Ab initio calculations of vibronic spectra for indole

29 September1995

CHEMICAL PHYSICS LETTERS

ELSEVIER

Chemical PhysicsLetters 244 (1995) 53-58

Ab initio calculations of vibronic spectra for indole Patrik R. Callis, James T. Vivian, Lee S. Slater Department of Chemistry and Biochemistry, Montana State University, Bozeman, MT 59717, USA

Received 3 May 1995; in final form 24 July 1995

Abstract

Detailed vibronic fluorescence spectra from the 1L b and IL a state origins of indole are computed from the geometry differences and ground state :~o:mal modes determined by GAUSSIAN 92 and a program to calculate Franck-Condon factors. The combination of using CIS/3-21G and HF/3-21G basis sets for excited and ground state geometries and MP2/6-31G* for the ground state vibrational modes captures many subtle details seen in the experimental 1L~, fluorescence.

1. Introduction

The indole chromophore of the amino acid tryptophan has been the object of numerous spectroscopic studies, motivated largely by the possibility of extracting useful protein structure and dynamics information [1,2]. The mechanism by which this might be possible is the spectral sensitivity to the local electric field due to the large change in dipole caused by excitation to the i L a state, one of two superimposed transitions comprising the strong 280 nm absorption band. The other state, 1L b, has only a small dipole change, but is more prominent in the low energy part of the spectrum because of its narrow band width. Analysis of modem optical experiments on tryptophan in proteins will almost certainly require detailed knowledge of the vibronic structure of these bands. That is, the vibrational frequencies in both excited states and in the ground state must be known, as well as the Franck-Condon (FC) factors connecting the vibronic levels, which give the characteristic intensity ratios. Recently we have reported a partially successful attempt to predict the vibronic spectra of

indole using a semiempirical approach [3]. However, it is evident from recent reports [4,5], for example, that force fields based on ab initio methods are superior for this purpose. In this Letter, we report ab initio ground state vibrational frequencies for indole obtained at the MP2/6-31G* level, which agree with experiment within 5% without scaling. The associated modes of importance to the vibronic spectra are presented. These modes, when used with the C I S / 3 - 2 1 G excited state and H F / 3 - 2 1 G ground state geometries [6] and the Franck-Condon factor program introduced in Ref. [3], are found to give good qualitative agreement with the experimental L b jet-cooled fluorescence spectrum - without empirical adjustments. In addition, the 1L a fluorescence is computed in the same manner and the effect of linewidth is demonstrated. •

1

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2. Methods

The ground and excited state geometries were determined [6] with the program GAUSSIAN 92 [7]

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P.R. Callis et al. / Chemical Physics Letters 244 (1995) 53-58

running on a Cray C 9 0 at the Pittsburgh S u p e r c o m puting Center. T h e 1L a and 1L b excited state g e o m e tries w e r e d e t e r m i n e d by m i n i m i z i n g the e n e r g y at the C I S / 3 - 2 1 G level and also w i t h the M P 2 correction [8]. Distinct 1L a and 1L b m i n i m a w e r e located and identified by their transition dipoles. T h e ground state geometries, vibrational f r e q u e n c i e s and normal m o d e s w e r e d e t e r m i n e d at several levels ranging in quality f r o m H F / S T O - 3 G to M P 2 / 6 - 3 1 G * The F r a n c k - C o n d o n factors w e r e obtained f r o m the g e o m e t r y difference b e t w e e n g r o u n d and excited state along w i t h the ground state normal m o d e s using our Fortran p r o g r a m based on the m e t h o d o f D o k torov, M a l k i n and M a n ' k o [9], w h i c h w a s recently applied using s e m i e m p i r i c a l e n e r g y surfaces [3]. The m e t h o d is exact w i t h i n the h a r m o n i c approximation, incorporating potential surface displacements, m o d e f r e q u e n c y changes upon excitation, and m o d e m i x i n g ( D u s c h i n s k y rotation). H o w e v e r , in this Letter w e use o n l y the ground state m o d e s and attempt only to describe the fluorescence. F C factors are d e t e r m i n e d for all 42 m o d e s for all fundamentals, overtones, and c o m b i n a t i o n s up to four total quanta, retaining those with v a l u e s greater than 10 -a times the origin value. The s u m o f the F C factors was typically about 0.95.

