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The cis and trans rotational isomers of 3-fluorostyrene. What is the energy difference between them?
26 August 1994
ELSEVIER
CHEMICAL PHYSICS
Chemical Physics Letters 226 ( 1994) 577-582
The cis and trans rotational isomers of 3-fluorostyrene. What is the energy difference between them? Christopher M. Harper, J. Michael Hollas Department of Chemistry, University ofReading, Reading RG6 ZAD, UK
Received 14 June 1994
Abstract Results obtained for 3-fluorostyrene from single vibronic level fluorescence in a supersonic jet, microwave spectroscopy and ab initio calculations have been interpreted to give cis-trans energy differences of 220 f 50, 26 + 45, and 43 cm-’ with cis the more stable. Calculations have suggested that the torsional potential may include a V3 term, in addition to the V,, Vzand V4 terms used to interpret the fluorescence data. It is shown that it is possible that all three results can be reconciled in this way.
1. Introduction
It has been shown from the S,-So laser-induced single vibronic level fluorescence (SVLF) [ 1,2], and confirmed by microwave spectroscopy [ 31, that styrene is planar, but only just. There is a very flat-bottomed potential for the C ( 1 )-C(a) torsional motion and it requires, for example, only 4.2 kJ mol- ’ (350 cm-‘) of energy to twist the vinyl group 50” out of plane. If we assume that the vinyl group in 3-fluorostyrene (3FS) is also coplanar with the benzene ring then we expect 3FS to exist as two rotational isomers, or rotamers, cis and trans as shown in Fig. 1.
2%
U@)=t
F
F
(b)
Fig. 1. The (a) cis and (b) trans rotamers of 3-fluorostyrene.
c V?l]l-cos
n
(@)I 3
(1)
the internal rotation function F( @), which describes how the internal rotation ‘constant’ Fvaries with torsional angle 9, is required. With reasonable assumptions regarding the geometry this function was found to be F($)/cm-‘=
1.4264-O.O829cos@
+O.l287cos2@,
0
0
co-)
The existence of these two rotamers was first shown from an investigation of the Si-So fluorescence excitation (FE) and SVLF spectra of 3FS seeded into a supersonic free jet [ 41. Levels for the C( 1 )-C(a) torsional vibration ~42 were observed up to ~42 = 8 in one rotamer and 4 in the other. In order to obtain the torsional potential, which has the general form
(2)
when @=O’ corresponds to the trans rotamer. Then the best fit of the calculated to the observed torsional levels in the ground electronic state S,, for both rotamers was obtained with the potential
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlOOO9-2614(94)00761-6
578
CM. Harper, J.M. Hollas 1 Chemical Physics Letters 226 (1994) 577-582
V(@)/cm-‘=4{467(
l-cos$)
+1070[1-cos(2~)]-255[1-cos(4~)]j,
(3)
when trans was assumed to be the more stable rotamer. When @=O’ corresponds to the cis rotamer, F(@)/cm-‘=
1.4264+0.0829cos$
+O.l287cos(2@)
(4)
and the best fit of the torsional levels was obtained with the potential V(@)/cm-‘=t{(220+50)(1-cos#) +(1040&80)[1-cos(2@)] -(247flO)[l-cos(4@)]},
(5)
when cis was assumed to be the more stable rotamer. The potentials of Eqs. ( 3 ) and ( 5 ) differ from that for styrene [ 21,
-(275*1)[1-cos(4@)] +(7.0?0.5)[1-cos(6$)]},
(6)
mainly by the inclusion of a Vi term which styrene, by virtue of its symmetry, cannot have. The effect of the Vi term in Eqs. (3) and (5) is to raise the minimum at @= 180” to an energy Vi above the @=O”minimum which represents the energy difference between the two rotamers of 3FS. The intensity ratio of the O”,bands of the two rotamers, in both the gas phase and in the supersonic jet, is about 3: 1 [ 41. (The energy barrier between the two rotamers is sufficiently high that no transfer of population from the high to the low energy rotamer in the jet is expected.) This intensity ratio strongly favours the choice of V, = 220 cm-’ and the potential in Eq. (5) for which the cis rotamer is the more stable. Shortly after this work, Villmaiian and Alonso published a paper on the microwave spectrum of 3FS [ 51 in which they were able to assign transitions to each of the two rotamers. The intensities of more than 15 pairs of a-type transitions were measured, the members of each pair belonging to different rotamers but having the same rotational assignment. The intensity ratios were interpreted to give an energy difference between the two rotamers of 26 f 45 cm-’
(two standard deviations), the cis rotamer being the more stable. Schaefer and Sebastian [6] carried out geometry optimised ab initio calculations of the torsional potential for 3FS at the STO-3G and 6-3 1G levels at 15” intervals of the torsional angle 0. The STO-3G potential was fitted to the model in Eq. ( 1) assuming Vi, V,, Vs, V4, V, and V, are all non-zero. The dominant parameters were V, and V, but they disagreed so badly with the values derived from experimental observations [4] that the STO-3G level of calculation was judged to be inadequate. The 6-31G level calculations were much more successful and the resulting potential was fitted in two ways: (a) Only Vi, VZand V4were assumed to be nonzero giving Vi =33 cm-’ ,
V,=1090cm-‘,
V4=-374cm-‘ .
