaldehyde. Number of Transition Measurements Energy 111‘212 61 125.6 101-202 19 .122.7 110-211 54 122.8 Average 125.2 85 for the ground to first excited state separation and the remaining 15% for E12. Correcting the overall average of 125.2 cm'1 for this factor gives an energy difference of 125.6 cm‘1 between the ground state and first excited state for the trans aldehyde. Ratios measured at Hewlett-Packard for four transitions again had either a strong pressure dependence or else disagreed markedly from the results ob- tained here. These energies given in Table XII in order of decreasing pressure were again not used for further calcu- lations. Data taken at Hewlett-Packard were used to determine the relative population of the cis and trans species in their ground states. The ground state of the 512-413 cis transi- tion is separated from the first excited state of the 413-514 trans transition by about six MHz. .Since these two lines are of comparable intensity they are by far a better pair to use for this purpose than any that could be found in the lower frequency regions. Eighteen measurements showed the first excited state of the trans species to have a peak intensity 1.55 times greater than the ground state of the cis Species and a linewidth1.14 times larger, making it’ 1.76 times more intense. Its calculated.intensity is 1.66 times greater than the calculated intensity of the cis transition from which can be concluded that the ratio of trans to cis molecules in their ground vibrational states is 1.06. At 280 C this corresponds to an energy difference of 12.5 cm’l. Because of the large amount of scatter in these 6 8 5.505 m.mma. 0.5m5 m.mmfi a.m05 5Nm|mm5 5.055 0.555 0.005 0.005 0.555 m50-555 0.055 0.555 5.505 5.005 0.005 0.005 m60-565 m.mm5 a.mmH m.mmd .m.5m5 N.mm5 a.mma m.5m5 N.N55 5.mm mmmuww5 .ATI- musmmmum 50305 muswmmum umnmwm ILY. Sewuwmcmue .MHCHOM5HMU .ouam 050m .mm5uoumuonmn cumxommluu053mm 0nu um Umc5muno mumo “mcmnmoamxonumu meonm050>o Imcmuu How mmumum 50c05muou m>5mmmoosm cmw3umn Annfiov SOHumummwm amumcm .HHx 05909 87 numbers (given in the Appendix) a rounded value of 10 cm'1 will be used in the calculation. Using the equations presented in Section II the reciprocal angle-dependent reduced mass for the torsion may be shown to be ”T = (2.57665 - 0.07175 cos a) cm'l . With the value of “T calculated at the cis and trans position (a = W'and 0, respectively) a harmonic oscillator type of calculation can be performed for the two species separately to obtain approximate potential constants. These are then varied until the calculated energy differences obtained by diagonalizing the torsional energy matrix agree with the three experimental numbers. Calculation of the potential function in this way gives V = - %Q_(1 ~ cos a) + $§%§,(1 — cos 2a) + NCO O) (1 — cos 5a) cm‘1 The function VLiS plotted in Figure 9 together with some of the lower energy levels. From Figure 9 the barrier to internal rotation Vmax is seen to be 1550 cm"1. Changes in the Vi caused by changes in the three energies E81, E51 and 685 can be calculated from AV; = 5.460231 - 6.46665; + 1.14 AESE 11.50628l + 15.26AE51 + 0.0016385 AVg Avg = 0.966381 + 6.996651 - 0.14AESE and, Avmak=11.12AEgl + 15.51AE51 + 0.506535 . 88 .mcwnmvamxonumo meoumoaumo 50m mam>05 >mumc0 0800 Cam cowuocsm Hmwucmuom .m musmwm 000 005 00 . 0 can IF 1 IV 6 - T. - \ / \ / - .6. AHIEUV> I 0005 050 mcmnu 1 coma 89 It is difficult to assign uncertainties to the three experimentally determined numbers because the source of the errors is not well understood. Not more than 5 or 4% error resulting from conventional sources can be assigned to any one intensity ratio. .Due to the large amount of data collected it is hoped that the final experimental averages are better than this, even though any one number might differ from the average by 20% or more. It is believed that E5; is accurate to better than 1.2 cm"1 while i.4 cm"1 may be optimistic for E81 and i220 cm"1 reasonable for ESE. With these numbers the uncertainty in the barrier is approximately 80 cm'l, in V1 60 cm‘l, in V2 70 cm'1 and in V3 40 cm‘l. 5.2 Cyclopropane Carboxylic Acid Fluoride Cyclopropane carboxylic acid fluoride was prepared by passing the corresponding acid chloride over antimony tri— fluoride in a vacuum system a number of times until the infra- red spectrum showed the acid chloride concentration to be no more than about 5%. Because of the greater mass of the chlorine atom compared to the fluorine atom, the two chlorine isotopes, and the quadrupole hyperfine splitting, the micro- wave spectrum of the acid chloride was expected to be con- siderably weaker than that of the fluoride. Hence, no prob- lems were expected as a result of the small amount of acid chloride in the sample. Low temperature (dry ice) storage was required to prevent the acid fluoride from decomposing into a dark partially solid substance. 