Ab initio investigations on the photophysics of indole

24 December 1999

Chemical Physics Letters 315 Ž1999. 293–298 www.elsevier.nlrlocatercplett

Ab initio investigations on the photophysics of indole Andrzej L. Sobolewski

a,)

, Wolfgang Domcke

b

a

b

Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland Institute of Theoretical Chemistry, Heinrich-Heine-UniÕersity, D-40225 Dusseldorf, Germany ¨ Received 5 August 1999; in final form 26 October 1999

Abstract Reaction paths and potential-energy profiles for detachment of the hydrogen atom of the NH group in excited singlet states of indole have been investigated using the CIS, CASSCF and CASPT2 ab initio methods. The potential-energy profile of the lowest p s ) excited singlet state is found to be essentially repulsive. It crosses the potential-energy functions of the 1 L b and 1 L a excited states of p p ) character as well as those of the ground state. The resulting multiple conical intersections can provide the mechanism for efficient internal conversion to the ground state. The polarities of the excited states are remarkably different, indicating a complex interplay of internal conversion and solvation dynamics of photoexcited indole in polar solvents. q 1999 Elsevier Science B.V. All rights reserved.

1. Introduction The electronically excited states of indole and substituted indoles have attracted considerable attention in the context of understanding the complex photophysical behavior of tryptophanyl side chains of proteins w1,2x. Tryptophan fluorescence has become an important indicator of the protein environment and structural changes, primarily because the fluorescence spectrum and quantum yield of the indole chromophore are highly sensitive to its local microenvironment. The emission spectrum of tryptophan in proteins varies from a structured band to a broad diffuse band where the maximum of the excitation coefficient spans a range of 40 nm. The fluorescence quantum yield varies from 0.35 to unmeasurably low values w1x. ) Corresponding author. Fax: q48-22-8430926; e-mail: [email protected]

Much of what we currently know about the mechanisms for the photophysical behavior of tryptophan is based on the detailed spectroscopic study of its aromatic chromophore indole. As in tryptophan, the quantum yield of the fluorescence and the spectral shape of the absorption band of indole and its derivatives are strongly medium dependent w3x. The anomalously large fluorescence Stokes shift of indoles in polar solvents is qualitatively explained by the inversion of the ‘locally excited’ ŽLE. S 1ŽL b . and ‘charge transfer’ ŽCT. S 2 ŽL a . states. It has been established that the 1 L b state is the lowest excited singlet state in the gas phase and in non-polar solvents, while the 1 L a state becomes the lowest-energy singlet state in polar solvents w4x. The solvent effect on the quantum yield of indole fluorescence is even more peculiar. Its characteristic feature is the breakdown of Vavilov’s law Žindependence of the fluorescence quantum yield on the excitation wavelength. in non-polar solvents and in

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 2 4 9 - X

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A.L. Sobolewski, W. Domcker Chemical Physics Letters 315 (1999) 293–298

water. Only in alcohols is Vavilov’s law obeyed w3x. This complex behavior can be explained by the presence of an efficient polarity-dependent Žand solvent specific. channel of radiationless deactivation. Hydrogen predissociation from the NH group in non-polar non-hydrogen bonding solvents and photoionization in water have been proposed as the mechanisms responsible for the non-radiative decay w3x. Investigations of the excess-energy dependence of the non-radiative decay rate performed for a series of indole derivatives under collision-free conditions correlate the threshold for non-radiative decay with the position of the 1 L a state w5x. It has been postulated that the 1 L a state of indoles is repulsive with respect to NH bond stretching w6x. A theoretical analysis of the vertical electronic spectrum of indole has recently been performed by Serrano-Andres ´ and Roos w7x with the aid of state-ofthe-art ab initio methods: complete-active-space self-consistent-field ŽCASSCF. and multi-configurational second-order perturbation theory ŽCASPT2.. This work also contains a comprehensive list of references to earlier semi-empirical and lower-level ab initio studies. The authors support the assignment of the first two absorption bands to 1 L b and 1 L a , with the 1 L a band origin located 0.31 eV above the 1 L b band origin in the gas phase. In addition, they predict a series of low-lying singlet Rydberg states just above the S1ŽL b . and S 2 ŽL a . valence excited states. The lowest Rydberg state of the series has a vertical excitation which is only 0.12 eV higher than that of the 1 L a state. The wavefunction of the Rydberg state is dominated by electronic configuration p s ) , and its dipole moment of 12.31 Debye is much larger than the dipole moments of the CT 1 L a and the LE 1 L b states Ž5.69 and 0.85 Debye, respectively. w7x. The presence of low-lying absorption bands with strong Rydberg character in the vaporphase absorption spectra of indole and 1-methyl-indole has already been suggested some years ago w8x. One can thus expect that the low-lying, and highly polar, Rydberg states may have a significant influence on the photophysical properties of indoles in polar solvents. In this Letter, we present the results of an ab initio study of the photophysical properties of indole in the lowest excited singlet states. It is found that

