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Photoejection of electrons from pyrrole into an aqueous environment: ab initio results on pyrrole-water clusters
5 May 2000
Chemical Physics Letters 321 Ž2000. 479–484 www.elsevier.nlrlocatercplett
Photoejection of electrons from pyrrole into an aqueous environment: ab initio results on pyrrole-water clusters Andrzej L. Sobolewski
a,)
, Wolfgang Domcke
b
a
b
Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland Institute of Theoretical Chemistry, Technical UniÕersity of Munich, D-80747 Garching, Germany Received 14 March 2000
Abstract Ab initio ŽRHF, CASSCF and CASPT2. calculations in the ground and lowest excited singlet states have been performed on pyrrole and pyrrole–water clusters. Full geometry optimization in the 1 p s ) state, which is energetically accessible from the optically allowed 1 p p ) state, reveals the flow of the electronic charge from pyrrole towards the water molecules, i.e., the formation of a charge transfer-to-solvent state. The computational results indicate that pyrrole–water clusters are good models for the investigation of the mechanistic details of the electron solvation process occurring upon ultraviolet photoexcitation of organic chromophores in liquid water. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Tryptophan is the most strongly near-ultraviolet ŽUV. absorbing species among the common amino acids. The photochemistry of tryptophan and its chromophore, indole, is therefore a topic of considerable interest in the radiation chemistry of proteins. The solution phase photophysics and photochemistry of indole and tryptophan is complex and very sensitive to the environment w1,2x. It has been established that electron ejection, i.e., formation of hydrated electrons, is a major decay channel for photoexcited indole or tryptophan in aqueous solution w3x. The quantum yield depends on the excitation wavelength and reaches a value , 0.3 at short wavelengths Ž200 nm. w4x. The charge-separation process ) Corresponding author. Fax: q48-22-843-09-26; e-mail: [email protected]
appears to be thermally activated with an activation energy of , 10 kcalrmol. It has been shown that the charge-separation process is fast Ž( 1 ps. and that recombination is negligible on a 100 ps timescale w5x. Considering the biological relevance of this phenomenon, a detailed understanding of the mechanism leading to the irreversible charge separation is of considerable interest. In a recent investigation of the photophysics of indole, we discovered a peculiarity of the excitedstate structure of this molecule which possibly can provide the clue for the understanding of the electron-ejection mechanism in the photoexcited indole–water system w6x. It has been found that the well-known S 1ŽL b . and S 2 ŽL a . p p ) excited states of indole are predissociated by a low-lying 1 p s ) state, the relevant reaction coordinate being the NH stretching coordinate. In this 1 p s ) state, previously classified as a Rydberg state w7x, a significant amount
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 4 0 4 - 8
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A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
of electronic charge is displaced from the N-atom towards the neighboring H-atom, resulting in an unusually large dipole moment of , 10 Debye. It is conceivable that in an aqueous environment the electron located in the diffuse s ) orbital of the highly polar 1 p s ) state can be transferred to nearby water molecules, resulting in a Žhydrated. indole cation and a hydrated electron. In the present work, we have investigated the possibility of this process by electronic-structure calculations on pyrrole–water clusters. As the photochemistry of pyrrole agrees in all essential features with that of indole Žsee below., the pyrrole–water system should be a good model for the indole–water system. In addition, the solution-phase photochemistry of pyrrole is of its own interest as pyrrole is a building block of many biologically relevant compounds. Using a basis set which includes a floating center for the representation of the moveable electron and employing geometry-optimization techniques, the charge-transfer process and associated microsolvation process have been explored and visualized.
