Vibrational Spectrum and Harmonic Force Field of Trimethylphosphinet

Raman spectra of both the -do and -d9 species in the liquid state, as well as the infrared spectrum of the perdeuterated species, and reconsidered the...
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J . Phys. Chem. 1990, 94, 4820-4831


Vibrational Spectrum and Harmonic Force Field of Trimethylphosphinet D. C. McKean,* G. P. McQuillan, Department of Chemistry, University of Aberdeen, Aberdeen AB9 2UE, U.K.

W. F. Murphy,* and F. Zerbetto Division of Chemistry, National Research Council of Canada, Ottawa, Canada K I A OR6 (Received: October 16, 1989; In Final Form: January 3, 1990)

Infrared and Raman spectra are reported for the isotopic species trimethylphosphine-do,-d3,-d6, and -d9, including ”C frequency shifts for the -do, -d6, and -d9 isotopomers. Fermi resonances affect a number of bands; these cases were analyzed to obtain unperturbed fundamental frequencies. The a2 and e torsional frequencies in the gas phase for the -do species were predicted from combination and difference band information. The molecular geometry and harmonic force field were calculated ab initio by using a 6-31G** basis set, and the force field was fit to the harmonized I2C frequency data by use of I O independent scale factors. This force field predicts well most of the I3C frequency shifts and greatly assists the detailed assignment of asymmetric methyl deformation and methyl rocking modes. The fit to all observed frequencies was further improved by varying 20 diagonal force constants and 1 1 off-diagonal ones, to yield a final force field.

Introduction Accurate knowledge of molecular potential energy surfaces has been obtained in recent years by combining spectroscopic data and a b initio calculations. This information is usually expressed in terms of the force constant matrix and is the starting point for comprehension of the dynamical behavior of the molecule, both isolated and in association with other molecules. It is perhaps surprising that such an investigation has not yet been undertaken in detail for the classical organometallic ligand, trimethylphosphine (Me3P). One problem has been that there is some doubt regarding some vibrational assignments for the gas-phase molecule; for example, the inactive methyl rocking frequency has only recently been located.’ There is an extensive literature on the vibrational spectroscopy of Me3P; pre-I970 vibrational studies were summarized by Park and Hendra2 and Durig et aL3 By that time, a molecular structure had been obtained from microwave and electron diffraction measurements, and measurement of the infrared spectrum of the gas and the Raman spectrum of the liquid for the -do species had provided data for calculation of the harmonic force field. However, these early analyses were later shown to be based on some incorrect vibrational assignment^.^^^ Park and Hendra2 measured the Raman spectra of both the -do and -d9 species in the liquid state, as well as the infrared spectrum of the perdeuterated species, and reconsidered the vibrational assignment. Durig et aL3 measured the far-infrared spectrum of both solid and gaseous Me3P, as well as the Raman low-frequency spectrum of the solid, to obtain information about the methyl torsional transitions and also the skeletal deformation modes. The torsional frequency assignments were later revised on the basis of measurements of Raman spectra of the low-temperature annealed solids, for both the -do and -d9 compound^.^ During this same period, a microwave study was carried out to reconsider the molecular ~ t r u c t u r e the ; ~ axis of the methyl group was found to be tilted with respect to the PC bond, and the CH, bond, trans to the phosphorus lone pair, was determined to be 0.022 8, longer than the other two methyl C H bonds (designated CH,). However, the size of the difference found is too large when compared with the 0.01 3-A C H bond length difference for trimethylamine (Me3N),6 where the lone-pair trans effect is much stronger. A later study of the isolated C H stretching frequencies in (CHD2),P7 predicted a 0.004-8, bond length difference (CH, > CH,) for Me3P. Ab initio calculations with a 4-31G basis set, although fairly successful in reproducing the observed bond length difference for Me3N,*could duplicate neither the frequency nor the bond length difference for Me,P,’ and, in fact, predicted the bond length variation to be the opposite of that

found from the frequency correlation. Very recently, the microwave spectrum of Me,P has been remeasured and used to rederive the molecular g e ~ m e t r y . ~In this analysis, the methyl C H bonds were assumed to be equivalent. The Me3P harmonic force field has recently been derived by scaling the a b initio force field calculated at the RHF/6-31G* level.’o In this work, the approach of Blom and Altona” and Pulay et al.I2 was followed in that a minimum number of scale factors, namely three, were used to adjust the ab initio force field to fit the literature experimental frequencies. In this respect, that resultlo should be considered as an effective force field, since anharmonic contributions have not been eliminated from the frequency values. The detailed Me3P force field was not reported in this work, which was concerned with the calculation and comparison of frequencies and some force constants for a range of substituted phosphines and phosphine oxides and sulfides. In the present work, we report infrared and Raman spectra for a number of Me,P isotopomers. We have added to the existing frequency data for the parent Me,P molecule and three deuterium substituted species ((CHJ2CD3P, designated as -d3, CH,(CDJ2P, designated as -d6,and the perdeuterated-d9 isotopomers), and also present new data on I3C frequency shifts for the (I3CH,),P, ’3CH3(CD3)2P,and (13CD3)3Pspecies. We calculated a quadratic force field at the 6-31G** level of theory and scaled it to fit the harmonized vibrational frequencies (see below). Several Fermi interactions were also treated to obtain unperturbed frequencies for use in the fit. The unusually large number of frequency data now available for this molecule, combined with its high symmetry, permits us to investigate different scaling criteria for the a b initio force field. We believe that the conventional scaling approach,”J2 where a minimum number of scale factors are used, is the safest when dealing with observed frequencies for a single isotopic species. However, if anharmonicity, including Fermi resonance, can be properly taken into account for several isotopic species, a more detailed refinement of the force constants is, in our opinion, both (1) McKean, D. C.; McQuillan, G. P. Spectrochim. Acta 1983, 39A, 293. (2) Park, P. J. D.;Hendra, P. J. Spectrochim. Acta 1968, 2 4 4 2081. (3) Durig, J. R.; Craven, S. M.; Bragin, J. J . Chem. Phys. 1970, 53, 38. 32A, (4)519, Rojhantalab, H.; Nibler, J . W.; Wilkins, C. J. Spectrochim. Acfa 1976,

(5) Bryan, P. S.;Kuczkowski, R. L. J . Chem. Phys. 1971, 55, 3049. (6) McKean, D.C. J. Mol. Struct. 1984, 113, 251. (7) McKean, D. C.; McQuillan, G. P. J . Mol. Struct. 1978, 49, 275. ( 8 ) Goddard, J. D. Can. J . Chem. 1982,60, 1250. (9) Bell, S . , University of Dundee, personal communication, 1989. ( I O ) Schneider, W.; Thiel, W.; Komornicki, A. J . Phys. Chem. 1988, 92, 5611. ( 1 I ) Blom, C. E.; Altona, C. Mol. Phys. 1976, 31, 1377.

*To whom correspondence should be addressed. ‘Issue as NRCC No. 31 396.

( 1 2 ) Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. SOC.1983, 105, 7037.

0022-365419012094-4820$02.50/0 0 1990 American Chemical Society

Spectra of Trimethylphosphine justified and useful. The force field determined in this way should be closer to the true harmonic potential than that calculated by scaling only. This paper is organized as follows: we first give experimental details and then outline the quantum chemical methods. In the succeeding section we discuss the spectral assignment and Fermi resonances. Then we report and discuss the harmonization procedure and the force field calculations, and finally we present our conclusions.

Experimental Section Samples were prepared by adding (isotopically labeled) methyl iodide to phosphine in a KOH/Me,SO ~ 1 u r r y . l ~The mixed isotopic species were obtained by combining the appropriately labeled methyl iodide and dimethylphosphine by means of the same reaction. I n some samples, the presence of trace methanol or dimethylphosphine impurities could be detected. This was most noticeable for the 13Csamples and caused problems in measuring 13C frequency shifts for several bands. Infrared spectra in the gas phase were recorded for the most part on a Nicolet 7199 FTIR spectrometer at a resolution of 0.25 or 0.12 cm-I. However, for the gaseous-d6 sample, and for all the solid spectra, the instrument used was a Perkin-Elmer Model 225 with a spectral slit width of about 1 cm-I. The solid-phase spectra were obtained by deposition on a CsI window cooled to 78 K, with subsequent annealing. In some cases, as noted in the table of results, solid solution spectra were recorded for isotopically dilute mixtures, in order to avoid crystal splitting effects which occur for some bands in the pure samples. For the Raman spectra, liquid samples were sealed in Pyrex capillaries which were mounted transversely to the directions of incidence and observation. Spectra were recorded at room temperature, except that if bubbles occurred at the laser focus, the samples were cooled to about -5 OC by a stream of cold nitrogen to inhibit boiling. The instrument was a Spex 14018 double monochromator with a cooled RCA C31034 photomultiplier and a Spex Datamate digital data acquisition system. The spectral slit width was about 2 cm-I, and two or three scans were accumulated at a sampling time of 1 s/point. Spectra were excited by about 300 mW of radiation at 514.5 nm. Parallel and perpendicular polarized components of the Raman spectra were recorded. Wavenumber shift and spectral sensitivity corrections were applied, and the trace (isotropy) and anisotropy scattering spectra were obtained from the polarized components in the usual way.I4 The reported wavenumber shifts are values of band maxima and are estimated to be accurate to about f0.7 cm-' for sharp bands in the trace spectra and to f 2 cm-' for the broader anisotropy scattering bands. The presence of laser discharge lines permitted a more accurate determination of I3C frequency shifts: up to fO.l cm-l in favorable cases. For some overlapping bands, such as the skeletal deformations in the -d3 and -d6 spectra, resolution enhancement techniquesI5 were applied to obtain consistent estimates of the individual band positions. The -d9 sample was contained in a large bore capillary, so that we could observe vapor-phase Raman spectra at the room temperature vapor pressure. The measured band positions are included in the table of results; they compare well with the infrared results for corresponding bands. Some preliminary Raman spectra of the I2C samples were measured on Cary 83 and Spex Ramalog spectrometers. The reported -d3 and -d6 C H / C D stretching frequencies are taken from spectra measured on the latter instrument. Method of Calculation The ab initio calculations were carried out at the RHF/6-31G** program"' The molecular level Of theory16 using the ( I 3) Jolly, W. L. Inorg. Synth. 1968, I I , 124. (14) Scherer, J. R.; Kint, S.; Bailey, G.F. J . Mol.Spectrosc. 1971, 39, 146. ( 1 5 ) Kauppinen, J. K.; Moffatt, D. J.; Mantsch, H. H.; Cameron, D. G. Appl. Spectrosc. 1981, 35, 271. (16) Francil, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S . ; Defreis, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. Harihan P. C . ;Pople. J. A . Theor. Chim. Acta 1973, 28. 213.

