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Conformational stability of (chloromethyl) phosphonothioic difluoride from temperature-dependent infrared spectra of rare gas solutions and r0 structural parameters
Journal of Molecular Structure 562 (2001) 145±156
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Conformational stability of (chloromethyl) phosphonothioic di¯uoride from temperature-dependent infrared spectra of rare gas solutions and r0 structural parameters q J.R. Durig*, J. Xiao Department of Chemistry, University of Missouri Ð Kansas City, 5100 Rockhill Road, Kansas City, MO 64110-2499, USA Received 9 October 2000; accepted 3 November 2000
Abstract Variable temperature (255 to 21508C) studies of the infrared spectra (3500±400 cm 21) of (chloromethyl)phosphonothioic di¯uoride (ClCH2P(S)F2) dissolved in liquid xenon and krypton have been recorded. From these data, the enthalpy difference has been determined to be 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21) with the trans conformer being the more stable rotamer. Complete vibrational assignments are presented for both conformers, which are consistent with the predicted wavenumbers obtained from ab initio MP2/6-31G(d) calculations utilizing two scaling factors. The optimized geometries, conformational stabilities, harmonic force ®elds, infrared intensities, Raman activities and depolarization ratios have been obtained from RHF/ 6-31G(d) and/or MP2/6-31G(d) ab initio calculations. Hybrid density function theory (DFT) calculations to obtain the structural parameters and conformational stability by the B3LYP/6-31G(d) method were also carried out. These quantities are compared to the corresponding experimental quantities when appropriate as well as with some corresponding results for some similar molecules. The r0 structural parameters have been obtained from a combination of the previously reported microwave rotational constants and ab initio MP2/6-3111G(d,p) predicted parameters. The results are compared to some corresponding quantities for some similar molecules. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Conformational stability; Structural parameters; Ab initio calculations; (Chloromethyl)phosphonothioic di¯uoride
1. Introduction For some time, we have been investigating the conformational stability of organophosphorus molecules of the general formula: YCH2P(Z)X2 where Y CH3, F and Cl; Z O, S, BH3 and lone pair; X F, Cl and CH3. In our earlier studies of q Taken in part from the dissertation of J. Xiao, which will be submitted to the Department of Chemistry in partial ful®llment of the PhD degree. * Corresponding author. Tel.: 11-816-235-6038; fax: 11-816235-5502. E-mail address: [email protected] (J.R. Durig).
ClCH2P(O)F2 [1] and ClCH2P(S)F2 [2], we were able to show that the initial conclusion [3] on the conformational stabilities of these two molecules that the gauche rotamers were the more stable forms in the liquids was in error. For the ClCH2P(S)F2 molecule, a temperature study of the Raman spectrum of the liquid was carried out from which an enthalpy difference for the two conformers of 149 ^ 31 cm 21 (1.78 ^ 0.37 kJ mol 21) was obtained with the trans conformer the more stable form. Also from the far infrared torsional transitions for both conformers, the potential function for the conformational interchange was obtained from which an enthalpy
0022-2860/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(00)00966-2
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J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
difference of 206 ^ 24 cm 21 (2.46 ^ 0.29 kJ mol 21) was estimated. Since it has been shown [4±8] that enthalpy determinations in rare gas solutions give values near those for the gas when the two conformers have similar dipole moments and molecular size, we initiated a variable temperature investigation of the infrared spectra of rare gas solutions of ClCH2P(S)F2. Additionally, we have carried out ab initio calculations to obtain predicted stabilities, vibrational frequencies, and structural parameters, particularly since the earlier vibrational assignment relied on transferred force constants to distinguish several of the conformer peaks. The results of this infrared spectra investigation and ab initio calculations are reported herein. 2. Experimental The sample of (chloromethyl)phosphonothioic di¯uoride was prepared from the corresponding dichloride (Alfa) by direct reaction with freshly sublimed antimony tri¯uoride. Sample puri®cation was performed with a low-temperature, low-pressure fractionating column. The purity of the sample was checked by comparing the mid-infrared spectra of the vapor to that previously published [2]. The mid-infrared spectra of the sample dissolved in liqui®ed krypton and xenon as a function of temperature (Fig. 1A) were recorded on a Bruker model IFS66 Fourier transform spectrometer equipped with a globar source, a Ge/KBr beamsplitter and a DTGS detector. The temperature studies ranged from 255 to 21008 and from 2105 to 21508 and were performed in a specially designed cryostat cell consisting of a 4 cm pathlength copper cell with wedged silicon windows sealed to the cell with indium gaskets. The complete system is attached to a pressure manifold to allow for the ®lling and evacuation of the cell. The cell is cooled by boiling liquid nitrogen and the temperature is monitored by two Pt thermoresistors. Once the cell is cooled to a designed temperature, a small amount of sample is condensed into the cell. The system is then pressurized with the rare gas, which immediately starts to condense, allowing the compound to dissolve. For each temperature investigated, 100 interferograms were recorded at a 1.0 cm 21 resolution, averaged,
Fig. 1. Comparison of experimental and calculated infrared spectra of (chloromethyl)phosphonothioic di¯uoride: (A) infrared spectrum of the sample dissolved in liquid xenon; (B) mixture of the calculated trans and gauche conformers with the experimentally determined DH of 244 cm 21; (C) pure gauche conformer; (D) pure trans conformer.
and transformed with a boxcar truncation function. The observed fundamental bands for the trans and gauche conformers are listed in Table 1. 3. Ab initio calculations The LCAO-MO-SCF restricted Hartree±Fock calculations were performed with the Gaussian 94 program [9] using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all the geometric parameters using the gradient method of Pulay [10]. Calculations were also carried out with full electron correlation by the perturbation method [11] to second order up to the 6-3111G(2d,2p)
Table 1 Observed and calculated frequencies (cm 21) and PEDs for (chloromethyl)phosphonothioic di¯uoride trans
gauche
B3LYP/6- Ab Fixed IR Raman Calc. Obs. Xenon PED 31G(d) initio a scaled b Int. act. c dep. c gas soln.
B3LYP/6- Ab Fixed IR Raman Calc. Obs. Xenon PED 31G(d) initio a scaled b Int. act. c dep. c gas d soln.
A0
3112 1467 1283 928 817 709 642 398 357 228 129 3175 1172 927 818 286 233 69
A 00
a b c d
n1 n2 n3 n4 n5 n6 n7 n8 n9 n 10 n 11 n 12 n 13 n 14 n 15 n 16 n 17 n 18
CH2 symmetric stretch CH2 symmetric deformation CH2 wag PF2 symmetric stretch PC stretch CCl stretch PS stretch PF2 wag PF2 deformation ClCP bend CPS bend CH2 antisymmetric stretch CH2 twist PF2 antisymmetric stretch CH2 rock PF2 rock PF2 twist Asymmetric torsion
3157 1500 1333 960 883 762 679 416 369 240 137 3227 1216 950 844 296 242 78
2962 1423 1264 910 838 723 644 416 369 240 137 3027 1153 901 800 296 242 78
8.2 68.79 15.3 12.23 9.1 1.15 278.1 2.22 47.8 16.55 86.0 8.12 16.2 12.81 51.2 4.73 16.1 3.74 1.2 7.33 2.0 0.30 2.4 49.87 0.5 8.23 138.8 0.86 3.3 2.77 3.1 4.72 0.7 0.29 5.0 0.04
0.13 0.71 0.74 0.12 0.52 0.20 0.05 0.43 0.36 0.51 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
2954 1404 1226 932 840 727 665 416 386 234 131 3009 1128 916 793 297 250 80
2940 1392 1223 926 840 721 663 413 ± ± ± 2995 1125 906 791 ± ± ±
100S1 3106 100S2 1470 98S3 1281 71S4,21S7 936 42S5,36S6,14S7 836 52S6,23S7,11S5 742 27S7,28S5,23S4,11S10 605 72S8,12S7 354 84S9 393 34S10,31S11 127 48S11,38S10 223 100S12 3173 98S13 1169 78S14,17S15 902 73S15,20S14 816 80S16,15S17 304 83S17,12S16 248 100S18 58
3155 1503 1328 971 880 792 646 368 408 134 236 3228 1212 930 854 318 260 67
2960 1426 1260 921 835 751 613 349 408 134 236 3028 1149 882 810 318 260 67
6.2 98.55 9.5 13.25 4.6 1.33 311.5 1.0 46.8 6.37 90.9 8.45 4.9 18.13 24.7 1.99 29.4 3.59 1.4 1.97 1.4 1.49 0.9 71.3 12.4 9.3 135.8 1.24 13.3 4.48 7.0 4.59 1.0 3.26 2.8 1.80
0.11 0.75 0.57 1220 1218 0.07 938 938 0.55 840 835 0.35 754 751 0.08 626 627 0.63 371 ± 0.75 ± ± 0.68 ± ± 0.72 ± ± 0.74 ± ± 0.74 ± ± 0.28 898 893 0.74 804 800 0.54 319 ± 0.63 ± ± 0.74 69 ±
100S1 100S2 98S3 41S4,25S7,22S15 35S5,30S6,20S4 48S6,15S7 45S7,28S5,13S4 55S8,32S9 29S9,19S11,18S10,18S8 50S10,24S11,15S16 45S11,19S9,12S11 100S12 97S13 79S14 62S15,15S4 53S16,12S9 71S17 96S18
The ab initio calculations are MP2/6-31(d). Scaled ab initio calculations with factor of 0.88 for the CH stretches, 0.9 for the heavy atom stretches and CH bends and 1.0 for all other coordinates at the MP2/6-31(d). Obtained from the RHF/6-31(d) basis set. Far infrared wavenumbers from Ref. [2].