3. Results T a b l e 1 c o m p a r e s the o b s e r v e d f u n d a m e n t a l vibrational frequencies o f indole w i t h those c o m p u t e d (not scaled) f r o m the M P 2 / 6 - 3 1 G * force field for the ground state. T h e s e are c o m p a r e d with o b s e r v e d v a l u e s f r o m Refs. [10,11]. A l s o in the table is a c o m p a r i s o n o f the o b s e r v e d and c o m p u t e d F C factors for the 1L b to g r o u n d transition, also unadjusted. It is seen that calculated and o b s e r v e d f r e q u e n c i e s are typically w i t h i n 5 % o f each other. In-plane freq u e n c i e s ( m o d e s 1 - 2 9 ) are consistently c o m p u t e d too high, w h i l e the out-of-plane ( m o d e s 3 0 - 4 2 ) freq u e n c i e s are consistently underestimated. The F C factors are s h o w n o n l y for in-plane fundamentals because w e are still in the process o f c o m puting the excited state modes. Within the h a r m o n i c assumption used here, out-of-plane intensities arise only f r o m f r e q u e n c y changes. It is seen that the c o m p u t a t i o n captures the c o m p l i c a t e d pattern o f observed intensities fairly well, especially c o n s i d e r i n g

Table 1 Comparison of experimental and calculated ground state vibrational frequencies and 1Lb-ground Franck-Condon factors for indole Mode number

Vibrational frequencies (cm- 1) MP2/ MV b BDOW c 6-31G * ~

42 41 40 39 38 37 36 35 34 33 32 31 30

205 225 338 388 391 546 589 702 714 761 797 841 866

207 240 420 516 570 601 715 738 791 850 904 925 979

208 241 420 480 570 602 715 738 765 849 925 -

29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14

401 554 619 781 897 915 1052 1110 1138 1173 1206 1252 1289 1336 1406 1458

13 12 11 10 9 8 7 6 5 4 3 2 1

1501 1540 1552 1587 1648 1702 3214 3218 3230 3242 3289 3308 3677

387 538 612 745 879 899 1014 1067 1083 1122 1150 1204 1227 1244 1278 1330 1347 1414 1458 1479 1520 1576 3051 3072 3118 3523

396 542 609 759 876 902 1015 1068 1085 1123 1143 1208 1248 1278 1334 1350 1410 1459 1479 -

1L b fluorescence Franck-Condon factors calc. a exp. d

0.0078 0.0038 0.0141 0.1002 0.0013 0.0081 0.0317 0.0159 0.0086 0.0015 0.0018 0.0006 0.0027 0.0331 0.0045 0.0960 0.0000 0.0010 0.0003 0.0005 0.0009 0.0020 0.0000 0.0003 0.0000 0.0005 0.0001 0.0001 0.0000

0.004 0.012 0.030 0.138 0.000 0.005 0.052 0.041 0.012 0.004 0.000 0.000 0.005 0.010 0.058 0.027 0.022 0.016 0.008 0.003 0.000 0.000 0.000 -

a This work: CIS/3-21G-HF/3-21G geometry difference; MP2/6-31G * modes and frequencies for both states. The origin FC factor is 0.23. b Ref. [11], observed, c Ref. [10], observed. d Estimated from Ref. [10]. The origin FC factor is about 0.19.

P.R. Callis et al. / Chemical Physics Letters 244 (I 995) 53-58

the large number of FC active modes and the range of their intensities. Fig. 1 is a graphical form of Table 1. It compares the computed and experimental tL b fluorescence spectra, presented as 'stick' spectra. The experimental intensities represent peak intensities obtained from the experimental jet spectrum published by Bickel et al. [10]. Fig. 2 shows a similar computation of the fluorescence from the ]L a state origin of indole and compares it to that shown in Fig. 1 for 1L b on a different scale. A variety of Gaussian line widths are applied to each line to expose the interesting changes in appearance created by the broadening, which is typical of many condensed phase spectra.

