J . Phys. Chem. 1988, 92, 6246-6249
6246
Vibrational Circular Dichroism of Methylthiirane Hoang Dothe, Marian A. Lowe, Department of Chemistry, Boston University, Boston, Massachusetts 02215
and Joseph S. Alper* Department of Chemistry, University of Massachusetts-Boston, (Received: April 20, 1988)
Boston, Massachusetts 021 25
Vibrational circular dichroism spectra of (R)-methylthiirane are calculated by using Stephens' equations for the vibrational-rotational strengths in the distributed origin gauge, the common origin gauge with the origin at the center of mass of the molecule, and the common origin gauge with the origin at the sulfur atom. The scaled quantum mechanical force field at a corrected theoretical geometry is used to calculate the atomic displacement matrix. All calculations are performed using the 6-31G* basis set. The three calculated spectra are compared with the experimental one. Best agreement is found with the origin at the center of mass.
Introduction Within the past few years, calculations of the vibrational circular dichroism (VCD) spectra of molecules which are in good agreement with the experimental VCD spectra have been perf ~ r m e d . I - ~These calculations have depended on accurate calculations of both the force fields and of the dipole and rotational strengths of the molecules. Purely ab initio force fields calculated by using S C F basis sets are not sufficiently a ~ c u r a t e . The ~ scaled quantum mechanical force field method (SQM) which combines data obtained from the experimental spectra with ab initio calculations has been shown to produce accurate force Rotational strengths in good agreement with experiment have been calculated with S C F basis sets using the formalism recently developed by StephensS8 Recently, we applied the SQM method to methylthiirane,' a molecule whose infrared and VCD spectra have recently been reported by Polavarapu et al. (PAE).9 Although the assignment of the experimental infrared spectrum was quite uncertain, we were able, using transferred scale factors, to obtain a force field which clarified the assignment and which gives excellent agreement between the calculated and experimental infrared spectrum. In the work reported here, we have calculated the VCD spectrum of (R)-methylthiirane (Figure 1) using our SQM force field and the Stephens formalism for the calculation of the rotational strengths. We find that the calculated VCD spectrum is extremely sensitive to the choice of origin used in the calculation of the rotational strengths. Fixing the origin at the center of mass of the molecule gives a calculated spectrum that agrees best with the experimental one. Spectra calculated by using the distributed origin gauge described by Stephensio give poorer agreement.
exact Hartree-Fock wave functions are used in the calculation of the tensors, then the rotational strengths are independent of the choice of origin even though the axial tensors are origin dependent. However, if basis sets of poorer quality than the exact Hartree-Fock set are used, the choice of origin does affect the value of the rotational strength. In this work, two choices of gauge have been used. In the common origin gauge (COG), all the axial tensors are calculated by using the same origin. The rotational strength of B fundamental transition in the ith vibrational mode of energy hwi is given by
Method and Calculations The dipole and rotational strengths, D and R, respectively, are functions of the atomic polar tensors, Pa,", and the atomic axial tensors, Ma,", where cy and p are the components of the tensor and u labels the nucleus.I0 Although the atomic polar tensors are independent of the position of the origin used in their calculation, the atomic axial tensors are not. If exact wave functions or even
(Mib)Do = C(MaO')uSoa,i
(1) Lowe, M . A,; Alper, J. S. J . Phys. Chem. 1988, 92, 4035.
( 2 ) Kawiecki, R. W.; Devlin, F.; Stephens, P. J.; Amos, R. D.; Handy, N. C . Chem. Phys. Letr., submitted for publication. (3) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Am. Chem. SOC.,in press. (4) Lowe, M. A.; Stephens, P. J.; Segal, G . A. Chem. Phys. L e u 1986, 123. 108. ( 5 ) Fogarasi, G.; Pulay, P. Annu. Rea. Phys. Chem. 1984, 35, 191. (6) Alper, J . S.; Dothe, H.; Lowe, M . A. Chem. Phys., in press. ( 7 ) Alper, J. S.; Lowe, M. A. Chem. Phys. 1988, 121, 189. (8) Stephens, P. J. J . Phys. Chem. 1985, 89, 748. (9) Polavarapu, P. L.; Hess, Jr., B. A,; Schaad, L. J.; Henderson, D. 0.; Fontana, L. P.; Smith, H. E.; Nafie, L. A,; Freedman, T. B.:Zuk, W . M.J . G e m . Phys. 1987. 86, 1140. (10) Stephens. P. .J. J . Phys. Chem. 1987. 91, 1712.
