I’HIHWI I > M 145 176 THS THE? PMCIRCD'WAVE 3TUDY (BF MGMQ~BEUTERQ étfiCfi‘50-fiHif'3-‘iiflfi CYCQQPROPANE Tiwcis far {in} {)3ng c4 52%. S. Mi’Ci'iASét-N We!“ M‘H‘w’ERSi'TY ”5" 54' m mewsms magma igfifi THVT‘B’S TH" ABSTRACT ma MICROWAVE STUDY or MONO-DEU'IERO, MONO-CHLORO CYCLOPROPANB by Thomas Krigas A short chronological outline of the cyclopropane bonding problem is given. The theoretical aspects of microwave spectroscopy are presented with the emphasis placed on the expressions for the energy levels, selection rules and the perturbations arising from.a nuclear quadrupole and/or from an electric field. Also discussed are the calculations, instrumentation and sample preparation. The pure rotational spectra of the deuterated species EEEEEEEH35C1 (cis), CHDCHZCH35C1(trans), and CHZCHzCD§5C1(sec) have been examined and L.____1 L_____: rotational constants assigned. when these are combined with the remain- ing four unique isotopic species that have been examined by Dr. G. D. Jacobs and Professor R. H. Schwendeman, a complete substitutional struc- ture is determined. The bond distances and angles are r(C,Cz) - 1.513 X, r(CCl) - 1.7h0 X, r(CzC3) - 1.515 X, r(CH)sec - 1.079 X, r(CH)cis - 1.086 X, r(CH)trans - 1.082 X, L can - 118.70, A c1CH - 115.80 and L 1101 - 116.20. It the z principal axis of the quadrupole tensor coincides with the C01 internuclear distance, the quadrupole coupling parameters are X 22 - -71.h Pic/sec and 11 bond - 0.029, orx zz - -73.5 Hc/sec, if a cylindrical charge distribution is assumed. In the light of this structure and its relationship to the structure of similar molecules, the bonding in qyclopropyl chloride is discussed. THE MICROWAVE STUDY OF MONO-DEU'IERO, MDNO-CHLORO CYCLOPROPANE By Thomas Krigas A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF'SCIENCE Department of Chemistry 196h To My Mother and Father ii ACKNOWLEDGMENT I wish to eXpress my appreciation to professor R. H. Schwendeman for his guidance and assistance which he so generously gave during this investigation. iii TABLE OF’CONTBNTS I. HISTORICAL BACKGROUND . . . . II. THEORY III. DESCRIPTION OF THE MICROWAVE SPECTROMETER . . . . . . 2.1 2.2 2.3 2.11 2.5 3.1 3.2 3.3 3.11 Introduction . . . . Energy Levels . . . Moments of Inertia and the Kraitchman.Equations. Nuclear Quadrupole Moments . Stark Effect ..... Klystron Oscillator Source ..... . . . Absorption Cell . . C 0 Detection System . . . Frequency Measurements . IV. MOLECULAR STRUCTURE OF CYCLOPROPYL CHLORIDE REFERENCES 11.1 11.2 11.3 11.11 11.5 Introduction . . . Sample Preparation . . . MOIecular Structure Quadrupole Analysis Discussion . . . iv I C O O O O U I O O Page Oct-wt» 10 13 15 15 1.7 18 18 21 21 22 2h ho L1 1.6 LIST OF TABLES TABLE Page I. Hypothetical unsplit frequencies (Me) for mono-deutero cyclopropylchloride.................. 28 II. Calculated and observed frequencies (MC) for the hyper- fine components in CHDCHZCH35C1 (trans). . . . . . . . . 29 L_____! III. Rotational constants (MC), moment of inertia (a.m.u. - z) and second moments (a.m.u. - 22) for various species of cyclopropyl chloride . . . . . . . . . . . . 31 0 IV. Coordinates (A) of the atoms in cyclopropyl chloride . . 33 o . V. Bond distances (A) and bond angles (degrees) for cyclopropylchloride.................. 35 VI. Comparison of coordinates (3), bond distances (X), and bond angles (degrees) of heavy atoms computed from the Kraitchman Equations assum ng (a) no reduction in bond lengths, and (b) 0.00005 reduction in bond lengths 36 0 VII. Changes (in A) in coordinates of the atoms or cyclo- firOpyl chloride produced by an increase of 0.001 a.m.u. z in quasi~inertial defect upon isotopic substitution . 39 VIII. Quadrupole coupling constants in C3H535Cl . . . . . . . h2 IX. Comparison of structural parameters of cyclopropyl chloride with those of related molecules . . . . . . . . h3 LIST OF FIGURES FIGURE Page 1. Block Diagram of the Microwave Spectrometer . . . . . . 16 2. A Projection of Cyclopropyl Chloride in the a, c-Plane Of SW try 0 O O I O O O O O O C O O I O O O O I O O I 23 vi I. HISTORICAL BACKGROUND In 1885, Baeyer(l) presented his strain theory to account for the difficulty of small ring formation and for their susceptibility to addi- tion reactions. ‘Hhen his erroneous assumptions of ring planarity for the larger rings (2) and his concept of the inflexible regular tetra- hedron (3) were reexamined, a modified theory evolved that was accepted for years. Since that time, a number of investigators employing heats of com- bustion (h), specific gravity, melting points, dipole moment (5), elec- tronic spectra (39. 6,7,8), rates of hydrotysis (9), H-D exchange (10) and dissociation reactions (10,11) have shown pro and con evidence for the existence of resonance energy with transmittance of conjugation in cyclopropane and its derivatives. This anomalous behavior for saturated hydrocarbons has also been treated theoreticalLy (12,13,1h). The most complete anatysis, that due to Coulson and Moffitt (15), treats the carbon-atom hybridizing ratios as parameters and calculates them by means of the variation technique. Their results for cyclopropane indi- cate delocalized "bent" bonds with shortened (C-C) distances and the HCH angle ' 116°. In an attempt to resolve some of this small ring controversy and in a continuation of ha109enated hydrocarbon studies at Michigan State University, the microwave spectrum of qyclopropyl chloride was examined. Previous structure studies of cyclopropyl chloride with electron dif- fraction (16) and microwave spectroscopy (17) have been carried out. The special attraction of microwave spectroscopy stems from two factors: It presents a region of the electromagnetic spectrum.previously 1 2 inaccessible (0.06 cm-t>'wavelength <:30 cm-l) in which many molecules exhibit pure rotational spectra; extremely high resolution is realized when the Hughes-Hilson designed, Stark-modulated instrument is used. With discarded military radar equipment capable of generating, transmitting, and measuring microwaves, microwave spectroscopy emerged in l9h6 as a powerful tool in structure determination. Uow pressure gas absorption spectra of’NH; (18) and 0C3 (19) in that year not only verified the validity of existing