'HEGH RESOLUWON ABSORPTEW. ZEEMA’N‘ AND ffiAGNEfiC FIDTA‘ESON SPECTRA. 53F NITROGEN DIOXIDE IN THE HEAR ENFMRED Thesis for the fiegree cf Ph. D, MICHEGAN STATE USNEVERSITY MELV'EN D. GLMAN‘ 1957' TflESIS End" LIBRARY Michigan State University ”mu-‘nn‘ This is to certify that the thesis entitled HIGH RESOLUTION ABSORPTION, ZEEMAN, AND MAGNETIC ROTATION SPECTRA OF NITROGEN DIOXIDE IN THE NEAR INFRARED presented by Melvin D. Olman has been accepted towards fulfillment of the requirements for WW/w 05.55% Major professor Date July 31, 1967 0469' 7,1. H__ ABSTRACT HIGH RESOLUTION ABSORPTION, ZEEMAN, AND MAGNETIC ROTATION SPECTRA OF NITROGEN DIOXIDE IN THE NEAR INFRARED by Melvin D. Olman The absorption, Zeeman, and magnetic rotation spectra of the (1,0,1) and (2,0,1) vibration-rotation bands of nitrogen dioxide have been obtained using Michigan State University's high resolution (~0.03 cm'1 at 4200 cm‘l), near-infrared spectrometer. Improved values of the ground state molecular constants of 1"N02 and 15N02 have been obtained from an analysis of combined ground state combina- tion differences and microwave transition frequencies. Accurate upper state rotational and centrifugal distortion constants and band origins have been obtained for the (1,0,1) and (2,0,1) bands of 1L’N02 and 15N02. In addition, the change in the effective spin-rotation coupling constant between the ground and the (2,0,1) vibrational states has been determined for each isotopic species. Theoretical expressions have been found which give the frequencies and transition probabilities for the Zeeman components of absorption transitions at all magnetic fields. The spectra predicted by these expressions match very close- ly the details of the experimental spectra at all magnetic fields available. Melvin D. Olman In the magnetic rotation spectra the strongest signals are found to come from Q-branch transitions. In the P branches there are one or more series of weaker signals which arise from transitions for which K_1 = 5, 6, and 7. The relative strengths of the Q- and P-branch signals and the dependence of the Q—branch signals on the magnetic field strength have been qualitatively explained on the basis of the theoretical Zeeman patterns. HIGH RESOLUTION ABSORPTION, ZEEMAN, AND MAGNETIC ROTATION SPECTRA OF NITROGEN DIOXIDE IN THE NEAR INFRARED BY 69 Melvin D? Olman A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1967 To MARY ACKNOWLEDGMENTS I am grateful to Professor C. D. Hause for his guidance and patience during the years of my graduate study. His dedication to teaching and his interest in his students should be an example for all. I owe much to Professor T. H. Edwards for his advice and comments during discussions cov- ering various aspects of this work. In addition to present- ing a very useful course on molecular structure, Professor Paul M. Parker has been helpful with questions of a theoret- ical nature. Several of my fellow graduate students have given both friendship and practical assistance. Mr. Donald B. Keck has been very helpful with both the experimental and the theo- retical parts of this work. Much of my understanding of the analysis of the spectra of an asymmetric top molecule has come from discussions with Mr. Kent Moncur and Mr. Lewis B. Snyder. Mr. Richard E. Blank did much of the preliminary work in the derivation of the expressions for the dipole moment matrix elements. I thank the staff of the Michigan State University Computer Center for the use of the C.D.C. 3600 computer and for their assistance. Very little of the work presented here could have been done without the use of a computer. iii The National Science Foundation has provided fellowship support and support through research grants to Professors C. D. Hause and T. H. Edwards which I have sincerely appre- ciated. Finally, I take this opportunity to express my appreci- ation to my wife both for the encouragement she has given me and for the many hours she has spent in the preparation of this thesis. iv ACKNOWLEDGMENTS LIST OF TABLES. LIST OF FIGURES LIST OF APPENDICES. INTRODUCTION. Chapter I THEORY. A. B. C. D. II A. L111 00 w SUMMARY . . REFERENCES. APPENDICES. TABLE OF CONTENTS ASYMMETRIC TOP ENERGIES. SPIN-ROTATION COUPLING ZEEMAN EFFECT. MAGNETIC ROTATION SPECTRA. EXPERIMENTAL EQUIPMENT ABSORPTION SPECTRA SPIN-ROTATION ANALYSIS ZEEMAN SPECTRA EXPERIMENT AND ANALYSIS MAGNETIC ROTATION SPECTRA. Page iii vi vii viii 18 22 39 44 44 45 58 63 68 73 74 77 Table II III IV VI VII VIII LIST OF TABLES Direction cosine matrix elements for prolate symmetric top. . . . . . . Experimental conditions for absorption spectra. Ground state rotational constants for N02 Upper state rotational constants and band origins fOr N02 0 o o o o o o Vibrational dependence of the rotational constants . . . . . . . . . . Predicted rotational constants for the (0,0,3) and (1,0,3) vibrational levels. Effective spin-rotation coupling constants fOr N02 0 o o o o o o o o o 0 (2,0,1) band spin-splittings. vi Page 31 46 50 54 57 57 60 61 Figure 10 LIST OF FIGURES Geometry of the N02 molecule . . . . . . . . . Asymmetric tOp energy level diagram. . . . . . Normal modes of vibration for N02. . . . . . . Energy level splittings and identifications at weak and strong magnetic fields . . . . . . Predicted splittings for the 331 level of the ground State Of IANOZO o o o o o o o o o o o 0 Predicted Zeeman splittings for the P5(10) line of the (2,0,1) band of ll*NOZ. . . . . . . Predicted Zeeman splittings for the Q7(7) line of the (2,0,1) band of 1“N02. . . . . . . Experimental Zeeman spectra for the band origin region of the (2,0,1) band of ll*NOZ . . Predicted Zeeman spectra for the band origin region of the (2,0,1) band of 1“N02. . . . . . Magnetic rotation spectrum of the (1,0,1) band 0f 1'+N02 O O O O O O O O O O O O O O O O 0 vii Page 11 28 28 40 41 66 67 69 LIST OF APPENDICES Appendix Page I COMPUTER PROGRAMS WRITTEN . . . . . . . . . . . 77 A. SCAN . . . . . . . . . . . . . . . . . . . 77 B. CALFIT . . . . . . . . . . . . . . . . . . 82 C. CDSORT . . . . . . . . . . . . . . . . . . 82 D. CDFIT. . . . . . . . . . . . . . . . . . . 86 E. SPECFIT. . . . . . . . . . . . . . . . . . 102 F. SPINFIT. . . . . . . . . . . . . . . . . . 104 G. PLOTZ. . . . . . . . . . . . . . . . . . . 106 II GROUND STATE COMBINATION DIFFERENCES FOR 1“NO, AND 15N02 . . . . . . . . . . . . . . . . . . . 117 III FREQUENCIES FOR (1,0,1) AND (2,0,1) BANDS OF IL‘NOZ AND 1 5N02 0 o o o o o o o o o o o o o o o 124 viii INTRODUCTION Nitrogen dioxide is one of the few stable, paramagnetic molecules with a single unpaired electron, and thus its spectrum and structure have been of interest to investiga- tors for some time. Microwave and far-infrared transition frequencies have been measured and ground state constants for several isotopic forms have been determined by Bird SE .1'2 and by Lees, Curl, and Baker.3 Arakawa and Nielsen4 El and Moore5 have reported the analysis of the medium resolu- tion vibration-rotation bands in the near-infrared, using the symmetric top approximation. Observation of the near- infrared magnetic rotation spectrum of N02 was reported by Aubel.6 The present work reports the analysis of the high resolution absorption, Zeeman, and magnetic rotation spec- tra of the (1,0,1) and (2,0,1) vibration-rotation bands of ll‘NOZ and 15N02 in the near-infrared. The rotational struc- ture of the absorption bands is analyzed using existing asymmetric rotor theory and yields improved values for the rotational and centrifugal distortion constants of the ground and upper vibrational states.' Effective spin- rotation coupling constants are determined from measurements of the zero-field splittings. As a result of the single unpaired electron, the ground electronic state of the nitrogen dioxide molecule is a 22 state.7 The coupling between the electron spin and the molecular rotation removes the degeneracy of the doublet and leads to a splitting of many of the observed transitions. In the presence of an external magnetic field, the coupling between the magnetic moment of the electron and the field leads to a Zeeman splitting of the energy levels and a cor- responding splitting of many of the observed transitions. Expressions which are valid at all field strengths are derived for the frequencies and transition probabilities of the several Zeeman components of an absorption line. Com- puter plots of the resulting theoretical Zeeman spectra at several field strengths are found to compare well with experimental spectra. It is found that the strongest magnetic rotation sig— nals arise from Q-branch transitions for which there is a maximum separation of AMN=+1 and AMN=-l transitions. Weaker signals in the P and R branches are found to come from spin- doublets. CHAPTER I THEORY A. ASYMMETRIC TOP ENERGIES Rigid Rotor The geometry of the planar triatomic molecule N02 is shown in Fig. l. The axes of the principal moment of iner- tia ellipsoid are designated by a, b, and c, and the cor- responding principal moments of inertia are designated Ia' Ib' and Ic’ with the axes labelled in the conventional way So that Ia ( Ib < IC. The b-axis is the C2v symmetry axis of the molecule. The general rigid rotor Hamiltonian is P2 P2 P2 Ho=_e_+.s_+_<.=_. (1) 21a 21b ZIC A more convenient form for Ho, for which the energies are in wavenumbers (cm-1), is = 2 2 2 H0 A Pa + B P + C PC , (2) b where the reciprocal moments of inertia, A, B, and C, are the usual rotational molecular constants and are related to the principal moments by A = h/(4cha), etc. The molecule is classified according to the values of A, B, and C. A spherical top molecule has A = B = C, and the result- ing expression for the energy depends only on the total rotational angular momentum quantum number N. A symmetric top molecule has two of the three recipro- cal moments equal. The axis associated with the third, unique, moment is the symmetric top axis. Here the energy depends upon N and the projection of N along the symmetric top axis K. Since the energy depends only on the square of K, levels having K non-zero are doubly degenerate. Mole- cules for which A > B = C, "a" being the unique axis, are called prolate symmetric tops, while those having A = B > C are oblate symmetric tops. In the general case of an asymmetric top molecule each of the reciprocal moments is unique (A > B > C). Since the resulting asymmetric tOp Hamiltonian cannot be diagonalized exactly, numerical methods must be used to get the molecular energies. The degree of asymmetry of the molecule is indicated by 8 K = 2B-A-C """A'-""C"" ' the molecule is called a prolate asymmetric top, while if Ray's asymmetry parameter, If B = C (r + -l), B = A (n + +1), it is called an oblate asymmetric top. For nitrogen dioxide K a -0.994 so that the molecule is nearly an accidentally symmetric prolate top (B = C). For such a case the energy can be written in the form9 N0 = 539 N(N+l) + (A - 339m , (3) where w is the Wang energy and must be computed numerically. The manner in which the energies of the lowest rota- tional levels change as K varies from -1 to +1 is shown in Fig. 2. Although the rotational angular momentum quantum number N is still a good quantum number, the asymmetry lifts the degeneracy in K. The value of K which a given energy level would have in the K = -1 (prolate) limit is labelled K_1, and its value in the x = +1 (oblate) limit is labelled K+1. Thus, although K itself is no longer a good quantum number, it is possible to identify a given energy level uniquely by N, K-1, and K+1, regardless of the degree of the asymmetry. The conventional notation for the identification of a given energy level is N Since nitrogen dioxide K-1K+1° is so nearly a prolate symmetric top, K will often be used here to mean K_1. Centrifugal Distortion Effects The rigid rotor Hamiltonian contains only terms which depend on the square of the angular momentum components. In an actual molecular system, the rotation of the nuclei leads to a centrifugal stretching of the molecular bonds which requires the inclusion of centrifugal distortion corrections in the Hamiltonian. These correction terms include P“- and P5-type operators. ----- —---a ("unique" axis) :b (C2v aXIS) xO-N-O = 134°4', rs = 1.1934 A Fig. 1. Geometry of the N02 molecule. (Structural constants from Bird gg'g£.1) N 0 1 ____________________ 1/:.10 :l 1 lll\31 l [/101 0 o -o 0oo o- o l l (Prolate) -l K+ +1 (Oblate) Fig. 2. Asymmetric top energy level diagram. 10 the general Hamil— ‘E: terms. As summarized by Hill, tonian which takes care of the vibrationally independent P“- type terms is P P P P . (4) H = 1 ZTquC u v 5 C From the commutation relations for the angular momentum operators and the relationships which develop among the 1's for a planar molecule,11 the eighty-one general 1's are reduced to only four independent T‘s for N02: Taaaa' Tbbbb' Taabb, and Tabab' (When the following expressions are used in the section on the analysis of the data, the 1's will be referred to as 11, 12, 13, and Tu: respectively.) Hill10 has given the resulting energies to first order as W1: X1+T X3+T Taaaa bbbbX2 + Taabb ababx“ ' (5) X1 ='%g r2[N2(N+1)2-61-2N(N+l)62] - (r-2)[2rN(N+1) + 2r63 - (r-2)]} x2 = %g{ll+s)2[N2(N+1)2-2N(N+1) + 1 -(l-s)261 + 2(1-52) [N(N+1)62 + 53]} x3 = %{(l+s)[rN2(N+l)2 - 2(r-1)N(N+l) + (r-2)] + r[(l-s)61 - 23N(N+l)62] - 2[l+s(l-r)]63} X“ = %{N(N+l) - - 63} and Os p—s H 2 _ u _ 2 2 (2w w )/bp 52 = ( - w)/bp 0': w H 2 _ u (w )/bp b = C-B = K-l p :A-B-C K+3 = 2 2 = 2 2 r Ce /Ae , 3 Ce /Be A B and Ce are the equilibrium rotational constants. e' e' Since equilibrium values of the constants are not known for N02, it is necessary to use ground state values in the cal- culation of r and s. The commutation relations reduce some of the P1+ terms in Eq. (5) to have the P2 dependence of the terms in Eq. (2) so that the observed rotational constants, which we shall label A', B', and C', are related to the reciprocal moments, A, B, and C, by the following equations, which are due to Hill:10 A. = A - % Tabab B. = B - % Tabab (6) C' = C + % Tabab ° Chung and Parker have cited an expression12 for the theoretical value of Tabab: 16 A B C , e e e (7) Tabab = - 2 where.m3 is the normal frequency of the v3 vibrational mode. Although the T'S as defined in Eq. (5) are independent of the vibrational state involved, one expects different vibrational states to have different centrifugal distortion energies. At the present time this can only be handled em— pirically by allowing the T's to have different values in different vibrational states. £3.325EE' In the analysis of the observed data, which includes transitions with N as large as 48 and K_1 as large as 8, it is found that a good fit of the data requires the inclusion of PB-type terms, in addition to the 1's. After 13 Pierce, Di Cianni, and Jackson, the following semi- empirical expression is used: _ 3 3 2 2 2 u W2 - HNN (N+1) + HNKN (N+l) + HKNN(N+1) (8) + HK , where the H's are to be determined experimentally. We can now write the rotational energy of a prolate asymmetric rotor molecule as w = 53-9 N(N+l) + (A - 539).. X1 + Tbbbbxz + T X3 + Tababx” (9) Taaaa aabb + HNN3(N+1)3 + H KN2(N+1)2 + H N(N+l) + HK , N KN In this expression A, B, and C, the four 1's, and the four H's are constants only for a given vibrational state. 10 Vibration-Rotation Bands The vibration-rotation bands observed here are due to transitions originating in the ground vibrational state and terminating in a vibrationally excited state. Being a tri- atomic molecule, nitrogen dioxide has three vibrational degrees of freedom so that there are three normal modes of vibration. These are shown schematically in Fig. 3. A vibrational state is labelled (n1,n2,n3), where ni denotes the number of quanta of Vi which have been excited for a molecule in that state. It is important here to recognize that the third normal mode v3 corresponds to an unsymmetri- cal vibration so that the vibrational wavefunction for a state in which an odd number of v3 quanta have been excited must be anti-symmetric, whereas the vibrational wavefunc- tions for all other states, including the ground state, are symmetric.14 By far the strongest bands observed here, and the only ones analyzed, have an odd number of v3 quanta in the upper vibrational states. From Figs. 1 and 3 it can be seen that for these bands the change in the dipole moment must be parallel to the a-axis. Thus they are called type-A or, since the a—axis is the limiting symmetric top axis, paral- lel bands. The selection rules for such bands are AN = 0, *l and AK_1 = 0. (With finite asymmetry, AK_1=*2 transi- tions are allowed, but for K = -0.994, their intensities are effectively zero.) ll Fundamental Frequency (Arakawa and Nielsen4) 1318 cm-1 V1 749.8 cm“1 V2 1617.8 cm-1 V3 Fig. 3. Normal modes of vibration for N02. 