0022-3654/88/2092-6246$01.50/0
where
Pip = CPa,'sua,i,
Mia = CMaB'Sua,i
Ua
ULI
relate the Cartesian coordinates X u , to the and where the normal coordinates Qi:
In the distributed origin gauge with the origins taken at the nuclei (DOG), the Ma," tensor for the u nucleus is calculated by using the equilibrium position of this nucleus as the origin and will be denoted (Magu)u.Stephens'O has shown that for this choice of gauge the rotational strength is given by
where oa
Li, = Ct~riRorPa~~Soa.r ULI
is
R,, is the
Cartesian component of the vector from any fixed arbitrary origin to the nucleus u and c,,~ is the completely antisymmetric third rank unit tensor. The dipole strength, being independent of the axial tensors, is independent of the choice of gauge and is given by h D(O-+I), = -(Pi.Pi) (3) 7
--
2wi
As described previously," the numerical evaluation of the atomic polar and axial tensors requires ground-state electronic wave functions evaluated at the equilibrium geometry and at geometries in which each atom is displaced from its equilibrium position along the three Cartesian coordinate axes. In addition, ( 1 1 ) Stephens, P. J.; Lowe, M. A. Annu. Rea. Phys. Chem. 1985, 36, 213.
0 1988 American Chemical Society
Vibrational CD of Methylthiirane
The Journal of Physical Chemistry, Vol. 92, No. 22, 1988 6247
1
-50
V
Figure 1. (R)-Methylthiirane.
I
A
TABLE I: Calculated Dipole Strengths and Rotational Strengths RC
-30
-
-50
-
COG frequency,' cm-'
ob
DOG^
come
sulfurf
-1.6 5.2 0.02 -6.4 6.7 -0.36 -8.3 3.2 5.5 3.8 4.7 5.3 -0.54 -6.1 -1.5 10.1 -0.07 6.6 -6.7 3.3 -4.4 0.95 -3.9 3.7
3.2 -10.5 3.6 9.4 -2.0 0.59 -3.5 -5.4 17.7 0.85 15.0 35.9 5.2 -173.7 40.9 73.2 -21.6 54.2 -36.8 22.1 -14.4 -1.7 -0.82 7.9
-2.7 -10.5 10.4 21.8 -9.2 -3.9 -8.0 12.2 31.5 7.2 -38.2 31.6 -5.3 -187.5 33.2 77.2 -21.9 52.7 -22.5 30.2 -18.4 -5.9 1.5 7.1
~
3098 3040 3018 2943 2919 2861 1452 1446 1434 1387 1341 1169 1151 1078 1043 992 908 896 86 1 628 585 317 301 220
7.6 19.2 22.7 33.7 29.9 54.8 10.2 17.9 10.3 5.4 18.5 22.5 8.9 94.7 35.8 11.5 9.3 11.6 7.3 35.2 309.6 2.4 26.8 1.6
'Frequencies calculated at corrected theoretical geometry, with SQM 6-31G* force field. * D in lo4" esu2.cm2. 'R in esu2-cm2. dDistributed origin gauge with origins at nuclei. eCommon origin gauge with origin at center of mass. /Common origin gauge with origin at sulfur. for the evaluation of the axial tensors, the ground-state wive function at the equilibrium geometry in the presence of an external magnetic field is required. The calculation of these wave functions and of the tensors P,", M,", and (M4")" was performed using the GAUSSIAN 80 program'* modified to incorporate the effect of an external magnetic field. The 6-31G* basis set was used throughout. The equilibrium geometry of methylthiirane is not known experimentally. Therefore the corrected theoretical geometry derived previously7 was used. The atomic displacement matrix, Sea,i,was obtained from the SQM force field. Finally the dipole strength was determined by using eq 3, the rotational strength in the COG from eq 1 , and the rotational strength in the DOG from eq 2. In the calculation of the atomic polar and axial tensors, displacements of f0.005 %, were taken along each of the Cartesian coordinate axes. In calculating the atomic axial tensors, a magnetic field of 1 X lo7 G was used. Calculations of dipole and rotational (12) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seegar, R.; DeFrees. D. J.; Schlegel, B.; Topiol, S.; Kahn, L. R.; Pople, J. A. QCPE;Indiana University: Bloomington, IN.
