J. Phys. Chem. 1995,99, 14277-14284
14277
Theoretical Investigations of the Proton Transfer Reaction in the Hydrogen-Bonded Complex of 2-Pyrimidinone with Water Andrzej L. Sobolewski Institute of Physics, Polish Academy of Sciences, 02 668 Warsaw, Poland
Ludwik Adamowicz*J Department of Theoretical Chemistry, Chemical Center, University of Lund, S-22100 Lund, Sweden Received: December 21, 1994; In Final Form: July 5, 1995@
The potential energy (PE) functions of the electronic ground and lowest mr* excited singlet states of the hydrogen-bonded cyclic complex of 2-pyrimidinone with water were theoretically investigated along the proton transfer (PT) reaction coordinate. The full geometry optimization was performed along the PT reaction path. In the geometry optimization the Hartree-Fock method and the configuration interaction method with single excitations (CIS) were used. The energy calculations at the optimized geometries were performed with the complete-active-space self-consistent-field (CASSCF) method and with the second-order perturbation theory, employing the CASSCF wave function as the reference. For the ground state, calculations were also performed with the Moller-Plesset second-order perturbation theory (MP2). We found that the hydroxy form of the 2-pyrimidin0ne:water complex is stable in the ground electronic state while the hydroxy-to-oxo transformation reaction of the complex is by about 0.67 eV exothermic on the lowest Inn*excited state PE surface. However, there is a barrier of about 0.19 eV along the PT reaction path on this surface. The top of the barrier is below the energy of the vertical excitation SO Inn*; thus, the photoexcited system has sufficient excess energy for the PT reaction to occur spontaneously.
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1. Introduction The photoinduced intramolecular excited-state proton (or hydrogen) transfer (ESIPT)is one of the most fundamental photochemical reactions and has attracted much attention for many years. (For a comprehensive review see ref 1 and the references therein.) The reaction can occur when either the acidic or basic moieties of the same molecule become more acidic or basic in the excited state. The majority of the reactions of this type involves the transfer of a proton from the oxygen donor to the oxygen or nitrogen acceptor along the intramolecular hydrogen bond. Apart from the existence of a hydrogen bond along the reaction coordinate, a necessary condition for the reaction to occur is the so-called reverse asymmetry of the ground- and excited-state potential energy (PE) functions along the proton transfer (PT) reaction coordinate. This means that the (stable in the ground state) subtract should become unstable (or metastable) with respect to the product on the excited-state PE surface. There is, however, one important class of compounds in which the PT reaction can occur but which does not fulfill any of the two above-mentioned conditions: i.e., neither they have any intramolecular hydrogen bonds, nor do their PE functions have the desired asymmetry with respect to the PT reaction coordinate. The transfer of the hydrogen atom in these systems occurs upon optical excitation under isolate molecule conditioni2 Moreover, the hydrogen atom is transferred exclusively from the ring nitrogen to the oxygen or sulfur acceptor, Le., against the existing endothermicity on the excitedstate PE surface. It has recently been proposed on the basis of theoretical results for 2-pyridone3 and fomamide4 that the photoinduced (possibly via multistep excitations to higher
* To whom correspondence should be addressed. Permanent address: Department of Chemistry, University of Arizona, Tucson, AZ 85721. * Abstract published in Advance ACS Abstracts, August 15, 1995. +
electronic states) dissociation and the subsequent ground-state association of the “mobile” hydrogen atom may provide a mechanism for this phenomenon. In a typical ESIPT system the hydrogen bond, along which the PT reaction occurs, does not need to be an intramolecular bond. It may also be an intermolecular hydrogen bond(s) between two components of a hydrogen-bonded complex. For the tautomerization reaction to occur, the complex should be cyclic; i.e., it has to be bonded via two hydrogen bonds which allow a concerted biprotic transfer reaction. Perhaps the most representative and the most frequently studied examples of the solvent-assisted ESIPT reaction are clusters of 7-azaindole and 7-hydroxyquinolinewith protic solvents. (See refs 5 and 6 and references therein.) The transfer of the proton through a molecular “bridge”, which connects remote proton-donor and proton-acceptor centers of the molecule, may also provide a mechanism for phototautomerization of the molecular system without intramolecular hydrogen bonds. The mechanism is similar to the one operating in a typical ESIPT system. The main effect of the formation of a cyclic H-bonded molecular complex is a decrease of the barrier separating the two tautomeric forms. For instance, the ground-state PT reaction in isolated 2-pyridone (2PY) is prohibited by a large (-13 500 cm-I) energy barrier,’ but the barrier decreases to about 80008 and 300 cm-’ for the 1:l and 1:2 complexes of 2PY with water, respectively. Similar effects have also been reported for formamide, its complex with water, and its dimer? Solvation also has an important effect on the relative stability of tautomers. Generally, the lactam form, which usually possesses a larger dipole moment than the lactim form, is more stabilized due to its stronger interactions with polar solvents. This effect has recently been studied in molecular jet by Nimlos et al.Io for 2PY and its clusters with water. They found that the energy of the lactim lactam tautomerization decreases from ACT = 150 cm-’ for the
0022-3654/95/2099-14277$09.00/0 0 1995 American Chemical Society
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Sobolewski and Adamowicz
