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On the vibrational assignment of thiophosphoryl fluoride
Spectroohimioa Acta,Vol.26A,pp.975to976.Pergsmon Prws1969.Printed inNorthern Ireland
On the vibrational assigment of thiophosphoryl fluoride H. F. SEUBVELL Department of Chemistry, Queen’s University, Kingston, Ontario, Canada (Received7 June 1968) &&a&--Normal coordinate oalculations have been carried out for thiophoephoryl fluoride (SPF,) using a simple valence foroe field and several mod&d valence foroe fields. These o&ul&ions have shown that the aI vibrations of SPF, cannot be assigned in a simple way to bending or stretchingvibrations. The degeneratee vibrations on the other hand can be assigned to PF stret&ing FPF bending and SPF bending vibrations. INTRODUCTION
amount of work has been published on the Raman [l-4] and infrared [3-61 spectra of thiophosphoryl fluoride SPF,. Three force constant calculations have also been reported [7-91. The earlier Raman work [l] was shown to be in error by later workers [2-41. However, there is now general agreement on the frequencies of the six fundamental vibrations obtained from both infrared and Raman data [2-S]. The SPF, molecule undoubtedly belongs to the point group C,, and the six fundamental vibrations comprise three totally symmetric u1 modes, 983, 698 and 442 cm-l and three doubly degenerate e modes 961, 404 and 275 cm-l [S]. The assignment of the fundamentals to a, and e symmetry types is based on Raman polarization data and infrared gas phase band contours. CAVELL [6] has suggested that the highest a, fundamental should be assigned as a P-S stretching vibration, while the 698 cm-l frequency should be attributed to the PF, symmetric stretohing mode. This assignment has been disputed by other workers [3,4]. The purpose of the calculation reported here is to investigate the normal coordinates of SPF, and decide on the correct assignment of the fundamentals. A CONSIDERABLE
hLCULATIONS
Previous calculations [7-91 are invalid because the original incorrect frequency data [l] was used. We have solved the secular equation in internal coordinates including one redundant coordinate. The internal coordinates employed are shown in Fig. 1. [I] M. L. DELWAand F. FRANCOIS, Cmpt. Rend. 226, 894 (1948); J. C&n. Phys. 46,87 (1949). [2] A. M~-GER, H. W. ROESKY and B. KREBS, 2. C&m. 7,169 (1967). [3] A. M&ER, B. KZBBS, E. Nu~KE and A. Rvo~g, Ber. Bunsengee.Phye. Ohem. 71,671(1967). [4] J. R. DURIUand J. W. CLARK, J. Chem. P&a. 46, 3057 (1967). [6] H. G. HORN, A. M~-LLER and 0. GLEMSER, 2. Nutqforsch. Ma, 746 (1966). [a] R. CAVEI&, Speotrochim.Acta =A, 249 (1967). [73 H. SIEBERT, 2. Anorg. AZZgem.Chem. 875,210 (1964). [S] J. S. ZIOXEK rmd E. A. PIOTROW~JII, J. Chem. Phya. &I, 1087 (1961). [9] G. NA~ARAJAN, J. 5’00.Id. Rea. (India) 2lB, 366 (1962). 973
H. F. SHUR~ELL
914
v F
2
? =* ‘1,4 @‘pF ) RpA r2,,, (Ar,F) R3= Ar3+ h,,) R4=*r4,5 (Arp5) Fig. 1. Internal COOAIMAX for SPF,.
All cdculrttions were carried out on an IBM 360/50 computer using a mod&d version [lo] of the Fortran program written by S~HA~ET~~HNEIDER [ll]. WILSON’s F-U matrix method was employed for the calculations [12]. The U matrix was calculated using bond lengths and angles taken from Ref. [13] (rp8 = 1.86 8, ~~~ = 1.43 A, aFPF = 100.3” and @SPF = 117.89. The F matrix was set up for & genera,1valence force field (G.V.F.F.). The potential function is: 2V = F,(R,2 + Rza + Rsa) + F$,a + 2F,,(&K
+ R,&
+
R,W
+
+
+
R,&i
2F,,(R,R,
R,R,
+
23’,@1%
+
R,R,
+
R,-& -W,,
+
2~,,CRJ,
+
JUGi
+
W,)
+
2K&W,
+
R&
+
2F,,V-W,
+
&R,
+
JW,)
-I-
=‘,W4,
-I-
&$,,
+
2F,,W,&,
+
R,-%
+
+
W&V,,
4$,
+
W4,
+ +
+
R,R,
+
+
R&J
W,
.W,
WA
&R,)
+
+
~~&V-G R2-h
+
-‘,,‘VW,
R,R,
+
&R,
+
2F,,V,&,
+
+
+
R2.h
+
Q4,
JWJ
+
+
+
+
+ Fa(&i” + Be2 + &2) + J’,(R,2 + Boa + %,2)
+
+
&R,,)
WL,) -I-
W,,)
WM
WU.