12 The C2v symmetry of the molecule, along with the zero nuclear spin of the 160 nuclei, requires that only states having a totally symmetric wavefunction be populated.15 This requires that for the ground state, only rotational levels for which the rotational wavefunction is symmetric (K+1 + K_1 even) be pOpulated, while the upper vibrational states of the bands observed can only have anti-symmetric (K+1 + K-1 odd) rotational levels populated. The result is that only half of the energy levels are populated, and thus only half of the allowed transitions occur in each vibration- rotation band. Analysis The frequency v of a rotational line in a vibration- rotation band is given by v = v0 + w'(N',Kll,K11) - w"(N",K21,K11) (10) where the primes refer to the upper vibrational state and the double primes to the ground state. v0 is the energy difference between the N=0 levels of the excited and ground vibrational states and is called the band origin. For the observed nitrogen dioxide bands the selection rules require that AN = N' - N" = o,t1 AK = AK-1 = K11 - K21 = o . Since only half of the allowed transitions occur, no 13 ambiguity will arise from the use of symmetric top notation to identify the transitions, AK ANK(N), where the letters P, Q, and R denote AK or AN = -l, 0, and +1, respectively, and N and K refer to the ground state values of N and K-1. The branches within a band are QPK(N), QQK(N), and QRK(N), or more commonly, the P, Q, and R branches. By taking differences between appropriate transition frequencies within an absorption band, one can obtain in- formation about rotational energy differences within just the ground or just the upper vibrational state. These are the usual ground or upper state combination differences (GSCD or USCD). The analysis of a set of combination differences pro- 10 ceeds as follows: Following the procedure used by Hill, the rigid rotor energy expression, Eq. (3), can be rewritten as N0 = Egg N(N+1) + (A - §;E)w (ll) B+C B- : CA + E T + n -2-C—: 3W0 3W0 3W0 where c = ———, E = __B:C—' and n = -—B:C— . 3A 3(T) 3(T) Since the Wang energy can be written as16 w = K_12 + 2C b n (12) n n p _ C-B . . . where bp — 2A3B:C ,.and the cn are numerical coeffICIents, 14 the following expressions can be obtained for c, a, and n: 3W0 B+C 3w ‘” + (A T) TA- _ B-C 8w -“+‘A'T’TAP'FE; _ _ 8w _ _ w bp 5T7. (13 a) P 3W0 8w 5 =—E::5-=N' a” (A'ETE’ IB+C 3(T) 3(T) = N(N+1) - m + b 35—” (13-h) P P 3W0 BW and "=—BT-T=(A‘%S)'1;T=‘gw° ‘13-” 3(T) 3(T) P Using ggl = = (since the limiting symmetric t0p axis is the z-axis) leads to C = (P22) 5 = N(N+1) - (14) n = ( - w)/bp . A computer subroutinel7 is used to calculate the Wang energies and the values of , , and for a (given set of A, B, and C values. A program was written to use these values and calculate W0, 2;, 5, and n for each level of interest. 15 If one has a set of observed energy levels and trial values of the rotational constants, K, B, and C, a set of calculated energy levels can be formed using Eq. (3) or Eq. (11). From the differences between the observed and calcu- lated energy levels, corrections to the rotational constants can be obtained by a leaSt—squaresfit to an equation of the form (15) B+C goAA + 5-A(-7—) + n~A<§§9). where AA = A - A, etc., and A, B, and C are the new experi- mental values of the rotational constants as determined by the least squares fit. By using these as new trial values, a refined set of constants can be determined. To include centrifugal distortion terms, Eq. (15) must be modified as follows: B+C w - w c-AA + g-A(-7—) + n-A(§§E) + inAri 1A obs calc = (16) + N3(N+1)3AHN + N2(N+1)2AH + N(N+1)AH NK KN 6 + AHK . .Here, the Ar's and AH's are the corrections to the trial 'values-of the 1's and H's. Since c, E, n, , , depend only on the trial values of A, B, and C, it is tuyt necessary to have starting values of the T'S and H's. 16 If their trial values are all taken as zero, the least squares fit will give their final values directly. In practice, only the differences of energy levels in a given vibrational state.are observed through the combina- tion differences. Thus Eq. (16) has to be changed to the following: [W1 - W2] [W1 - W2] obs - calc = (cl-mm + (51-52>A(-B-§-9) + (nl-n2)A(§§E) _ 3 3_ 3 3 + Eui1 x12)“i + [N1 (N1+l) N2 (N2+l) ]AHN (17) + [N12(N1+l)21 - N22(N2+l)22]AHNK u _ u + [N1(N1+l)1 N2(N2+1)21AHKN 6 _ 6 + [(PZ >1 (P2 >2]AHK where the subscripts l and 2 refer to the two states whose energy difference has been measured. It was found that only one or two iterations of A, B, and C were necessary before no further changes were made. If a fit of observed frequencies is desired, Eq. (17) must be modified to include the band origin v0 and to take into account the fact that there are different sets of rotational constants associated with states 1 and 2. If a calculated set of frequencies, is formed using Eq. vcalc' (10), corrections are found for v0 and for the upper and 1? ground state constants by applying the following equation to each observed frequency: vobs - vcalc — B'+C' AVO + C'AA' "l" E'A(—-2-—-) + n'A(T) 'l' ZXJl-ATi .1. I3 I 3 I I2 2 2 + N (N +1) AHN + N (N' +1) ' AHNK I I k I I 6 I I + N (N +1) AHKN + AHK (18) _ CuAA" _ E"A(B"+C") _ n"A(B _ ZXEAT; J. _ II 3 II 3 II _ II 2 II 2 2 II II N (N +1) AHN N (N +1) AHNK _ II II it II II _ 6 II II N (N +1) AHKN AHK . Here the primes and double primes refer to quantities in the upper and ground vibrational states, respectively, and the A's again refer to changes in the various coefficients. Several computer programs were written to aid in the reduction and analysis of the raw frequency data. They are described in more detail in Appendix I.~ SCAN reduces raw data from the Hydel system18 to fringe numbers. CALFIT de- termines the calibration constants for each chart. These are input to SCAN to convert the fringe numbers to frequen- cies. SPECFIT fits observed frequencies directly to deter— mine the band origin and the rotational constants for the two vibrational levels involved in a given band. CDSORT finds the differences of transitions within a given band 18 having a common upper (lower) level to form GSCD (USCD). CDFIT fits GSCD or USCD to determine rotational constants for a given vibrational level. B. SPIN-ROTATION COUPLING Energies So far, only the contribution that the rotational angu- lar momentum of the nuclei makes to the total angular momen- tum of-the molecule has been considered. In addition, there are the contributions of the spin of the single umpaired electron g and the non-zero nuclear spin of the nitrogen . atom E. The contribution of the nuclear spin to the energy levels is too small to be observed with the resolution available in the near infrared and is therefore neglected. With this simplification the total angular momentum is taken as that resulting from the addition of N and S. In the absence of external fields, N and S couple to form 2, the total angular momentum of the molecule. Since S = %, the possible values of J are N + % and N - %. Henderson,19 Lin,7 and Raynes20 have discussed the mechanism of the coupling between N_and §.in great detail. Ignoring off-diagonal terms in N as having little effect on the energies, Lin7 writes the spin-rotation Hamiltonian as §fl§ H = —————— e..N.N. , 5.. - 9.. , SR N(N+1) ij 1] 1 j l] 31 (19) 19 where the 2's are spin—rotation coupling coefficients which must be determined experimentally. Using the symmetric top, approximation that the off-diagonal elements of the s tensor are zero, and that Ebb = ecc' Lin's results can be written as e: +s a +6 _ bb cc bb cc K2 HSR- [—2—+ “a. - -—z—> mhfi (2°) ebb+ecc . 3 Since the microwave value of ———§——— 15 ~-0.0015 cm‘l, the first term was dropped as being insignificant. The result- ing Hamiltonian is HSR " KSR fig (21) +€ _ 2K2 _ ebb cc where KSR - my and E - Eaa -' —_T_ o (22) At an early stage in the analysis, the above symmetric top approximation-was tested by using the complete expres- sion of Curl and Kinsey21 for an asymmetric top. It was found that the fit to the experimental results did not change and that values of Ebb and Ecc could not be deter- mined as being significantly different from zero. Since = 1 2 [J(J+1) - N(N+1) - S(S+1)], (23) the spin-rotation energies can be written as + _ N wSR "‘KSR‘Z (24) W- = _ (N+1) SR SR "17" 20 t where WSR get the energy of the J1=Nt§ state. The coupling of N and S is the energy which must be added to Eq. (9) to to form g and the splitting of a typical level are shown at the left side of Fig. 4 (page 28). Note that the splitting given by Eq. (24) is not symmetrical about the zero—spin positions. Analysis For electric dipole transitions the selection rule for J is AJ = 0, *l, but transitions having AJ = AN are by far the strongest. Transitions having AJ # AN have not been observed in the infrared spectra of N02 so that all observed transitions are either W+ + W+ or W' + W". Thus the spin- rotation splittings of the observed spectral lines arise only from differences in the splittings of the levels which are involved in the transitions. If AJ # AN transitions can be found, they will provide direct observation of the spin splittings in the upper and lower states. If v represents the frequency of a given transition in the absence of spin-rotation splitting, the frequencies of the observed spin-split components (AJ = AN) will be given bY' v‘ = v + ng(e',N',K') - w;R(e",N",K") . (25) From this v+ - v' = W§R(e',N',K') - WSR(€"'N"’K") (26) - W§R(e',N',K') + W§R(e",N",K") . 21 Substitution of Eq. (24) gives v+—V-=£2—(N—':iu)—e'—K—2—(blu—+fle" (27) I N' (N'+l) N" (N"+l) where the fact that AK = 0 has been used. If the assumption is made that isotopic substitution does not change the electronic structure,20 the following expressions can be used: * 5 aa _ A* _ X‘ (28) I e 5 aa bb cc where the starred and unstarred coefficients correspond to the values of thelcoefficient for two isotopes of a given I. 6 1n molecule. Thus, 15 aa = ISA , etc., for each vibrational . s A level. aa Since the effective 5 observed is nearly equal to Eaa, the approximation e* _ A* ?—r em should be valid. A program SPINFIT (see Appendix I) was written to take input values of (v+ - v“), K, N, AN, and a weight for each observed splitting and perform a least squares fit to get values for e" and 5'. Data for ll'NOZ and 15N02 can be fit separately to get the e's for each molecule, or Eq. (29) can Ibe used to combine the two sets of data for the determina- 1“: 15e tion of -—— = I‘IA 15A for each vibrational state. 22 Due to the asymmetry of the splitting of the energy levels, the spin-free frequency of a line is not midway be- + .- tween the-two components, i.e., v # 3——;—1— . Thus it is necessary to use the results of an analysis of the data with Eq. (27) to correct the components of the doublet to a single spin-free frequency. Only after this has been done can the transition be included with the data which is fit to Eq. (17) or (18) to determine rotational and other constants. C. ZEEMAN EFFECT Energies In the absence of external forces and torques, molecu- lar energy levels are independent of the molecule's orien- tation in space so that there is a degeneracy of (2J+l) associated with each energy level. This corresponds to the (2J+l) possible values of MJ, the component of the total angular momentum J on the space-fixed Z-axis. The nitrogen dioxide molecule has a magnetic moment g which arises predominantly from the magnetic moment of the . . gsuB unpaired spin, gp= - ‘15—.E . Here, gs is the free electron g-factor, and "B is the Bohr magneton. Aside from its function in the spin-rotation coupling, the small magnetic moment arising from the end-over—end rotation of the mole- cule can be ignored. In the presence of an external magnetic field there *will.be a torque on the magnetic moment of the molecule 23 which will lift the MJ degeneracy through the action of the Zeeman Hamiltonian gs”B Hz='l‘.'§.=T§l§=2A\’ SZ, (30) _ l . . -1 . . l _ where Av - 2gsuBH 13 In cm and H 15 In gauss (2gsuB — 4.6754 x 10"5 cm'l/gauss). At low field strengths the N-g coupling predominates so that J is still a valid quantum number, and the wavefunction for rotation and spin may be written |N,S,J*,MJ> . (31) These are eigenvectors of the spin-rotation Hamiltonian [Eq. (21)], but not of the Zeeman Hamiltonian [Eq. (30)]. At higher field strengths the §f§ coupling predominates- and J is no longer a meaningful quantum number. N and E. couple to the-field (Z-axis) separately so that the wave- function may be written IN,MN,S,MS> . (32) These are eigenvectors of the Zeeman Hamiltonian but not of the spin-rotation Hamiltonian. For the general case of any magnetic field strength, an expression is found for the spin-rotation and Zeeman ener- gies. The approach is similar to that originally developed by'Eh In Hill for diatomic molecules and first published by .Alnw'in his treatment of the 22 state ofOH.22 24 The perturbation Hamiltonian is taken as H SR,Z HSR+ Hz ' (33) Since HSR is diagonal only in the IJ,MJ Hz is diagonal only in the IMN,MS> representation, H > representation, and SR,Z will have both diagongl and off-diagonal matrix elements in either of these representations. Thus the perturbation energies will have to be found by diagonalization of the energy matrix in either of these two representations. |J,MJ: representation. Initially the IJ*,M > represen- J tation was used. Using vector coupling coefficients for the addition of two angular momenta, the two |J*,M > wavefunc- J tions can be expressed as linear combinations of the two IMN,MS=t§> wavefunctions:23 A _ 2 |J+IMJ> _ [fifiig] |MN,MS=§> + [E_EE:£] IMfiIMS='2> 2N+1 2N+1 - a ; IJ-.MJ> - - [5—51-93] IMN.MS=1> + [M37] lMfi.MS=-l> 2N+1 2N+1 (34) I ' - _ where the values of MN and MN are fixed at MN — MJ i and Mfi = MJ+§ . Using the |J*,MJ> wavefunctions as the basis wavefunctions leads to a two-by-two matrix in which the off- diagonal elements couple only levels having the same value of MJ = MN + MS: 25 |J+IMJ> IJ-,MJ> M M 2 2 N+§ N+§ (35) M 5 M J 2 N+l J level does not exist for MJ = tJ+, the IJ+,MJ> level with MJ = *J+ must be treated separately. The resulting energy expressions for MJ # tJ+ are t WSR'Z(N,J ,MJ) (36-a) p( M - —§§ t % (AW)2 + 4(Av)(AW) J + 4(Av)2 5 , (N+§) while for MJ = 1J+ hf WSR'Z(N,J+,MJ=1J+) = —§5 N . Av . (36-b) Here, AW is the zero-field separation of the J+ and J- levels, and _ + _ - = AW — wSR wSR KSR(N+§) . IENIMS: representation. In the consideration of selec- tion rules and transition probabilities for the Zeeman components of a transition, it was found necessary to use the IMN,MS> representatiOn. Using the inverse of Eq. (34)24 26 ) i - > = §:Efl:i + = > _ N-MN - _ > IMN.MS-+l [ m1 J IJ .MJ “n+5 [mu] IJ .MJ-MN+l l l (37) N-MN N+MN+1 _ IMN+1.MS=-i> = [2.14.1] |J+.MJ=MN+1> + [El—1"] IJ ,MJ=MN+1> , the following energy matrix is obtained: IMNI+2> lMN+lr‘2> K K (MN'+“ "'szB MN + A“ —§5lN2+N-MN2-MN15 (38) AC éMa(¢Aa)n,m . (41) Here, A = X, Y, or Z and a x, y, or 2. Since the only N02 bands observed with reasonable in- tensity are type-A bands, where the change in the dipole moment is along the a- or z-axis, it will be assumed that the dipole moment has a non-zero component along only the z-axis, i.e., Mx = My = 0, Mz # 0. Although Cross, Hainer, and King and others write the matrix elements of M as , they are treat~ ing the special case of zero-spin angular momentum so that by J they mean the total rotational angular momentum N. Thus, the matrix elements, , must be formed in order to calculate the transition probabilities. With this understanding, the (0A ) can be written a n,m (0 Aa)N,K,MN;N',K',Mfi = (42) (¢Aa)N;N'(oAa)N,K;N',K'(¢Aa)N,MN;N',Mfi , where the 0A“ on the right hand side have been given by Cross, Hainer, and