J. Phys. Chem. 1996, 100, 9561-9567
9561
Solvent Effects on Molecular and Ionic Spectra. VIII. The 1(n,π*) Excited States of Pyridazine in Water J. Zeng,† N. S. Hush,†,‡ and J. R. Reimers*,† School of Chemistry, UniVersity of Sydney, NSW 2006, Australia, and Department of Biochemistry, UniVersity of Sydney, NSW 2006, Australia ReceiVed: January 19, 1996; In Final Form: March 14, 1996X
Our method (parts I-VII) for estimating solvent shifts of species that have strong specific interactions (e.g., hydrogen bonding) with the solvent is applied to calculate the absorption and fluorescence solvatochromic (solvent) shifts of dilute pyridazine in water. The interpretation of the spectroscopy of pyridazine is complicated by the possibility that the S1 state is nearly degenerate with one or more other electronic states. We evaluate solvent shifts for all possible low-lying states and conclude that if near degeneracies do indeed occur, then considerable, nonobserved changes in the absorption band shape would be expected with solvent variation. This lends strong support to the arguments suggesting that S2 is somewhat removed from S1. Only orthodox linear hydrogen bonding to the ground state is found to be consistent with observed solvent shifts; hydrogen bonding to the excited states of pyridazine is shown to be relatively weak, and the generally accepted interpretations of the solvent shifts of pyridazine are explicitly verified from a molecular point of view. This completes our detailed molecular analysis of the solvent shifts of the diazines in dilute solution.
I. Introduction We have developed a method for studying specific solvation effects of solvents on chromophores. Here, it is applied to a dilute aqueous solution of pyridazine (1,2-diazabenzene, Figure 1), completing a series of studies of pyridine1 and the diazines.2-5 We have also applied this method to look at charge-transfer transitions in aqueous solutions of inorganic complexes.6-8 Basically, the method proceeds via two independent stages. First, liquid simulations are performed in order to produce an ensemble of configurations representing the equilibrium structure of the fluid around the chromophore. Second, the liquid structure is taken and changes to the vertical excitation energy calculated by considering the solvent-solute electronic interactions. It is appropriate for use in situations in which strong solvent-solute interactions (such as hydrogen bonding) occur. In this case, simpler methods that treat the solvent implicitly using reaction-field technology (see, e.g.,refs 9-11) are inappropriate (see, e.g., refs 12-15). Other methods related4,5 to ours have also been developed.16,17 In principle, any viable scheme can be used for the first step, the generation of the liquid structure. We adopt2 Kollman’s scheme18-20 for the generation of intermolecular pair potentials and use these in a Monte Carlo simulation of the fluid. Although this method is intended for calculations of interaction potentials between molecules in their ground electronic states only, we have found1,3-5 that it can also be applied to describe the interactions between molecules in different electronic states. The potential contains two parts, atom-type-based interatomic Lennard-Jones interactions and molecule-specific electrostatic interactions. In the standard form, the electrostatic component of the potential is parametrized in terms of ab initio selfconsistent field (SCF) atomic point charges determined by fitting the ab initio molecular electrostatic potential (ESP). We use this form and a modified form in which atomic point charges and dipoles are used, as well as some nonatomic point charges and dipoles. The advantage of the revised scheme is that it †
School of Chemistry. Department of Biochemistry. X Abstract published in AdVance ACS Abstracts, May 1, 1996. ‡
S0022-3654(96)00175-X CCC: $12.00
Figure 1. Geometry of pyridazine62,78 in terms of the molecular inplane long (L) and short (S) axis.