(7)
However, it was not possible to get a good tit to the calculated potential with non-zero values for only these three V, parameters. In particular there was an uncertainty of 50 cm-’ for VI and the value of Vi is unacceptable compared to that derived from experimental data [ 41. (b) V,, V2, Vj, V,, Vs and V, were assumed to be non-zero giving V, =28 cm-‘,
V,=1084cm-‘,
V3=16cm-‘,
V,=-267cm-‘,
V,=-7.5cm-‘,
Vs=3cm-‘.
(8)
The values of V, and Vs are too small to be significant but, otherwise, the major differences between these values and those in Eq. (7) are a more acceptable value of V, and the inclusion of V3 which resulted in a better overall fit to the calculated potential. Further ab initio calculations were carried out [ 7 ] at the 6-3 1G P level, the P indicating that d orbitals on the fluorine atom were included. Geometry optimisation was done at the 3-21G P level. The energy difference between the two rotamers was calculated to be 43 cm-‘, with the cis rotamer being the more stable, a very similar value to that of 43.5 cm- ’ resulting from calculations without the fluorine atom d orbitals [ 6 1.
CM Harper, J.M. Hollas/Chemical PhysicsLetters226 (1994) 577-582
2. Possible uncertainties in the various estimates of the cis-trans energy difference Three different methods of determining the energy difference between the two rotamers of 3FS have been employed, SVLF spectroscopy, microwave spectroscopy and ab initio calculations. All agree that the cis rotamer is the more stable but the uncertainty in the microwave value of the energy difference leaves open the possibility that the opposite might just be the case. There is less agreement about the magnitude of the energy difference. Although the microwave (26 f 45 cm-’ ) and ab initio (43 cm-’ ) values are mutually consistent, the value of 220f 50 cm-’ from SVLF spectroscopy is considerably higher. First we need to examine any reasons why each of these values might be questioned. Estimates of relative intensities in microwave spectra are notoriously difficult and this is reflected in the large uncertainty quoted for the energy difference. There was a further difficulty encountered in this experiment [ 5 1. It was not possible to use the Stark effect to measure the dipole moment component A for either of the rotamers. This quantity is required because the intensities are proportional to pi which will be different for each rotamer. Instead, these dipole moments had to be estimated using the vector sum of the dipole moments of fluorobenzene and styrene. This approximation could lead to further uncertainty in the resulting energy difference. One problem with ab initio calculations is that uncertainties cannot be attached to the results. We can only attempt to judge the reliability from results obtained with similar systems using similar levels of calculation. For example, there have been two calculations of the energy difference between the trans and cis rotamers of 2-fluorostyrene. A calculation at the 6-3 1G level [ 6 ] has given an energy difference of 153 cm-’ while another, at the 6-3 1G Fc level [ 7 1, has given an energy difference of 200 cm-‘: both calculations predict that the more stable rotamer is trans. However, investigation of the FE and SVLF spectra of 2-fluorostyrene [ 81 have failed to detect a second rotamer, putting a lower limit of about 600 cm-’ on the energy difference. A study of the microwave spectrum of 2-fluorostyrene [9] has also resulted in the detection of only one rotamer. The rotational constants of this rotamer show conclusively that it is
579
trans. This failure of two experimental methods to detect the cis rotamer casts considerable doubt on the energy difference calculated by ab initio methods for 2-fluorostyrene. Since the calculated energy difference between the two rotamers of 3FS is much smaller (43 cm- l) than that for the rotamers of 2-fluorostyrene there must be doubt attached to this value also. There are also reasons to question the SVLF energy difference [4] of 220 & 50 cm-‘. Evidence to support this value was derived from the 3 : 1 intensity ratio observed for the 08 bands of the cis: trans rotamers in both the gas phase at room temperature and in the FE spectrum in a supersonic jet. This ratio is consistent with populations of the zero-point levels, at room temperature, being governed by the Bolzmann law. However, to estimate the cis: trans ratio from the FE or gas phase absorption spectrum we should use the ratio of the integrated intensities of all the bands in the S,-So spectra of each rotamer. In using just the 08 band intensities we are assuming that all the Franck-Condon factors governing vibronic band intensities are the same for both rotamers. A further assumption which is being made in using the 0; band intensities is that the magnitude of the Si-So electronic transition moment is the same for both rotamers. It has been pointed out [ 61 that there is a further assumption in obtaining the energy difference of 220 cm-’ from the observed torsional levels in the two rotamers [4]. This assumption is that the terms in the potential in Eq. ( 1) were restricted to Vi, V, and V4whereas fitting the ab initio curve [ 61 to a potential suggests that a V, term might be included, as in the results in Eq. ( 8 ) . In the work which we report here we have investigated this possibility to see what effect this additional term might have on the other parameters, particularly with regard to the possibility of reconciling the value of the energy difference obtained by SVLF spectroscopy with those obtained from microwave spectroscopy and ab initio calculations. 3. Fitting the torsional levels with various potential functions The torsional potential for 3FS in Eq. (5 ) was chosen to include only the V, term, in addition to the VZ