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Computed

0.20-

0.15-

500

1500

2500

3800

4800

5500

6800

Fig. 2. Computed fluorescence spectra from the ]L~ and t L a origins of indole using the same method as in Fig. 1. The four spectra were generated by appliing Gaussian line shapes with fwhm widths of 10, 400, 800, and 1200 cm -1 to each line to simulate inhomogeneous broadening under different conditions. The area under each curve is proportional to the corresponding width. The vertical axis is the computed F r a n c k - C o n d o n factor for the individual lines.

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200

600

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1000

1400

1800

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Fig. 1. The observed and computed fluorescence spectra from the I L b origin of indole under jet-cooled conditions. The observed spectrum is adapted from the peak heights in the spectrum reported by Ref. [10]. Note that v]4 is a Fermi doublet and has a total intensity similar to v23. The computed spectrum uses the G A U S S I A N 22 C I S / 3 - 2 1 G - H F / 3 - 2 1 G geometry difference and the ground state M P 2 / 6 - 3 1 G * modes and frequencies for both states.

Fig. 3 shows diagrams of the computed normal modes which are active in the spectra. For the outof-plane modes, the diameters of the circles on the atoms are in proportion to the atomic Cartesian amplitude normal to the plane. The phase is given by the presence or absence of shading. Of the in-plane modes, 29, 28, and 27 are virtually independent of the method of computation; QCFF/PI, AM1, and ab initio (STO-3G, 3-21G, 6-31G, and M P 2 / 6 - 3 1 G * ) all give very similar results. Significant variation in mode correspondence is found for other modes, especially the out-of-plane modes.

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P.R. Callis et al. / Chemical Physics Letters 244 (1995) 53-58

considering that no scaling of frequencies or displacements was done. The fit is particularly good below 1300 cm-1. Notable points of agreement are: (1) the similar FC magnitude of the origins; (2) the dominance of modes 26, 23, and 14; (3) the effective absence of modes 25, 19, 18, 10-8; (4) the moderate presence of modes 29, 28, 27, 24, 21, 20, and 17. Points of disagreement involve mainly modes 12-16. Experimentally there is strong intensity in modes 14 and 15, but the computation puts it into 16 and 14, with most going to 14. The computation also fails to find significant intensity in modes 12 and 13. Mode 28 is found to be Herzberg-Teller active (mixes 1La with 1L b) in absorption and emission [12]. It therefore appears more intense in experimental spectra than would be expected from the FC factor. The combination of methods used in Table 1 and Fig. 1 is the best we have found thus far. Although the MP2 correction generally improves computed geometries and frequencies, we find that the geometry difference computed with the CIS-MP2 excited state and MP2 ground state using the 3-21G basis gives a poor description of the 1L b fluorescence spectrum. This combination leads to a computed origin FC factor of 0.45 and has mode 27 much Fig. 3. Relative Cartesian atom displacements for twelve of the indole normal coordinates pertinent to the fluorescence spectrum. They were computed from the ground state MP2/6-31G * force field using GAUSSIAN92. For the out-of-planemodes the circle diameters are proportional to the Cartesian amplitude and the shading gives the relative phase.

Fig. 4 shows the Cartesian displacements (amplified 20 × ) accompanying the 1L b and iL a transitions as determined from the C I S / 3 - 2 1 G excited state and H F / 3 - 2 1 G ground state geometries. These are the geometry differences used to compute the spectra in Figs. 1 and 2. The corresponding geometry differences with the MP2 correction give very poor agreement with experiment.