rigid rotor energy solutions but pointed out that hyperfine splittings could arise from Stark effects and nuclear quadrupole moments. . Although both hyperfine splittings greatly complicated the spectra, each afforded additional sources of molecular information. The Stark effect is now commonly used to identify transitions and compute dipole moments. It has been shown by Townes and Bailey (20) that the nuclear quadrupole coupling constants can be related to amounts of ionic and covalent character and hybridization. To date, the most valuable facet of microwave spectrosc0py has been the determination of bond angles and bond distances. In the gener- ally accepted method (21), the differences in the moments of inertia of two isotopically substituted molecules give the coordinates of the substituted atom. Then when all non-equivalent atoms in a molecule have been isotopically substituted a complete structure is obtained. II. THEORY 2.1 Introduction The radar development program of World war II produced equipment capable of generating and measuring frequencies in the microwave region of the electromagnetic spectrum from 1 to 1000 kilomegacycles seconds". The benefit to molecular spectroscopy was immediately apparent. Here was an experimental method whereby essentially pure rotational transi- tions of manficompounds in their ground electronic and vibrational states could be studied. Fortunately, the necessary expressions relating these transition energies to molecular parameters had been determined by application of quantum.mechanics. The observable frequency is governed by the Bohr condition wZ-w, V " h (2-1) with W, representing the initial and W, the final energy state. Energy levels are found as solutions to the equation 11 W - W (2-2) where H is the quantum mechanical Hamiltonian Operator and V is the wave function describing the qystem. Born and Oppenheimer have shown that the total wave function for a molecule can.be separated into an electronic and a nuclear portion. If external forces and nuclear spin are neglected, the nuclear eigenfunction can be expressed as a product of a function for a vibrating non-rotor times a function for a rigid rotor. b Although the case of strong interaction has been worked out, vibra- tional frequencies are often on the order of 104 times those of rotation. For a particular vibrational state, the nuclear position may be considered fixed at the average value over the vibration. The remaining effect, that due to Coriolis coupling, is often ignored. 2.2 Energy Levels The Hamiltonian for a free rigid rotor in a body-centered corrdinate system becomes 2 P H ~i§ if? (2-3) 12’”: v P2 H -t‘;[—Lf;—L]+ h;- [f] (2-b) l 2 2 P P P H.§§£[IL.IL.IL] (2-5) x y z where (2-3) applies to linear, (2-h) to symmetric and (2-5) to asymmetric tops. Px and 1x are the components of angular momentum and moment of inertia respectively about the x-axis and similarly for the other axes. Rigid rotors are classified as linear if two moments of inertia are equal and the third is zero, as prolate symmetric tops if two moments are equal but greater than the third (cigar shaped), as oblate sym- metric tops if two are equal but less than the third (coin shaped), and as asymmetric if all three moments of inertia are different. Obviously, if a unique molecular axis can be distinguished, it has been labeled 2. The x, y, z co-ordinates map into the a, b, c co-ordinate designation preferred.by spectroscopists, subject only to the proviso I¢Z.Ib.2 Ia‘ (Moments of inertia are discussed in greater detail in Section 2.3). 5 In a molecule fixed Cartesian co-ordinate system, the matrix elements for angular momenta become (13),,“ J,K+1 " “alum J,x+1 '11sz * 1) ' “(K * ml 2 (2‘6) (PZ)J,K3 J,K . K (2-7) 2 _ z 1 _ z _ (py )J,K; J,K (Px )J,K; J,x 2U“ * 1) K 1 (2 8) 2 - 2 2 Z a .. (P )J,K3 J,K PX + Py 4- P2 J(.J +1) (2 9) The rotational quantum number, J, takes the values J - 0, l, 2 . . ., while K, the component of angular momentum along a unique molecular axis, becomes ii 0 0, il, 12, . . . 11, where J 3. Mil. In the preceding matrix elements K.may be replaced.by H'(Section 2.5), where M is the quantum number for the projection of the total angular momentum along a space- fixed axis. In the case where H is substituted for K the sign of i must be changed and x, y, 2 then refer to space-fixed axes. The correct energy expressions are obtained by combining the appro- priate Hamiltonian equation (2-3) through (2-5) with the angular momentum constraints (2~6) through (2-9). This leads to l we“ :- J(J + 1) (2-10) 8n2 I b for linear molecules. For an absorption transition, AJ - +1, the Bohr frequency condition (2-1) gives V - 280 + 1) (2-11) where J is the lower state quantum number and B is called the rotational constant. B 3 h (2-12) 8H: Ib ' Similar considerations for the symmetric top yield wr (prolate) - h[BJ(J + 1) + (A - B)K2] (2-13) "r (oblate) - h[BJ(J + l) + (C - B)Kz] (2-1h) with y - 2B(J + l) for both cases, since the selection rule requires that AJ - 1, AK - 0 where A and C are also rotational constants defined by A 2 h , C s h 2 8n Ia 81:1 1c In passing from a symmetric to an asymmetric top, the K double degeneracy is removed, because there is no longer a unique molecular axis. Nevertheless, J remains a "good" quantum number with the total angular momentum P still quantized in units of h/éwir3(3—:rl). There are still 2J + 1 levels for each J. The levels are ordered by a running subscript T, which takes the values -J, ~J+l, ..., OJ. An alternative notation is written as J The number L1 would be the angular K- ,K+ ' momentum about the a-axis in the limiting case of a prolate top, and K” corresponds to the limiting case of an oblate top with the angular momentum taken about the c-axis. It may be shown that T - K4 - Kn andx_,+Kfl - JorJ +1. Although no closed form solution has been obtained for the energy of an asymmetric top, there are two numerical methods commonly applied. Wang (22) has treated the example of a slightly asymmetric top. For a near-prolate top (B - C), the energy is written as wr-(B*°)J ->-> I - §m1(r,‘l - ”iri) 5 . (2-21) ...> here r1 - radius vector from the center of 21353 to the it]; mass -§ 1 - unit Wadic m1 - mass of the it}; atom. Typical Cartesian elements are . a . .