580
CM. Harper, J.M. Hollas /Chemical
and V4terms characteristic of the styrene potential, because this is the simplest way to create a cis-trans energy difference. A positive Vi raises, and also flattens, the minimum in the potential curve at $= 180 by Vi relative to the minimum at #=O’. This extra flattening pulls down the lower vibrational levels, consistent with the observation that, for example, the v,,=2-0 separation is 76.2 cm-’ for cis- and 91.4 cm-’ for trans-3FS [ 41. However, the $= 180” minimum can be raised by the inclusion of any V, terms in the potential, provided n is odd. Any raising of the minimum in this way is also accompanied by a degree of flattening. In principle, then, we can include any of l’,, V3,Vs, ... to produce the energy difference and flatten the minimum. The energy difference will be I’, + V, + V, + ... . We have tried various combinations of V, and V,, assuming that other values of V,, with n odd, are not significant. Table 1 Observed
and calculated 042
b
Vibrational
oc lc 2c 3c 4c 5C
6c 7c 8C Ot 1t 2t 3t 4t 5t 6t 7t 8t
VI VZ V3 V4 V6
torsion vibrational
level separations
level separations
Physics Letters 226 (I 994) 5 77-582
The computer program used to calculate energy levels from torsional potential functions uses 50 free rotor, sine and cosine, basis functions and uses the method of Lewis et al. [ lo]. First we tried the set of V, parameters in Eq. (8 ) suggested by Schaefer and Sebastian [ 61, but excluding Vs. The lower torsional levels calculated for both rotamers with this potential are given in Table 1 where they are compared with the available experimentally determined values and also those calculated with the potential in Eq. (5). Although those calculated with the Eq. (5) potential agree much better with the experimental values, the general pattern of levels calculated with that in Eq. (8) was sufficiently close to suggest that the inclusion of a V3term might well produce acceptable results. However, the calculated levels are particularly sensitive to the value of VI and the value of - 267 cm-’ from the ab initio potential was not acceptable. Therefore we used the more reli-
for 3-fluorostyrene
’
obs.
calculated
41.9 49.5 56.6 57.3 59.2 62.2 62.4 63.3
37.61 48.90 54.07 57.69 60.20 61.96 62.14 59.16 59.75
42.4 50.6 55.3 58.3 60.6 62.1 63.2 63.8 64.2
42.25 50.50 54.96 58.02 60.18 61.70 62.72 63.33 63.58
42.18 50.31 54.70 57.71 59.82 61.28 62.25 62.80 62.99
42.11 50.13 54.45 57.40 59.45 60.86 61.77 62.27 62.39
30.31 43.11 48.24 52.09 54.80 56.78 59.19 63.86 64.18
32.8 42.7 47.2 50.6 52.8 54.5 55.6 56.4 56.8
32.96 42.86 47.53 50.86 53.22 54.93 56.13 56.92 57.36
33.05 43.06 47.80 51.77 53.58 55.34 56.59 57.43 57.93
33.13 43.25 48.04 51.47 53.93 55.73 57.04 57.93 58.48
76.2 > 97.6
27.6 1084 15.9 -267 -7.5
8 The separations, G( v+ 1) -G(v), are in cm-‘. b ‘c’ and ‘t’ refer to the cis and trans rotamers, respectively.
220 1040 0 -247 0
135 1040 10 -247 0
51 1040 20 -247 0
-32 1040 30 -247 0
581
CM. Harper, J.M. Hollas /Chemical Physics titters 226 (1994) 5 77-582
able value of -247 cm-’ from the fit of the experimental data [ 41 and also used that value of 1040 cm-’ for V,. With V,= 1040 cm-’ and V,= -247 cm-‘, values of V,, less than the previously proposed value [ 41 of 220 cm- *, were chosen and, for each value, a search was made of positive values of V, until the most acceptable fit of the calculated to the observed levels resulted. These pairs of values are plotted in Fig. 2 which shows that they lie on a straight line given by I’, =220-8.40
I’, .
(9)
This equation shows that a large range of pairs of VI, V, values is possible and, therefore, a large range of energy differences V, + I’,. The energy levels for three such pairs, 135/10, 51120 and -32130 cm-’ are given in Table 1. These examples illustrate the general trend that, although agreement between the calculated and observed levels, which have an uncertainty of about l-2 cm-‘, is just acceptable for all pairs of values related by Eq. (9)) the agreement becomes rather less good as V, decreases and V, consequently increases. Since V, was quoted in Ref. [ 41 as having an estimated uncertainty of 10 cm-‘, similar searches for acceptable pairs of values of V, and V, were made for V4=-257, -251, -249, -245, -243, and -237 cm --I. These pairs also fall on straight lines which are illustrated in Fig. 1.