2. Computational method The ground-state geometry of pyrrole–water ŽPWn . clusters was optimized at the restricted Hartree–Fock ŽRHF. level. Optimization of the 1 p s ) excited-state geometry was performed using the complete-active-space self-consistent-field ŽCASSCF. method w8x. The standard split-valence doublezeta Gaussian basis set 6 y 31G ) ) with polarization functions on all atoms w9,10x was used. For the excited-state optimizations this basis set was supplemented with a set of s and p diffuse Gaussian functions localized at a floating center. The nuclear geometry of the cluster in the 1 p s ) state Žincluding the position of the floating center. and the exponent of the s and p diffuse functions were optimized in a self-consistent manner until the energy change was below the threshold for optimization. A similar technique has been used in calculations of the dipolebound anions of molecular complexes w11,12x. The active space for the CASSCF calculations includes all p valence orbitals of the pyrrole ring and the s ) orbital. The active space thus correlates
six electrons in six orbitals. C s symmetry of the PWn cluster was imposed in the course of the geometry optimization. Within the C s point group the wave function of the p s ) state transforms according to the non-totally symmetric AXX representation and thus cannot collapse to the ground state. The geometry optimizations were performed with the GAMESS package w13x. To incorporate electron-correlation effects for the excited states, single-point calculations at optimized geometries along the reaction path were performed with the aid of the CASPT2 method Žsecond-order perturbation theory based on the CASSCF reference. w14x. The CASPT2 calculations were performed with the MOLCAS-4 package w15x, using the ANO-L basis set of split-valence doublezeta quality with polarization functions on all atoms and diffuse s and p Gaussian functions at the floating center.
3. Results and discussion The experimental UV absorption spectrum of pyrrole exhibits a broad intense band centered around 6 eV which has been assumed to arise from p p ) valence-type excitations w16x. Superimposed on this band is a rich structure assigned to Rydberg-type excitations. To our knowledge, the lowest singlet– singlet transition of pyrrole has so far not been observed, although in N-methyl pyrrole the lowest singlet state at about 5.1 eV has been assigned to the 3s Rydberg state w17x. Ab initio calculations of the vertical excitation energies of pyrrole have been performed by a number of groups using a variety of methods Žsee Refs. w7,16,18,19x, and references therein.. There is some dispute about how the observed structures are to be assigned to Rydberg and valence transitions w7,16,18,19x. The calculations essentially assign, however, the lowest-energy singlet–singlet transition Žat about 5.0 eV. to the 1a 2 3s Rydberg state. The large dipole moment of 3.67 a.u. Ž9.32 Debye. obtained for this state w7x indicates that this state, like the 1 p s ) state in indole Žcf. discussion in Section 1., exhibits pronounced charge-transfer character. In Fig. 1 we present the p Ž1a 2 . and s ) Ž10a 1 . orbitals which were determined by a CASSCF calculation for the 1AXX Ž p s ) . state of pyrrole. The floating
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A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
Fig. 1. The p Ž1a 2 . and s ) Ž10a 1 . orbitals obtained by a CASSCF calculation for the 1A 2 Ž p s ) . state of pyrrole.
center of the diffuse basis function is located by geometry optimization on the NH bond at a distance ˚ from the nitrogen atom and the exponent of 0.694 A of the Gaussian s and p functions has the optimized value of 0.0205. This result clearly indicates that the lowest excited singlet state of pyrrole has Rydberg character, reflected by the diffuseness of the s ) orbital, but also involves a significant transfer of charge from the aromatic ring to the H-atom. Fig. 2 displays CASPT2 potential-energy ŽPE. profiles calculated along the minimum-energy path Ždetermined at the CASSCF level. for detachment of the H-atom of the NH group. For clarity, only the lowest 1 p s ) and 1 p p ) states and the electronic ground state are shown. It is seen that the geometryoptimized 1 p s ) state lies below the optimized 1 p p ) state. While the latter is bound as a function of the NH stretching coordinate, the former is essentially repulsive and thus can predissociate the 1 p p ) state. In a multi-dimensional picture, there exists a high-dimensional hyper-surface of intersection of the 1 p p ) and 1 p s ) surfaces; vibrational modes of A 2 symmetry lift these degeneracies, leading to a multi-dimensional conical intersection, which can promote ultrafast transitions from the 1 p p ) surface to the 1 p s ) surface. In fact additional electronic states Žother low-lying Rydberg-like states. also may be involved as intermediates in the 1 p p ) 1 p s ) decay. In any case, this transition can be expected to be fast, leading to the population of the lowest 1 p s ) state with high probability. The photochemistry of pyrrole is thus expected to be determined by the reaction dynamics on the lowest 1 p s ) surface.