Transition Distortion x 20

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4. Discussion 4.1. 1L b fluorescence

The agreement between observed and computed spectra seen in Fig. 1 is surprisingly good, especially

Fig. 4. Equilibrium geometry differences upon excitation to the indole iL b and 1La states, magnified by 20 fold, as computed from the CIS/3-21G excited state energy minimaand the HF/321G ground state energy minimum.

P.R. Callis et al. / Chemical Physics Letters 244 (1995) 53-58

stronger than mode 26. The reason appears to be that the MP2 correction has little impact on the CIS wavefunction with regard to geometry, whereas it has a large effect on the ground state geometry. This conclusion is reinforced by the observation that it matters little to the resulting spectrum whether we use the CIS or CIS-MP2 1L b geometry. Comparison with the spectrum which we [3] computed using QCFF/PI shows marked discrepancies, most notable being the absence of discernable activity in the ring bends, 29-27 and a complete reversal of the roles of 25 and 26. Mode 25 according to the present calculation is seen in Fig. 3 to be considerably antisymmetric with respect to reflection in a plane parallel to the long axis. However, the geometry displacement seen in Fig. 4 is more symmetric, a fact which largely accounts for the lack of mode 25 FC activity. Other missing modes, such as 18-20, are predominantly C - H bending modes; they are not active because the 'rr electron changes in the ~L b transition apparently have little effect on the CCH bond angles. The large activity of mode 14 is apparently because it is the mode which alternately stretches and contracts the bond lengths about the benzene ring. This projects well onto the bond length changes, which show the largest increases for the 8-9, 4-5, and 6 - 7 bonds. When the HF/3-21G modes are used for the computation, it is mode 17 which has this character and it is one of the most active modes in the computed spectrum.

4.2. 1L, fluorescence Because the CIS/3-21G ab initio calculation ~laces the 1 La minimum 940 cm- I below that of L b [6], the situation is similar to what could be expected from an indole perturbed by solvation or complexation with polar molecules. As such, it should help decide whether dispersed fluorescence from complexed indoles in cold jets i s 1L a o r 1L b. In particular, it should be noted that - just as for l Lb the origin is expected to be the strongest line in a jet spectrum, and that the spectrum will be sparse and structured below 1000 cm-1. However, t h e I L a spectrum in Fig. 2 is distinct from that of IL b in the number of significantly FC active modes and their relative intensities. A major difference is that the most active modes are the three

57

CC stretches Vs, v9, and vl0, predicted to be near 1600 cm -1. The sum of these three FC factors is nearly the same as the origin, and in the broadened spectra they lead to the characteristic maximum seen in experimental 1L a fluorescence and phosphorescence spectra near 1600 cm-1 [2,13]. Another difference is that mode 27 is comparable to 26, and both are much weaker than the origin. This aspect is also consistent with observed spectra in condensed phase when the emission is known to be IL a [2,13]. It is debatable whether jet-cooled I L a f l u o r e s c e n c e has been observed. For example, spectra by Tubergen and Levy [14] for the indole-water complex were assigned 1L a character on the basis of broadening, but the prominence of mode 26 and relative weakness of mode 27 in those spectra suggest that the fluorescence is 1L b on the basis of the calculations presented here.

4.3. Frequencies and modes Several analyses of the vibrations of indole have been made [11,15-17], including two based on HF/3-21G force fields [11,17]. In the latter, as is typical [20], in-plane vibrations were found to be estimated about 10% too high in frequency and out-of-plane frequencies were about 20% too high. As could be expected from numerous results for smaller molecules [20], the MP2/6-31G* computed frequencies are fairly accurate without scaling. It is the MP2 correction which is primarily responsible for this result. Although the frequencies are considerably lowered, the in-plane skeletal mode amplitudes are little changed by the quality of the calculation. A more detailed analysis of the MP2/6-31G* modes and frequencies is planned for future publication.

