Photophysics of 2-Hydroxypyridine: An ab Initio Study

Transcription

1 J. Phys. Chem. 996, 00, Photophysics of 2-Hydroxypyridine: An ab Initio Study Andrzej L. Sobolewski Institute of Physics, Polish Academy of Sciences, Warsaw, Poland Ludwik Adamowicz*, Department of Theoretical Chemistry, Chemical Center, UniVersity of Lund, S-2200 Lund, Sweden ReceiVed: March 24, 995; In Final Form: NoVember 4, 995 X The potential energy (PE) surfaces of the electronic ground and the lowest excited states relevant to photophysics of interconversion of the 2-hydroxypyridine/2(H)-pyridone system are characterized by ab initio calculations. The energy calculations at the optimized geometries are performed with the aid of the second-order perturbation theory, employing the complete-active-space self-consistent-field (CASSCF) wave function as the reference (CASPT2). Results confirm the earlier hypothesis based on the CASSCF calculations (Chem. Phys. Lett. 993, 2, 293) that the photoinduced dissociation-association (PIDA) mechanism is probably responsible for excited-state tautomerization observed in this system. Absorption of the second photon in the excited electronic state is suggested to provide the driving force for the PIDA mechanism.. Introduction The photomeric tautomerism in the 2-hydroxypyridine/2(H)- pyridone (2HP/2PY) molecular system has been the subject of many studies because it is representative of a large number of heterocyclic molecules that are relevant to biological functions. The 2HP/2PY tautomeric system is one of the few systems where the energy difference between the two tautomers is sufficiently small for both species to be observed in the gas phase and in inert matrices, 2,3 whereas in polar solvents and in the crystal phase the lactam 2PY form predominates. 3,4 The experimental measurements lead to the conclusion that under isolated molecule conditions (e.g. supersonic jet, gas phase, inert matrices) the free energy difference between the lactam, 2PY, and lactim, 2HP, forms is about ev in favor of the former one. 2,3,5-7 Theoretical studies of the reaction, although generally supporting the experimental findings, have resulted in a wide range of relative energies of the two forms. 8-9 All the studies, however, were consistent in predicting a large energy barrier for the proton transfer (PT) reaction in the ground state (=2 ev). 0,5,8,9 This is a direct consequence of lack of an intramolecular hydrogen bond in the system which could facilitate a PT reaction. The optical excitation within the lowest singlet manifold generally changes the acidity and basicity of molecular moieties and thus can significantly change the tautomeric equilibrium. The so-called excited-state intramolecular proton transfer (ESIPT) reaction occurs when the subtrate (stable in the ground state) becomes unstable (or metastable) with respect to the product on the excited-state potential energy (PE) surface (the reverse asymmetry). The majority of the ESIPT reactions involve transfer of a proton (or hydrogen) from the oxygen donor to the oxygen or nitrogen acceptor along the intramolecular hydrogen bond (for a recent review see ref 20). The existence of a hydrogen bond is a necessary condition for the ESIPT process to occur. This can be either an intramolecular hydrogen bond 20 or an intermolecular bond in the hydrogenbonded complex. 2,22 The considered 2HP/2PY molecular system belongs to an important class of compounds in which the excited-state PT Permanent address: Department of Chemistry, University of Arizona, Tucson, AZ X Abstract published in AdVance ACS Abstracts, February, 996. reaction has been observed, 3,23 but which under isolatedmolecule condition does not fulfill any of the two abovementioned conditions for ESIPT; that is, it does not have an intramolecular hydrogen bond, nor do its PE functions have desired asymmetry with respect to the PT reaction coordinate. However, the transfer of the hydrogen atom in this system does occur upon optical excitation in a low-temperature inert gas matrix, as it was confirmed via analysis and assignment of the IR spectra obtained before and after irradiation. 3,23 Because it manifests itself differently, as compared to a typical ESIPT system, where the occurrence of the PT reaction results in redshifted fluorescence, we propose to consider the process as an example of the photoinduced proton transfer (PIPT). In a typical PIPT reaction, contrary to the ESIPT process, the hydrogen atom is transferred exclusively from the nitrogen in the ring to the oxygen (or sulfur) acceptor, i.e., against the existing endothermicity on the excited-state PE surface. 23 This kind of transfer happens in the 2HP/2PY system where an excitation of the lactam 2PY form at λ = 300 nm increases the amount of the lactim 2HP form in the matrix, 3 despite a large endothermicity (=0.75 ev) of the PT reaction on the lowest ππ*-state PE surface. 24 The significantly different photophysics of typical ESPIT and typical PIPT systems, as mentioned above, lead to the conclusion that the physical mechanism of the PT reactions in the ESPIT and PIPT systems should be fundamentally different. In a series of papers published over the last 2 years, the results of extensive ab initio calculations of the PE surfaces relevant for the ESIPT reaction have been presented The general conclusion which emerges from the studies is the relevance of near-degeneracies and multidimensional surface crossings of the excited-state PE surfaces. It seems that in many ESIPT systems the reaction dynamics is largely determined by the intersection of the barrierless ππ* PE surface with the nπ* surface, which usually exhibits a significant barrier to PT. Therefore, the established paradigm of the reaction dynamics on a single isolated adiabatic surface is not appropriate for the ESIPT systems. In the parallel theoretical studies of the PT reaction in systems without intramolecular hydrogen bonds (the PIPT systems), a qualitatively new reaction mechanism was postulated. 8,30 It has been proposed that the PT reaction in these systems is /96/ $2.00/0 996 American Chemical Society