90 5.2a Spectra and Rotational Constants .Structures assumed for the cis and trans fluoride are shown in planar projection in Figures 10 and 11, respectively. The assumed parameters, the coordinates, and the rotational constants calculated from them are given in Tables XIII and XIV. .The a-type, J = 1-2 transitions, which occur in the same microwave frequency region for both the cis and trans Species, were identified first by their characteristic Stark effect. Some Q-branch transitions for the cis conformer were then identified, the correctness of the assignment being checked by a rigid rotor fit. Transitions in molecules in excited torsional states were readily observed for the J = 1—2 transitions of the cis species. .These were displaced approxi- mately 10 MHz from the ground state line and from each other. The intensity ratios between transitions in adjacent vibra- tional states was approximately 1.5. At least five and prob- ably six excited-state transitions (satellites) were seen in some cases but only four were measured. Satellites of the b-type Q-branch transitions, separated by about 70 MHz from the ground state lines and from each other, were detected. The frequencies of these lines together with those of the J = 1-2 transitions allowed all three, rotational constants to be calculated for the ground state and four excited states. Some measured transition frequencies are compared with calcu- lated frequencies in Table XV and the rotational constants, moments of inertia and second moments are given in Table XVI. 91 -L. 1A H1 Figure 10. Projection of cis-cyc10pr0panecarboxylic acid fluoride in its plane of symmetry. 3,5 1 Fc/ 6 1A -L 1H1 Figure 11. Projection of trans-cycloproPanecarboxylic acid fluoride in its plane of symmetry, Table XIII. fluoride in the 92 .Coordinates for cis-cyc10pr0panecarbox principal axis system. Atom a b c C; -0.57475 -0.65662 {0.00000 C2 0.74518 0.10706 0.00000 C3 -1.72665 -0.00855 0.75750 C4 —1.72665 -0.00855 -0.75750 0 0.82119 1.51467 0.00000 F 1.82896 -0.69787 0.00000 H1 -0.51071 -1.71472 0.00000 H2 -1.55945 0.95258 1.25514 H3 -2.41654 -0.67567 .1.25514 H4 -1.55945 0.95258 -1.25514 H5 -2.41654 -0.67567 -1.25514 aThe coordinates shown here were calculated assuming the following structural parameters: < cco = 125° r r (cc) (CF). 1.515 A r '1.55#A < OCF = 125° (CH) = 1.08 A :< H2C3H3 = 1160 r (C0) = 1.21 A ylic acid 95 Table XIV. Coordinates for trans-cyclopropanecarboxylic acid fluoride in the principal axis system.a Atom a b c C1 -0.57668 -0.72057 0.00000 C2 0.81664 -0.12548 0.00000 C3 -1.65501 0.02992 0.75750 C4 -1.65501 0.02992 -0.75750 0 1.82120 -0.79999 0.00000 P 0.85756 1.22456 0.00000 H1 -0.65095 -1.79901 0.00000 H2 -1.56400 0.94491 1.25514 H3 —2.41151 -0.55780 1.25514 H4 -1.56400 0.94491 -1.25514 H5 ~2.41151 —0.55780 -1.25514 3The coordinates shown here were calculated assuming the structural parameters given in the footnote of Table XIII. 94 .Nmz mo.o.fl mum mmwucosvmum om>ummnom Amm.mc ”a.moomd omoaumdoa Awo.m. pm.mdsma Aca.mc mm.mm-« 1am.mc mm.mmmma Asm.>c am.~¢m~a F«mumdm Aom.ac mm.«nm~a Amm.oc mo.doamd.fimm.mv mm.n~¢ma Ama.oc mm.ommma Amo.oc ma.onmmd ammupam . 1m~.oc mo.ommma Amm.ov o¢.oonna Add.mv sm.omnma F”muoom Amm.oc am.oam~a Amm.mv ~>.msm~d 1m¢.mc Hm.mmamd A>>.mc sm.mmmma Anm.mc mm.mowma mmsuofls lem.oc mauomoaa Amm.mo mm.madad Amm.mc Hm.nmada Aoo.mc «a.mmNAH adenbos Asm.mc «m.m~mma Amm.mc mm.mmmma 1mm.mv mo.mmmmd Amo.¢c s~.m«sma Amm.mc mo.mmm~a «mmumdm Ams.mc as.nomm 14m.mo pm.mmmm Amd.mv md.mdwm 1am.¢c ma.¢s«m mamnoom Ams.oc w~.oamna ammu.dm Amm.ov mm.owmma mamudam Am¢.mv o¢.mmmnfi -¢-0H¢ Amm.«c o>.«>««a amn:~.n ... . “as.mc «a.m«med mamunHm Aoo.ac‘oo.aaoma A«N.mv mm.msm¢« monumom 1am.mv am.m¢m«a «Handed Aom.>v m>.smmoa aamuo.a . Ado.mo,do.m«ooa Amm.mv mm.nnooa Aam.mv nm.mmooa “mo.oc 50.0H66a «omufloa ¢fl> nu> N.I.I> fifl> Ofl> cowuwmcmhfi .mkuosam uaon owaaxonumomammonmoHuaolmwu How ANM§¢ monocmsvmum Awaco muwmwv owns» ummHu vmumHsUHmo was mwu>ummno .>N manna 95 .22 no.0 .+. 6 “am: vacuum can Amc :Emv mwuumcfl mo mucmaoe m.ANmzq mucmumcoo Hmcowumuom mOoo H sm «NE WOoO H ed ugOHHON mm mHm WUQMUWCOU HNCOHUMUOH m5“ Gun mmfiUGHMHHmUGpN UU aamm.om ¢m>¢.om «mam.om omoo.om mmmp.ma m moom.>« «smN.>¢ mmmm.s« momm.s¢ msmm.>¢ Ana m mamm.>mfi swam.smfi m¢m~.mma mwnm.mmd mmao.mma m m U ammm.¢am Noam.mfim ewmm.mam mwam.mam m>mm.mam H omsm.mma momm.mma seem.mma nmmm.mmdA mm»~.mma nH mooo.mm m0~>.sm mmmm.em mmmm.sm memo.pm MH Hm.ammm mm.m¢m~ «m.¢¢m~ mm.o¢mm mm.mnmm o mm.«mom mm.mmmm mm.ommm mo.msmm so.>>m~ m sm.am¢e Nd.pm¢~ o¢.mm¢> em.oams mm.mmm> « d u > m u > N u > a u > o u > .wpwnosam oflom oflamxonumomcmmoumoHU>olmac How awn semv mucwfioa .H>x manna 96 Only two rotational constants (B and C) could.be accu- rately determined for the trans species of the acid fluoride because no b-type transitions were found. Since the asym- metry is fairly large, there is enough A dependence in the low J a-type transitions to determine A to within 1,20 MHz. .Some difficulty was experienced in finding satellites for the J = 1-2 transitions. Using the frequency separations found for the other three species (cis and trans aldehyde and cis fluoride) as a guide, transitions in excited torsional states were expected to lie within about 10 MHz of the ground state lines. When none were located, a wider search at a higher sensitivity (higher microwave power and higher sample pressure) was made with the same outcome. The difficulty turned out to be due to the small frequency difference be- tween excited states (about 1 MHz) which caused much overlap at normal and higher pressures. Ultimately transitions for only two excited torsional states could be found. However, the second excited state transitions seemed wider than the other two, probably because higher excited states occurred at almost the same frequency. Transition frequencies and rotational constants for the ground state and for the first two excited states are presented in Tables XVII and XVIII. 