provides a significantly improved description of the ab initio data. This is most noticeable around the hydrogen-bond-forming regions near the azine nitrogen atoms, and an improved shape of the hydrogen-bonding potential is obtained. Unfortunately, the Lennard-Jones parameters used in Kollman’s scheme are not optimized for this type of charge distribution, and as a result intermolecular potentials obtained in this fashion always overestimate the hydrogen-bond strength. In general, it appears that the original scheme provides the most realistic solvent structures, but in specific cases for molecules whose ESP is not adequately described using only charges, the revised scheme may be more appropriate. By use of the intermolecular pair potentials, it is also possible to make predictions concerning the structure and dynamics of van der Waals clusters of the solute and solvent molecules. These have been useful for qualitatively interpreting the results of liquid simulations and also for aid in the interpretation of experimental cluster data.4,5 For pyrazine,5 they provide unambiguous characterization of the nature of the first 1(n,π*) excited state. Fully quantitative accuracy is not expected, since the pair potentials are designed to model condensed phases and include implicitly many-body polarizability contributions. As a result, in particular, the cluster well depth is expected to be overestimated. Once liquid configurations are obtained, the change in the electronic absorption band center is evaluated using our method,4 which considers in detail the electrostatic interactions between the solvent and solute in its ground state and in its vertically excited state. The basic principles of this process were elucidated by Bayliss,21 McRae,22 and others, culminating in the work of Liptay.23,24 In these studies, however, the solvent © 1996 American Chemical Society
9562 J. Phys. Chem., Vol. 100, No. 22, 1996 is treated simply as a dielectric continuum. We model the electrostatic interactions using gas-phase solvent and solute charge distributions, allowing each molecule to be individually polarized. Note that we do not include contributions to the solvent shift arising from dispersion interactions. Such contributions, typically on the order of 300 cm-1, dominate solvent shifts in nonpolar media. They are less important for aqueous solutions of azines for which the solvent shift is on the order of 3000 cm-1. Our model can, in principle, also include contributions to the solvent shift arising from charge transfer between the solvent and solute molecules,4 and indeed, calculated solvent shifts are very sensitive to this effect. Supramolecular calculations (see, e.g., refs 17 and 25-28), which evaluate the electronic structure of the solvent plus solute, offer the advantage over our method that effects such as this, as well as dispersion contributions, are automatically included. Use of crude electronic structure methods25,26,28 produces significant charge transfer, while sophisticated methods, feasible only for small clusters, predict little. On the basis of the experimental results available for azine-water clusters, we have argued4,8 that the most accurate treatment of solvent-solute charge transfer currently available is to set it to zero. Studies of the solvent shifts of azines in water were very important for elucidating the general properties of hydrogen bonds,12,29,30 and our calculations1,4,5 have verified explicitly the basic physical picture obtained while expanding on the nature of hydrogen bonds to electronically excited receptors. This study of pyridazine completes a series of studies on the diazines pyridazine, pyrimidine,4 and pyrazine.5 For the diazines, a key question concerning the electronic structure of (n,π*) excited states (and hence the geometric structure, spectroscopy, and dynamics of these states) is whether or not the excitation remains localized on one of the nitrogens or delocalizes across both of them. We have discussed the physical consequences of both possibilities in detail for the case of pyrazine,5 but basically in a delocalized excited state the nitrogens remain symmetrically equivalent, while in a localized excited state a distortion in a nontotally symmetric in-plane mode occurs, which makes the nitrogens inequivalent. The final structure is controlled by the strength of the interaction between the lone pairs (which favors delocalization), and the energy stabilization resulting from the distortion of the geometry around a depleted nitrogen atom (which favors localization). Before the effects of through-bond31 interactions were known, it was felt32,33 that the lone-pair interactions would be weak in pyrazine, intermediate in pyrimidine, and strong in pyridazine. From this comes the notion that pyrazine’s (n,π*) excited states should break symmetry while pyridazine’s should not. Although through-bond interactions are now well established, remnants of the old thinking remain, with, for example, many authors considering the possibility of symmetry breaking in pyrazine,8,34 but none