2 3934 J. Phys. Chem., Vol. 00, No. 0, 996 Sobolewski and Adamowicz initiated by the motion of the mobile hydrogen atom on the predissociative PE surface toward dissociation. Strong nonadiabatic interaction present near the conical intersection between the PE surface of the dissociative A (πσ*) state and the ground state causes a nonradiative relaxation of the wave packet to the ground state, with a finite probability to set down in the minimum corresponding to the rare tautomeric form. The photoinduced dissociation-association (PIDA) mechanism of PT was initially proposed for the 2HP/2PY system, 8 but recently it was also found to occur in formamide. 30 In the meantime, Barone and Adamo 9 theoretically reinvestigated the 2HP/2PY system and concluded, contrary to the conclusions of ref 8, that the PIDA mechanism for proton transfer is not possible in this system. In the present paper we report new results of calculations of the 2HP/2PY system performed with the ab initio completeactive-space self-consistent-field (CASSCF) method and with the second-order perturbation theory method employing the CASSCF wave function as the reference (CASPT2). This more sophisticated theoretical treatment, which allows us to account for both the dynamic and static electron correlation effects, confirms the previous conclusion obtained at the CASSCF level 8 with respect to the relevance of the PIDA mechanism for the PT reaction in the 2HP/2PY system. It is shown that the conclusion of ref 9 results from artifacts of the approximate theoretical approach (configuration interaction scheme with only single-electron excitation from the Hartree-Fock reference (CIS)) used for description of the excited-state PE surfaces. 2. Theoretical Methodology 2.. Reaction Path Concept. When considering reaction paths on the PE surfaces of excited states, as required for the characterization of photochemistry, 3 two major complications arise. First, reliable ab initio energy calculations for excited states are typically much more involved than the ground-state calculations. Secondly, multidimensional surface crossings are the rule rather than the exception for the excited electronic states. The concept of an isolated Born-Oppenheimer (BO) surface, which is usually assumed from the outset in the reaction-path theory, is thus not appropriate for the excited-state dynamics. At surface crossings (so-called conical intersections 3-34 ), the adiabatic PE surfaces exhibit nondifferential cusps, which preclude the application of the established methods of the reaction-path theory As an alternative to nondifferentiable adiabatic PE surfaces, so-called diabatic surfaces 38 may be introduced, which are smooth functions of the nuclear coordinates. However, the definitions of these diabatic surfaces and of the associated wave functions are not unique and involve some subtleties Despite the lack of a comprehensive reaction-path theory for excited-state surfaces, the reaction-path concept can fruitfully be applied at a pragmatic level to advance the understanding of photochemical dynamics. There are two general issues of the reaction-path concept widely used in theoretical explorations of the PE surfaces. These are the concerted reaction-path (CRP) approach based on the straight-line, least-motion intramolecular coordinate which interpolates linearly between the equilibrium geometries of the reactant and the product, 42 and the minimum energy reaction path (MEP), 43 which is defined as the steepest descent path from the transition state down to the local minima of the equilibrium geometries of the reactant and the product. With respect to a quantitative characterization of the PE function along the reaction coordinate, in terms of local minima and barriers between them, the MEP concept is more relevant. However, it is well-known that for many reactions (PT process among them) the MEP is very sharply curved, so that the relevant dynamical motion can deviate far away from it. The CRP approach is free from such a curvature problem by the virtue of its definition, but can provide only a qualitative characterization of the PE surface. In the following presentation we use one of the two methods depending on the particular (qualitative or quantitative) features of the PE surface considered Computational Details. The ground-state molecular geometries of all molecular systems considered in this work were optimized at the Hartree-Fock (HF) level, whereas in the optimizations of the excited-state geometries, the configuration interaction scheme with single excitations (CIS) and the complete-active-space self-consistent-field (CASSCF) method were used. Most of the geometry optimizations were performed with the C s symmetry constraints (the systems were kept planar unless explicitly specified otherwise). The planarity of the system helps to perform the excited-state calculations. The lowest excited singlet states of all the systems considered in this work result from the ππ* and nπ* excitations and as such fall into two distinct symmetry representations, A and A, in the C s point group. Any out-of-plane deformation destroys the C s symmetry and mixes the A and A states together. It then often becomes practically impossible to get a converged solution for the higher of the two lowest close-lying excited electronic states of the same multiplicity and the same symmetry, which in the C s symmetry are distinct (i.e, the A (ππ*) and A (nπ*) states) and much easier to converge. Restricting the system to the C s symmetry in the calculations of the PE functions along the reaction coordinate also has important implications for treatment of the reaction dynamics. It is convenient in such a treatment to consider any distortion from the C s symmetry as a pseudo-nonadiabatic nuclear-electron interaction. This, of course, makes sense only if the distortions from the C s symmetry have a negligible influence on the energy. This point was carefully checked for the systems considered in this work. The split-valence Gaussian 3-2G basis set 44 was employed in geometry optimizations, and optimizations at the HF and CIS levels of theory were performed with the use of the GAUSS- IAN92 program package, 45 whereas for those performed at the CASSCF approximations the GAMESS issue of programs was used. 46 The single-point energy calculations were performed for the ground state with the use of the Moller-Plesset (MP2) perturbation theory and the double-ζ Gaussian basis set with polarization functions (the D95G** basis set of GAUSSIAN). The excited-state energies were calculated by means of the CASSCF method, 47 and the double-ζ-valence Gaussian basis set of Dunning and Hay 48 with polarization functions (DZVP basis set) was used. The remaining dynamic correlation effects were added in the subsequent step with the use of the secondorder perturbation theory, with the CASSCF wave function as the reference (CASPT2). 