King.25 Since all of the Zeeman work reported here is done with a lc>ngitudinal magnetic field, only transitions having AME = Mfi - MN = *1 will occur. With this restriction, all 30 matrix elements of M2 vanish. Combining this with the fact that AK = 0 for the transitions of interest and using Eq. (42) reduces Eq. (41) to = (43) M (T ) 2 A2 '(¢ (¢ ) N;N Az)N,K;N',K Az N,MN;N',MN*1 . The ¢Az of interest are given in Table I. The resulting matrix elements of MX and MY for the R, Q, and P branches are = ti =*Mz{[(N+l)2-K2)(N1MN+1) (NiMN+2)} 5 [4 (N+1) 2 (2N+1) (2N+3) 1‘5 = ti ; 2 2-5 ‘4‘“ = MzK[(N:MN)(NtMN+1)] [4N (N+1) ] = *i =¢Mz[(N2-K2)(NxMN)(NIMN-1)]5[4N2(4N2-1)]‘5 , where the quantum number K has been left out of the wave— functions since it is a constant for any given transition (AK = 0). Wavefunctions. In order to calculate the intensities of Zeeman components at all magnetic field strengths, it is necessary to find an expression for the mixing of the (N.K,M.N> wavefunctions which arises from H . (The mixing SR,Z 31 omN OOCOHONOM EOHMM lusecfl. n 2722;: 33: l . :22: 2:22.71: 522.5 222.5 A . m A I m HAZE..znzz.zxuxev Mm M..zxx.zxu is zero unless Mé = MS, the wavefunctions of Eq. (32) are the wavefunctions which should be used to calculate the transition probabilities. In the absence of a magnetic field the correct mixing of these wavefunctions to represent a given energy level is just that given by Eq. (34). As the magnetic field is applied, the mixing will decrease until at high fields a given energy level will be described by either IN,MN,S,+}> or|N,MN,S,-§>, in which case the intensities will be given by the usual symmetric top equations.26 An alternate approach is to treat the spin-rotation coupling as a perturbation. In the absence of the perturba- tion, the wavefunctions are IN,MN,S,*§>. The perturbation acts to mix the wavefunctions to produce the wavefunctions IJ*,MJ>. The amount of the mixing is determined by the ratio of the perturbation energy to the Zeeman energy. Thus the mixing is a maximum at zero magnetic field and decreases as the field is increased. In the limit of high fields the .Perturbation energy is much less than the Zeeman energy, and there is effectively no mixing. If the degeneracy of two states, Il> and l2>, is lifted by tlle action of a perturbation V, with matrix elements <11 V11 V12 , (45) (2| V21 V22 33 the resulting perturbation energies are V+V l Ei = -li§-ZZ * 3(V11‘V22) + V12V21 i I (45) where the upper sign gives E1 and the lower sign gives E2. Application of this to the matrices given in Eq. (35) or (38) gives Eq. (36-a) or (39-a). The perturbation will also cause a mixing of the wave- functions for the two states. This can be written as ll) C11|l> + C12|2> (47) l2) C21|l> + C22[2> , where In) denotes the resulting wavefunction for the level which had the wavefunction In> in the absence of the pertur- bation. The Cij are determined27 by = E. (48) and the normalization condition, C112 + C212 = l . (49) From this results C11: .[1 +(_VZJ._.)2]-i, 34 . [1 + (JILL—VJ-i, and C22 = V11-E2 V12 C = - C . 12 (v—J 2) 22 The choice of 1 must be consistent with the phase convention used in the evaluation of the Vij‘ It will be shown later that the upper sign must be used. Transition probabilities. Comparison of the matrices in Eqs. (38) and (45) shows that for the calculation of the transition probabilities for the Zeeman components, the V.. are 13 K V11 = -§§'MN + AV v22 = - 15—13 (MN-+1) - Av (51) f< V12 = V21 = -§B [N2+N-MN2-MN]£, and the Ei are E1 = WSR,z(N'MN'+5) (52) E2 = WSR'Z(N,MN+l,-§) . From these expressions, the Cij can be calculated using Eq. (50). Eq. (47) becomes ' 'NIMNI+2) = ClliNIMNI+2> + CIZINIMN+11‘2> (53'a) IIVIMN+1I'2) = CZIINIMNI+2> + CZZINIMN+1I'2> 0 (53-h) 35 For convenience, Eq. (53-h) is rewritten INIMNI-l) = CEIIN,MN-l,+£> + CEZINIMNI-2> I (53‘C) where C31 and C32 are equal to C21 and C22 with MN replaced by (MN-l) throughout. This replacement must be made in the V.. and E. also, yielding VT. and ET. 1 13 1 13 * "' * * V21 2 5 * V21 * C11 * 1 + '--—- , C21 - --- C11 * * * * VZZ‘EI VZZ'EI * Viz 2 -5 * Viz * C - . 1 + —————— , C1 - .—————— C 22 * * 2 * * 22 V11-32 V11-E2 (54) v‘fl =€§5 (MN—l) + Av F( ' ' vfz = —§§ [N2+N-MN2+MN]5 32* -- w..,. . (SS-a) except that |N,MN=-N,-)) = |J+,MJ=-J+> . (55-h) By calculating the Cij at zero field, substituting the results in Eqs. (SB-a,c) , and comparing with Eq. (34) using Eq. (55), the phases for the Cij in Eq. (50) can be fixed: 36 C11 and C22 are 3 0 . Writing the resulting ground state wavefunctions as IN".M§.+1) ClllNflrM§I+2> + ClZINnrM§+lI‘2> *Il lNulMfiI-é) = CZIIanM§-lr+2> + ngiNnrMfir-2> and those for the upper state as IN'.M§.+£> cillN'.M§.+)> + cile'.M§+1.-)> CzliN'IMfi-lr+2> + C22iN'rMfir‘2> iN'IMfiI-ll leads to the following matrix elements: (N",M§,+§|M|N',Mfi,+§) C¥1C11 (56-a) (56-b) (56-c) (56-d) (57-a) + CIZC12 = c3¥c§i (N".Mfi.+llfilN'.Mfi.-i) = C¥ICS1 (N",M§,-§|filN',Mfip+2) = CETCII (57-d) + C33C12 . 37 Consider a general element (nlMlm) C1<1|M|l> + c2<2|MI2> . (58) Since 3+ II with MZ = 0 for AMN=*l transitions, the transition proba- bility for a transition n + m is ll2 s II2 + I + c2<2|MxI2>|2 (59) + IC1<1|MY11> + c2<2mylz>|2. From Eqs. (44) = :i,and is real, so that lI2 -2[c1 + c2<2IMx|2>]2 (60) 2[(nIMXIm)]2 . Applying this to Eqs. (57), the transition probabilib ties for the Zeeman components of transitions in vibration- rotation bands of N02 are finally I(N".M§.+1I8IN'.M§.+T>I2 = ZICYICi1 <61-a) + CY2C12]2 38 l(N",M§,-§IM|N',Mfi,-£)|2 = *n *I 2[C21C21 (61—b) + CZZCZ£12 |(N".M§.+)IEIN'.Mfi.-1)l2 = 2[C¥1C3{ (6l-C) + CY2CE£12 |(N"IM§I'2IfiIN'IMfiI+2)i2 = zlczicil <61-d> + C22Ci2]2 . The non-zero matrix elements of M are given by Eq. (44). X From these and Fig. 4 it can be seen that the selection rules onMN for the perturbed energy states are AMN = 11 for the transitions of Eqs. (61-a) and (6l-b), AMN = 0, +2 for those of Eq. (6l-c), and AMN = 0, -2 for those of Eq. (61-dL Frequencies. Application of Eqs. (61) to calculate transition probabilities for P, Q, and R branches (AN = -l,‘ 0, and +1) gives non-zero intensities for only those compo- .nents having AJ = 0, *l, with AJ=AN transitions being much more intense . For R- and P-branch transitions (AN = *1) only one of the weak satellite (AJ # AN) lines occurs at zero field 39 since the second one would require AJ = *2, which is not allowed.. Correspondingly, Eqs. (61) predict zero transition probabilities for these transitions. In the Q branch (AN=0) there are two satellite lines predicted at zero field. As the magnetic field is applied, all of the satellite transi- tions lose intensity rapidly. The frequencies for the transitions given in Eqs. (61) are ..N«,M§,M§.N-,M§,Mé) = (.2) v(asym. rotor) + WSR,Z(N"MN'MS) - WSR,Z(N"'MN'MS)' Analysis. The program ZEMANINT was written to calcu-‘ late the frequencies using Eq. (62), along with the transi— tion probabilities from Eqs. (61), for the Zeeman components of any specified transition at various magnetic fields. Figures 6 and 7 show the predicted transition proba- bilities for a P- and a Q-branch transition, respectively, as calculated by ZEMANINT for fields of 0, 2000, 4000, and 6800 gauss. D. MAGNETIC ROTATION SPECTRA The magnetic rotation spectrum of a gas is the spectrum of radiation which is passed when a sample of the gas has been placed in a longitudinal magnetic field between crossed Polarizers. Normally there would be no radiation transmit- ted through the crossed polarizers, but ifthe gas exhibits 40 H=6800 l 'MMMHii i 'rMHE . l . .e M H = 400:) Jim _ mm l W)! ' H=2000 l I + H = O gauss l 1 . 1 I (l I 4|68.9 4|69.0 4l69.l cm" Fig. 6. Predicted Zeeman splittings for the P (10) line of the (2,0,1) band of 11'N02. The length of each ling is proportional to the rotational transition probability for that component. The lengths of the lines for the zero field case have been re— duced by a factor of 10 relative to the others. Lines drawn upward (downward) correspond to AM = +1 (-1) transitions. 41 H=6800 . . ‘ L ijq ( I :1 H=4000 ___LA I I I H=ZOOO | L 1 l l T I H = O gauss —LI i ( 4|75.7 4|75.8 4|75.9 cm'I Fig. 7. Predicted Zeeman splittings for the Q (7) line of the (2,0,1) band of 11+N02. Otherwise this figure is the same as Fig. 6. 42 magnetic optical activity at certain frequencies, there will be radiation transmitted at those frequencies. The magnetic rotation signal has been shown to be due to a combination of the Faraday effect and circular dichro- 28'29’6 An extensive review of "Magnetic Optical Activ- ity" has been presented by Buckingham and Stephens.30 ism. In the Faraday effect the plane of polarization of. incident radiation is rotated through an angle which is proportional to the difference between the indices of re- fraction for right and left circularly polarized radiation. Circular dichroism arises from a difference between the absorption coefficients for right and left circular polari- zation, so that an incident plane-polarized beam becomes somewhat elliptically polarized. Using a semi-classical approach, Aubel6 shows that Faraday rotation contributes to the magnetic rotation signal only in the wings of absorption lines, where there is very little absorption, while circular dichroism contributes only in regions where there is a sig- Iuificant difference in the amounts of right and left circu- larly polarized light which is transmitted. In the region of a nitrogen dioxide absorption line Iboth Faraday rotation and magnetic circular dichroism con- tribute to the magnetic optical activity, and thus to the magnetic rotation spectrum. Since the AMN=+1 and AMN=-l transitions are associated with different directions of circular polarization, the magnetic rotation signals depend 43 on the relative positions and intensities of the Zeeman components of the lines. Thus, it will be useful to refer to Figs. 6 and 7 when the observed magnetic rotation spectra are considered in Chapter II. CHAPTER II EXPERIMENT AND ANALYSIS A. EXPERIMENTAL EQUIPMENT Spectrometer All of the spectra were obtained using the high resolu- tion (~0.03 cm'1 at 4200 cm'l), vacuum, grating spectrometer at Michigan State University. Major modifications were made in the optical elements and grating drive-train during an eight month period from September, 1964 to May, 1965.- The absorption, magnetic rotation, and initial Zeeman records were obtained during the periods May 25, 1965 to June 24, 1965 and September 23, 1965 to November 2, 1965. At this time the spectrometer was essentially as described by Keck gp'gl.31 except that the vacuum polarizer assembly and new sources were not yet installed. In December of 1966 after these latter modifications had been completed, additional Zeeman records were obtained when it was found that data at several additional intermediate fields were necessary for a confirmation of the theory. Data Reduction The absorption spectra, recorded on strip charts, were 44 45 photographed; then the raw data were digitized using the Hydel system18 and reduced to absorption frequencies by the computer programs SCAN and CALFIT, which are described in Appendix I. Solenoid A Magnion solenoid capable of fields up to 6800 gauss was used for the Zeeman and magnetic rotation spectra. This solenoid has a seven-inch diameter air core which is forty- eight inches long. Over the central two-thirds of this length, which includes the region of the multiple-traverse absorption cell, the field is uniform to within better than *2%. B. ABSORPTION SPECTRA Experimental Conditions At least two calibrated, high-resolution absorption records were obtained for each of the four bands which have been analyzed and are reported here. The experimental con- ditions for these records are given in Table II. Each record was measured on the Hydel by two operators so that the absorption frequencies used in the analyses were ob- tained by averaging at least four different measurements. Initial Analysis The analysis of a given vibration-rotation absorption band started with an initial identification of several low N 46 N m H N H Hmcuo mcwumuw Aeume Aa.e.mc AoIHc AOINV AeIHV eehm oo o~z Hum 00 Hum who eoAumuhAHmo m A N H Aeoz home hmeuo o.meIe.ee e.~mum.am o.AeIe.me m.HmIm.om Ammmummev mamcm Aesxa some maflumuo . AAIEOV guess emo.o mmo.o emo.o mme.e uflam 0>Auumuum NH 8H NH ea lav nuees DAHm om.e mH.m om.e ma.m Ase nausea Beam ONIOH He omImH He lemony musmmmum me\ma\ea me\m~\ea me\m~\oa me\eH\OH me\mm\oa m.~.HIme\m~\m me\a~\oa amass: unmno AH.o.~v Ia.e.av Aa.o.~c la.e.av "chem Nozmu Nozed .Guuoomm coaumHOmnm «oasooaoz How MCOHDHDGOU Hmucmfiflummxm .HH manna 47 transitions for which K = 0, 3, 4, ..., since these transi- tions involve levels which are least affected by the asym- metry and could thus be easily identified by comparison with the structure of a symmetric top parallel band. Holding the ground state rotational constants fixed at the values deter- 1’3 it was possible to use mined by the microwave analysis, SPECFIT (see Appendix I) to determine approximate values for the band origin and upper state rotational constants. From these, a spectrum was predicted, and additional identifica- tions were made. Iteration of this procedure eventually led to a complete analysis of the band, with identification of nearly all of the observed transitions. For each vibrational state there is a very high corre- lation between the quantum dependences of Taabb and Tabab which prevents the simultaneous determination of good esti- mates for these two constants. Equation (7) has been used to fix Tabab at its theoretical estimate in each case so that a significant estimate of the value of Taabb can be found. Since the equilibrium values of the rotational con- stants are not known, the values for the ground vibrational state are used. (The value of mg is taken from the work of .Arakawa and Nielsen.4) Included in the final data are the corrected, spin-free frequencies for those transitions which show a resolved spin doubling . 48 Ground State Constants A program CDSORT (see Appendix I) was written to sort through the transitions within each band and form ground state combination differences (GSCD) and upper state combi- nation differences (USCD). Since both bands of each mole- cule which are analyzed here have the same ground state, the program also forms weighted averages of all of the GSCD found for each molecule. To these are added the reported microwave measurements of ground state energy differen- ces,1'3 with appropriately high weights. The infrared data has GSCD for N as high as 48 and K as high as 7, whereas the microwave analysis involves only levels with N up to 22 and K up to 2. Thus it is necessary to use the microwave constants only as very good initial estimates of the ground state constants from which final values are found. In addition, two of the empirical P6 terms, H and H KN K' the ground state of 1"N02. are found to have significant values for Table III summarizes the constants determined by the program CDFIT for the ground states of 1"N02 and 15N02 and lists the microwave constants for comparison where available. In each case, Eq. (17) was fit to the combined infrared and microwave data. At first, the rotational constants were held at the microwave values,l'3 and the 1's and H's were varied, but the data could not be fit without allowing the rotational constants to vary also. 49 For 11+N02 the rotational constants found here are with- in the uncertainty quoted by Lees gp‘gl.3 but have signifi- cantly smaller uncertainties. This is especially true since the uncertainties determined here are 95% simultaneous con- fidence intervals which are a factor of 4.0 larger than the standard errors of the coefficients, whereas the uncertain- ties given for the microwave values are simply the standard errors of the coefficients. . For 15N02 the rotational constants do not agree as well with the microwave values and have somewhat larger uncer- tainties. The 95% simultaneous confidence intervals are a factor of 3.6 larger than the standard errors of the coeffi- cients.r The observed GSCD used in these fits are listed in Appendix II along with their weights and their deviations from the GSCD calculated using the constants given in Table III. Upper State Constants Rotational and centrifugal distortion constants for the upper state of a vibration-rotation band can be determined in either of two ways--by fitting frequencies or by fitting upper state combination differences (USCD). Once the ground state constants are known, they can be used to subtract the ground state energies from the observed frequencies, leaving just the vibrational and upper state rotational energies, from which the band origin and upper state rotational 50 Table III. Ground state rotational constants for N02 (in cm’l). ll-I'NO2 Microwavea' This Work A 8.00213 . 