J. Phys. Chem. 1988,92, 5597-5602
5597
Ab Initio Calculation of Harmonic Force Fields and Vibrational Spectra for the Fluorophosphines PH,F&, ( n = 0-3) Jiirgen Breidung and Walter Thiel* Theoretische Chemie, Bergische Universitat-Gesamthochschule, 0-5600 Wuppertal I , West Germany (Received: July 21, 1987)
Ab initio self-consistent field calculations at the 6-31G** level are reported for PH3, PHzF, PHF2, and PF,. The calculated geometries, rotational constants, 'dipole moments, vibrational frequencies, centrifugal distortion constants, Coriolis coupling constants, and infrared band intensities of these molecules and their perdeuteriated isotopomers agree well with the available experimental data, particularly when the calculated force fields are scaled. The scaled theoretical symmetry force constants in the a' block of PHFz and the al block of PF3 are believed to be more realistic than the current empirical values. The vibrational spectra of the unknown molecules PHzF and PD2F are predicted.
1. Introduction In recent years, harmonic force fields have often been derived from a b initio Hartree-Fock calculations with basis sets of moderate size.'pz Since the resulting Hartree-Fock force constants are systematically too high, they can be improved by scaling It has been demon~tratedl-~ that such scaled theoretical force fields may assist in the assignment of vibrational spectra and allow predictions for unknown molecules and that the combination of theoretical and experimental information may lead to more reliable force fields for known molecules. The present paper reports ab initio calculations of the vibrational spectra of phosphine (PHJ and its fluoro-substituted derivatives (PHzF, PHF2, PF3). These tetraatomic molecules have been the subject of many ab initio studies, with particular emphasis on the calculation of inversion barriersew For phosphine, ab initio force fields have been published,'*12 and harmonic frequencies have been given by using standard basis sets.13-16 To the best of our knowledge, ab initio force fields are not yet available for the fluoro-substituted compounds. Experimentally, PHzFis still unknown, whereas the other three molecules are well characterized. There have been high-resolution infrared studies of all fundamental bands in PH317-19and PF3,m22
(1) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, pp 125-219. (2) Fogarasi, G.; Pulay, P. Annu. Reu. Phys. Chem. 1984, 35, 191. (3) Puiay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037. (4) Schneider, W.; Thiel, W. J. Chem. Phys. 1987, 86, 923. (5) Lehn, J. M.; Munsch, B. Mol. Phys. 1972, 23, 91. (6) Schmiedekamp, A.; Skaarup: S.;Pulay, P.; Boggs, J. E. J. Chem. Phys. 1977, 66, 5769. Boggs, J. E.; Seida, D. J. Chem. Phys. 1981, 75, 3645. (7) Marynick, D. S.J. Chem. Phys. 1980, 73, 3939. Marynick, D. S.; Dixon, D. A. J. Phys. Chem. 1982,86,914. Marynick, D. S.; Rosen, D. C.; Liebman, J. F. J. Mol. Struct. 1983, 94, 47. (8) Yabushita, S.; Gordon, M. S. Chem. Phys. Lett. 1985, 117, 321. (9) Dixon, D. A.; Arduengo, A. J., 111; Fukunaga, T. J. Am. Chem. SOC. 1986, 108, 2461. (10) Schlegel, H. B.; Wolfe, S.; Bernardi, F. J . Chem. Phys. 1975, 63, 3632. (11) Kutzelnigg, W.; Wallmeier, H.; Wasilewski, J. Theor. Chim. Acta 1979, 51, 261. (12) Civis, S.;Carsky, P.; Suirko, V. J. Mol. Specrrosc. 1986, 118, 88. (13) Gordon, M. S.;Binkley,*J.S.;Pople, J. A.; kietro, W. J.; Hehre, W. J. J. Am. Chem. SOC.1982, 104, 2797. (14) Pietro, W. J.; Franc], M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J. Am. Chem. SOC.1982, 104, 5039. (15) Franc], M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S.;DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (16) DeFrees, D. J.; McLean, A. D. J. Chem. Phys. 1985, 82, 333. (17) Yin, P. K. L.; Rao, K. N. J. Mol. Spectrosc. 1974, 51, 199. (18) Baldacci, A.; Devi, V. M.; Rao, K. N.; Tarrago, G. J . Mol. Spectrosc. 1980, 81, 179. ~~
0022-3654188 12092-5597$01 SO10
TABLE I: Symmetry Coordinates and Scale Factors for PH3 and PF3 sDecies svmmetrv coordinatea factor"
TABLE 11: Symmetry Coordinates and Scale Factors for PHF2 and PH2F species symmetry coordinate" factor"
a'
a"
SI= Arl S2 = 2-'/2(Ayi, + Ay12) s 3 = 2-qAR2 + A R 3 ) s4 = A623
c, Cr
Ss
c7
s,
2-1/2(Ay13- AyI2) = 2-qAR2 - A R 3 )
"The entries refer to PHF2.24For PH2F, replace r
CR
c8
-
CR
R and #I
-
a.