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
Species Vib. Description No.
147
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J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
basis set. In addition, density function theory (DFT) calculations made with the Gaussian 94 program [9] was restricted to the hybrid B3LYP method. The determined structural parameters are listed in Table 2. The energy difference that resulted from these various calculations ranged from 341 cm 21 (4.08 kJ mol 21) from the RHF/6-31G(d) calculation to 170 cm 21 (2.03 kJ mol 21) from the MP2/63111G(d,p) calculation with the trans conformer always the more stable form. In order to obtain a complete description of the molecular motions involved in the normal modes of (chloromethyl)phosphonothioic di¯uoride, a normal coordinate analysis has been carried out. The force ®eld in Cartesian coordinates was obtained with the Gaussian 94 program [9] from the MP2/6-31G(d) calculation. The internal coordinates de®ned in Table 2 and shown in Fig. 2 were used to form the symmetry coordinated listed in Table 3. The B-matrix elements [12] were used to convert the ab initio force ®eld from Cartesian coordinates into the force ®eld in desired internal coordinate [13]. The resulting force ®eld for both trans and gauche conformers are available from the authors. These force constants were used in a mass-weighted Cartesian coordinate calculation to reproduce the ab initio vibrational frequencies and to determine the potential energy distributions (PED) for both conformers, which are given in Table 1. The diagonal and off-diagonal elements of the force ®eld in internal coordinates were then modi®ed with scaling factors of 0.88 for the CH stretches, 0.9 for the heavy atom stretches and CH bends and 1.0 for all other coordinates. The calculation was repeated to obtain the ®xed scaled force ®eld and scaled vibrational frequencies. The infrared and Raman spectra were simulated as shown in Figs. 1 and 3, respectively. The frequencies, Raman scattering activities, and infrared intensities were obtained from the output of the ab initio calculations. The Raman scattering cross-sections, 2s j =2V; which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted frequencies for each normal modes [14±17]. To obtain the polarized Raman crosssections, the polarizabilities are incorporated into Sj by S j 1 2 rj =1 1 rj ; where r j is the depolarization ratio of the jth normal mode. The Raman scattering cross-sections and the predicted scaled frequencies
were used together with a Lorentzian function to obtain the calculated spectra. The predicted Raman spectra of the pure trans conformer of ClCH2P(S)F2 is shown in Fig. 3D and that of pure gauche conformer in Fig. 3C. The predicted Raman spectrum of the mixture of the two conformers with an enthalpy difference of 244 cm 21, with the trans conformer being the more stable form is shown in Fig. 3B. In Fig. 3B, the predicted Raman spectra of the mixtures of the two conformers are shown using the experimentally determined DH value of 244 cm 21 with the trans conformer being the more stable rotamer. These spectra should be compared with the experimental Raman spectrum of the liquid shown in Fig. 3A and the simulated Raman spectrum closely resembles the observed spectrum. Although there are some differences in the calculated versus experimental intensities, i.e. the PyS stretches are predicted too weak and ClCP bend is predicted too strong, these data demonstrate the utility of ab initio calculations in predicting the spectrum for conformer identi®cation and vibrational assignments for these types of organophosphorus molecules. The infrared spectra were also predicted from the MP2/6-31G(d) calculations and Raman scattering activities determined from the RHF/6-31G(d) basis set. Infrared intensities were calculated based on the dipole moment derivatives with respect to the Cartesian coordinates. The derivatives were taken from the ab initio calculations transformed to normal coordinates by: ! X 2mu 2m u Lj 2m i 2Xj j where Qi is the ith normal coordinate, Xj the jth Cartesian displacement coordinate, and Lij the transformation matrix between the Cartesian displacement coordinates and normal coordinates. The infrared intensities were then calculated by: " # 2m y 2 Np 2mx 2 2m z 2 1 1 Ii 2 2Qi 2Qi 2Qi 3c The predicted infrared spectra of the trans and gauche conformers are shown in Fig. 1C and D, respectively. The mixture of the two conformers is shown in Fig. 1B. These spectra can be compared to the experimental spectra of the samples dissolved in
Table 2 Ê , bond angles in degrees, rotational constants in MHz and dipole moments in Debye), rotational constants, dipole moments and energy for Structural parameters (bond distances in A (chloromethyl)phosphonothioic di¯uoride Parameter
Internal RHF/6-31G(d) coodinates
r(PyS) r(P±F1) r(P±F2) r(P±C) r(C±Cl) r(C±H1) r(C±H2) /SPC /PCCl /CPF1 /CPF2 /H1CP /H2CP t (SPCCl) t ((F1PCS) t (F2PCS) t (H1CPCl) t (H2CPCl) A B C um au um bu um cu um tu 2(E 1 1435)H DE (cm 21) a b
R X1 X2 T S r1 r2 h d p1 p2 a1 a2
gauche
MP2/6-31G(d)
trans
trans
gauche
gauche
MP2/6-311 1 G(d,p)
MP2/6-3111G(2d,2p)
This study a (r0)
trans
trans
trans
gauche
gauche
1.893 1.888 1.907 1.902 1.887 1.882 1.883 1.879 1.897 1.892 1.879 1.548 1.556 1.583 1.592 1.583 1.591 1.581 1.590 1.564 1.574 1.547 1.548 1.550 1.583 1.586 1.583 1.586 1.581 1.584 1.564 1.568 1.547 1.814 1.817 1.831 1.836 1.813 1.816 1.809 1.812 1.802 1.806 1.805 1.775 1.772 1.797 1.792 1.772 1.770 1.770 1.797 1.780 1.778 1.766 1.080 1.079 1.092 1.092 1.091 1.091 1.091 1.091 1.083 1.082 1.091 1.080 1.080 1.092 1.092 1.091 1.092 1.091 1.091 1.083 1.083 1.091 116.5 121.0 116.2 121.1 116.5 120.9 117.1 121.2 116.6 120.9 116.7 114.0 112.7 114.6 112.6 114.2 112.1 114.3 112.0 113.7 111.3 113.6 103.0 98.8 102.8 98.3 102.4 98.3 102.5 98.8 102.4 98.4 102.5 103.0 101.8 102.8 101.5 102.4 101.1 102.5 101.4 102.4 101.0 102.5 108.4 109.0 108.0 108.6 108.0 108.7 107.4 108.0 107.8 108.6 107.4 108.4 108.5 108.0 108.6 108.0 108.6 107.4 108.4 107.8 108.7 107.4 180.0 64.2 180.0 62.2 180.0 61.8 180.0 60.7 180.0 59.4 180.0 128.6 127.8 128.8 128.0 129.0 128.5 129.0 128.6 129.1 128.8 129.1 2128.6 2131.3 2128.8 2131.4 2129.0 2131.3 2129.0 2131.0 2129.1 2131.2 2129.1 2121.2 2120.8 2121.2 2120.6 2121.5 2120.8 2121.6 2120.6 2121.3 2120.2 2121.6 121.2 120.3 2121.2 120.5 121.5 120.6 121.6 120.9 121.3 120.4 121.6 3830 2661 3679 2564 3724 2588 3752 2596 3807 2587 3872 b 1124 1348 1098 1322 1122 1358 1123 1362 1127 1382 1140 b 1068 1120 1044 1095 1068 1122 1070 1125 1072 1130 1084 b 1.824 1.555 1.326 1.288 1.592 1.521 1.352 1.645 1.283 1.426 1.559 2.517 1.591 2.047 1.829 2.225 2.202 1.755 1.872 1.905 0.000 1.673 0.000 1.542 0.000 1.729 0.000 1.788 0.000 1.614 2.400 3.399 2.071 2.868 2.425 3.202 2.584 2.997 2.269 2.875 0.702569 0.701052 3.805474 3.803919 1.580697 1.579797 2.134169 2.133393 2.306039 2.305084 333 341 198 170 210
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
trans
B3LYP/6-31G(d)
Calculated using the rotational constants reported in Ref. [2]. Calculated values obtained from the r0 values in this study.