0.00037 8.002509 . 0.00010b B 0.433686 4 0.000033 0.4336646 . 0.000004 C 0.41044 4 0.00010 0.4104925 . 0.000014 Taaaa (-9.99 . 0.13)x10-3 (-ll.365 . 0.28)Xl0’3 Tbbbb (-l.382 : 0.005)><10-6 (-1.4180 . 0.023)x10"6 Taabb (6.147 . 0.007)><10-S (6.905 . 0.24)><10-5 _ -6 _ -6 Tabab ( 8.182 . 0.33)x10 8.215 x 10 HKN (-1.11 . 0.6)><10-7 HK (2.8. t 1.1)x1o'5 No. of GSCD 162 Std. dev. 0.0048 (I.R. data) 51 Table III (Continued) lSNOZ MicrowaveC This Work A 7.63047 * 0.00012 7.630617 * 0.00029b B 0.433735 1 0.000006 0.433717I,.=t 0.000016 C 0.409440 * 0.000006 0.4094916 * 0.000030 ._ -3 _ -3 Taaaa ( 9.12 t 0.13)x10 ( 9.15 t 0.5)X10 Tbbbb (-1.382 . 0.005)x10-6 (-1.400 : 0.04)><10-6 Taabb (5.87 1 0.06)Xl0‘5 (5.87 * 0.4)x10“5 _ -6 _ -6 Tabab- ( 8.16 t 0.03)x10 8.175 x 10 HK 0.0 No. of GSCD 149 Std. dev. 0.0043 (I.R. data) m aLees, Curl, and Baker. b95% simultaneous confidence intervals. cBirdeg£.§£. 52 constants can be determined using SPECFIT. The alternate method is to use CDSORT to form USCD to which Eq. (17) can be fit to determine the upper state constants. For the bands analyzed here, the first method is best for several reasons: (1) For a parallel band (AK_1 = 0) several of the con- stants (e.g., A and HK) of a vibrational level cannot be determined by fitting just energy differences. Thus a frequency fit would have to be used to determine these constants and the band origin regardless of how the other constants are determined. There is also the danger that certain of the other constants might not be linearly inde- pendent. (2) The uncertainties of the constants are significant- ly smaller for this method. (3) Since it was found (see below) that some of the observed lines do not fit well, possibly indicating the existence of a perturbation, it is more meaningful to fit the energies directly rather than just the energy differ- ences. The K=3 series of the (2,0,1) band of each molecule could not be fit as well as the rest of the data. For 10 < N < 48 there is a progressive deviation of the observed ‘positions from.those predicted by the best constants that can be determined. This deviation is as large as 0.12 cm'1 at N’= 48. The other series of the (2,0,1) bands and all of 53 the series of the (1,0,1) bands fit much better with-the largest systematic deviations being no larger than 0.07 cm‘i Since GSCD obtained from the K=3 series of the (2,0,1) bands agree with those of the (1,0,1) bands and fit well with the other GSCD, there must be a perturbation of some sort affecting the (2,0,1) vibrational levels. A Coriolis perturbation can probably be ruled out since the nearest- lying band which could have a Coriolis interaction with the (2,0,1) band is ~240 cm"1 away. In addition, one would expect a Coriolis interaction to affect more than one of the K levels for a given N. A failure in the analysis scheme, which is based on only a first-order treatment of centrifu- gal distortion, can be ruled out since the GSCD fit well for all values of N and K used. Since the deviations of the K=3 series of the (2,0,1) bands are not understood, these series are.not included in the final fit to determine the (2,0,1) upper state rotation- a1 constants and band origins, although they are used to form the averaged GSCD. The resulting upper state constants and band origins for the (1,0,1) and (2,0,1) bands of 1“N02 and 15N02 are given in Table IV. Evaluation 2; Rotational Constants and Prediction g£(0,0,3) and (1,0,3) Rotational Constants The relations for the vibrational dependence of the rotational constants of a triatomic molecule-are written as 54 Table IV. Upper state rotational constants and band origins for N02 (cm‘l). 14N02 (1,0,1) (2,0,1) v0 2906.0737 . 0.006a 4179.9383 t 0.007 A 7.8540. t 0.0010 7.92649 4 0.0010 B 0.4285979 . 0.000017 0.4262833 t 0.000018 c 0.4050070 . 0.000015 0.4022531 : 0.000016 Taaaa (-1.1558 4 0.016)><10"2 (-l.l84g . 0.019)><10"2 Tbbbb (-1.4309 . 0.030)x10-6 (-1.4443 . 0.031)x10-6 Taabb (7.469 2 0.17)><10"5 (6.521 : 0.08)><10'S Tabab -8.215 x 10'5 -8.215 x 10'5 HKN (-1.129 . 0.19)><10"7 0.0 HK (2.893 t 0.04)><10'S (2.763 . 0.05)x10‘,'S No. lines 710 563 identified No. lines 369 286 weighted¢0 Std. dev. 0.0096 0.0104 of fit 55 Table IV (Continued) ISNO2 (1,0,1) v0 2858.7071 t 0.008 A 7.49181 1 0.0032 B 0.4287542 4 0.000024 C 0.404166“ 1 0.000020 Taaaa (—l.411 t 0.13)><10"'2 Tbbbb (-l.3632 t 0.042)x10’5 Taabb (6.572 t 0.30)x10's Tabab -8.l75 x 10'5 HKN 0.0 HK (3.69 t 0.9)><10'S No. lines 482 identified No. lines 288 weighted#0 Std. dev. 0.0118 of fit (2,0,1) 4120.3673 . 0.004 7.53981 . 0.0005 0.426487S 2 0.000013 0.401450o . 0.000011 (-0.9533 . 0.0041x10‘2 (-1.4068 . 0.022)x10-6 (5.837 . 0.12)..10"5 -8.l75 x 10"5 (0.827 : 0.14)x10"7 0.0076 a95% simultaneous confidence intervals throughout. R nln2n3 (63) I w o o o I 'M Q .‘3 ‘ where R = A, B, or C, and the subscript e denotes the equi- librium value of the constant. From this, the following expressions for a? and a? in terms of the known values of R000 , R101 , and R201 can be Obtained: 01 = R101 ' R201 (64) R 03 R000 + R201 - 2R101 . The resulting values of these a's for the two molecules are given in Table V. The values of 0% cannot be determined since n2 = 0 for all of the bands studied here; thus, equi- librium values of the rotational constants could not be determined. Frequencies were obtained for the (1,0,3) and (0,0,3) bands of each molecule. The analysis of the (0,0,3) band of 1"N02 has just been started.32 Others have tried to analyze 4’5 but have not lower resolution spectra of these bands, been entirely successful, due largely to the wide spacing of the Q branches of the bands. These authors have tried to explain the large Q-branch spacing as arising from overlap- ping type-B (perpendicular) bands. 57 Table V. Vibrational dependence of the rotational constants. 14N02 15N02 6? -0.07245 . 0.0014 -0.04800 . 0.0033 6? 0.002314 . 0.000025 0.002267 . 0.000027 6? 0.002754 . 0.000022 0.002716 4 0.000023 6% 0.22092 . 0.0017 0.18681 4 0.0046 6% 0.002753 . 0.000030 0.002696 4 0.000040 6% 0.002732 4 0.000030 0.002609 . 0.000043 Table VI. Predicted rotational constants for the (0,0,3) and (1,0,3) vibrational levels. l‘INO2 ISNOZ A003 7.33975 * 0.0029 7.0702 * 0.008 8003 0.425405 * 0.00005 0.425629 * 0.00007 C003 0.402297 1 0.00005 0.401665 * 0.00008 A103 7.41220 1 0.0033 7.1182 * 0.009 B103 0.423092 1 0.00006 0.423362 . 0.00008 C103 0.399543 4 0.00006 0.398949 4 0.00008 58 With the present determination of a? and a? , the val- ues of the upper state rotational constants for these bands were calculated and used to predict a spectrum. The calcu- lated rotational constants for the (0,0,3) and (1,0,3) vibrational levels are given in Table VI. The predicted spectra have Q-branch positions which closely match the observed Q branches, showing that the wide Q-branch spacing is due to the relatively large values of 0% . It should be remarked here that the magnetic rotation spectra have large signals at these Q-branch positions, which also confirms the identification. Thus it appears that only the type-A (0,0,3) and (1,0,3) bands occur in these regions. C. SPIN-ROTATION ANALYSIS Experimental Initial spin-splitting measurements were taken from the absorption records. Later, after modifications had been completed on the spectrometer which slightly improved its resolution, new Zeeman records were obtained. The spin- splitting measurements from the zero-field Zeeman runs have been used for the final determinations of the spin-splitting constants. (2,0,1) Bands At least 50 spin-doublets have been identified in each of the (2,0,1) bands. The 0* and v' components were as- signed by comparing their intensities with the statistical 59 weights of the levels involved. Of these, 25 1"N02 and 24 15N02 spin-splittings have been assigned non-zero weights. Equation (27) was first used to fit the ll'N02 and 15N02 data separately. The program SPINFIT (see Appendix I) was then modified so that the data from the two molecules could be combined to test the approximation expressed by Eq. (29). In each case, the fits were first performed holding the ground state effective e's at the values which result from the microwave work3 and then allowing both upper and lower state effective e's to vary. The results are summarized in Table VII. The uncertainties on all except the microwave values are 95% simultaneous confidence levels, which in this case are a factor of 2.5 larger than the standard errors of the coefficients as given by the least squares routine. Comparison of the first and third rows of the table shows that the approximation of Eq. (29) is valid for these data and leads to more accurate values of the £201 . Since this determination of the 5000 values does not overlap the values calculated from the microwave work, and the microwave values are generally expected to be far more accurate, the most meaningful results of these fits are probably the values of (€201 - €000) given in the third row of-Table VII. In Table VIII are listed the observed and calculated splittings and weights from the fit which led to the effec- tive 2's in the third row of Table VII. 60 .uoxmm can .mam>HODCH mocmcflmcoo msoocmuHsEHm mmm n .HHDU .mmmq mo mmsHm> o>m30uoafi Eoum coumasoamum m aowflma ~o~43~ aawu fl "GNU emooo.o. hmoo.e. mmee.o. emooe.o. oeoo.o. Heoo.o. ml .1 hoeoo.o emea.o Amma.o Ammoo.o mema.o mama.o eeeaml seemes «aqqmmu u qquuu oaoo.o. eaoo.o. oaoo.o. oaoo.o. Iowans Ismael mmoo.o emea.o moammea.o emoo.o Hmna.e weeeama.o "amen. I _e~032 meoe.o. mmee.o. “meo.e. mooo.o. emoo.e. Hmoo.o. oooeml .lowhml omoo.o «mma.o mmma.o mmoo.o Amma.o omma.o .ooou. .Aoueel eaoo.o. eaoo.o. mooooo.o. eaeo.o. eaoo.o. ~ooooe.o. low .ASN w w mmoo.o meea.e moammea.o emeo.o ~mea.o heeeama.e ml 31 occuluoNu Homu ooou occulfioww AoNu ooou UCHHM> mugmvaOU NOZmH N023” .moz MOM mucmumcoo mcflamsoo c0wumuoulcwmm o>wuommmm .HH> manna Table VIII. 61 (2,0,1) band spin-splittings (cm‘l). 1“NO, lsN02 Branch K_l N OBS CALC WT OBS CALC WT P 1 2 0.0520 0.0579 0.1 P- 2 3 0.1051 0.0849 0.1 0.0930 0.0803 0.1 P 2 4 0.0496 0.0443 1.0 p 3 4 0.1223 0.0997 0.1 0.1027 0.0939 1.0 P 3 5 0.0670 0.0610 0.1 0.0505 0.0572 0.1 P 3 6 0.0424 0.0409 0.1 0.0292 0.0383 0.2 P 3 7 0.0249 0.0272 0.05 p 4 5 0.1081 0.1018 0.1 p 4 6 0.0770 0.0680 0.1 P 4 7 0.0474 0.0483 0.2 p 4 8 0.0360 0.0386 0.1 P 5 7 0.0883 0.0809 0.1 0.0842 0.0755 0.1 P 5 8 0.0644 0.0602 0.7 p 5 9 0.0413 0.0463 1.0 0.0432 0.0429 0.2 p 5 10 0.0313 0.0365 0.1 0.0391 0.0337 0.1 p 6 12 0.0409 0.0346 0.1 p 7 11 0.0463 0.0529 0.5 P 7 12 0.0414 0.0431 0.3 R 1 1 -0.0649 -0.0620 1.0 -0.0714 -0.0593 1.0 R 2 2 -O.1038 -0.0949 1.0 -0.1040 -0.0910 1.0 R 2 3 -0.0490 -0.0496 1.0 R 2 4 -0.0363 -0.0329 0.1 -0.0321 -0.0317 0.1 62 Table VIII (Continued) 14N02 15N02 Branch K_1 N OBS CALC WT OBS CALC WT R 3 3 -0.1236 -0.ll6l 1.0 R 3 4 -0.0715 -0.0739 1.0 R 3 5 -0.0464 -0.0516 1.0 R 3 6 -0.0367 -0.0383 0.2 —0.0347 -0.0371 0.1 R 4 4 -0.1271 -0.1315 0.1 -0.1330 -0.1266 0.1 R 4 5 -0.0709 -0.0886 0.1 R 4 6 -0.0551 -0.0681 0.1 -0.0572 -0.0659 0.1 R 4 7 -0.0446 -0.0528 0.1 -0.0548 -0.0512 0.1 R 4 8 -0.0429 -0.0411 0.1 R 4 9 -0.0353 -0.0338 0.1 R 6 9 -0.0800 -0.0782 0.1 R 6 15 -0.0352 -0.0334 0.2 R 7 18 -0.0321 -0.0336 0.1 63 (1,0,1) Bands The lower energy in the (1,0,1) region, which limits the spectrometer's resolution, and the larger values of (A' - A") for the (1,0,1) bands, which cause a greater over- lapping of different K sub-bands, prevent the measurement of many spin-splittings. Only one or two splittings can be assigned non-zero weights out of the ~40 observed in each band, so a fit has not been attempted. D. ZEEMAN SPECTRA Experimental Conditions High resolution Zeeman spectra of the (1,0,1), (2,0,1), and (0,0,3) bands of each molecule were obtained under the same conditions as the absorption spectra (Table II) and with longitudinal magnetic fields of 500, 1000, 2000, 4000, and 6800 gauss. Comparison 2; Experimental Results with Theogy In addition to the transition probabilities given in Eqs. (61), the prediction of the Zeeman spectra requires information about other factors such as the Boltzmann popu- lation'distribution, the line shape of the Zeeman components, and the slit function shape and half-width. The population of a rotational level is proportional to N = e-E(N,K)/kT R (65) 64 where the symmetric top approximation can be used for the rotational energy: E(N,K) = B N(N+1) + (A4B)K2, where — B+C B = —7— . The percentage transmission at line center is given by _ 2 e “NRlu' x 100 , (66) where In)2 is the rotational transition probability and 0 includes other factors in the line strength such as the pressure dependence, the vibrational transition probability, and the normalization of the pOpulation distribution. Since these factors are not all known here, a must be treated as a parameter which is allowed to vary in order to get the best match to the observed spectra. Thus, the percentage absorp— tion at line center is _ 2 (1 - e “NR|“| )x 100 . (67) The program PLOTZ (see Appendix I) was written to cal- culate and plot the percentage absorption as a function of frequency, using ZEMANINT as a subroutine to calculate line positions and transition probabilities for the Zeeman com- ponents. Because the slit function is generally larger than the line width, the observed spectra show mainly the shape and width of the slit function. Thus, the line shape of each component can be approximated by a rectangular line shape with height given by Eq. (67) and with a width equal to the minimum plotter unit, which is 0.01 inch or 0.0033 65 cm'1 for the scale of the Spectra used here. This is proba- bly not far from the true line width, and any errors are masked by the slit function. On the basis of the shapes of single lines in the ab- sorption spectra, the slit function is taken to have a Gaussian shape with a half-width at half-intensity of 0.016 cm‘l. Figure 8 shows the experimental Zeeman spectra of the band origin region of the (2,0,1) band of 1"N02 at fields of 0, 1000, 2000, and 6800 gauss. Figure 9 shows the corres- ponding theoretical spectra as calculated and plotted by PLOTZ, using a = 0.07 . The program finds the apparent per- centage absorption as a function of frequency by the follow- ing procedure: (1) The product-NRIIII2 and the frequency is calculated for each Zeeman component of each of the lines which are to be plotted. If more than one component occurswithin a small frequency interval (which is the minimum plotter unit, or 0.0033 cm‘l), the values of NRIIII2 in that interval are summed. (2) The percentage absorption at each point is calcula- ted using Eq. (67). (3) The specified slit function is used to integrate over the region of interest, giving the predicted spectrum. The zero-field asymmetric top frequencies used for the tran- sitions are those calculated from the constants given for 66 . .N025H to when AH.e.NV 0B0 to eoemmh cflvfluo pawn map How muuoomm cmEooN Hmucoaflummxm .m OWHFW mmado O u I mmn b h P b p D b b h b IPimy‘b 5 IF » h pi?) b h p Pg) éd)» b b bhibirhi-ibpbbhbbhbbin b L p b 1p/u\h<~ < Lier p h h n p n r h) AW 5‘ b > h rb P¢¢< Ski I pirbibbhDDFALIIPLLiDFLhILirFLLDiPhLL th p h L ‘1 b h b b P b Li P h b i? hi I} (I b h D (D D F - L b b L L L b L (I I— V i, 1’ I. I— r P b (r . (P h p D P _ P b. b! PthbL p?» b» p n p pr »> h. PIIP. D i hrliP .- h i b b b L b > b F b p b P F (PL 5 b h p f D) b v > L P b b h F FL P p (p Lirb b h b h h p p h h C < . 00min: 68 this band in Table IV. The strongest line plotted at zero field corresponds to ~35% absorption. Varying a has little effect on the relative intensities of the different rotational transitions and very little effect on the Zeeman structure of a given rotational transi- tion.