and the vibrational spectrum of PHFz has been assigned by two independent g r o ~ p s . ~Ground-state ~,~~ molecular constants have been derived from the microwave spectra of PH3,25PHFz,z6and PF3.z79z*The experimental infrared and microwave data have been used to construct empirical harmonic force fields for PH3,299M PHF2:3*24 and PF3.22927 In this situation, our present theoretical study serves four purposes: First, for the known molecules, the calculated spectroscopic constants are compared with the available experimental data to establish the accuracy of the calculations. Second, the vibratonal spectrum of the as yet unknown PHzF molecule is predicted. Third, a consistent set of scaled theoretical force (19) Tarrago, G.; Dang-Nhu, M.; Goldman, A. J. Mol. Spectrosc. 1981, 88, 311. (20) Reichman, S.; Overend, J. Spectrochim. Acta, Part A 1970, 26, 379. (21) Reichman, S.J. Mol. Spectrosc. 1970, 35, 329. (22) Small, C. E.; Smith, J. G. J. Mol. Spectrosc. 1978, 73, 215. (23) Durig, J. R.; Zozulin, A. J.; m o m , J. D.; Streusand, B. J. J . Raman Spectrosc. 1979, 8, 259. (24) Dunning, V. D.; Taylor, R. C. Spectrochim. Acta, Part A 1979, 35, 419. (25) Tarrago, G.; Dang-Nhu, M. J. Mol. Spectrosc. 1985, I l l , 425. (26) Kuczkowski, R. L. J. Am. Chem. SOC.1968.90, 1705. (27) Hirota, E.; Morino, Y. J. Mol. Spectrosc. 1970, 33, 460. (28) Kawashima, Y.; Cox,A. P. J. Mol. Spectrosc. 1977, 65, 319. (29) Duncan, J. L.; McKean, D. C. J. Mol. Spectrosc. 1984, 107, 301. (30) McRae, G. A.; Gerry, M. C. L.; Cohen, E. A. J. Mol. Spectrosc. 1986, 116, 58.
Q 1988 American Chemical Societv
5598 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
Breidung and Thiel
TABLE III: Molecular Geometries"
PH2F PHF2 PF3
L E E T T E' T
1.407 1.4116 (6) 1.413 (2) 1.406 1.406 1.412 (6)
E E
1.600 1.581 1.582 (2) 1.564 1.563 (2) 1.561 (1)
95.5 93.36 (8) 93.45 (9) 93.1
42 30 98.8 99.0 (2) 97.3 96.9 (7) 97.7 (2)
98.7 96.6 96.3 (5)
26 27 28
'Equilibrium values, unless noted otherwise. bT theoretical, 6-31G**; L theoretical, large basis L; E experiment,uncertainty of last digit given in parentheses. C r rstructure. TABLE I V Rotational Constants (cm-I)
calcd molecule PH3 PH2F PHFz PF3
obsd
A.
B.
C.