481
It is seen in Fig. 2 that the repulsive 1 p s ) PE profile intersects the PE function of the ground state ˚ resulting in at an NH distance of about 1.8 A, another conical intersection. In the isolated molecule, this conical intersection leads to ultrafast Žfemtosecond. internal conversion to the ground state. This explains why fluorescence of pyrrole has not been observed so far in the gas phase. A weak fluorescence is observed in N-methyl pyrrole w17x, indicating that the NH group of pyrrole is involved in the reaction leading to radiationless decay. In the following, we discuss the electronic structure of the 1 p s ) state in PWn clusters Ž n s 1–5.. A detailed discussion of the energetics of the photochemistry of PWn clusters requires extensive CASPT2 calculations which will be reported in a future publication w20x. Here we focus on the character of the s ) orbital in order to visualize the charge separation process in the photoexcited clusters. Fig. 3 shows the geometric structures of PWn , n s 1–5, clusters which correspond to the minimum of the 1 p s ) surface. Ground-state optimized cluster structures Žsee below. were used as initial-guess structures for the excited-state geometry optimization. For small clusters Žup to three water molecules., the same final minimum-energy structure in the
™
Fig. 2. Minimum-energy path PE profiles for the lowest 1 p p ) state Žcircles. and for the lowest 1 p s ) state Žsquares. as a function of the NH distance. The PE function of the ground state Žtriangles. was calculated at the optimized geometry of the 1 p s ) state.
A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
482
XX Fig. 3. The s ) orbital of the 1A Ž p s ) . state of the PWn clusters.
1
p s ) excited state displayed in Fig. 3 has been obtained, independent of the initial guess. This indicates that these structures represent well-developed minima on the 1 p s ) surface, under C s symmetry constraint. For larger clusters, several different minima of the 1 p s ) surface can be found. For the PW4 cluster, for example, several C s excited-state geometries can be found by using initial guesses which eliminate different water molecules from the ground-state PW5 cluster. Fig. 3 shows, in addition, the s ) orbital. It is seen that already in the presence of a single water molecule ŽPW1 . the s ) electron cloud has largely been transferred from the H-atom of the NH group to the water molecule Žcf. Fig. 1.. It appears to form a dipole-bound state of water which is tilted towards the positive charge of the pyrrole cation. When further water molecules are added, the s ) electron cloud successively moves away from the chromophore. The water molecules form a cage encapsulating the electron cloud. The resulting negatively charged water cluster is connected by hydrogen bonds to adjacent H-atoms of pyrrole. Since in all systems the p orbital remains localized on the
aromatic ring, the structures of Fig. 3 may be classified as charge-transfer-to-solvent ŽCTTS. systems. They can be considered as precursors for the electron solvation process in large clusters or in liquid water. To our knowledge, this phenomenon has been obtained here for the first time at the level of an ab initio electronic-structure calculation. Some of the properties of the 1AXX Ž p s ) . state of the PWn clusters at the optimized geometry are collected in Table 1. It is seen that the separation of the s ) orbital from the pyrrole ring, measured by the NX distance Ž X being the floating center., increases ˚ for PW1 to NX s monotonically from NX s 1.84 A ˚ 4.08 A for PW5 . The increasing charge separation is reflected by the increase of the dipole moment of the CTTS state from 11.48 Debye for PW1 to 14.57 Debye for PW5 . The exponent of the floating Gaussian basis set functions, on the other hand, is essentially constant, indicating that the spatial extension of the hydrated electron does not depend on the cluster size. The spatial extension of the electron cloud in the CTTS state is remarkably smaller than that deter-
Table 1 Energy Ž E ., distance of the floating center from nitrogen ŽNX., exponent of the diffuse function Žh ., and dipole moment Ž m . obtained at the XX CASSCF level of theory for the 1A Ž p s ) . state of the pyrrole–water clusters
E Žau. ˚. NX ŽA h m ŽDebye.