till the recent work by Fischer and Wormell35 have considered it in pyridazine. Experimentally, the observed36-38 photoelectron spectra of the diazines indicate similar n-orbital splittings of about 2 eV, and since the localization tendency is a local atomic property, dramatic differences between the diazines in terms of their stability to localizing distortions are not expected: for pyrimidine and pyrazine, the final result for these molecules (delocalized structures) arises as a fine balance between the competing forces, and a fine balance is also expected here for pyridazine. The interpretation of key features in the electronic absorption spectrum remains unclear. S1, the lowest allowed singlet excited state, is known39 to be of 1(n,π*) type. In this, the two nitrogen atoms remain equivalent and the electronic wave function has
Zeng et al. B1 symmetry. In orbital terms, this state arises38 from an excitation from the highest-lying lone pair orbital n- (the antisymmetric combination of the two atomic orbitals) to the lowest-lying π*-orbital. This state must be partnered by a (forbidden) state of A2 symmetry arising from a transition from the n+-orbital (symmetric combination of the two atomic orbitals) to the same π*-orbital, and the two states must form a conical intersection at some point in their coordinate space. If, as is the case in pyrimidine and pyrazine, the tendency to delocalize just overcomes the tendency to localize, then there will be strong vibronic coupling between these states through modes of b2 symmetry. For pyridazine, the scenario is more complicated than those for pyrimidine and pyrazine, since transitions to the second-lowest π*-orbital are of similar energy. Hence, there are four low-lying 1(n,π*) states, two of B1 symmetry and two of A2. Difficulties in the assignment of the observed spectra of pyridazine start40 at a vibronic level of overall B1 symmetry located 373 cm-1 above the S1 origin. Ransom and Innes considered40 a variety of options for this level and concluded that it is in fact the origin of the second B1 electronic state. Other evidence supporting this assignment has also been found.41 However, all serious calculations, from the original CNDO results42 to the most sophisticated ab initio calculations,35,38,43,44 place the second B1 state very much higher in energy, and the original assignment appears untenable. These calculations place one of the A2 states (n- to second π*) at sufficiently low energy such that the observed band could be a vibronic origin (b2 vibration) of this state. Evidence suggesting45 that it indeed does contain significant character from another electronic state comes from the photochemistry of pyridazine S1: decomposition occurs with an activation energy of 373 cm-1. The quantum yield for this process when excited by high-energy radiation is quite low (0.1 at 383 K, excess energy of 700-800 cm-1).46 However, if this level is a vibronic level of an A2 state, then the origin of this state would be expected to be below that of S1, and hence, high quantum yields for dissociation would be expected. Finally, as argued by Ranson and Innes,40 this band is unlikely to be a vibronic level of an A2 state, since the associated transitions in fluorescence following a single vibronic excitation are not apparent.47 An alternative possibility for the S1 origin + 373 cm-1 band is that it corresponds to a vibration of a1 symmetry based on the S1 origin. Ransom and Innes40 originally considered this possibility but eliminated it on the grounds that no feasible vibrational mode could be found. This possibility has, however, received strong support by Wanna and Bernstein48 who examined high-resolution spectra of a variety of pyridazine clusters. They found that this level always followed the S1 origin, whereas if it belonged to a different excited state, then the two states would be expected to solvate differently, and hence, large variations in the relative band positions would be expected. Similarly, relatively small shifts are observed in cyclohexane and benzene crystals39 compared to the shifts of the S1 origin, a scenario strongly suggesting that the 373 cm-1 band is a strongly coupled vibronic level of S1. Finally, a low-frequency band just 225 cm-1 above the 0-0 line of the corresponding B1 (n,π*) triplet state is observed49 in the pyridazine crystal, and in this case the 3(n,π*) state is known to be well removed from other electronic states.39,50,51 These observations suggest that vibrational modes not investigated by Ransom and Innes should be considered. On the basis of the close analogy expected between the diazines, a possibility is that the 373 cm-1 band arises from two-quanta absorption in the b2 mode 6b. This mode is of the