4.4947 0.8 184
4.6251O 0.5087 0.2980 0.2610
3.8630" 0.5012 0.2293 0.1610
C"
ref
4.4524
3.9190
25
0.2967 0.2608b
0.2286 0.1600 (2)b
26 28
B"
All
0.8190
'Values for basis L: Be, 4.6128; C,, 3.8553. bEquilibriumvalues:28 Be, 0.2618; C,, 0.1606 (3). constants is given for all four molecules with the hope that this may, in some cases, improve our knowledge especially of the off-diagonal coupling constants. Fourth, we derive transferable scale factors for the calculated force constants in internal or symmetry coordinates that will be used in a subsequent theoretical study" of the vibrational spectra of the fluorophosphoranes PH,F5-, (n = 0-5).
2. Details of the Calculations All quantum-chemical calculations were carried out at the HartreeFock level by using the GRADSCF program system.32 The 6-31G** basis1S*33,34 was chosen as the standard basis set for all molecules, with the following rec~rnmended'~J~ exponents for the polarization functions: H , 1.10; F, 0.80; P, 0.55.The sensitivity of the results with respect to the basis set was checked for PH3 by calculations using several other basis sets. Since most of the calculated properties did not change very much when improving the basis, we shall report only some results obtained with our largest set L. This basis set uses a triple-[ representation of the valence orbitals of hydrogen36 and phosphor~s,~' Le., H (5s)/ [3s] and P (13slOp)/[6sSp]; it is augmented by one set of gpolarization functions at hydrogen with an exponent of 0.65, which is appropriate for P-H bond^,^^,^^ and by two sets of d-polarization functions at phosphorus with exponents" of 0.30 and 0.85. Molecular geometries were always completely optimized within the constraint of a given point group symmetry (C3"for PH3 and PF3, C,for PH2Fand PHF2). The Cartesian force constants and the Cartesian dipole moment derivatives were evaluated analytically3*at these theoretical equilibrium geometries. The quantum-chemical results were converted to spectroscopic constants in the usual manner.4 Briefly, the harmonic frequencies uk = (2n)-'Xk*/2were obtained directly from the eigenvalues Xk of the mass-weighted Cartesian force constant matrix, while the corresponding eigenvectors (Iik) define the normal coordinates Qk = CIikqiin terms of mass-weighted Cartesian displacements qi.39940
The infrared intensities Ak were c a l c ~ l a t e dfrom ~ ~ the ~ ~ squared derivatives of the electric dipole moment with respect to the normal coordinates Qk.For the symmetric-top molecules PH3 and PF3, the Coriolis constants for the degenerate modes and the centrifugal distortion constants DJ, DjK, and DK were computed from standard f o r m ~ l a s . ~ ~ , ~ ~ The following conventions were adopted for defining the internal and symmetry coordinates of PX1X2X3(X = H, F): The xz plane is always taken as a plane of symmetry, and the z axis as symmetry axis for PH3 and PF3. Atom P lies in the origin, and atom XI in the xz plane with Cartesian coordinates x1 < 0, z1 < 0; furthermore, we have x2> 0, y 2 > 0, z2 < 0 for atom X2. Considering the internal coordinates, r refers to a P-H distance, R to a P-F distance, a to a HPH angle, p to a FPF angle, and y to a HPF angle, with the indexes denoting specific substituent atoms X i . The symmetry coordinates Siare defined as usua123,24-41 in terms of internal displacements from the equilibrium geometries (see Tables I and 11). For scaling the theoretical harmonic force fields in symmetry coordinates, we employed the same procedure3 as in our previous study.4 A scale factor ci is introduced for each diagonal force constant Fii associated with symmetry coordinate Si. The scaled off-diagonal force constants Fijs are then defined in terms of the unscaled force constants Fij as
[,
Since identical scale factors apply for qualitatively similar distortions, there should be altogether five independent scale factors (Le., c,, cR, c,, cg, cy),,for the five types of internal coordinates listed above. The assignment of these scale factors to symmetry coordinates is shown in Tables I and 11. Optimum values of the scale factors for a given molecule are obtained by minimizing the root-mean-square (rms) deviation: 3N-6 (r
=[
C
i= 1
(31) Breidung, J.; Thiel, W.; Komornicki, A. J . Phys. Chem., following article in this issue. (32) Kornornicki, A. GRADSCF: An ab initio Gradient Program System, Version 9.2; Polyatornics Research Institute: Mountain View, CA, 1985. (33) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2251. (34) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (35) Keil, F.; Kutzelnigg, W. J . Am. Chem. SOC.1975, 97, 3623. (36) Dunning, T. H., Jr. J . Chem. Phys. 1971, 55, 716. (37) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980, 72, 5639. (38) Kmg, H. F.; Komornicki, A. In Geometrical Deriuatiues of Energy Surfaces and Molecular Properties; Jorgensen, P., Simons, J., Eds.; Reidel: Dordrecht, 1986; pp 207-214.