PW1
PW2
PW3
PW4
PW5
y284.76311
y360.79737
y436.83765
y512.86766
y588.90569
1.840 0.016 11.48
2.519 0.018 12.60
2.811 0.018 11.45
3.613 0.020 12.85
4.081 0.017 14.57
A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
mined for the dipole-bound anions of water clusters w11,12x. Extension of our basis set by an additional s orbital at the floating center and optimization of both Gaussian exponents has no essential effect on the shape of the s ) orbital. This can be explained by the different nature of the interactions which bind the hydrated electron in the CTTS state compared to dipole-bound anion clusters. In the former case, the most important binding contribution at long range results from Coulombic attraction between the hydrated electron and the cationic core. This results in
483
a relative compactness of the electron cloud in the CTTS state. With increasing cluster size, water molecules form a shell which effectively screens the Coulombic attraction between the two species, leading to a spatial separation of the electron cloud from the cation. Fig. 4 shows the comparison of the equilibrium geometries of the PWn clusters in the electronic ground state and in the 1 p s ) state. In the ground state, we obtain the well-known ‘ice-like’ lattice of water molecules H-bonded to the NH moiety of pyrrole. The geometric structure of the cluster changes drastically after electronic excitation to the 1 XX A Ž p s ) . state. For larger clusters, in particular, there is little correspondence between the geometries in both electronic states. Generally, in the 1AXX Ž p s ) . state the water molecules form a shell around the s ) cloud and their geometric arrangement exhibits only marginal reminiscence of the H-bonded lattice of the ground state. Our calculations thus confirm massive rearrangement of the surrounding solvent in the CTTS process. For technical reasons, C s symmetry of the cluster was enforced in the calculations. This introduces some limitations on the possible structures of the clusters. However, even with this restriction, the calculations reveal the existence of several almost isoenergetic isomers for larger clusters. This indicates a flat PE surface with several local minima in the 1AXX Ž p s ) . state, a fact which may be important for future simulations of the molecular dynamics of the electron photoejection process in pyrrole–water clusters. 4. Summary
XX Fig. 4. The geometries of the PWn clusters in the S0 and 1A Ž p s ) . states, optimized with the RHF and CASSCF methods, respectively. The black dot indicates the center of the diffuse basis functions.
The exploratory ab initio electronic structure calculations presented in this work show that electron ejection is a spontaneous Žexothermic. process after UV photoexcitation of the chromophore in pyrrole– water clusters. The calculations reveal, furthermore, the detailed mechanism of this remarkable process. A key role is attributed to the low-lying 1 p s ) state of pyrrole which is populated by internal conversion after photoexcitation of the optically allowed 1 p p ) state. The characteristic feature of the 1 p s ) state is a pronounced dislocation of the electronic charge from the aromatic ring towards the H-atom of the
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NH group. In clusters of pyrrole with water, the diffuse electron cloud on the H-atom is further transferred to the surrounding water molecules, forming a CTTS state. When four or more water molecules are present, the characteristic cage structure of the hydrated electron develops. The water layer screens the Coulombic attraction between the electron cloud and the pyrrole cation, resulting in stabilization of the CTTS state. In bare pyrrole, the 1 p s ) state forms a conical intersection with the electronic ground state Žcf. Fig. 2., which causes ultrafast internal conversion to the ground state. The photon energy is thus converted into heat with high efficiency. The presence of water removes the conical intersection w20x and opens the CTTS channel: the energy of the photon is now converted into chemical energy Žcharge separation.. The pyrrole–water cluster may be one of the simplest systems where this biologically highly relevant process can be investigated in microscopic detail. The phenomena which we have investigated here for pyrrole–water clusters occur in a very similar manner in indole–water clusters. The calculations on indole–water clusters are in progress. Further investigations have to show whether the formation of hydrated electrons is a general feature of the photochemistry of heterocycles in aqueous environments.
Acknowledgements This work has been supported by a visitor grant of the Deutsche Forshungsgemeinschaft for A.L.S.