14278 J. Phys. Chem., Vol. 99, No. 39, 1995 monomer to -750 and -2048 cm-' for the 1:l and 1:2 complexes, respectively. Complexation with water also changes the exothermicity of the tautomerization reaction on the excited Inn* state PE surface from -6051 cm-' for 2PY to -5748 cm-' for 2PY:(H20)1 and to -6545 cm-' for 2PY:(H20)2.I0 Upon inspection of the above results, one sees that the ESIPT reaction in complexes of 2PY with water, although possible under jet conditions, is highly unlikely under bulk conditions since the subtract lactim form has higher energy on the groundstate PE surface than the product lactam form (the common asymmetry example). Note that the lactim lactam reaction in 2PY and its complexes with water is highly exothermic on the excited-state PE surface. This is a general trend observed for many ESIFT systems and results from the fact that after a nn* excitation the aromatic nitrogens are becoming more basic, and this results in an increased stabilization of the lactam form. Summarizing the above discussion one can conclude the following: (i) In the molecular systems with an intramolecular hydrogen bond(s), the ESIPT process favors the lactim-to-lactam transformation. (ii) In the isolated molecular system without an intramolecular hydrogen bond(s), the reverse, lactam-tolactim, photoinduced transformation has been observed. (iii) Complexation with protic solvents can provide hydrogen bonds for the system along which the ESIPT lactim-to-lactam form in the ground state more than the lactim form. This, in tum, leads to a decrease of the asymmetry of the PE function of the system-a necessary condition for the closed-cycle ESIPT process. Having the above observations in mind, one can search for a molecule which can be a good ESIPT system after complexation with water. When not involved in a complex with water, such a system under isolated conditions should almost exclusively exist in the lactim form. The endothermicity of the lactim-tolactam reaction on the ground-state PE surface should be large enough so that the complexation with one or two water molecules does not significantly change the tautomeric equilibrium. The results of experimental studies indicate that in some cases the relation between the molecular structure and the tautomeric equilibrium can be estimated.2 It has been found, for example, that in a series of diazinones and diazinethiones the relative stability of the lactam and lactim tautomers depends on the relative position of the lactam group with relation to the second nitrogen atom in the ring. In the diazinone series, the relative abundance of the lactam/lactim tautomers changes from the exclusive dominance of the lactam form for 3-pyridazinone to the exclusive dominance of the lactim form for 2-pyrimidinone." The situation in diazinethiones is similar; however, the substitution of the exocyclic oxygen atom by sulfur atom leads to some increase of the stability of the fully aromatic (tiol) form in those compounds. The above-mentioned findings for diazinones suggest that the water complex of 2-pyrimidinone (2PMD) or its ti0 analog may be a good candidate for an ESIPT system. The free energy difference determined for 2PMD from the IR spectroscopy in low-temperature inert gas matrix is about 1600 cm-l (0.19 eV) in favor of the lactim (hydroxy) form.I2 This value is in close agreement with A& = 0.18 eV obtained in the most extended ab initio calculations of Les and A d a m 0 ~ i c z . l In ~ the H2Odoped Ar matrix, the intensity decrease of the R bands assigned to the OH group of 2PMD and the increase of the intensity of the bands assigned to the C=O group have been observed.I4 This suggests a shift of the tautomeric equilibrium position due to interaction with water. Theoretical calculations reveal that closed H-bonded structures are the most stable among the 1:1 complexes of 2PMD with water for both the hydroxy and oxo
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tautomers, with the complex of the former being by about 750 cm-' more stable than with the latter.I5 Thus, complexation with water stabilizes the oxo (lactam) form of 2PMD by the amount of energy similar to that observed for 2PY.I0 If this trend continues for higher clusters of 2PMD with water, one may expect that complexation of 2PMD with two water molecules may lead to the oxo (lactam) form being already more or equally stable than the hydroxy (lactim) form. This supposition seems to be supported by the low-temperature matrix data.I4 In conclusion, the 1:l or 1:2 H bonded complexes of 2PMD with water should provide, in principle, an opportunity for observation of the ESIPT process since it is reasonable to expect a strong exothermicity of the lactim-to-lactam PT reaction on the Inn* excited-state PE surface for this system. The question which we address in this work concems the height of the barrier on the excited-state PE surfaces for the PT reaction in this system. 2. Methodology and Results
The molecular geometries of all molecular systems considered in this work were optimized at the Hartree-Fock (HF) level for the ground state, whereas in the optimizations of the excitedstate geometries the configuration interaction scheme with single excitations (CIS) was used. Most of the geometry optimizations were performed under the C, symmetry constraints (the systems were kept planar unless explicitly specified otherwise). Maintaining the planarity of the system is very important with respect to the excited state calculations. The lowest excited singlet states of all the systems considered in this work result from the nn* and nz* excitations and as such fall into two distinct symmetry representations, the A' and A", in the C,point group. Any out-of-plane deformation destroys the C, symmetry and mixes the A' and A" states together. It is then practically impossible to get a converged solution for the higher of the two lowest close-lying excited electronic states of the same multiplicity and symmetry, which in the C,symmetry are distinct (Le., the A'(zz*) and A"(nn*) states) and easy to converge. Restricting the system to the C, symmetry in the calculations of the PE functions along the reaction coordinate has also important implications for treatment of the reaction dynamics. It is convenient in such a treatment to consider any distortion from the C,symmetry as a pseudononadiabatic nuclear-electron interaction. This, of course, makes sense if the distortions from the C,symmetry have a negligible influence on the energy. This point was carefully checked for the systems considered in this work. We also need to stress that the study presented in this work are exploratory and are aimed to provide only a qualitative characterization of the proton transfer reaction assisted by water molecule. The approximations made in the calculations should and have been tested here for their reliability in providing a quantitative picture of the process and not a quantitative one. The split-valence Gaussian basis sets 3-21G and 6-31G**l6 were employed in geometry optimizations, and all the optimizations were performed with the use of the GAUSSIAN92 program package. The single-point energy calculations were performed for the ground state with the use of the MollerPlesset (MP2) perturbation theory and the double-zeta Gaussian basis set with polarization functions (the D95G** basis set of GAUSSIAN). The excited state energies were calculated by means of the CASSCF method,'* and the double-zeta-valence Gaussian basis set of Dunning and HayI9 with polarization functions (DZV** basis set) was used. The remaining dynamic correlation effects were added in the subsequent step with the use of the second-order perturbation theory with the CASSCF wave function as the reference (CASFT2).20 CASPT2 calcula-
J. Phys. Chem., Vol. 99, No. 39, 1995 14279
H-Bonded Complex of 2-Pyrimidinone with Water
“‘0’0”‘
Q &f.yQH c4
c2
H2
HI
c2
H4
H2
c3
H3
H3
Figure 1. Hydroxy and the oxo forms of 2-pyrimidinone.