(v? - vref)2]'/2(3N - 6)-'/2
(2)
between the frequencies vi" calculated from the scaled theoretical force field and the experimental reference frequencies viEf. Two choices are possible for the latter: When harmonic experimental frequencies u:b"" are used, the scale factors account for systematic errors due to approximations in the theoretical calculations, Le., the neglect of electron correlation and the basis set truncation. (39) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (40) Califano, S . Vibrational States; Wiley: New York, 1976. (41) Duncan, J. L.; Mills, I. M. Spectrochim. Acta 1964, 20, 523.
The Fluorophosphines PH,F3-, ( n = 0-3)
The Journal of Physical Chemistry, Vol. 92, No, 20, 1988 5599
- -- -
either a single frequency (e.g., c, vI, c8 u4 in PHF2) or, more v2/v4 in commonly, a pair of frequencies (e.g., c, v l f v3, c, molecule calcd obsd ref vZ/vq in PF3; CR v3!v6, cy v2f us in PH3; CR -+ V ~ ! V ? , C! PH3 0.891' 0.574 44 PHF2). Optimization of this scale factor will then correctly PHZF 1.678 reproduce the corresponding frequency in the first case or the PHF;! 1.657 1.32 (1) 26 corresponding degeneracy-weighted average of frequencies in the PF3 1.381 1.025 (9) 45 second case, which is indeed found (see Table VI). Hence, errors o v a h e for basis L: 0.744. in the scaled theoretical frequencies mainly arise from errors in the calculated splittings between the pairs of frequencies listed When the observed fundamental frequencies upbsd are used as above. Obviously, these splittings are predicted a t the 6-31G** reference data, the scale factors must also absorb anharmonicity level reasonably well, with errors of 10 cm-' or less, which leads effects, in an average sense. to low overall rms deviations (see Table VII). In this connection, it should be noted that the scaled theoretical frequencies for PH3 3. Results and Discussion remain practically unchanged when improving the basis set from 6-3 1G** to basis L, although the unscaled theoretical frequencies In this section we present our calculated geometries, rotational are slightly better for the larger basis L (see footnote d of Table constants, dipole moments, vibrational frequencies, centrifugal VI). distortion constants, Coriolis coupling constants, harmonic force Turning to individual molecules, the experimental frequencies fields, and infrared intensities and compare them with the available for PH3 and PF3 are well established from high-resolution experimental data. ~ o r k . ' ~Two - ~ ~independent s t ~ d i e sof~ PHF2 ~ , ~ ~yield frequencies Table I11 lists the molecular geometries. The agreement bethat agree to 2 cm-' or better for vl, v2, v4, and us but differ tween theory and is satisfactory since the appreciably for the P-F stretching modes v3 and v6 (see Table VI, calculated distances and angles often lie within the uncertainties especially footnote e). We prefer the assignment of ref 24, which of the experimental equilibrium values, especially for PHF2 and implies an error of 3 cm-l in our calculated splitting between this PF,. The calculations underestimate the P-H bond length by pair of frequencies, whereas the assignment of ref 23 would imply 0.006 A, and overestimate the HPH angle in PH3 by 2 O ; these an error of 26 cm-I, which seems unreasonably large in view of errors for PH3 are largely removed when correlation corrections the general accuracy of such 6-31G** frequency splittings (see are included a t the MP2 l e ~ e l . ' ~The . ~ ~calculated equilibrium above and Table VI). structure of the unknown PH2Fmolecule is close to other recent When the fundamental frequencies of unknown molecules such prediction^.