49 CASPT2 calculations were performed with the CASSCF function optimized for each state separately (unless otherwise specified) with the use of the nondiagonal zero-order Hamiltonian as it is implemented in the MOLCAS-3 quantum chemistry software. 50 All the calculations were performed on the IBM RS/ workstation. 3. Results of Calculations and Discussion 3.. Energies of Electronic Transitions. The molecular systems considered in this study are presented schematically in Figure. The geometrical parameters computed at the HF/ 3-2G and CIS/3-2G approximation for the ground and for the lowest excited singlet states of the 2HP/2PY system are wellknown (see for instance ref 9), so we do not present them in

3 Photophysics of 2-Hydroxypyridine J. Phys. Chem., Vol. 00, No. 0, Figure. Oxo (lactam) and hydroxy (lactim) forms of 2-pyridone. this paper. The point we would like to discuss in more detail concerns the (presumed) planarity of these systems in the lowest excited singlet states (the structures are essentially planar in the ground state). At the CIS/3-2G level, the A (nπ*) state is the lowest singlet excited state of both 2HP and 2PY forms. The normal mode analysis performed at the C s -optimized geometry of the A state gives two imaginary frequencies for both forms, and they mostly involve the out-of-plane deformation of the OH or NH groups. The out-of-plane energy-lowering distortions of these molecular moieties were confirmed by the CIS/3-2G optimizations without any symmetry constraints (C ). The stabilization energy with respect to the C s -optimized geometry was about 300 cm - for 2HP and 800 cm - for 2PY at this level of theory. The bright (for optical excitation from the ground state) A (ππ*) state is the second singlet state in both forms at the CIS/3-2G level. The normal mode analysis performed at the C s -optimized geometries gives all real frequencies for the 2PY form and all but one (the imaginary frequency corresponds to the OH out-of-plane bending) real frequency for 2HP. An attempt to optimize 2HP in the A state without symmetry constraints causes a collapse of the system to the lowest close-lying A state. The energetical ordering of the two lowest excited singlet states, (nπ*) and (ππ*), is reversed at the CIS/6-3G** level. Now the 2HP form remains planar in the A (ππ*) state, while 2PY shows one imaginary frequency corresponding to the out-of-plane deformation of the ring. The C -optimized geometry of 2PY shows, however, only minor energetical stabilization of the S state (e00 cm - ). The soft out-of-plane deformation of 2PY in the A (ππ*) state, suggested by our calculations, is in accord with experimental observation. 5 In conclusion we can say that, although the out-of-plane deformations in the lowest singlet states may be present, they do not seem to cause significant effects on the energy scale relevant to this study. Thus, the system were kept planar in this work, if not explicitly specified otherwise. The single-point energy calculations of the ground and lowest excited singlet states were performed at the C s -optimized geometries according to the methods specified in the preceding section. In the CASSCF calculations, 0 electrons (of a total number of 50) were correlated in nine active MOs. The active space in this case is denoted as (20,0/2,7), where the first two numbers indicate the number of core (doubly occupied in each configuration) molecular orbitals in the A and A symmetry representations of the C s point group, respectively, and the second two numbers indicate the similar symmetry distribution for the active orbitals. In other words, the active space includes all the (first shell) π orbitals (from a to 7a ) and two σ orbitals (2a of the n type and 22a of the σ* type). The double-ζvalence Gaussian basis set of Dunning and Hay 48 with polarization functions (DZVP) was employed in the energy calculations. The exponents of the polarization functions were 0.75, 0.80, 0.85, and.0 for carbon, nitrogen, oxygen and hydrogen atoms, respectively. Calculated energies are listed in Table. Inspecting the CASPT2 results presented in Table, one can notice that the lactim 2HP form is by 0.07 ev more stable than TABLE : CASSCF and CASPT2 Energies, Energies Relative to the Ground State ( E), and the Weight of the CASSCF Reference Function in the First-Order Wave Function (ω) Calculated with the DZV P Basis Set for 2PY and 2HP at Molecular Geometries Optimized in Different Electronic States for Both Tautomeric Forms state[geometry] CASSCF (au) E (ev) CASPT2 (au) the lactam 2PY form. This is in reasonable agreement with the experimental observations, 2-3,5-7 as well as with the other theoretical results. 8-9 At this level of theory, the lowest excited singlet state in both systems is the A (ππ*) state. This is the state allowed for absorption from the ground state. The abovelying A (nπ*) state is essentially dark in this respect. The quantities which can be directly compared to the experiment are the energies of the vertical electronic excitations, i.e., the differences between the energies of the ground and the excited singlet states, calculated at the ground-state equilibrium geometries. The CASPT2 energies of the S 0 f S (ππ*) transition calculated for the 2HP and 2PY forms ( E ) 4.75 ev and E ) 4.37 ev) can be compared to the maxima of the first absorption bands observed in solution for these systems at 4.59 and 4.20 ev, respectively. 