tions were performed with respect to the CASSCF function optimized for each state separately with the use of the nondiagonal zero-order Hamiltonian as it is implemented in the MOLCAS-2 quantum chemistry software.2’ All the calculations were performed on the LBM RS/6000-590 workstation. A. 2-Pyrimidinone Monomer. The geometry parameters of the two tautomeric forms of 2-pyimidinone (Figure 1) optimized in the ground and in lowest excited singlet states with the use of the 3-21G basis set are presented in Table 1, and those obtained with the 6-31G** basis are presented in Table 2. The reason for using two different basis sets was to compare the results obtained with the molecular structures generated with the use of the two basis and to determine whether the 3-21G simpler basis is capable of providing the qualitative answers which we seek in this work. If this were the case, we would be able to investigate the PES for the proton transfer reaction at much lower cost. Upon inspection of the results obtained with both basis sets, one can notice a significant variation, particularly of the bond lengths, between the two tautomeric forms. At the HF/3-21G level of theory the oxo form to 2-pyrimidinone is more stable than the hydroxy form in the ground state, as well as in both the lowest excited singlet states. The stability of the structures was checked by computing harmonic force fields at the C,-optimized geometries. At the HF/6-31G** level the hydroxy form is slightly more stable in the ground state, but in both excited singlet states the oxo form has lower energy. It appeared that both tautomeric forms of the 2-pyrimidinone are planar in the ground state at the HF level of theory with both basis sets, but in the lowest excited singlet state only the hydroxy form in the ‘A”(nn*) state is planar. The oxo form in the ’A’(nn*) state and the hydroxy form in both excited singlet states considered possess one imaginary vibrational frequency at the C,-optimized nuclear geometry. In all the cases it is an out-of-plane vibration which corresponds to the imaginary frequency. From the spectroscopic point of view the lowest A’(nn*) singlet state, which is allowed from the ground state in the absorption process, is of the primary importance. Unfortunately,this state at both the CIS/3-21G and CIS/6-31G** levels of theory is higher in energy than the “dark” (for absorption from the ground state) A”(m*) state (see Tables 1 and 2). The ordering of the two excited states is reversed when the dynamic electron correlation effect is taken into account (Tables 3 and 4). The presence of the close-bellowlying ‘A”(nn*) state makes the optimization of the geometry of the “spectroscopic” ‘A’(nn*) state impossible without the C,symmetry constrains. In an attempt to optimize the geometry for this state without any symmetry constrains, just after a few optimization steps the system collapses into the lower ‘A”(rut*) state and, in the case of the hydroxy form, the planarity is restored. There is, of course, no symmetry distinction between the n and n molecular orbitals when the symmetry plane does not exist, but the electronic states can still be qualitatively characterized in terms of the nn* and m*electronic excitations since the latter has still a negligibly small oscillator strength
for the absorption from the ground state. We assume, by the analogy to other similar compounds,22that distortions from the C, symmetry of the considered systems have a relatively minor effect on the energy scale pertaining to this work and should not influence qualitative conclusions of this work. However, without a doubt this approximation has to be carefully checked in a more quantitative study. The single-point energy calculations of the ground and lowest excited singlet states were performed at the C,-optimized geometries obtained with the 3-21G and 6-31G** basis sets according to the methods specified in preceding section. In the CASSCF calculations, 10 electrons (of the total number of 50) were correlated in eight molecular orbitals. The active space is denoted as (20,0/1,7), where the first two numbers indicate the number of closed (doubly occupied in each configuration) molecular orbitals in the A‘ and A” symmetry representations of the C, point group, respectively, and the second two numbers indicate the similar symmetry distribution for the active orbitals. Thus, the active space includes all the (first shell) n orbitals (from la” to 7a”) and one n orbital (21a’). The double-zetavalence Gaussian basis set of Dunning and HayIg with polarization functions (DZV**) was employed in the energy calculations. The exponents of the polarization functions were 0.75, 0.80,0.85, and 1.0 for carbon, nitrogen, oxygen, and hydrogen atoms, respectively. The first-order interaction space in the CASPT2 calculations had the dimension of about 1.2 x lo6. The energies calculated for the lowest singlet states of the two tautomeric forms with the geometries obtained with the use