^^^ as PHzF from scaled theoretical force fields are predicted, it is Table IV shows the rotational constants. The agreement between the calculated equilibrium values and the observed2s~26~28 assumed that the scale factors are transferable between related known and unknown molecules, at a given theoretical level. This ground-state values is as good as expected. PH2Fis predicted to hypothesis has been verified empirically by several previous behave like a nearly prolate symmetric-top molecule since Be and s t ~ d i e s ' ~and - ~ is ~ -further ~ ~ supported by our present data for C, differ by less than 1.5%. the scale factors C , and c8, which are quite similar in PHF2and According to Table V, the calculated dipole moments (6-31G**) PF3 (see Table VII). However, the scale factors c, in PH3 and are consistently higher than the 0 b s e r v e d ~ ~ 9ones, ~ 9 ~by ~ 0.32 (PH3), PHF, differ strongly, at least when scaling with respect to v,Obsd 0.34 (PHF,), and 0.36 D (PF,). When such systematic errors (see Table VII). When an explanation of this discrepancy is looked are corrected for, the dipole moment of PH2F should be 1.35 f for, the experimental fundamental P-H stretching frequencies for 0.03 D, which agrees quite well with an empirical estimate46of PH3 and PHF2 seem to be beyond doubt, even though it should 1.30 D. When the large basis L is used, the calculated dipole be noted that the comparatively low P-H stretching frequency moment of PH3 remains too high but the error drops to 0.17 D, of PHF2 in the gas phase shifts to an appreciably higher value indicating a substantial improvement through basis set extension. and in argon matrices.54 Since in the liquid or solid state23q24-s3 Table VI compares the calculated and observed vibrational the scale factors c, in PH, and PHF2are similar when scaling with frequencies. An approximate description for each normal mode respect to wpbd (see Table VII), one may argue that the above is included which is feasible due to the fact that each normal discrepancy is caused by anharmonicity effects; in our opinion, coordinate turns out to be dominated by a single symmetry cohowever, the anharmonicity correction applied" to vIobsdof PHF2 ordinate. The experimental harmonic frequencies wpW in Table seems to be unrealistically large, so that the discrepancy would VI have been derived22*24~29 from the observed fundamental frepersist when a more realistic anharmonicity correction is used. quencies v,Obsdby using approximate anharmonicity corrections In this situation we have decided to adopt as our standard scale and must therefore be regarded as rather uncertain estimates. It factors c, and c, from PH3, cR and c8 from PF3, and cy from PHF, is obvious from Table VI that the unscaled 6-31G** frequencies (see Table VII). As discussed above, the transferability of these wi overestimate wpbsd by 7 f 3% and upbsd by 10 f 5%. These scale factors3' is backed by general previous e ~ p e r i e n c e ' ~ , ~and '-~~ errors are fairly typical for SCF calculations with medium-size , caution should be. exercised by the present results for cRand c ~but basis sets.43 with respect to the transferability of c,. Therefore, we believe that The scaled 6-31G** frequencies airand vi" in Table VI have the predicted fundamental frequencies vi" of PH2Fin Table VI1 been obtained by using wpbsdand vpbsd, respectively, as reference are accurate to about 10 cm-' in the case of v,, v3, v,, and v6 but data in the scaling procedure (see section 2). The corresponding may be appreciably less accurate in the case of v 1 and vs (see also scale factors and rms deviations are collected in Table VII. The footnotefof Table VI, rms deviation of 5 cm-' for v2-v6). agreement between the scaled theoretical and the experimental Table 1 of the supplementary material (see the paragraph at frequencies is excellent, which is not surprising for the following the end of the paper) lists the centrifugal distortion constants for reason. Because of the close correspondence of normal and PH3and PF3. The calculated constants do not change much when symmetry coordinates (see above) and the chosen assignment of scale factors to symmetry coordinates (see Tables I and 11) it is evident that, for each molecule, a given scale factor mainly affects (47) Pulay, P.; Fogarasi, G.; Boggs, J. E. J . Chem. Phys. 1981, 74, 3999.