Pyridazine in Water correct symmetry to couple S1 to the presumably nearby A2 state and has the effect of localizing the (n,π*) excitation on one of the two nitrogens. Large vibronic coupling involving this mode could thus be envisaged, and a large reduction of its frequency below that of 630 cm-1 observed39 in the ground state could occur. Indeed, the CIS calculations of Fischer and Wormell35 predict that this band reduces to 317 cm-1, and since bands of this type are highly sensitive to electron correlation, have anharmonic potentials, and involve considerable nonadiabatic effects, a further reduction of the frequency such that 2ν6b ) 373 cm-1 is conceivable. If this assignment is correct, then simplistic Franck-Condon analysis indicates that a strong line is expected in the single-vibronic-level (SVL) fluorescence spectrum41,47 at twice the ground state frequency of ν6b, i.e., twice 630 cm-1 (ref 39). But there is no evidence of such a line. The calculations of Fischer and Wormell35 also suggest the possibility that the 373 cm-1 line could originate from twoquanta absorption in the a2 mode 16a. They found that, at the CIS level, this mode had a shallow double-minimum potential. Again, the expected line at 2 × 410 cm-1 is not found in the SVL spectrum.41 The clearest feature in the SVL data is ν6a, but the SVL intensities41 are extremely non-Franck-Condon. The extent to which Franck-Condon analysis is applicable to pyridazine is unclear. Clearly, further experiments and highlevel calculations are required in order to interpret the 1(n,π*) absorption of pyridazine. In particular, independent confirmation of the symmetry of the 373 cm-1 band is required, the original40 assignment of B1 being obtained from low-resolution rotational contour analysis, the accuracy of which has been questioned5 for pyrazine. Here, we attempt to interpret the observed12 solvent shifts of pyridazine absorption and fluorescence in dilute aqueous solution. Since the identity of the excited state(s) is not completely known, we consider the solvent shifts of the lowest two B1 states and the lowest A2 state. We consider the nature of hydrogen bonding to the ground and excited states and consider also the properties of the pyridazine-water cluster. 2. Calculation Methods (a) Solvent Shift Evaluation. The method used to evaluate the solvent shift at the center of the pyridazine 1(n,π*) absorption and fluorescence bands is described in detail elsewhere.4 It requires as data sample liquid configurations as well as a representation of the solute’s initial and final state electrostatic potentials and polarizabilities. These are evaluated as described below. (b) Liquid Simulations. Full details of the simulation techniques used, including error analysis methods, are given elsewhere. Briefly, convergence-accelerated2,52 rigid-molecule constant number, temperature, and pressure (NPT ensemble53) Monte Carlo54,55 calculations2,3 are performed at T) 298 K and P ) 1 atm for a sample containing one pyridazine molecule and 102 water molecules. Periodic truncated octahedral boundary conditions56-58 are used, and these provide many advantages.2 Equilibration is performed for at least 107 moves, considerably longer than the longest relaxation “times” found in such systems,2 and a total of 4 × 107 configurations are generated. Error bars quoted are 1 - σ and based on analysis subsamples of size (2-10) × 106. Every 200th configuration is analyzed in order to determine the radial distribution functions, and every 4000th configuration is subsequently analyzed to determine the solvent shift. Pairwise additive intermolecular potentials are constructed using Kollman’s (second) function form,18 which specifies the TIP3P59 water-water potential and includes contributions from both Lennard-Jones and Coulomb
J. Phys. Chem., Vol. 100, No. 22, 1996 9563 TABLE 1: Cartesian Coordinates,62,78 in Å, in Terms of the Molecular Long (L), Short (S), and Normal (N) Axes for the N, C, and H Atoms of Pyridazine as Well as for an Additional Point Charge X that are Used in Individual Potentials potential all
11A1/X 11B1/X 11A2/X 21B1/X
atom
N
S
L
N1,2 C3,6 C4,5 H7,10 H8,9 X11-X14 X15-X18 X11-X14 X15-X18 X11-X14 X15-X18 X11-X14 X15-X18
0 0 0 0 0 (.0225 (.0914 (.0427 (.0211 (.0439 (.0089 (.3842 (.3760
-1.1842 -.0159 1.2291 -.1618 2.1614 2.1100 -.0793 .8639 -.6538 .7732 -.8385 1.4223 -.2093
(.6660 (1.3243 (.6927 (2.4035 (1.2397 (1.1127 (1.6371 (.8362 (1.5958 (.9075 (1.4965 (.4855 (1.8827
TABLE 2: Atomic Charges, in e, Used in Each Potential atom
11A1
11A1/X
11B1
11B1/X
11A2/X
21B1/X
N1,2 C3,6 C4,5 H7,10 H8,9 X11-X14 X15-X18
-.3280 .3763 -.2475 .0259 .1732
-.3280 .3763 -.2475 .0258 .1732 .0100 -.0099
-.1135 .0480 -.2506 .1339 .1823
-.1136 .0479 -.2507 .1338 .1822 .1954 -.1952
-.1669 .1109 -.2680 .1480 .1756 .1811 -.1809
-.0916 .0264 -.2078 .1090 .1637 .0417 -.0415