of the 3-21G are listed in Table 3, and those obtained with the geometries obtained with the 6-31G** basis are presented in Table 4. Upon inspecting the results presented in Tables 3 and 4, one can notice that the relative stability of the two tautomeric forms of 2-pyrimidinone is reversed (now the hydroxy form is preferred by AE = 0.19 eV, as calculated with the 3-21G geometries, and by AE = 0.21 eV, as calculated with the 6-31G** geometries, over the oxo form) as compared to the HF/3-21G result of Table 1 (AE = -0.05 eV). This is in an agreement with the experimental observationsI2as well as with the other theoretical res~1ts.I~One should notice that the CASPT2 energies calculated with the 3-21G geometries are for both tautomers slightly lower than the energies obtained with the 6-31G** geometries. This indicates that the 3-21G geometries may be closer in certain parameters to the experimental geometries. In the excited singlet states the oxo form is more energetically stable than the hydroxy form (by AE = 0.74 eV and A = 0.77 eV in the ‘A‘(nn*) and ‘A“(nn*) states, respectively, in the calculations with the 3-21 geometries, and by AE = 0.68 eV and A = 0.44 eV in the ‘A‘(nn*) and IA”(rut*) states, respectively, in the calculations with the 6-31G** geometries). Although, the energy differences calculated with the 3-21G and 6-31G** geometries for the ‘A”(nn*) state are noticeably different, for the ‘A’(nn*) state, which is of interest in the present work, they are very similar. This again gives us a reason to expect that we will get qualitatively correct answers, if we use the 3-21G geometries in our study. The quantity, which can be directly compared to the experiment, is the energy of the “vertical” electronic excitation, i.e., the difference between the energy of the ground and excited singlet states calculated at the ground state equilibrium geometry. The energies of the SO Inn* transition (AE = 4.82 eV and AE = 4.14 eV) calculated with the 3-21G geometries for the hydroxy and oxo forms can be compared to the maxima of the first absorption bands observed at 4.80 eV for the hydroxy form of 2PMD in the gas phase and at 4.16 eV for the oxo form in ethanol.23
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Sobolewski and Adamowicz
14280 J. Phys. Chem., Vol. 99, No. 39, 1995
TABLE 1: -HF/3-21G and CIS/3-21G Optimized Parameters of Geometry (Bond Lengths in angstroms, Bond Angles in degrees) and Enerdes (au) of the Two Tautomeric Forms of 2-Pyrimidinone hydroxy form parameter CiNi NiC4 c4c3
c3c2
C2N2 N2Ci CIOI OIHI" C4H2 C3H3 ~
c2H4 CiNiC4 NiW3 c4c3c2
C3C2Nz C2N2Ci N2CiNi N2Ci01 CiOiHi' NIGH> C4C3H3 N2C2H4 energy a
so 1.368 1.331 1.380 1.385 1.327 1.322 1.342 0.966 1.070 1.068 1.070 117.8 121.6 116.2 122.2 117.2 125.0 117.0 110.8 116.7 121.9 116.4 -335.6634
'A'(JtJC*)
oxo form I A"(
nn* )
so
IA'(JCJt*)
IA"(nn*)
1.361 1.360 1.413 1.416 1.364 1.338 1.319 0.970 1.066 1.070 1.066 115.7 120.2 119.3 120.2 115.9 128.7 116.4 111.0 117.7 120.3 117.5
1.296 1.387 1.371 1.398 1.371 1.316 1.336 0.967 1.066 1.070 1.064 123.6 119.0 118.1 116.1 126.3 116.6 119.9 111.6 116.9 121.4 118.7
1.404 1.359 1.340 1.431 1.284 1.394 1.208 0.999 1.070 1.066 1.072 123.8 120.0 116.0 124.4 120.9 114.8 124.9 115.4 116.5 122.4 116.8
1.451 1.351 1.412 1.382 1.371 1.333 1.224 1.000 1.067 1.069 1.066 121.5 117.8 119.6 121.9 120.0 119.2 126.7 115.8 118.9 119.1 116.3
1.386 1.410 1.334 1.445 1.335 1.373 1.206 0.998 1.067 1.069 1.064 124.2 121.1 119.1 112.3 134.7 108.2 127.3 115.2 115.2 122.0 122.0
-335.4224
-335.4724
-335.6652
-335.4649
-335.4925
These parameters should for the oxo form be replaced by NlHl and CINIHI.respectively.
TABLE 2: HF/6-31G** and CIS/6-31G** Optimized Parameters of Geometry (Bond Lengths in angstroms, Bond Angles in degrees) and Energies (au) of the Two Tautomeric Forms of 2-Pvrimidinone hydroxy form parameter CiNi NiC4 c4c3
c3c2
C2Nz NzCi CIOl OIHI" C4H2 C3H3
c2H4 CiNiC4 NiW3 c4c3c2
C3C2Nz C~N~CI NzCiNi N2Ci01 CiOiHP NiC4H2 C4C3H3 N2CzH4 energy
so 1.319 1.321 1.379 1.385 1.317 1.317 1.322 0.946 1.076 1.072 1.077 116.2 122.5 115.3 123.1 115.7 127.0 115.9 108.4 116.2 122.4 116.0 -337.5796
lA'(Jcn*)
oxo form
so
IA"(nn*)
'A'(JCJC*)
1.351 1.344 1.414 1.415 1.346 1.333 1.298 0.949 1.072 1.074 1.072 114.8 120.4 118.9 120.6 114.7 130.5 115.1 108.1 117.8 120.5 117.6
1.291 1.377 1.364 1.407 1.351 1.307 1.314 0.947 1.071 1.075 1.069 122.0 120.2 118.0 115.2 127.2 117.4 119.6 108.6 116.6 121.7 119.4
1.394 1.350 1.342 1.432 1.281 1.382 1.193 0.995 1.074 1.071 1.079 124.0 119.6 115.4 125.5 119.4 116.0 124.5 115.0 116.5 122.6 116.1
-337.3494
-337.3748
-337.5729
1
I A"(nn*)
1.434 1.342 1.414 1.391 1.350 1.339 1.201 0.996 1.07 1 1.073 1.072 122.1 116.8 119.5 122.8 118.6 120.1 125.7 115.1 119.0 119.2 116.5
1.380 1.400 1.333 1.450 1.323 1.360 1.190 0.994 1.071 1.073 1.068 123.9 120.9 119.5 111.8 135.2 108.7 127.1 114.6 115.5 122.0 122.2
-337.3747
-337.3881
These parameters should for the oxo form be replaced by NlHl and ClNlHl, respectively.