— Zn 1|!(y1 +26), 110' Iyx gmixiyi, where xxx? Iyy,and.lzz_are called moments of inertia and IXY’ Ixz and Iyz are called products of inertia. An expedient calculational device is to define a planar dyadic P. -> ..., P 211nm r, (2-22) with a, and r: defined as before. This leads to the following typical realtions: l Isoc - Pyy + Pzz’ Pxx ' 5(1)? + Izz ' Ixx)’ PX? . - IXY. (2-23) According to a theorem of mechanics, there are three mutually per- pendicular axes about which the moment of inertia is a maximum or minimum. In this axis system a, b, c, the matrix representations of both dyadics I and P are diagonal with the implicit center of mass conditions 212nm - o, §m1bi - o, ignite, - 0. Upon isotopic substitution of the 9-9-1- atom of mass m by m + Am, the principal axis of the substituted molecule will in general be translated and rotated from those of the original molecule. The coordinates of the substituted atom in terms of the principal axes of the parent can be expressed with the planar dyadic by making use of the parallel axis theorem. The P matrix becomes 2 Pea ‘ ”as ”35133 “ascs pl .. “ash, Pbb + “1332 uh c (2-2h) vases ”bscs P + ”c 10 MAm where p. - m , and M - 2 m1. Diagoralization of this matrix cor- i responds to a rotation into the principal axis system of the substituted molecule. Kraitchman has shown that the co-ordinates are P' - P P' — P -l bb bb cc cc I a I - p. [(P' - P )(l + )(1 * p———"—)] (2-25) 3 aa aa bb ~ aa cc ' Pas Calculation of! b land lc lis a matter of cyclic permutation of the subscripts. The sign of a co-ordinate is evaluated from other source s of inform- ation, or through chemical intuition. Then'uhen all non~equiValent sites in the molecule have been substituted, each atomic position will be known. 2.hL Nuclear Quadrupole Moments All nuclei possess an intrinsic spin analogous to that possessed by an electron. The angular momentum.I, due to the spinning nucleus, is quantized in units of h/bn. When I> l/? a nuclear charge asymmetry results, creating a complex spectrum. This hyperfine splitting is caused by the interaction.betueen the nuclear quadrupole moment and the gradient of the molecular electric field at the nucleus in question. The required orientation restrictions are fulfilled by defining the total molecular angular momentum quantum number F F-J+I,J+I-1,...I’J-Il (2-26) such that F'ZLO' Hyperfine splittings are usually small compared to rigid rotor energy level spacings. In this case, the selection rules become AJ - O, 11, AF - 0, 11, AI I‘O. The strongest components are produced when AF - AJ. ll Tao successful expressions for nuclear quadrupole energ splittings of asymmetric tops have been derived. The first uses the numerically attractive reduced energy function £11,, (X ) (28). Here the interaction energy HQ is no . 367D. (xaaf ch) NONI) - lg'géfl] + (xaa' ch) [BOO - 937K711 as) (2-27) where the quadrupole coupling constant X“ is 2 X83 - éQ(§;—2E)EV. e - electronic charge 0 ' electric quadrupole moment, 2 (fig; the average electric field gradient at the i3}- nucleus, a I CC+1 -I I+1JJ+1 - + Y(F) It Casimir's function - and C - F(F+l) - I(I+1) - J(J+l). Casimir's function Y(F) is tabulated from J '- l to J II 10 for \mrious I and all possible values of 1“ (26,29). The third constant Xbb is found from Laplace's equation. X as + Xbb 4» ch - 0. If the molecule is a near symmetric top, then wQ - final - J(J+l) - 3C2b2)9m + (C1+2C2b+3C3bz)qn1\IY(F) (2-28) where 2 V 7K 22 ) av. - 22m e _a mi, 7\ _ e’v/axti- Jail/Hi , Xxx” Xxx qm X 22 12 with 2m being the molecular principal axis most nearly representing a symmetry axis. Prior to the spectral analysis, the hyperfine splitting calcula- tions are made on the basis of assumed values of the rotational constants. Once transitions have been assigned and better rotational constants are available, an iterative process of calculation quickly converges both the rotational and quadrupole constants to their experimental values. Nuclear quadrupole studies are also valuable in explaining the type of bonding between the quadrupolar atom.and its adjacent neighbors. The coupling constants obtained from equations (2-2?) or (2-?8) have their frame of reference in the inertial principal axis system. By means of a similarity transformation, the coupling constant matrix can be rotated into the quadrupole principal axis system. This is accom- plished either by assuming that one axis lies along the chemical bond, or by assuming that a cylindrical charge distribution exists about one axis. Townes and Bailey have shown (30,31) that charge distributions in E: 1 molecule arising from adjacent atoms and closed shells of electrons do not contribute appreciably to the quadrupole coupling. Moreover, the amount of ionic character I of a Cl bond is related to the quadrupole coupling constant in the bond direction by I - (1 - 32 + d2 + II) - (Xzz/eoq atom) (2-29) where s and d are estimates of the amount of hybridization from s and d orbitals, and II is the amount of double bond character. 13 2,5 Stark Effect Another complexing spectral factor is introduced when a unidirec- tional electric field is applied to a molecular system. The energy split- tings that occur are known as the Stark effect. This interaction energy between the electric field and the molecular dipole destroys the 2J+l degeneracy of rotational levels. Components of angular momenta along the space fixed direction of the electric field are quantized in units of h/bn.and are characterized by M, the magnetic quantum number. M takes the values M - J, J-l ... -J. Stark splittings are often small compared to rotational levels. Therefore, Stark expressions are obtained by standard perturbation cal- culations. The so-called "first" and "second“ order Stark effects indi- cate the order of perturbation necessary in the calculation. Stark orders also refer to the power of the dipole moment, electric field, and magnetic quantum.number which appear in the final equations. Rotational levels of symmetric tops that exhibit first order Stark ‘will be split into 2J+1 components whereas linear and asymmetric tops which exhibit second order (terms of NZ only) will be split into J+l levels. If Stark-modified spectrometers produce fields parallel to the microwave electric field, the selection rule AM - 0 holds. As a con— sequence, the number of Stark components is equal to the lowest J level involved in the transition. After the assignment has been made, the dipole moment can be evalu- ated. If the perturbation expansion calculation is made for the asymmetric rotor with the perturbing term HE, the first order energies are zero. The second order splittings from the rigid rotor energy levels are 1h AWL? - 52 [Fix “3 + F3”? p; + Fit p: 3 (2-30) where pa, uh, uc, are components of the dipole moment in the a, b, c directions; and F11, ... are functions of J, ‘t’ and M2 in the a, b, and c direction: and can be nmnerically evaluated. A Stark component for the transition J,T -—-> J', T ' is due to the difference between two shifted energy levels found from equation (2—30) . That is . 