interactions. For the Lennard-Jones contributions, we use the same parameter set as described previously.2 The Coulombic part of Kollman’s intermolecular potential is specified to be the interaction between the TIP3P water charges and (electronic-state dependent) atomic pyrazine charges. These are usually determined by fitting2 the SCF ab initio electrostatic-potential (ESP) obtained using the double-ζ plus polarization60 (DZP) basis set. Indeed, we generate atomic charges in this fashion for the ground state and lowest B1 state. These potentials are named 11A1 and 11B1, respectively. We also generate improved potential functions with improved fits to the ESP, and these are called 11A1/X and 11B1/X, respectively. Using the same approach, we also determine potentials named 11A2/X and 21B1/X for the A2 and second B1 state, respectively, and a total of six simulations are run. (c) Gas-Phase Electronic Structure. Molecular charge distributions are evaluated ab initio using a double-ζ plus polarization basis set60 via HONDO61 at the observed62 groundstate equilibrium geometry shown in Table 1 and Figure 1. Provided that no localizing distortion of the excited states occur, we have found that the calculated solvent shifts are reasonably insensitive to the details of the geometries used in the calculations (optimized excited-state geometries have been determined by Fischer and Wormell35 at the CIS level of theory). In accord with the specifications of the intermolecular potential surface used, most calculations are performed at the SCF level. However, this is not feasible for 21B2, and for this we employ a small complete-active-space SCF calculation (CASSCF). The calculated ESP atomic charge distributions, evaluated as before,4 are shown in Table 2 for the 11A1 and 11B1 potentials. All the remaining potentials contain atomic point dipole contributions on each nitrogen atom (these allow the large contributions to the molecular dipole moment from local s-p hybridization to be explicitly included) and two symmetry-related sets of floating point charges and dipoles, named X11-X14 and X15-X18, to model the π-ring charge density. The coordinates used and point charges and dipoles fitted are shown in Tables 1, 2, and 3, respectively. For each electronic state considered, available experimental
9564 J. Phys. Chem., Vol. 100, No. 22, 1996
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TABLE 3: Atomic Point Dipoles, in Debye, Used in Various Potentials atom
N 1A
1 N1,2 X11-X14 X15-X18
0 -1.0244 -2.5072
N1,2 X11-X14 X15-X18
0 -13.9232 (.7581
N1,2 X11-X14 X15-X18
0 -14.4260 (6.4043
N1,2 X11-X14 X15-X18
0 -.5928 -.5181
S
L
.7253 .0058 -.4439
-1.6795 -.0208 (.2086
-.0066 -1.0403 -.3660
-.4390 -.5691 (.5925
.0470 -1.0291 -.3763
-.9108 -.6270 (.6029
.2998 -.3117 -.1505
-.5527 -.2169 (.1211
1/X
11B1/X
11A2/X
21B1/X
TABLE 4: Resulting Root-Mean-Square Error, in kcal mol-1 e-1, of Fitting the ab Initio ESP Data to the Point Charge/Dipole Models, as Well as the Dipole Moment (in Debye) Calculated from the ESP Model (ESP), from the Full Electronic Wave Function (WF) and from CASPT2 Calculations44 µ / (debye) surface
ESP error
CASPT2
WF
ESP
1 1 A1 11A1/X 11B1 11B1/X 11A2/X 21B1/X
1.91 .23 1.17 .26 .29 .25
4.37a
4.43
1.59
1.95
1.97 1.74
2.21 1.87
4.30 4.43 1.90 1.96 2.21 1.87
a
79
Experimental value is 4.22 D.
dipole moments and those evaluated by Fu¨lscher et al.44 using a CASSCF calculation followed by a multireference secondorder perturbation-theory calculation (CASPT2) are compared with those obtained from our ab initio wave functions in Table 4. Also shown are the dipole moments obtained from the various fits to the ESP and the root-mean-square (rms) error in the fit. The comparison indicates that the charge distributions are reasonable. The deficiencies of the charge-only distribution for the ground state are apparent in Figure 2 in which contours of the molecular ESP are plotted as determined from the charge distributions and as determined from the ab initio wave function. Clearly, the charge-only potential 11A1 constricts the hydrogenbonding potential to be too steep in-plane and too shallow outof-plane. Note also that the SCF methodology appears to be more quantitatively reliable for pyridazine than for pyridine,1 pyrimidine,4 and especially pyrazine5 for which it predicts a qualitatively incorrect electronic structure. However, as is well known,38,43,44 care must be taken with this and related methods such as CIS. The solvent-shift calculations treat the solute as being polarizable, requiring as input the molecular polarizability of pyridazine in both its ground and excited states. We find that, for azines in water, the calculated solvent shift is insensitive to the solute polarizability, and for reasons of computational efficiency we calculate it using finite field CNDO/S-CI methods.42,63 The results are (RLL, RSS, RNN) ) (55, 55, 10) au for S0, the in-plane components being close to both the ab initio SCF results64 of (69, 69, 39) au and the observed results65 (assuming RLL ) RSS) of (65, 65, 39) au. For 11B1 the calculated polarizability is (80, 60, 10) au, for 11A2 it is (60, 70, 15) au, and for 21B1 it is (80, 80, 20) au.
Figure 2. Contours of the ground-state ESP for pyridazine in the NS and LS planes as evaluated from the ab initio wave function (WF) and the 11A1 and 11A1/X models. Contour levels are 0, (2, (4, (8, (16, and (32 kcal mol-1 e-1. They are drawn outside the shell at 1.4 × the molecular van der Waals radii, and - - - indicates the shell at ×2.5 inside which the model charges/dipoles are fitted. Distances are in angstroms from the center-of-mass.