2 Having optimized the structures in the S state for both tautomers, we can estimate the energies of the 0-0 lines in absorption. The obtained values (Table 2) are E ) 4.28 ev and E ) 3.68 ev for 2HP and 2PY, respectively. These can be compared with E ) 4.47 ev and E ) 3.7 ev observed by Nimlos et al. 24 in a molecular jet. One sees that theoretically predicted values are in good agreement with the experiment. Thus, it is reasonable to conclude that the theoretical methods selected for the geometry optimizations and for the energy calculations of the low-lying electronic states of the 2HP/2PY system provide results which are consistent with experimental observations within a fraction of an electronvolt. Therefore, we can expect similar precision in the description of the PE surfaces relevant to the photophysics of these systems PT Potential Energy Functions. In characterization of the reaction path for PT in terms of local minima and the transient points between them, we follow the simplified version of the MEP approach. In this approach one of the 3N-6 (where N is the number of atoms) intramolecular degress of freedom of the system is defined as the reaction coordinate, and the remaining (3N-7) coordinates are optimized at each step of the reaction. There are no strict rules for choosing the reaction coordinate, and in principle, this can be any of the 3N-6 intramolecular coordinates, since in this static approach all the kinetic energy terms are neglected. In practice, this should be the coordinate which changes the most when the reaction proceeds. In a typical ESIPT system, the PT reaction, where the light hydrogen nucleus is moving between two heavier (X and Y) heteroatoms, being chemically bonded to one of them and forming a hydrogen bond to the other and Vice Versa, can ω E (ev) 2PY S 0[S 0] A [S 0] A [S 0] S 0[ A ] A [ A ] A [ A ] HP S 0[S 0] A [S 0] A [S 0] S 0[ A ] A [ A ] A [ A ]

4 3936 J. Phys. Chem., Vol. 00, No. 0, 996 Sobolewski and Adamowicz TABLE 2: CASSCF/3-2G and UHF/3-2G Optimized Parameters of Geometry (Bond Lengths in Angstroms; Bond Angles in Degrees) and Energies (au) of 2PY and 2HP and Their Prefulvenic Forms A (nπ*) A (ππ*) prefulvenic form parameter 2PY 2HP 2PY 2HP 2PY 2HP N C C C C 2C C 3C C 4C C 5N C 3C C O C 2H C 3H C 4H C 5H N H (a) C N C C C 2C C 5N H a C 2C O C 3C 2H C 5C 4H C 4C 5H C 2C 3H C C 2C 4C C 3C 4C 5N C 5N C C C 5N C O C 5C 3C 2H C 3C 5N H a N C 2C 3H C 2N C 5H C 2C 3C 4H energy a These parameters should for the 2HP form be replaced by O H, C O H, and N C O H, respectively. Figure 2. Cartesian trajectories of the hydrogen atom along the CIS/ 3-2G optimized MEP in the A (ππ*) (a) and in the A (nπ*) (b) excited singlet states for stretching of the NH (circles) and OH (squares) bond lengths. Triangles in (a) denote trajectory obtained for fixing the NCH bond angle. be described with the use of the reaction coordinate of the type X-H Y. It is then quite natural to choose the X-H distance as the reaction coordinate. 27,28 In the 2HP/2PY system there is no intramolecular hydrogen bond which the proton follows when the reaction proceeds. Thus, it is not obvious that the choice of the OH (or NH) stretching provides the optimal reaction coordinate for the process. An alternative to this would be, for instance, to chose as the reaction coordinate the angle which specifies the position of the hydrogen nucleus with respect to the ring. To compare MEPs for different choices of the reaction coordinate for MEP, in Figure 2a we present the CIS/3-2G optimized Cartesian trajectories of the mobile hydrogen atom in the S (ππ*) state for the three reaction coordinates: the NH and OH bond lengths and the NCH bond angle. Inspection of the results leads to the conclusion that the MEP Cartesian trajectory depends generally on the reaction coordinate. There Figure 3. PE functions of the ground (circles) and the A (ππ*) excited singlet (squares) states along the MEP for proton transfer in the 2HP/ 2PY molecular system calculated in the MP2/D95** and in the CASPT2/DZVP approximations for both states, respectively. The reaction coordinate is the NCH bond angle. are, however, three points common to all the reaction coordinates. These are the equilibrium geometries of the two tautomeric forms and the transition point between them. This means that although the shape of the PE function generally depends on the reaction coordinate, the energetics at the extrema do not, as expected from the definition of MEP. This provides a justification that the MEP approach as used in this work is indeed capable of tracing the reaction path through its saddle point. In Figure 3 the PE functions for the PT reaction in the ground state and in the S (ππ*) state calculated along MEP vs the NCH bond angle are presented. The PE function of the excited state was calculated in the CASPT2/DZVP approximation (at the CIS/3-2G geometries) with the active space as defined in the preceeding section, while the ground-state PE function was obtained at the MP2/D95G** level (at the HF/ 3-2G geometries). One sees, upon insection of the results