5.2b Dipole Moments For both the cis and the trans species Stark effect measurements were made on a-type R—branch transitions. As expected, analysis of the Stark shifts showed that one 97 Table XVII. Observeda.and calculated (last three digits only) frequencies (MHz) for-trans-cyclopr0pane- carboxylic acid fluoride. Transition v = 0 v = 1 v = 2 11;-212 10105.55 (5.51) '10109.72 (9.67) 10115.05 (5.08) 110-211 10887.86 (7.89) 102-202 10472.68 (2.60) 202-503 15649.25 (9.25) 15652.48 (2.52) 15654.68 (4.68) 212-513 15145.64 (5.65) 15150.08 (0.00) 15155.20 (5.14) 503-404 20757.68 (7.68) 20765.05 (5.00) 513-414 20165.54 (5.40) 20174.11 (4.20) 20181.08 (1.10) 522-423 20974.61 (4.65) 605-707 55612.02 (2.56) 625-723 56551.54 (2.19) aObserved frequencies are i.0.05 MHz. 98 Table XVIII. Rotational constants (MHz),a moments of inertia (amu A2) and second moments (amu A2) for trans- cyc10pr0panecarboxy1ic acid fluoride. v = 0 v = 1 v = 2 A 7580.. 7561- “ 7518. B 2819.77 2818.90 2818.20 C 2428.58 2450.25 2451.62 Ia 68.479 68.656 69.059 Ib 179.2260 179.2815 179.5258 Ic 208.0955 207.9525 207.8551 Paa 159.421 159.289 159.051 Pbb 48.674 48.664 48.784 Pcc 19.805 19.992 20.274 aUncertainties‘in rotational constants are as follows: A, $.20 MHz; B, i.0.05 MHz; C, i.0.05 MHz. 99 component of the dipole moment was zero for each species. The calculated dipole moments together with the measured and calculated slopes of the Stark shifts are given in Tables XIX and XX for the cis and trans conformers, reSpec- tively. The failure to find any b-type transitions for the trans fluoride is partially explained by the ratio of the squares of the a and b components of the dipole moment. Because transition intensities are prOportional to the squares of a dipole moment component, the b-type transitions are expected to be approximately 70 times less intense than the a—type transitions. In addition to confirming the assumption that the molecule has a plane of symmetry, the dipole moments can serve as additional evidence for the correctness of the assignment of the spectra to the appro— priate Species. This is helpful because the rotational constants of the two Species are not very different. By using dipole moments of some simpler compounds (acetaldehyde (5), 2.7 Debye; ethyl fluoride (29), 1.9 Debye) as a guide the ratio of “a to ”b can be calculated for both species and compared to the actual ratios. The calculated ratios are 1.25 and 5.42 for the cis and trans species, respectively. This compares to 1.76 and 7.82 for the eXperimental values in the same order. 5.2c Relative Intensities and the Torsional Potential Function. The frequency separation between excited state lines of the cis a-type J = 1-2 transitions is approximately 10 MHz 100 Table XIX. Stark effect and dipole moment of cis-cyclo- propanecarboxylic acid fluoride. Transition (av/BE2)2£:. (av/8E2):alc. 161-202 M = 0 —49.47 -49.15 101-202 M = 1 81.56 81.27 110-21; M = 0 51.47 50.66 202-503 M = 0 -12.25 -12.20 202—503 M = 2 44.77 45.11 212-513 M = 1 45.19 44.40 ”a = 2.85 1.0.05 D 0b = 1.65 1.0.05 D ”c = 0.0 0 = 5.28 1.0.05 D aHZ/(volt/cm)2. u = 0.7152 D b ocs Uncertainty in observed’SlOpes is i 1.5%.. Table XX. Stark effect and dipole moment of trans—cyclo- pr0panecarboxylic acid fluoride. Transition (av/8E2):£:. (av/5E2):alc° 101-202 M = 0 75.00 72.42 110-211 M = 0 67.16 67.75 212-513 M = 0 -2.45 -1.88 111-212 M = 0 72.15 72.17 ”a = 5.44 i.0.05 D ”b = 0.44.: 0.05 D uc = 0.0 = 5.47 1.0.05 D aHz (volt/cm)2. u = 0.7152 D ocs Uncertainty in observed slopes is i,1.5%. 101 which is very convenient for making relative intensity measurements. Unfortunately, there are other weak transi- tions in the same frequency region which are more difficult to saturate than the transitions of interest (i.e., their intensity relative to that of the 1-2 transitions increases with an increase in the radiation level). Saturation is an ever-present factor in the intensity measurements in this compound because the Spectrum is rich and transitions are generally closely spaced, which means that low pressures are required to minimize overlap. To avoid saturation, power levels would have to be used at which the sensitivity of the Spectrometer would be low; therefore, saturation and high sensitivity were almost always chosen as the Operating con- ditions. When the relative-intensities of transitions in more than one excited state are measured, all possible combina- tions are used to determine the energy difference. For most transitions in the cis species relative intensities of the ground state and the first two excited state lines were measured. Three energy differences are obtained from these three intensities, E01, E12 and E13/2. Table XXI contains the experimental energy differences for nine transitions in the cis-Species. The data for four of these nine transi- tions are considered to be more accurate than for the others because they occur in the X-band frequency region and the frequency separation between the transitions is relatively 102 Table XXI. Energy separation (cm-l) between successive torsional states for cis-cyc10pr0panecarboxylic acid fluoride. Number of Transition Averages Energy 111-212 18 61.10 101-262 17 65.21 202-503 5 66.21 508‘515 2 74.07 707-716 10 69.55 715-725 6 60.66 