2 .2 2 C 2 .. hI/J’T 33"?" E [AFa Pa + AFbub + AF pc] (2 31) Hence, a plot of frequency of one Stark component versus the value of E"- for several transitions will afford slopes that allow determination of pa, “b’ and ”c where the total dipole moment is z . 2 z _ u via + vb *“c' (2 32) III. DESCRIPTION OF'THE MICROWAVE SPECTROMEIER A brief description of the microwavespectrometer at Michigan State University will follow the diagram shown in Figure l. The conventional component outline of a spectrometer into source of energy, absorption cell, detector, and a frequency measuring device will be adopted. For a more complete description, see Jacobs (32) and Tobiason (33). ,3. 1 Energy Source The klystron oscillator has a regulated D.C. filament supply used to heat the thermionic cathode. The necessary voltages for the klystron grid, anode and reflector are produced by an FXR type 28153 power sup- ply. The major line voltage fluctuations are eliminated by a Sorensen Model 10008 voltage regulator. In this laboratory, microwave radiation is generated by reflex klystrons. The electrons emitted by the cathode are accelerated by a positive voltage on the plate and controlled by a grid. Most of the electrons are allowed to pass the plate and enter a deformable cavity. At this point an.alternating voltage modulates their velocity forming bunches of electrons. The bunches are repelled by a highly negative electrode at the far end of the tube. Depending upon the cavity size and the phase of the returning electrons, the bunches give up some of their energy to the cavity. Klystrons, available in this laboratory, cover a frequency range from 8 to 37.5 kilomegacycles (ko). 15 16 .uouofiouuoomm o>m30uom2 ofi mo £5.3de xoofim .H oupwwh manoud< P I >33 ‘ n ...l , 3:3 .8on L, J J renew menu 304. uoBOnH odd 3% gonzo x nm - v 02 com Hccmm Bun-COD, max COHHmshg uo>mooom FF ‘ —— O .t» M A J. 06mm _ - nouMHoGoD hammam I .. - neaoouofi 5008 omoonozwomo «dofimdh ‘ .7 ozfimcow—r 3mm Econ Hann— doaumrvm quooom . ommnnm. _ I - - 08mm H I. H . y . _ aca— - ommfio> zamam Hunger/om , no nooo ‘ r - - , o m acmcouoL r noBOnm amusem— oGSQEmounm , a i - v 4 v9.58 twamsm peanuocoo HouucoU ox H uoBOnm m3 oumavm @3395 gnommouo: .«3 co 1 :3 "mama .83253 882 axon: a. a a o n M v i - o .m H .m an “ Eolllgessmfi erg. Ha Haw/PH. P 11. _ U I comm X _ A J o o L - J . A C .33 M Q , H3950 #38300qu ”Wu—o coating 3. .5 24.32:: as a a: 03.9.58 Eoumumm ~93on 0:05 warm cannon > W330 m “X h v at» .x ~300qu ca... .2253 Emma swans mmcm noBOnm o3: ‘ oozouudoo “5:03:00 17 332 Sample Absorption Cell The sample cell used in this work has a length of ten feet and is constructed of brass with a silvered interior. The interior dimensions are O.LOO" x 0.900" which allows conduction of frequencies down to 8 ko. Tapered transitions are used to connect K and R-band klystrons to the cell. Mica windows cover both ends of the absorption cell making it a vacuum—tight receptacle. Sample introduction is effected from.an ex~ ternal vacuum system sealed to the cells through tapered joints. In addition to holding the sample, the cell performs four other tasks. Its vacuum-sealed system.allows low enough gas pressures (10"1 to 10—3 mm. Hg) to cancel much of absorption line broadening. Secondly, the sample may be recovered intact by vacuum distillation to the ex— ternal vacuum line. Third, it permits one to regulate the sample tempera— ture, thereby guaranteeing sufficient energy level population for observ- ing particular transitions. The fourth task performed is important enough for special considera- tion. Running the length of the cell is a teflon—insulated silver electrode. This electrode, when coupled with a 100 kc square-wave generator (3h), enables one to apply an alternating electric field to the sample. This Stark modulated microwave spectrometer (35) is used to determine dipole moments, identify transitions, and help eliminate instrument noise. The base of the square-wave voltage can be varied to any desired DuC. bias. At a particular D.C. level the amplitude of the voltage has a range from.0 to 1250 volts. Therefore, the sample experiences a periodic field, no-field cycle every 10 microseconds. 18 3.3 Detection System Detection is accomplished by silicon crystals that rectify the A.C. output from the absorption cell. The D.C. output from the crystal is sent to an ammeter to indicate the power present at the crystal. Since the microwave voltages of the A.C. output containing the absorption signal are of the order of fractions of microvolts, considerable ampli- fication is necessary. This is accomplished by sending the output through a 100 kc-series resonant combination into a tuned preamplifier- amplifier system. From there, the signal is sent to the phase-sensitive detector which amplified and transmits only those signals in phase and 180° out of phase with the 100 kc square-wave reference signal. The accompanying noise amplification is decreased by the 100 kc tuned load arrangement and numerous filter circuits that reject fre- quencies differing appreciably from 100 kc. The phase sensitive detector rejects 100 he noise that is out of phase. The absorption.peaks and.Stark components can be displayed in either of two ways. First, the signal from the phase sensitive detector is im~ pressed on the y-axis of an oscilloscope, while the klystron frequency and.x~axis of the scope