TABLE V Dipole Moments (debye) . _ .
+
-+
(48) Pongor, G.;Pulay, P.; Fogarasi, G.; Boggs, J. E. J . Am. Chem. SOC. 1984, 106, 2765.
(42) Helms, D. A.; Gordy, W. J. Mol. Spectrosc. 1977, 66, 206. (43) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (44) Davies, P. B.; Neumann, R. M.; Wofsy, S. C.; Klemperer, W. J. Chem. Phys. 1971, 55, 3564. (45) Birnbaum, G. J. Chem. Phys. 1967, 46, 2544. Shulman, R. G.; Dailey. B. P.; Townes,C. H. Phys. Rev. 1950, 78, 145. (46) Morse, J. G.; Parry, R. W. J . Chem. Phys. 1967, 46, 4159.
(49) Sellers, H.; F'ulay, P.; Boggs, J. E. J . Am. Chem. SOC.1985, 107, 6487. (50) Niu, 2.;Dunn, K. M.; Boggs, J. E. Mol. Phys. 1985, 55, 421. (51) Xie, Y.;Boggs, J. E. J. Comput. Chem. 1986, 7, 158. (52) Xie, Y.; Fan, K.; Boggs, J. E.Mol. Phys. 1986,58, 401. (53) Rudolph, R. W.; Parry, R. W. Inorg. Chem. 1965, 4, 1339. (54) Burdett, J.; Hodges, L.; Dunning, V.; Current, J. J. Phys. Chem. 1970, 74,4053.
5600 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
Breidung and Thiel
TABLE VI: Vibrational Frequencies (cm-I)
calcdbsc molecule PH,d
mode ai y1 v2
e
Y3 v4
PH2F
a' v 1 y1
v3 v4
a" v 5 v6
PHF2ef
a' v 1 v2 y3 Y4
a'' v5 Y6
PF3
a1 y1 y2
e
Y3
v4
description" P-H s-stretch HPH s-deform P-H d-stretch HPH d-deform P-H s-stretch HPH scissors HPF s-bend P-F stretch P-H a-stretch HPF a-bend P-H stretch HPF s-bend P-F s-stretch FPF scissors HPF a-bend P-F a-stretch P-F s-stretch FPF s-deform P-F d-stretch FPF d-deform
obsdb
wi
Ui"
V,sC
2576 1123 2574 1257 2569 1252 1077 903 2566 999 2568 1118 934 377 1064 931 916 513 956 364
241 1 1017 2409 1139 2404 1134 1001 821 2402 928 2398 1039 856 361 989 858 891 490 871 349
2326 997 2324 1116 2320 1111 915 815 2317 904 2242 1012 838 357 963 840 884 488 864 347
2405.4 1012.4 2411.4 1141.1
2321.13 992.13 2326.88 1118.30
ref 18, 29 19, 29 18, 29 19, 29
2398 1049 860 360.5 979.2 854.4 897.08 489.83 867.81 348.49
2242 1016.5 839 357 959 839 891.92 487.72 859.8 346.6
24 24 24 24 24 24 20,22 20,22 21,22 22
W p w
vpb"d
" Following the conventions of Shimanouchi, T. Tables of Molecular Vibrational Frequencies; NSRDS-NBS 39: Washington, DC, 1972. See text for notation. '6-31G**, scale factors, see Table VII. duivalues for PH, with basis L: 2537, 1107, 2535, 1239. The scaled wi" and vi" values with basis L differ by less than 1 cm-I from the corresponding 6-31G** values. rupbsd values for PHF2 from ref 23: 2240, 1015, 848, 358, 958, 825. f u i K values for PHF2 by using standard scale factors (see Table VII): 2319, 1012, 844, 359, 963, 846. TABLE VII: Scale Factors c! and rms Deviations u (cm-')
molecule type c, CR PHI" w 0.8757 Y 0.8154 w 0.8719 0.8380 PHF2 v 0.7621 0.8026 w 0.8281 PF3 Y 0.8146 stdb w 0.8757 0.8281 Y 0.8154 0.8146
c,
C@
0
0.8206 0.7881
3.6 3.5 0.9206 0.8640 6.1 0.9017 0.8194 2.5 0.9195 2.9 0.91 13 3.8 0.8206 0.9195 0.8640 0.7881 0.9113 0.8194
"Scale factors for PH3 with basis L: w 0.9027, 0.8448; v 0.8405, 0.8 1 13. Used for unknown molecules such as PH2F.