‘ The value of a used is found to give the best overall match between the observed and theoretical intensities. E. MAGNETIC ROTATION SPECTRA Experimental Magnetic rotation spectra at various fields were ob- tained for each of the bands studied. Figure 10 shows slave-recorder tracings of the magnetic rotation spectra of the (1,0,1) band of 1"N02. The P-branch region (below 2890 cm'l) was run at a field of 3500 gauss, and the Q-branch region at 2500 gauss. The strongest signals are from QK(N) transitions with K = 4 through 9. The P-branch signals come from PK(N) transitions with K = 6 and 7 and N = 13 through 24. Analysis The strongest magnetic rotation signals invariably come from the Q-branch transitions. The signals from the Q branch for a given K increase as the field is increased until a certain field is reached, after which they decrease. The field at which a Q branch gives the maximum signal var- ies with the value of K for the branch. Study of the 69 .wmsmm comm um nocmunlo ecu can .mmcmm oomm um can MOB ALIEO ommm zoaonv cowmmn socmunIm one .Noz:~ mo pawn AH.o.Hv ms» mo Eduuommm coflumuou ofiumcmmz .oa .ma@ 7:3 DOWN . OJQN ODON e m m t. m m .v. 25.0 70 variations of the Zeeman patterns of a Q-branch transition indicates that there is a field strength at which the AMN=+1 transitions from the two components of the spin-doublet superimpose. Thus, at this field there is a strongly ab- sorbing region of AMN=+1 transitions at line center, with weaker AMN=-l absorption in the wings of the line. For each Q branch this is the field for which the magnetic rotation signals are the strongest. For the 07(7) transition shown in Fig. 7 this occurs at a field strength near 2000 gauss. The fact that the field at which this maximum signal occurs is found, experimentally, to depend on K can be at- tributed to the fact that the zero-field separation of the spin-doublets varies as K2. At low K values, a smaller field will move the AMN=+1 components to superposition, while at high K values, the field must be considerably stronger. If the field is increased above the point of strongest signal, the AMN=+1 and AMN=-l transitions move closer to_one another, as shown in Fig. 7, until at high fields there is so much overlapping that little magnetic rotation signal can be expected. Experimentally, as the field is increased, the signal decreases until at the maxi- mum field (6800 gauss) there is essentially no magnetic rotation spectrum. Calculation of the index of refraction and absorption coefficient curves for right and left circu- larly polarized light at the various fields should show maximum differences corresponding to the fields at which maximum signals are found, and small differences at higher fields. 71 As shown in Fig. 6, the Zeeman patterns for P-branch lines are not the same as the Q-branch patterns. As the field is applied, the stronger components tend to remain near their field-free positions so that there is never a. grouping of strong AMN=+1 or AMN=-l transitions in a single region, as there is for the Q-branch lines. This explains the weaker signals which are found in the P branch.. The only R-branch signals appear to come from low N transitions near the band origin. The lack of further signals from R— branch lines, which have Zeeman patterns similar to those of the P branch,-is probably due to the great amount of over-~ lapping of transitions which would tend to cancel Faraday rotation and circular dichroism effects. The strongest P—branch signals for the (2,0,1) band of ll'N02 come from the K=5 series with N = 8 to 12, at a field of 2000 gauss. From this it appears that the strongest P- branch signals are to be expected from lines whose spin- doublet is just resolved (0.03-0.04 cm‘l) so that in the region between the doublet components the monochromator passes a band of frequencies for which there has been pre- dominantly AMN=+1 (or -1) absorption. From the Zeeman patterns shown in Figs. 6 and 7 it appears that the observed magnetic rotation signals have contributions from both Faraday rotation and circular di- chroism. Thus, a complete explanation of the experimental spectra will require a detailed quantitative analysis. 72 Strong magnetic rotation signals were obtained from. what are here identified as the Q branches of the type—A‘ (0,0,3) bands of 1"N02 and 15N02. No signals could be: obtained from the weak (0,0,2) type-B bands. This supports ‘theconclusion reached in Section B of this chapter that the signals, and thus the Q branches found in the (0,0,3) region, must come from the type-A (0,0,3) band and not from an underlying type-B band. SUMMARY Analysis of infrared ground state combination differ- ences combined with microwave transition frequencies has led to the determination of more accurate estimates of the ground state molecular constants of 1"N02 and 15N02, includ- ing empirical P6 terms. Accurate upper state rotational and centrifugal distortion constants and band origins have been obtained for the (1,0,1) and (2,0,1) bands of 1"N02 and 15N02. In addition, the change in the effective spin- rotation coupling constant between the ground and the (2,0,1) vibrational states has been determined for each isotopic species. Theoretical expressions have been found which give the frequencies and transition probabilities for the Zeeman components of absorption transitions at all magnetic fields. The Spectra predicted by these expressions match very close- ly the details of the eXperimental spectra at all magnetic fields available. Use of these expressions should lead to a quantitative explanation of the observed magnetic rotation spectra. 73 13. 14. 15. G. REFERENCES R. Bird gppgl., J. Chem. Phys. 10, 3378 (1964). A. Gebbie gp‘gi., Nature 200, 1304 (1963). M. Lees, R. F. Curl, Jr., and J. G. Baker, J. Chem. Phys. 1;, 2037 (1966). T. Arakawa and A. H. Nielsen, J. Mol. Spectry. 3, 413 (1958). E. Moore, J. Opt. Soc. Amer. 43, 1045 (1953). L. Aubel, Thesis, Michigan State University (1964). C. Lin, Phys. Rev. llg, 903 (1959). S. Ray, Z. Physik. 18, 74 (1932). C. Wang, Phys. Rev. 21, 243 (1929). A. Hill, Thesis, Michigan State University (1963). ~M. Dowling, J. Mol. Spectry. g, 550 (1961). T. Chung and P. M. Parker, J. Chem. Phys. 43, 3869 (1965). Pierce, N. Di Cianni, and R. H. Jackson, J. Chem. Phys. 33, 730 (1963). Herzberg, Infrared and Raman Spectra pf Polyatomic Molecules, Molecular Spectra and Molecular Structure L; (D. Van Nostrand Company Ltd., New York, 1945), p. 133. Ibid.’ p. 462. 74 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 75 C. H.-Townes and A. L. Schawlow, Microwave SpectroscoPy (McGraw-Hill Book Co., Inc., New York, 1955), p. 86. The routine used to calculate asymmetric rotor energies was furnished by J. Hand, Chemistry Department, Michigan State University. The Hydel system was originally used to digitize cloud chamber data. Professor T. H. Edwards recognized its usefulness for reduction of spectroscopic data andv developed the photographic method for converting our: data to 35 mm film frames. The system can reproduce measurements to better than 0.03 mm on the original charts, which corresponds to 0.0002 to 0.0008 cm'l, de- pending on the dispersion, chart speed, fringe order, etc. The Hydel system is described briefly by T. L. Barnett, Thesis, Michigan State University (1967). R. S. Henderson, Phys. Rev. 122, 723 (1955). W. T. Raynes, J. Chem. Phys. 21, 3020 (1964). R. F. Curl, Jr. and J. L. Kinsey, J. Chem. Phys. 32, 1758 (1961). G. M. Almy, Phys. Rev. _3_§, 1495 (1930). E. U. Condon and G. H. Shortley,.zhg Theopy pf Atomic Spectra (The MacMillan Company, New York, 1935), p. 73. E. Merzbacher, Quantum Mechanics (John Wiley and Sons, New York, 1961), p. 514. P. C. Cross, R. M. Hainer, and G. W. King, J. Chem. Phys. 12, 210 (1944). 26. 27. 28. 29. 30. 31. 32. 33. 76 Townes and Schawlow, pp. cit., p. 96. Merzbacher,.pp. cit., p. 387. R. T. A. D. R. M. Serber, Phys. Rev. 41, 489 (1932). Carroll, Phys. Rev. 52, 822 (1937). D. Buckingham and P. J. Stephens, "Magnetic Optical Activity," Annual Review pf Physical Chemistry, Volume 11 (Annual Reviews, Inc., Palo Alto, Califor- nia, 1966), pp. 399—432. B. Keck SE 31., "Symposium on Molecular Structure and Spectroscopy," Columbus, Ohio, 1966, Paper H-2. E. Blank, M. D. Olman, and C. D. Hause (to be pub- lished). A. Efroymson, "Multiple Regression Analysis," E3552? matical Methods for Digital Computers (John Wiley and Sons, Inc., New York, 1960), Ch. 17, pp. 191-203. APPENDIX I COMPUTER PROGRAMS‘WRITTEN Many computer programs were written in the course of the work described in this thesis. The most important.of these are described below. All least squares sections are based on a routine written by M. A. Efroymson33 of Esso Research and Engineering Company, and the calculations of the asymmetric rotor energies are based on a program written 17 by J. Hand while at Michigan State University. A. SCAN This program converts digitized data from the Hydel system18 into the fringe positions and frequencies of the absorption lines as recorded on the chart. Error flags are printed out if the fringe spacing varies by more than 10%, if the rotation angle is greater~ than 10.005 radians, or if any of the rotation card data points is off by more than 10 microns on the film. Since the use of the Hydel system and SCAN to reduce data is now a standard procedure in this laboratory, it is not necessary to provide a description of the program here. A listing of the program SCAN follows. 77 78 uncanan SCAN . DIMENS!ONXN(6).YH(6)}FRNGX(100).PSEPC100):FGSEP(100)o11(2):!2(2). 11HIADCO).NANE(2 );NHEAD(10)aDELX(6),IIPR(3).!PEN(2) DATA¢IPEN38H6FIR8T .8H68ECOND ) PRINT 9701 READ 7.NAME.:rno~E VORNAT (2A8.56X.AB) IF¢IFDONE-8HNEH SCAN)5.0 If¢lfDONEu8HOLD SCAN) 0.9 PfltNT 10 FORMAT (00N0 NAME CARD 0 - - ABORT.) 00 TO 102 INIHnO 00 TO 1 6 1N8H91. . 1 HEAD 3. lHEAD,1FOONE PfllNT 3: IHE‘D 17(IFDONE-8HEND HEAD) 1,2 2 NFRMsNCALIIPno NIFIIHI1 X'SE'IVSEPIOtO ASSIGN 3600 To N00 101 READ 100. (XN(1)0 YN(!). I I1o6)o ICODEaIFR 17(10005-6) 202.200a208 203 17(10005-8) 7000a‘a102 202 If!4-ICODE)5010.4000.204 204 !ICIOODE-2) 20!.2000.200 205 !F(-!CODE) 1000.109110! . 1o! PRINY 106.(XH(!)oYN(!)o!'1.6) GO TO 101 102 PRINT 97013870. 200 NCODRDQO ' !'(XH(6)) 100.107 10’ DO 103 0.105 NCOORD-NCOORD-1 103 17(XM(N000RD)) GO TO 104 GO TO 101 100 DO 201 I!1.NCOORD 201 INCI)IOM72*XM(1)-THETAwYM(I) !F(10006-5) 3000a5000,0000 1000 XVINIXM XFRNGIYH 'RNGQX'RNG'iuo GO To 101 . 2000 SUMXDSUHYISUMYYISUMYXD0.0 GO TO N00 82 CONTINUE NOPRIO ASSIGN 6205 YO NIR DO 20 1.. 106 SUMY a-SUHY t VHC!) BUMX I SUMX * xnt!) A SUNYY I SUHYY a VMCI)0YH(I) 20 SUNYX a BUMYX ¢ YM(1)¢XH(1) a.“ N. Q 79 THETA I (SUMYX - SUMYASUHXlé.)/(5UNYY a SUHTPSUMY/6.) TH!TA2I0.5¢THETAOTHETA OHT201.0-THETA2 IBAD s 0 DO 30 I 9 109 DELXII) . Isunx-IusIA.sunvI/¢. . YHEYAAYMII) . XM(I) IFIABSFIOELXIIII .GT. 10.0) IBAD l.1 30 CONTINUE . 00 To (101031001H 31 Ir¢.NOI. INEH) ENCODE (6.11aIFR) XFRM PRINT 9201.IHEAD.I'R.~AHE IFITHETAZ .GT. 0.0000125) PRINT 6210 IFIIBAD) PRINT 6209 GO TO 101 3000 008007J82aNCOORDa2 IP :,IP t 1 XFSEPIXFSEP01.0 PSEPIIPIIXMIJI.XMIJ-1) VSERIPSEPIIR)¢FSEP 3007 CONTINUE 00 To 101 3600 NFRHINFRH¢1 IPPRINFRMIQIFR Ir¢.~ov. INEH) E~cooec4.11LIPFnI~rnnII xrnn 11 RORNAT ('4) GO TO I 82.3602)oN'RM 3502 rs;n.rsewxxr85- NllN'Rflll PRINT6010IPENIN133IPFRIN1). NAMEaTHETA,OELXoIPSEP(I) IONI’o IP) 601 FORMATIAOaPEN SEPARATION VRAME IS No.0A6/ ' HEASURED BY RZAOI 1. ROTATION ANGLE I!vf10.6o RADIANSA/o ROTATION FITS teasers...:. n ZICRONSo/O OBTERVED PEN SEPARATIONSII20P53) 3608 NIIIIRtl IPITHETAZ .GT. 0.0000125) PRINT 6210 IVIIBAD) PRINT 6909 PRINT 3609. FOE! 3609 FORMAT (0 AVERAGE PEN SEPARATION 70R THIS FRAME ISOF6.1O MICRONsi) IOERIXFSERIOc 0 IVINFRN. 50. 2) 00 TO 82 IH-Z ASSION 32 T0 N00 PSEPBUH - 0 DO 3701 Jl1nIP 3701 PSEPSUHQPSEPOUHQPSEPIJ) PENSEP l PSEPSUH/ IR PRINT9300,PENSEP 00 To 32. coon NOALI1 . A o YMI1) . XHI2100.00001 BIXNIIIOVH13)00.00001 I'TY"(2’ 3L1. 00°, 9"9 BIVH(2)OBGO.°°U°1 PRINT 9400a A. D 00 T0 101 5000 5001 5010 5011 6000 620! 6206 6204 6003 6006 6012 6011 9000 6001 7000 100 106 6206 6209 6210 9201 80 DO 5001 J I 1.NCOOR0 NOVR I NOFR * 1 RRNOXINOFR) 9 XMIJ) rOIEPINOFRHFRNOXINOFR)IFRNGXINOFR'1I CONTINUE GO TO 101 ITINOFR) GO TO 200 IFI.NOT.INEN) 00 T0 200 XTRNOIXH rn~epxrnNG-1.o DO 5011 Il1a5 XHIIIIXHII¢1I YHIIIIYHIIO1) XH‘61'YH‘60'OAO GO TO 200 GO TO NIR PRINT 9500.X7RNGaTHETA.DELXo(FOSEPII),I!2.NOFR) ASSIGN 6204 TO NIR AVESERIO.10('R‘NGXINOFR)-FRNOXI1))IINOFRe1n) IBAO I 0 DO 6206 I33.NOPR IPIABSFIFOSEPII)-FOSEP¢I-1)) .GT. AVESEP) I860 9-1 IFIIBAD) PRINT 6208 H00 IFINCAL) PRINT 9650.1,9 PRINT 9655 DO 6001 Js1aNCOORD NEXT-8H XIR I PENSEP t-XHIJ) DO 6003 1R10N0'R IIIXIR.LE,FRNGXII)) 00 TO 6004 LuNaNOFR-1 . NEXTIOHRX RIGHT 00 TO 6011 LoI-1 00 TO (6012:5011III NEXT-6H5! LEFT Ll1 FRNO1DPRNGtL*(XIR-FRNOXIL))lFGSEPILt1) IFI.NOT.NOAL) GO TO 9000 FREQlIAOBtFRNO1 PRINT 9651aNEXT.VRNO1,PREO1 00 TO 6001 PRINT 9651aNEXTngNO1 CONTINUE GO TO 101 REA08pNHEADSPRINT3oNHEADIGOTO101 FORMAT (10A8) VORHAT (9(2‘50X)0110A6) FORMAT ItOTHIS CARD HAS A BLANK 0R ZERO 0005* 5X6I2P5.xI I) FORMAT (oocBOXoFRINGE SPACINO VARIATION .GT. 10!.) FORMAT I 81XAROTATION FIT .OT. 10 HICRONSO) IORHAT (OOOOOXOTHET‘ I8 .OT. 0.005 RADIANST) TORNATI05t/t1i9All' LINE POSITIONS FOR¥706"5' A4.6X'HEASURBD 9* 81 1 02A!) 9300 FORMAT ('6PEN SEPARATION ON THE FILM ptF6.1t MICRONsi) 9400 FORMATIR6THE FOLLOHING CALIBRATION CONSTANTS HAVE BEEN INRUT A 1 I0F11.5¢ B !'F13.10) 9900 FORMAT (* FIRST FRINGE IS N0.tF5.8X cnOTATION ANGLE ISiF10.6t RADI 1AN8t/t ROTATION FITS TOA6IF3¢,¢)¢ MICRONSt/AOFRINGE SEPARATIONS IN 1 MICRONS'II5X10FBII 9650 FORMATI'OALIBRATION CONSTANTS USED AREI§XtA 9*F11g535X’B I'F18.10) 9651 FORMAT (*9.A9,F10.4.F15,A) 9655 FORMAT (*0*9X*FRINGE NUMBER FREQUENCY!) 9701 FORMAT (*St/R1A9A8) END 82 B. CALFIT This is a least squares routine specialized to fit the fringe numbers of calibration lines to their known frequen- cies using the formula, (frequency) = A + B-(fringe number). The values of A and B are input to SCAN to allow it to.con- vert observed fringe numbers to frequencies. If the worst data point is off more than 0.005 cm‘l, it is deleted, and the fit is repeated. This process will be repeated until up to five data points have been deleted. STRUCTURE OF DATA DECK Card Typg Format Columns Information 1 10A8 1-80 Heading cards to be printed out. The last one must have "END HEAD" in col- umns 73-80. Data cards (up to 500) 2 3F15 1-15 Known calibration frequency. 16-30 Observed fringe number. 31-45 Assigned weight. 3 A8 73-80 "END DATA" to signal end of data. 4 Start new set of data with another card type 1, pp blank card to stop execution. C. CDSORT This program inputs and stores all of the identified transition frequencies of a given band. It forms frequency differences for those transitions having common upper or lower quantum numbers and stores these differences as 83 weighted GSCD or USCD. The differences are also printed out along with the frequencies of the lines involved.‘ After all such differences have been found and averaged, the resulting set of USCD are output as punched cards ready for input to CDFIT. Transitions for the next band of the same molecule-are then input, and the above is repeated, with the new GSCD being averaged with those of the first band. After all of the desired bands have been processed, the resulting set of averaged, weighted GSCD is output. STRUCTURE OF DATA DECK Card Type Format Columns Information 1 I5 1-5 1, 2, or 3 will request program to find GSCD, USCD, or both. A8 6-13 Molecule [e.g., "14N02"]. A8 14-21 Band [e.g., "(2,0,1)"1. 2 (X,6I3,F15,Fl3) Identified transitions for this band. The format is identical to that used for SPECFIT data. 3 A8 73-80 "END DATA" signals end of data. 4 Card types 1-3 for the next band of this molecule, 23 blank card to signal that last band of this molecule has been input so that averaged GSCD will be output. 5 Card type 1 for new molecule, pp blank card to stop. A listing of the program CDSORT follows. 21 22 26 25 118 117 311 312 313 84 unoann cosoav . cannon 4(2000.2)oJJI6).FREO(2000).HHTI2000)nKKI630.2.2). 