are swept synchronously by a saw-tooth voltage. Thus, one obtains a plot of frequency versus absorption. Second, a recorder can be combined with an automatic klystron drive to permit permanent records to be made. 3.h Frquen y Measurements Approximate frequency measurements are performed by a cavity-type wavemeter coupled to the waveguide. The size of the cavity is controlled by a micrometer plunger. Oscillations are produced in the wavemeter 19 when the cavity has the proper dimensions. The small absorption of energy is displayed on the oscilloscope. In this manner, a frequency can be measured within S - 20 Me of the actual value. Here accurate measurements are made by measuring the difference frequency between the unknown microwave frequency and a harmonic of a precisely known frequency V microwave - m.V standard 1 )/ difference. (3-1) The standard frequencies are generated by a Hanson Laboratories RD - lhO high-stability one Mc oscillator, a Gertsch Products AM - 1A, VtH.F. interpolator, and a Gertsch FM - hA microwave frequency multiplier. The generator assembly has an overall precision of 1 part in 107 when the oscillator is adjusted by beating its 10th harmonic against the 10 Mc carrier of radio station'WWV'from the National Bureau of Standards. The lMc RD - lhO oscillator is multiplied 19 to 38 times by the AM.- 1A. The output of the multiplier is mixed with the output of a stable l~2 Me low-frequency oscillator. The single signal of some frequency between 20 and b0 Me is input to the FH - hA. Here, a 500— 1000 Mo variable—tuned oscillator is locked to a frequency which is 1 10 Mc from the AM - 1A signal. ‘A crystal diode that is rectifying the microwave signal mixes the standard output of the generator assembly and the microwave signal. Of the many harmonics produced only the dif- ference frequencies less than 500 Mo are sent to the receiver. The difference frequency is plotted on the y-axis of the second beam of the detection oscilloscope, while the x-axis is the klystron frequency varied with the sawtooth voltage. When this frequency marker is placed directly on the center of the absorption line, the difference frequency can.be read directly from the receiver. The two receivers 20 available in this laboratory are a Collins 30 Mc model Sth and a Halli- crafters SX - 62 - A. The overall precision of the frequency measure- ment process is essentially limited.by the receiver. A frequency of 20,000 Mc is precise to 1 part in 107 when it is measured by the Collins, while the Hallicrafters is reliable to approximately 1 part in 105. IV. I‘DLECULAR STRUCTURE OF CYCLOPROPYL CHLORIDE b.1 Introduction The investigation of cycloprqpyl chloride was prompted by both the small ring "strain” discussions (Section I) and as a continuing study of halogenated hydrocarbons in this laboratory. Once the assignment was completed, the structural parameters and quadrupole constants could be compared with those found in related molecules. The first partial molecular structure of cyclopronyl chloride was given by O'Gorman and Schomaker (16). Using electron diffraction experiments, they reported r(C‘C) ' 1.52 t 0.023 r(C-Cl) * 1.76 t 0.022 4(01- c- ring) - 56° : 2°, where they assumed r(C-H) I 1.093. In 1958, Friend and Bailey (17) studied the Cl - 35 and Cl - 37 species by microwave spectroscopy. They arrived at values for B, C, and the quadrupole coupling constants from the assignment of R-branch, a-type transitions; ,Quadrupole coupling constants for the solid assuming cylindrical symmetry have been evaluated from.pure quadrupole resonance spectroscopy (36). At 77%, the reported value is X 22 - — 68.126 Kc. The work of Friend.and Bailey was reinvestigated at Hichigan.State University'by Dr. G. D. Jacobs (32). Besides remeasuring the transi- tions reported earlier, he assigned a series of low J, Q-branch, c-type transitions that are highly sensitive to the A rotational constant. The spectra of the CHICH213CH35C1 and CH215CHZCH35C1 isotopes were w w 21 22 recorded by Professor R. H. Schwendeman while the study of the mono- deutero species are the subject of this thesis. b.gfi Sample Preparation In the substitution method for structure determination, the molecular parameters of hydrogen atoms can be found by isotopically labeling with deuterium. The equations below represent the synthesis scheme used in preparing the mono-deutero isomers CHDCHZCH35Cl(cis), CHDCHzCH35Cl(trans), L_.___J t_____; and CHZCHZCD35C1(sec). Figure 22 is a projection of cyclopropyl chloride on its a, c plane of symmetry. C3H5C1 + 21.13.2221... LiCl + C3H5Li c3114.: + nae—£9» cansn + 1.101) 031150 + c12 “EL—e C3H4001 + C3H5C1 +Hc1 + DCl. The lithium.salt, CsHaLi was prepared by the method of Hart and Cipriani (37). In this reaction, 7.6 milliliters of distilled oyc10propyl chloride was added over a one hour period to 1.3 grams of lithium in dry diethyl ether at 0°C. All the apparatus used was flame dried and con- tinuously flushed with argon. At this point, the reaction was allowed to come to room temperature followed by refluxing for one-half hour. The D20“ was added dropwise to the same reaction vessel now maintained at -78°C. As the system was slowly warmed, the evolving CzhsD gas was collected in a liquid air trap. From this point on, all steps were performed in the vacuum line. The photochlorination reaction was carried out in a modification of the '*The 99.5% D 0 was obtained from.Liquid Carbonic, 767 Industrial Rd., San Carlos, zCalifornia. 23 \I‘ .xubmsexm mo mcmHQIUam ucp cm upmnoflzu Hangmaofiomu mo cowbummoma a .m unwowm ea; .0 $55: 3.6 o \ _o 30 3.8 o 33.... 