TABLE 5: Properties of Pyridazine-H2O Clustersa surface 1A
1 1 11A1/X 11B1 11B1/X 11A2/X 21B1/X
EHB
Enon-HB
Ev
dynamics
-6.97 -9.18 none -3.75 -5.10 -3.16
-3.00 -3.15 -4.68 -3.59 -3.81 -3.16
-1.08 -1.23 -4.62 -2.08
dissoc chaotic periodic periodic
aE HB ) energy of isomer with hydrogen bond to nitrogen; Enon-HB ) energy of isomer with water above the π-plane; Ev ) vertical excitation energy from 11A1 or 11A1/X minimum, as appropriate. All energies are in kcal mol-1. A qualitative description of the FranckCondon excited-state dynamics is also shown.
3. Pyridazine-Water Clusters Results for pyridazine-H2O are shown in Table 5, obtained using the six effective pair potential functions. The groundstate charge-only surface 11A1 produces a hydrogen-bonded structure of Cs symmetry in which the water is located above the ring, with one hydrogen dropping down to provide a hydrogen bond with each of the (equivalent) nitrogen atoms; the H atom effectively bridges the two nitrogen atoms. Quite a different hydrogen-bonded structure is found for the groundstate charge + dipole surface 11A1/X, with the water molecule located in-plane with pyridazine, offering a linear O-H-N hydrogen bond to just one of the two nitrogens. The well depth of -9.18 kcal/mol is most assuredly too deep, but it appears to be a general feature that using the improved electrostatic description with Kollman’s standard functions improves the shape of the hydrogen-bonding well but overestimates its depth. Only the 11A1/X structure is consistent with the experimental results for diazine-water clusters in dilute aprotic solution.66 For the excited states, no stable hydrogen-bonded isomer is found for the charge-only surface 11B1, while the other three charge + dipole surfaces produce weak hydrogen bonds of standard shape to just one of the nitrogen atoms. Stable isomers for all surfaces are found in which the water molecule is located above the pyridazine ring, binding the aromatic π-cloud. As
Pyridazine in Water
J. Phys. Chem., Vol. 100, No. 22, 1996 9565
TABLE 6: Results from Liquid Simulationsd surface 1
1 A1 11A1/X obsd 11B1 11B1/X 11A2/X 21B1/X
∆H
∆V
coord no.
-16.1 -18.5 -14.9a -9.1 -9.6 -10.2 -8.3
70 65 70.4b 68 66 75 76
∼3 2.0 2c .5 .2 .8 .1
a Reference 71. b Reference 77. c Qualitative estimate. See reference 71 and text. d ∆H ) enthalpy of hydration, in kcal/mol, with an uncertainty of (2 kcal mol-1; ∆V ) partial specific volume, in cm3 mol-1, with an uncertainty of (6 cm3 mol-1. The number of N-H hydrogen bonds per pyridazine is also shown.
has been found for other azines,4,5 the strength of these interactions tends to increase slightly after excitation from the ground state, whereas the hydrogen-bond strength decreases significantly so that the two types of interactions become comparable in energy. Also shown in Table 5 are the vertical excitation energies from the appropriate ground-state hydrogen-bonded minimum to the excited states. These energies are all negative, and so the complexes are all bound in the excited state. Molecular dynamics trajectories starting in the Franck-Condon region show three distinct types of behavior: dissociative trajectories in which the hydrogen bond immediately breaks and isomerization occurs; chaotic trajectories that remain in the hydrogenbonding well for long times but have an energy actually exceeding the transition-state energy for isomerization; periodic trajectories in which simple harmonic motion occurs. All types of trajectories have been found for pyridazine-H2O as indicated in Table 1. In all cases, the simple periodic trajectories arise when the predicted ground- and excited-state hydrogen-bonded minima have very similar geometries. Qualitatively, we see that small changes in the potential surface can produce large changes in the excited-state dynamics and thus in the nature of the spectroscopy of the cluster. In experimental molecular-beam studies of pyridazine-H2O, Wanna and Bernstein48 failed to detect any signal, suggesting that the cluster in its S1 state either dissociates or isomerizes very rapidly, as predicted by the dynamics on our 11B1 surface. This negative result is somewhat open to question, since these authors made similar observations67 for pyrazine-H2O and pyrazine(H2O)2. Yet these clusters are known to be very stable in their excited states under matrix isolation.68 Qualitatively, the experimental scenario is similar to the predicted one in that stable excited-state hydrogen bonds have been found for some azines and not for others, and apparently, seemingly small changes can have large affects.4 4. Results for Pyridazine-Water Solution Results obtained for the structure and thermodynamics of water around pyridazine in its ground and excited electronic states are shown in Table 6, and pyridazine nitrogen or centerof-mass (CEN) to water hydrogen or oxygen radial distribution functions g(r) are shown in Figure 3. Both ground-state simulations 11A1 and 11A1/X produce distinct hydrogen-bonding peaks in gN-O(r) at around 2 Å, with corresponding peaks in gN-O(r) and gCEN-H(r). The charge + dipole potential 11A1/X produces the most sharply defined structure with one (different) hydrogen-bonded water attached to each nitrogen. For the point charge potential 11A1, as may be anticipated from its cluster properties, one water molecule is placed above and below pyridazine’s plane, with about three hydrogen atoms being
Figure 3. Radial distribution functions g(r) obtained from the six simulations for pyridazine nitrogen (N) and center-of-mass (CEN) to water oxygen (O) and hydrogen (H) atoms.