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the 1 L b and 1 L a potential-energy ŽPE. functions are bound with respect to the in-plane detachment of the hydrogen atom of the NH group, but are predissociated by the repulsive PE function of the low-lying 1 p s ) state. Vibronic coupling of the p p ) valence 1 L b and 1 L a states with the 1 p s ) state by out-ofplane modes connects the former states, via a low barrier, to the conical intersection of the latter state with the ground state, providing a mechanism for efficient internal conversion.

2. Computational methods The ground-state geometry of indole was optimized by the restricted-Hartree–Fock ŽRHF. second-order Møller–Plesset ŽMP2. method w10x. Optimization of the excited-state geometry was performed using the configuration interaction with singles ŽCIS. method w11x. The standard split-valence double-zeta Gaussian basis set 6-31G with polarization functions on all the heavy atoms and on the hydrogen atom of the NH group w12,13x was supplemented with a set of diffuse functions. Since we were interested in the theoretical description of the lowest p s ) Rydberg-like state with the s ) orbital essentially localized on the NH moiety, the s- and p-diffuse functions Žexponent 0.0639. were centered on the nitrogen atom and the diffuse s-function Žexponent 0.036. was placed on the adjacent hydrogen atom. For the construction of the reaction path for hydrogen detachm ent, the coordinate-driven minimum-energy-path ŽMEP. approach was adopted, i.e. for a given value of the NH bond length Ž R NH . all remaining intramolecular coordinates were optimized with C s symmetry, i.e. planarity of the molecular frame being imposed. The symmetry constraint has allowed us to optimize the lowest excited singlet states of AX Ž p p ) . and AXX Ž p s ) . symmetry, respectively. The MP2 and CIS calculations were performed with the aid of the GAUSSIAN 98 program package w14x. To incorporate electron-correlation effects for the excited states, single-point calculations at optimized geometries along the reaction path were performed with the CASPT2 method w15x. The CASPT2 calculations were performed with the MOLCAS-4

A.L. Sobolewski, W. Domcker Chemical Physics Letters 315 (1999) 293–298

package w16x, using the ANO-L basis set of split-valence double-zeta quality with polarization functions on all heavy atoms and the reactive hydrogen atom, supplemented by diffuse functions as defined above. The active space for the CASSCF and CASPT2 calculations includes all the p orbitals as well as two additional s ) orbitals of Rydberg type, localized mostly on the NH moiety. The active space correlates 10 electrons in 11 orbitals and it is denoted as Ž1–10aXX ,28–29aX . in the C s point group. Dipole moments and transition dipole moments were calculated from the CASSCF wavefunctions by means of the CASSI Žcomplete-active-space state interaction. method w17x. The CASPT2 energies were used in calculation of the oscillator strengths.

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and oscillator strengths. The three lowest excited singlet states are, in ascending order, L b Ž p p ) ., L aŽ p p ) . and AXX Ž p s ) .. The dipole moments increase in the same order. The wavefunction of the AXX Ž p s ) . state is determined by the electronic configuration 5aXX 27aX , the latter orbital being the s ) Rydberg-type localized on the NH moiety and having a node along the NH bond. This fact and the high polarity of the AXX Ž p s ) . state indicate that it is not a ‘regular’ Rydberg state which by definition is supposed to be centered at the center of positive charge of the cation. To avoid confusion, in the following we refer to the AXX state as to the p s ) excited singlet state with diffuse s ) orbital. The three lowest excited singlet states of indole are distinct from each other with respect to their spectroscopic properties. The absorption spectrum of indole is dominated by the transition to the allowed 1 L a state, while transitions to the lowest valence 1 L b state and to the 1AXX state are nearly forbidden. They can, however, gain intensity via vibronic coupling with the close-lying allowed S 0 1 L a transition. The distinct spectroscopic properties of the states are reflected by differences in their wavefunctions which determine the charge distribution and the effective dipole moment of each electronic state Žsee Table 1.. In Fig. 1 we present the CASSCF charge distribution ŽMulliken definition. in the ground state of indole and its change due to excitation to the lowest singlet states. The small dipole moment of the S 0 state, pointing from the center of mass towards the nitrogen atom, results from the almost symmetrical distribution of charge within the molecular frame. Optical excitation to the lowest excited singlet state