4. Conclusions
The most important conclusion regarding the fitting of the experimentally observed [ 41 torsional vibrational energy levels of the two rotamers of 3FS to a single potential is that, if we relax the previously assumed restriction that, of the V, terms in the potential with n odd, only V, is significant, the levels can be fitted satisfactorily with both V, and V, nonzero. The pairs of acceptable values are illustrated by the graphs in Fig. 2. The energy difference, V, + V,, between the trans and cis rotamers can be anywhere between about 220 cm-’ and zero. Table 1 illustrates, for example, the acceptability of VI + V3= 7 1 cm-’ and Fig. 3 compares the potential curve for this value of V, + V, with that for VI = 220 cm- ’ and v,=o. The inclusion of the V3term in the potential, therefore, makes it possible to reconcile the cis-trans energy difference obtained from laser-induced fluorescence spectroscopy, microwave spectroscopy and ab initio calculations. The general conclusion from this exercise is that, for a molecule of this type existing as two planar rotamers, it may not be possible to determine the energy difference from the observed torsional vibrational levels unless the energy levels can be obtained with considerably higher accuracy. Of course, the detailed shape of the potential is different for different . v,=-257 A v,=-251 +
v,=-249
l
va=-247
v
v.j=-245
r
v,=-243
.
v4=-231
Fig. 2. Graph illustrating the values of V, and V,, with V,= 1040 cm-’ and various values of V.,, which result in acceptable agreement between observed and calculated vibrational levels.
582
CM
Harper, JM. Hollas /Chemical
Physics Letters 226 (1994) 577-582
a 1100 1000
800 800 700 800 500 400 300 200
0"
180”
9
Fig. 3. Potential curves and vibrational energy levels for V, = 1040 cm-l,
v,=_247
00 180” @ cm-’ and (a) VI=220 Cm-', Vs=O;
(b) V,=51
cm-‘, V,=20cm-I.
values of V, + Vs. In particular, although V, has a similar effect to that of Vi in raising the trans minimum, it has a relatively greater effect in flattening it: compared to the effect of Vi, a little V, goes a long way in this respect. But these results show that the energy levels are not sufficiently sensitive, compared to the experimental uncertainties of l-2 cm-’ in the energy levels, to a change in the shape corresponding to quite a large change in I’, + V3. This leads to a question to which there is, at present, no reliable answer. Is the torsional potential more likely to involve just Vi rather than Vi and VJ (and, possibly I’,, I’,, etc.), all of which are allowed by symmetry? The ab initio potential [ 6,7 ] indicates an important V3term and the present calculations show that its inclusion can result in vibrational energy levels which are in acceptable agreement with those observed [ 41. Perhaps the most conclusive evidence for the inclusion of a I’, term is the fact that, if it is included, the resulting cis-trans energy difference can be reconciled with that of 26 f 45 cm-’ from the microwave spectrum [ 5 1. This value has a very large uncertainty attached to it and was obtained only with necessary assumptions regarding the values of the dipole moments of the two rotamers. It is, nevertheless, so far outside the value of 220+ 50 cm-’ obtained from the fluorescence spectra, including the Vi term only [ 41, that we are persuaded that the cis-trans energy difference is more likely to be nearer to about 70 cm-’ (0.84 kJ mol-' ), with the cis rotamer the more stable.
The only remaining evidence which seems to favour the higher value of 220 cm-’ is the $-So, 08 band cis-trans intensity ratio of 3 : 1 observed in the gas phase and in the jet. If this evidence is rejected it has to be on the grounds of there being either appreciably different Si-So Franck-Condon factors or electronic transition moments for the two rotamers. Acknowledgement We are grateful to Professor R.D. Gordon for the use of his computer program for calculating eigenvalues for torsional potentials. References ] J.M. Hollas and T. Ridley, Chem. Phys. Letters 75 (1980) 94.
] J.M. Hollas, H. Muss, T. Ridley, P.H. Turner, K.H. Weisenberger and V. Fawcett, J. Mol. Spectry. 94 ( 1982) 437. ] W. Caminati, B. Vogelsanger and A. Bauder, J. Mol. Spectry. 128 (1988) 384. [4] J.M. Hollas and M.Z.bin Hussein, Chem. Phys. Letters 154 (1989) 228. [ 51 R.M. Villamait~n and J.L. Alonso, Chem. Phys. Letters 159 (1989) 97. [6] T. Schaefer and R. Sebastian, Chem. Phys. Letters 163 (1989) 212. [ 71 J.J.C. Teixeira-Dias and P.J.A. Ribeiro-Claro, Struct. Chem. 3 (1992) 95. [8] J.M. Hollas and M.Z.bin Hussein, Chem. Phys. Letters 154 (1989) 14. [ 9 ] R.M. VillamaiUn, J.C. Lopez and J.L. Alonso, J. Am. Chem. Sot. 111 (1989) 6488. [10]J.D.Lewis,T.B.MalloyJr.,T.H.ChaoandJ.Laane,J.Mol. Struct. 12 (1972) 427.