The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4821 TABLE I: Internal Coordinates and Equilibrium Geometry of Trimethylphosphine (Bond Lengths in A, Angles in degrees) coord descripn indexesa ab initiob expc expd R PC str 2-4 1.8526 1.843 f 0.003 1.845 CH, str 5-7 1.0866 1 . 1 12 f 0.005 8-13 1.0852 1.090 f 0.010) 6 CPC def 2-4 100.145 98.9 f 0.2 98.99 H,CH, def 8-13 107.564 108.2 f 0.8 H,CH, def 108.578 109.4 f 0.4) 5-7 PCH, def 5-7 112.605 1 11.4 f 0.2 1 1 1.62 PCH, def 8-13 109.689 109.8 f 0.4 109.14 i Me torsionC 2-4


{ {

Indexes for bond stretching coordinates according to atom number (Figure I ); for deformation coordinates according to appropriate bond coordinate indexes. bThis work. Reference 5. Five-parameter geometry from ref 9. eTorsion coordinates defined as in ref 19.

Figure 1. Molecular configuration of trimethylphosphine with the atom labeling used in this work.

geometry was optimized by minimizing the total molecular energy within the constraint of C,, symmetry. The symmetry constraint was then relaxed and the minimum energy conformation was located starting from a geometry slightly perturbed from the structure previously found. The calculation converged again to the C3, geometry, which indicates that this is a stable energy minimum for Me3P. The structural parameters so determined are presented in Table I. The a b initio harmonic force field was calculated at the optimized geometry and transformed from Cartesian to symmetry coordinates by using the method previously described.l* The B matrix relating the internal coordinates to the atomic Cartesian coordinates was also calculated from the a b initio optimized geometry; the vibrational symmetry coordinates, which transform according to the irreducible representations of the C,, molecular point group, are displayed in Table 11. The deformation coordinates correspond to standard methyl group coordinate^,'^ orthogonal to the redundancy conditions. However, the CH, and CH, stretching internal coordinates were kept separate, in order to facilitate our study of their behavior in the vibrational problem. Since a b initio R H F force fields overestimate normal-mode frequency,'* we scale the ab initio force field by multiplying each force constant matrix element,& by the scale factor product spj. The scaled force constant matrix is used to calculate the vibrational frequencies with the standard FG matrix formulation,20and the scale factors are varied to yield the best agreement with the harmonized frequencies. This approach is equivalent to the conventional procedure,16 but the resulting scale factors must be squared to compare them with results reported by others. (17) Dupuis, M.; Spangler, D.; Wendoloski, J. J. NRCCSoftware Catalog, Proeram OG01. Lawrence Berkelev Laboratorv. Livermore. CA. 1980: Vol. I . Schmidi, M.; Elbert, S.; Lam, B.-GAMESS User's Guide; N. Dakota State University, 1987. (18) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig, J. R., Ed.;Elsevier: New York, 1985; Vol. 14, pp 125-219. (19) Shimanouchi, T.; Matsuura, H.; Ogawa, Y.; Harada, I. J . Phys. Chem. Ref. Data 1978, 7 , 1323. (20) Wilson, Jr., E. B.; Decius, J. C.; Cross, P. C . Molecular Vibrations, McGraw-Hill: New York, 1955.


The Journal of Physical Chemistry, Vol. 94, No. 12, 1990

McKean et al.

TABLE 11: Symmetry Coordinates for Trimethylpbosphine



sym CH, str sym CH, str sym PC str Me sym def

Me asym def’ Me rock’ sym PC3 def

asym CH, str Me asym def” Me rock” torsion ex

S12= 6-’l2(2r7- r s - r 6 ) SI,= 1 2 - ’ / ~ ( 2 r-~rlI , - r I 2 2rlO- r9 - r 8 ) SI4 = 2-’(rI1 - r12 r9 - ~ 8 ) SIs = 6-1/2(2R4- R2 - R,) S I 6 = 0.165(2a1 - a5 - a 6 ) + 0.173(2a13- a l la12 + 2010 - a9 - ag) - 0.166(287 - /35 - 8 6 ) 0.161(281, - 011- 812 + 2P10 - P9 - 88) SI7 = 0.338(2a7 - as- a 6 ) - 0.162(2a13- a l la12 + 2 a 1 0 - a9 - a 8 ) SI8 = -2-’(aIl - (YI2 + a9 - as) si9 = O.330([email protected] 85 - 86) - 0.170(2/31, 812 + 2P10 - 8 9 - 08) s20 = 2-’(PIl - PI2 + P 9 - 88) S21= 6-1/2(264- a2 - 6,) S 2 2 = 2-1/2(~2 - 13)

asym CH, str sym CH, str asym CH, str asym PC str Me sym def

= 2-’/’(r5 - r6) = 2-l(rIl - rI2- r9 + r8) S25 = - 1 2 1 / ~ ( 2 r ~-,rlI - r 1 2- 2r10 + r9 r8) s 2 6 = 2-1/2(R2- R,) s 2 7 = 0.286((~5 - (Y6) + 0.299(all - a12- a9 + as) - 0.288(P~- P6) - 0.279(811- 812 - 0 9 +

asym CH, str sym CH, str asym CH, str asym PC str Me sym def



s23 S24




= 0 . 5 8 6 ( ~ ~-5ag) - 0.280(all - a12- a9 + as) = 12-1/2(2a13- all - a I 2- 2 a l o + a9 + a s ) S,o = O.571(p5 - 86) - O.2%(8,1 - 812 - 89 + @g) S,I = -12-1/2(2813- f i l l - PI2- 2ol0 + 09 + BE) s32 = 2 4 4 a 2 - 6,) s 3 3 = -6-’/*(274 - ~2 - 73) s2g S29

Me asym def‘ Me asym def” Me rock’ Me rock” asym PC, def torsion

Me asym def’ Me asym def” Me rock’

Me rock” asym PC, def torsion

Displacement coordinates; the deformation coordinates have been implicitly normalized by a length of 1 A, to maintain consistent units. The internal coordinates are labeled according to the indexes given in Table I. *The methyl asymmetric deformation and rocking coordinates are identified according to their a’ or a” transformation properties with respect to the methyl group uu symmetry plane (see text). Standard deviation estimates for the scale factors were calculated from the variance of the fit.21

Results: Assignment of the Spectra The symmetry of Me3P is described by the C,, molecular point group (see Figure 1). The structural parameters are given in Table I, where the ab initio calculated structure is compared with the structure recently determined in a study of the microwave spectrum9 and the results of a previous microwave study.s Within the C3, group, the 33 normal vibrations transform according to 7al + 4a2 + 1 le. In the following, we shall use parentheses to denote the molecular symmetry of the various modes, Le., (al), (a2), (e). In addition, it will be convenient to describe the symmetry behavior of some modes with respect to the u, symmetry plane of each methyl group: this is denoted by brackets, i.e., [a’], [a”]. In particular, the (e) species contains both [a’] and [a”] asymmetric C H stretching (vas), asymmetric methyl deformation (21) Clifford, A . A. Mulrivariafe Error Anolysis; Applied Science: New York, 1975.







3300 3100 2900 ‘2300 2100 CM-’ Figure 2. Infrared spectra in vapor phase: (A) (I2CH3),P(3300-2750 cm-I); (B) (I2CD,),P (2300-1900 cm-I).