the basis set of PH3 is improved but are fairly sensitive to the scaling of the theoretical force field. This is due to the fact that the frequencies appear in the corresponding formula^^^,^ as inverse squares, so that an overestimate of the unscaled frequencies by 10% (see above) will lead to an underestimate of the centrifugal distortion constants by about 20%. The constants calculated from the scaled force fields agree well with the experimental values, the deviations being about 10%for PH3 and less than 5% for PF3. Similar agreement was found in our previous s t u d 9 of the halides H3MX (M = C-Sn, X = F-I). Table 2 of the supplementary material contains the Coriolis constants for PH3 and PF,, i.e, Yt for the coupling between the degenerate modes and YSt for the coupling between a pair of nondegenerate and degenerate modes. The calculated Coriolis constants are insensitive to an enlargement of the basis set and to scaling. The observed 3; values are obtained by dividing the Coriolis terms (CY), by the corresponding rotational constants C,;22*55 the observed Ygt constants are available only in absolute v a l ~ e . ~The * ~agreement ~~ between the theoretical and experimental values is generally satisfactory, although slightly worse than in our previous study4 of the halides H3MX. Two points should be noted, however: The experimental value Y3 = 0.419 for PF3 is probably perturbed by an anharmonic resonance22 and therefore does not satisfy the [sum rule (Y, + Y4 = Be/2Ce- I ) , which would require Y3 = 0.444 (using experimental data for Y4, Be, Ce),much closer to our calculated value f3 = 0.452. Furthermore, the constant (13 = 0.39222for PF3 has been found to be highly correlated with other molecular constants and could therefore be determined only by a fairly complicated procedure ( 5 5 ) Graner, G.; Biirger, H. J . Mol. Spectrosc. 1986, 115, 393.
TABLE VIII: Scaled Theoretical and Empirical Force Fields for PH3 (mdyn/&" harmonic force fieldb*d effective force fielde 6-31G** basis L ref 29c 6-31G** basis L ref 3OC 3.366 3.341 (33) 3.135 3.134 3.194 (20) F11 3.367 0.150 0.100 (21) 0.144 0.142 0.156 (10) Fi2 0.152 0.641 0.612 (7) 0.615 0.616 0.594 (4) F22 0.641 3.327 3.339 (33) 3.098 3.098 3.165 (18) F33 3.327 -0.041 -0.041 -0.036 (10) F34 -0.044 -0.043 -0.048 (8) 0.710 0.730 (10) 0.680 0.682 0.710 (4) FM 0.708 a Angle-bending coordinates have been scaled with a unit bond length of 1 A; uncertainty of the last digit is given in parentheses for the empirical values. *Derived to reproduce the harmonized experimental frequencies wpW. Derived to reproduce the observed fundadunscaled CEPA values (ref l l): 3.557, mental frequencies vp". 0.088, 0.690, 3.553, -0.036, 0.783. CEmpirical.
TABLE I X Scaled Theoretical and Empirical Force Fields for PF, (mdyn/AY
F11 Fi2
F22 F33 F34
F4
6-31G** 5.930 0.368 2.054 5.031 -0.219 1.250
harmonicb ref 22 6.415 (124) 0.682 (106) 1.985 (25) 5.021 (80) -0.272 (43) 1.235 (13)
ref 27 6.25 (13) 0.64 (14) 1.96 (4) 4.98 (5) -0.30 (8) 1.22 (3)
effectiveC ref 56 6.18 (10) 0.49 (9) 2.01 (2) 4.96 -0.32 1.20
'See footnote a of Table VIII. bSee footnote b of Table VIII.
