J. Phys. Chem. A 2001, 105, 8241-8247
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MC/MO Study of the Solvent Effect on the Excitation Energies of the (CH3)2NO Radical in Hydrogen-Bonding and Non-Hydrogen-Bonding Solvents Toru Yagi, Kenji Morihashi, and Osamu Kikuchi* Department of Chemistry, UniVersity of Tsukuba, Tsukuba 305-8571, Japan ReceiVed: April 10, 2001; In Final Form: June 15, 2001
A combination of Monte Carlo (MC) simulation and ab initio molecular orbital (MO) calculation was applied to dimethyl nitroxide (DMNO) in H2O, CH3OH, CH3CN, and (CH3)2CO solutions, and the solvent effect on the electronic structure and n-π* and π-π* excitation energies was analyzed. The solution structures were generated by MC simulations, and the ROHF-SCI calculation with the MIDI-4 basis set was carried out for each solution structure. The electronic structure and excitation energies in the four solutions were obtained by averaging the 100 solution structures for each solution. Solvent effect was calculated by the point charge model and supermolecule model. In the point charge model, all solvent molecules were approximated by point charges at atomic nuclei, while in the supermolecule model the solute molecule and some of the solvent molecules were treated as a supermolecule surrounded by other solvent molecules approximated by point charges. The calculated n-π* excitation energy increased (blue shift) in the four solvents as compared to that in the gas phase. The magnitude of the solvent effect reflects the dielectric constant of the solvent. The calculated En-π* value in CH3OH was larger than that in CH3CN, whose dielectric constant is larger than that of CH3OH. This is due to the hydrogen-bonding ability of CH3OH and agrees well with experiment. The π-π* excitation energy was predicted to decrease in the four solvents, although the red shift was overestimated. The solvent effect was well elucidated by using the Mulliken charges of DMNO in the ground state and the excited states and the electrostatic potential generated by the solvent molecules.
I. Introduction Nitroxide radicals are very popular radicals in various research areas.1-24 ESR spectra of dimethyl nitroxide (DMNO), (CH3)2NO, have been observed in H2O and CHCl3;2,3 the hyperfine coupling constant (hfcc) of the N atom (aN) is larger in H2O than in CHCl3. Di-tert-butyl nitroxide (DTBN), ((CH3)3C)2NO, is a stable radical, and its aN value has been determined in various solvents.1,4,5,7-14 The aN value of DTBN is larger in polar solvents. The solvent effect on the excitation energies of nitroxide radicals has been reported since the mid-1960s.4,14,25-28 For dialkyl nitroxide radicals,4,14,26 the n-π* excitation energies were observed in many solvents and cover from 21 500 to 23 000 cm-1. For cyclic nitroxide radicals,25,27 the n-π* and π-π* excitation energies were observed in various solvents. The n-π* excitation energy shifts largely as in the case of the dialkyl nitroxide radicals. However, for the π-π* excitation energy, the shift by the solvent effect is small and does not show a clear tendency. The excitation energies of the H2NO radical were calculated first by Kikuchi6 and recently by Ricca et al.16,17 The π-π* excitation energy was overestimated to some extent in these studies. In many cases, the solvent effect on the electronic structure of the nitroxide radical was studied by ESR experiment.2-4,14,25 Symons et al. showed a high correlation between the n-π* excitation energy and aN and suggested that the solvent effects on these two quantities originated in the same cause.14 In our previous theoretical works,20-22 the hfcc’s of the N atom of DMNO were evaluated by using the MC/MO method, and the difference in the hydrogen-bonding or non-hydrogen-bonding solvents was reproduced well. However, there have been no
theoretical studies of the solvent effect on the excitation energies of DMNO. In this paper, the MC/MO combined method was applied to calculate the n-π* and π-π* excitation energies of DMNO in four solvents: H2O, CH3OH, CH3CN, and (CH3)2CO. The solution structures were generated by MC simulation, and the excitation energies were calculated by the ROHF-SCI/MIDI-4 method. The SCI method may not be sufficient to calculate quantitatively the excitation energies of free radicals. In this study, we were concerned with the effect of the solvent on the ground state and the SCI excited wave functions. The electronic structure of DMNO in these solutions and the solvent effect on the excitation energies were clarified. II. Methods of Calculation A. Monte Carlo Simulation. The C2V molecular structure was assumed for DMNO and optimized by ROHF/MIDI-4d calculation in vacuo, while experimental geometries were adopted for H2O, CH3OH, CH3CN, and (CH3)2CO.29 For the H2NO radical, a pyramidal structure has been calculated to be more stable than the planar one.30,31 However, the energy difference between the planar structure and pyramidal one is very small in aqueous solution.15 Moreover, the methyl groups in DMNO conjugate with the NO π group and the present assumption of the planar geometry of DMNO may be reasonable. MC simulations for the H2O, CH3OH, CH3CN, and (CH3)2CO solutions were carried out for the NPT ensembles according to the standard Metropolis method.32 Each solution included one DMNO molecule and 215 solvent molecules in a cubic cell, and the periodic boundary condition was employed. A cutoff
10.1021/jp0113230 CCC: $20.00 © 2001 American Chemical Society Published on Web 08/09/2001
8242 J. Phys. Chem. A, Vol. 105, No. 35, 2001
Yagi et al.
length for the potential was half of an edge of the cubic cell. The system pressure was set at 1 atm and the temperature at 298 K. The Owicki-Scheraga-Jorgensen preferential sampling technique33-35 was employed. Each simulation covered at least 2000K steps for equilibration, followed by additional 3000K steps for averaging. MC simulations were carried out using the SIMPLS program coded for the present purposes. B. Point Charge Model and Supermolecule Model. After establishing equilibrium for the solution structure in the MC simulation, the solution structures were picked up and the solvent molecules were treated in two ways as described below. One is a point charge model and the other is a supermolecule model. In the point charge model, solvent molecules located inside the cutoff length from the solute molecule were represented by point charges; the magnitudes of the point charges were the same as those used in the potential functions for the MC simulation. In the supermolecule model, some of the solvent molecules close to the solute molecule were selected and treated explicitly as a supermolecule together with the solute molecule. Thus the ab initio MO calculation was carried out for the supermolecule including one DMNO and the selected solvent molecules which was surrounded by other solvent molecules approximated by point charges. The H2O molecules included in the supermolecule were selected in the order of the distance parameter, R ˜ AB, defined between the sites of the solute and solvent molecules:
R ˜ AB )
RAB r A + rB
(1)
where rA and rB are van der Waals radii of sites A and B, respectively, and RAB is the distance between these sites. In this selection, the H2O molecules distribute around the DMNO uniformly. C. Calculation of Excitation Energies. The following Hamiltonian was used for the MO calculation:
H ˆ )
( ) () 1
∑k - 2∇k2
+
1
∑ k