(b,,(Me)) and methyl rocking (p(Me)) vibrations, while the (al) and (a2) species involve only vibrations of type [a’] and [ a ” ] , respectively. Selected infrared spectra are shown in Figures 2-6, and the Raman spectra of the -d3and -d6 species are displayed in Figures 7 and 8. In Tables 111-VI we list the frequencies of the bands observed in the spectra of -do, -d3,-d6, and -d9 isotopomers. Also included are frequency shifts observed upon isotopic substitution of 12Cby 13C. We discuss the assignment, as far as possible, in terms of gas-phase absorption spectra, so that we may describe the vibrational properties of the isolated molecule by the force field calculation. When necessary, we also refer to the absorption spectra of the solid sample and the Raman spectra of the liquids, where frequency shifts are applied, if required, to account for intermolecular interaction effects on the condensed phase spectra. In the following, we shall discuss the assignment of isolated fundamental bands in the various regions of the spectrum and then consider the decoupling of Fermi resonance interactions as well as the attribution of hot bands. CH (CD) Stretching Modes. These spectra, shown for -do and -d9 in Figure 2 , are virtually independent of the number of CH3 or CD3 groups present, so that the coupling between methyl groups must be weak. We can thus assign the bands in this region according to the local methyl group vibrations. The symmetric C H stretch is involved in a Fermi interaction and will be considered later. In the previous study of the isolated C H stretching frequencies of the (CHD2)3Pspecies,’ the shorter CH, bond is shown to have a higher frequency than the CH, bond. This means that the [a”] v,(CH,) band, which involves only the two CH, bonds, will occur at a higher frequency than the [a’] one. The band at 2976.1 cm-I was thus assigned as the [a”] component and the 2962.2-cm-I band as u,,(CH,)[a’]. The latter band has more parallel character, in keeping with this assignment. Similarly, the bands at 2229.9 and 2219.0 cm-I in the -d9 spectrum are the [a”] and [a’] uas(CD3)bands, respectively. Methyl Asymmetric Deformation Modes (6,,(Me)). Two well-defined bands are seen in the methyl deformation region of the infrared spectra of both the -do and -d9 species (see Figure 3). The higher frequency band, at 1442.1 (1051.4) cm-l in the -do (-4) spectrum, has more parallel character and can be assigned with confidence as va,(CH3)(al). The lower band at 1430.0 (1044.6) cm-I is accompanied by a less defined shoulder at 1414.5 (1033.6) cm-I; these two features are due to the two (e) modes, which must then be designated according to [a’] and [a”] local symmetry. In the partially substituted species, a similar pattern is found in the 6,,(CH3) region of -dgand the 6,,(CD3) region of -d6. In each of these latter cases, a fourth peak is also observed, which may be the (a2) mode which becomes allowed under lower symmetry. Moreover, the two other 6,(Me) modes in these lower symmetry species are observed for S,,(CH,) of -d6 at about 1430 cm-I, split by 4 cm-l, and for 6,,(CD3) of -d, at about 1040 cm-I, split by 4.9 cm-I. For the detailed assignment of these bands, we have turned to the unscaled ab initio force field, which predicts that the (al) mode

The Journal of Physical Chemislry, Vol. 94, No. 12, I990

Spectra of Trimethylphosphine

TABLE 111: Vibrational Spectrum of Trimethylphosphine (CH3)3P(I infraredb assignment





3260 vw 3231.7 vw, 11 3181 3168 sh 3 157.4 vw 3148.5 vw 3143 sh 2976.1 vs 2962.2 vs 2902.9 vs, 11

-I5 15.4 -IO

2852.1 m 2837 m, bd 2826 m 28 19.9 m, )I 2703.0 vw 2557.8 vw 1442.1 s, 11 1430.0 s, bd 1414.5 sh 1361 vw 1312.0 m


2846 w, bd

2.4 12.0 20 2.4 2.9 2

2810 s 2714. 2686 2543 1431.5 ss 1428 ss 1413.5 ss 1360 m 1312 m, ss 1303.8 vw 1295.5 ss 1276.5 ss

1298.4 m,11 1283.8 m 1225 vvw 1134 w -1015 sh 969.6 m, 11 965.6 m, 11 961.6 m 952.5 sh, I( 949.5 vs, 11 947.9 vs, 11 939.3 vs 907 sh 828.1 vw 708 vs 654.9 vw,

10.0 9.7 3.6

-0.3 9.3


2963.5 vs 2953.5 vs 2897 vs

2965 s 2955 s 2893.0 vs 2867 w 2842.5 w 2824 w

8.4 10.5 3.9

2810.5 m


1435.5 tr, vw 1421 an, w


1307.4 tr, vw


1293.7 tr, w 1277.5 an, vw

0.0 7


1016 vw 5.7 5.6 6.2

993.5 vw

992 tr, vw


961 s, bd

948.1 tr, w


944.5 vs

938 an, w



834.1 w, 831.1 w 719.6 vw 736 vvw 709 ss 682 vvw 667 vvw 654 w 649 vw 307 w w

828 an, vw


707.3 an, m


653.4 tr, vs


302.2 tr, w 261.3 an, m

4.5 4.8




3263 vw 3238 vw 3195 vw, bd 3172 sh





298< 255‘

‘Frequency data (in cm-’) from infrared spectrum of gas phase, ug, and crystalline, uC. samples, and Raman spectrum of liquid sample, u1. Frequency shifts, Au, are reported for the I3C isotopic species. Fundamental and overtone transitions are assigned according to the principal vibrational symmetry coordinate; combination bands are labeled according to the fundamental frequencies involved. Fermi resonances are identified by lines connecting the interacting levels. Abbreviations used: s, strong; ms, moderately strong; m, medium; w, weak; v, very; 11, parallel band; sh, shoulder; bd, broad; ss, bands observed in isotopic solid solution (these regions have significant structure in the pure crystal spectrum); tr, trace scattering; an, anisotropy scattering. Weak bands between 1440 and 2300 cm-I, which were not used in the assignment, have been left out of the table. CReference3.

clearly has the highest frequency of the four modes in the -do and -d9 species, and that the (e)[a”] mode falls significantly higher than the (e)[a’] mode. However, the calculated splittings in the 6,,(CH3) modes of -d6 and the 6,,(CD3) modes of the -d3 are smaller than observed, with the [a”] mode only slightly higher than the [a’] one. The possibility of an alternative assignment was checked in an empirical force field calculation wherein the magnitudes of the two (e) 6,(Me) principal force constants were reversed compared to the ab inito prediction. The calculated frequencies did not agree at all with the observed ones; for example, the splittings for 6,,(CH3) -d6 and 6,,(CD3) -4 were found to be over 10 cm-I compared to the observed values of 4-5 cm-I. Both the scaled and the semiempirical force fields reproduce well the preferred assignments given in Tables IV and V. Methyl Symmetric Deformation Modes ( & ( M e ) ) . The 6,(CH3)(al)modes are strongly affected by Fermi resonance in the -do and -d3 species, as discussed below. On the other hand, the solitary b,(CH3) band at 1290.2 cm-I in the -d6 species appears to be unperturbed. The 6,(CD3)(a,) modes and the G,(Me)(e)

modes and their (a’) and (a”) counterparts in the lower symmetry species may all be easily identified as indicated in the tables. Methyl Rocking Modes (p(Me)). For the methyl rocking mode assignment, we are again guided by the a b initio force field which indicates that the (e)[a”] modes should be higher in frequency than the (e)[a’] ones. These (e) modes in the -do and -d9 species and all the p(Me) bands in the lower symmetry -d3 and -d6 species can be identified with no particular difficulty, except for the -d6 p(CD,)(a”) mode, which probably underlies the stronger PC stretching band at 603 cm-l in the liquid Raman spectrum (Figure 7). In the -do spectrum the p(Me)(e) modes are identified as 939 cm-’ [a”] and 828 cm-’ [a’], and the p(Me)(az) mode may be observed in the crystal spectrum at 779.6 cm-l (Figure 4). The latter assignment was proposed earlier’ and has been confirmed in the more recent ab initio study.I0 However, an explanation for the complicated structure in the 900-970-cm-’ region, including the p(Me)(a,) band, will be deferred until later. The p(CH3)(a,) bands in the lower symmetry species and the p(CD3)(al) bands may be identified as indicated in the tables. In the -d3 species,


The Journal of Physical Chemistry, Vol. 94, No. 12, 1990

McKean et al.

TABLE IV: Vibrational Spectrum of Trimethylphosphine (CHI)K D P infrared Raman assignment C H 3 ) [a”] Vns(CH,) [a‘] us(CH3) 26ns(CH3) 6as(CH,) + 6,(CH,) 26SCH3) va,(CD,)la”I uas(CD,) [a’] us(CD3)

2826.5 s 2721 vw


207 1.4 w


7 3

26ACD3) 6,,(CH,)(a‘)[a’] 6,,(CH3)(a’)[a”] 6,,(CH3)(a”)[a”] 6,,(CH3)(a”)[a’] 716 + 620

~,~’c~,~:a8.‘,“” 3 674 + 618(a’)

6,(CH&a”) impurity? 6,,(CD3)(a”)[a”] 6,,(CD,)(a’)[a‘] 6,(CD,) dCH&a’) P ( CHI) (a’) p ( C H 4 (a”) p(CH&a”) uas(PC,)(a”) u,,(PCp)(a’) p(CD3)(a’)[a’] 292 216 + 166(a‘) Me3P-do impurity d C D W ’ ) [a”] u,(PC,)(a‘) &,(a‘) a,k(a‘) 6,k(a“)



2905 2607 vw 2229 ms 2219.1 s 2122.5 s,


1996.5 w, q 1437.2 s, 11 1430 sh 1426 s, bd 1412 sh 1304 m 1293 s 1284 m 1280 sh 1044.4 m 1039.5 m 1010.5 s, 11 942.0 s 913.5 s 887.0 s 816.5 w 717.5 s 687.3 s 674.0 s

618.0 w



2965.0 vs 2953.5 vs 2897 vs 28 15 ms 2690 vw, bd

2976.3 vs 2962.3 vs

2550 vw 2220.0 ms 2214.3 ms 2114.3 s 2060.5 w

2967 2956 2894 2820

m. bd m, bd vs w

--2220 m, bd 2115 vs 2063 w

2050 sh 1986.5 w 1433 sh 1424 s 1412 sh 1334 w 1306.8 w 1287.3 ms

1988 w 1425.6 tr, vw 1421 an, m ,

1304 tr, vw, sh 1289.5 tr, w 128 1 an, vvw












500 CM-’

Figure 3. Infrared spectra in vapor phase: (A) (”CHg),P; (B) (’,CD&P ( 1 500-550 cm-I).