Figure 4. Contours of the probability of finding one of the closest two water molecules per configuration distances rO-N1 and rO-N2 away from pyridazine atoms N1 and N2, respectively, obtained from the 11A1 and 11A1/X liquid simulations.
simultaneously involved with hydrogen bonds to both nitrogen atoms. These differences are highlighted in Figure 4 in which probability contours are for the distances rO-N1 and rO-N2 of one of the two closest water molecules per configuration to the two nitrogen atoms, N1 and N2, respectively. For the simulations using 11A1, the contours center around the line rO-N1 ) rO-N2, while for 11A1/X a widespread or rO-N2 value occurs for each rO-N1 value and vice versa. Little trace of hydrogen-bonding to nitrogen atoms is evident in the results from the excited-state simulations, also shown in Table 6 and Figure 3, with perhaps the exception of 11A2/X for which the excited-state hydrogen-bond strength is the greatest (see Table 5). This result is in accord with experimental deductions12,39 but arises not because of the lack of a significant pro-hydrogen-bond interaction but rather because of a combination of the weakening of the hydrogen-bond strength and the increased strength of the competitive interactions with the
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TABLE 7: Calculated Solvent Shifts, in cm-1, Evaluated from a Given Set of Liquid Configurations Using Various Models for the Initial-State and Final-State Charge/Dipole Distributions liquid
initial
11A
11A
1
11A1 11A1/X 11A1/X 11B1 11B1/X 11A1/X 11A2/X 11A1/X 21B1/X a
1
11A1/X 1 1 A1 11A1/X 11B1/X 11B1/X 11A1/X 11A2/X 11A1/X 21B1/X
final
∆νa
11B1 11B1/X 11B1 11B1/X 11A1/X 11A1/X 11A2/X 11A1/X 21B1/X 11A1/X
2800 230 3000 4100 650 800 2900 600 3850 700
Observed12 3800 cm-1 absorption and 700 cm-1 fluorescence.