5 Photophysics of 2-Hydroxypyridine J. Phys. Chem., Vol. 00, No. 0, presented in Figure 3, that both tautomeric forms are separated by a moderate barrier (=.5 ev) on the ground-state PE surface. This is in agreement with other theoretical predictions. 0,5,8,9 On the S (ππ*) PE surface, the 2PY f 2HP tautomerization reaction is endothermic by about 0.54 ev (see Table ) and the transient point is.25 ev higher above the local minimum of the 2PY form. Qualitative features of both PE functions are similar to those reported in ref 8 and obtained at a lower level of theory. However, the appearance of a shallow minimum in the middle of the PE function for the S state requires a comment. This minimum, or rather a plateau, appears only at the CASPT2 level of theory, whereas in the CIS and CASSCF calculations a well-defined maximum in this region of the reaction path was found. It is likely that the minimum is an artifact of the perturbational treatment, because at this point we also observe a noticeable decrease of the weight of the CASSCF reference in the first-order wave function. The general conclusion which emerges from the results presented in Figure 3 and in Table is that the thermally or optically induced 2PY f 2HP reaction is rather unlikely in either the S 0 or S state. Let us now tern our attention back to the A (nπ*) state. This state is essentially dark for absorption from the ground state and lies just above the bright A (ππ*) state (Table ). MEP calculated for this state along the NH and OH stretching coordinates gives proton trajectories presented in Figure 2b. One sees that for small displacements they are similar to the trajectories obtained in the A (ππ*) state, but for larger displacements they are qualitatively different. There is a sharp (discontinuous) change in each of the trajectories at R(NH) and at R(OH) of about.4 Å related to passing over the barrier. Further stretch of either one of the reaction coordinates leads to a local minimum (near the intersection of both trajectories of Figure 2b), after which the energy increases. There is no real PT reaction observed along either one of the reaction coordinates. This is, to some extent, in accord with the result of Barone and Adamo, 9 who claim that they were unable to detect a saddle point for the PT reaction on the A (nπ*) PE surface. There is a simple reason for that; the proton trajectory obtained at the A (nπ*) PE surface results from artifacts of the CIS approximation which cannot properly handle the dissociation. In Figure 4a we present proton trajectories vs the NH and OH stretches obtained at the CASSCF/3-2G level of theory with the (20,2/2,4) active space. The first few points of both trajectories are very similar to those obtained at the CIS level (Figure 2b), but after passing the barrier the proton freely dissociates on the CASSCF A PE surfaces. This is qualitatively the same picture as presented in ref 8 and obtained at a more approximate level of theory. Finally, we conclude this section with a discussion of the results which we obtained by performing symmetry-unrestricted search for transition states in the lowest singlet excited states of the 2PY and 2HP systems with the use of the CIS method with the 6-3G** basis. The purpose of this search was to verify whether or not restricting the system to a planar configuration, which is done in the majority of the calculations presented in this work, introduces any error in the results. The transition-state search performed for the 2HP system in the lowest singlet state resulted in a structure with the hydrogen atom of the hydroxy group significantly displaced from the molecular plane (with R OH ).277 Å). The dihedral angle between the hydrogen, oxygen, and C and C2 atoms was equal to 3. The analysis of the symmetry of the wave function along the optimization path from the 2HP equilibrium to the transition state indicated that for most of the path the structure was planar, and only near the transition state did a sharply increasing Figure 4. Cartesian trajectories of the hydrogen atom along the CASSCF/3-2G optimized MEP on the A PE surface (a) calculated for stretching of the NH (black circles) and the OH (black squares) bond lengths. Circles and squares denote positions of hydrogen at the successive steps of energy optimization without any geometry constraints. In (b) positions of hydrogen atom are marked by geometry optimizations on the A PE surface with the NH and OH distances fixed. contribution from a πσ* configuration to the essentially pure ππ* wave function cause an out-of-plane bend of the hydrogen atom. After passing the transition point the structure returned back to the planar conformation with the wavefunction dominated by the πσ* configuration. It was apparent from the results of the calculation that the transition state was located on the dissociation path of hydrogen and not the path leading to the 2PY tautomer. A very similar result was obtained in the search for a transition state on the lowest singlet excited state surface of the 2PY system. Here also the transition state corresponded to an out-of-plane displacement of the hydrogen atom bonded to N2 (by 26.5 with the length of the NH bond to.557 Å). The molecule, initially planar in the ππ* state, was distorted from planarity near the transition state due to a sharply increasing contribution from a πσ* configuration, which after passing the transition point starts to demoniate the wave function and the molecule becomes planar again. The above investigation indicates that from a narrow domain around the transition point the PT process in the 2PY/2HP system can be studied with C s -constrained geometries. Also, it indicates that in the lowest excited single state of both tautomers, both transition states correspond to dissociation of the hydrogen from the system, and not to an intramolecular proton transfer Photophysics of the Mobile Proton. Behavior of the mobile hydrogen atom on the A PE surface of the 2HP/ 2PY system presented in Figure 4a follows qualitatively the same pattern as revealed in ref 8. It was suggested in that paper that there is an intersection between the bonding nπ* and dissociative πσ* PE surfaces along the NH and/or OH stretching coordinates. When one tries to visualize the PE functions along the trajectories of Figure 4a, a technical problem arises. Namely, there is a range of the NH (or OH) bond length where there are two solutions for the MEP at a given value of the reaction coordinate. It is the region of the NH (OH) distance near the barrier, where the MEP depends on the direction the barrier is approached from (stretching or compression of the bond length). This indicates that the reaction path for dissociation of the proton is probably sharply curved near the barrier, and the MEP approach does not describe properly the phenomenon. This problem can be avoided to some extent in the CRP treatment. Two points (molecular geometries) are needed in order to define the CRP. For the case on hand, the lower limit of the CRP reaction coordinate (Q ) 0) is defined to be the equilibrium geometries of 2HP and 2PY systems on the A