1273.2 m 1034.8 m, bd 1032.8 m 1005.3 ms 947 vs 912.5 vsb 892.6 s, 888.0 sb 821 m 716.0 vs 687.3 sh 679.5 msb 675.3 sh 648 vw 619.6 m 292 vw

1086 tr, vw 1038 an, vw 1005.6 tr, w 940.2 tr, vw 908.7 tr, vw 884.5 an, vw 816.7 an, vw 714.5 an, m 686.8 tr, m 673 an, ah 652.8 tr, w 647.8 an, w 617.7 tr, vs 288.7 tr, w 253.6 an, m 239.4 an, m

‘See footnote to Table Ill. No I3C substituted sample was avilable for this isotopic species. b T h e spectrum of the isotopically diluted sample includes features a t 917 sh, 912 w, 891.5 w, 880.0 m, and at 689.5 m, 687 m, 679.5 w, and 675.5 sh.

four of the rocking modes each include significant contributions from both [a’] and [a”] symmetry coordinates. For these modes, this designation is dropped in Table V. PCStretching Modes (u(PC3)).In the -do and -d9 species, the oa,(PC3)(e) modes can be identified as listed in the tables, but the identification of u,(PC3)(a,) modes for the -do species is complicated by additional bands in this region, as discussed below. For the -d9 species, u,(PC3)(al) could only be observed in the Raman spectrum of the liquid. In the lower symmetry -d3 species, the three u(PC3) modes are easily identified (Figure 8, Table IV), as is the v,(PC,)(a’) mode in the -d6 (Figure 7, Table V). However, the two u,(PC3) modes in -d6 lie close together and can be more easily identified by consideration of the crystal spectrum, as discussed below. Skeletal Bending (ask) and Torsional Modes. The &,(al) and SSk(e)modes for the -do species were assigned with confidence in the earlier study of the gas-phase absorption s p e c t r ~ m .These ~ assignments are confirmed by the I3C shifts found here for the liquid-phase Raman spectra; these spectra also yield the Ask modes for other isotopic species. In the Raman study of low-temperature condensed-phase spectra of -do and -d9,4 the (e) and the (az) torsions were located at 225 (158) and 210 (152) cm-’, respectively (-d9frequencies in parentheses). We shall discuss below the use of combination band information to estimate the gas-phase torsional frequencies.

i )I


, , 700 CM-’ Figure 4. Infrared spectra of annealed polycrystalline films a t 78 K of (I2CHJ3P: (a) thick film, (b) thin film. I








,\Jl ,


Infrared Crystal Spectra and Crystal Structure. As far as we are aware, no crystal structure has been determined for solid Me3P. From their study of the low-temperature phase, Rojhantalab et aL4 proposed that crystalline Me3P is isomorphous with Me3PS, which has two molecules in the unit cell on C, sites. This assumption is consistent with features in the infrared spectrum observed here, as displayed for the -do species in Figure 4. For example, we observe p(CH3)(a2)in the spectrum of the -dospecies, due to the lowered site symmetry. Also, there are two main peaks associated with G,(Me)(a,) in both the -do and -d9species, whereas the extra structure in this band for the -dospecies, shown in Figure 4, is not observed for the -d9 species. In addition, the S,(Me)(e) and ua,(PC3)(e) bands are split, as seen in the figure. In the spectrum of a 3% solid solution of -do in -d9,all of these features collapse into single bands. The same is true for the uas(PC3)band in -d9,when observed in a -do matrix. This suggests that these splitting are primarily due to the factor group. Since the (e) modes are not split in the dilute matrix, one might conclude that the site symmetry should be higher than C,. However, the partially deuterated species provide a more sensitive probe of the site symmetry. The nondegenerate C H 3 rocking modes near 900 cm-I are split in both the -d3 and -d6 pure solid and in the solid solution. This can only be explained by a site symmetry, lower than C3, which produces two types of methyl

The Journal of Physical Chemistry, Vol. 94, No. 12, I990 4825

Spectra of Trimethylphosphine TABLE V: Vibrational Spectrum of Trimethylphosphine CH3(CD3)2P“ infrared assignment Vas(CH,) [a”] Vas(CH3) [a’]



2976.0 s 2962.1 vs 2903.0 s 2829.4 m 2229.0 s 2219.2 vs 2122.1 vs, 2075.2 m 2073.6 m 2069.3 m 1995.5 m 1991.8 m 1430.4 m 1426.4 m


A% 9.9 9.6 3.46 4.7 0 0 0

Raman 2964.5 s 2954.5 s 2896.0 vs 2820 m 2220.8 s 2214.3 s 21 15.4 vs

2965 m, bd 2956 m, bd 2895 vs 2818 m

2058 w, bd

2061 vw

8.1 0.4 0.1 0.2

893.7 s


764 s

1 .o

711.1 ms


665.2 s 640 sh



0.0 6.2

{ -604 vw -600 vvw

1986 vw 1423 w, bd

1023.5 w 1008.3 ss, s 1001.6 ss, s 912 ss, w 906 ss, sh 900.5 ss, w 895 ss, w 768.0 vs 735.6 vw 713.4 vs 693 vw 671.1 666.3 vs 642.3 w 629 vw 620vw 611.4 sh

1285.6 tr, w 1038.7 an, w

8.6 0.7

1008.8 tr, m 1003.2 an, w 902.3 tr, w

0.2 0.2 6.2

893.9 an, vw


761.5 tr, vw

605.7 m. 604.2 m

709.2 tr, w 692.4 tr, w 666.1 tr, w 665.1 an, m 642.4 an, w

4.5 -0 6.9

603.0 tr, vs


273.4 tr, vw 242.5 an, m 224.4 an, m

1.7 2.9 0.7

-0.8 337 vw, bd 276 vw 243.5 vvw

4,(a‘) Ma“) &,(a‘) ‘See footnote to Table Ill Crystal-phase value.

2219 m, bd 21 14 vs

1995 vw 1984 w 1421.4 mw 1417.9 ms 1411.6 w 1285.6 m 1040.6 ss, ms 1035.3 ss, ms

0 0 2.3 2.5

1290.2 m 1048.7 m 1044.2 m 1041.5 s 1032.8 1013.8 s 1007.7 s 904.9 vs




I3C shifts were also measured for the crystal spectrum, and are available from one of the authors (D.C.M.).

groups. Furthermore, the additional structure in the -do &(Me) bands near 1300 cm-l may mean that there are more than two molecules per unit cell. Nonfundamental Transitions and Fermi Resonances. The identification of the well-defined fundamental frequencies, as presented in the preceding paragraphs, provides a basis for the assignment of multiple quantum transitions and the perturbation of fundamental levels through Fermi interaction. In particular, the presence of several low-lying torsional and skeletal vibrational levels means that hot bands can be expected. Torsional Modes. The occurrence of sum and difference transitions provides information for estimating the location of the torsional transitions. Since methyl torsional frequencies increase markedly on going from the gas phase to the solid,22+23 the band frequencies found in the solid4 must be reduced appropriately for consideration of combination transitions in the gas-phase spectra. For example, within the complicated structure in the 970900-cm-’ region of the -do species (Figure 5 ) , we have already identified the p(CH3)(e) band at 939.3 cm-’. The p(CH3)(al) band is expected at somewhat higher frequency. The observed spectrum consists of a pattern of six prominent narrow Q branches, accompanied by other weak ones, a pattern that is repeated in the I3C spectrum, shifted 6 cm-I to lower frequency, except that (22) Groner, P.; Durig, J. R. J . Chem. Phys. 1977, 66, 1856. (23) Durig, J. R.; Griffin, M. G. J . Chem. Phys. 1977, 67, 2220.



O’ 980


7 -




9’00 CM-’

Figure 5. Infrared spectra in vapor phase of (I2CH,),P and (I3CH,),P, 990-900 c d .

there is no I3C counterpart of the I2C band at 952.5 cm-I. There are two binary levels which can give additional parallel (a,) bands in this region. One of them is vs(PC3)(al) 6,k(al), predicted at 953 cm-I. From the ab initio force field, this transition should have a I3C shift of some 21 cm-’, and it could therefore be assigned to the “disappearing” 952.5-cm-I band in the ‘*C spectrum. The second binary level is p(CH3)(a2) t(CH3)(a2),which should fall at about 775 + 190 = 965 cm-l. Here, we have reduced the



4826 The Journal of Physical Chemistry, Vol. 94. No. 12, I990

McKean et al.