149
150
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
Fig. 2. Internal coordinates of (chloromethyl)phosphonothioic di¯uoride.
liqui®ed xenon shown in Fig. 1A. As a whole, the simulated infrared spectrum closely resembles the observed spectrum, which provides excellent evidence for the quality of the ab initio calculation. The optimized geometry was obtained from the MP2/6-31G(d) calculation for the trans conformer and then was utilized to obtain a potential surface scan. In this potential surface scan, only the torsional dihedral angle was allowed to vary on 10 increments from 08 (trans) to 180.08 (cis), which is a transition state. The resulting potential function indicated an
additional minimum at 1208, which corresponds to the gauche conformer. Optimization at the trans and gauche minima from the MP2/6-31G(d) calculations gives the energy of 21436.580687 and 21436.579797 hartree (1 hartree 219474 cm 21), respectively, which are consistent with a more stable trans conformer and with the gauche rotamer lying 198 cm 21 higher in energy. Combined with optimization at the cis position and the other transition state from the MP2/6-31G(d) calculation, this procedure leads to a more meaningful potential surface. The calculated potential surface scan as well as the potential surface using the optimized minima and maxima on the potential surface are shown in Fig. 4.
4. Conformational stability In order to gain information about the enthalpy difference between the two conformers similar to what is expected for the gas, variable temperature studies in lique®ed xenon and krypton were carried out. The sample was dissolved in lique®ed xenon and krypton and the spectra were recorded at different temperatures varying from 255 to 21508 depending on the solvent. Only small interactions are expected to
Table 3 Symmetry coordinates for (chloromethyl)phosphonothioic di¯uoride Species
Description
Symmetry coordinate a
A0
CH2 symmetric stretch CH2 symmetric deformation CH2 wag PF2 symmetric stretch PC stretch CCl stretch PS stretch PF2 wag PF2 deformation ClCP bend CPS bend
S1 r1 1 r2 S2 4m 2 a1 2 a2 2 11 2 12 S3 11 1 12 2 a1 2 a2 S4 x1 1 x2 S5 T S6 S S7 R S8 p1 1 p2 2 l1 2 l2 S9 4f 2 l1 2 l2 2 p1 2 p2 S10 d S11 h
A 00
CH2 antisymmetric stretch CH2 twist PF2 antisymmetric stretch CH2 rock PF2 rock PF2 twist Asymmetric torsion
S12 S13 S14 S15 S16 S17 S18
a
Not normalized.
r1 2 r2 11 2 12 2 a1 1 a2 x1 2 x2 11 2 12 1 a1 2 a2 l1 2 l2 1 p1 2 p2 l1 2 l2 2 p1 1 p2 t
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
Fig. 3. Raman spectra of (chloromethyl)phosphonothioic di¯uoride: (A) experimental spectrum of the liquid; (B) calculated spectrum of the mixture of both conformers with experimentally determined DH value; (C) pure gauche conformer; (D) pure trans conformer.
151
occur between the dissolved sample and the surrounding noble gas atoms; consequently, only small frequency shifts are anticipated when passing from the gas phase to the lique®ed noble gas solutions [4±8]. A signi®cant advantage of this study is that the conformer bands are better resolved in comparison with those in the infrared spectrum of the gas. This is particularly important since most of the conformer bands for this molecule are expected to be observed within a few wavenumbers of each other. Also the areas of the conformer peaks are more accurately determined than those from the spectrum of the gas. The best separated bands in the infrared spectra of the xenon and krypton solutions are assigned to the P± C stretch. Figs. 5 and 6 show the spectral changes for the bands belonging to the two conformers in the infrared spectrum of the xenon and krypton solutions, respectively. The lower wavenumber band has been con®dently assigned to the trans conformer. It is obvious that the increase in the intensity of the infrared bands assigned to the trans conformer as the temperature decreases con®rms the stability of the trans rotamer over the gauche rotamer. The improved resolution of the spectral allowed the enthalpy difference between the two conformers to be determined from the same conformational pair used in the previous study (PS stretch) as well as
Fig. 4. Potential function of the asymmetric torsion of (chloromethyl)phosphonothioic di¯uoride: (A) surface scan at MP2/6-31G(d); (B) ®t to the far infrared data from Ref. [2]; (C) optimization at MP2/6-31G(d).
152
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Fig. 5. Temperature-dependent infrared spectra of (chloromethyl)phosphonothioic di¯uoride dissolved in liquid xenon in the PC stretching region.
additional conformational bands belonging to the PC and CCl stretches. In order to obtain the enthalpy difference between the two conformers, 10 spectral data points were obtained over each temperature range (255 to 21008 for xenon and 2105 to 21508 for krypton) for each conformer pair (Table 4). The intensities of each conformer pair were ®t to the equation: 2ln k DH=RT 2 DS=R: The DH value was determined from a plot of 2ln K versus 1/T, where DH/R is the slope of the line and K is the intensity ratio Ig/It. It is assumed that DH is not a function of temperature over the temperature range. From the plot of the natural logarithm of the ratio as a function of the reciprocal of the absolute temperature, an average DH value of 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21) was obtained with the trans conformer being the more stable rotamer. The error limits are given by the standard deviation of the measured areas of the intensity data. These error limits do not take into account small associations with the lique®ed rare gas or other experimental factors such as the presence of overtones or combination bands in near coincidence with the measured fundamentals. 5. Vibrational assignment
Fig. 6. Temperature-dependent infrared spectra of (chloromethyl)phosphonothioic di¯uoride dissolved in liquid krypton in the PC stretching region.
A rather complete vibrational assignment of the infrared and Raman spectra of (chloromethyl)phosphonothios di¯uoride has been previously reported [2]. However, the normal coordinate calculations were based upon the transferred force constants from the ClCH2P(O)F2 and CH3P(S)F2 molecules whereas we carried out normal coordinate analysis utilizing ab initio force constants from the MP2/631G(d) calculations. The resulting PED indicated a reversal in the assignment of the two CH2 stretch modes compared to the previously reported one [2]: the band at 2954 cm 21 is now assigned to the CH2 symmetric stretch and the band at 3009 cm 21 is assigned to CH2 antisymmetric stretch. This assignment is also supported by the measured depolarization ratios from the Raman spectrum of the liquid [2]. The infrared spectrum of the sample dissolved in the liquid rare gas solutions makes it possible to
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
153
Table 4 Temperature and intensity ratios for the conformational study of (chloromethyl)phosphonothioic di¯uoride a T (8C)
1000/T (K)
255 260 265 270 275 280 285 290 295 2100 DH (cm 21) 2105 2110 2115 2120 2125 2130 2135 2140 2145 2150 DH (cm 21)
4.587 4.695 4.808 4.926 5.051 5.181 5.319 5.464 5.618 5.780
a
5.952 6.135 6.329 6.536 6.757 6.993 7.246 7.519 7.812 8.130
K I628 =I663 £ 102
K I751 =I722 £ 102
K I841 =I836 £ 10
6.210 5.600 5.195 3.793 4.777 3.898 4.360 3.694 3.731 263 ^ 67
6.917 6.715 6.100 6.594 5.488 5.675 5.616 5.438 4.963 194 ^ 31 4.612 5.976 4.573 6.159 3.753 4.171 4.032 2.861 4.002 2.704 198 ^ 57
2.916 2.717 2.597 2.502 2.402 2.276 2.175 2.078 1.948 1.809 262 ^ 6 1.455 1.396 1.300 1.207 1.096 1.014 0.929 0.815 0.783 0.604 251 ^ 6
3.731 3.723 3.333 2.918 2.332 2.060 2.196 1.840 1.716 296 ^ 29
Average DH 244 ^ 16 cm21 (2.92 ^ 0.19 kJ mol 21) with the trans-conformer the more stable species.
assign most of the fundamentals for the gauche conformer as well and the assignments of the observed bands are listed in Table 1. As a result of the improved resolution of the bands from the infrared spectrum of the rare gas solutions, the n 5 fundamental is clearly distinguished for the gauche rotamer from the corresponding mode for the trans conformer. According to the calculated vibrational frequencies, a reversal in the assignments from that previously reported [2] is suggested for the two bands at 938 and 932 cm 21, which was previously assigned to the PF2 symmetric stretches of the trans and gauche conformers, respectively.
torsional transitions of the trans and gauche conformers published [2] earlier (Table 5). The torsional dihedral angular dependence of the internal rotational constants F(f ) can be represented as a Fourier series: F f F0 1
k1
Fk cos kf
Table 5 Observed and calculated (cm 21) asymmetric torsional transitions for (chloromethyl)phosphonothioic di¯uoride (far-infrared data from Ref. [2]) Conformer
Transition
Obs. a
D (obs. 2 calc.) b
trans
1Ã0 2Ã1 3Ã2 4Ã3 17 Ã 0^ 2^ Ã 17
80.11 78.29 76.62 74.58 69.31 66.77
20.24 20.12 0.19 0.18 0.31 20.31
6. Asymmetric torsion The potential function for conformer interconversion has been redetermined utilizing the DH value obtained from the rare gas solutions, the dihedral angle 118.28 (1808 2 61.88, which is the value of the dihedral angle SPCCl) of the gauche rotamer from MP2/6-31G(d) calculation and the asymmetric
8 X
cis
Average DH 244 ^ 16 cm21 (2.92 ^ 0.19 kJ mol 21) with the trans-conformer the more stable species. b Calculated using the ®tted potential constants listed in Table 6 for the MP2/6-31G(d) geometry. a
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Table 6 Potential constants (cm 21), barriers to internal rotation (cm 21), enthalpy differences and dihedral angle for (chloromethyl)phosphonothioic di¯uoride Parameter
MP2/6-31G(d)
Ref. [2]
This study a
V1 V2 V3 V4 V6 trans to gauche barrier gauche to gauche barrier Enthalpy (cm 21) difference Dihedral angle (gauche)
141 78 1004 45
2167 479 947
138 101 927 97 44 1110 815 244 118.20
a
1132 948 198 118.16
49 1280 571 206 126
Calculated using the assignments in Table 5 and the Fourier coef®cients (Fi) calculated from the MP2/6-31G(d) geometry.