817-826 6 60.66 1019-1023 5 65.56 11110-1129 5 64.50 Average 65.71 105 small. These four transitions are the 111-212, 101-202, 716-725 and 817-825. .The last two are included because the ground state of the 715-725 occurs between the ground state and first excited state of the 817-825 and going to lower frequency excited state lines of the two transitions alternate. Because the ratio of the intensities of the two transitions in a given vibrational state can be calculated, some cor- rection to the measured intensity ratios can be applied by forcing the ratio of the 817-826 to 716-725 intensities to be as calculated in all vibrational states. Correcting the average energy separation from Table XXI according to equa- “1 as the eXperimental energy differ- tion (5-1) gives 65.5 cm ence between the ground state and first excited state for the cis fluoride. Two transitions measured at Hewlett-Packard (Table XXII) had associated with them the same problems discussed before and were not considered in further calculations. Only one transition could be used in deand for the trans fluoride, the 111-212. Twenty-six values for the energy difference between the ground state and first excited state yield a value of 89.8 cm'l, while Six measurements for the 212-513 transition in P-band average to 91.5 cm’l. The individual numbers can be found in the Appendix. Three transitions measured at Hewlett-Packard (Table XXIII) -1 averaged to 88 cm and were not included. Since only the first excited state was measured in all cases, no correction Table XXII. 104 Energy separation (cm'l) between successive torsional states for cis-cyclopropanecarboxy1ic acid fluoride; data obtained at the Hewlett- Packard Laboratories, Palo Alto,.California. Transition *S-Higher Pressure Lower Pressure —*- 707‘808 624-725 57.9 72.7 81.5 86.5 81.2 77.2 77.6 84.4 Table XXIII. Energy separation (cm‘l) between successive, torsional states for trans-cyclOprOpanecar- boxylic acid fluoride; data obtained at the Hewlett-Packard Laboratories, Palo Alto, California. Transition ‘<—-Higher Pressure Lower Pressure'-* 525-726 606-707 313-414 61.4 75.5 85.8 98.5 86.8 87.5 105.9 99.2 95.6 105 is required and the value of 90 cm"1 is taken to be the vibrational excitation energy for the trans fluoride. For the cis trans separation, 18 ratios for the intensi- ties of the cis 101-202 transition to the trans 111-212 transition put the trans ground state 196 cm'1 higher in energy than the cis ground state. Two ratios measured at Hewlett—Packard gave 191 and 221 cm’l. All these numbers are given in the Appendix. Because of the large uncertainty in 1 this energy a rounded value of 200 cm“ will be used. With a reduced mass of pr = (0.8641 - 0.01066 cos a) cm-1 the above three numbers for E81, E51 and 885 predict the following potential function and barrier for the hindered rotation 550 2 v v = 1790 cm-1. max (1-cos a) + £§%Q_(1 - cos 2a) + ééé-(1 - cos 5a) A plot of this function together with some energy states is shown in Figure 12. The dependence of the three potential constants and the barrier on the three energies is approxi- mately Avl = 9.1 AES;-12.4 AEgl-1.1 4855 Avg = 18,7 A331 + 24.7 ABE; Av3 = -9.6 ABS; + 12.9 ABE; - 0.1 6885 AVhax = 18.4 4881 + 25.0 ABE; — 0.5 4885 106 .mowuozam owum owahxonumu locomoumoaozo How mHm>mH mmuocw 080m ocm cowuocsm Hawucmuom .Nfi musmwm ohm omd om 0 0m: _ 4 D T m / ’ 1 O V L - / I 1 00m 1750; J oooa mflo moon» 1 come ’ 107 As is evident from these equations, a less accurate barrier will be obtained for the fluoride than was obtained for the aldehyde. Using 4 cm‘1 for the uncertainty in E81, 5 cm'1 for E51 and 50 cm'1 for the uncertainty in 885. the uncertainties in the potential constants are approximately 150 cm"1 for V1, 200 cm’1 for V2, 105 cm‘1 for V3 and 215 -1. cm for V . max VI . DISCUSS ION In Spite of the fact that the magnitudes of the potential barriers to internal rotation have been determined for a large number of molecules and the fact that a priori theoretical calculations indicate that there are no unknown forces in- volved (50), the physical models which have been put forth to describe the origin of the potential barriers have not been very useful (5). One of the reasons for studying internal rotation potential functions in asymmetric molecules is to provide more data from which a model may be constructed. In this section comparisons of internal rotation potential func- tions will be made between the two compounds studied in this thesis and between them and related molecules. In a molecule such as H202 it is presumably possible to write the potential for the internal rotation about the oxygen oxygen bond as a series, V = %-Z Vi(1-cosi8) where 8 is the internal rotation angle measured from one of the planar con- figurations. In more complicated molecules the interaction between any two atoms might still be written as such a sum and the total potential as the sum of all such pairdwise interactions1 (51). If this is assumed, then from the many 1If the molecule does not have a plane of symmetry at any angle 8, a Fourier sine series with its own coefficients must be added. 