Although the agreement seems to be more a fortunate coincidence than a reflection of the accuracy of the theoretical approach, it provides some assurance that the method is reliable enough to make qualitative predictions. In view of the above, we can conclude that the theoretical approach selected for the present study of the low-lying electronic states of 2-pyrimidinone based on C,-optimized geometries obtained with the 3-21G basis set provides results which are consistent with the experimental values. Therefore, it is reasonable to expect similar precision for slightly larger, but similar, systems which will be discussed in the next section. B. 2-Pyrimidin0ne:Water Complex. The HF/3-21G optimized tautomeric forms of 2PMD:HzO complexes in the
ground state are presented in Figure 2, and the parameters of the structures optimized in the lowest excited singlet states (CIS/ 3-21G) are shown in Table 5 . Only the parameters which describe the geometry of the "reaction center" (close to the hydrogen bonds) are shown because the other parameters remain practically identical to those in the monomers. All the structures are generally nonplanar (notice that one of the hydrogen atoms of water is significantly tilted out of the molecular plane). This has, however, a minor effect on the energy. The C,-optimized structures have the ground state only by about 310 and 220 cm-' for the hydroxy and oxo forms, respectively, higher than the energies of the structures optimized without symmetry constraints. Thus, the relative energy difference between the
J. Phys. Chem., Vol. 99, No. 39, 1995 14281
H-Bonded Complex of 2-Pyrimidinone with Water TABLE 3: CASSCF and CASPT2 Energies, Energies Relative to the Ground State (AE) and the Weight of the CASSCF Reference Function in the First-Order Wave Function (0)Calculated with DZV** Basis Set for 2-Pyrimidinone at Molecular Geometries Optimized in Different Electronic States of Its Two Tautomeric Forms with the Use of the 3-216 Basis Set state [geometry1
so [Sol Inn* [So]
Inn* [SO] So [ ' J C X * ] 'ZZ* ['xx*] Inn* ['nn*]
CASSCF
AE
CASPT2
(au)
(ev)
(au)
AE (ev)
OJ
Hydroxy Form -337.7126 -337.5163 -337.5115 -337.7079 -337.5282 -337.5200
5.34 5.47 0.13 5.02 5.24
-338.6289 -338.4517 -338.4460 -338.6291 -338.4676 -338.4591
Figure 2. Hydroxy and the oxo forms of 2-pyrimidinone:water
0.776 0.760 0.747 0.772 0.756 0.750
4.82 4.97 -0.005 4.39 4.62
0.778 0.756 0.768 0.772 0.758 0.769
0.19 4.33 4.47 0.33 3.65 3.85
Oxo Form
so [Sol
0.07 5.16 4.58 0.54 4.29 3.95
-337.7100 Inn* [So] -337.5228 'nn* [SO] -337.5443 So ['zJc*] -337.6927 'JUT* [ I ~ J C * ]-337.5549 Inn* [Inn*] -337.5675
-338.6220 -338.4698 -338.4646 -338.6169 -338.4947 -338.4872
TABLE 4: CASSCF and CASPT2 Energies, Energies and the Weight of the Relative to the Ground State (AZ?) CASSCF Reference Function in the First-Order Wave Function (0)Calculated with DZV** Basis Set for 2-Pyrimidinone at Molecular Geometries Optimized in Different Electronic States of Its Two Tautomeric Forms with the Use of the 6-31G** Basis Set state CASSCF A,?? CASPT2 AE [geometry1
(au)
(au)
OJ
(eV)
-338.6281 -338.4504 -338.4448 -338.6285 -338.4660 -338.4677
0.778 0.760 0.758 0.774 0.757 0.763
4.83 4.98 0.01 4.41 4.36
-338.6202 -338.4678 -338.4682 -338.6170 -338.491 1 -338.4841
0.779 0.758 0.769 0.774 0.758 0.771
0.21 4.36 4.62 0.30 3.73 3.92
(eV)
Hydroxy Form
so [Sol Inn* [So] Inn* [SO]
so [Inn*] Inn* ["*I Inn*
[Inn*]
-337.7131 -337.5150 -337.5147 -337.7093 -337.5270 -337.5395
5.39 5.40 0.10 5.06 4.72
Oxo Form
so [Sol [So] Inn* [So] so [Inn*] 'En*
'JCJC*
["*I
Inn* [Inn*]
-337.7100 -337.5225 -337.5394 -337.6971 -337.5504 -337.5661
0.08 5.18 4.72 0.43 4.42 4.00
two tautomers is by only about 110 cm-' changed by imposing the C, symmetry on the systems. The minor effect of the forced planarity on the relative energy of the complexes results from the fact that it has almost no influence on the intramolecular geometry parameters. Only the intermolecular coordinates of the complex are slightly modified upon relaxation of the C, symmetry. This provides a justification for optimizing the excited state geometries within the C, point group. Besides, this was the only way we have been able to obtain the optimal structure for the higher, at this level of approximation, of the two close-lying singlet states (the A'(nn*) singlet state which is the state of interest), which in the C, symmetry group belong to different representations (A" and A', respectively). All attempts to lift the C, symmetry restriction and optimize the geometry of the state closely resembling the A'(nn*) singlet state with the use of a state-specific approach were unsuccessful. Although the 'A"(m*) state has at the CIS/3-21G level of theory lower energy than the spectroscopically allowed A'(nn*) singlet state, the electron correlation is expected to shift this state to higher energy (above the 'A'(nn*) state), by analogy to the results obtained for the monomer. Therefore, the IA"(m*) state is quite likely to be unimportant for the molecular dynamics on the excited PE manifold, and for this reason we did not
complex.