TABLE VI: Vibrational Spectrum of Trimethylphosphine (CD,),PQ Raman


-~ assignment




2360 w, bd 2229.9 ms 2219.0 s. 11 21 22.0 s, 11 2082.5 w 2071.0 w 2065.6 w. 11 2045.4 vw 2029.5 vw 1993.8 w, 11 1051.4 ms, 11 1044.6 ms 1033.6 ms 1016.8 s

14.8 14.6 8.1 -6.5 8.7 7.8

-263.3 3.5 -3 13.9

1007.6 s


838.0 w, 11 787.8 vw, 11 783.5 ms, )I 758 s 646.0 m 624.8 sh 614sh

11.6 7.9 7.0 6.9 7.3 6.0

2220 s 2214 ms 2115.6 s 2070 w. bd

2219.3 2121.7

2057 w 1983 mw 1049 ms 1037 m 1033 sh 101 1.2 ms, 1009.5 ms 1004.3 s, 999.8 s 996.7 vs, 989 vw 840.0 vw, 836.5 sh 813.5 w, 810 sh 786.5 ms, bd 729.9 vvs 646.5 ss. s 628 7 m




2221 s 2218 s 21 14.9 vs 2081 w



2057 w


2020 w 1983 w


1038.3 an, w


1012.4 tr, m


1001.7 an, w 783.5

778.8 tr, vw 754 an, w 646.4 an, m 624 an, sh

6 5 7.6 -3


593.8 v w

592.2 253.6 215.4

592.3 tr, vs 257.7 tr, w 220.9 an, w

10.3 1.4 2.4

Osee footnote to Table 11. The Raman spectrum was also observed for this species in the gas phase, as described in the text.

solid-state frequencies by 4.5 and 20 cm-’ to estimate the gas-phase values. This transition has a predicted I3C shift of 5 cm-I, similar to that predicted for the p(CH3)(al) fundamental, and is thus a plausible assignment for one of the observed Q branches. Thus, if we choose the observed bands at 965.6 and 949.5 cm-’ as the principal Q branches due to the p(CH3)(a2) + t(CH3)(a2)overtone and the p(CH,)(a,) fundamental, respectively, which interact via Fermi resonance, we can make rough estimates ( f 5 cm-l) of 960 and 956 cm-I for the unperturbed frequencies. (There is no evidence for Fermi interaction involving the us bsk level.) This would mean that the (a2) torsion lies at 185 f 5 cm-I. This identification is supported by the solid-phase spectrum (Figure 4). Here the bands at 944.5 and 961 cm-I are clearly due to p(CH3)(e) and p(CH3)(al). The weak band at 993.5 cm-I is the combination p(CH,)(a2) t(CH3)(a2),as predicted from solidstate frequencies of the two fundamentals (779.6 210 = 989.6 cm-I). The Fermi interaction between this combination and p(CH,)(a,) is greatly reduced, so that the essentially unperturbed p(CH3)(al) in the solid is about 5 cm-I higher than our estimate of the decoupled gas-phase value (956 cm-I). This gassolid shift is consistent with that found for p(CH3)(e): 5.3 cm-’. The remaining Q branches in the gas-phase spectrum which disappear in the solid spectrum may be due to hot bands of the (e) torsion, whose upper level must also be involved in Fermi interactions. From the prediction of the gas-phase (a2) torsional frequency of 185 f 5 cm-I, we could expect the (e) torsional mode to fall near 200 cm-l in the gas phase. This allows us to identify the weak parallel band at 1225 cm-l as 6,,(CH,)(e) [a”] - t(CH,)(e), which yields a prediction of 205 cm-I for the (e) torsion. These assignments are supported in an analysis of the combination bands in the 3100-3300-cm-’ region (Figure 2). The two bands at 3231.7 and 3260.0 cm-I undergo a 13Cshift of about 15 cm-’. which reveals the involvement of hsk modes: v,,(CH,)[a”] + bSk(e)= 3231 cm-’; v,,(CH,)[a’] + &,(a,) = 3260 cm-’. The shifts of these two bands to high frequencies on going to the solid is consistent with the larger increase in the bsk frequency compared to the smaller decrease in that of v,,(CH3). The broad feature centered at 3 I76 cm-I in the gas-phase spectrum has a I3C shift of roughly 1 1 cm-’ and must stem from v,,(CH,) + t(CH,) combinations. The Q branches at 3 181.7, 3 168.0, and 3 157.4 cm-I t(CH,)(e), vasare most easily identified as v,,(CH,)[a”] (CH3)[a’] + t(CH,)(e), and o,,(CH,)[a”] + t(CH,)(a,), which




leads to predictions, by band frequency differences, that the (e) torsion is 205.6 and 205.8 cm-’ and the (a2) torsion is 181.3 cm-I. These may be taken as reasonable estimates of the fundamental frequencies, since the anharmonicities of such combination bands are expected to be On the basis of this information, we therefore place the (e) and (a2) torsions in the gas phase at 206 f 1 and 182 f 3 cm-I, respectively. A fourth Q branch at 3148.5 cm-I is possibly a hot band of an (e) torsional level. From the frequencies in the solid spectrum, t(CH,) bands corresponding to those identified the v,,(CH,) in the gas-phase spectrum are predicted to occur at 3188, 3178, and 3174 cm-I. The broad band in the solid spectrum at 3195 cm-l has a shoulder but no other lower frequency features; this further supports the above hot band assignment for the gas-phase spectrum. For the -d, species, a combination band at 788 cm-I may be identified with u,,(PC,)(e) + t(CD,)(e), yielding a predicted (e) torsional frequency of 142 cm-’. This value does not compare well with the force field prediction of 149 cm-I (see below), which is not surprising for an anharmonic torsional mode. PC Stretching Modes. The infrared band near 650 cm-’ in the -do spectrum, due to v,(PC,), has a Q branch whose structure differs for the I2C and I3C species (Figure 6). If the highest frequency component of each Q branch is taken to be the fundamental, a shift of 15.8 cm-] is found; this differs significantly from the shift of 16.7 cm-’ found in the liquid-phase Raman spectrum. I f the Q-branch structure is taken to be due to hot bands, this behavior could be rationalized by attributing the highest frequency component in the I3C spectrum to the hot band from the (e) torsion. The upper level of this transition, v,(PC3) + t(e) (844 cm-l) is in weak resonance with the p(CH3)(e) fundamental at 821.4 cm-l. This would explain why the liquid-phase I3C shift is lower for vs(PC3): the torsional frequencies rise markedly in the condensed phase, leading to a reduced perturbation of the upper level of the hot band, since it is further separated from the interacting fundamental than in the gas phase. In the -d6 species, the (a’) and (a”) va,(PC3) modes almost coincide. The infrared band at 665.2 cm-l in the gas phase does not shift on I3C substitution, so it is clearly the (a”) mode. Also,




(24) Winther, F.;Hummel, D. 0.Spectrochim. Acta 1969, 25A. 417,425.

Spectra of Trimethylphosphine

The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4827

1% I


660 650



640 630 CM-’

IO cm-’

Figure 6. Bands due to u,(PC,) in (12CH3)oP and (13CH3)3P.

Figure 8. Raman spectra in the liquid phase of (CH,),CD,P: (top) trace, (bottom) anisotropy spectra. For display purposes, the intensity scale of the anisotropy spectrum is expanded by 1OX with respect to that of the

trace spectrum.


L )r VI




00 400 600 800 1000 1200 1400 cm-’ Figure 7. Raman spectra in the liquid phase of CH,(CD3)2P (top) trace, (bottom) anisotropy spectra. For display purposes, the intensity scale of the anisotropy spectrum is expanded by 30X with respect to that of the

trace spectrum. the Raman trace band at 666.1 cm-’ in the liquid must have (a’) symmetry. These bands are both observed in the infrared solid spectrum: a weak band at 671.1 cm-I and a stronger one at 666.3 cm-l undergo 13C shifts of 9.5 and -0.8 cm-I, respectively. This indicates that the two motions are coupled in the lower symmetry crystal environment. Methyl Symmetric Deformation Modes. For the -do species, a conspicuous resonance is observed in the spectrum of the I2C species near 1300 cm-’ (Figure 3) between 6,(CH3)(al) and 2v,(PC3). The observed gas-phase frequencies are 1312.0 and 1298.4 cm-I. In the corresponding I3C species, u,(PC3) shifts appreciably to reduce the interaction, so that the overtone 2us(PC3) can then be seen only in the liquid-phase Raman spectrum. To estimate an unperturbed frequency, 6;(CH3)(al), we assume that it coincides with the overtone 2v:(PC3). Then we find the unperturbed frequency to be 1305 cm-I, with a Fermi interaction parameter of 6.8 cm-’. A Fermi resonance also affects the 1293-cm-’ G,(CH3)(a’) band in the -4 species, where the interacting level is u,(PC3)(a’) u,,(PC3)(a’), as seen from the intensity of the combination band in the trace Raman spectrum. However, the combination band frequency is nearly the sum of the related fundamental frequencies so we taken the observed frequency to be that of the unperturbed fundamen tal.


CH and CD Stretching Modes. The upper levels of the u,(CH,) bands are involved in the ubiquitous resonance interaction with 26,,(CH3) levels. Since the various 6,,(CH3) fundamentals are split, as discussed earlier, it is most convenient to analyze the resonance shift from the data for the -d6 species. In this case the average of the two 6,,(CH3) modes is 1428.4 cm-I, which leads to an estimated unperturbed 26,0(CH3) frequency of 2846.8 cm-I, if we allow IO cm-I for the effect of anharmonicity. From the observed overtone frequency of 2829.4 cm-I, the resonance shift is then 17.4 cm-’ and the uncoupled u,(CH3) fundamental frequency is 2885.6 cm-I. These frequency values correspond to a Fermi resonance interaction parameter of 31.3 cm-I, which may be compared to the value of 34 cm-I in CH3CLZ5 The overtone 26,(CH3) is expected at 2570.4 cm-I, but was not observed. It is not expected to affect v,0(CH3) by more than 4 cm-I, so we adopt 2882 f 5 cm-’ as the unperturbed frequency. This value agrees with that previously found.’ We perform a similar analysis of the -d3spectrum to obtain v?(CD3). Here, both 26,(CD3) (2071.4 cm-I) and 26,(CD3) (1996.5 cm-’) are observed. If we again use the average 6,,(CD3) frequency (1042.0 cm-I), and assume anharmonicity contribution of 7 cm-’ to both 26,,(CD3) and 26,(CD,), the two overtones contribute shifts of 5.5 and 17.2 cm-I, respectively, to the fundamental vs(CD3). The resulting value of u:(CD3) is then 2100 f 5 cm-l. Since there is little evidence of coupling between the C H stretching modes on different methyl groups, we have used these values as unperturbed v?(CH3) and u:(CD3) frequencies for all of the I2C isotopic species. Fundamental frequencies for the -do, -d3,-d6,and -d9 isotopic species of Me,P are presented in Table VII. Where only condensed-phase data are available, appropriate shifts have been applied to obtain estimates of the gas-phase frequencies. The I3C frequency shift data were taken from infrared or Raman measurements, or an average of the two, depending on our assessment of the relative accuracy of the two results.