6 3938 J. Phys. Chem., Vol. 00, No. 0, 996 Sobolewski and Adamowicz Figure 5. CASPT2/DZVP PE functions of 2PY (a) and 2HP (b) for the ground (circles), A (squares), A (triangles connected via solid line), and 3 A (triangles connected via dashed line) states calculated along the CRP for hydrogen dissociation. The CRP is spanned by equilibrium geometry of a given tautomeric form in the A state (Q ) 0) and by geometry with the hydrogen atom in positions and 3 of Figure 4b for (a) and (b), respectively. The CASSCF/3-2G geometries were optimized on the A PE surface. PE surface. The upper limit of the CRP reaction coordinate for the molecular system with the mobile hydrogen atom should correspond to its dissociation. This is, of course, the situation of minor importance from the spectroscopic point of view, because the most interesting region of the reaction is near the barrier. Comparing trajectories of the proton presented in Figures 2b and 4a, one sees that the calculated trajectory is rather sensitive to the theoretical method used in determination of the MEP. The CASSCF approximation, which handles properly the near-degeneracy effects, but takes into account only a small part of the dynamic electron correlation, predicts almost radial dissociation of the proton with respect to the molecular frame. On the other hand, the CIS approximation, which does not handle properly the near-degeneracy effects resulting from breaking the chemical bond, predicts essentially angular motion of the proton instead of dissociation. The proper description of both effects, i.e., the near-degeneracy and dynamic correlation effects will probably result in a proton trajectory which is closer to the CASSCF result. Thus, in the following we decided to optimize the molecular geometry for the upper limit of CRP by fixing the distance of the proton from both heteroatoms. The points at which the proton was located with respect to the molecular frame in the optimization procedure are indicated in Figure 4b. The geometry optimizations at these points were performed at the CASSCF/3-2G level with the (20,2/2,4) active space. Among them, points and 3 were used for the definition of the upper limits of the CRP coordinates (Q ) ) for dissociation of the proton from the 2PY and 2HP molecules, respectively. As is usually the case, the CRP was defined as the vector of the internal displacement (bond lengths and bond angles) that connects the initial and final geometries of the two tautomeric forms. Next, a number of intermediate nuclear configurations were generated by incremental increase of the reaction coordinate from Q ) 0 to Q ), and the energies of the ground and lowest excited states were calculated at each configuration. The energies were calculated at the CASPT2/ DZVP level with the (20,0/2,7) active space. The resulting PE functions are presented in Figure 5, and they look similar for 2HP and 2PY and are not qualitatively different from the appropriate functions of ref 8 obtained at the CASSCF/DZV level of theory (Figure 4b,c of ref 8). One can notice upon inspection of the results presented in Figure 5 that only PE surfaces of the A state and the ground state are relevant to the proton (pre)dissociation. The energy of the A Figure 6. CASPT2/DZVP PE functions of the ground (circles), the A (squares with solid line), and the 3 A (squares with dashed line) states of the 2HP/2PY system calculated with the hydrogen atom fixed in positions -3 and -3 of Figure 4b for (a) and (b), respectively. state rises sharply along the reaction coordinate and does not lead to dissociation. The first conclusion resulting from the results presented in Figure 5 is that both tautomeric forms are well protected in the A state against dissociation of the proton. Barriers of about.5 ev can be estimated for both 2HP and 2PY systems with respect to their equilibrium in the A (nπ*) state. Let us notice that geometries of the transition structures were not optimized, so the real saddle point may have a somewhat lower energy. We do not expect, however, that this can significantly lower the barrier. In any case, it seems that the barriers are too high for any noticeable tunneling or for any thermal transfer of the proton to the dissociative part of the PE surface. If, however, the wave packet can be optically prepared on the excited PE surface to effectively tunnel through the barrier and to reach the repulsive A (πσ*) PE surface, it will exhibit a significant tendency toward dissociation of the hydrogen atom. On the other hand, just behind the barrier there is an intersection between the excited A and groundstate PE surfaces. This intersection occurs only when the C s symmetry (the planarity) of the system is conserved. Any outof-plane deformation of the system will cause an avoided crossing of the two surfaces, resulting in a conical intersection. Strong nonadiabatic interactions present near such an intersection will cause an irreversible nonradiative relaxation of the wave packet to the ground state. In the condensed phase the system should be effectively cooled down in the ground state to a local minimum corresponding to one of the two tautomeric forms. One may wonder, Is there a nonzero probability for the wave packet to reach the other tautomeric minimum due to such a process? In Figure 6 we present energies calculated for the 2HP/2PY system with the hydrogen atom placed in one of the positions indicated in Figure 4b. In the CASSCF/3-2G optimization procedure, only the relative position of the hydrogen atom with respect to the heteroatoms (N and O) was fixed. The rest of intramolecular degrees of freedom were fully optimized by minimizing the energy of the A (πσ*) state. The first cross section through the PE surfaces (shown in Figure 6a) is just behind the barrier on the A PE surface, and the second (shown in Figure 6b) corresponds to the hydrogen atom being shifted by Å toward its dissociation. It is interesting to note that there is an energy gradient on the A (πσ*) PE surface (singlet or triplet) attracting the hydrogen atom toward the middle point (of roughly equal distances from nitrogen and oxygen atoms). There is a region where the ground-state PE surface approaches the A PE surface and where the conical intersection is located. It is thus likely that the wave packet propagated on the repulsive A (πσ*) PE surface can reach the ground-state PE surface near