ELSEVIER
CHEMICAL PHYSICS
Chemical Physics Letters 226 ( 1994) 577-582
The cis and trans rotational isomers of 3-fluorostyrene. What is the energy difference between them? Christopher M. Harper, J. Michael Hollas Department of Chemistry, University ofReading, Reading RG6 ZAD, UK
Received 14 June 1994
Abstract Results obtained for 3-fluorostyrene from single vibronic level fluorescence in a supersonic jet, microwave spectroscopy and ab initio calculations have been interpreted to give cis-trans energy differences of 220 f 50, 26 + 45, and 43 cm-’ with cis the more stable. Calculations have suggested that the torsional potential may include a V3 term, in addition to the V,, Vzand V4 terms used to interpret the fluorescence data. It is shown that it is possible that all three results can be reconciled in this way.
1. Introduction
It has been shown from the S,-So laser-induced single vibronic level fluorescence (SVLF) [ 1,2], and confirmed by microwave spectroscopy [ 31, that styrene is planar, but only just. There is a very flat-bottomed potential for the C ( 1 )-C(a) torsional motion and it requires, for example, only 4.2 kJ mol- ’ (350 cm-‘) of energy to twist the vinyl group 50” out of plane. If we assume that the vinyl group in 3-fluorostyrene (3FS) is also coplanar with the benzene ring then we expect 3FS to exist as two rotational isomers, or rotamers, cis and trans as shown in Fig. 1.
2%
U@)=t
F
F
(b)
Fig. 1. The (a) cis and (b) trans rotamers of 3-fluorostyrene.
c V?l]l-cos
n
(@)I 3
(1)
the internal rotation function F( @), which describes how the internal rotation ‘constant’ Fvaries with torsional angle 9, is required. With reasonable assumptions regarding the geometry this function was found to be F($)/cm-‘=
1.4264-O.O829cos@
+O.l287cos2@,
0
0
co-)
The existence of these two rotamers was first shown from an investigation of the Si-So fluorescence excitation (FE) and SVLF spectra of 3FS seeded into a supersonic free jet [ 41. Levels for the C( 1 )-C(a) torsional vibration ~42 were observed up to ~42 = 8 in one rotamer and 4 in the other. In order to obtain the torsional potential, which has the general form
(2)
when @=O’ corresponds to the trans rotamer. Then the best fit of the calculated to the observed torsional levels in the ground electronic state S,, for both rotamers was obtained with the potential
0009-2614/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDlOOO9-2614(94)00761-6
578
CM. Harper, J.M. Hollas 1 Chemical Physics Letters 226 (1994) 577-582
V(@)/cm-‘=4{467(
l-cos$)
+1070[1-cos(2~)]-255[1-cos(4~)]j,
(3)
when trans was assumed to be the more stable rotamer. When @=O’ corresponds to the cis rotamer, F(@)/cm-‘=
1.4264+0.0829cos$
+O.l287cos(2@)
(4)
and the best fit of the torsional levels was obtained with the potential V(@)/cm-‘=t{(220+50)(1-cos#) +(1040&80)[1-cos(2@)] -(247flO)[l-cos(4@)]},
(5)
when cis was assumed to be the more stable rotamer. The potentials of Eqs. ( 3 ) and ( 5 ) differ from that for styrene [ 21,
-(275*1)[1-cos(4@)] +(7.0?0.5)[1-cos(6$)]},
(6)
mainly by the inclusion of a Vi term which styrene, by virtue of its symmetry, cannot have. The effect of the Vi term in Eqs. (3) and (5) is to raise the minimum at @= 180” to an energy Vi above the @=O”minimum which represents the energy difference between the two rotamers of 3FS. The intensity ratio of the O”,bands of the two rotamers, in both the gas phase and in the supersonic jet, is about 3: 1 [ 41. (The energy barrier between the two rotamers is sufficiently high that no transfer of population from the high to the low energy rotamer in the jet is expected.) This intensity ratio strongly favours the choice of V, = 220 cm-’ and the potential in Eq. (5) for which the cis rotamer is the more stable. Shortly after this work, Villmaiian and Alonso published a paper on the microwave spectrum of 3FS [ 51 in which they were able to assign transitions to each of the two rotamers. The intensities of more than 15 pairs of a-type transitions were measured, the members of each pair belonging to different rotamers but having the same rotational assignment. The intensity ratios were interpreted to give an energy difference between the two rotamers of 26 f 45 cm-’
(two standard deviations), the cis rotamer being the more stable. Schaefer and Sebastian [6] carried out geometry optimised ab initio calculations of the torsional potential for 3FS at the STO-3G and 6-3 1G levels at 15” intervals of the torsional angle 0. The STO-3G potential was fitted to the model in Eq. ( 1) assuming Vi, V,, Vs, V4, V, and V, are all non-zero. The dominant parameters were V, and V, but they disagreed so badly with the values derived from experimental observations [4] that the STO-3G level of calculation was judged to be inadequate. The 6-31G level calculations were much more successful and the resulting potential was fitted in two ways: (a) Only Vi, VZand V4were assumed to be nonzero giving Vi =33 cm-’ ,
V,=1090cm-‘,
V4=-374cm-‘ .