214 method used by Roberts (38) for large scale production of C2H5Cl. The light source was a General Electric Ultraviolet Sun Lamp. The CszD was split into three equimolar samples. Each sample was mixed with chlorine in a two-to-one molar ratio. This mixture was irradiated for two-minute intervals with six to eight passes necessary to react all of the chlorine. Between each.pass, chlorinated products were trapped in a bulb cooled by a dry-ice, trichlorc>ethylene bath (-79°C). The volatile components were removed from the bath by repeated distillation to ~196°C. The monochloro product was distilled three times from ~lO°C to -79°C leaving the polychlorinated material in the bulb cooled to ~ 0°C. The total yield of desired.product was 0.68 millimoles or 0.68% of'purity greater than 95%. Identification and purity of all compounds were monitored by infrared spectroscony and gas chromatography. M Molecular Structure Before the spectra are examined, an initial calculation is required to obtain approximate values for the principal moments of inertia, energy levels and transition frequencies. A hand calculation was carried out based upon the structure proposed by Friend and Bailey (17). From the proposed bond distances and.angles, the atomic positions can be defined in an arbitrary Cartesian coordinate system (x, y; z). The coordinates of the center of mass (xm,;ym, 2m) in this axis system are found from the first moment conditions. gmixi - graiy1 v- glitz1 - 0. Translation of the origin to (xm) ym, em) defines a center of mass coordin- ate system (x', y‘, z'), where 25 x' - x - xm y' s y - ym (14-1) 2' - z - em. The eigenvalues of the second moment matrix and therefore the moment of inertia matrix can be computed by a similarity transformation. This Operation is equivalent to a rotation of the axes into the principal in- ertial axis system of the molecule. For qyclopropyl chloride x and y were chosen to lie in the plane of symmetry. As a consequence, 2 will remain invariant during the transformation and may be identified with the b—axis of Figure 2. Coordinates a1 and c1 are given by a - x ' cos 6 +ly ' sin.9 ‘ ‘ 1 (11-2) - I c c1 - xi sin 9 +'y1 cos 9. Returning to equation (2~2h), the second moments of the substituted molecule may be found by second order perturbation; a typical element is 2 z 2 z u a 2b u 2a. c _ z s s s s s s _ Paa, Paa+usa3 *[P -P ] + [r-T 1M3) bb aa cc as where P s the second moment of CHZCHZCH35C1 in its principal axis as , , system, Peel. the second moment of the substituted molecule in its princi- pal axis system, (a from the calculation discussed above. s’ bs’ c8) - the coordinates of the substituted atom determined The moments of inertia are given with respect to their second moments in equation (2-23), while the rotational constants are found.by dividing o the corresponding moment of inertia into 505, 531 Mc/sec--.a.m.u.-Az. 26 An independent check on the hand calculation.was performed by "MISTIC" the digital computer at Michigan State University. The pro- gram written by R. H. Schwendeman is described in detail elsewhere (39). It should be realized from Figure 2 that the allowed transitions are limited to a and c types, because both the C01 bond and dipole moment lie in the a,c~plane of symmetry. Since the asymmetry para— meter,’( , is approximately —O.9S for all three deuterated species, the near prolate top equation (2-15) was applied. When these restric- tions are used in conJunction with the Bohr frequency condition (2-1), the R—branch a-type transition frequencies are l)- 2(J+1) [9-3-9] + [A - 9-3-9] (M2 + Aclb + Aczbz) (Li—i.) while the Q-branch c—type transition Jo,J —->.J1’J frequencies are V-f [A - Egg] (Ax! + AC1b + ACzbz...). (h-S) The preliminary calculations indicated a large number of ground vibrational state, R-branch, low J transitions in the 15 to 30 ko region. A mixture of the deuterated isomers was introduced into the Hughes—Wilson type spectrometer with mom: Stark modulation (see Section III). An appreciable population density of low J energy levels was maintained by cooling the sample with dry ice. measurements on stronger transitions were made by oscillosc0pe display with sweep reversal, while pen-and-ink recordings were employed for the weaker transitions. The assignment of transitions for CHDCHZCH35C1 (cis and trans) l—.——J and CHZCHZCD35CI were Judged on three criteria: one, the transition frequ;;;;:1two, the quadrupole splittings, multiplicity and intensity; and three, the identification of a duplicate group of v . 0 transitions 2? arising from the Cl-37 mono-deutero isomers each of which is displaced to a lower frequency from its Cl-JS analogue. The quadrupole coupling constants fro the deuterated species are nearly the same as those of the parent molecule CHZCHzCH35C1(32). The hypothetical rigid rotor frequencies are calculated-from the experi- mental multiplets by the following equation where “a l7 - a function of the quadrupole coupling parameters qm and11.qm. ”i - the experimental transition frequencies ' I the hypothetical unsplit frequency 10 Table I is a list of these hypothetical unsplit frequencies. Although at least ten transitions were assigned for each isomer, the ”fit” can usually be considered complete when only two R-branch and two 0- branch transitions give consistent values of A, B and C to within one- tenth of a megacycle. The value of A determined from the 03—9 110 transition of CHzCHzCH35Cl was used to predict Q-branch transition i..._..._I frequencies. This procedure consistently computed values 0.h megacycles higher than was actually observed. The difference was attributed to centrifugal distortion. Therefore, an empirical factor of O.h megacycles was added to all Q-branch transitions before the rotational constants were calculated. Table II is a comparison of calculated Egrsgs_Observed frequencies for the hyperfine components in trans-deutero cyclopropyl chloride. The rotational constants, moments of inertia and second moments for all isotopic species are given in.Table 111. Since the requirement of iso- topic substitution at eveny non-equivalent atom has been met, the structure of qyclqprOpyl chloride can be determined by the method of Kraitchman(5ection 11-3). Table I. Hypothetical unsplit frequencies (Mc) for mono-deutero cyclo- propyl chloride. 28 cnuc CHIIIH 0135c1 CHDCH c1135c1 Transition $23253, 1 L"'T§is) Zrans) 101‘-> 202 1&377-h9 1&770-3h 1bh57.93 11r-4> 212 lh676.73 lthh.hl lbléS.SS 110 -> 211 15083.15“ 15067.26 111761.58 202 -> 303 22309.35 221111. 58 21673.06 21,» 313 22013.22; 21723.13at 212th.88 211 -> 312 22597.50 22138.86 303 -.> "01. 