The relaxation of the structural parameters B(f ) during the internal rotation can be incorporated into the above equation by assuming that they are small periodic functions of the torsional angle of the general type: B f a 1 b cos f 1 c sin f The structural parameters (Table 2) obtained from the optimized geometries for both the trans and gauche conformers were used to obtain the kinetic constants. The torsional potential is also represented as a Fourier cosine series in the internal angle (f ): V f
6 X Vi 1 2 cos if 2 i1
The kinetic terms, the asymmetric torsional frequencies for both conformers, the experimental enthalpy and the gauche dihedral angle were used to ®t the potential function utilizing a computer program developed in our laboratory [18]. As an iterative process, this calculation was continued until the differences between the observed and calculated frequencies as well as the dispersions in the potential constants were minimized. From the calculated potential function, the trans to gauche and gauche to gauche barriers are determined to be 1100 and 815 cm 21, respectively, with the enthalpy difference between the two conformers of 244 cm 21. These results are listed in Table 6 along with the results previously reported [2]. Although
the potential coef®cients are signi®cantly different from the values from those obtained earlier, the trans to gauche and gauche to gauche barriers have very similar values. The spacings for the hot band torsional transitions for the trans and gauche conformers essentially determine the potential barriers for the conformational interchange. The large differences in the values for V1 and V2 terms between this study and the results reported [2] earlier are due to the fact in the earlier study the dihedral angle (1268) of the gauche conformer is much larger than value of 118.28 obtained from the MP2/6-31G(d) calculation. The V1 and V2 terms are strongly correlated and the use of the gauche dihedral angle for the potential function determination reduces the correlation between these two terms. Utilizing ab initio calculation MP2/6-31G(d), we have also determined the barriers to internal rotation about the P±C bond. It is not surprising that the calculated potential constants, V1 through V3 and the barriers to internal rotation, trans to gauche and gauche to gauche, are very close to the experimental value (Table 6). The ab initio calculation predicts the values of the torsional fundamentals of 78 and 67 cm 21 for the trans and gauche conformers, respectively, in good agreement with the observed values. In addition, this calculation predicted the enthalpy difference of 198 cm 21 between the two conformers, which is not far from the experimental value. The agreement of the two potential functions is shown in Fig. 4.
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
7. Discussion The determination of the enthalpy difference for the conformers of (chloromethyl) phosphonothioic di¯uoride from the rare gas solutions clearly shows that the trans conformer is the more stable rotamer with an average DH value of 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21). Since only small interactions are expected to occur between the dissolved molecules and the rare gas atoms, this value should be relatively close to the value for the vapor state [4±8]. This enthalpy difference is in agreement with the ab initio calculations and is close to the value predicted from the MP2/6-3111G(2d,2p) calculation. It should be noted that as the size of basis sets at the MP2 level increased beyond 6-31G(d), the prediction of the enthalpy difference was not signi®cantly improved. Also the DH value predicted from the RHF/6-31G(d) and B3LYP/6-31G(d) calculations are very close but signi®cantly larger than the experimental one. Using two scaling factors of 0.88 and 0.90, the wavenumbers for the fundamentals predicted from the MP2/6-31(d) calculations are in good agreement with the observed values. Excluding those for the two carbon±hydrogen stretches, the average errors in the frequency predictions for the normal modes are 12 and 10 cm 21 for the trans and gauche conformers, respectively. Thus this set of scaling factors is suf®cient to predict the wavenumbers for the observed fundamentals for this type of organophosphorus molecules. We also used density functional calculation by the B3LYP method with the 6-31G(d) basis set to predict the wavenumbers of the fundamentals. The agreement is reasonably good with the observed values with the average error for the normal modes of 20 cm 21 for the trans conformer, which is better than the MP2/6-31G(d) calculation before scaling (the average error 31 cm 21). Therefore, smaller scaling factors are needed for B3LYP/6-31G(d) calculations for this type of organophosphorus molecules. The calculated PED of ClCH2P(S)F2 is relatively pure for both trans and gauche conformers. Most of the modes are made up by 40% or more of the description provided except for n 7 and n 10 for the trans conformer and n 5 and n 9 for the gauche conformer. However, n 7 for the trans conformer and n 9 for the gauche conformer have major contributions from four
155
motions. Thus, for these modes the description provided is more for book-keeping than providing the description of the motions involved. There is little difference between the corresponding diagonal force constants for the two conformers except for those of the ClCP bend. For ClCP bending Ê 22 smaller force constant, the value is 0.061 mdyn A for the gauche conformer than that of the trans Ê 22). The conformer (0.626 versus 0.687 mdyn A difference can be rationalized on the basis of the structural change with the conformational change (2.38 larger for the trans conformer). The change in the ClCP angle is from the interaction between the F and Cl atoms resulting in a larger force constant in the trans conformation. Therefore, the difference in the wavenumber for the fundamentals for the two conformers is mainly due to the differences in the mixing as indicted by the PEDs. It is clear that the rotational constants predicted from the ab initio calculations match reasonably well with the ones obtained from the microwave study [2]. The rotational constants (previously reported from the microwave spectra [2]) of B 1 C 2224 MHz for the trans conformer is predicted to have values of 2192, 2190, 2193, 2199 MHz, respectively, from the RHF/6-31G(d), MP2/6-31G(d), MP2/6-3111G(d,p), MP2/6-3111 G(2d,2p) calculations. There is poorer agreement of this value with the one predicted from B3LYP/631G(d) (2142 MHz) calculation. Because of the limited number of experimental rotational constants, we used a program developed in our laboratory, which incorporates the predicted differences among the structural parameters obtained from the ab initio calculations in the determination of the molecular geometry assuming the errors associated with ab initio calculations are mainly systematic. The program consists of iterative procedure, which starts from the ab initio predicted structural parameters and modi®es them in order to ®t the observed rotational constants. It restricts the change of all or of a selected number of equivalent geometric parameters in a way that keeps the differences among them unchanged form those predicted by the ab initio calculations. In addition to the ®tting of the observed rotational constants, the program also minimizes the differences between the initial (ab initio) structural parameters and their current values during the interactions. However,
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generally these differences are given a small weight in the overall ®t. In that sense, the initial values of the structural parameters and the number of the sets of rotational constants in¯uence the outcome of the structural ®t. In Table 2, we have listed the adjusted r0 structural parameters obtained by the application of the described method. It should be noted that the initial geometry was taken from the MP2/63111G(d,p) calculation with the exception of the P±F distance, which was taken from the RHF/631G(d) since it has been demonstrated to predict a more reasonable value [19]. Under the restriction of the Cs symmetry of the trans conformer, all geometric parameters were allowed to change in the structural ®t. This provided a good and reasonable ®t between the observed and calculated rotational constants (Table 2). We believe that the adjusted parameters produced in this way are more meaningful than the ab initio values alone. The major differences between the structural parameters for the two conformers are the SPC, PCCl and CPF1 angles. For the gauche conformer, the SPC angle is predicted to be 4±58 larger and the PCCl and CPF1 angles are predicted to be smaller by about 2±38, respectively. It would be interesting to carry out a structural determination by the electron diffraction technique using the restriction from the ab initio calculation and microwave spectroscopy. Acknowledgements J.R.D. acknowledges the University of Kansas City Trustees for a Faculty Fellowship award for partial ®nancial support of this research.