7 Photophysics of 2-Hydroxypyridine J. Phys. Chem., Vol. 00, No. 0, Figure 8. Prefulvenic forms of 2PY (a) and 2HP (b) optimized in their ground state at the UHF/3-3G approximation. Figure 7. CASSCF/DZVP PE functions of the four lowest excited singlet states of A symmetry calculated along the MEP optimized in the A state at the CASSCF/3-2G approximation for 2PY (a) and for 2HP (b) vs stretching of the NH and OH bond lengths, respectively. its transition point for PT, and thus the system can further relax into one of the local minima. Thus, in principle, the PT reaction can take place. The scenario sketched above is similar to the photon-induced dissociation-association (PIDA) mechanism of PT proposed in ref 8. The question remains, How can the wave packet propagated near the equilibria on the excited A or A PE surfaces reach the repulsive A (πσ*) PE surface? The barrier on the A PE surface are rather prohibitive with respect to effective tunneling or a thermal excitation. The experiments where the photoinduced PT reaction was detected 3,23 were performed under stationary conditions. One thus cannot exclude that a second photon is absorbed by the system during its lifetime in the excited state. In relation to that, it would be interesting to explore higher excited states, in particular the πσ* states, which can be adiabatically correlated to the repulsive part of the A PE surface. In Figure 7 we present the PE functions of the four lowest singlet states of the A symmetry calculated for different stretchings of the NH (Figure 7a) and the OH (Figure 7b) bonds. Because all the states belong to the same symmetry representation in the C s point group, it is almost impossible to obtain converged CASSCF wave functions for all the (but the lowest) roots. The PE functions presented in Figure 7 were obtained in the state-averaged CASSCF/DZVP calculations with the (20,2/2,7) active space. We should mention that even the state-averaged approach has a convergence problem in the region of strong mixing between the states. Fortunately, the first three points presented in Figure 7 allow us to qualitatively characterize the PE functions of the higher excited states of the A symmetry. The two lowest states have near the equilibrium geometry a mostly nπ* character, and the next two are dominated by the πσ* electronic configurations. Among them, the state number three (when counting from the bottom) correlates adiabatically to the dissociative part of the A PE surface for a larger stretching of the reaction coordinate. The wave packet excited (presumably by the second photon) to this state is accelerated in the direction of the proton dissociation. Thus, there is a chance to pass through the region of strong nonadiabatic interactions between the PE surfaces and to reach the dissociative A (πσ*) PE surface. This may provide the driving force for the PIDA mechanism to operate in the proton-transferring system without an intramolecular hydrogen bond Nonradiative Deactivation Channel. The photophysics of the 2HP/2PY system discussed in the preceding section results in a conclusion that the PIPT reaction via the PIDA mechanism should be essentially symmetric with respect to the doorway tautomeric form. Thus, longer wavelengths of exciting light should induce the lactam (2PY) to lactim (2HP) transformation, whereas a shorter wavelength should induce the reverse process. While there are some experimental works reporting the lactam-to-lactim PIPT transformation in 2HP/2PY and in similar systems, 3,23 there exists no evidence for the reverse reaction. A possible explanation for this, as was already suggested in ref 8, is that an efficient radiation-less transition to the ground state takes place after excitation of the lactim (aromatic) form within the lowest ππ* singlet manifold. It has been postulated that strong nonadiabatic interactions between the excited and ground states of the aromatic 2HP molecule along the reaction path to its biradical prefulvenic form may be responsible for its efficient internal conversion to the ground state. The above-mentioned postulate of ref 8 has been drawn by analogy to benzene and pyrazine, where such interactions determine the excited-state dynamics. 52,53 More recently, this type of internal conversion has also been elucidated for other systems. 25,28 In the following we present results of explorations of the prefulvenic reaction path for the 2HP/2PY system interconversion. First, it appears that the full aromaticity of the (aza)aromatic ring is not the necessary condition for the formation of a stable (or metastable) prefulvenic form, as has been previously suggested. In Figure 8 we schematically present the geometry of one, among the six possible, prefulvenic form of 2PY and 2HP molecules. Both tautomeric forms represent local minima on the PE surface of the ground state at the UHF/3-2G approximation. The UHF/3-3G optimized parameters of their geometries are listed in Table 2 and are very close to those reported previously for other similar systems. 25,52,53 A characteristic feature of such structures is a strong out-of-plane distortion of one of the ring atoms (C 4 for the case on hand) and formation of a new chemical bond between a pair of neighboring atoms (C 3 and C 5 in Figure 8). The biradical character of such structures is due to localization of one electron on the out-of-plane tilted atom (C 4 ) and localization of another electron on the aryl part of the ring (N -C -C 2 ), which is almost planar. Both structures pictured in Figure 8 belong to the C point group, and there is no symmetry distinction between their excited electronic states. This means that it would be difficult to apply the MEP approach to study the reaction path on the excited PE surface, since there is a high probability that the optimized wave function of the higher electronic state collapses to the ground state. Thus, CRP is the method of choice for characterization of this reaction path. The initial and final CRP points are the geometry of the CASSCF/3-2G optimized A (ππ*) state (Q ) 0) and the geometry of the UHF/3-2G optimized ground state of the prefulvenic form (Q ) ). The geometrical parameters of the initial and final 2PY and 2HP structures are listed in Table 2. The CASPT2/DZVP PE functions of the ground and first excited singlet states calculated