[lo] W. V. F. BROODY, private communication. [ll] J. H. SCECAOHTSOHNEIDER, T&mica1 Report No. 57-65, Shell Development Co. (1965). [12] E. B. WILSON, JR., J. C. DECKS and P. C. CROSS, MoZecuZar Vihtionrr. MoGraw-Hill (1956). [13] Q. WILLIAMS, J. SEEIUDAN and W. GORDY, J. Chmn. Phys. 20,164 (1962); N. J. HAWKINS. V. W. COEIENand W. 8. KOSHI, J. C?ma. Phys. 20,628 (1962).
976
On the vibrational assignment of thiophosphorylfluoride
This potential function involves the sixteen force constants listed in Table 1. Since only six vibrational frequencies are available, some simplification must be made. One method would be to transfer force constants from related molecules, as was done by NAUABAJA~[9]. However, this method was rejected in favour of the following procedure. Table 1. Desclriptionsof fame oon&ant~ of the G.V.F.F. potent&l fun&ion 1. 2. 3.
4. 6.
6.
7.
8.
9. 10. 11. 12. 13.
14. 16.
16.
F* = PF stretahing P, = PS atmtohing
Fa=FPFbending F/J= SPF bending
F,,= PF &ret&-PF stretch intmaotion Fr:, = PF atretah-PS eke&h interaction pip = PF &&oh-FPF bend internotion. where
the PF bond forms one side of the FPF angle. Pm’ = ILLfor 7. but the PF bond doee not form one aide of the FPF augle.
F,p = F,p'= Fm = F&T = Faa = Fp,q= F,x@= Fag'=
PF stmtoh-S9F bend intareetion, where the PF bond forme one side of the SPF nngle. esfor 9, but the PF bond does not form one eide of the SPF en&. PS stretch-FPF bend interaction Pfdetreteh-SPF bend i&areetion FPF bend-FPF bend intenwtion SPF bmd-SPF band intern&ion FPF bend-SPF bend intern&ion with a oommon PF bond. aefor 16, but with no oommon PF bond.
The best possible fit between observed and calculated frequencies was first obtained using only four diagonal force constants, PS and PF stretching constants and SPF and FPF bending constants. All other force constants were set equal to zero. This is a simple valence force field (S.V.F.F.). The results of these preliminary oalculations are shown in Table 2. Table 2. Resulta using a S.V.F.F.
1.
2. 3. 4.
Fame oonsta.nts* (mdynlA) 6.620 FPF 6.748 FPS 0.686 FFPF 0.290 FSPF
obs. 983 al 698 ( 442 961 e 404 L276
Frequenoiee (am-l) calo. 1018 644 417 961 407 276
Potential energy distribution Fl
0.463 0.629 0.018 0.929 0.044 0.026
El2
F8
Ei
0.396 0.433 0.171 0.000 0.000 0.000
0.114 0.029 0.612 0.044 0.966 0.001
0.037 0.009 0.199 0.027 0.001 0.973
* In this table FmF hm been divided by vpF2and Fspp has been divided by T~F. 38, consistent
to give
unite.
The next step was to find which of the twelve interaction constants were signiflcant. It was found that no single interaction constant was more important than all of the others. Several sets of force constants, involving the four principal constants and one interaction constant, produced a reasonable fit between observed and calculated frequencies. Finally, to each set of force constants described above a second interaction constant was added and in many cases an excellent fit between observed and calculated frequencies was obtained. It was found that F,, a PF stretch-PS stretch interaction constant was the most significant. Including this, together with either F1,, 8, or P,, in the force field lead to excellent fits between observed and calculated frequencies. Another six force constant field that gave an almost perfect fit involved P,, a PF stretch-FPF bend interaction, together with P,,.
976
H.