-70, I
h
sok
w20
-
0-
15m
llar
l&
tiw
IlW
ldoo
000
BW
Frequency (cm-1)
Figure 2. Spectra of (R)-methylthiiranein the 800-1 500-cm-' region. (a) Calculated VCD spectrum, distributed origin gauge; (b) calculated VCD spectrum, common origin gauge with the origin at the sulfur atom;
(c) calculated VCD spectrum, common origin gauge with the origin at the center of mass; (d) calculated infrared spectrum; (e) experimental infrared and VCD spectra, reprinted with permission from ref 9. strengths using these displacements and magnetic field were compared with the recent analytical calculations of Jalkanen et for the N H D T isotopomer of ammonia. In all cases, the agreement was within 5%. Two different common origins, one taken at the center of mass of methylthiirane and the other at the equilibrium position of the sulfur atom, were examined. Results and Discussion
Calculated dipole and rotational strengths are given in Table I. The VCD spectra obtained by using the COG at the center of mass, the COG at the sulfur, and the DOG are shown, together with the experimental spectrum of PAE in Figures 2 and 3. A Gaussian line shape with a half-width of 8 cm-' is assumed in the (13), Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Chem. Phys., in press.
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The Journal of Physical Chemistry, Vol. 92, No. 22, 1988
42-
10'E
0-2. -4. -6. -6
I
4
-154
I
-154
I
3100
3wo 2900 Frequency (cm-1)
2m
I
j
WAVENUMBER (cm-')
Figure 3. Spectra of (R)-methylthiirane in the C-H stretching region. Spectra a-e as in Figure 2.
calculated spectra. As seen in Table I and Figures 2 and 3, the rotational strengths show significant variation from one gauge to another. This variation is indicative of the limited basis set used in these calculations. Examination of Figure 2 shows that in the region 800-1500 cm-l the spectrum calculated by using the COG at the center of
Dothe et al. mass agrees most closely with the experimental spectrum. Major features of the experimental spectrum are well reproduced. Disagreements between calculation and experiment occur for weak experimental features where two or more bands are close together. For the band at 1446 cm-I, the calculated rotational strength is negative whereas the experimental spectrum shows a small positive peak. For the weak negative peak at 1151 cm-', the calculated VCD intensity is weak and positive. No VCD is observed for the band at 895 cm-' while the calculated intensity is fairly large. Given that the discrepancies occur for modes that are not isolated, all of them may be due to inaccuracies in the calculated force field. It should be noted that the SQM force field was based on experimental data for only one isotopomer of methylthiirane. It is possible that the availability of IR spectra of various deuteriated isotopomers will result in a better assignment of the fundamentals and thus an improvement in the SQM force field. The spectrum calculated by using the sulfur atom as the common origin agrees somewhat less well with the experimental spectrum, since it does not reproduce the pronounced positive band associated with the isolated mode at 1346 cm-'. This problem is similar to one encountered in (S)-methyloxiranel where calculations performed with the oxygen atom as the common origin failed to predict the negative band at 1369 cm-]. Repeating the methyloxirane calculation with the center of mass taken as the common origin successfully reproduces the observed negative band. The spectrum calculated by using the DOG is in the poorest agreement with the experimental one. In addition to predicting the wrong sign of the band at 1038 cm-', the relative strengths of the calculated bands are very different from those seen in the experimental spectrum. As seen from Figure 3, none of the three calculated VCD spectra agrees well with the experimental spectrum in the C-H stretching region. In view of the relatively poor agreement with experiment of the calculated frequencies and intensities of the bands in this region, this result is not surprising. The poor agreement is likely to be due in part to inadequacies in the calculated force field. The assignment in this region is uncertain. The matrix-isolated IR spectra in this region was reported by PAE to show a considerable dependence on the matrix material. Moreover, there are more bands found in this region than there are fundamentals, so that Fermi resonance may well be a problem. Data