8 3940 J. Phys. Chem., Vol. 00, No. 0, 996 Sobolewski and Adamowicz Figure 9. CASPT2/DZVP PE functions of the ground and the first excited singlet state of 2PY (a) and 2HP (b) calculated along the CRP from the minimum of the S state at planar geometry (Q ) 0) to the minimum of the prefulvenic form (Q ) ). Figure 0. CASSCF/DZVP adiabatic (solid) and diabatic (dashed) PE functions calculated near the avoided crossing region of Figure 9a (a) and the NAC element (b). with respect to the state-averaged CASSCF wave functions are presented in Figure 9. Upon inspection of the PE functions presented in Figure 9, one can notice that they look qualitatively similar for both systems; that is, their shape results from avoided crossing of two electronic states. A different degree of configuration mixing has a dramatically different effect on the photophysics of the two molecules. First of all, 2PY is rather well protected in its (almost) planar form at the equilibrium of the S (ππ*) state. This is not the case for the 2HP form. The nuclear frame of this molecule is much softer with respect to the out-of-plane deformation along the reaction coordinate. Also, the barrier which separates the equilibrium in the S (ππ*) state from the region of the avoided crossing with the ground state is much lower in this case. Let us notice that the transient point on the S PE surface was not optimized in the present treatment. Thus, the barrier may be lower than indicated in Figure 9b. In other words, the wave packet propagated on the S PE surface of 2HP can rather easily reach the region of strong coupling to the ground state and relax due to nonadiabatic interactions. To visualize the effect of the interstate coupling, the stateaveraged CASSCF/DZVP PE functions of the ground and excited singlet states near the interaction region are presented in Figures 0a and a for 2PY and 2HP, respectively. The CASSCF adiabatic PE functions can approximately be diabatized by a block-diagonlization of the configuration interaction matrix (see for details refs 25, 54, and 55). The quasi-diabatic PE functions are also presented in Figure 0a,b, and they intersect each other as expected. The derivative of the adiabaticto-diabatic mixing angle ν (R) with respect to the reaction coordinate R determines the nonadiabatic-coupling (NAC) element. This derivative is presented in Figure 0b and b Figure. CASSCF/DZVP adiabatic (solid) and diabatic (dashed) PE functions calculated near the avoided crossing region of Figure 9a (a) and the NAC element (b). for 2PY and 2HP, respectively. Because there is no real intersection between adiabatic PE surfaces, the NAC element does not show any singularity at the intersection as it does for the conical intersection. 54 Nevertheless, the NAC element reaches a much higher value for 2HP than for 2PY. Moreover, any additional out-of-plane deformation of the system will amplify the coupling. Thus, one can except that photophysics of 2HP in the first excited singlet state will follow a similar pattern as predicted for benzene and pyrazine; that is it will be dominated by radiation less decay to the ground state. In closing, we can confirm the hypothesis of ref 8 that nonadiabatic interactions between the S and S 0 states in 2HP provide a channel for an efficient nonradiative decay of electronic excitation to the ground state. This process is ineffective in depopulating the lowest excited states of 2PY because this molecule is well protected by barriers near its equilibrium geometry. 4. Conclusions Extensive ab initio explorations of multidimensional PE surfaces, reported in this work, were performed with the intention of developing a better understanding of the photophysical behavior of the 2HP/2PY molecular system. Among many possible photoreaction channels, we have focused our attention on those which are expected to be relevant to the tautomerization (PT) reaction due to optical excitation. The picture of photophysics of the 2HP/2PY system which emerges from our study is rather complex. Present results, obtained with the aid of the state-of-art ab initio technology for excited states of larger polyatomic systems, confirm generally the earlier suggestion that the excited-state dissociation followed by the ground-state association of the hydrogen atom is the intrinsic feature of the photoinduced proton transfer (PIPT) reaction in systems without intramolecular hydrogen bonds. The direction of the PT reaction, which according to the experimental observations, occurs exclusively from the lactam (oxo) form to the lactim (hydroxy) form, is explained by the existence of an efficient channel for radiation less deactivation of the lowest excited singlet state of 2HP. This deactivation process is due to strong nonadiabatic interactions with the ground state along the reaction path leading to the prefulvenic form. This channel is supposed to be fast enough to effectively compete with any other reaction which can occur after optical excitation within the lowest singlet manifold of the lactim form. The lactam 2PY form is protected by a significant barrier on the PE surface of the lowest excited singlet state from the region of strong nonadiabatic interactions with the ground state, and thus internal conversion to the ground state seems to be unimportant for the dynamics on the excited-state PE surface.