References [1] B.J. van der Veken, P. Coppens, R.D. Johnson, J.R. Durig, J. Chem. Phys. 83 (1985) 1517. [2] B.J. van der Veken, P. Coppens, R.D. Johnson, J.R. Durig, J. Phys. Chem. 90 (1986) 4537. [3] E. Steger, M. Kuntze, Spectrochim. Acta 23A (1967) 2189. [4] M.O. Bulanin, J. Mol. Struct. 99 (1995) 578. [5] B.J. van der Veken, F.R. De Munck, J. Chem. Phys. 97 (1992) 3060. [6] M.O. Bulanin, J. Mol. Struct. 347 (1995) 73. [7] W.A. Herrebout, B.J. van der Veken, A. Wang, J.R. Durig, J. Phys. Chem. 99 (1995) 578. [8] W.A. Herrebout, B.J. van der Veken, J. Phys. Chem. 100 (1996) 9671. [9] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian 94 (Revision B. 3), Gaussian Inc., Pittsburgh PA, 1995. [10] P. Pulay, Mol. Phys. 17 (1969) 197. [11] C. Moller, M.S. Plesset, Phys. Rev. 46 (1934) 618. [12] E.B. Wilson, J.C. Decius, P.C. Cross, Molecular Vibrations, McGraw-Hill, New York, NY, 1955. [13] G.A. Guirgis, X. Zhu, Z. Yu, J.R. Durig, J. Phys. Chem. 104 (2000) 4383. [14] M.J. Frisch, Y. Yamaguchi, J.F. Gaw, H.F. Schaefer III, J.S. Binkley, J. Chem. Phys. 84 (1986) 531. [15] R.D. Amos, Chem. Phys. Lett. 124 (1986) 376. [16] P.L. Polavarapu, J. Phys. Chem. 94 (1990) 8106. [17] G.W. Chantry, in: A. Anderson (Ed.), The Raman Effect, vol. 1, Marcel Dekker, New York, NY, 1971 (chap. 2). [18] P. Groner, R.D. Johnson, J.R. Durig, J. Mol. Struct. 142 (1986) 363. [19] J.R. Durig, J.B. Robb II, J. Xiao, T.K. Gounev, J. Mol. Struct. 516 (2000) 131.
www.elsevier.nl/locate/molstruc
Conformational stability of (chloromethyl) phosphonothioic di¯uoride from temperature-dependent infrared spectra of rare gas solutions and r0 structural parameters q J.R. Durig*, J. Xiao Department of Chemistry, University of Missouri Ð Kansas City, 5100 Rockhill Road, Kansas City, MO 64110-2499, USA Received 9 October 2000; accepted 3 November 2000
Abstract Variable temperature (255 to 21508C) studies of the infrared spectra (3500±400 cm 21) of (chloromethyl)phosphonothioic di¯uoride (ClCH2P(S)F2) dissolved in liquid xenon and krypton have been recorded. From these data, the enthalpy difference has been determined to be 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21) with the trans conformer being the more stable rotamer. Complete vibrational assignments are presented for both conformers, which are consistent with the predicted wavenumbers obtained from ab initio MP2/6-31G(d) calculations utilizing two scaling factors. The optimized geometries, conformational stabilities, harmonic force ®elds, infrared intensities, Raman activities and depolarization ratios have been obtained from RHF/ 6-31G(d) and/or MP2/6-31G(d) ab initio calculations. Hybrid density function theory (DFT) calculations to obtain the structural parameters and conformational stability by the B3LYP/6-31G(d) method were also carried out. These quantities are compared to the corresponding experimental quantities when appropriate as well as with some corresponding results for some similar molecules. The r0 structural parameters have been obtained from a combination of the previously reported microwave rotational constants and ab initio MP2/6-3111G(d,p) predicted parameters. The results are compared to some corresponding quantities for some similar molecules. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Conformational stability; Structural parameters; Ab initio calculations; (Chloromethyl)phosphonothioic di¯uoride
1. Introduction For some time, we have been investigating the conformational stability of organophosphorus molecules of the general formula: YCH2P(Z)X2 where Y CH3, F and Cl; Z O, S, BH3 and lone pair; X F, Cl and CH3. In our earlier studies of q Taken in part from the dissertation of J. Xiao, which will be submitted to the Department of Chemistry in partial ful®llment of the PhD degree. * Corresponding author. Tel.: 11-816-235-6038; fax: 11-816235-5502. E-mail address: [email protected] (J.R. Durig).
ClCH2P(O)F2 [1] and ClCH2P(S)F2 [2], we were able to show that the initial conclusion [3] on the conformational stabilities of these two molecules that the gauche rotamers were the more stable forms in the liquids was in error. For the ClCH2P(S)F2 molecule, a temperature study of the Raman spectrum of the liquid was carried out from which an enthalpy difference for the two conformers of 149 ^ 31 cm 21 (1.78 ^ 0.37 kJ mol 21) was obtained with the trans conformer the more stable form. Also from the far infrared torsional transitions for both conformers, the potential function for the conformational interchange was obtained from which an enthalpy
0022-2860/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0022-286 0(00)00966-2
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difference of 206 ^ 24 cm 21 (2.46 ^ 0.29 kJ mol 21) was estimated. Since it has been shown [4±8] that enthalpy determinations in rare gas solutions give values near those for the gas when the two conformers have similar dipole moments and molecular size, we initiated a variable temperature investigation of the infrared spectra of rare gas solutions of ClCH2P(S)F2. Additionally, we have carried out ab initio calculations to obtain predicted stabilities, vibrational frequencies, and structural parameters, particularly since the earlier vibrational assignment relied on transferred force constants to distinguish several of the conformer peaks. The results of this infrared spectra investigation and ab initio calculations are reported herein. 2. Experimental The sample of (chloromethyl)phosphonothioic di¯uoride was prepared from the corresponding dichloride (Alfa) by direct reaction with freshly sublimed antimony tri¯uoride. Sample puri®cation was performed with a low-temperature, low-pressure fractionating column. The purity of the sample was checked by comparing the mid-infrared spectra of the vapor to that previously published [2]. The mid-infrared spectra of the sample dissolved in liqui®ed krypton and xenon as a function of temperature (Fig. 1A) were recorded on a Bruker model IFS66 Fourier transform spectrometer equipped with a globar source, a Ge/KBr beamsplitter and a DTGS detector. The temperature studies ranged from 255 to 21008 and from 2105 to 21508 and were performed in a specially designed cryostat cell consisting of a 4 cm pathlength copper cell with wedged silicon windows sealed to the cell with indium gaskets. The complete system is attached to a pressure manifold to allow for the ®lling and evacuation of the cell. The cell is cooled by boiling liquid nitrogen and the temperature is monitored by two Pt thermoresistors. Once the cell is cooled to a designed temperature, a small amount of sample is condensed into the cell. The system is then pressurized with the rare gas, which immediately starts to condense, allowing the compound to dissolve. For each temperature investigated, 100 interferograms were recorded at a 1.0 cm 21 resolution, averaged,
Fig. 1. Comparison of experimental and calculated infrared spectra of (chloromethyl)phosphonothioic di¯uoride: (A) infrared spectrum of the sample dissolved in liquid xenon; (B) mixture of the calculated trans and gauche conformers with the experimentally determined DH of 244 cm 21; (C) pure gauche conformer; (D) pure trans conformer.
and transformed with a boxcar truncation function. The observed fundamental bands for the trans and gauche conformers are listed in Table 1. 3. Ab initio calculations The LCAO-MO-SCF restricted Hartree±Fock calculations were performed with the Gaussian 94 program [9] using Gaussian-type basis functions. The energy minima with respect to nuclear coordinates were obtained by the simultaneous relaxation of all the geometric parameters using the gradient method of Pulay [10]. Calculations were also carried out with full electron correlation by the perturbation method [11] to second order up to the 6-3111G(2d,2p)
Table 1 Observed and calculated frequencies (cm 21) and PEDs for (chloromethyl)phosphonothioic di¯uoride trans
gauche
B3LYP/6- Ab Fixed IR Raman Calc. Obs. Xenon PED 31G(d) initio a scaled b Int. act. c dep. c gas soln.
B3LYP/6- Ab Fixed IR Raman Calc. Obs. Xenon PED 31G(d) initio a scaled b Int. act. c dep. c gas d soln.
A0
3112 1467 1283 928 817 709 642 398 357 228 129 3175 1172 927 818 286 233 69
A 00
a b c d
n1 n2 n3 n4 n5 n6 n7 n8 n9 n 10 n 11 n 12 n 13 n 14 n 15 n 16 n 17 n 18
CH2 symmetric stretch CH2 symmetric deformation CH2 wag PF2 symmetric stretch PC stretch CCl stretch PS stretch PF2 wag PF2 deformation ClCP bend CPS bend CH2 antisymmetric stretch CH2 twist PF2 antisymmetric stretch CH2 rock PF2 rock PF2 twist Asymmetric torsion
3157 1500 1333 960 883 762 679 416 369 240 137 3227 1216 950 844 296 242 78
2962 1423 1264 910 838 723 644 416 369 240 137 3027 1153 901 800 296 242 78
8.2 68.79 15.3 12.23 9.1 1.15 278.1 2.22 47.8 16.55 86.0 8.12 16.2 12.81 51.2 4.73 16.1 3.74 1.2 7.33 2.0 0.30 2.4 49.87 0.5 8.23 138.8 0.86 3.3 2.77 3.1 4.72 0.7 0.29 5.0 0.04
0.13 0.71 0.74 0.12 0.52 0.20 0.05 0.43 0.36 0.51 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
2954 1404 1226 932 840 727 665 416 386 234 131 3009 1128 916 793 297 250 80
2940 1392 1223 926 840 721 663 413 ± ± ± 2995 1125 906 791 ± ± ±
100S1 3106 100S2 1470 98S3 1281 71S4,21S7 936 42S5,36S6,14S7 836 52S6,23S7,11S5 742 27S7,28S5,23S4,11S10 605 72S8,12S7 354 84S9 393 34S10,31S11 127 48S11,38S10 223 100S12 3173 98S13 1169 78S14,17S15 902 73S15,20S14 816 80S16,15S17 304 83S17,12S16 248 100S18 58
3155 1503 1328 971 880 792 646 368 408 134 236 3228 1212 930 854 318 260 67
2960 1426 1260 921 835 751 613 349 408 134 236 3028 1149 882 810 318 260 67
6.2 98.55 9.5 13.25 4.6 1.33 311.5 1.0 46.8 6.37 90.9 8.45 4.9 18.13 24.7 1.99 29.4 3.59 1.4 1.97 1.4 1.49 0.9 71.3 12.4 9.3 135.8 1.24 13.3 4.48 7.0 4.59 1.0 3.26 2.8 1.80
0.11 0.75 0.57 1220 1218 0.07 938 938 0.55 840 835 0.35 754 751 0.08 626 627 0.63 371 ± 0.75 ± ± 0.68 ± ± 0.72 ± ± 0.74 ± ± 0.74 ± ± 0.28 898 893 0.74 804 800 0.54 319 ± 0.63 ± ± 0.74 69 ±
100S1 100S2 98S3 41S4,25S7,22S15 35S5,30S6,20S4 48S6,15S7 45S7,28S5,13S4 55S8,32S9 29S9,19S11,18S10,18S8 50S10,24S11,15S16 45S11,19S9,12S11 100S12 97S13 79S14 62S15,15S4 53S16,12S9 71S17 96S18
The ab initio calculations are MP2/6-31(d). Scaled ab initio calculations with factor of 0.88 for the CH stretches, 0.9 for the heavy atom stretches and CH bends and 1.0 for all other coordinates at the MP2/6-31(d). Obtained from the RHF/6-31(d) basis set. Far infrared wavenumbers from Ref. [2].