References w1x R. Santus, M. Bazin, M. Aubailly, Rev. Chem. Intermed. 3 Ž1980. 231. w2x D. Creed, Photochem. Photobiol. 39 Ž1984. 537. w3x L.I. Grossweiner, G.W. Swenson, E.F. Zwicker, Science 141 Ž1963. 805. w4x J. Zechner, G. Kohler, N. Getoff, I. Tatischeff, R. Klein, ¨ Photochem. Photobiol. 34 Ž1981. 163. w5x J. Peon, G.C. Hess, J.-M.L. Pecourt, I. Yuzawa, B. Kohler, J. Phys. Chem. A 103 Ž1999. 2460. w6x A.L. Sobolewski, W. Domcke, Chem. Phys. Lett. 315 Ž1999. 293. w7x L. Serrano-Andres, M. Merchan, I. Nebot-Gil, B.O. Roos, M. Fulscher, J. Am. Chem. Soc. 115 Ž1993. 6184. ¨ w8x B.O. Roos, Adv. Quant. Chem. 69 Ž1987. 399. w9x J.S. Binkley, J.A. Pople, W.J. Hehre, J. Am. Chem. Soc. 102 Ž1980. 939. w10x M.S. Gordon, J.S. Binkley, J.A. Pople, W.J. Pietro, W.J. Hehre, J. Am. Chem. Soc. 104 Ž1982. 2797. w11x D.M.A. Smith, J. Smets, Y. Elkadi, L. Adamowicz, J. Chem. Phys. 107 Ž1997. 5788. w12x F. Weingend, R. Ahlrichs, Phys. Chem. Chem. Phys. 1 Ž1999. 4537. w13x M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 Ž1993. 1347. ˚ Malmqvist, B.O. Roos, A.J. Sadlej, K. w14x K. Andersson, P.-A. Wolinski, J. Phys. Chem. 94 Ž1990. 5483. w15x K. Andersson et al., MOLCAS, Version 4, User’s Guide, University of Lund, Sweden, 1997. w16x M.H. Palmer, I.C. Walker, M.F. Guest, Chem. Phys. 238 Ž1998. 179. w17x R. McDiarmid, X. Xing, J. Chem. Phys. 105 Ž1996. 867. w18x A.B. Trofimov, J. Schirmer, Chem. Phys. 214 Ž1997. 153. w19x O. Christiansen, J. Gauss, J.F. Stanton, P. Jørgensen, J. Chem. Phys. 111 Ž1999. 525. w20x A.L. Sobolewski, W. Domcke, in preparation.
Chemical Physics Letters 321 Ž2000. 479–484 www.elsevier.nlrlocatercplett
Photoejection of electrons from pyrrole into an aqueous environment: ab initio results on pyrrole-water clusters Andrzej L. Sobolewski
a,)
, Wolfgang Domcke
b
a
b
Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland Institute of Theoretical Chemistry, Technical UniÕersity of Munich, D-80747 Garching, Germany Received 14 March 2000
Abstract Ab initio ŽRHF, CASSCF and CASPT2. calculations in the ground and lowest excited singlet states have been performed on pyrrole and pyrrole–water clusters. Full geometry optimization in the 1 p s ) state, which is energetically accessible from the optically allowed 1 p p ) state, reveals the flow of the electronic charge from pyrrole towards the water molecules, i.e., the formation of a charge transfer-to-solvent state. The computational results indicate that pyrrole–water clusters are good models for the investigation of the mechanistic details of the electron solvation process occurring upon ultraviolet photoexcitation of organic chromophores in liquid water. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Tryptophan is the most strongly near-ultraviolet ŽUV. absorbing species among the common amino acids. The photochemistry of tryptophan and its chromophore, indole, is therefore a topic of considerable interest in the radiation chemistry of proteins. The solution phase photophysics and photochemistry of indole and tryptophan is complex and very sensitive to the environment w1,2x. It has been established that electron ejection, i.e., formation of hydrated electrons, is a major decay channel for photoexcited indole or tryptophan in aqueous solution w3x. The quantum yield depends on the excitation wavelength and reaches a value , 0.3 at short wavelengths Ž200 nm. w4x. The charge-separation process ) Corresponding author. Fax: q48-22-843-09-26; e-mail: [email protected]
appears to be thermally activated with an activation energy of , 10 kcalrmol. It has been shown that the charge-separation process is fast Ž( 1 ps. and that recombination is negligible on a 100 ps timescale w5x. Considering the biological relevance of this phenomenon, a detailed understanding of the mechanism leading to the irreversible charge separation is of considerable interest. In a recent investigation of the photophysics of indole, we discovered a peculiarity of the excitedstate structure of this molecule which possibly can provide the clue for the understanding of the electron-ejection mechanism in the photoexcited indole–water system w6x. It has been found that the well-known S 1ŽL b . and S 2 ŽL a . p p ) excited states of indole are predissociated by a low-lying 1 p s ) state, the relevant reaction coordinate being the NH stretching coordinate. In this 1 p s ) state, previously classified as a Rydberg state w7x, a significant amount
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 4 0 4 - 8
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A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
of electronic charge is displaced from the N-atom towards the neighboring H-atom, resulting in an unusually large dipole moment of , 10 Debye. It is conceivable that in an aqueous environment the electron located in the diffuse s ) orbital of the highly polar 1 p s ) state can be transferred to nearby water molecules, resulting in a Žhydrated. indole cation and a hydrated electron. In the present work, we have investigated the possibility of this process by electronic-structure calculations on pyrrole–water clusters. As the photochemistry of pyrrole agrees in all essential features with that of indole Žsee below., the pyrrole–water system should be a good model for the indole–water system. In addition, the solution-phase photochemistry of pyrrole is of its own interest as pyrrole is a building block of many biologically relevant compounds. Using a basis set which includes a floating center for the representation of the moveable electron and employing geometry-optimization techniques, the charge-transfer process and associated microsolvation process have been explored and visualized.