consider this state in the present work with respect to the ESIPT reaction. The single-point energy calculations of the ground and lowest excited singlet state were performed with the method specified in the preceding section. In the CASSCF calculations 12 electrons (of the total number of 60) were correlated in the active space of nine molecular orbitals. The active space is denoted as (24,0/1,8) in the C, point group. The first-order interaction space in the CASPT2 calculations had the dimension of about 2.05 x IO6. The energies calculated for the lowest singlet states are listed in Table 6. Let us first notice that the interaction with water stabilizes the oxo form of 2-pyrimidinonerelatively more than the hydroxy form. The hydroxy form is now by only 0.05 eV more stable than the oxo form. This is consistent with the other theoretical r e s ~ 1 t . l Complexation ~ with water lowers slightly the energy of the SO Inn* transition of both tautomeric forms as compared to the monomer case (AE= 4.67 eV and AE = 4.12 eV for the hydroxy and the oxo forms, respectively) and shifts to higher energy the SO lm*transition, as expected. In the cyclic complex of 2PMD with water, with two hydrogen bonds formed between the ring nitrogen atom and the hydrogen atom of the hydroxy group of 2PMD and with the oxygen atom and one of the hydrogen atoms of the water molecule (Figure 2), tautomerization reaction which converts one form of 2PMD into another can be considered as a concerted double-proton transfer reaction. The calculations of the reaction path for this process were performed by increasing incrementally the length of the OlHl bond (see Figure 2) and optimizing the rest of the degrees of freedom. The OlHl separation considered in this optimization ranged from the value of the length of the OlHl bond in the hydroxy tautomer to the length of the 0,*.*H1 hydrogen bond in the oxo tautomer of the 2PMD:H20 complex. Naturally, those lengths were different in different electronic states. If only one coordinate is selected to study a process as complex as the double-proton transfer reaction, it is important that the other degrees of freedom are fully relaxed at every value of the reaction coordinate. In this way an effective lowestenergy reaction path can be found. An alternative approach to describe a proton-transfer reaction would be to take two coordinates (the obvious choice being the two distances of the hydrogen between the hydrogen and the donor and acceptor atoms) and calculate the potential energy surface for the reaction. Actually, when two protons participate in the reaction, like it is in the process studied in the present work, a four-coordinate approach would need to be applied. Certaintly, there are reactions where due to very complicated reaction path an effective single-coordinate model cannot be applied. However, it seems unlikely that the reaction studied here belongs to this category. The exchange of protons between water and the pyrimidinone molecule follows a rather direct path (though some complications may appear around the transition point), and provided that the intra- and intermolecular relaxation is ac-
-
-
Sobolewski and Adamowicz
14282 J. Phys. Chem., Vol. 99, No. 39, 1995
TABLE 5: HF/3-21G and CIS/3-21G Optimized Parameters of Geometry (Bond Lengths in angstroms, Bond Angles in degrees) and Energies (au) of the Two Tautomeric Forms of 2-Pyrimidinone:Water Complex hydroxy form parameter
So"
oxo form
'A'(nn*)
Sob
So"
Sob
'A'(nn*)
1.338 1.332 1.332 1.320 0.993 118.2 123.3 113.7 3.054 1.603 2.021 0.973 0.961 63.9 60.7 114.2 18O.Od
1.338 1.332 1.331 1.321 0.994 118.2 123.4 113.1 3.091 1.637 1.986 0.977 0.965 63.4 56.2 110.7 121.4
1.396 1.356 1.336 1.293 1.081 115.4 126.7 114.8 3.004 1.499 1.910 0.980 0.960 62.1 60.8 116.1 180.0d
1.391 1.350 1.384 1.225 1.844 123.1 116.1 114.6 3.060 0.977 1.019 1.738 0.962 59.7 54.0 112.4 180.W
1.391 1.350 1.383 1.225 1.852 123.2 116.2 114.0 3.099 0.979 1.020 1.768 0.965 59.9 47.1 105.6 106.8
1.455 1.347 1.335 1.232 1.970 120.6 120.1 115.4 3.181 0.971 2.670 1.736 0.962 56.5 53.4 111.9 180.0d
-41 1.2792
-41 1.2806
-41 1.0455
-41 1.2840
-41 1.2850
-41 1.0801
a Optimized under the C, symmetry constraints. Optimized without any symmetry constraints. These parameters should for the oxo form be replaced by C I N I H ~C102H1, , H I O Z H ~and . C1H106, respectively. Value fixed in optimization.