aromatic π-system. Similar results have been found for pyrimidine4 and pyrazine.5 Calculated absorption and fluorescence solvent shifts are shown in Table 7. In each case, a set of liquid configurations (ground-state for absorption, excited-state for fluorescence) are selected, and then each molecule is assigned a charge/dipole distribution in its ground and excited states, as well as a polarizability as previous described. For S1 absorption, the predicted solvent shift obtained using the 11A1 liquid configurations and the 11A1 and 11B1 charge distributions is 2800 cm-1. This is considerably less than the observed12 value of 3800 cm-1 (relative to isooctane, which is typically quite close to vapor results4). We have found that this procedure, for reasonably small solvent shifts such as this, is accurate to about 700 cm-1, and it is possible that this low value serves to further extend the error bar of this method. However, for other azines, the calculated solvent shift has been too large rather than too small.2,4,5 Alternatively, the solvent shift evaluated using the 11A1/X liquid structure and the 11A1/X and 11B1/X potentials is 4100 cm-1, slightly larger than the observed value. Although use of charge + dipole functions in general increases the magnitude of the blue shift, the increase here is much more pronounced and is attributed to the qualitative change in the hydrogen-bonding predicted by the 11A1 and 11A1/X potentials (see Figure 2). The calculated absorption solvent shifts for the 11A2 and 21B1 states are 2900 and 3850 cm-1, respectively. For 11A2, the calculated differential solvation difference compared to 11B1 is -1200 cm-1. This is much larger than the relative shifts observed in the S1 origin and +373 cm-1 lines in nonpolar aprotic solvents,41,48 and if about half the observed band intensity in the S1 region is associated with transitions to each state, then considerable nonobserved12 changes to the absorption band shape would result. Hence, it is difficult to envisage how the observed liquid solvent-dependence could be interpreted in terms of a picture in which 11A2 absorbs significantly in the region of 11B1. This finding significantly strengthens conclusions drawn by Wanna and Bernstein48 based on cluster-shift data and strongly questions the conclusions drawn from crystal-shift data by Ueda, Udagawa, and Ito.41 Studies of dilute pyridazine in a regular ice polymorph or studies of doubly dilute pyridazine with water in some other host may thus answer some of the outstanding questions concerning the role of the 11A2 state. For 21B1, the calculated solvent shift is very similar to that obtained for 11B1, and hence, the observed solution spectra could be consistent with these states being nearly degenerate. For fluorescence, calculated solvent shifts showed very little range, just 600-800 cm-1, all very close to the observed value12 of 700 cm-1. One possibility for pyridazine fluorescence, possible if the 11A2 state lies in the gas phase just above the
11B1 state, is that after solvation the 11A2 state becomes adiabatically the lowest singlet excited state. In this case, fluorescence would most likely originate from vibronic levels of 21B1, making fluorescence-solvent-shift data very difficult to interpret. Our results indicate that this is not likely to be the case, as indeed also indicated by the experimental observation that the band shape is not dramatically different in water than in other solvents.12 For pyridazine, the experimental observation alone is insufficient to establish this, however, since the standard diagnosis for the presence of a low-lying S2 state assumes that the S1 and S2 geometries are essentially identical.41 5. Conclusions Our liquid simulations raise the possibility of two different hydrogen-bonding arrangements in pyridazine, a result arising from the closeness of the two hydrogens and the steric strain associated with fitting two water molecules into a small volume. One structure, that produced by the 11A1/X potential, is orthodox with one linear hydrogen-bonded water attached to each nitrogen, while the other, that produced by the 11A1 potential, has a multitude of nitrogen-bridging hydrogen bonds. Although many experimental studies involving hydrogen-bonding to pyridazine have been made, none give sufficiently detailed microscopic structural information to unambiguously discriminate between these two options. In general, doubly dilute solutions of diazines with water66 and other69 proton donors in aprotic solutions form just one hydrogen bond per diazine, but two hydrogen bonds per diazine is typical for a dilute azine in a neat proton-donor liquid.70 Indeed, based on enthalpy of hydration (∆H) arguments,71 the diazines are believed to form two hydrogen bonds in aqueous solution. As shown in Table 6, this is more consistent with the results from the 11A1/X simulation than with those from 11A1. Furthermore, after (implicit or explicit) corrections are included for known72 differences such as the “R-effect”, there appears to be little difference73,74 among the hydrogen-bonding properties66,69,71,72,75-77 of pyridazine, pyrimidine, and pyrazine. Possible structures with nitrogen-bridging hydrogen-bonds have previously been considered75 and tentatively rejected based on this observation, and this conclusion is supported by recent extensive calculations.73 Here, we provide further support to the hypothesis that two linear hydrogen bonds to pyridazine are formed in dilute aqueous solution, since the observed 1(n,π*) solvent shift appears to be consistent only with this option. This is reinforced by the pyridazine-H2O cluster calculation, the nitrogen-bridged structure predicted by the 11A1 potential being inconsistent with experimental results in dilute aprotic solution.66 This study completes our analysis of the absorption and fluorescence solvent shifts of the diazines. Again, we see that the solvent structure, and in particular the details of the hydrogen bonding to the chromophore, plays a significant role in the determination of the solvent shift. Clearly, the liquid structure must be considered at a molecular level when specific solventsolute interactions occur. Our method for evaluating the solvent shifts contains various aspects such as the determination of the electronic structure of the isolated chromophore in its ground and excited electronic states, the realistic representation of the ESP emanating from the solute, the determination of solvent-solute effective pair potentials and, hence, liquid configurations, and the determination of an accurate n-body polarizable form of the intermolecular interactions. Although the procedures that we have implemented are usually sound, each step, for any particular chromophore, must be considered in detail to ensure that physically sensible results are obtained. Clearly, the develop-
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