108 109 methyl group barriers found for ethane-like molecules the V3 term for two hydrogens, or other single-bonded atoms, Should be about 150 cm‘1 (52). .Nothing is known about the individual V1, V2 or other terms from the data on these compounds Since all terms other than V3, V6 etc., cancel because of the geometry of the methyl group. Similar complete or partial cancellation can occur in other molecules so that care must be exercised in comparing values of the various measured V's in different molecules. For example in the acid fluoride studied, the interaction between the two ring carbons and the fluorine atom can be represented by the following potential -1.62 V; (C-F)(1-cos8) - 0.62 V2(C-F)(1-cos 29) + 0.62 vs (C-F)(1-cos 59) +.1.62 v. (C-F)(1-cos 49) + 2v5 (C-F)(1-cos 59) + . . . where the Vi(C-E) are the potential constants for the inter- action of the fluorine atom with a ring carbon atom. The 150 cm‘1 for the V3 term between two hydrogen (bond and all) corresponds to a repulsion energy Since the staggered configuration is the lower energy one. Even though the same number can not be eXpected to represent the V3 part of the hydrogen-hydrogen potential in acetaldehyde, since both the geometry and the bonding are different, any value near this number would indicate a negative V3 for the hydrogen-oxygen interaction. .Similar conclusions can be drawn for the V3 part of the potential between a hydrogen atom and other doubly bonded atoms and also for the cycloPrOpane ring. Because many molecules of a given type have very nearly the same V3 110 value, even when hydrogens are replaced by fluorine or other atoms or groups, it seems justified to take this value as being characteristic of that type of molecule and attribute differences to other factors (51). For example V3 values for CH3COX (52) are often near 425 cm“1 and for CH3CXCH2 (52) near 790 cm'l. For cyclopropane derivatives the ring could be considered as a Single group which would be Similar to a carbon-carbon double bond (V3 for methyl cyclopropane (55) is 1010 cm“1). Because of the possible importance of steric effects, however, interactions between individual atoms will be considered instead of between an atom and the ring as a unit. In both the aldehyde and the fluoride the distance of closest approach of the atoms of the top (hydrogen and oxygen or fluorine and oxygen) to the hydrogens on the out-of-plane ring carbons occurs approximately 720 (é-w) apart and is rather small for hydrogen and fluorine--being about 2.5 A in both cases (the sum of van der Waal's radii is 2.4 R for H-H and 2.5 R for H-F (59)). In addition, the CC0 angle is expected to be less in the aldehyde than in the fluoride (5,55). If it is assumed that this close approach will result in more positive (repul- sive) V1, V3 and V5 terms for the pairs of atoms involved, then the change in V1 and V3 obtained in going from the alde- hyde to the fluoride can be interpreted as a steric effect. Table XXIV contains the potential constants for the two molecules studied here and for acryloyl fluoride. 111 Table XXIV. Potential constants (cm‘l) for cyclOprOpyl carboxaldehyde, cyclopr0panecarboxylic acid fluoride and acryloyl fluoride. Molecule V1 V2 V3 Cyclopropyl carboxaldehyde -80.1 60 1555.1 70 96 :{40 CycloprOpanecarboxylic acid fluoride -550 i.150 1800 i 200 545 i 105_ Acryloyl fluoride -95 2550 65 The interactions which are expected to change most be- tween the aldehyde and fluoride are the F-CH (or H-CH) and the O-CH interactions represented by V(For H-CH) and V(O-CH) . Included in CH is the combination of the ring carbon and attached hydrogen. The net contribution of these two terms to V1, V3 and V5 are v1 = 1.62 V1(0-CH) — 1.62 V;(F or H—CH) V3 =-0.62 V3(O-CH) + 0.62 V3(F or H-CH) v5 = -2 V5(0-CH) + 2 V5(F or H-CH) where V(A-B) is the interaction potential for one A atom and one B atom. The decrease of V(O-CH) together with the in- crease of the VKF-CH) term in the fluoride compared to the aldehyde (where it is V(H—CH)) act in the same direction to make V1 smaller and V3 and V5 larger in the fluoride compared to the aldehyde. .Since V5 is taken to be zero, its actual 112 contribution to the potential function is absorbed by V; and V3, making them more positive than they would otherwise be. The actual magnitude of these effects is not known but it is possible for them to account for most of the differ- ence in V1 and V3 between the two compounds. If the steric effect were not present, the V3 term would be less than that obtained for the aldehyde. In view of the larger change in V1 between the aldehyde and the fluoride the value V1 would have if the atoms (F or H and CH) did not approach as closely might be large and positive. ‘This would make it more nearly equal to the value implied for acrolein (7) and 1,5-butadiene (56) for which the trans species is much more abundant than the cis isomer (if present). In addition, a similar V3 value for the aldehyde and fluoride would add another type of compound to the ones fOr which a substitution of fluorine fOr hydrogen does not change V3 except for special effects. A V3 value for the two compounds about one—half as large as the value for acetaldehyde (V3 = 408 cm'l) would be eXpected if pair-wise interactions (for any two given atoms) in different molecules were of compar- able magnitude and no special steric effects were present. The arguments given above suggest that the V3 value for the two compounds in the absence of steric effects would be smaller than 200 cm”; although the accuracies in the numbers compared limit the confidence one can have in such conclu- sions. .115 