4.4. Geometry changes The geometry differences in Fig. 4 correlate very well with reported bond order changes from INDO/S [18] and are quite similar to those found with scaled QCFF/PI [3]. The 1L b displacement is dominated by expansion of the benzene ring, in keeping with large decreases in bond order in each of the bonds while those in the pyrole ring are smaller. Most of the atom displacements are radial, thus explaining the lack of activity in the stretching modes, except

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P.R. Callis et al. / Chemical Physics Letters 244 (1995) 53-58

for 1114, the 8 - 9 stretch. The fairly detailed agreement found here lends considerable validity to the geometry difference computed using the CIS excited states. A much different geometry was proposed for the 1L b state of indole, based on a MCSCF wavefunction [19]. The FC factors which can be inferred from the latter give a vastly different pattern from the observed one. For 1L a, the bond-order changes alternate around the ring, with particularly large decreases in the 2 - 3 and 6 - 7 bonds and moderate increases in the 3 - 9 and 1 - 2 bonds. Thus, the large activity of the CC stretching modes is understood.

5. Conclusions The use of ab initio C I S / 3 - 2 1 G - H F / 3 - 2 1 G transition geometry differences leads to calculated fluorescence spectra from the 1L b and 1L a states of indole that contain characteristic detail. The geometry differences using the MP2 correction give poor agreement because of its small effect on the excited state. However, the use of MP2 and higher quality basis sets for the ground state modes and frequencies improves the fit somewhat. The results strengthen the validity of the CIS ab initio excited state wavefunctions and semiempirical wavefunctions with similar characteristics.

Acknowledgement This work was supported by US PHS NIH Grant No. GM31824 and grant No. CHE92005P for computer time from the Pittsburgh Supercomputing Center.

References [1] A.P. Demchenko, Ultraviolet spectroscopy of proteins (Springer, Berlin, 1986). [2] S.V. Konev, Fluorescence and phosphorescence of proteins and nucleic acids (Plenum Press, New York, 1967). [3] J.T. Vivian and P.R. Callis, Chem. Phys. Letters 229 (1994) 153. [4] M.Z. Zgierski and F. Zerbetto, J. Chem. Phys. 99 (1993) 3721. [5] P.S. Swiderek, G. Hohlneicher, S.A. Maluendes and M. Dupuis, J. Chem. Phys. 98 (1993) 974. [6] L.S. Slater and P.R. Callis, J. Phys. Chem. 99 (1995) 8572. [7] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, B.G. Foresman, B.G. Johnson, H.B. Schlegel, M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Arnders, K. Raghavaachari, J.S. Binldey, C. Gonzalez, R.L Martin, D.J. Fox, D.J. DeFrees, J. Baker, J.J.P. Stewart and J.A. Pople, GAUSSIAN 92, Revision A (Gaussian, Pittsburgh, 1992) [8] J.B. Foresman, M. Head-Gordon, J.A. Pople and M.J. Frisch, J. Phys. Chem. 96 (1992) 135. [9] E.V. Doktorov, I.A. Malkin and V.I. Man'ko, J. Mol. Spectry. 64 (1976) 359. [10] G.A. Bickel, D.R. Demmer, E.A. Outhouse and S.C. Wallace, J. Chem. Phys. 91 (1989) 6013. [11] M. Majoube and G. Vergoten, J. Raman Spectry. 23 (1992) 431. [12] B. Fender and P.R. Callis, Chem. Phys. Letters 239 (1995) 31. [13] M.V. Hershberger, A.H. Maki and W.C. Galley, Biochemistry 19 (1980) 2204. [14] M.J. Tubergen and D.H. Levy, J. Phys. Chem. 95 (1991) 2175. [15] I. Harada, T. Miura and H. Takeuchi, Spectrochim. Acta 42A (1986) 307. [16] W.B. Collier, J. Chem. Phys. 88 (1988) 7295. [17] T.L.O. Barstis, L.I. Grace, T.M. Dunn and D.M. Lubman, J. Phys. Chem. 97 (1993) 5820. [18] P.R. Callis, J. Chem. Phys. 95 (1991) 4230. [19] C.F. Chabalowski, D.R. Garmer, J.O. Jensen and M. Krauss, J. Phys. Chem. 97 (1993) 4608. [20] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986).