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3. Results and discussion 3.1. Spectroscopic properties

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The geometry of the ground state of indole optimized at the MP2 level with the basis set as specified above is similar to the MP2r6-31GŽd.-optimized geometry of Ref. w18x and the data are therefore not presented here. The CASSCFrCASPT2 results obtained for the ground-state geometry are given in Table 1. The CASPT2 energies reproduce the experimental observations Žmaxima of absorption bands. within the accuracy expected for this method Ž0.2 eV.. They are similar to the CASPT2 results of Ref. w7x although the basis sets and molecular geometry are slightly different. The same applies to the dipole moments

Table 1 Calculated and experimental excitation energies ŽeV., oscillator strengths, and dipole moments ŽDebye. for the ground and the lowest excited singlet states of indole State

S0 S1Ž p p ) . S2Ž p p ) . S3Ž p s ) . a b

Experimental data from Ref. w8x. Experimental data from Ref. w9x.

Excitation energy

m

Oscillator strength

CASPT2

Exp

4.30 4.65 5.05

4.4 4.8

a

CASSI

Exp

0.02 0.09 3 = 10y5

0.04 0.12

b

1.87 1.55 6.12 11.03

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A.L. Sobolewski, W. Domcker Chemical Physics Letters 315 (1999) 293–298

Fig. 1. Mulliken charge distribution in the ground state of indole and its change due to optical excitation to the lowest singlet states obtained with the CASSCFrANO-L method at the MP2-optimized geometry. The arrows indicate the value and the direction of dipole moment in each electronic state.

ŽL b . causes only marginal changes in the charge distribution and resulting dipole moment. Upon excitation to the 1 L a state, a significant amount of electronic charge is transferred from the pyrrole ring to the phenyl moiety; the resulting moderate dipole moment is approximately parallel to the long molecular axis. Excitation to the lowest singlet state of AXX symmetry causes much more radical changes in the charge distribution. More than one electron charge is

transferred from the rings Žmostly from the nitrogen atom. to the hydrogen atom of the NH group. The resulting large dipole moment of the 1AXX state is approximately parallel to the NH bond, and almost perfectly in the opposite direction with respect to that of the ground state and rotated by about 133 degrees with respect to the dipole moment of the 1 L a state. Such a massive rearrangement of the charge distribution between the excited electronic states implies a very different dynamical response of a polar environment to intramolecular electronic transitions. In addition, the strong polarity of the NH bond in the 1 XX A state indicates the possibility of ‘solvation’ of the electron in a polar solvent such as water w19x. 3.2. Potential-energy profiles The CASPT2 PE profiles calculated along the CIS-determined MEP for detachment of the hydrogen atom of the NH group are presented in Fig. 2a. Only the geometry of the lowest excited state of a given symmetry and multiplicity can be optimized. Both valence excited p p ) singlet states ŽL b and L a . belong to the same symmetry representation ŽAX . and can only accidentally be optimized individually w7x. This is not the case when one optimizes the excited-state geometry along the MEP. In the CIS

Fig. 2. CASPT2 PE profiles Ža. and CASSCF dipole moments Žb. of the Žcircles. electronic ground state and the lowest excited singlet states: Ždiamonds. L b , Žsquares. L a , and Žtriangles. A‘ states. The solid lines indicate properties calculated at the optimized geometry of a given electronic state.