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
Species Vib. Description No.
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basis set. In addition, density function theory (DFT) calculations made with the Gaussian 94 program [9] was restricted to the hybrid B3LYP method. The determined structural parameters are listed in Table 2. The energy difference that resulted from these various calculations ranged from 341 cm 21 (4.08 kJ mol 21) from the RHF/6-31G(d) calculation to 170 cm 21 (2.03 kJ mol 21) from the MP2/63111G(d,p) calculation with the trans conformer always the more stable form. In order to obtain a complete description of the molecular motions involved in the normal modes of (chloromethyl)phosphonothioic di¯uoride, a normal coordinate analysis has been carried out. The force ®eld in Cartesian coordinates was obtained with the Gaussian 94 program [9] from the MP2/6-31G(d) calculation. The internal coordinates de®ned in Table 2 and shown in Fig. 2 were used to form the symmetry coordinated listed in Table 3. The B-matrix elements [12] were used to convert the ab initio force ®eld from Cartesian coordinates into the force ®eld in desired internal coordinate [13]. The resulting force ®eld for both trans and gauche conformers are available from the authors. These force constants were used in a mass-weighted Cartesian coordinate calculation to reproduce the ab initio vibrational frequencies and to determine the potential energy distributions (PED) for both conformers, which are given in Table 1. The diagonal and off-diagonal elements of the force ®eld in internal coordinates were then modi®ed with scaling factors of 0.88 for the CH stretches, 0.9 for the heavy atom stretches and CH bends and 1.0 for all other coordinates. The calculation was repeated to obtain the ®xed scaled force ®eld and scaled vibrational frequencies. The infrared and Raman spectra were simulated as shown in Figs. 1 and 3, respectively. The frequencies, Raman scattering activities, and infrared intensities were obtained from the output of the ab initio calculations. The Raman scattering cross-sections, 2s j =2V; which are proportional to the Raman intensities, can be calculated from the scattering activities and the predicted frequencies for each normal modes [14±17]. To obtain the polarized Raman crosssections, the polarizabilities are incorporated into Sj by S j 1 2 rj =1 1 rj ; where r j is the depolarization ratio of the jth normal mode. The Raman scattering cross-sections and the predicted scaled frequencies
were used together with a Lorentzian function to obtain the calculated spectra. The predicted Raman spectra of the pure trans conformer of ClCH2P(S)F2 is shown in Fig. 3D and that of pure gauche conformer in Fig. 3C. The predicted Raman spectrum of the mixture of the two conformers with an enthalpy difference of 244 cm 21, with the trans conformer being the more stable form is shown in Fig. 3B. In Fig. 3B, the predicted Raman spectra of the mixtures of the two conformers are shown using the experimentally determined DH value of 244 cm 21 with the trans conformer being the more stable rotamer. These spectra should be compared with the experimental Raman spectrum of the liquid shown in Fig. 3A and the simulated Raman spectrum closely resembles the observed spectrum. Although there are some differences in the calculated versus experimental intensities, i.e. the PyS stretches are predicted too weak and ClCP bend is predicted too strong, these data demonstrate the utility of ab initio calculations in predicting the spectrum for conformer identi®cation and vibrational assignments for these types of organophosphorus molecules. The infrared spectra were also predicted from the MP2/6-31G(d) calculations and Raman scattering activities determined from the RHF/6-31G(d) basis set. Infrared intensities were calculated based on the dipole moment derivatives with respect to the Cartesian coordinates. The derivatives were taken from the ab initio calculations transformed to normal coordinates by: ! X 2mu 2m u Lj 2m i 2Xj j where Qi is the ith normal coordinate, Xj the jth Cartesian displacement coordinate, and Lij the transformation matrix between the Cartesian displacement coordinates and normal coordinates. The infrared intensities were then calculated by: " # 2m y 2 Np 2mx 2 2m z 2 1 1 Ii 2 2Qi 2Qi 2Qi 3c The predicted infrared spectra of the trans and gauche conformers are shown in Fig. 1C and D, respectively. The mixture of the two conformers is shown in Fig. 1B. These spectra can be compared to the experimental spectra of the samples dissolved in
Table 2 Ê , bond angles in degrees, rotational constants in MHz and dipole moments in Debye), rotational constants, dipole moments and energy for Structural parameters (bond distances in A (chloromethyl)phosphonothioic di¯uoride Parameter
Internal RHF/6-31G(d) coodinates
r(PyS) r(P±F1) r(P±F2) r(P±C) r(C±Cl) r(C±H1) r(C±H2) /SPC /PCCl /CPF1 /CPF2 /H1CP /H2CP t (SPCCl) t ((F1PCS) t (F2PCS) t (H1CPCl) t (H2CPCl) A B C um au um bu um cu um tu 2(E 1 1435)H DE (cm 21) a b
R X1 X2 T S r1 r2 h d p1 p2 a1 a2
gauche
MP2/6-31G(d)
trans
trans
gauche
gauche
MP2/6-311 1 G(d,p)
MP2/6-3111G(2d,2p)
This study a (r0)
trans
trans
trans
gauche
gauche
1.893 1.888 1.907 1.902 1.887 1.882 1.883 1.879 1.897 1.892 1.879 1.548 1.556 1.583 1.592 1.583 1.591 1.581 1.590 1.564 1.574 1.547 1.548 1.550 1.583 1.586 1.583 1.586 1.581 1.584 1.564 1.568 1.547 1.814 1.817 1.831 1.836 1.813 1.816 1.809 1.812 1.802 1.806 1.805 1.775 1.772 1.797 1.792 1.772 1.770 1.770 1.797 1.780 1.778 1.766 1.080 1.079 1.092 1.092 1.091 1.091 1.091 1.091 1.083 1.082 1.091 1.080 1.080 1.092 1.092 1.091 1.092 1.091 1.091 1.083 1.083 1.091 116.5 121.0 116.2 121.1 116.5 120.9 117.1 121.2 116.6 120.9 116.7 114.0 112.7 114.6 112.6 114.2 112.1 114.3 112.0 113.7 111.3 113.6 103.0 98.8 102.8 98.3 102.4 98.3 102.5 98.8 102.4 98.4 102.5 103.0 101.8 102.8 101.5 102.4 101.1 102.5 101.4 102.4 101.0 102.5 108.4 109.0 108.0 108.6 108.0 108.7 107.4 108.0 107.8 108.6 107.4 108.4 108.5 108.0 108.6 108.0 108.6 107.4 108.4 107.8 108.7 107.4 180.0 64.2 180.0 62.2 180.0 61.8 180.0 60.7 180.0 59.4 180.0 128.6 127.8 128.8 128.0 129.0 128.5 129.0 128.6 129.1 128.8 129.1 2128.6 2131.3 2128.8 2131.4 2129.0 2131.3 2129.0 2131.0 2129.1 2131.2 2129.1 2121.2 2120.8 2121.2 2120.6 2121.5 2120.8 2121.6 2120.6 2121.3 2120.2 2121.6 121.2 120.3 2121.2 120.5 121.5 120.6 121.6 120.9 121.3 120.4 121.6 3830 2661 3679 2564 3724 2588 3752 2596 3807 2587 3872 b 1124 1348 1098 1322 1122 1358 1123 1362 1127 1382 1140 b 1068 1120 1044 1095 1068 1122 1070 1125 1072 1130 1084 b 1.824 1.555 1.326 1.288 1.592 1.521 1.352 1.645 1.283 1.426 1.559 2.517 1.591 2.047 1.829 2.225 2.202 1.755 1.872 1.905 0.000 1.673 0.000 1.542 0.000 1.729 0.000 1.788 0.000 1.614 2.400 3.399 2.071 2.868 2.425 3.202 2.584 2.997 2.269 2.875 0.702569 0.701052 3.805474 3.803919 1.580697 1.579797 2.134169 2.133393 2.306039 2.305084 333 341 198 170 210
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trans
B3LYP/6-31G(d)
Calculated using the rotational constants reported in Ref. [2]. Calculated values obtained from the r0 values in this study.