TABLE 6: CASSCF and CASPT2 Energies, Energies Relative to the Ground State (AE)and the Weight of the CASSCF Reference Function in the First-Order Wave Function (0)Calculated with DZV*(*) Basis Set for 2-Pyrimidinone:Water Complex at Molecular Geometries Optimized in Different Electronic States of Its Two Tautomeric Forms AE CASFT2 (eV) (au) Hydroxy Form so [Sol -413.753 1 -414.8508 Inn* [So] -413.5585 5.29 -414.6791 Inn* [SO] -413.5414 5.76 -414.6612 So [ I x J c * ] -413.7417 0.31 -414.8475 Inn* [ ' ~ n * ] -413.5645 5.13 -414.6940 Oxo Form s o [Sol -413.7539 -0.02 -414.8491 Inn* [So] -413.5708 4.96 -414.6973 Inn* [SO] -413.5862 4.54 -414.6875 So ['JUT*] -413.7401 0.35 -414.8458 Inn* ['nn*] -413.5977 4.23 -414.7185 state rgeometrvl
CASSCF (au)
AE o
(eV)
0.747 0.730 0.710 0.743 0.725
4.67 5.16 0.09 4.26
0.748 0.729 0.740 0.743 0.729
0.05 4.17 4.44 0.14 3.60
counted for, a single-coordinate approach should facilitate a reasonable model to study the reaction, particularly if only a qualitative characterization is desired. The full optimization of the reaction path was performed for the ground state and for the lowest A'(nn*) excited singlet state. The obtained PE functions and the profiles of the variations of some of the intramolecular coordinates involved in the PT reaction are plotted vs reaction coordinate in Figures 3 and 4 for the SO and 'A'(nn*) states, respectively. One sees that the two tautomeric forms of the 2PMD:HzO complex are represented by local minima on the SOPE surface and are protected from each other by a relatively high barrier (Figure 3a). The situation is qualitatively different on the IA'(nn*) PE surface. Here the hydroxy form is much higher in energy, and there is almost no barrier for the F T reaction which leads to the energetically lower oxo form (Figure 4a). It is interesting to examine the variations of some of the intramolecular coordinates along the reaction path. They are qualitatively similar for both PE surfaces, so let us discuss in more detail those corresponding to the ground state (Figure 3b). The first conclusion resulting upon inspection of the results presented in the figure is that the variations of the intramolecular coordinates along the reaction path are far from being linear.
0.8
1
1.0
1.2 1.; 1.6 1.8 ' 3 REACTION COORDINATE (Angstroms;
Figure 3. Variation of the HF/3-21G ground-state energy (a) and some of the bond distances (b) 02Hj (circles), O ~ H I(squares), NlH5 (triangles), 0 1 0 2 (+), and Nl02 ( x ) of 2-pyrimidinone:water complex along the FT reaction coordinate (the OIHI bond length).
v
E
W
-41 1.07
2
W
7
-47 1.09
E ; 2.4
1.0
1.2 1.4 1.6 1.8 2.C REACTION COORDINATE ( A n g s t r o m s )
Figure 4. Same as in Figure 3, but calculated at the CIS/3-21G optimized geometry of the IA'(nn*)state. This is typical for the PT reaction m e c h a n i ~ m ? ~The ~ ~most ~*~~ characteristic is the 02H5 bond length of the water molecule. It remains practically unchanged vs the reaction coordinate (the OlHl bond length) up to a certain point. When the hydrogen atom (HI) becomes almost equally distant from both heavy
J. Phys. Chem., Vol. 99, No. 39, 1995 14283
H-Bonded Complex of 2-Pyrimidinone with Water distance changes atoms (R(OIH1) * R(02H1) 1.3 A), the OZHS abruptly and, simultaneously, the 02H1 and the NlH5 distances shorten and new chemical bonds are formed. Both the 02H1 and the NlH5 distances remain practically constant for the farther stretches of the reaction coordinate. The hydrogen jumping (PT reaction) is accompanied by a significant decrease of the distance between the participating molecules of the complex at the transient point. This is visualized as a dip in the curves representing the variation of the distance of the oxygen atom of water from oxygen (01) and nitrogen (NI) atoms of 2PMD. The decrease of the distance between the heavy atoms accompanying the PT process contributes to lowering of the barrier for the PT reaction. The other intramolecular coordinates do not show any drastic changes along the reaction path. The mechanism of the double-PT reaction in the hydrogenbonded molecular complex of 2PMD with water is apparently very similar as found previously for the PT reaction in the hydrogen-bonded complexes of cytosine with water?’ with HNO>4 and for the intramolecular single-PT proce~s.’~In all cases vibrational motion of the “mobile” hydrogen atom along the PT A-H- *Breaction coordinate is accompanied by relative motion of the A atom toward the B atom. This shortens the distance for the proton migration and, in effect, significantly reduces the energy barrier for the reaction. Qualitatively, the same mechanism of the PT reaction operates in the excited electronic states. This is illustrated in Figure 4 for the nn* singlet state PE surface. The PE functions obtained from the optimization procedure along the PT reaction coordinate represent a rather crude estimation since simple levels of theory (HF or CIS approximations) with relatively small basis set (3-21G) were employed. In order to obtain more quantitative information on the PE functions for the considered systems, we performed energy calculations at the HF/3-21G and CIS/3-21G optimized geometries with the use of more sophisticated methods. The CASPT2/DZV* * energies calculated at the equilibrium geometries have already been discussed (Table 6). For the ground state, however, a relatively simpler method, the Moller-Plesset perturbation theory (MP2), can be applied since the electronic wave function of this state is dominated by a single determinant along the entire range of the PT reaction coordinate. In Figure 5 we present the ground state MP2 PE function calculated along the PT reaction coordinate of the 2PMD:Hfl complex. The D95G** double-zeta basis set with polarization functions implemented in GAUSSIAN92I7 was employed. This method gives results virtually identical to those obtained at the CASPT2/ DZV** approximation, as it is shown in Figure 5 . We should mention that the MP2/D95G** PE function of the ground state was calculated at the HF/3-21G geometries optimized with the C, symmetry constraints for the 2PMD:H20 complex. To verify the effect of the C, symmetry constrains on the energy, three geometrical points along the PT coordinate were recalculated at the molecular geometries optimized with full relaxation of all nuclear degrees of freedom. The considered geometries were the equilibrium geometries of both tautomeric forms and the transition structure between them. One sees, upon inspection of Figure 6, that full relaxation of molecular geometry has only minor effect on the PE function on the energy scale pertaining to this work. The MP2/D95G** energy calculated at the relaxed geometry is only by 720 and 200 cm-I for the hydroxy and the oxo forms, respectively, lower than the energies obtained with the same method at the C, optimized geometries. The net effect of geometry relaxation is a slight increase of the energy difference between the two tautomeric forms with preference of the hydroxy form. This also decreases the barrier for the