A.L. Sobolewski, W. Domcker Chemical Physics Letters 315 (1999) 293–298

approximation, the state of L a character is the lowest excited singlet state among the states of the AX symmetry. Thus the MEPs used for the CASPT2 PE profiles presented in Fig. 2a were determined for the AX Ž1 L a . and 1AXX states. The PE profiles of the 1 L b and the S 0 states were calculated at the geometries optimized in the 1 L a and 1AXX states, respectively. Inspecting the results presented in Fig. 2a one sees that PE profiles of the ground and the lowest valence excited states rise with increasing NH distance in an approximately parallel manner. The minimum of the lowest 1 p s ) state Žof AXX symmetry. lies about 0.5 eV above the minimum of the 1 L a state. Dissociation of the hydrogen atom in the former state is prohibited by a barrier of only 0.1 eV Ž, 2 kcalrmol.. The 1AXX state intersects the valence excited singlet states as well as the ground state along the R NH reaction coordinate. These intersections develop into conical intersections when out-of-plane displacements are taken into account. This produces a barrier on the PE surface of the lowest excited singlet state with respect to hydrogen detachment reaction, which protects the electronically excited system against the region of strong non-adiabatic interactions with the ground state at the conical intersection with the latter. The CASSCF dipole moment functions of the states of interest are presented in Fig. 2b. The dipole moments of both valence states and the ground state are weakly dependent on the reaction coordinate, whereas the dipole moment of the 1 p s ) state decreases abruptly with increasing NH distance. In effect, the latter state dissociates to a neutral hydrogen atom and a neutral indolyl radical. Interactions with a polar solvent are expected to have a complex influence on the 1AXX state owing to its large dipole moment w19x. 3.3. Photophysical implications The mechanism which is expected to govern the photophysics of indole excited with some excess of energy above the origin of the S 1 state under isolated-molecule conditions is the access to an efficient non-radiative channel provided by the hydrogen-detachment reaction of the NH group. The threshold for this photophysical process is predicted to be located at about 5 eV for optical excitation from the

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ground state. This value agrees well with experimental observations w5,8x. Our results unequivocally attribute the threshold for hydrogen detachment to predissociation of the 1 L a state by the lowest AXX Ž p s ) . state. This is in apparent contradiction to earlier propositions which assign the radiationless channel to properties of the PE function of the 1 L aŽ p p ) . state w6x. This contradiction is largely semantic since the symmetry distinction between the AX Ž p p ) . and AXX Ž p s ) . states applies only when the molecular symmetry plane is conserved. Any outof-plane distortion may mix the states. While the dipole moments of the 1 L a and the AXX states are of similar value near their intersection, the directions of the dipole moments in the two states are very different from each other Žthey are similar to those presented in Fig. 1.. Thus solvation of the different excited singlet states, which depends not only on the polarity of the solvent, but also on specific dynamical solute–solvent interactions, is expected to modulate the barrier for internal conversion to the ground state, and is thus being responsible for the complex photophysics of indole in solution.

4. Conclusions A brief summary of the results of the present work can be given as follows: Ži. The lowest 1AXX Ž p s ) . state of indole has strong CT character, one electron being transferred from the ring to the hydrogen of the NH group. Its PE function is repulsive with respect to in-plane detachment of the hydrogen atom. Žii. As a function of the NH distance, the PE profile of the 1AXX Ž p s ) . state crosses the PE profiles of the 1 L aŽ p p ) . and 1 L b Ž p p ) . states and the ground state. The associated multiple conical intersections between the states presumably provide the mechanism for efficient internal conversion from the excited singlet states to the ground state. The threshold for this photophysical process is predicted to be located within the 1 L aŽ p p ) . absorption band. Žiii. The competition of vibronic interactions and solvation of the weakly-polar 1 L b Ž p p ) . valence state, the moderately polar 1 L aŽ p p ) . valence state and the highly polar predissocia-

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tive 1AXX Ž p s ) . state is expected to provide the key to understanding the complex photophysics of indole in solvents of different polarity. Acknowledgements This work has been supported by the Deutsche Forshungsgemeinschaft and the Committee for Scientific Research of Poland ŽGrant No. 2P03B 035 13. References w1x P.R. Callis, Methods Enzymol. 278 Ž1997. 113. w2x Y. Chen, M.D. Barkley, Biochem. 37 Ž1998. 9976. w3x I. Tatischeff, R. Klein, T. Zemb, M. Duquesne, Chem. Phys. Lett. 54 Ž1978. 394. w4x H. Lami, N. Glasser, J. Chem. Phys. 84 Ž1986. 597. w5x N. Glasser, H. Lami, J. Chem. Phys. 74 Ž1981. 6526.

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