(7)
However, it was not possible to get a good tit to the calculated potential with non-zero values for only these three V, parameters. In particular there was an uncertainty of 50 cm-’ for VI and the value of Vi is unacceptable compared to that derived from experimental data [ 41. (b) V,, V2, Vj, V,, Vs and V, were assumed to be non-zero giving V, =28 cm-‘,
V,=1084cm-‘,
V3=16cm-‘,
V,=-267cm-‘,
V,=-7.5cm-‘,
Vs=3cm-‘.
(8)
The values of V, and Vs are too small to be significant but, otherwise, the major differences between these values and those in Eq. (7) are a more acceptable value of V, and the inclusion of V3 which resulted in a better overall fit to the calculated potential. Further ab initio calculations were carried out [ 7 ] at the 6-3 1G P level, the P indicating that d orbitals on the fluorine atom were included. Geometry optimisation was done at the 3-21G P level. The energy difference between the two rotamers was calculated to be 43 cm-‘, with the cis rotamer being the more stable, a very similar value to that of 43.5 cm- ’ resulting from calculations without the fluorine atom d orbitals [ 6 1.
CM Harper, J.M. Hollas/Chemical PhysicsLetters226 (1994) 577-582
2. Possible uncertainties in the various estimates of the cis-trans energy difference Three different methods of determining the energy difference between the two rotamers of 3FS have been employed, SVLF spectroscopy, microwave spectroscopy and ab initio calculations. All agree that the cis rotamer is the more stable but the uncertainty in the microwave value of the energy difference leaves open the possibility that the opposite might just be the case. There is less agreement about the magnitude of the energy difference. Although the microwave (26 f 45 cm-’ ) and ab initio (43 cm-’ ) values are mutually consistent, the value of 220f 50 cm-’ from SVLF spectroscopy is considerably higher. First we need to examine any reasons why each of these values might be questioned. Estimates of relative intensities in microwave spectra are notoriously difficult and this is reflected in the large uncertainty quoted for the energy difference. There was a further difficulty encountered in this experiment [ 5 1. It was not possible to use the Stark effect to measure the dipole moment component A for either of the rotamers. This quantity is required because the intensities are proportional to pi which will be different for each rotamer. Instead, these dipole moments had to be estimated using the vector sum of the dipole moments of fluorobenzene and styrene. This approximation could lead to further uncertainty in the resulting energy difference. One problem with ab initio calculations is that uncertainties cannot be attached to the results. We can only attempt to judge the reliability from results obtained with similar systems using similar levels of calculation. For example, there have been two calculations of the energy difference between the trans and cis rotamers of 2-fluorostyrene. A calculation at the 6-3 1G level [ 6 ] has given an energy difference of 153 cm-’ while another, at the 6-3 1G Fc level [ 7 1, has given an energy difference of 200 cm-‘: both calculations predict that the more stable rotamer is trans. However, investigation of the FE and SVLF spectra of 2-fluorostyrene [ 81 have failed to detect a second rotamer, putting a lower limit of about 600 cm-’ on the energy difference. A study of the microwave spectrum of 2-fluorostyrene [9] has also resulted in the detection of only one rotamer. The rotational constants of this rotamer show conclusively that it is
579
trans. This failure of two experimental methods to detect the cis rotamer casts considerable doubt on the energy difference calculated by ab initio methods for 2-fluorostyrene. Since the calculated energy difference between the two rotamers of 3FS is much smaller (43 cm- l) than that for the rotamers of 2-fluorostyrene there must be doubt attached to this value also. There are also reasons to question the SVLF energy difference [4] of 220 & 50 cm-‘. Evidence to support this value was derived from the 3 : 1 intensity ratio observed for the 08 bands of the cis: trans rotamers in both the gas phase at room temperature and in the FE spectrum in a supersonic jet. This ratio is consistent with populations of the zero-point levels, at room temperature, being governed by the Bolzmann law. However, to estimate the cis: trans ratio from the FE or gas phase absorption spectrum we should use the ratio of the integrated intensities of all the bands in the S,-So spectra of each rotamer. In using just the 08 band intensities we are assuming that all the Franck-Condon factors governing vibronic band intensities are the same for both rotamers. A further assumption which is being made in using the 0; band intensities is that the magnitude of the Si-So electronic transition moment is the same for both rotamers. It has been pointed out [ 61 that there is a further assumption in obtaining the energy difference of 220 cm-’ from the observed torsional levels in the two rotamers [4]. This assumption is that the terms in the potential in Eq. ( 1) were restricted to Vi, V, and V4whereas fitting the ab initio curve [ 61 to a potential suggests that a V, term might be included, as in the results in Eq. ( 8 ) . In the work which we report here we have investigated this possibility to see what effect this additional term might have on the other parameters, particularly with regard to the possibility of reconciling the value of the energy difference obtained by SVLF spectroscopy with those obtained from microwave spectroscopy and ab initio calculations. 3. Fitting the torsional levels with various potential functions The torsional potential for 3FS in Eq. (5 ) was chosen to include only the V, term, in addition to the VZ