149
150
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Fig. 2. Internal coordinates of (chloromethyl)phosphonothioic di¯uoride.
liqui®ed xenon shown in Fig. 1A. As a whole, the simulated infrared spectrum closely resembles the observed spectrum, which provides excellent evidence for the quality of the ab initio calculation. The optimized geometry was obtained from the MP2/6-31G(d) calculation for the trans conformer and then was utilized to obtain a potential surface scan. In this potential surface scan, only the torsional dihedral angle was allowed to vary on 10 increments from 08 (trans) to 180.08 (cis), which is a transition state. The resulting potential function indicated an
additional minimum at 1208, which corresponds to the gauche conformer. Optimization at the trans and gauche minima from the MP2/6-31G(d) calculations gives the energy of 21436.580687 and 21436.579797 hartree (1 hartree 219474 cm 21), respectively, which are consistent with a more stable trans conformer and with the gauche rotamer lying 198 cm 21 higher in energy. Combined with optimization at the cis position and the other transition state from the MP2/6-31G(d) calculation, this procedure leads to a more meaningful potential surface. The calculated potential surface scan as well as the potential surface using the optimized minima and maxima on the potential surface are shown in Fig. 4.
4. Conformational stability In order to gain information about the enthalpy difference between the two conformers similar to what is expected for the gas, variable temperature studies in lique®ed xenon and krypton were carried out. The sample was dissolved in lique®ed xenon and krypton and the spectra were recorded at different temperatures varying from 255 to 21508 depending on the solvent. Only small interactions are expected to
Table 3 Symmetry coordinates for (chloromethyl)phosphonothioic di¯uoride Species
Description
Symmetry coordinate a
A0
CH2 symmetric stretch CH2 symmetric deformation CH2 wag PF2 symmetric stretch PC stretch CCl stretch PS stretch PF2 wag PF2 deformation ClCP bend CPS bend
S1 r1 1 r2 S2 4m 2 a1 2 a2 2 11 2 12 S3 11 1 12 2 a1 2 a2 S4 x1 1 x2 S5 T S6 S S7 R S8 p1 1 p2 2 l1 2 l2 S9 4f 2 l1 2 l2 2 p1 2 p2 S10 d S11 h
A 00
CH2 antisymmetric stretch CH2 twist PF2 antisymmetric stretch CH2 rock PF2 rock PF2 twist Asymmetric torsion
S12 S13 S14 S15 S16 S17 S18
a
Not normalized.
r1 2 r2 11 2 12 2 a1 1 a2 x1 2 x2 11 2 12 1 a1 2 a2 l1 2 l2 1 p1 2 p2 l1 2 l2 2 p1 1 p2 t
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
Fig. 3. Raman spectra of (chloromethyl)phosphonothioic di¯uoride: (A) experimental spectrum of the liquid; (B) calculated spectrum of the mixture of both conformers with experimentally determined DH value; (C) pure gauche conformer; (D) pure trans conformer.
151
occur between the dissolved sample and the surrounding noble gas atoms; consequently, only small frequency shifts are anticipated when passing from the gas phase to the lique®ed noble gas solutions [4±8]. A signi®cant advantage of this study is that the conformer bands are better resolved in comparison with those in the infrared spectrum of the gas. This is particularly important since most of the conformer bands for this molecule are expected to be observed within a few wavenumbers of each other. Also the areas of the conformer peaks are more accurately determined than those from the spectrum of the gas. The best separated bands in the infrared spectra of the xenon and krypton solutions are assigned to the P± C stretch. Figs. 5 and 6 show the spectral changes for the bands belonging to the two conformers in the infrared spectrum of the xenon and krypton solutions, respectively. The lower wavenumber band has been con®dently assigned to the trans conformer. It is obvious that the increase in the intensity of the infrared bands assigned to the trans conformer as the temperature decreases con®rms the stability of the trans rotamer over the gauche rotamer. The improved resolution of the spectral allowed the enthalpy difference between the two conformers to be determined from the same conformational pair used in the previous study (PS stretch) as well as
Fig. 4. Potential function of the asymmetric torsion of (chloromethyl)phosphonothioic di¯uoride: (A) surface scan at MP2/6-31G(d); (B) ®t to the far infrared data from Ref. [2]; (C) optimization at MP2/6-31G(d).
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Fig. 5. Temperature-dependent infrared spectra of (chloromethyl)phosphonothioic di¯uoride dissolved in liquid xenon in the PC stretching region.
additional conformational bands belonging to the PC and CCl stretches. In order to obtain the enthalpy difference between the two conformers, 10 spectral data points were obtained over each temperature range (255 to 21008 for xenon and 2105 to 21508 for krypton) for each conformer pair (Table 4). The intensities of each conformer pair were ®t to the equation: 2ln k DH=RT 2 DS=R: The DH value was determined from a plot of 2ln K versus 1/T, where DH/R is the slope of the line and K is the intensity ratio Ig/It. It is assumed that DH is not a function of temperature over the temperature range. From the plot of the natural logarithm of the ratio as a function of the reciprocal of the absolute temperature, an average DH value of 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21) was obtained with the trans conformer being the more stable rotamer. The error limits are given by the standard deviation of the measured areas of the intensity data. These error limits do not take into account small associations with the lique®ed rare gas or other experimental factors such as the presence of overtones or combination bands in near coincidence with the measured fundamentals. 5. Vibrational assignment
Fig. 6. Temperature-dependent infrared spectra of (chloromethyl)phosphonothioic di¯uoride dissolved in liquid krypton in the PC stretching region.
A rather complete vibrational assignment of the infrared and Raman spectra of (chloromethyl)phosphonothios di¯uoride has been previously reported [2]. However, the normal coordinate calculations were based upon the transferred force constants from the ClCH2P(O)F2 and CH3P(S)F2 molecules whereas we carried out normal coordinate analysis utilizing ab initio force constants from the MP2/631G(d) calculations. The resulting PED indicated a reversal in the assignment of the two CH2 stretch modes compared to the previously reported one [2]: the band at 2954 cm 21 is now assigned to the CH2 symmetric stretch and the band at 3009 cm 21 is assigned to CH2 antisymmetric stretch. This assignment is also supported by the measured depolarization ratios from the Raman spectrum of the liquid [2]. The infrared spectrum of the sample dissolved in the liquid rare gas solutions makes it possible to
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
153
Table 4 Temperature and intensity ratios for the conformational study of (chloromethyl)phosphonothioic di¯uoride a T (8C)
1000/T (K)
255 260 265 270 275 280 285 290 295 2100 DH (cm 21) 2105 2110 2115 2120 2125 2130 2135 2140 2145 2150 DH (cm 21)
4.587 4.695 4.808 4.926 5.051 5.181 5.319 5.464 5.618 5.780
a
5.952 6.135 6.329 6.536 6.757 6.993 7.246 7.519 7.812 8.130
K I628 =I663 £ 102
K I751 =I722 £ 102
K I841 =I836 £ 10
6.210 5.600 5.195 3.793 4.777 3.898 4.360 3.694 3.731 263 ^ 67
6.917 6.715 6.100 6.594 5.488 5.675 5.616 5.438 4.963 194 ^ 31 4.612 5.976 4.573 6.159 3.753 4.171 4.032 2.861 4.002 2.704 198 ^ 57
2.916 2.717 2.597 2.502 2.402 2.276 2.175 2.078 1.948 1.809 262 ^ 6 1.455 1.396 1.300 1.207 1.096 1.014 0.929 0.815 0.783 0.604 251 ^ 6
3.731 3.723 3.333 2.918 2.332 2.060 2.196 1.840 1.716 296 ^ 29
Average DH 244 ^ 16 cm21 (2.92 ^ 0.19 kJ mol 21) with the trans-conformer the more stable species.
assign most of the fundamentals for the gauche conformer as well and the assignments of the observed bands are listed in Table 1. As a result of the improved resolution of the bands from the infrared spectrum of the rare gas solutions, the n 5 fundamental is clearly distinguished for the gauche rotamer from the corresponding mode for the trans conformer. According to the calculated vibrational frequencies, a reversal in the assignments from that previously reported [2] is suggested for the two bands at 938 and 932 cm 21, which was previously assigned to the PF2 symmetric stretches of the trans and gauche conformers, respectively.