Results: Force Field Calculations Harmonization. The determination of a molecular harmonic force field is complicated by the fact that the band positions observed in the vibrational spectra correspond to the anharmonic frequencies. If vibrational data for only one isotopic species are used, the determination of an effective harmonic force field from the observed frequencies is possible,i8 whereby, to a first approximation, the anharmonic effects are absorbed into the quadratic terms. However, if vibrational data are available for several isotopic species, this procedure is not satisfactory. In such ( 2 5 ) Bensari-Zizi, N.; Alamichel, C. J . Mol. Specfrosc. 1983, 99, 98.


McKean et al.

The Journal of Physical Chemistry, Vol. 94, No. 12, 1990

TABLE VII: Observed, Harmonized, and Calculated Frequencies for Trimethylphosphine (in cm-')'' ( "CHd3P U



2962.2 3085.6 2882* 3002.1 1442.1 1486.7 1305* 1331.6 956* 956 654.9 654.9 298 298 a2 2976.1 3100.1 775 182


775 182


0.8 -5.9 5.7 3.5 -3.3 -2.4 -0.9 -1.0 (1463.7) -4.0 0.6

9.7 0.7 2.4 -8.0 2.4 -2.6 8.5 1.7 -0.6 7.8 -3.0 16.7 0.7 4.5 -2.0 (1469.0) -1.7 -3.6 0.6 12(CH3)2CD3P EA1



2976.3 2962.3 2882. 2219.1 2 I oo* 1437.2 1430 1294* 1039.5 1010.5 942.0 913.5 687.3 674.0 618.0 284.2 249. I

3100.3 3085.7 3002. I 2287.6 2163.0 1481.6 1474.2 1320.4 1062.7 1026.6 942.0 913.5 687.3 674.0 618.0 284.2 249.1





2962.1 2882* 2229.0 2219.2 2100* 1426.4 1290.2 1048.7 1044.2 1013.8 904.9 764 711.1 666 603 268.9 219.9

3085.5 3002.1 2297.9 2287.8 2163.0 1470.5 1316.5 1072.2 1067.6 1029.9 904.9 764.0 71 1 . 1 666.0 603.0 268.9 219.9


a , 2219.0 2100* 1051.4 1016.8 783.5 592.2 253.6 a2 2229.9






2.2 -5.1 -0.9 4.0 1.9 -0.3 1.8 3.9

1.7 -7.7 0.3 2.2 1.8 1.2 0.9 3.0 -0.1 0.6 -2.8 --2.0 -2.3


-1.3 -3.6 -3.1 -5.6 8.9 2.3 -1.2 2.4 (149.7)

( "CD,),P w 2287.5 3.3 2163.0 1.7 1074.9 4.8 1032.9 -1.5 -0.6 783 5 592.2 3.2 253.6 -1.7 2298.8 2.8 (1059.4) (583.4) (1 29.0)


0.1 0.0 1.3 (149.4)




10.5 2.6 2.6 8.9 7.8 16.7 4.5

10.6 3.8 2.3 9.3 8.4 16.3 4.1 11.2 2.8 4.3 0.1


AWSE 11.1 3.4 2.4 8.9 8.2 16.5 4.1 11.2 2.9 4.3



1.6 1.9 -1.2 0.6 3.4 0.4 -0.9 2.0 (1063.3) 581.6 129.0)

(I3CD,)3P AU A U A ~ 14.6 15.5 16.1 5.3 3.3 3.4 3.5 14.3 14.8 15.2 7.0 7.0 7.3 10.3 10.3 10.3 1.4 1.4 2.1 15.8 3.5 4.2 AY


( I'C H ,),P fSE




10.0 10.9 2976.1 3100.1 -2.7 -0.7 10.5 3.0 2.4 9.7 2962.2 3085.6 2.4 2.6 2882* 3002.1 -4.7 -7.6 2.9 3.1 1430 1474.2-1.4-1.1 -2.1 1414.5 1458.2 -7.0 -0.3 -2 1283.8 1310.0 2.3 1.7 9.3 9.7 939.3 939.3 -0.1 -1.0 9.4 9.4 828.1 828.1 1.3-3.0 5.0 5.0 708 708 -2.0 -1.3 14.4 14.4 1.0 -1.4 4.8 4.8 255 255 206 206 -1.2 -0.9 "(CH,)2CD3P



-2.5 --0.5 1.7 1.4 -5.5 -7.9 4.2 2.2 I .8 2.0 4.8 2.0 -0.2 -0.7 -1.1 -2.5 -0.1 -1.4 -2.1 -1.2 -5.4 -3.5 3.8 3.3 -4.1 -1.5 3.3 0.3 1.6 0.3 -1.1 0.3 1.9 -1.1 (206.9) (206.5) 13CHJ(CD3)2P AU AW AwA1 AwsE 9.6 10.4 10.7 1 1 . 1 3.9 3.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5 2.7 2.6 2.6 8.1 8.8 9.5 9.2 0.4 0.4 0.0 0.0 0.1 0.1 0.0 0.0 0.1 0.1 0.0 0.0 6.2 6.2 6.4 6.3 1.0 1.0 1.2 1.1 4.8 4.8 5.6 4.9 7.7 7.7 6.4 7.4 1.7 1.7 1.9 1.9 1.7 1.7 1.7 1.7 0.7 0.7 0.7 0.7 0.1 0.1




16.2 5.1 3.5 14.8 7.3 10.6 2.1 15.8 3.5 4.2 0.1


11.2 11.2 3.4 2.6 2.7 9.4 8.9 4.8 14.5 5.0 0.4





3100.3 3085.7 3002.1 2297.8 1470.1 1455.6 1306.1 1067.6 887.0 816.5 717.5 644.0 234.9

-1.4 3.1 -4.7 -0.1 1.9 -9.5 -I .6 2.6 -1.7 I .2 -1.2 4.7 2.8 (1 9 1.4) (I41 .O)

-1.4 2.4 -7.6 0.5 -1 .o -3.0 -2.1 I .2 -2.3 - I .7 1.3 1.4 1.5 (191.2) (140.9)







2976.0 2229.0 2219.2 2100* 1430.4 1041.5 1032.8 1007.7 893.7 665.2 640

3100.0 2297.9 2287.8 2163.0 1474.6 1064.8 1056.0 1023.8 893.7 665.2 640.0

PW 10.8 0.0 0.0 0.0 2.5 0.2

6.6 0.0 0.0

6.6 0.0 0.0


-1.2 0.8 2.7 1.9 1.6 -0.1 -0.6 -0.9 1.3 3.2 1.6 (603.3) -0.4 (199.1) (134.1)

9.9 0.0 0.0 0.0 2.3 0.2


-2.2 1.0 4.9 2.2 3.2 2.2 -4.8 -2.0 1.3 2.2 0.7 (600.8) 2.2 (199.4) (134.1)






14.8 14.6

15.7 15.5

(12CD3),P AwsE


11.2 10.7 3.9 2.6 2.7 9.6 8.9 4.7 14.2 5.1 0.2

2976.3 2962.3 2882* 2229 1426 1412 1280 1044.4 887.0 8 16.5 717.5 644 234.9

I2CH3(CD,)2P a"





2229.9 2219.0 2100* 1044.6 1033.6 1007.6 758 646.0 624.8 215.4

2298.8 2287.5 2163.0 1068.0 1056.8 1023.7 758.0 646.0 624.8 215.4

0.0 4.6 2.2 -0.2 -3.9 -1.6 1.3 1.8 8.0 1.4 (149.1)


11.2 0.0 0.0 0.0 2.7 0.0 0.0 0.0 6.6 0.3 0.0 0.0 2.5 0.1 0.0


11.2 0.0 0.0 0.0 2.7 0.0 0.1 0.1 6.7 0.3 0.0 0.0 2.4 0.1 0.1

(13CD,)J' 1.2 2.4 1.9 0.1 0.6 -0.1

2.2 2.8 1.2 -0.1 (148.9)

3.5 3.7 3.0 3.1 14.8 15.3 6.9 6.9 7.4 7.4 6.0 6.0 2.4 2.4


16.2 16.0 5.3 3.7 3.7 15.9 7.3 6.9 6.1 3.0 0.2

16.2 16.1 5.2 3.7 3.9 15.4 7.2 7.5 6.0 2.9 0.2

'' For the I2C isotopic species, Y and w denote the observed and harmonized frequencies, respectively. The asterisk denotes modes which have been decoupled from Fermi resonances (see text). Error vectors (calc - obs) are given for the two reported force fields: CAI. scaled a b initio force field; eSE, semiempirical force field. For unobserved bands, the calculated frequencies, in parentheses, replace the error values. I3C shifts are given for the observed ( A u ) and harmonized ( A w ) frequencies, and for the frequencies calculated from the two force fields, AwAI and AwSE.

cases, the typical result for motions involving hydrogens is that X H frequencies are calculated higher than observed, while X D

ones are calculated too low. For a molecule as large as trimethylphosphine, it is clearly not possible to estimate the an-