580
CM. Harper, J.M. Hollas /Chemical
and V4terms characteristic of the styrene potential, because this is the simplest way to create a cis-trans energy difference. A positive Vi raises, and also flattens, the minimum in the potential curve at $= 180 by Vi relative to the minimum at #=O’. This extra flattening pulls down the lower vibrational levels, consistent with the observation that, for example, the v,,=2-0 separation is 76.2 cm-’ for cis- and 91.4 cm-’ for trans-3FS [ 41. However, the $= 180” minimum can be raised by the inclusion of any V, terms in the potential, provided n is odd. Any raising of the minimum in this way is also accompanied by a degree of flattening. In principle, then, we can include any of l’,, V3,Vs, ... to produce the energy difference and flatten the minimum. The energy difference will be I’, + V, + V, + ... . We have tried various combinations of V, and V,, assuming that other values of V,, with n odd, are not significant. Table 1 Observed
and calculated 042
b
Vibrational
oc lc 2c 3c 4c 5C
6c 7c 8C Ot 1t 2t 3t 4t 5t 6t 7t 8t
VI VZ V3 V4 V6
torsion vibrational
level separations
level separations
Physics Letters 226 (I 994) 5 77-582
The computer program used to calculate energy levels from torsional potential functions uses 50 free rotor, sine and cosine, basis functions and uses the method of Lewis et al. [ lo]. First we tried the set of V, parameters in Eq. (8 ) suggested by Schaefer and Sebastian [ 61, but excluding Vs. The lower torsional levels calculated for both rotamers with this potential are given in Table 1 where they are compared with the available experimentally determined values and also those calculated with the potential in Eq. (5). Although those calculated with the Eq. (5) potential agree much better with the experimental values, the general pattern of levels calculated with that in Eq. (8) was sufficiently close to suggest that the inclusion of a V3term might well produce acceptable results. However, the calculated levels are particularly sensitive to the value of VI and the value of - 267 cm-’ from the ab initio potential was not acceptable. Therefore we used the more reli-
for 3-fluorostyrene
’
obs.
calculated
41.9 49.5 56.6 57.3 59.2 62.2 62.4 63.3
37.61 48.90 54.07 57.69 60.20 61.96 62.14 59.16 59.75
42.4 50.6 55.3 58.3 60.6 62.1 63.2 63.8 64.2
42.25 50.50 54.96 58.02 60.18 61.70 62.72 63.33 63.58
42.18 50.31 54.70 57.71 59.82 61.28 62.25 62.80 62.99
42.11 50.13 54.45 57.40 59.45 60.86 61.77 62.27 62.39
30.31 43.11 48.24 52.09 54.80 56.78 59.19 63.86 64.18
32.8 42.7 47.2 50.6 52.8 54.5 55.6 56.4 56.8
32.96 42.86 47.53 50.86 53.22 54.93 56.13 56.92 57.36
33.05 43.06 47.80 51.77 53.58 55.34 56.59 57.43 57.93
33.13 43.25 48.04 51.47 53.93 55.73 57.04 57.93 58.48
76.2 > 97.6
27.6 1084 15.9 -267 -7.5
8 The separations, G( v+ 1) -G(v), are in cm-‘. b ‘c’ and ‘t’ refer to the cis and trans rotamers, respectively.
220 1040 0 -247 0
135 1040 10 -247 0
51 1040 20 -247 0
-32 1040 30 -247 0
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CM. Harper, J.M. Hollas /Chemical Physics titters 226 (1994) 5 77-582
able value of -247 cm-’ from the fit of the experimental data [ 41 and also used that value of 1040 cm-’ for V,. With V,= 1040 cm-’ and V,= -247 cm-‘, values of V,, less than the previously proposed value [ 41 of 220 cm- *, were chosen and, for each value, a search was made of positive values of V, until the most acceptable fit of the calculated to the observed levels resulted. These pairs of values are plotted in Fig. 2 which shows that they lie on a straight line given by I’, =220-8.40
I’, .
(9)
This equation shows that a large range of pairs of VI, V, values is possible and, therefore, a large range of energy differences V, + I’,. The energy levels for three such pairs, 135/10, 51120 and -32130 cm-’ are given in Table 1. These examples illustrate the general trend that, although agreement between the calculated and observed levels, which have an uncertainty of about l-2 cm-‘, is just acceptable for all pairs of values related by Eq. (9)) the agreement becomes rather less good as V, decreases and V, consequently increases. Since V, was quoted in Ref. [ 41 as having an estimated uncertainty of 10 cm-‘, similar searches for acceptable pairs of values of V, and V, were made for V4=-257, -251, -249, -245, -243, and -237 cm --I. These pairs also fall on straight lines which are illustrated in Fig. 1.