torsional transitions of the trans and gauche conformers published [2] earlier (Table 5). The torsional dihedral angular dependence of the internal rotational constants F(f ) can be represented as a Fourier series: F f F0 1
k1
Fk cos kf
Table 5 Observed and calculated (cm 21) asymmetric torsional transitions for (chloromethyl)phosphonothioic di¯uoride (far-infrared data from Ref. [2]) Conformer
Transition
Obs. a
D (obs. 2 calc.) b
trans
1Ã0 2Ã1 3Ã2 4Ã3 17 Ã 0^ 2^ Ã 17
80.11 78.29 76.62 74.58 69.31 66.77
20.24 20.12 0.19 0.18 0.31 20.31
6. Asymmetric torsion The potential function for conformer interconversion has been redetermined utilizing the DH value obtained from the rare gas solutions, the dihedral angle 118.28 (1808 2 61.88, which is the value of the dihedral angle SPCCl) of the gauche rotamer from MP2/6-31G(d) calculation and the asymmetric
8 X
cis
Average DH 244 ^ 16 cm21 (2.92 ^ 0.19 kJ mol 21) with the trans-conformer the more stable species. b Calculated using the ®tted potential constants listed in Table 6 for the MP2/6-31G(d) geometry. a
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Table 6 Potential constants (cm 21), barriers to internal rotation (cm 21), enthalpy differences and dihedral angle for (chloromethyl)phosphonothioic di¯uoride Parameter
MP2/6-31G(d)
Ref. [2]
This study a
V1 V2 V3 V4 V6 trans to gauche barrier gauche to gauche barrier Enthalpy (cm 21) difference Dihedral angle (gauche)
141 78 1004 45
2167 479 947
138 101 927 97 44 1110 815 244 118.20
a
1132 948 198 118.16
49 1280 571 206 126
Calculated using the assignments in Table 5 and the Fourier coef®cients (Fi) calculated from the MP2/6-31G(d) geometry.
The relaxation of the structural parameters B(f ) during the internal rotation can be incorporated into the above equation by assuming that they are small periodic functions of the torsional angle of the general type: B f a 1 b cos f 1 c sin f The structural parameters (Table 2) obtained from the optimized geometries for both the trans and gauche conformers were used to obtain the kinetic constants. The torsional potential is also represented as a Fourier cosine series in the internal angle (f ): V f
6 X Vi 1 2 cos if 2 i1
The kinetic terms, the asymmetric torsional frequencies for both conformers, the experimental enthalpy and the gauche dihedral angle were used to ®t the potential function utilizing a computer program developed in our laboratory [18]. As an iterative process, this calculation was continued until the differences between the observed and calculated frequencies as well as the dispersions in the potential constants were minimized. From the calculated potential function, the trans to gauche and gauche to gauche barriers are determined to be 1100 and 815 cm 21, respectively, with the enthalpy difference between the two conformers of 244 cm 21. These results are listed in Table 6 along with the results previously reported [2]. Although
the potential coef®cients are signi®cantly different from the values from those obtained earlier, the trans to gauche and gauche to gauche barriers have very similar values. The spacings for the hot band torsional transitions for the trans and gauche conformers essentially determine the potential barriers for the conformational interchange. The large differences in the values for V1 and V2 terms between this study and the results reported [2] earlier are due to the fact in the earlier study the dihedral angle (1268) of the gauche conformer is much larger than value of 118.28 obtained from the MP2/6-31G(d) calculation. The V1 and V2 terms are strongly correlated and the use of the gauche dihedral angle for the potential function determination reduces the correlation between these two terms. Utilizing ab initio calculation MP2/6-31G(d), we have also determined the barriers to internal rotation about the P±C bond. It is not surprising that the calculated potential constants, V1 through V3 and the barriers to internal rotation, trans to gauche and gauche to gauche, are very close to the experimental value (Table 6). The ab initio calculation predicts the values of the torsional fundamentals of 78 and 67 cm 21 for the trans and gauche conformers, respectively, in good agreement with the observed values. In addition, this calculation predicted the enthalpy difference of 198 cm 21 between the two conformers, which is not far from the experimental value. The agreement of the two potential functions is shown in Fig. 4.
J.R. Durig, J. Xiao / Journal of Molecular Structure 562 (2001) 145±156
7. Discussion The determination of the enthalpy difference for the conformers of (chloromethyl) phosphonothioic di¯uoride from the rare gas solutions clearly shows that the trans conformer is the more stable rotamer with an average DH value of 244 ^ 16 cm 21 (2.92 ^ 0.19 kJ mol 21). Since only small interactions are expected to occur between the dissolved molecules and the rare gas atoms, this value should be relatively close to the value for the vapor state [4±8]. This enthalpy difference is in agreement with the ab initio calculations and is close to the value predicted from the MP2/6-3111G(2d,2p) calculation. It should be noted that as the size of basis sets at the MP2 level increased beyond 6-31G(d), the prediction of the enthalpy difference was not signi®cantly improved. Also the DH value predicted from the RHF/6-31G(d) and B3LYP/6-31G(d) calculations are very close but signi®cantly larger than the experimental one. Using two scaling factors of 0.88 and 0.90, the wavenumbers for the fundamentals predicted from the MP2/6-31(d) calculations are in good agreement with the observed values. Excluding those for the two carbon±hydrogen stretches, the average errors in the frequency predictions for the normal modes are 12 and 10 cm 21 for the trans and gauche conformers, respectively. Thus this set of scaling factors is suf®cient to predict the wavenumbers for the observed fundamentals for this type of organophosphorus molecules. We also used density functional calculation by the B3LYP method with the 6-31G(d) basis set to predict the wavenumbers of the fundamentals. The agreement is reasonably good with the observed values with the average error for the normal modes of 20 cm 21 for the trans conformer, which is better than the MP2/6-31G(d) calculation before scaling (the average error 31 cm 21). Therefore, smaller scaling factors are needed for B3LYP/6-31G(d) calculations for this type of organophosphorus molecules. The calculated PED of ClCH2P(S)F2 is relatively pure for both trans and gauche conformers. Most of the modes are made up by 40% or more of the description provided except for n 7 and n 10 for the trans conformer and n 5 and n 9 for the gauche conformer. However, n 7 for the trans conformer and n 9 for the gauche conformer have major contributions from four
155
motions. Thus, for these modes the description provided is more for book-keeping than providing the description of the motions involved. There is little difference between the corresponding diagonal force constants for the two conformers except for those of the ClCP bend. For ClCP bending Ê 22 smaller force constant, the value is 0.061 mdyn A for the gauche conformer than that of the trans Ê 22). The conformer (0.626 versus 0.687 mdyn A difference can be rationalized on the basis of the structural change with the conformational change (2.38 larger for the trans conformer). The change in the ClCP angle is from the interaction between the F and Cl atoms resulting in a larger force constant in the trans conformation. Therefore, the difference in the wavenumber for the fundamentals for the two conformers is mainly due to the differences in the mixing as indicted by the PEDs. It is clear that the rotational constants predicted from the ab initio calculations match reasonably well with the ones obtained from the microwave study [2]. The rotational constants (previously reported from the microwave spectra [2]) of B 1 C 2224 MHz for the trans conformer is predicted to have values of 2192, 2190, 2193, 2199 MHz, respectively, from the RHF/6-31G(d), MP2/6-31G(d), MP2/6-3111G(d,p), MP2/6-3111 G(2d,2p) calculations. There is poorer agreement of this value with the one predicted from B3LYP/631G(d) (2142 MHz) calculation. Because of the limited number of experimental rotational constants, we used a program developed in our laboratory, which incorporates the predicted differences among the structural parameters obtained from the ab initio calculations in the determination of the molecular geometry assuming the errors associated with ab initio calculations are mainly systematic. The program consists of iterative procedure, which starts from the ab initio predicted structural parameters and modi®es them in order to ®t the observed rotational constants. It restricts the change of all or of a selected number of equivalent geometric parameters in a way that keeps the differences among them unchanged form those predicted by the ab initio calculations. In addition to the ®tting of the observed rotational constants, the program also minimizes the differences between the initial (ab initio) structural parameters and their current values during the interactions. However,
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generally these differences are given a small weight in the overall ®t. In that sense, the initial values of the structural parameters and the number of the sets of rotational constants in¯uence the outcome of the structural ®t. In Table 2, we have listed the adjusted r0 structural parameters obtained by the application of the described method. It should be noted that the initial geometry was taken from the MP2/63111G(d,p) calculation with the exception of the P±F distance, which was taken from the RHF/631G(d) since it has been demonstrated to predict a more reasonable value [19]. Under the restriction of the Cs symmetry of the trans conformer, all geometric parameters were allowed to change in the structural ®t. This provided a good and reasonable ®t between the observed and calculated rotational constants (Table 2). We believe that the adjusted parameters produced in this way are more meaningful than the ab initio values alone. The major differences between the structural parameters for the two conformers are the SPC, PCCl and CPF1 angles. For the gauche conformer, the SPC angle is predicted to be 4±58 larger and the PCCl and CPF1 angles are predicted to be smaller by about 2±38, respectively. It would be interesting to carry out a structural determination by the electron diffraction technique using the restriction from the ab initio calculation and microwave spectroscopy. Acknowledgements J.R.D. acknowledges the University of Kansas City Trustees for a Faculty Fellowship award for partial ®nancial support of this research.
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