F. SKLTRVELL
In all cases the sets of force constants were physically reasonable and it is evident that the valence force field for SPF, contains many significant interaction constants. In order to further refine the force field it would be necessary to have additional experimental data, such as centrifugal distortion constants, Coriolis interaction constants and frequency data from isotopically substituted molecules (unfortunately fluorine has only one isotope). However, in order to discuss the assignments, an exact force field is not essential. All of the calculations described above lead to the same assignment, and it is unlikely that a complete force field would change these assignments significantly. In order to discuss the assignments of the fundamental modes, the eigenvectors of the product of the P and B matrices were calculated. These comprise the L matrix of the transformation: R = LQ, where R is a vector of internal coordinates and Q is a vector of normal coordinates. L is obtained from the diagonalization of CfF [12] and may be used to classify the frequencies, since the elements Llk of the eigenvector corresponding to the i-th frequency, give the ratios of the amplitudes of the displacements of the internal coordinates Ra for that normal vibration. However, it has been shown [14] that this is not the most reliable method for classifying normal vibrations. A better method involves the calculation of the distribution of potential energy in the internal coordinates for each normal mode [ 141. Alternatively the contribution to each frequency from the various force constants can be calculated [lo, 111. We have used the latter method. Potential energy distributions were calculated for all sets of force constants that gave a good fit between observed and calculated frequencies. In all cases the distributions among the four principal force constants were similar to those shown in Table 2. From these P.E.D.‘s, it is evident that it is not possible to assign any of the a, fundamentals to any single mode of vibration. CONCLUSIONS Calculations using a simple valence force field and mod&d fields containing one and two interaction constants have shown that the highest a, fundamental (vr) of the SPF, molecule is essentially a mixture of PF and PS stretching vibrations. The va mode also contains both PF and PS stretching vibrations. The third a, fundamental is essentially a symmetric FPF deformation mode, but here again there is a contribution from PS stretching. Thus the descriptions given by previous workers [3,4, 61 for the a, fundameritals of SPF, are not correct. However, the descriptions given previously for the degenerate e modes are confirmed. It is also evident that many interaction constants are important in the force field of SPF,. However, it is reasonable to conclude that the PF and PS stretching constants are both near 6.0 mdyn/A, the FPF bending constant is approximately 0.7 mdyn/A (1.6 mdyn -A) and the SPF bending constant is approximately 0.3 mdyn/A (0.8 mdyn - A). Aoknowle&mmt~The author is very grateful to Dr. W. V. F. BROOKEIof the University of New B runswiokfor the use of his programs. The financial assistmoe of the National Research Council of Canada is also gratefully acknowledged. [14] Y. MORINO and K. KUCF~ITSU, J. Chem. P&a. SO,1089 (1962).
On the vibrational assigment of thiophosphoryl fluoride H. F. SEUBVELL Department of Chemistry, Queen’s University, Kingston, Ontario, Canada (Received7 June 1968) &&a&--Normal coordinate oalculations have been carried out for thiophoephoryl fluoride (SPF,) using a simple valence foroe field and several mod&d valence foroe fields. These o&ul&ions have shown that the aI vibrations of SPF, cannot be assigned in a simple way to bending or stretchingvibrations. The degeneratee vibrations on the other hand can be assigned to PF stret&ing FPF bending and SPF bending vibrations. INTRODUCTION
amount of work has been published on the Raman [l-4] and infrared [3-61 spectra of thiophosphoryl fluoride SPF,. Three force constant calculations have also been reported [7-91. The earlier Raman work [l] was shown to be in error by later workers [2-41. However, there is now general agreement on the frequencies of the six fundamental vibrations obtained from both infrared and Raman data [2-S]. The SPF, molecule undoubtedly belongs to the point group C,, and the six fundamental vibrations comprise three totally symmetric u1 modes, 983, 698 and 442 cm-l and three doubly degenerate e modes 961, 404 and 275 cm-l [S]. The assignment of the fundamentals to a, and e symmetry types is based on Raman polarization data and infrared gas phase band contours. CAVELL [6] has suggested that the highest a, fundamental should be assigned as a P-S stretching vibration, while the 698 cm-l frequency should be attributed to the PF, symmetric stretohing mode. This assignment has been disputed by other workers [3,4]. The purpose of the calculation reported here is to investigate the normal coordinates of SPF, and decide on the correct assignment of the fundamentals. A CONSIDERABLE
hLCULATIONS
Previous calculations [7-91 are invalid because the original incorrect frequency data [l] was used. We have solved the secular equation in internal coordinates including one redundant coordinate. The internal coordinates employed are shown in Fig. 1. [I] M. L. DELWAand F. FRANCOIS, Cmpt. Rend. 226, 894 (1948); J. C&n. Phys. 46,87 (1949). [2] A. M~-GER, H. W. ROESKY and B. KREBS, 2. C&m. 7,169 (1967). [3] A. M&ER, B. KZBBS, E. Nu~KE and A. Rvo~g, Ber. Bunsengee.Phye. Ohem. 71,671(1967). [4] J. R. DURIUand J. W. CLARK, J. Chem. P&a. 46, 3057 (1967). [6] H. G. HORN, A. M~-LLER and 0. GLEMSER, 2. Nutqforsch. Ma, 746 (1966). [a] R. CAVEI&, Speotrochim.Acta =A, 249 (1967). [73 H. SIEBERT, 2. Anorg. AZZgem.Chem. 875,210 (1964). [S] J. S. ZIOXEK rmd E. A. PIOTROW~JII, J. Chem. Phya. &I, 1087 (1961). [9] G. NA~ARAJAN, J. 5’00.Id. Rea. (India) 2lB, 366 (1962). 973
H. F. SHUR~ELL
914
v F
2
? =* ‘1,4 @‘pF ) RpA r2,,, (Ar,F) R3= Ar3+ h,,) R4=*r4,5 (Arp5) Fig. 1. Internal COOAIMAX for SPF,.