4. Conclusions
The most important conclusion regarding the fitting of the experimentally observed [ 41 torsional vibrational energy levels of the two rotamers of 3FS to a single potential is that, if we relax the previously assumed restriction that, of the V, terms in the potential with n odd, only V, is significant, the levels can be fitted satisfactorily with both V, and V, nonzero. The pairs of acceptable values are illustrated by the graphs in Fig. 2. The energy difference, V, + V,, between the trans and cis rotamers can be anywhere between about 220 cm-’ and zero. Table 1 illustrates, for example, the acceptability of VI + V3= 7 1 cm-’ and Fig. 3 compares the potential curve for this value of V, + V, with that for VI = 220 cm- ’ and v,=o. The inclusion of the V3term in the potential, therefore, makes it possible to reconcile the cis-trans energy difference obtained from laser-induced fluorescence spectroscopy, microwave spectroscopy and ab initio calculations. The general conclusion from this exercise is that, for a molecule of this type existing as two planar rotamers, it may not be possible to determine the energy difference from the observed torsional vibrational levels unless the energy levels can be obtained with considerably higher accuracy. Of course, the detailed shape of the potential is different for different . v,=-257 A v,=-251 +
v,=-249
l
va=-247
v
v.j=-245
r
v,=-243
.
v4=-231
Fig. 2. Graph illustrating the values of V, and V,, with V,= 1040 cm-’ and various values of V.,, which result in acceptable agreement between observed and calculated vibrational levels.
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CM
Harper, JM. Hollas /Chemical
Physics Letters 226 (1994) 577-582
a 1100 1000
800 800 700 800 500 400 300 200
0"
180”
9
Fig. 3. Potential curves and vibrational energy levels for V, = 1040 cm-l,
v,=_247
00 180” @ cm-’ and (a) VI=220 Cm-', Vs=O;
(b) V,=51
cm-‘, V,=20cm-I.
values of V, + Vs. In particular, although V, has a similar effect to that of Vi in raising the trans minimum, it has a relatively greater effect in flattening it: compared to the effect of Vi, a little V, goes a long way in this respect. But these results show that the energy levels are not sufficiently sensitive, compared to the experimental uncertainties of l-2 cm-’ in the energy levels, to a change in the shape corresponding to quite a large change in I’, + V3. This leads to a question to which there is, at present, no reliable answer. Is the torsional potential more likely to involve just Vi rather than Vi and VJ (and, possibly I’,, I’,, etc.), all of which are allowed by symmetry? The ab initio potential [ 6,7 ] indicates an important V3term and the present calculations show that its inclusion can result in vibrational energy levels which are in acceptable agreement with those observed [ 41. Perhaps the most conclusive evidence for the inclusion of a I’, term is the fact that, if it is included, the resulting cis-trans energy difference can be reconciled with that of 26 f 45 cm-’ from the microwave spectrum [ 5 1. This value has a very large uncertainty attached to it and was obtained only with necessary assumptions regarding the values of the dipole moments of the two rotamers. It is, nevertheless, so far outside the value of 220+ 50 cm-’ obtained from the fluorescence spectra, including the Vi term only [ 41, that we are persuaded that the cis-trans energy difference is more likely to be nearer to about 70 cm-’ (0.84 kJ mol-' ), with the cis rotamer the more stable.
The only remaining evidence which seems to favour the higher value of 220 cm-’ is the $-So, 08 band cis-trans intensity ratio of 3 : 1 observed in the gas phase and in the jet. If this evidence is rejected it has to be on the grounds of there being either appreciably different Si-So Franck-Condon factors or electronic transition moments for the two rotamers. Acknowledgement We are grateful to Professor R.D. Gordon for the use of his computer program for calculating eigenvalues for torsional potentials. References ] J.M. Hollas and T. Ridley, Chem. Phys. Letters 75 (1980) 94.
] J.M. Hollas, H. Muss, T. Ridley, P.H. Turner, K.H. Weisenberger and V. Fawcett, J. Mol. Spectry. 94 ( 1982) 437. ] W. Caminati, B. Vogelsanger and A. Bauder, J. Mol. Spectry. 128 (1988) 384. [4] J.M. Hollas and M.Z.bin Hussein, Chem. Phys. Letters 154 (1989) 228. [ 51 R.M. Villamait~n and J.L. Alonso, Chem. Phys. Letters 159 (1989) 97. [6] T. Schaefer and R. Sebastian, Chem. Phys. Letters 163 (1989) 212. [ 71 J.J.C. Teixeira-Dias and P.J.A. Ribeiro-Claro, Struct. Chem. 3 (1992) 95. [8] J.M. Hollas and M.Z.bin Hussein, Chem. Phys. Letters 154 (1989) 14. [ 9 ] R.M. VillamaiUn, J.C. Lopez and J.L. Alonso, J. Am. Chem. Sot. 111 (1989) 6488. [10]J.D.Lewis,T.B.MalloyJr.,T.H.ChaoandJ.Laane,J.Mol. Struct. 12 (1972) 427.