5.0
I
W
i
’.O
0.0
so
I
,.e-.. #e‘
~~
,
1
1.0 1.2 1.4 1.6 1.8 2.0 REACTION COORDINATE(Angstroms)
Figure 5. PE functions of the 2-pyrimidin0ne:water complex vs the PT reaction coordinate calculated with the MP2/D95G** method at
the HF/3-21G optimized geometry of the ground state (circles) and with the CASPT2/DZV** method at the CIS/3-21G optimized geometries of the ‘A’(m*) state (squares). The C, symmetry was imposed on the system in the calculations. The CASFT2/DZV** results for the ground state are denoted by triangles, and those obtained with the
PT reaction, but only by about 10%. Therefore, there is no need to change the conclusion that the barrier height (-0.5 eV) on the ground state PE surface is rather prohibitively high to allow any thermally induced PT reaction to occur effectively. There may be some doubts whether the transition point for the reaction determined in the minimum-energy path (MEP) approach represents the saddle-point for the process. In order to check this, we localized the saddle point for the PT reaction in the ground state of the 2PMD:H’O complex with the aid of the transition point search procedure (opt = ts option of GAUSSIAN92) at the HF/3-21G level of theory. The normalmode analysis performed at the transition structure found with this procedure gave only one imaginary vibrational frequency (o= 1662i cm-’) in which essentially only the motions of the “mobile” hydrogens were involved, confirming that the structure found represents the saddle point for the PT reaction. The transition structure can be characterized by describing the location of the “mobile” hydrogens with respect to the rest of (the reaction coorthe molecular frame. Thus, the OHhydroxy dinate) bond length has a value of 1.252 A, and NH = 1.313 A, and the hydrogens are separated from the water’s oxygen by the distances 1.174 and 1.183 A, respectively. These values fit well to the curves presented in Figure 3b and obtained with MEP approach. The HF/3-21G energy calculated at the saddle point, E = -411.2591 au, agrees very well with the height of the barrier on Figure 3a. We also recalculated the energy at the saddle point at the MP2/D95G** level of theory. The obtained value of the barrier for the PT reaction on the ground state PE surface of AE = 0.60 eV fits well with the maximum of the curve of Figure 4 obtained with the MEP approach. The above analysis provide justification for using the MEP approach in studying the reaction path of the PT reaction on the ground state PES. Therefore, it is reasonable to expect that the MEP approach facilitates also an adequate method to study the lowest excited state PE surfaces which are of interest in this work. The PE function of the A‘(nn*) excited singlet state calculated at the CASPT2/DZV** level of theory looks qualitatively very similar as that obtained for at the CIW3-21G level of theory (see Figure 4a). The barrier for the PT reaction (0.19 eV) is significantly smaller than in the ground state and the reaction is by 0.67 eV exothermic.
Sobolewski and Adamowicz
14284 J. Phys. Chem., Vol. 99,No. 39, 1995
Upon inspection of the results presented in Table 6 and in Figure 5 , we can conclude that the PT reaction in the 2PMD: HzO complex can be induced via optical excitation within the lowest absorption band. Our results suggest that the barrier for the PT reaction on the ‘A’(nn*) PE surface, if present, is below the energy of the vertical electronic excitation from the ground state. Let us notice that there is an obvious discontinuity in the PE function of the ground state calculated at the level of the MP2 approximation (Figure 5 ) . It seems to be an artifact of the perturbation approach since the PE calculated at the same points within the Hartree-Fock approximationis continuous (compare also Figure 3a).
3. Discussion of Results The ab initio calculations of PE functions, reported in this work, were performed with the intention of developing a better understanding of the possible photophysical behavior of 2-pyrimidinone. Among many possible photoreaction channels, we have focused our attention on the water-assisted double proton transfer reaction which can be responsible for production of the rare oxo tautomeric form. Turning our attention back to the PE functions presented in Figure 5, as well as in Figures 3 and 4, it is clear that the hydrogen-bonded complex of 2-pyrimidinone with water is rather stable with respect to the thermally induced F T reaction on the ground-state PE surface. The oxo form of the complex has only slightly higher energy on the ground-state PE surface, but its production via thermal heating of the hydroxy form seems to be prohibited by a relatively high banier (0.6 eV). However, this conclusion has to still be verified with a calculation at a higher level of theory with a more extended basis set. The situation is radially different in the first excited singlet state (A’(nn*)). Here the hydroxy form is protected against the PT reaction by relatively small barrier (-0.2 eV), and the oxo form is by about 0.67 eV more stable than the hydroxy form. The energy of the barrier on the ‘A‘(nn*) PE surface relative to the ground state of the hydroxy form (AE = 4.45 eV) is below the energy of the “vertical” excitation from the ground state (AI?= 4.67 eV). Thus, after an optical excitation the system has a large enough excess of energy for the PT reaction to occur in the first excited singlet state. Acknowledgment. This study was supported by grant from the Office of Health and Environmental Research of the Department of Energy (DEFG 0393ER61605) and by the grant from the Committee for Scientific Research of Poland (2 2395 92 03). L.A. thanks the Natural Science Research Council of Sweden for supporting his stay at the Theoretical Department, University of Lund. L.A. also thanks Prof. Bjom Roos for his hospitality.
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