2. Computational method The ground-state geometry of pyrrole–water ŽPWn . clusters was optimized at the restricted Hartree–Fock ŽRHF. level. Optimization of the 1 p s ) excited-state geometry was performed using the complete-active-space self-consistent-field ŽCASSCF. method w8x. The standard split-valence doublezeta Gaussian basis set 6 y 31G ) ) with polarization functions on all atoms w9,10x was used. For the excited-state optimizations this basis set was supplemented with a set of s and p diffuse Gaussian functions localized at a floating center. The nuclear geometry of the cluster in the 1 p s ) state Žincluding the position of the floating center. and the exponent of the s and p diffuse functions were optimized in a self-consistent manner until the energy change was below the threshold for optimization. A similar technique has been used in calculations of the dipolebound anions of molecular complexes w11,12x. The active space for the CASSCF calculations includes all p valence orbitals of the pyrrole ring and the s ) orbital. The active space thus correlates
six electrons in six orbitals. C s symmetry of the PWn cluster was imposed in the course of the geometry optimization. Within the C s point group the wave function of the p s ) state transforms according to the non-totally symmetric AXX representation and thus cannot collapse to the ground state. The geometry optimizations were performed with the GAMESS package w13x. To incorporate electron-correlation effects for the excited states, single-point calculations at optimized geometries along the reaction path were performed with the aid of the CASPT2 method Žsecond-order perturbation theory based on the CASSCF reference. w14x. The CASPT2 calculations were performed with the MOLCAS-4 package w15x, using the ANO-L basis set of split-valence doublezeta quality with polarization functions on all atoms and diffuse s and p Gaussian functions at the floating center.
3. Results and discussion The experimental UV absorption spectrum of pyrrole exhibits a broad intense band centered around 6 eV which has been assumed to arise from p p ) valence-type excitations w16x. Superimposed on this band is a rich structure assigned to Rydberg-type excitations. To our knowledge, the lowest singlet– singlet transition of pyrrole has so far not been observed, although in N-methyl pyrrole the lowest singlet state at about 5.1 eV has been assigned to the 3s Rydberg state w17x. Ab initio calculations of the vertical excitation energies of pyrrole have been performed by a number of groups using a variety of methods Žsee Refs. w7,16,18,19x, and references therein.. There is some dispute about how the observed structures are to be assigned to Rydberg and valence transitions w7,16,18,19x. The calculations essentially assign, however, the lowest-energy singlet–singlet transition Žat about 5.0 eV. to the 1a 2 3s Rydberg state. The large dipole moment of 3.67 a.u. Ž9.32 Debye. obtained for this state w7x indicates that this state, like the 1 p s ) state in indole Žcf. discussion in Section 1., exhibits pronounced charge-transfer character. In Fig. 1 we present the p Ž1a 2 . and s ) Ž10a 1 . orbitals which were determined by a CASSCF calculation for the 1AXX Ž p s ) . state of pyrrole. The floating
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A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
Fig. 1. The p Ž1a 2 . and s ) Ž10a 1 . orbitals obtained by a CASSCF calculation for the 1A 2 Ž p s ) . state of pyrrole.
center of the diffuse basis function is located by geometry optimization on the NH bond at a distance ˚ from the nitrogen atom and the exponent of 0.694 A of the Gaussian s and p functions has the optimized value of 0.0205. This result clearly indicates that the lowest excited singlet state of pyrrole has Rydberg character, reflected by the diffuseness of the s ) orbital, but also involves a significant transfer of charge from the aromatic ring to the H-atom. Fig. 2 displays CASPT2 potential-energy ŽPE. profiles calculated along the minimum-energy path Ždetermined at the CASSCF level. for detachment of the H-atom of the NH group. For clarity, only the lowest 1 p s ) and 1 p p ) states and the electronic ground state are shown. It is seen that the geometryoptimized 1 p s ) state lies below the optimized 1 p p ) state. While the latter is bound as a function of the NH stretching coordinate, the former is essentially repulsive and thus can predissociate the 1 p p ) state. In a multi-dimensional picture, there exists a high-dimensional hyper-surface of intersection of the 1 p p ) and 1 p s ) surfaces; vibrational modes of A 2 symmetry lift these degeneracies, leading to a multi-dimensional conical intersection, which can promote ultrafast transitions from the 1 p p ) surface to the 1 p s ) surface. In fact additional electronic states Žother low-lying Rydberg-like states. also may be involved as intermediates in the 1 p p ) 1 p s ) decay. In any case, this transition can be expected to be fast, leading to the population of the lowest 1 p s ) state with high probability. The photochemistry of pyrrole is thus expected to be determined by the reaction dynamics on the lowest 1 p s ) surface.