on isotopically substituted methylthiirane would be a great help in refining the force field. Although this work has shown that the use of the COG produces significantly better VCD spectra for methylthiirane than does the DOG, this gauge does not provide better results for all molecules. Jalkanen et aI.I3 have shown that for chiral ammonia, NHDT, the DOG is superior and argue that this gauge should be used for all molecules. Their arguments supporting the superiority of the DOG rely heavily on their calculations on NHDT. They found that the errors in the calculated values of the atomic polar tensors are less than those in the values of the axial tensors and that the relative importance of the axial tensors in the calcuiation of the rotational strengths is reduced by using the DOG. We cannot estimate the relative errors in the values of the axial and polar tensors for methylthiirane at this point. However, we have found that in the DOG, for most of the vibrational modes of methylthiirane, the contribution to the rotation4 strength from the term in eq 2 involving the axial t_en_sor,P-M, is the same ofder of magnitude as that of the term P-L which does not involve M . Thus use of t_he_DOGgauge does not tend to minimize the importance of the P-M term in methylthiirane. In addition, as we have seen, the DOG rotational strengths are worse than those calculated by using COG. The results presented here indicate that at this time there is no simple rule for determining which gauge should be chosen for a VCD calculation. The effect of origin seems to depend on both the molecule being studied and the basis set used. For methyioxirane, we have found that, at the 4-3 1G level, using the COG at the center of mass gives a calculated VCD spectrum that is slightly less accurate than the DOG,',* while the COG with the origin at the oxygen atom gives significantly worse re~u1ts.l~There
J . Phys. Chem. 1988, 92, 6249-6258
is good evidence for the hypothesis that, if a fixed origin calculation is performed, then the origin should be chosen at the center of mass. For NHDT, the accuracy of the calculated value of the axial atomic tensor for the nitrogen atom decreases more rapidly than that for the hydrogen as the distance of each atom from the origin is increased.13 This conclusion is borne out by the good agreement obtained for the methylthiirane VCD spectra by fixing the origin at the center of mass. The sensitivity of the choice of gauge is a troubling feature of the calculation of VCD spectra. As the quality of the basis sets used increases, this dependence should diminish. However, our preliminary calculations of rotational strengths of methylthiirane for selected normal modes using the larger 6-31G** basis set gave essentially the same results as those obtained by using the 6-31G* set. At this time, it is impracticable to use basis sets routinely that are much larger than the 6-31G** basis for molecules as large or larger than methylthiirane. Consequently, a more detailed theoretical analysis of the choice of gauge is required. Inaccuracies in calculated VCD spectra arise from inaccuracies in the force field, the atomic polar tensors, and the atomic axial (14) Dothe, H.; Lowe, M. A,; Alper, J. S., unpublished results.
6249
tensors. Results of calculations for the molecule thiirene indicate that atomic polar tensors may not be calculated very accurately even at a post-SCF level. Extremely accurate S C F and post-SCF calculations (DZP-CISD) have been performed on this molecule.15 The improvement in the force field achieved by performing the DZP-CISD calculation rather than one at the S C F level was considerable, but the intensities did not show nearly the same degree of improvement and discrepancies with experiment remained.I5 Since atomic axial tensors may be even less accurate than the atomic polar tensors, the above results indicate that, while the SQM force fields are probably sufficiently accurate for VCD calculations, improvements in methods of calculating atomic polar and axial tensors may be needed in order to reproduce the details of experimental VCD spectra.
Acknowledgment. M.A.L. gratefully acknowledges a grant from the National Science Foundation (CHE-8519526) for financial support for this work. Registry No. (R)-Methylthiirane, 17406-93-8. (15) Allen, W. D.; Bertie, J. E.; Falk, M. V.; Hess, Jr., B. A,; Mast, G. B.; Othen, D. A,; Schaad, L. J.; Schaefer 111, H. F. J . Chem. Phys. 1986,84, 4211.