The same arguments can be used to explain the potential function of acryloyl fluoride, 2550 (1-cos a) + 2 (1-cos 2a) + 65 V = — '2—- (l-COS 5a) NICO 01 This function was calculated using the estimates of Keirns and .Cur.1(57) of 115 cm":L for both the cis and trans torsional frequencies and 50 cm“; for the energy of the cis isomer relative to the trans. The reduced mass, (1.299 + 0.062 cos a) cm"1 was calculated by the method described above. ;V1,.V3 and V5 contain the two terms Vi(0-C=C) - Vi(F-C=C). A nearest distance of about 2.5 A would'tend to increase Vi(F-C=C) giving a smaller V1 than would exist without strain. This would again be more like other conjugated double bond systems where the trans is the more abundant. A larger V3 is also indicated although this could be modified some by the V5 term. Conjugation seems to be at least partly responsible for the V2 terms in the potential functions considered here. Evidence for the conjugating prOperties of a cyclOprOpyl ring.has also been obtained from ultra violet Spectra (58) of unsaturated molecules containing cycloprOpane and from dipoleamoment data (59). The difference between the V2's of the aldehyde and fluoride is almost within the large uncertainties in these numbers. The lone pair electrons on the fluorine may increase the conjugation of the system resulting in the larger V2 term for the fluoride. The still langer V2 obtained for acryloyl fluoride could be due to 114 the fact that conjugation is more effective with a vinyl group than with the ring (40). A V2 similar to that found for acryloyl fluoride would be expected for acrolein. The results obtained from a microwave study of that compound (7,41) were interpreted as being consistent with a small V2 term and possibly a gauche Species as the second isomer instead of the cis found for the three related compounds discussed here. Since only the trans Species was identified in the gas phase no definite conclusions can be drawn, but from the above discussion a cis form for acrolein is more likely than a gauche form. If steric effects are indeed as important as implied above, then some correlation between V; and V3 might be ex- pected for related compounds. (If might also be mentioned that a value of V3 near zero for the compounds studied would be predicted if V3 (O-CH) is equal to V3(0) + V3(CH), that is, if each pair-wise interaction can be written as a sum of two terms, one for each of the two atoms involved. L. VII. A STUDENT SPECTROMETER The minimum requirement for a student spectrometer intended for use in undergraduate physical chemistry courses was the ability to diSplay and accurately measure the fre- quency of the J = 0-1 transition of OCS together with its Stark component. Figure 15, which is a block diagram of the complete instrument, should be referred to for the following descrip- tion. Radiation from a Varian X—15 klystron (8.2 - 12.4 GHz) passes through an attenuator, a cavity frequency meter (wavemeter), and into a 5 db directional coupler where it is divided into two parts, half going to a mixer and harmonic generator for frequency measurement and the remainder passing through the sample Cell and finally into the detector. The sample cell is of standard construction, consisting of a three foot piece of X-band brass waveguide enclosing al29 .inch long silver septum which is supported by two equally long grooved teflon strips. Many of the circuits used in the components of this instrument made use of integrated circuits and were modifications of similar circuits described in an RCA integrated circuit manual (42). 115 .Hmuwfionuommm pompoum mo Emnmmfio xoon .ma musmfim 116 ouumuwo z>n hammsm “mam no» , m>wu on IfiHmEm IlllumHHwomo Iwmcmm Hmucsoo >oomlo Hm3om umx ma mmmnm Hmumfim>m3 couumhax memwo p _ \% hammsw mmoom kumz Nmmz m \N .— D O C _ I Chumwax 4.0.2.250 Hm3om Houmscmuud p _ 1 “may Iwamem Hmwm nouowumn um: 04m . .1398 .83 mz_mm.d ImeEm . NmM ma f . b p MOHQDOO. - _ .8... F _ . A Emummm finsom> OB Houmumcmm owSOEHmn ocs “ox“: 117 Since the role of each part of a microwave spectrometer was described earlier, this section will deal mainly with the circuit details of the components of the student Spectrometer. A battery Operated tuned preamplifier (45) supplies most of the gain of the system: a schematic of the preampli- fier is shown in Figure 14. The input circuit separates the small 15 kHz component of the signal coming from the detector from the much larger DC component sending the former to later stages while the DC part is passed to ground through a current meter of either 0.2 or 1.0 milliampere sensitivity. In order not to load the first series-tuned.LC section, an n channel field-effect transistor is used to.pick off the 15 kHz signal from the junction of the 0.005 uf capacitor and the 25 mh choke and pass it to the three-stage integrated circuit amplifier (CA 5055). Variable feedback on the first stage, brought about by adjusting R1 is used to change the gain. The maximum gain of this integrated circuit is 129 db or 8 million. Series LC tuning is used between the first and second and between the second and third stages of the preamplifier resulting in'a bandwidth of about three kilo- Hertz. .Maximum gain of the preamplifier is 400,000 at a frequency of 15.5 kHz, while the maximum undistorted output is slightly less than two volts. The phase-sensitive detector (Figure 15) is a Shunt- type gate (44) consisting of a CA 5019 integrated circuit, 118 .Hmfimwamem owssu me ma .wd musmam no oosnosa u 0 Houma ucmuusu mmom «o ooa m ooo mm . .III1T||_o m, a A «m m a 9 a - 9.o| m .Aumoo.o oa L<m I ..