1CDIFFI600a2)ICONTI630.2) DIMENSION 18(2) DATA (IN-6H anpu~o .an UPPER I READ 10nI$.MOL.IHEAD.TOL IF(.NOT. TOL) TOL00.01 IFIXSI 405 IHEAO I BRAVERAGE IFINSTOR) STOP NSTOPII91 MOLsIMOL 00 TO 220 NINSTOPIO IMOLIMOL N'N‘1 READ 101.44.?Reo¢~>.HHII~I.IDENT IFIIDENT-OHEND DATA) 6.8 IFIFREOIN) .LE. 100.0) 00 TO 9 ENCODE (6a11aJINa1)) JJI1).JJ(2):JJI3) ENOOOE (8.11aJIN.2)) JJI4).JJ(5)0JJ(6) GO TO 7 NODATAIN-1' GO TO (1.22.23.24I.IS¢1 I01 I1I2 ISIO 00 TO 25 II! I101 ISRO GO TO 25 I91 I8II1i2 PRINT 2.MOL4IHBAD.IHII).NOOATA NOOI0 DO 111 Ml1aNODATA M1IM¢1 D0'111‘NIH10NODATA IFIJIN.I) .NE, JIM.I)) GO TO 111 ODIFREOIN)-FRE0IM) MMnM NNIN , IFICD).118.111I117 "HUN NNIM CDIICD GO TO I3111312IAI N1-MM3N8'NMSGO T0 313 N1INN$N2QMM OEOOOE (8.11aJIN1aI1I) JJI1).JJ12)0JJ(3) DECODE (30113J1N2A11’) JJ“’OJJ‘9’fJJ‘6’ FMnFREOIMM) FNIFREOINN) 85 HNIHHTINN) HMRHHTIMM) NT!2.00HN6HH/(HN‘HH*0.0001) , PRINT121.JJ.CD.HT.IJINN,K).KI1.2),Fn.HN.(JIM".K)0K31.2).FM.HM IFIJJIZ).LR.8) IFINTI122.111 PRINT 55 GO TO 111 122 NODQNODP1 NMITOOJJIZITJJIII¢20 IFIJJI1)-JJ(4)-2) NM-NM-ZO IFIODHTINM.I)) 201.203 201 A¢CDHTINM,I)Au$ . IFIABSFIOD-CDIFFINM.I)) .8T..TOL) PRINT 204.70L CDIFFINM.I)IICDIFFINM,IIPCDHTINH.I)oCDAHT)/A CDHTINM01)!A GO TO 111 203 CDIFTINM.I)¢CD ODHTINM01)lNT _ KKINM.1.I)PJIN1.I1) KKINM.2.I)-J(N2.I1) 111‘CONTINUE PRINT3,NCD GO TO (21.220).I 220 NPUNCHuO PRINT 2 DO 211 K!1.9 KMn70PK¢1 DO 211 Mo1.70 MNnKM-M CDHHTIODHTIMN,I) IFICDRHT) 213.211 213 J1-KKIMN.1.I) J:.KKIMN.2.II CDICOIFFIMNII) . PRINT 100.J1.J2.C0.CDHHT PUNCH 1°01J10J20CDJCDHHT NPUNCMINPUNCH¢1 211 CDHTIMNoI)'0.0 PUNCH 126 PRINT125pNPUNCH.MOL.IHII) GO TO (1021)01 2 FORMATIA1O3A808TATE COMBINATION DIFFERENCES FROMPIAP FREQUENCIESOI 1/3I2I' J K- K99)16X0HHTRSX)/*0*21XPOOHB DI'FOZIISXPFREGUENCYTIII 3 FORMATIQTtIAO”OOMBINATION DIFFERENCES HITH NON-ZERO HEIGHTS.) 10 FORMAT (I6.2A8.F10) 11 FORMAT (I2non2oon2) 59 rORMAT (Ptc122xvK .GT. 80) 100 FOIHATszAOIXROAFAS390,13.2, 101 FORMAT (X6I3.715.P13.29XA8) 121 FORMAT I2IX3IJI.F11.4,76.2.2I5X.2A10.711.4o[6.2)I 124 FORMAT I72XPEND‘DATA.) 12! FORMATIRTPUNCHED'I49 AVERAOBOA9,RTTSTATECOMBINATION DIFFERENCES.) 206 FORMAT (fitt122XADIFF 0T076.3) END 86 D. CDFIT Built around the asymmetric rotor energy level rou- tinel7 and the least squares routine,32 this program generates a set of calculated energy levels, along with values of c, 5, and n, from a set of trial constants. Observed combination differences are then read in and come pared with combination differences formed from the calcula- ted energies.. The set of observed minus calculated combi— nation differences are fit by the least squares section to determine corrections to the trial values of the constants [cf. Eq. (17)]. The particular set of constants which is allowed to vary in a given fit is specified on a parameter card. After the fit the deviation (times the square root of the weight) of the worst data point is compared with an in- put tolerance, and if the tolerance is exceeded, the data point is given a zero weight, and the fit is repeated.' Another input tolerance specifies how many times this pro- cess will be repeated. Any number of parameter cards can be read in. This allows the determination of corrections for several differ- ent sets of variables. For each parameter card, all weights are reset to their initial values so that deleted points will be included again. 87 STRUCTURE OF DATA DECK Card Type Format Columns 1 IS l-S IS 6-10 2A8 21-36 A8 37-44 Trial constants (three 2a 3F15 1-45 2b 3F15 1-45 3 4F15 1-60 4 4F15 1-60 Information Maximum value of N (:48) contained in input data if fitting GSCD. Maximum value of N (<48) contained in input data if fitting USCD. If "observed minus calculated" is larger than this number, the data point is deleted on input. (Set to 10.0 if left blank.) Identification of combination differ-‘ ences fitted [e.g., "(2,0,1)-(1.0.1)fl. Molecule [e.g., "14N02"]. cards for GSCD; four cards for USCD) Values of A, B, and C for ground state: this card is needed only when fitting USCD. A, B, C. Tl! T2: T3: TR- HN' HNK' HKN’ HK' Data (one card for each observed combination difference; up to 300 data points may be input) 5 613 2-19 F20 20-39 F10 40-49 Values of N, K_1, K+1 for upper and lower rotational level, respectively. Observed combination difference. Weight assigned to this observation. "END DATA" signals end of data. Parameter cards (one card for each set of constants to be 6 A8 73-80 varied) 7 1311 1-13 Non-zero numbers in any of these col- umns will enter the corresponding constants in the fit. The 13 con- stants are (B+C)/2, (B-C)/2, A, T}, 88 Card Type Format Columns Information T2! T3! 70: HNI HNKI HKNI HKI BI and F10 21-30 This number gives the minimum value a variable's diagonal element in the least squares matrix can have if the variable is to be entered.. If left blank, it is set to 0.0001. 12 49-50 A non-zero number will cause all of the least squares steps to be printed out. If left blank, only the final coefficients and standard errors for each fit will be printed out. I5 60-65 Maximum number of data points to be deleted after the initial fit. F5 66-70 Tolerance for deleting data points after the initial fit. A8 73-80 "END HEAD." Otherwise will read and print succeeding cards until "END HEAD" is encountered in columns 73- 80. 8 A8 73-80 "LAST FIT" signals end of execution. A listing of the program CDFIT follows. .2 1 3 en. 89 PROGRAM 6 D FIT . DINENSION I1113I§I21121013(2)oI5ISIINVARTC11T DATA!I1!7HI8*C)/2.THIBIO)/231HAoSHTAAAAoSHTBBBBT5HTAABBg5HTA8A8.2H 1HNAJHHNK.JHHKN.2HHK.1HR01HCT3H ‘ASH‘ BnSH CPSHKAPPAASHTAAAA.5HTB 1888.5HTAA88.5HTA8A8.3H HNIAH HNK06H HKNn3H HK.TH GROUND.7H UPPER) CONMON 11/ OLDCNSTI1ZI| EOgIVALENCEIOLDCNSTI1).AI.(OLDCNSTIZIcfl):IOLDCNSTIS).C).IOLDCNSTI4 1). APPA) , OONMON/2/EI4loi6o25).DATAI160500IoVECTOR‘15015).INDEXI16005IGMAI14 1).OOENI14).SIGMOOI1401NKI1S)TNUSEISOOI.CORR(13)aADDI12).CNST(12)n 2IHI10).N1(13).NOTINI13) EOUIVALENOECE.DATA)0(E(7uoi)oVECTOR)o(517226,.INDEXIAIE17240).SIGM 1A).(5(7254).COEN).(E17268).SIGMCO).(E(72BZIINKIT(5(7295)0NUSE)- 2IEI7795).CORR).(8(781OIoADO)A(517825)0CN5T)0(517840).IH).(E(7850)o 3N1).IEI7868)0NOTIN) COMMONIJ/NTI300I00150’oTI25)cTT‘25)ARIZSIIHH125IAPIK125IaPIKJI25)a 1PIIKI25I EQUIVALENOE INT.O)I(HTI51).T)0(NTITO).TTIPINT(101).R)9(HTI126):HH) 10(HTI151IPFIK).INTI1T6IcPIKJ).(HTI201).PIKK) OONMONIAIHI25.25).JK12.300) EQUIVALENOE (HAJK’ COMMON/BIORSI300)oCALCI300)oCONSTI130300’oNDENTISOO).KKJI6)o 12(11:2I.ENO(2) READ OOOOPNNAXGoNMAXUTODEVHAAA15‘ IFINMAXO) 3.6 N581 N695 NHAXINMAXO OOTO6 STOP IFI,NOT,NMAXU) GO TO 2 N892 NC!1 NMAxINRARU READ 7010 APOaC RR!(C/A)*‘2 SSQICIBIPP2 . . _ READ 701IIOLOCN8TIIIPTPNC¢12T IFINMAX.OT,48) NPAXIAB . IFI .NOT. ODEVMAX) CDEVHAXIlOcO CAPPAIIZ.98'A-C)l(AuC) TFICAPPAI7}718 . BRIIOARPA'1.OIIICAPPA*300) 8090.56(A¢8) ABOlO-Rc L193 L29MM291 LSQMN182 . 11‘1IITHIA081/23I1(2)ITHIAIBII2311IBII1HCOT1T120'1HA 5 I1(13)!1HB GO TO 9 BREIOAPPA01.0)/ICARPA'3.0) BO!0.5'IB*O) ABOIAOBO L1!MM1I1 14 an 23 24 29 as 2T In 32 90 LZTMMZnZ L393 7 I . I1I1)87H(80C)/?$I1I2):!HI89C)/2$I1(3)!1HASI1(12)'1H8 I I1I13)I1HC E(1.6)!E(1.7)=§I1o10)3811A11)3E11o16IIEI1015)8E(206)IE(2:7)=E(2.10 1)36(2.11)IE(2.14)lE(2115)31.$E(2012)!E(3112)!16.03EI2o16)85(3.16)= 266,:EIEI109)IEI1.9)!EI1.13)8.OSEIZ.6)IE(2.8)!E(3.6)IE(3.8)=4. BPZIBPOBP 511.3)!10'Fp 511.22.10‘39 EI2)92.-SORTF(4.*12.‘382) [1,11222-‘p'6(2’ 8(2.3)91.'8.*BR E(2.2)!-E(2o3)*2.0 EI3.x.{)05.~3.08P-80RTII16.¢24.TBP¢24.PBP2) EI3.3.2I-1o.-6.PEP-E¢3.3) EIS.2.1)I5.*3.oBP-SORTII16,-24.98Pt24.08P2) 5(3.21203100.6.939951302’ E13:1010'2,’SQRT'(4,‘OD9.8’2’ 5(3111203‘.‘E(3’ 0013’J921NHAX LLASTla IDENTI1 XJ9J AJPLSIRJAXJ+XJ ABSQAJPLSiBPOo.5 DO 14 II1TJ XIQIPI DII.ao.soaPosoPTTIIAJPLs-XIIttz-XII DI1)I1.6142135624tDI1) L80.5*IXJ*2.0) DO 26 I!1AL IP3!I03 . DO 26 IJ'1.L ”(1:1J0900. . _ 60'0‘2682‘02312,626,0‘TPS'IJ’ ”(IoI) I II*I'2)**2 GOTO 26 . H(!.IJTIDII‘1*1I GOTO 26 HIIaIJIIHIIJoI) CONTINUE GO TO 93 LID.56(XJ61.0) DO 35 IllnL' IK'IPI IPSQI¢S no as IJ-13L ”(tniJTQDO , OoTo¢35.31.32.30.35)nIIFSTIJ’ “(I.TJIQHIIJTI) GOTO 35 “I‘liTQD‘TK’ GOTO 35 GOTOI33.34).I 33 34 39 36 39 40 41 42 43 44 45 48 49 n 51 5! 54 59 as 60 51 91 H:1.¢A85 GoTo 35 H(I.I) ! IIKslIROZ CONTINUE GO TO 53 L80.5'IXJ*1.0) DO 44 II1TL IK!I*I IP33I¢3 DO 44IJ91.L ”(latJIQDO‘ ‘ , - GOT0149040041339144011IPS'IJ’ HII.IJ)!H(IJ.II OOTO 44 "(IAIJ’QDIIKI OOTO 44 OOTOI42.43).I H51.IA85 0070 44 HII.I) ! (IK-1I042 CONTINUE GO TO 53 L80.56XJ 00 51 I'11L IPSIIOS no 51 IJI1.L H(!A!J"ni f , . GOTOI51,49.50.48.51).II93'IJI “(I.IJIQHIIJTI) OOTO 51 HII.IJ)!DII*I*1) GOTO 51 ”(111’ I ORI.I CONTINUE CONTINUE LK!LI1 . OOTOI130154)0L DO 123 K310L . IFIJ03’60060055 IFIK-LK)56.56.58 E(J.IDPNT.K)-2.PEIJ-1.IDENT.KI.EIJsz.IDENT.K) GOTO 60 TUMI0.085UN=H(L.L) DO 59 IJ'1ILK SUNISUNOHIIJTIJ) TUMCTUMAEIJoIDENTaIJ) BIJ.IDENT.L)ISUM-TUM LOOP-LOORZIK LO0P1I1 LOOR3l0 'UNTESTBSPE', LINIL-LOOP LIM - LIN . 2 KJILOORIi 62 63 64 66 66 67 68 66 70 71 72 73 74 75 76 77 78 79 an of a: as a. as a. 37 as 86 90 91 92 KLILOORAI R:E(J.IDENT.K)uH 0070(64.62).L00P MN I HI1.2)'H(1:2) DO 63 IIZAKJ HHII) I HII:I+1)¢HII.IA1) RII)IEIJ.IDENT.K)'HII.IIPHHII'1IIRII91) 8(L)'EIJ.IOENT.K)-H(L.L) GOTOI67.65):LIN HHIL) I HILoL-1)OHIL.L91) DO 66 ItiaLlM LI'L'I . HHILI) I HILI.LI-1)4H(LI.LI'1) RILIIIEIJTIDENT.K)2H(LI.LII-HHILIT1IIRILIT1I RIKL)IEIJnIDENT.“)QHIKLoKLI-HHIKLtlI/RIKL91) HHIKL) I HIKL.KL¢1)¢H(KL.KL'1) IFILO0P1-1)69.70w IF (LO0P1'10) 92.92.70 IFILOOPcL)71a7A DO 72 IBKL.L TTII)IHII.I-1)IRII) TILOOP7'10 DO 73 IIKL.L TII)'TT(I)0TIIv1) IFILno#-1)75.78 DO 76 IQ1PKJ TTII)!H(IaI*1)/RII) TILOOP7810 DO 77 I810NJ TILOOP-I)4TTILOOP'I)*TILOOP*I*1) DFUNCT'OPO DO 79 I81IL DFUNOTQDFUNCT+T(I)*T(I) SUM-1.ISORTF(DFUNCT) DO 80 II1aL TIIHTIIHBUM IFILOOF1-1IO1.82 IPILOOP1~11>92.62 ITTY'1 I81 . IFIIfiITTY'L)85.85.88 TEST 8 TIITTYIOTIITTY) - TIITTYPI)¢TIITTT*I) IFITEST)86.87.A7 ITTYIITTY*I 8070 83 III+1 GOTO 84 LOOPIITTY IFILOOP-LOOPIIR9392 IFILOOP1911)90.91 LOOPIILOOP1¢1 GOTO 61 LOOPZILOOP LOOP1311 92 93 94 99 96 97 98 99 100 101 102 104 108 105 100 109 110 113 11! 117 116 114 119 129 134 93 6070 61 IFILOOP1I12)93.110.110 IFILOORP1)94.98 IFILDOP-LIO9I97 FUNCTUEIJ.IDENT.K)PHILOOR.LOOP)-HH(KL)IR(KL) PRODag, DO 96 IflisLK IJ-L-IP1 PROD 8 1. P PRODPHHIIJWRIIJHRIIJ) DFUNCTQPROD GOTO 102 FUNCT'EIJPIDENT.K)PHILOORpLOOP)"HHIKJI/RIKJ) PRODI1. DO 98 II1TLK PROD I 1. . PROD-HHIIIIRIII/RII) DFUNCTUPROO GOTO 102 FUNcTIEIJ.IDENT.K)PHILOOP.LOOP)'HH(KL)/R(KL)?HH(KJ)/R(KJ) PROD-1. DO 1CD 1.11KJ PROD 8'1. t-PRODOHHII’IRIIIIRII’ DFUNCTIPROD-I. PROD-1, D0 101 I'1ILIN IJ'L-IP1 PROD I 1, o PRODPHHIIJ)/R(IJ)/R(IJ) DFUNCTIDFUNCT¢PROD LOOPZCLOOP L00918LO0P1*1 LOOPSILOOP3+1 ' IFIFUNTEST-ABSFIFUNCT)1106.1060104 IFILOOP1-12I1os.106.11o L0091'11 GOTO 108 [FILOOF3I10710811091109 E(J.ID!NT.K)'EIJ.IDENT.K)TFUNCTIOFUNCT GOTO 61 PRINT 702 aoTo 128 CONTINUE D0114I'10L. 90T011130115011501177:IDENT PIKII)III*I-2)002 OOT0116 PIKII)!(I*I'1)O92 OOT0116 PIKII)I4PIPI PIKKIIhPIKIIHPIKII) PIKJIII P PIKKIIIPPIKII) IJKI1$ITOPILK$IFILOOP01I120:132 IFILOOP-LI125.134 E(J.IDENT*12IK)IPROEIDFUNCT' E(J.IDENTPR.K)QPROC/DFUNCT E(J.IDENT¢4.K)IPROD/DFUNCT 94 GOTO 128 129 ITOP'KJOLOOPOITIJKIZ KLILOOPO1 LINIL-LOOP 134 PROEIPIKJ PROcIPIKK PRODIPIK_ OO126II1.IT0P HHRRIHHIIIIRIII/RII) PROE a PIKJII+1I . PPOE'HRPR PROC a PIKKII+T) O PROCTHHRR 126 PROD - PIK (10;) . PRonPHHPR 80T0I131o135).IJK 135 E(J.IDENT¢92.KIPPROE E(J.I0ENT¢A.KIPPROO EIJ.IDENT94.')IPROO ITOPILIN 132 PROG-PIKKIL) PROEIPIKJIL) RRODIPIKIL) DO 127 IP1.IT0P IJlL-IP1 HHRR-HHIIJIIRIIJIIRIIJT PROE n PIKJIIJ-1) a PROEPHHRR PROC a PIKKIIJ-1) 4 PROCPHHRR 127 PROD I PIK (IJu1) 6 PROOAHHRR GOT011312133701JK 133 E(J.IDENT¢12TKIQIEIJaIDENT¢120K)*PROEIPIKJILOOP0)lDFUNCT E(J.IDENTPA.K)PIEIJ.IDENToA.KI+PROCPPIKKILOOPI)IOFUNCT EIJ.IO!NT¢4.K)I(E(J.IDENTPA.KIoPROn-PIKILOOP))/DFUNCT 120 CONTINUE 130 CONTINUE 133 LLASTILLASTPL IDENTOIOENTP1 00T0I20.27}36.45.139).IOENT 139 CONTINUE INOATAPO eon INOATAIINDATAP1 259 READ 850.KKJ.OO.HHT.ID IFIID-AHENO DATA) 255.256 255 IFIKKJI1I-NMAXI-260.260o257 257 PRINT 258.KKJ.OO.NHT.I0 258 FORMAT (PM .GT, NMAX . . . LINE IGNOREDP5X6IS.712.4.75.2.A10) GO TO 259 ‘ 260 M32 MM!4 270 JPKKJIMM) 1 IFIJ) 250.251 251 ENOIM)-o.0, DO 249 I'lall 249 2(I.M)!0.0 , 00 TO 270 250 NLQJ-KKJIMMAMMQIAKKJIMMiMM1)*4 NMIL/4 276 279 277 27g 273 330 331 203 202 95 leqtNtNL*1 XJPJ XJZaxJOXJold XJ‘ I XJ228J? EJLN'ECJnLoN’ 2(3.H)IZETA=E(J.L*4.N) FZ‘CE(J3L‘81~) 2(1.N)IXIIXJ2-IETA DEL2I(ZETAcEJLNI/8P EN!BC¢¥J2*ABC*EJLN IF (CAPPA) 275,275,276 DEL1IIZETAoZETA-PZ4)IapzaETA-ETA 2(2.M)IETAI-DEL2 DELS'IIE7A¢BP¢ZEYAIOZEYA-PZQIIBP 2(4.M)-.0625v(xJ4-OEL1-2.tIJ2*DEL2v(1.«RR-RRItI2.*XJ2-ZETA+2.-DEL3 10(1.URRvRR)'PZ4)’ 2(5.M".0625'CYJ"UEL1*2.*YJ2'UEL2'(1.”SS'SS)O(2..XJ2'ZETA'2.tDEL3 1-(1.vSS-SS)-P24II ZI6."’30.125*(XJ4*DEL1!2.'¢1o“RR’SS"XJZ'ZET"2..‘RR'SS’*DEL3 10(1.-RR-RRI*I1,-SSsSSItPZ4I ZI7.")lo.29*¢XJ4¢DFL1'2.0XJ2‘ZETltPZ4I GO TO 277 DEL1I(EJLNo(2.025TA-EJLNIwPZ4IIBP2 2(2.N)IETAsDEL2 OEL3'IEJLNtZETA-P24I/BP 2(‘.N)l.0695'(RR‘R9*(XJ4-DEL1‘2.'XJZ‘DEL2)0(RR'2.)*(2.ORRtXJ2iZETA 1*2.¢RRODEL3-IRR-2.)0P24)) 2(5.N)'.06250(I1.*SSI*I1.08$I'IXJ4-2.0XJ2*ZETA*PZ4IvI1.vSS)t 1(1,.SSI¢DEL1¢2.0¢1.:SSaSS)o(XJZGDELZoDELSII 2(6.N)I.1250¢I1.oSS)t(RRcXJ492.¢IRR-1.)cXJZtZETA+(RR92,)cpz4) 1tRRtII1.-SS)'DEL1'2.*SStNJ?*DEL2)'2.*I1.*SS¢(1o-RR)I‘DELS) ZI7.NI-o.SOIXJ2*ZETA-PZ4sDEL3) 2(8.N)-XJ4.XJ2 2(7.MIIZI7.H’-n.9*ZEYAto,1250X!vo.625'ETA 2(91M"XJ‘.ZET‘ 2(1o.n)st2tPZ4 . 2(110H‘IE(J9L012nN, no 279 1-4311 ENIEN¢!(!.H)*0LDCNSTI1.1) ENG(H)IEN MH'M'MI1 IFIMM-1I 3300270 CALCIINDATA)'CC=ENGI1)IENG(2) OBSIINUAYAIIOO NDENTIINDATAIsID DI'F'Ofi'CC ADIFfslBSFIDIFFI DO 331 I!1.11 , CONSTII.INDATAICZII.1>-Z(I.2I CONsYItzglNDlTAI-0.5t(2(1.1)c2(1.2I02I2.1)-Z(2.2I) CONSYI13.INDATAIIO.5t(2I1.1)¢Z(1.2I'ZI2.1)¢ZI2.2)I IFIHHTI 203.200 _ Ir‘inofloHHY’ 20002020202 _ IFIADIFFOHHTaCOEVHAXI 200.201.201 201 200 261 295 172 173 173 179 15! 157 499 175 500 253 252 254 512 523 501 146 540 96 PRINY 1000.INDATA.KKJ.OO.CC.NHT HHYI0.0 UTIINDATA)-HHT ENCODE (8:2611JKIioINDATAII KKJII’QKKJIZ’IKKJIS) ENCODE (8.261.JKI2.INDATA)I KKJI4).KKJ(5).KKJI6) FORMAT (12.x.12,x,12) GoToson CONTINUE INDATAITNDATA-1 EFINIE'OUI I 1.08.10 READ156.NKLTOL.INF0.NDELMAx.XDEVMAx.1HT10) IFI.NOY. IOLI YOL'0.0001 IFTIHItoI-SHLAST FITI173.2 RE‘D!51.IH FRINT151.IH IFIIHI1OI-BHEND hEtDIl74.17S NOVAR I 1 001571.1113 NV‘RYIIIIO IFINKII))188.157 N1INOVARI'I1III NVARY(M0VAR)'I NOVARINOVAfloi CONTINUE SDEVMAx-XDEVHAxatZ NOVMI - NOVAR . 1 NOVPLINOVHI*2 NDEL-O XD‘TAISUMHHT'0.0 NOINIKINOENTINOHININOHAXIO VAR-FLEVELIO.0 DO 176 I ' ioNOVPL DO 176 J a 1.NOVPL VECTORII.JI I 0.0 [FINOELI501.SOO DOSzSN-1,INDATA IFTHTINI1252.253 NUSEINIIO GO TO 254 NUSEINII1 XDATA:XDATA¢1.0 suMuUT-SUNUHTouTINI NUMufl no 512 1-1.N0v~1 DATAII.N)ICONST(NVARY(I).NI DATATNOVAR;NI=OBS(NI-CALCIN) AVEHHT¢SUHHHYI XtATA 00910Nn1.INOATA IFINUSEINII146.510 UH73HTINI/AVEHHT DO 540 1,: 1. NOVAR VECTOR!IaNOVPLIIVECTOflII.NOVPLI*DATAII.N)*NHT no 54o J‘8 IoNOVAR VECTOR!I.JI=VECTCR(InJI¢DATAII.NI*DATAIJ.NI'HHT 510 530 601 999 180 602 603 650 792 794 610 300 830 870 80! 1001 1002 1010 97 CONYINUE VECTORINOVPLoNOVPLI I XhATA IFIINFO)580.659 PRINTiSaIIoI'iochnII PRINY 17IVECTORINOVAR.N0VPL)0(VECTORIIaNOVPLI.I=1¢N0VHII NGOIfl NONIN-I NOHAXsNOVNI IFINO MAI-6) 599.599.6G1 NONAXIG NGOul , PRINT 1520(IaIINCHINaNOHAXI DO 180 JINOMIN.NCVMI JJIJ ‘ IFIJJ 06?. 6 o‘NDo NGOI JJlé PRINT 1530J.IVECTOR(I0JI.IIN0 MIN.JJI PRIN7 15IoIVECYOHII0N0VAP).I'NOMIN.NOMAXI IFINGOI 60?:603 NOMINI7 NOHAXtNOVH! NGOsO GO TO 599 CONTINUE PRINYIBS. VECTORINOVAR.NOV1RI NOSTEP I '1 NuflaERIO DEVR I VECTORIKOVPLoNOVPL) ' 1.0 00 800 I x 1.NOVAR IFIVECYORIIoIII 79207941816 PRINY 793. I 6070172 PRINT 7950 I QIGHAIII 9 100 60 70 800 SIGHAIII I SORT? (VECTOR (IaIII VECTORIIOII ' 100 DO 830 I ' laNOVNI IP1 I I . 1 DO 830 J,I 191. BOVAR VECTORIJgIIIVECTCRIIgJIIVEcTORIIoJI It SIGHAIIII SIGMAIJ)) IFIINFOI87011001 PRIN719’.II.II1,NOVHII DO 885 II2.NOVMI IHllI'i _ ‘ ‘ PRIN7160.I.IVECTCRIIIJJaJ3taIH1) PRINIléliIVECTDRIIoNOVARIaT=10NOVMII NOSTEP I NOSIE’ I 1 IF IVECYORI NOVAflnNOVAHII 1002.100201010 NSIPH1 s NOSTEP I 1 PRINT 1004; NSTPNi GO TO 1331 SIGY I SIGHIINOVARI I SORTF IVECTORINOVAflaNOVARII DEER) DE'R IDE'RI1.0i IF (DEFR I 1017.1017. 102fi 1017 1020 1042 1060 1080 1100 904 1170 1160 1110 1210 1050 903 1240 1300 1310 1301 1320 1340 134a 1354 1361 1370 1391 1392 98 PRINT 1019 .NOSTEP GO TO 1381 VHINIVHAXIn NOINIO DO 1050 I I 1.NOVNI Ir (VECTORII.III 1042- 1050: 1060 PRINT 1044. I. NCSTEP GO TO 1301 IFIVECTORII.I)-TCLI 1050. 1080. 1000‘ VARIVECTORIIINOVARIOVECTORINOVAROII/VECTORII;I) IFIVARI1100. 1050. 1110 NOIN I NOIN I 1 INOEXINOINI I I COENINOIN) I VECTORII.NOVARI . SIGHAINOVAR) I SIGMA III SIGMCOINOIN) =_SORTFIVECTORIIoIIIISIGY/SIGNAII) If IVHIN! 