29733.08 291196.117 28871.67 322 -> 1123 295117.12 28922.62a 321 -> 1122 297811.89 29602.33 28977.56 1‘01; -> "11; 10111.5 505 -> 515 9502.97 91469.53 606 -> 6165 8906.633 871.11.515‘ 9221.25 70., -> 717 826h.66a 81:13.19al aUncertainty is t 0.05 No except for frequencies marked "a'I for which uncertainty is t 0.10 Mc. 29 Table II. Calculated and observed frequencies (M0) for the hyperfine components in CHDCHZCH35CI (trans) w Observed Calculated Transition F - F' Frequency Frequency 1 - 2 5/2 - 7/2 1hh59.16 01 02 3/? _ 5/2 1Lb59.21 1hh59.22 5/2 - 5/2 1hbhh.82 1hbbh.8h 1 - 2 5/2 - 7/2 1h168.93 1h168.82 11 12 3/2 - 5/2 1h15h.52 12152.5h 5/2 - 5/2 lh163.73 1h163.8h 3/2 - 3/2 1t158.17 1h158.1o 1 - 2 5/2 - 7/2 1h765.28 lh765.07 1° 11 3/2 - 5/2 111750.95a 1u750.79 5/2 - 5/2 1h?S6.13 11759.78 3/2 - 3/2 1&757.h6 1t757.h3 2 - 3 7/2 - 9/2 21673.78 02 03 5/2 - E/2 21673'7h 21273.86 3 2 - 2 21 70.30 1/2 - 3/2 21670'18 21670.21 2 - 3 7/2 - 9/2 221bo.27 11 12 1;? _ 3;? 221u0.30 22139.63 5 2 - 7 2 22136.72 3 2 - 5/2 22136'h6 22136.07 2 — 3 7/2 - 9/2 212b6.31 12 13 1/2 - 3/2 212b6.53 212u6.73 5 2 - 7 2 212h2.76 3/2 - 5/2 212h2°91 212h3.18 3 - b 9/2 - 11 2 28872.20 5 2 - 7 2 28870.63 3/2 - 5/2 2887°°35 28870.52 7/2 - 7/2 28877.32 28877.23 322 - 1.23 9/2 - 11 2 289211.90 28928.73 7/2 - 9 2 28919.00 28919.03 5/2 - 7/2 28920.70 28921.03 3/2 - 5/2 28926.78 28926.73 Table II. Continued. T’““5‘t‘°“ Observed Calculated F - F' Frequency' Frequency 6 - 6 15/2 - 15/2 9220.18 9220.18 06 16 13/2 - 13/2 9222.80 9222.92 11/2 - 11/2 9222.20 9222.27 9/2 - 9/2 9219.62 9219.5h 7 - 7 17/2 - 17/2 8u12.35 07 17 11/2 - 11/2 8b11°95 8h11.88 15 2 - 15 2 811111.69 13/2 - 13/2 ablh'36 8h1h.21 aInterfering transition. 31 o n to: Bee .coaumu«cnsaoo mpm>~ud acmemvcmacow .m .mu .nwmv mam AFHV emocuummumd 0 e e O I. A ~M a s a m 0: "mm mom a can: nopomu commum>coou .~ 1 .:.a.m H~O0.0 a eu mam m Mu< 1 .s.a.m mooo.o H .« auscuaom mm ucumaummm mmuumcm no «cameos c zucumaumocsn o .e: 8.0 a .0 Be m 3x 4.0 e .< 33:9.“ 3 usages 3:388 "escapee?“ 5 35338:.“ E III, m®QM.OH awomeflw Omomemwfi JOH®.MJN awhwefimn thwewm OmewaM Jwe4©hm N.N©0m~ HAmcmugv HUnnmmmmmmmw MOMN.MH 4fl40.NN AOOMJ.ONH HNNJem4A O~©0.~m~ wubwomm mwemamm J©.mmmm Ooamfimd mammUv HUnnmwmmmmmw 28.2 32.8 mama: mamas aha: «Rena 438m 3.3% 383 manna $3.2 88.8 82.3“ 88.2” 33.5 $3.: maémmm 2.3% .388 enoenfinlfidwmz 34on 338 48am: mameaa $3.3“ $8.8 fiéem Nana... seems esseczeegc 63.2 «328 $3.34 mead: $545 33% 233mm has” «amen mustang OQNN.OH mHJM.ON NmHN.mMfl 04mmLQMH mNJd.mNH HHNMoOfi Odemmom fidomoafi NoommOH NHUnnmmmwwwmw 8e be 3e eH nH «H o m e 3.8% fl .upmucaco «smouaonohu no newsman msOHum> you wa~w a .sem.mv mucmsoa pcoomm pcm o.aauw a .:.a.mv magnum“ Ho «menace .maozv mucmumcoo Hmcouumuom .HHH canmfi 32 The resultant coordinates are shown in Table IV where CHzCHZCH35Cl has L...__J been taken as the I'parent" molecule. It will be recalled that Kraitchman's equations are derived for a rigid molecule. However, in a physically real situation, the zero-point vibrations change upon isotopic substitution producing slight deviations from.these formulas. With zero-point errors likely to be as high as 1% in the bond distances and angles calculated, the approximations necessary to interpret the data prove the most serious limitation to microwave, especially when one considers that frequency measurements are accurate to about 0.0001%. Earlier workers often reported structures (called to structures) calculated by adjusting the bond distances and angles to fit the observed moments of inertia of a small number of isotopic substitutions. Costain (to) has compared these r0 structures to both the substitutional struc- tures obtained from Kraitchman‘s equations (rs) and the equilibrium structures (re) of simple molecules that have been vibrationally anal- yzed. He found the rs structuresto be closer to the re structures with much smaller mean deviations than is the case of the r0 method. This pragmatic Justification of the substitution procedure is impaired when heavy atom coordinates are less than 0.153 from an axis (29., the c-coordinates of Cl, C, and C3 in.cyclopropyl chloride). Fortunately, the c-coordinates of C2 equals that of C3. The two inde- pendent heavy atom c-coordinates, C; or C3 and Cl, can be corrected for zero-point vibrational effects by applying the two conditions 2 micl - Zmlaici - 0. i i 33 o Coordinates (A) of the atoms in cyclopropyl chloride. Table IV. Atom a b c -Cl 1.2861 0 0.08h1 c1 -o.3287 o -o.56n7 02,3 -1.h093 : 0.7577 0.1760 H (sec) -0.h022 0 «1.6h07 H (015) ~l.0925 t 1.2h93 1.0908 H (trans) -2.1552 i 1.2765 -O.L109 o m,a1 - 0.2368 a.m.u. - A o . mici - 0.251h a.m.u. - A _ O _ __ 2 miaici 0.10h5 a.m.u. A Hf\1 HfV9 ”.txj Ia - 30.L873 a.m.u. - 33 0 1b - 129.0huo a.m.u. - A2 Ic . 138.987b a.m.u. - £2 3h Inserting the new coordinates into Kraitchman's equations yields structure 11 of Table V. A degree of satisfaction is achieved by noting that within experimental error structure 11 agrees with Structure I obtained with no correction terms. Because detailed vibrational analyses of complicated molecules are neither experimentally or theoretically feasible, Laurie (hi) has suggested a calculation to estimate the uncertainty of rs structures. When a site is substituted by a heavier isotope, the coordinates obtained give an apparent average bond shortening which may be as large as 0.00013. Although it is difficult to ascribe the vibrational effect to any single effect, for calculational purposes Laurie takes the point of view that when a heavy atom is substituted all the bonds to that atom are actually shortened. Then the second moments and their corresponding coordinates are computed for the following hypothetical molecules: (1) C3H535Cl with the parameters in Table V, (2) C5H537Cl with the parameters in Table V except r(CCl) shortened by 0.000052, (3) CHZCH213CH3501 with the para- l._.__...._! 0 meters in Table V except r(CCl) and both r(C,Cz) shortened by 0.00005A, and (h) 13EE32EESH35C1 with the parameters in Table V except r(C2C3) and the appropriate r(CICz) shortened by 0.000052. Table VI contrasts coordinates and parameters of the r3 structure and the one obtained by the bond shortening. Note that the small change estimated upon isotopic substitution results in significant changes in the structural parameters. The greatest change is in the a-coordinate of C, where three bonds are involved in the shortening. The large change is due to the large un- certainty inherent in the substitution method when coordinates are less 0 than 0.15A (see above) as they are in the c-coordinates of C1, C2 and C3. 