‘I -l-ll-.‘.l 'l'“ '- Il‘ll'll (l 119 .HmwmemEm 0cm Honomumo m>wuamcmmlmmmnm .md musmflm L%. . . MW. . hW. . 1: . - n m ,9 W1 NO I—I (#000040 I - HQ. % usmuso . m. m (“WM/x).— Bn. H m HA m 93 no: :31 mi. owl , L- 09 hfi Mm +fi muao> o + Hmcmnm moswummmu 120 four of whose six well-matched diodes are used in this appli- cation. A twin T filter proved necessary to remove the 15 kHz Signal from the output of the detector at low time con- ‘stants. A low-gain DC amplifier (45) using a CA 5000 inte- grated circuit boosts the output by a factor of five to give a maximum undistorted output of 2.5 V peak-to-peak. The reference signal for the phase-sensitive detector is supplied by the 15 kHz oscillator (Figure 16) which is also used to drive the modulator or power amplifier described below. The 10,000-ohm variable resistor in the tank circuit of 91 allows some frequency variation by changing the effective value of the capacitor. R2, 02 and Q3 are used for phase shifting, allowing a variation of about 150°. The remaining transistors and the integrated circuit are used to square the signal and to amplify it to the 17-volt level which is needed for the phase-sensitive detector. A modified high-fidelity amplifier (46) (Figure 17) serves as the power amplifier which supplies a high voltage square wave to the septum of the waveguide. .The integrated circuit and Q; change the 15 kHz sine wave from.the oscil- lator into a square wave which is then passed on to the last two stages. Because the input to 02 is large compared to its supply voltage, it is either saturated or off. Therefore, the output of Q2 can be changed by changing the supply voltage to this stage. Since the last four transistors are just cur- rent amplifiers, the output of the square-wave generator is 121 .HOumHHwomo mocmummmu me ma Heuomumo m>fluwmcmmlmmmnm 08 .AJ .mH wusmflm umwmwamam Hm3om 09 >md / xma sma mo So.m s5.4 So omo omo Sm.a xs.o mm...” \q 29 m 4 N . Jilin. ... 49m 51 91|||||1T|| : H.o i. [1. o r 1. H 0 mm 0061 Mo in. Mo>4 mm.m o.o m. . fl .2. 1. v «.0 x00« .4. fi >4oo o .r Sma omn- ohm sod xo>9 . 2% xma mum 122 .Auoumasoosv umamaamem HmBOm. .59 095595 Ca 00 .————< H -—|I—-—- =, M0 Mmm 4 a «.o u o m>m3 mumzvm >ONIO omm rl. Xn.m Mam OH lT Sm.“ 95.9 o.o 29* mo 8... W T .fil1flnhwn NTI T494. 8 . “T o do Sod 1 so.m Sm.m so.m _>od 125 controlled by this supply voltage. A step-up transformer having a turns ratio of about 25:1 produces a high voltage AC signal that only Slightly resembles a square wave. The output network (47) of the square-wave generator trims the tOp and bottom of the square wave and ties it to ground. The 1 microfarad capacitor isolates the square wave from ground so that it may be biased by an amount equal to the DC input voltage at that point. The variable voltage for the last two stages is generated in the modulator power supply (Figure 18) and can be as large as 24 volts at‘1 ampere which is enough to produce a 740 volt peak-to-peak square wave. However, due to heating of the output transistors, the transformer, and the two resistors in the wave-shaping’net-‘ work, the maximum safe limit on the square wave is about 550 volts. This output voltage requires 15 volts at 460 milli- amperes from the power supply. The waveform of the square wave is very clean but the rise and fall times are a relatively high 8 and 5.5% respectively. A second power supply having -5, 5, 10 and 15 volt low- ripple outputs provides power for the oscillator, the DC amplifier, and the first part of the power amplifier. .Due to the low resolution (0.1%) of the cavity frequency meter, frequency measuring equipment had to be supplied in order to be able to make relative frequency measurements accurate to about 50 kHz. 124 2N5055 \” 0-24V 00K 1100 5.5K || 24V -<;—————d -- 100 T Figure 18. Modulator power supply. Dual 100 pf 2N5819 0.55 mH 100 n . _ . , 1. ll W 21 47 pf J_ ‘ -4.7 pf / 1 120 T ' 0.001 -10 E' : ‘1.— T I ! 1470pf '— 7 4'7Lf4'71pf - i F‘4I if 302 _L0.001 10x : Figure 19. 5 MHz oscillator. 125 The method adopted makes use of a stable, crystal- controlled variable 5.MHz oscillator (51) disgrammed in Figure 19. The capacitor tuning allows frequency changes of approximately 20 kHz while the variable inductor permits small changes in the center frequency. It was found that the oscillator would not lock to the crystal frequency when turned on unless the supply voltage was increased gradually starting at a low voltage. A 100 ohm resistor and 10 microfarad capacitor provide this relatively slow voltage buildup; however, if the center frequency is changed by too great an amount from the 5.MHz point, erratic behavior may result. A frequency-multiplying chain, removed from a National Radio Company Atomichron, accepts 5 MHz and multiplies it in stages to 10, 50, 90, 270 and 540 MHz. The power output of this instrument is sufficient to obtain difference fre- quencies directly when its output at 540 MHz is multiplied and mixed with the microwave Signal. The beat signals are not quite strong enough to allow accurate frequency measure- ments, so a tuned amplifier in the form of a broadcast-band radio tuner increases the voltage of the difference frequency if it happens to be 1.65 MHz. Changing the 5 MHz frequency by 20 kHz will change the 540 MHz signal by 2.16 MHz. ‘When the 540 MHz output is multiplied to the microwave range of interest--about 12000 MHz--the change will be 40 MHz. This is not enough variation to make it possible to place a har— monic of the 540 MHz signal anywhere in the X-band range. 