1160.1170.904 PRINT 906 GOTO172 VNIN s VAR NOMTN - I 00 T0 1050 f IFIvAR . VNIN)1OSO.1050.1170 IF (VAR - VMAx11050.1050.1210 VMAX o VAR NOMAX I I CONTINUE IF (NOINI 903.1240.1300 PRINT 907 GO TO 17? STDYISIGY GO TO 1350 IPIINFOI1310.1320 Ix-aHENTERING , IFINOENT .LE. OI IXIBHREHOVED Ircwunaen) FLEVELIFL PRINT 169.NOSTEP.IX.K.K.FLEVEL.SIGV 001301J310N0IN NIINDEXIJI PRINT163.N.N1(NI.COENIJ).SIGHCOIJ).VECTORIJ) IFINUHRER) GO TO 1580 FLIFLEVEL rLEVEL a VMIN 4 OEPR I VECTOR INOVAR.NOVARI IFIEFOUT I FLEVEL) 1350: 13504 1340 K I NOHIN NOENT I 0 GO TO 1391 FLEVEL g VMAX 4 OEPR I (VEcTORINOVAR.NOVAR)e VMAX) IF (EFIN - FLEVEL) 1370.136101360 IF (ERIN) 1300.1380.1370 K I NOMAX NOENT I K IFIKI 139211392.1400 PRINT 1395. NOSTEP 00T0172 1400 1430 1440 1410 1480 1520 1360 1381 1560 9201 9203 9202 9200 9211 9210 9212 9206 9207 920! 1663 1662 99 VECTORIK.KIIVKI1.OIVECTORIK.KI Do 1410 I I 1.00VAR IF (I-KI 1430.1410 DO 1440 J I 10 NOVAR IFIJ.NE.KI VECTORII.JIIVFCTOR(I.J)-VECTORII.K)*VECTORIK.J)*VK CONTINUE CONTINUE DO 1400 I = 1. AOVAR IFII.NE.K) VECTOR II.KI 8 a VECTOR II.KIIVK CONTINUE DO 1520 J a 1. NOVAR IFIJ.NE.K) VECTOR(K1J) 8 CONTINUE 90701001 VECTOR IKoJIOVK PRINT167II5I1).I5(2I4ISINSI.I5I3I0XDATA4N0VHI.IVENHToNDELMAX. 1XDEVNAX.STDY1NOSTEP NUMBERI1 GO TO 1310 NOTINUMIO 009200II1413 CORRIIIlOOO IFINKIIII 9201.9?00 NUMINUM61 DO 9202 J'SONOIN IFIINDEXIJI'NUM) 9202:9203 CORRIIIICOENIJI GO TO 9200 CONTINUE NOTINOT t 1 NOTTN(NOT)INUH CONTINUE IFINGTI 921109219 DO 9210 II11N07 JauoTINIII PRINT 1234JaNllJIoVECIORIJI ADDIL1IICORRI3I ADDILzIICORthnRRI2IICORRI12’ ADUIL3IICORRICDR9I2IICORRI13’ DO’ZO7II5012 ‘DDIIIICORRII'1I D09208I11112 CNSTIIIIADDIIIOOLDCNSTIII CNSTI41II2.ICNSTI2IICNSTucMSIISII/ICNST'CNSTISII ADDI4IICNSTI4)IOLDCNSTI4I _ ”RINT17101I21IIICLHCNSYIIIpADDII79CNSTIIIa[31:12) NFITISO , VFITIDEVMAXISHTIYIfllflofl 001660~3103NDA7AK ‘ IFIN'IT-flfl’ 16623166311663 PRINT 166 NFIT'D NFITIN'ITIl HTNINUSEINIIHTINI HHTIHTN/AVENHT 100 YPRED . 090 00 1630 I s 1;NCIN 1630 YPREDIVPREDICOENII!.DATAIINDEXII),NI CCICALCINI OOIOBSINI DI'F'OOICC DEV-DIFF-YPRED ADEVIDEVIDEVINTN . IFIAOEvunEVNAXI 1661.1610.1610 1610 NHAxIN DEVMAXIAOEV 166i FPRDIOO-DEV , L IFI10.-NTIN)I1652.1652.1651 1651 VFITIV'ITOHTNIOEVIIZ XII-XIR41. 0 SHTBSWTtHI N PRINT165.N. (JKII.NI.141.2).HTN. OO. CC.FPRD.OIfFovPRFD.DEV.NDENT(N) GO TO 1660 1652 PRINT26SIN;(JKII;NII3.102)OHYNDOODCCOFPRD!DIFFIYPREDIDEVI~DENTINI 1660 CONTINUE VFITIVTIT-XIP/I(XIRsNOINIISNT) STDrTT-soRTFIVFIT) PRINT150. VFIT. STOPIT IFINHELMAXUNDELIT72017211624 1624 IFIDEVMAx-SDEVNAXI172.172.1620 1620 NUSEINNAX)30 NOEL-NOELO1 onTAsxDATA-1.0 SUHUHTISUNUHT-UTINHAXI PRINT 1000.NNAX OOT0495 15 FORMAT (013UN 0F VARt/oo 17 FORMAT I12I1I.AI 123 PORNAT II11.A9¢ NO CORREcTION FOUND*726.5) 7'11I11I 154 FORMAT¢.05TAT rRON LINES NNTO LT 10.04/40VAR, c-F1n.6a STD. DE 1V I6F7.4/ITII 151 roRNAT I10A8) 152 FORMAT (.vRAH SSCP MATRIXI/I21.SI22) 153 rORNAT IXI2.6F?2.4I 154 FORMAT It 706720.63 155 FORMAT ¢. Y‘VS vcr15.41 154 FORMAT I13I1.7X.'10.18¥I2.iOXIS.F5.2XAO) 15¢ TORNAT IO-PAFTIAL CORR. COEFF.0100016I8) 160 FORMAT 0 for P lines and <0 for R lines). F10 20-29 Assigned weight. 12 41-42 Isotope, i.e., "14" or "15." 3 A8 73-80 "END DATA" signals end of data.- Card Type Format Columns 105 Information Parameter cards (there can be any number, but they should be all of the same type, i.e., either 4a or 4b) 4a For fitting data from only one isotOpe to determine 5' and/or e" and/or for predicting spin-doubling for one isotope. 411 1-4 I6 5-10 ZFlO 11-30 A non-zero number will enter the cor- responding variable in this fit. The four possible variables are e", e', (e'+e")/2, and (e'-e")/2. If all four columns are left blank, the pro- gram will predict spin-splittings using the values of a given in col— umns 11-30. Maximum value of K for which spin- splittings will be predicted starting with K = 1. If left blank, will not predict any splittings. Initial values of e" and e' for this fit. 4b For fitting both isotopes to determine 1“e"/1‘*A" = lsefl/ISAN and/or lhcl/ 411 1-4 5-10 2F10 11-30 4FlO 31-70 5 As 73-80 NAT = 15€./15A.. Same as for card type 4a except that the four possible variables are e"/A", e'/A', (e'/A'+e"/A")/2, and (E'/A'-E"/A")/2. Blank. Initial values of e"/A" and e'/A' for this fit. Values of 11+A", 1“A', 15A", 15A'. "LAST FIT" signals last fit has been performed on this set of data. 6 Start new set of data with another card type 1, 2E blank card to stop execution. 106 G. PLOTZ For each specified field strength this program calcu- lates the transition probabilities for the Zeeman components of specified transitions and plots a predicted spectrum, integrating over a Gaussian, Lorentzian, or triangular slit function to determine the apparent percentage absorption at each point. It also can plot a vertical line at the center- of each component which is proportional to the absorption by nthat component. STRUCTURE OF DATA DECK Card Type Format Columns Information 1 2F10 1-20 Values ijE" and e' to be used for- the following data. 2A8 23-38 Identification [e.g., "(2,0,1) OF 14N02"]. R1 41 Slit function to be used: "G" for Gaussian, "L" for Lorentzian, or "T" for triangular. R1 44 If left blank, program will plot a vertical line at the center of each component. The height of each line is proportional to the percentage‘ absorption by that component. The envelope of the resulting predicted Spectrum is then plotted. An "F" suppresses plotting of the vertical lines; an "E" suppresses plotting of the envelope. F5 45-50 Wavenumber scale giving number of inches on the plot for each cm‘l. (The total width of the plot must be less than 27 inches.) F5 51-55 Intensity scale giving number of inches for height of a 100% absorbing line. 107 Card Type Format. Columns Information F5 56-60 Half-width at half-intensity of slit function. F5 61-65 Value of a [cf. Eq. (66)]. IS 66-70 Non-zero number to suppress printing of positions and transition probabil-‘ ities of individual Zeeman components. F5 71-75 Value of ground state A for spectrum to be plotted. F5 76-80 Value of (B+C)/2 in the ground state for spectrum to be plotted.‘ 2 6F10 1-60 Up to six magnetic fields at which the Zeeman Spectrum is to be calcu- lated and plotted.w Only the first field may be zero. Data cards (one for each asymmetric rotor transition which is to be included in the spectra; as many as desired) 3 R1 4 "P", "Q", or "R", signifying AN = -l,. 0, or +1. 13 5-7 Value of K_1. I3 8-10 Value of N in ground state. F10 11-20 Predicted asymmetric top frequency. 4 Blank card to signal end of data. 5 Data for next set of plots, starting with new card type 1, 23 blank card to stoP execution. A listing of the program-PLOTZ follows. 1 9000 S 900! 9003 20 21 108 PROGRAM PLOTZ COMMON DELNUC63.XKAP(2). XNU(2) XN, XN1,XM.XH1.SPIN1.SPIN2pPOR, ZFRACT. NDELN.NL:NES. DELN, JMAX.KK, NoPRINT DIMENSION FIELD C6:.!HEAD¢2). 595(2) COMMON/QIFRQI6.250)aZINT(6.250!.‘NU(1500).A(1500’aHNC6).J.LABEL(Z) 1.XTEST,YTEST EQUIVALENCE (PRO.FNU).(2!NT.A) COMMON/1/XX(6.1SOO).Yytbnisoo) COMMON/21$Y.SX.SYI 3X! SCZS.VC. VS,MEYHOD.SCALEoHS. GAM.ISPRS CONNON/S/DUMHYI1’oSHAPECSOO).NPTS FGAN.XGAN. ALPHA IFLINoIFENV CALL PLOT! 0..31.a0n100.a100.) CALL 'L07(0.00.a1) CALL PLOT(4.a2..2) STATHT-1.43883/300. NH(1)INPLOTSuo REID 9OD°OEPS,IHEAD;HETHODa{SPRSaSC‘LEaHsoGAM.ALPHA1NOPRINT 1.AZERO.BBAR g FORMAY (2710aZXZABoZXR1.ZXR1.X4FS.15.2F5’ IF¢EPS) 0,5 CALL PLOT (15..0.a01) PRINT 9005 IORNAT ('50) 870?. . NPLOTSuNPLOTS¢1 NUIQBO¢NPLOTS CALL PLOYCNUB,0..3! 17¢ .NOT. AZERO) AZEROIB.002509 1r: .NOT. BEAR : BEAR no.4220736 NEAD 9003. FlELD FOINAT «9:10: DELNU(1)IO.00004675360715LD(1) D0 20 1'206 MN¢1100 DELNU!13.0.0000467536cF1EthI, IFCDELNU¢!)) 20.21 CONTINUE 107 JN‘XI‘O1 IFLINUISPRS-22 IFENv-IFLINoi 802530.35/SCALE sxp100,¢SCALE 3YI100.flHS 8x!:1.0/SX 3Y10130’8Y 8Y1!!SY!*5.0 Yea-25.05Y! Y8..'5..8Y1 XTESTISX! YTBSY'O.°1' FGANnIGAMIQ.O¢0AMt8Xto.5 XGAMIFGAH¢SXI¢0.9 f0ANnO.5/XGAM CALL PROFILE 109 IFCNOPRTNT) PRINT 9006.1HEA0.(f!ELD(J).JI1aJHAX) 9006 FORNAT('OZEEHAN COMPONENTS HILL BE CALCULATED AND PLOTTED FOR THE 170LLOHING LINES OF THE *ZAaltocuMULAT!VE NO. OF COMPONENTS AT THE ZFOLLONING FIELDSt6F61) 2 READ 90°10NDEL1KKINN0FREQ 9001 FOINAT!3XR1:2!3a'10’ NDELNINDELIiRQ IF¢NDELN/2) 00 T0 6 fKJIBBARt(NN0NN¢NN)0(AZER0-88A3)*(th02) BOLTzIEXPft-STATHTtFKJ) ”LINESIO {FITNTF(FREQT 'RACTIFREG-FF XKZIKKttZ XNuNN XNZIXNotZ XNinNNtNDELN XNiZIXNlOXNI XKAP¢1$I0.SOEP8(1)*XK2/(XNZtXN) XKA9(2)IO.505P9(2)*XK2/(XN120XN1T XNU(1’I XKAP(1)¢(XN*0.5) XNU(2)I XKAPT2)0(XN1¢0.5) IleOPRINT) 24,25 24 PRINT 9008.NDEL,KK.NN,FREQ 9000 FORMAT (5XR1111o*(*120)tF15.4) 00 T0 20 25 PRINT 9002.NDEL,KK.NN,THEAoofREOo(FIELDCITol'ioJHAX) 9002 POINATttflclifllfiEHAN FREQUENCIES AND INTENSITIES F03 *R1.11*(0!2t) 20f QZABt LINE CENTER I'F10.4/09*10X*NNA HN9*91003F13) 26 00 T0 (100.200.300)1(NDELNc2) 100 PQNIO.50.(XN2-IK2)/(4.00XNZtOZ-XNZT MHINlI-NN MNINZINHAXZIMHINJINH!N1¢1 HHAXlINNOZ MMAXSIHHAXlti 00 T0 400 200 POE-0.50*XK2/(!N2tXN)o-2 MMINSIMMTNIIMMINZI-NN NHAX2INNAX38NN HHAXiIMHAXZIi 00 T0 400 300 PORI(XN12IXK2)/(B.OXN12¢(XN2¢XN*XN‘0.75)T MM!NSQNNAXSIMHINisNHIN23-NN MHAXinNMAXZINN 00 T0 400 ‘00 CONTINUE, 3PTN1II1|0 DO 401 Kl1.2 SPTNIOSPTNal-SPINI DELHI'130 DO ‘01 0'10: DELHI-DELM 00‘401 NINMTN1,NMAX1 XHIDELMQH 401 402 405 404 407 409 406 400 403 27 9000 26 9007 9004 10 110 XH18XH¢DELM CALL‘ZEEHAN !P(.NOT. KK) GO TO 404 IPTN1'4100 spr2I0$.O . DO 402 HIHHIszflflAXZ XMIXMiIH CALL ZEEMAN 591N13'100 SP!N2061.0 DO 405 NIHHIN3,HMAX3 XMOXHIQN CALL=ZEENAN CONTTNUE DO 403 J!1.JHAX DO 406 3011NLTNES IP1-101 DO 406 KIIP1nNLIN5$ SUMAIZINTtJaKT¢ZINTTJgT)*1.OE'10 DIFFIFROCJaKTGPRQTJaT) GO TO (‘07.‘09;4°9.‘°6’0‘Dlrr/XYEST93.O’ PROTJ01307ROCJoK’ PR0(J0K)IFROTJ.K"DIVV DIPPI-DIPF ZINT(Jpl)OZINT(J0K) ZINTTJoK’ISUMA-ZINT‘JaK’ 00 TO 406 FROTJDITI('R°(JoI)‘ZINTCJaT)tFRQ‘JcK)OZINT(JoKT)/§U"‘ ZINT‘Jp!"SUMA Z!~T‘JIK,.O|O courtNUE DO 403 I'loNLINfls T'CZTNT‘Jnl) .LT: YTEST) GO TO 408 NIMHTJTIHHCJifil XX!J.N)I'RDTJOT"" YT!J:N)IZINT(J.ITOBOLTZ CONTTNUE CONTINUE IftNOPRINT) 27.26 PRINT 9009-4NH(JT0J31;JMAX) TORNAT (04052X616) GO TO 2 . . PRINT 9°07O‘H"¢J’IJ.10JH4x, FORMAT (*ONLINESTPTELO) 406113) 00 TO 2 DO 10 JIanHAx NHIHHTJ’ DO 9’T010N" PNUCT)!XXCJ.T) 6(1)!YY‘JOIT - ENCODE (0:9004nLAUEL41TT FIELDCJ) IORNAT (0H 90!!) LADEL‘ZDIOH GAUSS CALL'DUH 111 GO TO 1 END SUBROUTINE ZEEMAN COMMON DELNUT6I.XKAPIZTIXNUIZIIXNIZIAXMTZAIS‘ZTJPQR:'ROCTINDEL 1.NLINES.DELN.JHAX.KK,NOPRINT COMMON/4/PR0(6,250IIZINT(6.250I.DUMI11I O’NENSION V112)0V2(21.V312)oEPTZ).EM(ZTaE‘2’ NLINES-NLINESO1 DHIDELMOXH¢1I DHPQDHADELM DHMQDH'DEL" DO 1100 JuiaJNAx IFIKKI 3:4 4 17(J 05°: 1’ GO TO 3 DO 6 I-2.JNAX PRO (I.NLINESIIPRO I1.NLINESI 6 ZINTII.NLINESIIZINT(1.NLINESI GO TO 7 3 CONTINUE DQDELNUIJI DO 1101 10103 XHNnXNIII E(III-o.50-XKAP(IIts:IIGSORTFIDvD¢2.0tDtxxAPII). ZIXNN00.5-S(II)¢ XNUIIIctz) IFIXNII) .50. S(IIoXHNI EIII‘SIII'IXKAPCIItXHNoD) IPISII) cLT. 0.0) XMNnXHN-ln0 v1IIIuXKAPIII¢XNN «a VZIIII-VlIII-XKAPIII VSIIIIXKAPIIItBORTF(xNIIIw¢2¢xNIII-XNMbIXNNt1.0II EPIII:0.50(V1IIIOV2(III 0 SOITP(0.25'IV1II)-VZIIIIOtZoVOIIIt-II III ,NOT. V31!) I 591!) a V11!) 1101 ENIIII-EPIIItv1III9VZIII ~ FROIJoNLINE§1§PRAOT¢E(2:.E¢1) IFCSI1IOBIZII 2000.131000 1 IPISI1II400002.3000 1000 OONTINUH R1QVSI1IIIV2I1IOIPI1II R120R1002 IZIVSIZI/(VZIRIOIPIZII R228R2¢t2 61-1.0/¢(1.0cn121vt1.oa022)3 0290100120022 , 03.2.0-01-n2-ca IFINDELI 1001010025100! 1001 n1g¢xucII-ona.¢XN¢1I-oM-1.0) DZ:(XN¢1I-DNPI0(xNI1I-0NP-1.OI 00 TO 1100 1002 DiIIXNt1I-DMIttXNI1ItDNt1.0) DZIIXNI1IODMPIOIXNI1IADMP01.OI GO TO 1100 1003 D1QIXNI1I¢DN01.OIvIXN¢1ItDH¢2.0I DZI(XN¢1I¢DHP¢1.0IvIXNI1I¢DHPa2.0I 00 TO 1100 2000 CONTINUE 2001 2002 2003 3000 3001 3002 3003 4000 4001 112 P1QV311I/(V1T1I-EHI1II R12§R1062 R2.V3(2)l(V1(2)-EM(2II R22lfl2tt2 . 02I1.0/¢(1.0‘R12IGI1.04R22I) 0100200120R22 0392.00R10R2t02 IFINDELI 2001.2002.2003 . OllIXNI1I-DNNIoIXNI1I-DNN-1,0) DZICXNI1I-DMIOIXNI1I-DN-1.0I 00 TO 1100 D1u(xN(1)-DNN).(XNI1I¢DHN¢1.0) DZI(XN(1I-DNIoQXNI1I*OHO1.OI GO TO 1100 _ D1IIXNI1I¢DHH41.0IOIXNI1I¢DNNo2.0I D2ICXNI1’ODH41.0IOIXNI1)*DN¢2.OI GO TO 1100 CONTINUE R1IV311I/(V211I-EPI1II R12IR1002 R2IVSIZI/(V112I-EHIZI) RZZIRZOOZ PSI1.0/((1.00R1ZItI1.00R22II 01:2220R3 CZIR124R3 03'2.00R10324R3 TVTNDEL’ 3001.3002.3003 XNPIXNI1I¢XNI1I DilXNPo(XNPc1.0) DZIXNPOIXNP¢1.0I GO TO 1100 XNPIXNI1IOXNI1I XNNOXNC1I-XMI11 DI'XNPO‘XN".1.°) 020(XNP41.0I0XNH 00 TO 1100 ‘ XNH19XN11I-XHI1I41.0 D1IXNH1tIXNN1a1.0I DZQXNM101XNM1-1.0I GO TO 1100 CONTINUE R1IV311IIIV111I-EHI111 R129R1002 ‘ P2IV3¢21IIV2(21'EPIZII P229R2002 - P301,0/((1.00R121011.OOR22II O1IR12tR3 C2IR220R3 03-2.00R10R2*R8 IP(NDELI 4001.4002.4003 XNHIXNI1I-XN11I D1QXNN¢IXNN¢1.0) DZIXNH.(XNHI1.0I 00 TO 1100 4002 4003 1100 113 XNDIXNI1I¢XNI1I XNNIXNI1IOXHI1I D1IIXNH¢1.0I0XNP DZIXNMO(XNP¢1.0I GO TO 1100 XNP1HXNI1I¢XHI1I*1.0 D19XNP1OIXNP1-1.0I DZIXNP1OIXNP161c01 ZINTIJ.NLINES)uPOR~IC1tn1¢c2.02.c3osonrr(01.02:y 7 CONTINUE 9000 202 33 I'INOPRINTI GO TO 2 PRINT 9000.50XN1(FROIJaNLINEOInZINTIJoNLINESI0J91IJMAXI FORMAT IXF24/2ni'zfil21274,9(0P.F9.4,3P.F4II RETURN END SUBROUTINE SUN DIMENSION 90313000) COMMON/4/XNUI1900InAI15001. NNI6I0NOPL0T. LABELIZInXTESTIYTEST COMMON/2’3Y48X, SYI. SXI15C25.YC.Y9.NETHODpSCALEoH5.GAN.ISPRO COMMON/5/OUHNTI1IaSHAPEI500InNPT5. FOAflngAHo ALPHAOIFLINOI'ENV IINNINOPLOTI DO 4 Jl1aI LIJ¢1 DO 4 KanI SUNAuAIJItAIKI XNHXNUIKIIXNUIJI GO TO (303.314I01XN/XTEST¢3.0I XNUIJIIXNUIJIOXN XNUIKIIXNUIKIIXN XNQIXN AIJIQAIKI AIKIOSUHA-AIKI GO TO 4 XNUIJIIIXNUIJIOAIJIOXNUIKIQAIKII/SUHA 6IJ’03UNA AIKIlOOIO CONTINUE II90 DO 8 JI1|I _ I'IAIJI 0LT. TTEOTI GO T0 8 IIIII¢1 XNUIIIIOXNUIJI AIIIIIAIJI CONTINUE ItII PRINT 202oIoLADELoIXNUIJIaAIJIoJ91III FORMAT 1"4I4t FREQUENCIES PLOTTED AT 02A8/151‘F1OI40F933II) CALL~PL°TCUll°oOOI X!0.0 DO 33 Nl1o2 CALL CHARI'.75,XcL49§LINI.030.a.15 XIX‘1.! CALL pLOTI0.00.n2I ZIINTFIXNUI1I'0.2I 200 30 21 22 23 24 12 114 LTIXTOINTPIXNUIII41,2.Z) LEILTt10 SIZE-XTtSOALE Xlo.1 L00 DO 5 KnLoLE XIX¢.1 VI Y8 , CALL ”L0T1000X0108TnSXI IIIK .60. KISOSI YlYovs CALL PLOTIYoXo1I CALL pLOTIOHXoIJ Ll-LT01 NRQZ¢LT XCILT XIXC-SCZB XCIXC¢1.305029 CALL CHAR‘ YCoXCIZHCN.2o0...1o.1I XOIXCOSCZS YVIO.790YC _ CALL CHARIYToXCaZH'1a2aouo.06..06) DO 6 K11.LF ENCODEI‘oZOOaLAINR FONNATII4I CALL CHAR (YC.X.LA.4.0...1..1> NRINR-1 XOX.1. MAXPOSISX . LINIL30SCALE'10. IPILIH .GT. 3000) LIN - 3000 DO 7 IN'10LIN PODIINIIOI MINI-NPTS CALL pLOT (0.0.0co2) DO 9 K810I XXQXNUIKI-z INIXXtSX YYIAIK) Yll.005NPP¢00,1¢ALPHA4YYI IPIIFLINI 30.9 CALL 'LOT (0.0.XXc1I CALL PLOT I Y ,xx,1) CALL “LOT (0.0.XXa1I POSIINIIPOSIINTOYY IPI.NOT. IPSNVI GO TO 20 DO 21 INI1ALIH IPIPOSIINII 00 TO 22 MIN-IN-1 DO 23 INO1oLIN IPIPOSILIN-INII 00 TO 24 HANDLIM'IN41 DO 12 INlNINaNAX POUIINI'1.0IEXIP¢-ALPHAtPOSIINII MINQHIN-NPTS 115 ITININ .LE. NPTSI MININPTS¢1 MAXIMAXPNPTS IPINAX .05. (LIN-NPTSII MAXQLIN-NPTSct XIININOIIOSXI CALL PLOTIOoDo! 01I HINIIINPTS HAX19 NPTS DO 10 INININAHAX XlXOSXI V90 00 11 INQNIN1.MAX1 11 YQYOPOSIINOINIOSHAPEIXABSFIINII 10 CALL PLOTIYoxoiI 20 CALL 9LOT(0.30..2I X'OQU Y.-‘. IFISIZ! .OT. 12.0, GO TO 25 NHINOPLOT'INOPLOT/ZIoz YaMNc4-4 XI '300NM415 29 CONTINUE CALL PLOTI T o X001100n01000I CALL PLOTIO.:0..2I RETURN END SUBROUTINE PROFILE COMMON/ZISTISX.STI.SXI.SC2§.YC.Y3,NETHODoSCALEnH3.OAH.ISPRS CONNON/5/DUMNY11IaSHAPEISODIaNPT5.POAN.XOAN04LpHAIIFLIN.IFENV OAN2IXGAN002 OANZLN200.69319/GAH2 N90 SHAPEINII1.0 TEST! SYI ITINETHOD035I 213:4 4 ASOION 400 TO NOD NANBIOHTRIANOL! DO TO 5 3 ASDIGN 300 TO NOD NANElOHLDRENTl GO TO 5 2 ASOION 300 TO NOD NAMEIOHOAUSSIAN 5 CONTINUE X00.D DO 100 II1JDOD XIX¢SXI X29X0t2 00 TD N00 400 SHAPEIII'1.0'XOFOAN DO TO 102 300 SHAPIIIIDOAH2/(X2OOAN2I GO TO 102 200 SNAPDIIIOEXPIOOANOLN2OX2I _ 102 ITISHAPEIIIITESTI 101.100.100 100 101 500 116 CONTINUE NPTSnBOO NPTSSI PRINT 500.SCALI.HS.ALPHA.NAME.XGAM.GAM.NITS.(SHAPEIJI.JoN.NPTsI TonMAch1THE NEXT LINES HILL 8: PLOTTED AT0F6,3t CN-1/INCH AND 100 1! ABSORBING LINES HILL B!of5.2¢ INCHES NIOHtIA THE LINES ARE ASSUM ZED To BE DELTA FUNCTIONS HITM HEIGHTS GIVEN BY I1.-EXPF('0F§,8.10H 30¢M>**2II./5Xa NHERE (N) 13 THE DIPOLE MOMENT MATRIX ELEMENTt/t A. 4A9. SLIT FUNCTION HAS USED To INTEGRATE OVER THESE LINSS.t/4XAITS SHALF-NIDTH AT HALF-INTENSITY 18.77.40 CN-1 (INPUT ASAT7,44 cHu1).t 6/0 TMEAE ARE A MAXIMUM OPoI4¢ QLOTTER UNITS FROM EACH LINE CENTER 7 TO ITs LAST POINT PLoTTED,0/6NOTHE INTENsITIEs AT EAcH or THESE p aoINTs Ton A LINE or UNIT HEIGHT AREA/I10x20F6.3II ’ RETURN END UPPER N KI K6 n 0» lar-H-PwaH-Hunvnuuar-H-Hunk-Huath-Hwac:cpau:cuauacaauacaanar-nlauiv-r- ' a u: & .