Fluorescence Properties of P,&Diarylfndenes Gregory M. Anstead and John A. Katzenellenbogen* Department of Chemistry, University of Illinois, Urbana, Illinois 61801 (Received: April 29, 1988)
The absorbance and fluorescence properties of three 2,3-diarylindenes substituted with donor and acceptor functions were studied and compared with the corresponding donor/acceptor-substituted stilbenes. The parent systems, 2-phenyl-3-(4methoxyphenyl)-6-methoxyindene (lc) and 4-methoxystilbene (2c), show absorption and emission spectra typical for stilbene systems. Relative to the stilbene 2c, absorbance of indene ICshows a small bathochromic shift (1500 cm-I) and a somewhat larger Stokes shift (7000 versus 5000 cm-’); neither absorbance nor emission shows much solvent sensitivity. The meta-substituted (2b) both show absorbances systems 2-( 3-nitrophenyl)-3-(4-methoxyphenyl)-6-methoxyindene(lb) and 4’-methoxy-3-nitrostilbene having little solvent dependence that are shifted ca. 1200 cm-’ relative to the unsubstituted analogues (ICand 2c); however, their fluorescence spectra are now very solvent sensitive, with Stokes shifts for both systems ranging from ca. 11 000 cm-I in cyclohexaneto ca. 16000 cm-’ in chloroform. The very large Stokes shift of l b and 2b can best be explained by the emission arising from a twisted intramolecular charge-transfer (TICT) state, in which the two ?r systems are mutually perpendicular, with complete charge transfer from donor to acceptor. In addition to this TICT band, the indene system l b also shows a shorter wavelength emission that is ascribed to a locally excited state (LE). The relative intensities of the dual-emission (LE and TICT) bands of this are very solvent dependent. The absence of an LE band in the stilbene 2b suggests that it can access the twisted conformation required for the TICT state more readily than can the diarlyindene lb. The para-substituted systems 2-(4-nitrophenyl)-3-(4-methoxyphenyl)-6-methoxyindene(la) and 4’-methoxy-4-nitrostilbene (2a) show absorbance bands shifted bathochromically by 5000-6000 cm-I relative to the unsubstituted systems IC and 2c. The Stokes shift is again very solvent dependent but is smaller than for the para-substituted systems, in the range 5500-9000 cm-I for la and 8000-12000 cm-I for 2a, consistent with emission from a simple intramolecular charge-transfer state (ICT) involving a more planar system having only partial charge separation. The greater Stokes shift of the stilbene 2a relative to the indene la may be due to the greater planarity of the stilbene system. The relative emission intensities of the indene systems varies p-NOz > H > m-NO2,that of stilbenes H > p-NOz > m-NOz,consistent with the forbidden nature of the TICT, with the indenes la and l b being far more intense than the corresponding stilbenes. The donor/acceptor-substituted 2,3-diarylindenesystems provide interesting structure-dependent fluorescence characteristics that may be exploitable in biological applications.
Introduction The utility of fluorophores as molecular probes is based on the sensitivity of their emissive behavior (wavelength, quantum yield, polarization, and lifetime) to the environment.] This characteristic enables one to distinguish fluorophores that have been localized *To whom correspondence should be addressed at 461 Roger Adams Laboratory, Box 37, 1209 W. California Street, University of Illinois, Urbana, IL 61801.
in different environments, such as different subcellular compartments’ or those that are bound to macromolecules versus free in ( 1 ) (a) Azzi, A. Q. Reu. Biophys. 1975, 8, 237. (b) Brand, L.; Gohlke, J. R. Ann. Reo. Biochem. 1972, 41, 843. (2) Taylor, D. L.; Wang, Y.-L. Nature (London) 1980, 284, 405. (3) Weber, G.; Farris, F. J . Biochemistry 1979, 18. 3075.
0022-3654/88/2092-6249$01.50/00 1988 American Chemical Society