The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4829

Spectra of Trimethylphosphine harmonic force field from either analysis of experimental spectra

or by a b initio calculation. In such a case, empirical corrections for anharmonicity may be made by using Dennison’s rule:26 the harmonic frequencies of corresponding modes of two isotopomers, w and w’, are related to the observed frequencies, u and v’, by w = u/(l

- x),


= v‘/(l - x ?


where x’ = u ’ x / u

An approach which has met with some success in the application of this procedure to cases of molecules containing C H bonds is to associate harmonization factors, x, with certain types of internal coordinate motion: C H stretching, 0.04; C H deformation, 0.02; and skeletal stretching, 0.01-0.01 5.27 The recent determination of harmonic frequencies for the CH31 molecule permits the verification of such factors in this case, as follows:28 C H stretch, x, = 0.043, x4 = 0.047; C H 3 deformation, x2 = 0.027, x5 = 0.035; C H 3 rock, x6 = 0.014; CI stretch, x3 = 0.027 (the indexes refer to the usual normal mode numbering). These are on the whole somewhat larger than those previously used and show variations for the CH stretch and deformation motions. Since similar data are not yet available for CD31, the isotopic relation for Dennison’s rule (eq 2, above) cannot be verified for this case. However, previous demonstrations of the utility of this approach for several molecules (e.g., ethane,29ethylene,30acetonitrilet7) provide some confidence that it can play a useful role in the determination of a harmonic force field. For the present case, harmonization factors were selected after noting the effect of such corrections to the observed frequencies on the fit of the semiempirical force field. In the end, we applied harmonization corrections to C H stretching modes (x = 0.04) and CH3 deformation modes (x, = 0.02, x,, = 0.03). It was clear that different values were required for the symmetric and asymmetric deformation modes, as found from the CH31 results,2s but in contrast to the previous approach.27 We decided not to apply such corrections to methyl rocking modes: such motions are most highly coupled to skeletal stretching ones here, particularly in the deuterated species, and the relevance of the isotopic relation (eq 2) becomes especially doubtful in such cases. Also, from the CH31 results, it appears that the factor for methyl rocking motions would be smaller. For similar reasons, we made no corrections to PC stretching frequencies. It should be noted that the harmonization procedure is most relevant when the frequencies concerned vary significantly on isotopic substitution. Otherwise, the effect of the anharmonic shift can be taken into account on a numerical basis through a change in the harmonic force constants. The set of harmonized frequencies used in the fitting procedure are listed in Table VII. The success of the Dennison rule corrections can be gauged by comparing how well the harmonized frequencies obey the Redlich-Teller product rule,20compared to the behavior of the observed ones. If the frequency product rule is used to verify the validity of the harmonization procedure (see Table VIII), the effect of low-lying vibrations such as skeletal bends and methyl torsions must be taken into account. Experimental errors in the frequencies of such modes, due to difficulties in observing the bands in the spectrum, lead to disproportionate errors in the frequency products. Thus, while the deficit in the a l -do/-d9observed frequency product ratio is 4.2%, that for the e symmetry vibrations is only 3.5% even though there are four additional hydrogen motions involved. Furthermore, the product ratio for the harmonized -do/-d9e frequencies is larger than the theoretical value, a clearly unacDennison, D. M. Rev. Mod. Phys. 1940, 12, 175. Duncan, J. L.; McKean, D. C.; Tullini, F.;Nivellini, G . D.; Perez . J . Mol. Specrrosc. 1978, 69, 123. Duncan. J. L.: Ferauson, A. M.; Mathews, S. J . Chem. Phys. 1989, 91,‘783. (29) Duncan, J. L.; Kelley, R. A.; Nivellini, G . D.; Tullini, F. J. Mol. Specrrosc. 1983, 98, 87. (30) Duncan, J. L.; Hamilton, E. J . Mol. Srrucr. 1981, 76, 65.

TABLE V I I I Isotopic Product Rule Ratios ( R ) and Deficits (A)#for Various Isotopic Species of Trimethylphosphine, As Calculated from Theory, and from Observed and Harmonized Frequencies a, R

e A. 7%


d,/d, ( W theory 5.337 12 5.11360 -4.2 obseried harmonized 5.293 10 -0.8

e Rb

A. %

18.704 61 18.04224 -3.5 19.02307 +1.7

A. %

13.446 59 12.43689 -7.5 13.11299 -2.5


1.06278 theory 1.06342 observed harmonized 1.06383

1.079 78

1.077 82 1.07666 -0.108 1.077 20 -0.050

1.088 38

1.087 17 1.08131 -0.54 1.08225 -0.45 a” A, %

0.0065 0.100

I2C/”C (d,)

1.06494 theory observed harmonized a’ d3/& (I2c) theory observed harmonized


A, %


2.807 40 2.72746 2.778 58

-2.8 -1.0

4.77246 4.54245 4.721 66

-4.8 -1.1

Ratio reduced by removal of torsional a A = 1 OO(R,,,, - Rthmry)/Rtheary. frequencies (see text).

ceptable situation since a residual (negative) deficit is expected from the contributions from methyl rocking and the skeletal modes, which were not harmonized. When the product ratio is reduced by removing the torsional frequencies (the theoretical value was multiplied by frequencies calculated from the scaled ab initio force field), the resulting deficit is much more acceptable. Another indication of susceptibility to errors in low-frequency values is the positive deficit for the a , I2C/l3C (-do)product ratio. Here, the large I3C shift observed for the skeletal bend cannot be reproduced by either calculated force field (see below). The adopted harmonization procedure is of value in that it permits a more precise replication of the harmonized frequencies by the vibrational force fields. The validity of the correction procedure is supported by the reduction found for the product rule deficits (Table VIII), compared to the product ratios for the observed frequencies. Residual deficits are expected from the nonharmonized methyl rocking and skeletal motions, but could also be due to problems with the harmonization procedure itself, especially for the C H stretching vibrations. Scaled ab Initio Force Field. Our approach to the force field determination is to scale the calculated a b initio force field, by means of the procedure described earlier, to fit the harmonized frequencies. The large number of data for various isotopically substituted species has permitted a more extensive scaling analysis than normally undertaken. We have experimented with various approaches to scaling, whereby we have obtained optimum fits to the -do, -d3,-d6, and -d9 harmonized frequencies for the I2C isotopic species. We then confirmed the suitability of the resulting scaled force field by comparing frequencies calculated for the I3C species with those determined in the harmonization analysis. In scaling the a b initio force field, all frequencies included in the fit were given equal weight. Assigning an equal percentage uncertainty to each frequency was also tried; essentially the same results were obtained for the two fits. In our initial efforts, we used scale factors associated with each of the six types of internal coordinate: C H and PC bond stretching, CH2, PCH, and PC2 deformation, and methyl torsion. The resulting calculated frequencies were characterized by a separation of the symmetric and asymmetric methyl deformation modes which was consistently about 15 cm-’ less than observed. Since the &(Me) coordinates include contributions from both CH2 and PCH deformation internal coordinates, an improved fit was achieved when we associated scale factors with the seven different types of symmetry coordinates: C H and PC bond stretching, methyl symmetric and asymmetric deformation and rocking, PC2 deformation, and methyl torsion. On investigation, we found that

McKean et al.

4830 The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 TABLE IX: Scale Factors for the ab Initio Force Field type of SYm coord index scale factor sym coord I . 12, 23 0.9438 f 0.0006 CH, str 2. 8. 13, 14, 24. 25 0.9505 f 0.0004 CH, str 3 PC str ( a , ) 0.9465 f 0.0032 0.9368 f 0.0028 15, 26 PC str (e) 4, 16, 27 0.8948 f 0.0009 methyl sym def 5, 9, 17, 18, 28, 29 0.9221 f 0.0006 methyl asym def 6, 20, 31 methyl rock 0.8810 f 0.0019 I O , 19, 30 methyl rock 0.8975 f 0.0021 7 . 21, 32 0.9604 f 0.0050 PC3 def 1 I . 22. 33 methyl torsion 0.9357 f 0.0120

further improvements in the fit could be achieved by using separate scale factors for the following types of symmetry coordinates: CH, and CH, bond stretching, P C (al) and PC (e) bond stretching, and for methyl rocking coordinates divided according to the amount of steric interaction between adjacent methyl groups during the rocking motion. In the final result, the members of each of these pairs of scale factors differ by more than their combined standard deviation estimates. Thus, I O scale factors associated with various symmetry coordinates, as presented in Table IX, were used to determine our preferred, scaled a b initio force field for trimethylphosphine (Table X). The mean deviation for the 98 fitted frequencies was found to be 3.44 cm-I. This force field was then used to predict I3C frequency shifts for the -do,-d6,and -d9species, which are included in Table V I I I . in a detailed assessment of the calculated frequencies, we note that the calculated symmetric C H 3 stretches are consistently -5 cm-I higher than the harmonized values, while the corresponding CD3 frequencies are some 2 cm-' too low. These deviations could be due to an inadequate harmonic correction, although they are within the likely errors of the Fermi resonance analysis. The poor reproduction of the I3C shifts for these modes is probably due to similar effects. In contrast, however, the I3C shifts for the asymmetric methyl stretching modes are reproduced to within 0.5 cm-' . The need for separate scale factors for the CH, and CH, stretching coordinates is demonstrated by comparing the isolated C H stretching frequencies observed for (CHD2j3P7with those calculated, as shown in Table XI. The single C H scale factor