¢ pmppnppuuppuppnpuuppuaoonoaoooooaommuuooa ' I s a LOWER N K. K. APPENDIX II OBSERVED 5.877769 4.132328 0.510467 1;361426 1.306371 0.887373 0.534214 75.4661 68.9791 62.4419 55.9010 52.6209 49.3302 46.0366 42.7336 32.7793 29.4409 19.3873 19.2712 .2.5135 76.8945 77.1156 73.6207 73.7948 70.3499 70.4552 67.1206 63.7889 63.7702 60‘5071 60.4167 53.6810 50.3017 46.9138 40.7027 37.4019 36.7240 34.0835 30.7670 29.9089 26.5007 OBS-CALU 90.000000 -0.000000 0.000006 0.000020 -0.000001 -o.000003 0.000001 0.0001’ 0.0204 0.0041 0.0034, 0.0026 -0.0016 "0.0010 »-0.0014 000039 0.002? 000024 '.0.°112 ‘-0.0109 00.0073 0.0043 00.0079 '0000‘2 Q0.0021' .0000‘9 0.0003 .0.0007 ‘90.0014 0.0061 0.0022. 0.0035 0.0029 -¢0.0000 --0.0029 0.0069 4-0.0034- 0.0020 0.0018 .0'0061' 00.0031 117 HEIGHT 1000000 2000000 250000 40000 40000 40000 900 0.24 0.17 0.10 0.82 0.46 0.46 1.00 1.00 0102 1.00 0.17 0.32 0.17 0.20 0073 0.31 0.77 0.13 0.37 0.33 0.13 0.51 0.24 0.67 0.46 1.00 1.46 0.18 0.47 0.18 1.00 0.67 0.67 1.00 GROUND STATE COMBINATION DIFFERENCES FOR 14N02 14 MICRO 14 MICRO 14 MICRO 14 MICRO 14 MICRO 14 MICRO 14 MICRO 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 . 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 . 14N02 14N02 14N02 14N02 14N02 _ “manta-.5); NUCNG‘UO‘IONUOUIO‘HOUI‘JO ”MN“ “000 “Kahlua““a“NNMNNNNNNMNNNMNNNNNNNNNNMNNNNNPPPHPPHHPHFMHPH 0.3 ”NODOONOOO Cd.“bb 0964040301 N01“ 08“) 13 11 V0 b..&&b HNCfl‘UIOPNCd‘mOO-‘NUUI “(10$ POO TONGA 0WD ..n NGWDOONOVDO 00$“.‘ ON“.UIO «caol‘ 4=kru 944 ”PHVHWUTHPHWVQOPH bbb.‘ CNN)“ PPNNMNNGUOI& .ONN&OGO&OO ur- auu 1“.) PO‘UQOMOOmmObOODD OI 0 (dUGQGGGUGNNMNMNNMMNNNNNNMNMNNNNN”NMNMNNHFH-HFPHO‘PHMRI-OFT” muo- 018% N V 118 24.1250 20.7952 19.6712 17.4757 14.1500 10.8203 7.4898 5.9054 4.1758 5.3330 5.4073 3.9307 3.5632 2.4253 1.7390 80.8618 77.4641 74.6917 74.0491 71.3944 70.6298 03.7914 54.7041 53.5220 50.0093' 46.6690 43.2496 41.2985 31.2060 2946213 24.4665 22.0261 19.4372 17.7300 16.0555 14.3494 12.6724 5.9095 9.2599 0.4750 7.5866 5.0694 3.3766 2.5329 80.3439 70.4196 76.9545 75.0470 73.5426 60.3348 64.9669 54.8639 53.2104 100.0001 ~O0.0066 90.0020 00.0009 0.0002 «0.0014- -0.0028 60.0051 0.0130 ‘I0.0057 0.0040 0.0007 0.0006 -90.0026 0.0041: v90.0049 -°0.0014 0.0014 0.0073 .0.0034 0.0294 00.0072 90.0027 0.0053- 0.0055 00.0029 00.0005 00.0009 0.0050 0.0009 0.0041 1-0.0028 ‘0.0006 90.0014 0.0052’ 0.0024. 90.0010 0.0021. 90.0014 0.0023 0.0077 0.0008 0.0002' .03001“ 0.0000 0.0013. 0.0199. 040101' 0.0009 90.0060 0.0044~ 90.0009 90.0021' ~eo.0010 1.00 0.46 0.10 0.99 1.00 0.82 0.18 0.82 0.18 0.17 0.18 0.18 0.58 0485 1.13 0.42 0471 0.17 0.17 1.28 0.17 0.13 1.37 0.77 0.17 0.02 1.00 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 ‘ 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 ounmwuuuuumuumuuuQIAno;baa-none...besauaauauuuuuaauuuuauca FNNNMNN OP‘UIOOO G‘WTONGONGOWO PPHPNNNUUU‘Aé OVO‘OMU‘OOPNOHVOF‘W «0a a». oumumuuuuumuuuuuubtbebu.35“...egtnuuauauuuuuaauuauuuon N \2 (dble PFNNMN ODONPFGGWW‘JOPPGUVOPUHU unavsnwuna Inhaownaxo *- O 119 51.4914 49.0347 46.4554 44.7520 43.0756 37.9975 34.6269 12.6710 10.9706 9.2037 7.6099 10.9786 0.4404 7.6020 6.7560 549129 5.0677 4.2253 3.3769 70.4237 76.7564 71.7003 60.3525 64.9779 54.0657 51.4973 40.1213 37.9962 34.6321 29.5590 27.0676 24.4997 12.6703 9.2950 0.4533 6.7616 5491.00 59.9257 50.2382 54.0675 53.1037 46.4500 44.7667 41.3079 27.0012 14.3699 13.5160 10.9710 10.1411 9.2973 6.4470 7.6092 6.7624 61.6272 I0.0036v 90.0023 00.0003 0.0032 0.0003 90.0010 0.0047 0.0038 00.0004 90.0062 0.0091 0.0003 60.0050 0.00134 90.0003 0.0012 0.0005i 0.0026 00.0013 00.0101 90.0109 '.0.0007 0.0085 0.0005 .0 .0039 -90.0007 90.0061. 0.0056= 90.0019 00.0055 0.0040 ‘60'0013‘ 0.0031: 0.0058 0.0035; I0.0034‘ 1.0.0032 ‘00.0066 '00.0080~ 9-0.0060: 0.0031: 0.0064. 0.0015 0.0070 60.0025; 90.0129' 0.0011 0.0021‘ -90.0025‘ 0.0030. 0.0019' 040013 0.67 0.32 0.33 0.82 1.16 0.50 1400 0.70 0.67 0.10 0.67 0.17 0437 0.67 1.32 1.66 1.17 1.49 1.00 0.10 0.27 0.17 0431 0.10 0.31. 0.52 1.10 0.82 0.67 0.02 0.02 0.29 0.17 0.13 0.58 0.10 0.95 0.70 0.02 1.17 0.17 0.46 0,10 0.46 0.82 1.00 0.31 0.15 1.46 1.00 0.67 0.47 0.15 0.50 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02' 14N02' 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 “VOOOOOOOOOOOOOOOOOO \IVOOOOOOOOOOOOOOOOOO 120 56.5091 46.4507 43.0941 41.3916 30.0195 34.6531. 32.9811 3102713 29.5913 27.8988 16.9130 16.0579 15.2185 13.5280 11.8305 10.1333 7.6146 6.7746 13.5202 12.6800 0.0150 00.0010 0.0075 '0.0°79 ~c0.0042 0.0060 0.0226 0.0017' 0.0107 0.0079 0.0124 0.0000 0.0059 0.0047 60.0032 90.0104: 0.0063; 0.0115‘ 00.0080 90.002] 0.17 0.02 0.50 0.31 0.50 0.10 0.18 0.33 0.30 0.17 0.10 0.20 0.13 0.46 0.02 0.16 0.24 0.17 0.10 0.07 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 14N02 UPPER N K0 K4 3 1 3 5 1 5 7 1 7 10 0 10 12 0 12 21 2 20 46 0 46 30 0 30 36 0 36 34 0 34 32 0 32 30 0 30 20 0 20 26 0 26 24 0 24 22 0 22 20 0 20 10 0 10 16 0 16 14 0 14 6 0 6 4 0 4 40 1 47 46 1 45 45 1 45 44 1 43 42 1 41 39 1 39 37 1 37 36 1 35 35 1 35 32 1 31 30 .1 29 29 1 29 20 1 27 ‘26 1 25 25 1 25 24 1 23 16 1 15 15 1 15 14 1 13 13 1 13 11 1'11 9 1 9 7 1 7 6 1 5 5 1 5 4 1 3 3 1‘ 3 LOHER N KC K4 4 o 4 6 0 6 8 0 6 9 1 9 11 1 11 22 1 21 44 o 44 36 0 36 34 0 34 32 0 32 30 0 30 28 0 28 26 0 26 24 0 24 22 0 22 20 0 20 18 0 18 16 0 16 14 o 14 12 o 12 4 o 4 2 0 2 46 1 45 44 1.46 43 1 43 42 1 41 40 1 39 37 1 37 35 1 35 34 1 33 33 1 33 30 1 29 28 1627 27 1 27 26 1 25 24 1 23 23 1 23 22 1 21 14 1 13 13 1 13 12 1 11 11 1 11 9 1 9 7 1 7 5 1 5 4 1 3 3 1 3 2 1 1 1 1 1 121 OBSERVED 3.762178 1.969932 0.133759 1.743310 3.657656 0.094000 75.2507 62.2704 59.0236 55.7663 52.4936 49.2237 45.9307 42.6465 39.3476 36.0390 32.7199 29.3914 26.0561 22.7131 9.2717 5.0942 00.2960 76.9902 73.4650 73.6045 7003614 63.6451 60.3765 60.3457 57.0025 53.6166 50.2526 4792107 46.0775 43.4075 40.6260 40.0961 26.4097 24.0012 23.0007 20.7612 17.4449 14.1246 10.0022 9.4021 7.4001 15.9925 4.1540 OBS-CALCI 0.000008 0.000000 ‘00000016 -0.000009 ”0.000000 -0.000000 90.0150 90.0049 '0.0032 0.0011 90.0039 0.0009 90.0019 90.0029 '0.0011' 0.0007 90.0002‘ 100.0007 0.0007 0.0023 0.0002' -0.0073 0.0132: 0.0035? 0.0002 0.0050 1-0.0000 '0.0054 0.0046- '00.0012' '0.°°’l 90.0091 00.0009 00.0029‘ 0.0031. ‘.00001, 0.0007 '099019 0.0019 0.0007 0.0043 90.0029 0.0000 0.0005 90.0001 60.0060 0.0000 0.0050 ‘.03000‘ HEIGHT 25000 100000 25000 25000 250000 100000 0.13 0.10 0.10 0133 0.67 0.17 0.63 1.10 2.00 0.42 2.00 1.00 1.00 0.10 0.13 0.17 0.13 0.50 0.42 0.77 1113 0.15 0.67 0.33 0150 0.17 1.00 0.10 0.79 1.67 1.10 0.52 0.46 1.00 0.33 1.10 1.33 1.67 1.00 GROUND STATE CONBXNATION DIFFERENCES F0R 15N02 15 H1000 15 41000 15 41030 15 MICRo 15 MICRO 15 MICRO 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 _ 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 15N02 . 15N02 15N02 15N02 15N02 uuaaauaaaauuuuauuuuamwmn»nnmunnnmnnnmmnnnnnnnnmmupppup 122 6.6022 9.4903 3.5673 2.4195 1.7351 60.6419 77.6669‘ 77.4346 74.5584 74.0391 71.2632 '70.6230 67.9529 67.2039 64.6107 63.7743 60.3500 94.6149 60.0706 47.9452 46.6609 43.2292 39.0094 36.4055 32.9953 29.5931 26.2030 7.5885 5.6954 5.0992 5.0650 012161 3.3719 ‘215291 70.3217 73.4959 70.1059 64.6966 96.1764 56.5549 54.0031 40.0033 44.6966 43.0209 41.3276 39.6360 37.9539 34.5844 32.0959 31.2162. 29.5296 2614667 22.7772 21.0902 90.0000 90.0057 0.0002 90.0000 0.0000 0.0019 00.0035‘ 90.0067 90.0050 0.0037 0.0109 90.0001 0.0166 10.0015‘ 90.0039 60.0090 0.0006 90.0069 90.0060 0.0069 0.0079 .0.002. 90.0057 0.0025' '0.0007 90.0013~ 0.0057 90.0011 90.0007 0.0010 0.0006, .0.0009 0.0071' '0.0171. 90.0098 'W "°1°0127, -90.0045¥ 0.0126 90.0034 90.0109 .000012 90.0102 90.0026 0.0000‘., ’00.0056- 0100601 “1 0.0031 0000212 0.0017- 0.10 0.50 0.13 0152 0.02 0.15 0.15 0.17 0.10 0.10 0.15 0.67 0.24 0.67 0.17 0.15 1.00 0.10 0.17 0.10 0.24 0.67 1.10 0.10 0.02 1.37 0.56 1.00 0.10 0.37 0.67 2.00 1.17 1017 0.37 0.13 0.37 0000 0180 0035 0.46 0.10 0.17 0.15 0.25 0.10 0.26 0.18 -0610 1.17 0.10 m0.10 1.00 4900 15N02 15N02 15N02 . 15N02 15N02 15N02 15N02 15N02‘ 16602 15602 15N02 15N02 15N02 15602 15602 15602 15N02 15N02 15N02 15602 15N02 15602 15N02 15602 15N02 15602 15N02 13602 15602 15602 15N02 15602 13602 15602 16602 15602 15N02 15N02 13602 19602 15N02 15N02 _ 15N02 15602 15N02 15602 15N02 15602 16602 15604 15N02 16602 15N02 19602 oooo‘uuuuuuuuuuuuuuuua..gAgaa¢b.as¢&.aa§¢sabauuauauaua PHWWVVUHOO (d‘ NO ”NM“ 0090 NNM '0‘. 20 «.ONGObOOO OOOOUUWUUUUUUWWUQUU‘I.‘O..‘..t.&‘b&b.‘&.‘$bfl“€dflfflflfluuGI PPGWWVFWV‘V p “WVVOOOP ’26 .10 123 19.4000 17.7166 16.0296 9.2838 8.4355 7.5955 6.7475 5.9063 4.2230 ‘3.3817 73.3293 58.1761 56.4955 56.8117 53.1289 51.4500 66.3886 44.7043 43.0222 39.6519 31.2119 29.5202 27.8309 26.1556 19.4122 16.0118 14.3403 9.2830 8.4360 7.5749 539121 4.2306 63.2260 58.1675 56.5108 39.6527 36.2845 36.5969 32.9063 31.2178 29.5367 26.6727 12.6530 11.8178 10.9739 10.1237 9.2845 ‘7.6007 56.5071 29.5279 29(4927 13.5008 v0.0018 0.0022 0.0049 ~0.0001 0.0037 ..o.oooo 0.0015 0.0058 0.0075 00.0014 ~30.0013 c0.0006 0.0020 0.0018 0.0089 0,0014 0.0030 0.0059 0.0071 00.0017 00.0069 v0.0096 0.0020 0.0067 .0 .019: 00.0034 0.0020 90.0033 90.0188 0.0053 0.0117 '0.0027 -00.0126 0.0135 00.0004 0.0031 '0.0001, 00.0045‘ ~00.0046 000012 'Q0.0017 690.0060 0.0026 0.0022 00.0062; 0.0004 0.0063 '00 .006‘ Q°.°19. 0.0073 '0‘007’ 0.77 0.67 0.10 0.30 0.17 15~02 15~02 15~oa zswoz 15~oz 15~oz 15~oz aswoz 15N02 15~02 15~oa 15~02 15~02 15~oz 15N02 15~02 15~02 15~oz 15~02 15~02 15~02 xsnoa 15~oa 15~oz 15~02 15~oz 15~02 15~02 tsuoz xsnoz xsnoz 15002 15N02 asnoz 15~oz tsnoz 15~02 15N02 15N02 15~oz 15N02 xsnoa 15~02 15N02 xsnoz 15N02 15N02 xsnoz 1s~oz 15N02 15~02 15~oz '01!“U‘I“U1I“I1IU1D1I‘1018‘1013‘131VU1DU‘O1YV‘D1JU‘I1331D1IV‘O‘IV‘B X AINHUN3NH“F‘Hfl‘fi‘flfl‘fl‘FW‘fl‘FH‘fi‘HW‘f‘FH‘F‘HW‘U‘HH‘CDOHDCDQHDCDGM3CMO¢3 FREQUENCIES OBS 2856.019 2859.289 2864.373 2874.016 2878.592 2883.002 2887.247 2891.334 2895.265 2899.033 2902.639 2853.423 2856.074 2858.688 2861.264 2863.793 2866.279 2868.727 2871.136 2873.500 2875.835 2878.124 2880.383 2882.564 2884.746 2886.876 2888.991 2891.006 2893.002 2894.981 2896.908 2898.793 2900.963 2902.446 2906.202 2854.606 2857.230 2859.808 2862.367 2864.874 2867.333 096 .0.008 0.009 0.013 "03026 0.003 0.004 0.003 '0.000 .03080 0.003 0.004 0.005 "00005 "00006 .90004 0.003 0.002 "03001 "90001 "9.°01 .90908 0.001 0.002 0.013 "0081‘ "00000 0.002 0.029 "°.904 "09915 "03003 "93092 '90903 0.002 0.000 "O'OOG 0.004- '.0301‘ "9.902 "90002 "90908 APPENDIX 1:! FOR THE (1.0.1) BAND 0F 16N02 H7 00---.-.-.-.u-.--.o..--ooo-.o.on-sconce... 80"“NQO.~.CHHC’CHHCND¢DCMO‘:"CHDC3CN°\.‘law‘fllaufi‘aNFV“GH°C3°H3C3FW‘ ID¢3CHDCDCH3CFOO‘CH‘€MDCSFW‘CMOO‘FW‘FMDCDCM3CMOC3OMDCMOCDFW‘FHDCMOCD 124 ‘31.ITV‘D10‘HIIYU‘DITU‘DYTUTUIY“.1TU‘D1I‘VO‘D‘T‘1D1TV‘D1IU‘DII‘101D“B INI§GaNthlNufifibFwfibbflwibbfluflr‘flflflbbHwfirbfluflhbflufirtcwo::cno¢:cwo¢3cna¢3 K 085 2856.669 2861.819 2866.834 2871.665 2876.323 2880.815 2835.130 2889.311 2893.316 2897.170 2900.863 2904.382 2855.340 2857.966 2890.560 2863.100 2865.608 2868.056 2870.484 2872.851 28750182 2877.473 2879.724 2881.926 2884.098 2886.212 2838.291 2890.327 2892.325 2894.277 2896.193 2893.052 2899.878 2901.662 2903.401 2853.016 2855.699 2858.296 2860.874 2863.415 2865.918 2868.376 0'0 '00005 .0902: .0000; 0.00.1 0.002 0.001 I0.012 0.001 .0000; 0.006 0.010 0.007 '0.006 '0.007 0.002 .00083 0.005 .00006 0.006 .9009: .0000: ”09083 0.003 '00001 0.000 0.001 0.001 90.000 0.003 0.003 0.009 .0000: 0.001 0.002 0.001 .00013 .00015 00.006 I0.007 -o.oo5 30.000 "01001 I. .4 GNU\8UPVF3HWDFVHCDHW3¢DGVfl‘lFHD\JOWQCFHflOQWOt‘NHUF‘NUOGDGHD¢SCVNF‘FHU .--C--v----‘----‘--—.-----------------------. O‘CMO<3CMOIDCMOGQFDCH‘O‘FWDCMDO‘CDFHDt‘CMDIDChat:CWOGDfi.FN‘CJFW‘CMD¢3C) ‘D1I‘Hl‘IW‘D1VV1I1VU15"01VU1I‘1U1I‘HU1IV‘D1I‘“01531.1!“‘01!31'11‘0019‘1U‘V919‘1010‘1913U IDOHbIIOL§15.5.453L‘lbILOGIGIGHHGIGIGHHGdOIHHHEIGIGHHGIG‘GHHG‘GINHVEDNHQEDQHUQDNHURO“UNUSEDHI 2869.762 2872.155 2874.471 2876.789 2879.053 2881.266 2883.440 2885.575 2887.691 2089.709 2891.735 2893.707 2895.636 2897.523 2899.366 2901.166 2902.940 2853.815 2856.446 2859.044 2861.595 2864.104 2866.572 2869.007 2871.395 2873.734 2876.026 2878.299 2880.522 2882.705 2884.838 2886.956 2888.994 2891.006 2892.997 2894.909 2896.795 2898.652 2900.459 2851.581 2854.225 2856.824 2859.383 2861.903 2864.373 2866.834 2869.243 2871.596 2873.911 2876.193 2879.731 2880.624 2882.781 2884.896 '9.°03 0.008 "0.018 0.000 0.005 "00008 .0308; '0.003 0.019 "03017 .0000: '0.001 v0.00: '0.001 '0.004 "01007 0.004 "0.911 "°g°11 *0.004 "9.903 "0.004 "°|9°4 0.004 0.005 “0.001 "0.014 “0.008 "00003 "09001 '.03006 0.014 ”0.003 "'0.005 0.014 "0.°°’ "0.007 0.003 0.005 0.066 0.062 0.052 0.042 0.034 0.017 0.032 0.034 0.024 0.015 0.015 0.012 0.005 0.005 0.003 O.-.O.-.......-...-.-O..O..----.....-....OOOOCOOOOOODO auacaamaaaUHDCDCHHF.HWficworbunacaauacma~dcrucaow‘cauua~Iamauhocacrfl~aauac3ouacaauucwocac: “‘1U1T‘1D1r‘101r‘1flirt‘01ri‘l1ri‘u1rt‘D1TU‘D1IV‘D1TI’D1ID‘U1TV1D11t‘0111‘0131V01l13U‘O1rt‘n .sJ-aupasauudsausa-onuJ-.maéuucdcianu(noun(nouucuauu«donnedouucunamnun3~u003Nnonumlunnnaono ””3””0OOOOOOOOOOOOOOOOOO‘OFOOOOFOFOOOOOOOOOPHOOPO‘OOPOO8'" 2870.795 2873.170 2875.517 2877.800 2880.065 2882.264 2884.450 2886.579 2888.667 2890.691 2892.703 2894.662 2896.573 2898.457 2900.278 2902.068 2852.455 2855.093 2857.723 2860.293 2862.827 2865.323 2867.776 2870.187 2872.563 2874.878 2877.195 2879.409 2881.614 2883.777 2885.904 2887.983 2890.004 2891.993 2893.944 2895.857 2897.727 2899.556 2901.390 2852.922 2855.532 2858.110 2860.648 2863.156 2865.608 2868.056 2870.421 2872.755 2875.062 2877.316 2879.532 2881.712 2883.844 2885.941 .00001 -I0.005 0.004 "ooolo '0.000 no.0‘5 ‘500001 'I0.000 0.002 ~0.016 00.005 900002 60.005 0.009 0.003 0.00? .00006 v0.019 00.003 U0.008 "00007 "0.009 00.001 «0.001 0.006 .00006 00.005 90.005 .0000: .06000 0.007 0.010 98.905 60.019 I0.010 .0000, '.00005 '0000‘ I"0.000 0.076 0.058 0.047 0.036 0.030 0.022 0.045 0.025 0.016 0.020 0.013 0.008 0.010 0.004 0.004 .--.---------Q-------,--.--0---.-‘C---..-_--.---.--.--------C “HOCDCN°<3.2NH3‘3F9NH‘..CDCHU\afiua‘3QIOH‘CDCMO'“C’GV“'~C~U°..FHD¢3“‘CHNC3CH°63C3CH=C3UH“‘ic’ C3FH‘F‘HW‘CNOCDCNDCMO€3CMO¢3CHDCWOIDCMD*‘FW‘CWOGDCHDCDCHDCIOW:CMDCJOW‘"HDCDFM‘CDFWDCNO9‘ ‘0133'B1TU‘D1T‘1D19‘1.1V?‘U1rfi1fl1lV‘D1IV‘DITV‘I1IV‘D1YV‘D1IU‘DTJU1U1YV1D1T‘1I1I‘1U1T‘1917U 'M‘iNri‘ini‘flGDOWDCIOMDCIOHIIbOMDGIOJDCbOHILIUHO\IUNU\IUNI\DUIUHIUNU\IUIUHIUIUL§lb.h.lb.ub 2886.956 2888.994 2891.006 2892.958 2894.856 2896.721 2850.238 2852.871 2855.475 2858.048 2860.568 2868.049 2065.509 2007.910 2870.278 2872.601 2874.070 2877.127 2079.820 2001.470 2003.590 2885.667 2887.698 2889.709 2891.644 2090.060 2895.424 2097.209 2859.044 2861.524 2863.964 2866.357 2868.727 2071.045 2073.324 2075.557 2877.759 2879.894 2662.021 2884.098 2606.126 2000.122 2090.071 2091.904 2893.852 2887.238 2859.719 2862.157 20.4.55: 2866.900 2869.248 2871.497 2878.788 '90813 .80809 0.011 0.013 0.001 "90990 '0.002 “0.027 "90036 "80936 00.036 "00091 .0003; "°0088 '00012 "°.918 "°0°11 '-0.013 .0000: '00008 '0.004 '00091 "°0°°6 "00812 0.012 "D0083 0.012 0.001 "0.009 ”00087 ‘.00007 .00086 “90012 0.000 0.001 0.002 0.006 "°0913 .00990 0.004 0.001 0.007 0.006 0.011 0.013 "°0003 0.010 0.013 0.014 0.007 0.041 0.015 0.021 83C)GHMt‘CHQCDCM08‘CDaNDCS:HU\NCDUHDNIUHUCSHHDF‘CMDCDCMOIDCIfluacaNF“‘icuflt‘fiuficaflflo‘MCMocac3 I‘0193101rfi1lIrv‘01F'1D1Tt‘01rt‘91r‘1l1FU‘u1IIPD1DIrU‘D1rt1n1rt‘fl1rt‘01!t1u1r‘1019t‘01rt‘n ~6~ru~6~ru~6~low)Ihouhahouhahouhabowpa»ocrauu~nunauruxlunu\nunaumuxlunaunuua~nausarglpa.b ...O..-.C.--...O--...-.-......--.--C-.-------........ . 1°CDCH3CM°¢3CHDCMD..FW3FH‘CWDO.CHDCMOCDCHDCMO.‘CHOF‘FW‘HHDCWOCDCMDCHDCMDC)CW3CHDC¥°C3C) 2887.983 2890.004 2891.983 2896.909 2895.792 2897.698 2899.442 2851.564 2854.165 2856.753 2859.289 2861.819 2869.255 2866.728 2869.098 2871.435 2876.734 2876.026 2878.223 2880.888 2882.564 2884.637 2889.693 2888.697 2890.689 2892.606 2094.504 2896.836 3857.780 2860.293 2862.752 2865.171 2867.551 2869.888 28720189 2879.471 7 2876.678 2878.838 2880.972 2883.067 2885.130 2887.129 2889.103 2891.006 2892.928 2894.758 2858.481 2860.944 2863.353 2865.740 2868.055 2870.350 2872.598 28790824 "0.007 0.001 0.008 0.006 .00086 0.009 500002 ~I0.055 I0.051 00.046 00.055 60.028 00.027 10.014 I0.017 '00021 00.028 0.010 .00011 60.028 0.017 60.004 I0.002 00.010 0.012 '0.001 0.009 .00005 90.016 -60.003 I0.006 '0000‘ .0080; 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