481
It is seen in Fig. 2 that the repulsive 1 p s ) PE profile intersects the PE function of the ground state ˚ resulting in at an NH distance of about 1.8 A, another conical intersection. In the isolated molecule, this conical intersection leads to ultrafast Žfemtosecond. internal conversion to the ground state. This explains why fluorescence of pyrrole has not been observed so far in the gas phase. A weak fluorescence is observed in N-methyl pyrrole w17x, indicating that the NH group of pyrrole is involved in the reaction leading to radiationless decay. In the following, we discuss the electronic structure of the 1 p s ) state in PWn clusters Ž n s 1–5.. A detailed discussion of the energetics of the photochemistry of PWn clusters requires extensive CASPT2 calculations which will be reported in a future publication w20x. Here we focus on the character of the s ) orbital in order to visualize the charge separation process in the photoexcited clusters. Fig. 3 shows the geometric structures of PWn , n s 1–5, clusters which correspond to the minimum of the 1 p s ) surface. Ground-state optimized cluster structures Žsee below. were used as initial-guess structures for the excited-state geometry optimization. For small clusters Žup to three water molecules., the same final minimum-energy structure in the
™
Fig. 2. Minimum-energy path PE profiles for the lowest 1 p p ) state Žcircles. and for the lowest 1 p s ) state Žsquares. as a function of the NH distance. The PE function of the ground state Žtriangles. was calculated at the optimized geometry of the 1 p s ) state.
A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
482
XX Fig. 3. The s ) orbital of the 1A Ž p s ) . state of the PWn clusters.
1
p s ) excited state displayed in Fig. 3 has been obtained, independent of the initial guess. This indicates that these structures represent well-developed minima on the 1 p s ) surface, under C s symmetry constraint. For larger clusters, several different minima of the 1 p s ) surface can be found. For the PW4 cluster, for example, several C s excited-state geometries can be found by using initial guesses which eliminate different water molecules from the ground-state PW5 cluster. Fig. 3 shows, in addition, the s ) orbital. It is seen that already in the presence of a single water molecule ŽPW1 . the s ) electron cloud has largely been transferred from the H-atom of the NH group to the water molecule Žcf. Fig. 1.. It appears to form a dipole-bound state of water which is tilted towards the positive charge of the pyrrole cation. When further water molecules are added, the s ) electron cloud successively moves away from the chromophore. The water molecules form a cage encapsulating the electron cloud. The resulting negatively charged water cluster is connected by hydrogen bonds to adjacent H-atoms of pyrrole. Since in all systems the p orbital remains localized on the
aromatic ring, the structures of Fig. 3 may be classified as charge-transfer-to-solvent ŽCTTS. systems. They can be considered as precursors for the electron solvation process in large clusters or in liquid water. To our knowledge, this phenomenon has been obtained here for the first time at the level of an ab initio electronic-structure calculation. Some of the properties of the 1AXX Ž p s ) . state of the PWn clusters at the optimized geometry are collected in Table 1. It is seen that the separation of the s ) orbital from the pyrrole ring, measured by the NX distance Ž X being the floating center., increases ˚ for PW1 to NX s monotonically from NX s 1.84 A ˚ 4.08 A for PW5 . The increasing charge separation is reflected by the increase of the dipole moment of the CTTS state from 11.48 Debye for PW1 to 14.57 Debye for PW5 . The exponent of the floating Gaussian basis set functions, on the other hand, is essentially constant, indicating that the spatial extension of the hydrated electron does not depend on the cluster size. The spatial extension of the electron cloud in the CTTS state is remarkably smaller than that deter-
Table 1 Energy Ž E ., distance of the floating center from nitrogen ŽNX., exponent of the diffuse function Žh ., and dipole moment Ž m . obtained at the XX CASSCF level of theory for the 1A Ž p s ) . state of the pyrrole–water clusters
E Žau. ˚. NX ŽA h m ŽDebye.