126 However, enough subharmonics at 270 and 90 MHz are present to give detectable difference frequencies when multiplied and mixed with a microwave signal. For complete coverage the 50 MHz component would have to be large enough to give beat signals, but only a few 50 MHz markers can be seen. Fortunately, the transitions of interest can be measured with 90, 270, or 540 MHz markers. A stable low-ripple DC high-voltage supply is used to apply a well defineanC voltage to the septum. A Heath Universal Digital Instrument (Model EU805) measures this voltage and also counts the frequency of the 5 MHz oscillator. The signal from the output of the phase-sensitive de- tector is applied to one beam of a dual beam oscilloscope while the voltage across the crystal current meter and the output of the 1.65 MHz tuned amplifier may be applied to the second beam, either separately or in parallel. The instrument described above is sensitive enough that it is possible (not necessarily for the students) to readily see on the oscilloscOpe the J = 0-1 transition of 16012C348 in natural abundance and to just barely see the same transi- tion in 16013C328, also in natural abundance. It is believed that the most dramatic improvement in sensitivity would result from an increase in the sample cell length since the current cell length is only one-fourth, or less than one-fourth, that of a typical cell for microwave spectroscopy. LIST OF REFERENCES 10. 11. 12. 15. 14. 15. LIST OF REFERENCES J. D. Kemp and K. S. Pitzer, J. Chem. Phys. 4, 749 (1956). C. E. Cleeton and N. H. Williams, Phys. Rev. 42, 254 E. B. Wilson, Jr., Adv. Chem. Phys. 2, 567 (1959). D. 0. Harris, H. W. Harrington, A. C. Luntz, and W. D. Gwinn, J. Chem. Phys. 44, 5467 (1966). R. W. Kilb, C. C. Lin, and E. B. Wilson, Jr., J. Chem. Phys. 22, 1695 (1957). L. S. Bartell and J. P. Guillory, J. Chem. Phys. 45, 647 (1965). E. A. 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APPENDIX APPENDIX EXPERIMENTAL RELATIVE-INTENSITY DATA .The relative intensity ratios (r) obtained from oscil- loscope measurements or recorder tracings are reported here as energies calculated from E(cm’1) = 0.695 T ln r. 1. Cis-cycloproPyl carboxaldehyde 503-512 transition Temperature Energies (cm'l) 25° 86.7 92.1 97.5 126.5“ -9° 155.8 98.5 122.5 125.5 129.5 -75° 118.4 114.6 118.0 115.0 4121.5 106.1 118.5 125.9 .105.6 434-413 transition Temperature Energies (cm-l) 25° 112.1 110.0 107.5 105.8 98.9 99.0 98.4 100.7 116.5 101.5 97.5 108.9 105.9 -4° 125.0 118.0 119.0 119.0 116.0 105.0 100.0 -75° N101.1 102.1 105.9 .106.5 .120.0 .114.2 105.6 111.4 110.6 102.0 99.5 102.4 150 115.0 102.8 99.8 119.0 7150.5 105.4 151 535-512 transition Temperature Energies (cm’l) —4° 114.0 110.0 2. Trans-cyclopropyl carboxaldehyde 111-212 transition Temperature vEnergies (cm-1) 25° 125.2 -750 127.1 151.1 154.9.152192126.9 121.51125.4 128.7 129.4 127.1 125.0 121.7 154.5 122.5 120.8 117.8 117.2 122.4 124.9 125.6 121.6 117.8 125.1 122.5 120.5 120.0 122.0 120.6 118.2 125.6 122.6 120.9 127.0 116.2 115.5 121.1 125.6 112.1 121.5 125.6 114.1 120.5 128.9 117.8 117.8 122.0 126.1 115.9 128.5 127.9 126.4 126.4 122.2 125.9 124.1 122.6 118.9 117.8 122.7 124.0 101-232 transition Temperature Energies (cm’l) 25° 122.5 121.7 ~75° 129.6 122.0 155.0 124.2 150.6 155.9 122.6 124.4 116.6 116.1 107.6 116.0 117.8 111.6 126.1 128.8 120.5 113-211 tfansition Temperature Energies (cm-1) -75° 125.8.129.5 117.2 120.5 122.0 125.5 110.4 127.5 122.9 127.2 122.1 118.0 152.8 112.5 117.8 120.8 Temperature -750 cont'd 124.2 127.5 155.8 128.9 125.5 128.5 116.0 116.0 125.9 119.8 125.7 150.4 125.7 111.9 115.5 114.6 122.0 120.7 152 Energies (cm- 1) 5. Cis—trans ground state energies of cyclopropyl carboxalde- hyde at 28 C. -2506 ‘11 .8 15.1 16.7 -600 21.7 -408 -509 -205 22.1 25.4 50.7 4.7 4. Cis-cyclopr0panecarboxylic acid fluoride at -75°C. and Energies (cm'l) Transition .111-212 44.5 70.6 57.6 57.2 67.2 49.0 75.4 62.2 47.5 70.6 101-202 64.2 68.9 66.4 55.9 80.9 62.9 57.6 60.5 60.5 55.1 715-725 61.9 75.5 60.9 74.5 59.0 817-823 52.6 61.1 57.2 202-503 64.8 69.2 64.6 603-615 76.7 72.9 707-716 71.4 75.5 72.5 75.9 74.1 64.5 1019-1023 70.1 60.0 65.4 11110‘1129 55.4 77.0 62.1 62.8 58.5 66.4 74.9 56.5 62.9 62.2 49.1 65.4 64.2 45.1 67.5 .10.9 15.8 50.7 57.5 58.9 62.7 72.0 54.9 .55.6 68.4 75.5 62.5 60.4 58.5 55.8 58.9 155 5. Trans-cyc10pr0panecarboxylic acid fluoride at -75°C. Transition Energies (cm'l) 111-212 108.5 112.8 114.6 108.5 119.2 125.9 110.4 116.4 100.8 104.0 80.4 92.0 100.5 89.8 85.2 82.6 91.5 77.0 70.6 66.4 75.4 82.4 77.0 88.5 86.1 85.4 212-513 105.4 110.4 110.4 70.6 80.9 64.7 6. Trans-cis ground state energy of cyclOpropanecarboxylic acid fluoride at -75°C (MSU) Transitions Energies (cm-1) cis 101-232 188.5 200.5 205.2 177.0 197.5 196.9 207.1 trans 111-212 195.0 202.8 191.9 194.6 189.9 191.1 197.6 202.1 186.5 194.6 186.7 At the Hewlett-Packard Laboratory, Palo Alto, California cis 624-725 202.4 256.5 218.5 227.4 trans 633-737 (Igltlflllflnanwm 3 0 3 9 Em Am "I m3