All cdculrttions were carried out on an IBM 360/50 computer using a mod&d version [lo] of the Fortran program written by S~HA~ET~~HNEIDER [ll]. WILSON’s F-U matrix method was employed for the calculations [12]. The U matrix was calculated using bond lengths and angles taken from Ref. [13] (rp8 = 1.86 8, ~~~ = 1.43 A, aFPF = 100.3” and @SPF = 117.89. The F matrix was set up for & genera,1valence force field (G.V.F.F.). The potential function is: 2V = F,(R,2 + Rza + Rsa) + F$,a + 2F,,(&K
+ R,&
+
R,W
+
+
+
R,&i
2F,,(R,R,
R,R,
+
23’,@1%
+
R,R,
+
R,-& -W,,
+
2~,,CRJ,
+
JUGi
+
W,)
+
2K&W,
+
R&
+
2F,,V-W,
+
&R,
+
JW,)
-I-
=‘,W4,
-I-
&$,,
+
2F,,W,&,
+
R,-%
+
+
W&V,,
4$,
+
W4,
+ +
+
R,R,
+
+
R&J
W,
.W,
WA
&R,)
+
+
~~&V-G R2-h
+
-‘,,‘VW,
R,R,
+
&R,
+
2F,,V,&,
+
+
+
R2.h
+
Q4,
JWJ
+
+
+
+
+ Fa(&i” + Be2 + &2) + J’,(R,2 + Boa + %,2)
+
+
&R,,)
WL,) -I-
W,,)
WM
WU.
[lo] W. V. F. BROODY, private communication. [ll] J. H. SCECAOHTSOHNEIDER, T&mica1 Report No. 57-65, Shell Development Co. (1965). [12] E. B. WILSON, JR., J. C. DECKS and P. C. CROSS, MoZecuZar Vihtionrr. MoGraw-Hill (1956). [13] Q. WILLIAMS, J. SEEIUDAN and W. GORDY, J. Chmn. Phys. 20,164 (1962); N. J. HAWKINS. V. W. COEIENand W. 8. KOSHI, J. C?ma. Phys. 20,628 (1962).
976
On the vibrational assignment of thiophosphorylfluoride
This potential function involves the sixteen force constants listed in Table 1. Since only six vibrational frequencies are available, some simplification must be made. One method would be to transfer force constants from related molecules, as was done by NAUABAJA~[9]. However, this method was rejected in favour of the following procedure. Table 1. Desclriptionsof fame oon&ant~ of the G.V.F.F. potent&l fun&ion 1. 2. 3.
4. 6.
6.
7.
8.
9. 10. 11. 12. 13.
14. 16.
16.
F* = PF stretahing P, = PS atmtohing
Fa=FPFbending F/J= SPF bending
F,,= PF &ret&-PF stretch intmaotion Fr:, = PF atretah-PS eke&h interaction pip = PF &&oh-FPF bend internotion. where
the PF bond forms one side of the FPF angle. Pm’ = ILLfor 7. but the PF bond doee not form one aide of the FPF augle.
F,p = F,p'= Fm = F&T = Faa = Fp,q= F,x@= Fag'=
PF stmtoh-S9F bend intareetion, where the PF bond forme one side of the SPF nngle. esfor 9, but the PF bond does not form one eide of the SPF en&. PS stretch-FPF bend interaction Pfdetreteh-SPF bend i&areetion FPF bend-FPF bend intenwtion SPF bmd-SPF band intern&ion FPF bend-SPF bend intern&ion with a oommon PF bond. aefor 16, but with no oommon PF bond.