PW1
PW2
PW3
PW4
PW5
y284.76311
y360.79737
y436.83765
y512.86766
y588.90569
1.840 0.016 11.48
2.519 0.018 12.60
2.811 0.018 11.45
3.613 0.020 12.85
4.081 0.017 14.57
A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
mined for the dipole-bound anions of water clusters w11,12x. Extension of our basis set by an additional s orbital at the floating center and optimization of both Gaussian exponents has no essential effect on the shape of the s ) orbital. This can be explained by the different nature of the interactions which bind the hydrated electron in the CTTS state compared to dipole-bound anion clusters. In the former case, the most important binding contribution at long range results from Coulombic attraction between the hydrated electron and the cationic core. This results in
483
a relative compactness of the electron cloud in the CTTS state. With increasing cluster size, water molecules form a shell which effectively screens the Coulombic attraction between the two species, leading to a spatial separation of the electron cloud from the cation. Fig. 4 shows the comparison of the equilibrium geometries of the PWn clusters in the electronic ground state and in the 1 p s ) state. In the ground state, we obtain the well-known ‘ice-like’ lattice of water molecules H-bonded to the NH moiety of pyrrole. The geometric structure of the cluster changes drastically after electronic excitation to the 1 XX A Ž p s ) . state. For larger clusters, in particular, there is little correspondence between the geometries in both electronic states. Generally, in the 1AXX Ž p s ) . state the water molecules form a shell around the s ) cloud and their geometric arrangement exhibits only marginal reminiscence of the H-bonded lattice of the ground state. Our calculations thus confirm massive rearrangement of the surrounding solvent in the CTTS process. For technical reasons, C s symmetry of the cluster was enforced in the calculations. This introduces some limitations on the possible structures of the clusters. However, even with this restriction, the calculations reveal the existence of several almost isoenergetic isomers for larger clusters. This indicates a flat PE surface with several local minima in the 1AXX Ž p s ) . state, a fact which may be important for future simulations of the molecular dynamics of the electron photoejection process in pyrrole–water clusters. 4. Summary
XX Fig. 4. The geometries of the PWn clusters in the S0 and 1A Ž p s ) . states, optimized with the RHF and CASSCF methods, respectively. The black dot indicates the center of the diffuse basis functions.
The exploratory ab initio electronic structure calculations presented in this work show that electron ejection is a spontaneous Žexothermic. process after UV photoexcitation of the chromophore in pyrrole– water clusters. The calculations reveal, furthermore, the detailed mechanism of this remarkable process. A key role is attributed to the low-lying 1 p s ) state of pyrrole which is populated by internal conversion after photoexcitation of the optically allowed 1 p p ) state. The characteristic feature of the 1 p s ) state is a pronounced dislocation of the electronic charge from the aromatic ring towards the H-atom of the
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A.L. Sobolewski, W. Domcker Chemical Physics Letters 321 (2000) 479–484
NH group. In clusters of pyrrole with water, the diffuse electron cloud on the H-atom is further transferred to the surrounding water molecules, forming a CTTS state. When four or more water molecules are present, the characteristic cage structure of the hydrated electron develops. The water layer screens the Coulombic attraction between the electron cloud and the pyrrole cation, resulting in stabilization of the CTTS state. In bare pyrrole, the 1 p s ) state forms a conical intersection with the electronic ground state Žcf. Fig. 2., which causes ultrafast internal conversion to the ground state. The photon energy is thus converted into heat with high efficiency. The presence of water removes the conical intersection w20x and opens the CTTS channel: the energy of the photon is now converted into chemical energy Žcharge separation.. The pyrrole–water cluster may be one of the simplest systems where this biologically highly relevant process can be investigated in microscopic detail. The phenomena which we have investigated here for pyrrole–water clusters occur in a very similar manner in indole–water clusters. The calculations on indole–water clusters are in progress. Further investigations have to show whether the formation of hydrated electrons is a general feature of the photochemistry of heterocycles in aqueous environments.
Acknowledgements This work has been supported by a visitor grant of the Deutsche Forshungsgemeinschaft for A.L.S.
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