calculation predicts a difference of 19.4 cm-' between the two bands compared to the observed value of 35.5 cm-I. Thus, separate CH, and CH, scale factors are required to compensate for a deficiency in the a b initio calculation which produces a too-small C H force constant difference. A similar effect could explain the small C H bond length difference (0.0014 A) compared with the 0.0036-A value predicted from the frequency correlation dependence.6 It will be interesting to see whether the ab initio geometry and force field can be improved when it becomes feasible to include electron correlation in the calculations. I f we examine the fit of the lower frequency modes, we find a few instances where the results are less satisfactory: the (e) band observed at 1414.5 cm-' in -do and that observed at 624.8 cm-l in -d9 (but note that both of these occur as shoulders in the spectra), and the (a') band a t 666 cm-l in -d6. Problems in the calculation of I3C shifts could possibly be due to failure to take weak Fermi interactions into account. However, the poor results for the I3C shifts of the G,(CD3)(e) mode of -d9 (1007.6 cm-I, observed) and the 6,(CH3) mode of -d6 (1 290.2 cm-I, observed), as well as the adjacent modes of -d6 at 71 1 and 666 cm-l, were a concern. The latter -d6 discrepancies must be due to difficulties in properly describing the coupling between the coordinates involved, which has the largest effect for this isotopic species where these modes are closest in frequency. This small number of discrepancies out of the 98 calculated frequencies emphasizes the satisfactory overall fit obtained from the scaled a b initio force field. In particular, the ordering of the methyl asymmetric deformation modes and the methyl rocking modes, which was a concern of an earlier paper.' has been confirmed. Semiempirical Force Field. In considering the results of any scaled a b initio force field, it must be remembered that the selected scaling procedure is an empirical treatment to account for basis set deficiencies and other effects such as omission of electron correlation from the a b initio calculation. Thus, the potential for achieving an improvement over the scaled a b initio force field must be kept in mind. I n the present case, such an improvement was sought by refining the diagonal force constants. except for the torsional ones, in an empirical force field fitting procedure of all of the frequency data, including the 13Cfrequency shifts. At first, off-diagonal force constants were held fixed to the scaled a b initio force field values; later, selected ones were allowed to vary in the fit, to try to achieve an improvement in the agreement between

TABLE X: Quadratic Force Field for Trimethylphosphine (in aJ A-2)' a , block l 2 3 4 I 5.0946 5.2664 2 0.045 I 3 0.0888 0.0590 3.0857 4 0.0688 0.0938 -0.2293 0.5048 5 -0.1027 0.0760 -0.0235 0.0061 -0.0698 -0.0292 0.0066 6 0.075 1 7 -0.0980 0.0792 0.3313 -0.0406 a, block 8 9 8 5. I825 9 0.1333 0.5559 IO 0.0833 0.0035 II 0.0073 -0.01 1 I e block 12 13 14 15 16 17 12 5.0743 13 0.0520 5.2585 0.0041 5. I937 14 0.0050 I5 0.0205 0.0466 0.0236 2.9493 0.0991 -0.0049 -0.1990 0.4862 16 0.09 I 2 17 -0.1086 0.0809 -0.0043 -0.0186 0.0061 0.5532 18 0.0050 -0.0020 0.1383 -0.0068 -0.001 1 0.0009 19 0.0331 -0.0477 0.0095 0.0560 -0.0018 0.0066 20 0.0028 -0.0085 0.1083 -0.0443 0.0082 -0.0032 0.0185 -0.02 I9 0.0686 -0. I455 0.0263 -0.0023 21 22 0.0044 -0.0030 0.0052 0.0048 -0.0012 0.0020



0.5628 0.01 27 -0.0179 IO

0.5092 -0.2607


1.3738 11

0.4238 -0.0 I 4 I 18



0.5644 -0.0003 0.0058 -0.0038 -0.0079

0.4762 0.0289 0.1 134 0.0109

0.4976 0.2465 -0.0143

0.0601 21

1.0719 0.0338



"6-31GS* force field scaled by symmetry coordinate factors in Table IX (see text). Elements given in terms of the symmetry coordinates of Table 11.

Spectra of Trimethylphosphine TABLE XI: Isolated CH Stretching Frequencies (in cm-') for Trimethylphosphine. Comparison of Observed Frequencies with Those Predicted from Scaled ab Initio Force Fields calculated with single C H separate CH5, str scale factor CH, str scale factors observed" WCH,b 3053.7 3038.5 YCH, 293 1 .6c 2917.OC 2919.0 d 3074.0 3080.1 *CH, PCH. 295 1 .Oc 2956.9c 2954.5 Aue 19.4 39.9 35.5 OReference 7. bAverage of a, and e C H stretching frequencies for (CH,D2),P molecule of C,, symmetry. "Deharmonized" frequency: u = 0 . 9 6 ~ . dAverage of a and e C H stretching frequencies for (CH,D2),P molecule of C3 symmetry. Frequency shift: Au = uCH, "CH,.

the calculated and harmonized observed frequencies. There were minor differences in the numerical procedure, compared to that used to determine the scaled ab initio force field, in that the a , and e, blocks were refined separately from the a2 and eyones, due to the organization of the fitting program. Also, well-determined frequencies were assigned 1% uncertainties, as to offset any problems in previous work from our lab~ratories,~' in anharmonicity corrections for higher frequency modes. We found that when eleven off-diagonal force constants were varied from their scaled a b initio force field values, a significant improvement in the overall frequency fit was obtained. Of these 1 1 force constants, four occur in the a , block and seven in the e block. Since the e, and ey blocks were refined separately, small differences were found for the latter force constants, always well within the calculated dispersion. The average e, and ey results are reported in Table XII, and the frequency error vector and shifts are included in Table VII. The mean deviation in the frequency fit of the 98 12C frequency values is 2.54 cm-' compared to the value of 3.44 found for the scaled a b initio force field. We note in particular the significant improvement in reproducing the I3Cshifts and absolute frequencies of the -d6 and -d9 species which caused problems for the scaled a b initio force field. All of the off-diagonal constants fitted in the semiempirical force field involve at least one of the skeletal PC stretching or PC3 deformation coordinates. Further, these elements include the largest off-diagonal ones in the force constant matrix. It appears that the selected scaling procedure for the a b initio force field has the most difficulty with such force constants; a possible explanation is that force constants involving skeletal motions have been found to be most sensitive to electron correlation effects in the a b initio c a l c ~ l a t i o n . ~ lThus, - ~ ~ allowing such elements to vary from the values determined in the scaling procedure could be a valuable approach when difficulties occur in the fit. (31) Cough, K. M.; Murphy. W. F.; Raghavachari, K. J . Chem. Phys. 1987, 87, 3332.

(32) Guo, H.; Karplus, M. J . Chem. Phys. 1988, 89, 4235.

The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4831 TABLE XII: Semiempirical Harmonic Force Field for Trimethylphosphine Expressed in Symmetrv Coordinates (in aJ A-*Y ~

block element 1 9 1

292 3,3 4,4 5,5 66 7,7 83 939 10,lO 12,12 13,13 14,14 15,15 16,16 17,17 18,18 19,19 20,20 21,21

value element value 5.1290 f 0.0370 394 -0.2489 f 0.0091 5.2389 f 0.0380 -0.0349 f 0.0226 3,6 3.0870 f 0.03 12 397 0.3394 f 0.0436 0.5095 f 0.0033 -0.2488 f 0.0200 6,7 0.5692 f 0.0037 0.51 13 f 0.0095 1.3390 f 0.0421 5.1858 f 0.0313 0.5601 f 0.0061 0.421 1 f 0.0040 5.1101 f 0.0314 15,16 -0.21 86 f 0.0068 5.2342 f 0.0323 0.0788 f 0.0082 15,19 5.1864 f 0.0263 15,20 -0.0491 f 0.0127 2.9672 f 0.0259 15,2l -0.2158 f 0.0504 0.4893 f 0.0030 0.0939 f 0.0405 16,21 19,21 0.5473 f 0.0030 0.0820 f 0.0176 0.5649 f 0.0031 20,21 0.2773 f 0.0186 0.4826 f 0.0028 0.4927 f 0.0087 1.1316 f 0.0441

OElements not given were constrained to the scaled a b initio force field values in Table X. The e block elements are the average of the values found in the separate a' and a" calulation (see text).


A nearly complete set of infrared and Raman vibrational frequency data has been measured for the -do,-d3,-d6,and -d9 isotopic species of trimethylphosphine, as well as 13Cdata for the -do, -ds, and -d9 species. Empirical anharmonic corrections have been applied to produce estimates of the harmonic vibrational frequencies for each of these species. A vibrational force field analysis was carried out on the basis of this frequency data. First, the RHF/6-31G** a b initio force field was suitably scaled to reproduce the harmonic frequencies of the I2C isotopic species. This scaled a b initio force field was then further improved by varying the diagonal force constants and selected off-diagonal force constants to fit the harmonic I2C and tbe I3C frequency shifts. The quality of the final fit is extremely satisfactory for a molecule of this size. The large number of available data and the application of harmonic corrections to the observed frequencies thus has permitted us to extend the previous harmonic force field study of substituted phosphines and substituted phosphine oxides and sulfides,I0 and to produce an accurate, detailed harmonic force field for trimethylphosphine. Acknowledgment. We thank the SERC for the Aberdeen FTIR facility, and Dr. A. R. Morrisson for recording some of the infrared spectra. We gratefully acknowledge the travel support provided by a NATO Grant for International Collaboration in Research. We also thank the University of Glasgow for providing some preliminary Raman data. Registry No. D, 7782-39-0; "C, 14762-74-4; Me3P, 594-09-2.