The best possible fit between observed and calculated frequencies was first obtained using only four diagonal force constants, PS and PF stretching constants and SPF and FPF bending constants. All other force constants were set equal to zero. This is a simple valence force field (S.V.F.F.). The results of these preliminary oalculations are shown in Table 2. Table 2. Resulta using a S.V.F.F.
1.
2. 3. 4.
Fame oonsta.nts* (mdynlA) 6.620 FPF 6.748 FPS 0.686 FFPF 0.290 FSPF
obs. 983 al 698 ( 442 961 e 404 L276
Frequenoiee (am-l) calo. 1018 644 417 961 407 276
Potential energy distribution Fl
0.463 0.629 0.018 0.929 0.044 0.026
El2
F8
Ei
0.396 0.433 0.171 0.000 0.000 0.000
0.114 0.029 0.612 0.044 0.966 0.001
0.037 0.009 0.199 0.027 0.001 0.973
* In this table FmF hm been divided by vpF2and Fspp has been divided by T~F. 38, consistent
to give
unite.
The next step was to find which of the twelve interaction constants were signiflcant. It was found that no single interaction constant was more important than all of the others. Several sets of force constants, involving the four principal constants and one interaction constant, produced a reasonable fit between observed and calculated frequencies. Finally, to each set of force constants described above a second interaction constant was added and in many cases an excellent fit between observed and calculated frequencies was obtained. It was found that F,, a PF stretch-PS stretch interaction constant was the most significant. Including this, together with either F1,, 8, or P,, in the force field lead to excellent fits between observed and calculated frequencies. Another six force constant field that gave an almost perfect fit involved P,, a PF stretch-FPF bend interaction, together with P,,.
976
H.
F. SKLTRVELL
In all cases the sets of force constants were physically reasonable and it is evident that the valence force field for SPF, contains many significant interaction constants. In order to further refine the force field it would be necessary to have additional experimental data, such as centrifugal distortion constants, Coriolis interaction constants and frequency data from isotopically substituted molecules (unfortunately fluorine has only one isotope). However, in order to discuss the assignments, an exact force field is not essential. All of the calculations described above lead to the same assignment, and it is unlikely that a complete force field would change these assignments significantly. In order to discuss the assignments of the fundamental modes, the eigenvectors of the product of the P and B matrices were calculated. These comprise the L matrix of the transformation: R = LQ, where R is a vector of internal coordinates and Q is a vector of normal coordinates. L is obtained from the diagonalization of CfF [12] and may be used to classify the frequencies, since the elements Llk of the eigenvector corresponding to the i-th frequency, give the ratios of the amplitudes of the displacements of the internal coordinates Ra for that normal vibration. However, it has been shown [14] that this is not the most reliable method for classifying normal vibrations. A better method involves the calculation of the distribution of potential energy in the internal coordinates for each normal mode [ 141. Alternatively the contribution to each frequency from the various force constants can be calculated [lo, 111. We have used the latter method. Potential energy distributions were calculated for all sets of force constants that gave a good fit between observed and calculated frequencies. In all cases the distributions among the four principal force constants were similar to those shown in Table 2. From these P.E.D.‘s, it is evident that it is not possible to assign any of the a, fundamentals to any single mode of vibration. CONCLUSIONS Calculations using a simple valence force field and mod&d fields containing one and two interaction constants have shown that the highest a, fundamental (vr) of the SPF, molecule is essentially a mixture of PF and PS stretching vibrations. The va mode also contains both PF and PS stretching vibrations. The third a, fundamental is essentially a symmetric FPF deformation mode, but here again there is a contribution from PS stretching. Thus the descriptions given by previous workers [3,4, 61 for the a, fundameritals of SPF, are not correct. However, the descriptions given previously for the degenerate e modes are confirmed. It is also evident that many interaction constants are important in the force field of SPF,. However, it is reasonable to conclude that the PF and PS stretching constants are both near 6.0 mdyn/A, the FPF bending constant is approximately 0.7 mdyn/A (1.6 mdyn -A) and the SPF bending constant is approximately 0.3 mdyn/A (0.8 mdyn - A). Aoknowle&mmt~The author is very grateful to Dr. W. V. F. BROOKEIof the University of New B runswiokfor the use of his programs. The financial assistmoe of the National Research Council of Canada is also gratefully acknowledged. [14] Y. MORINO and K. KUCF~ITSU, J. Chem. P&a. SO,1089 (1962).