35 0 Table V. Bond distances (A) and bond angles (degrees) for cyclopropyl chloride. Parameter 0::tance or aggge Totglcertgxgziimental 001 1.780 1.780 +.011 -.003 1.003 c102,; 1.513 1.512 +.006 -.008 1.008 0203 1.515 1.517 +.003 -.001 1.001 CH (sec) 1.079 1.080 1.003 1.001 CH (cis) 1.086 1.086 +.006 -.008 1.008 CH (trans) 1.082 1.079 +.010 -.001 1.003 c001 118.7 118.9 +.3 -.6 1.3 ClCH 115.8 115.7 +.3 -. 2.2 CCH (sec) 116.1 116.0 +.8 -.5 1.3 clcsu (cis) 115.5 115.5 +.6 -.2 1.2 clean (cis) 116.9 116.9 +.6 -.6 1.8 clcsn (trans) 117.8 118.1 +.h -1.o t.h 0,05H (trans) 118.7 118.7 +.5 -.6 2.3 HCH 116.2 116.0 +.6 -. t.) aStructure I is taken directly from Kraitchman's equations. b Structure II is calculated by correcting the coordinates of the heavyatomsso tEmc -0andZmac .0 whereZ'ma becomes . i i . i i i ’ , i i 0.236? a.m.u. — . 1 1 1 36 O 0 Comparison of coordinates (A), bond distances (A), and bond Table VI. angles (degrees) of heavy atoms computed from the Kraitchman equation assuming (a) no reduction in bond lengths, and (b) 0.00005 reduction in bond lengths. Parameter No Reduction 0.00005 3 Reduction a(Cl) 1.2861 1.2852 C(Cl) 0.08hl 0.0837 a(c,) —0.3287 -O.318h C(C1) -0.56h7 —0.56hh a(Cz’3) 4.1093 4.11091 b(Cz’3) i0.7577 t0.756? C(C2,3) 0.1760 0.1759 r(CC1) 1.7b0 1.729 r(c,cz) 1.513 1.520 r(CzC3) 1.515 1.513 < ccci 118.7 118.9 37 A new approach to uncertainty calculations has been proposed by Tobiason and Schwendeman (h2). In planar molecules such as H20 and H200 the second moments perpendicular to the molecular plane should be zero. However, the out-of—plane vibrations give rise to a slight deviation called the inertial defect. If the a-axis is perpendicular to the place of the molecule, then Paa - Z miaiz - o (Ll-7) i no longer holds exactly, but 2 I .. a . 2Paa. (Ibb + ICC 18.8.) + Aaa 2138.8 + Aaa (’4 8) does, where Paa - the effective second moment about the a-axis Paae I the equilibrium second moment about the a-axis Aaa - the inertial defect. If equation (h-B) is placed in Kraitchman's equation (2-25) where in the general case has is a quasi-inertail defect that retains its signifi- cance as a lumped, ground-state vibrational correction term, one gets ~1 Pbb' ' Pbb Agpcc' - Pcc Aaa' ' Aaa 2a“ 1‘15—7‘5— 1'? 51> 2 bb aa cc aa P - P (8 i- P - P -A 1 cc' cc b' Abb 6’ bb' bb cc' cc 0 P - P o-Fr————75——— -+ 0»Fr————————- [2( 9‘3" a?) [Q cc - aa) 13bb ' a; bb - Pea) cc- aa>] Terms involving products of changes in the inertial defect have been .8, .. la ignored as have the differences between equilibrium.and effective second moments in the denominator of equation (h-9). Such terms are ordinarily smaller than those retained. 38 If the magnitudes of (A - Asa) etc., are roughly equal, the last Abb' " A131: two terms may be dropped since F—-_:TF-_' and similar quantities are bb aa quite small in comparison. The coordinate uncertainties [eel — 'a' can aa' then be related to bond distances and angles by employing the total' differential. If rs t is the distance between atoms 3 and t, then 3 ”9,: " 59 (as’ bs’ cs‘ at, bt’ Ct) Jr gr r gr /rs,t ‘J-Eflfa’ ’30.:‘2/at 40.3—53.1}.be + ... 43-3-31-5 ffct' (1,40) Of course, angle uncertainties require changes in three atoms. Table VII contains the values for [ae[-- [as] etc., for each atom assuming 0.001 a.m.u. - R2 for A(Aaa). Laurie indicated that the vibra- tional contribution to the coordinate is positive while the experimental uncertainty can have either sign. The experimental portion was calculated using an estimated 0.002 a.m.u. — 22 change in the inertial defect. Both the experimental and total uncertainties in the structural parameters are listed in Table V, where the total uncertainties were obtained by multiplying the differences in Table VII by the corresponding numbers in parentheses. The positive uncertainty is a sum of all positive terns added as though each were acting in a maximal sense without cancella- tion from negative contributions and similarly for the total negative uncertainty. One should bear in mind that these rather pessimistic total uncertainties are a measure of the closeness of approach of the substitutional structure to the equilibrium structure, whereas the experimental error Just gives the uncertainty in the substitutional structure. 39 0 Table VII. Changes (in A) in coordinates of the atoms of cycl ropyl chloride produced by an increase of 0.001 a.m.u. - 1 in quasi-inertial defect upon isotopic substitution. Atom ae - a b‘2 - b c - c c1 0.0001 (6)a ... 0.00158 (2) 0 0.00077 (8) ... 0.000h7 (2) 0 0.00019 (2) 0.00036 (2) 0.00155 (2) H (sec) 0.00061 (8) 0.00020 (8) H (cis) 0.00023 (8) 0.00022(8) 0.00030 (8) H (trans) 0.00013 (8) 0.0002u (8) 0.00075 (8) aThe numbers in parentheses are the factors by which the correspond- ing differences were multiplied to obtain the uncertainties in Table V. ho ole Ana sis Equation (2-28) for the quadrupole energy of a near symmetric top with one quadrupole nucleus can be written as HQ - aqm + qu . Transition frequencies are 1) - Aaqm + Afiqm . (la-11) The frequency difference between hyperfine components within a given transition becomes / 1) - (Aa)qm + (Amqm . (8-12) The constants c/(Aa) and /(AB) were computed using the observed rotational constants, and q!a and qm 3} were fit by least squares. With the a-axis most nearly representing a symetry axis in cyc10propyl chloride, the quadrupole coupling constants are 7‘3. ' qum X - . _ ( bb X“) 807mm (h 13) (Xaa * 7(bb + ch) . 0' The coupling constants (7(3) in the principal axis system (a, b, c) must be first referred to the quadrupole tensor axis system (x, y, 2) before their contribution to the bonding is discussed. This is so since the principal coupling constants are the values which are assumed in inter- pretations of quadrupole coupling.of the molecule. In first order quad- rupole effects the off diagonal matrix elements (7( ab etc.) are zero and therefore dropped. A simple rotation of axes will carry (a, b, c) into (x, y, z). with a plane of symmetry such as the a, c-plane in cyclopropyl chloride the 111 transformation equations are 7Q Xaa cos 02 -ch sin 92 22 cos 92 - sin 62 (it'll-i) “FL . ‘7