I.V. Rostov

Studies of the ground and excited-state surfaces of the retinal chromophore using CAM-B3LYP

The isomerization of the 11-cis isomer (PSB11) of the retinal chromophore to its all-trans isomer (PSBT) is examined. Optimized structures on both the ground state and the excited state are calculated, and the dependence on torsional angles in the carbon chain is investigated. Time-dependent density functional theory is used to produce excitation energies and the excited-state surface. To avoid problems with the description of excited states that can arise with standard DFT methods, the CAM-B3LYP functional was used. Comparing CAM-B3LYP with B3LYP results indicates that the former is significantly more accurate, as a consequence of which detailed cross sections of the retinal excited-state surface are obtained.

A frequency-resolved cavity model (FRCM) for treating equilibrium and non-equilibrium solvation energies: 2: Evaluation of solvent reorganization energies

Abstract The frequency-resolved cavity model (FRCM), a generalized continuum reaction field model, which allows for distinct effective solute cavities pertaining to optical (op) and inertial (in) solvent response, has been implemented and applied to the evaluation of solvent reorganization energy ( E s ) for a number of intramolecular electron transfer (ET) processes in polar media. Specifically, effective radii are defined for the solute atoms: r ∞ = κ · r vdW (where κ is taken as a universal scale factor) and r in = r ∞ + δ (where δ is specific to a particular solvent). Optimal values of κ and δ are determined through the use of solvation free energy data for small atomic and molecular ions, together with the experimental estimates of solvation reorganization energy ( E s ) for intramolecular ET in the steroid-based radical ions studied by Closs, Miller and co-workers [G.L. Closs, L.T. Calcaterra, N.J. Green, K.W. Penfield, J.R. Miller, J. Phys. Chem. 90 (1986) 3673; M.D. Johnson, J.R. Miller, N.S. Green, G.L. Closs, J. Phys. Chem. 93 (1989) 1173; J.R. Miller, B.P. Paulson, R. Bal, G.L. Closs, J. Phys. Chem. 99 (1995) 6923]. With these optimal parameters, E s is then evaluated for a number of other intramolecular ET processes, yielding results which are in generally good agreement with experimentally based estimates, and which give support for some of the assumptions employed in the analysis of the experimental data. Calculations with conventional solute atom radii ( r ∞ = r in , with κ =1.2 and δ =0) fitted to equilibrium solvation data yield E s values exceeding the FRCM results by factors of ≥2.

Quantum-chemical evaluation of energy quantities governing electron transfer kinetics: applications to intramolecular processes

Abstract Important energy quantities governing electron transfer (ET) kinetics in polar solutions (reorganization energy, Er, and net free energy change, ΔU) are evaluated on the basis of quantum-chemical self-consistent reaction-field (SCRF) models. Either self-consistent field (SCF) or configuration interaction (CI) wavefunctions are used for the solute, which occupies a molecular cavity of realistic shape in a dielectric continuum. A classical SCRF model together with unrestricted Hartree-Fock SCF wavefunctions based on the semiempirical PM3 Hamiltonian is applied to the calculation of the solvent portion of Er (denoted Es) for two different series of radical ion ET systems: radical cations and anions of biphenylyl/naphthyl donor/acceptor ( D A ) pairs linked by cyclohexane-based spacer groups and trans-staggered radical anions of the type (CH2)2m, m = 2–5. Results for Es based on two-configurational CI wavefunctions and an alternative reaction field (the so-called Born-Oppenheimer model, which recognizes the fast timescales of solvent electrons relative to those involved in ET) are also noted. Results for inner-sphere (i.e. intra-solute) reorganization, Ei, and for ΔU are also reported. The semiempirical Es results are quite similar to corresponding ab initio results and display the form of the two-sphere Marcus model for Es as a function of D A separation. Nevertheless, in the one case where direct comparison is possible, the calculated Es result is more than twice the magnitude of the estimate based on experimental ET kinetic data. To reconcile this situation, a generalized SCRF model is proposed, which assigns different effective solute cavity sizes to the optical and inertial components of the solvent response, using ideas based on non-local solvation models.

Comparing long-range corrected functionals in the cis–trans isomerisation of the retinal chromophore

Earlier results for the 11-cis to all-trans isomerisation of the retinal chromophore after photoexcitation, studied using time-dependent density functional theory with the hybrid CAM-B3LYP functional, are compared with new results using other long-range corrected DFT functionals. The TDDFT S0 and S1 minimum energy paths have been compared with the approximate coupled-cluster method RI-CC2. All calculations were consistent in producing an additional avoided crossing minimum on the S 1 minimum energy path lying approximately halfway between the 11-cis and all-trans S1 minima. In this minimum on the S1 potential energy surface, the retinal chromophore has inverted bond order in its carbon chain and lower energy than it has in both the 11-cis and all-trans S1 minima.

Calculation of a Complete Enzymic Reaction Surface: Reaction and Activation Free Energies for Hydride-Ion Transfer in Dihydrofolate Reductase.

We present a two-dimensional grid method for the calculation of complete free-energy surfaces for enzyme reactions using a hybrid quantum mechanical/molecular mechanical (QM/MM) potential within the semiempirical (PM3) QM approximation. This implementation is novel in that parallel processing with multiple trajectories (replica-exchange molecular dynamics simulations) is used to sample configuration space. The free energies at each grid point are computed using the thermodynamic integration formalism. From the free-energy surface, the minimum free-energy pathway for the reaction can be defined, and the computed activation and reaction energies can be compared with experimental values. We illustrate its use in a study of the hydride-transfer step in the reduction of dihydrofolate to tetrahydrofolate catalyzed by Escherichia coli dihydrofolate reductase with bound nicotinamide adenine dinucleotide phosphate cofactor. We investigated the effects of changing the QM region, ionization state of the conserved active-site Asp27 residue, and polarization contributions to the activation and reaction free energy. The results clearly show the necessity for including the complete substrate and cofactor molecules in the QM region, and the importance of the overall protein (MM) electrostatic environment in determining the free energy of the transition state (TS) and products relative to reactants. For the model with ionized Asp27, its inclusion in the QM region is essential. We found that the reported [Garcia-Viloca, M.; Truhlar, D. G.; Gao, J. J. Mol. Biol. 2003, 327, 549] stabilization of the TS due to polarization is an artifact that can be attributed to truncation of the electrostatic interactions between the QM and MM atoms. For neutral (protonated) Asp27, our calculated reaction free energy of -4 ± 2 kcal/mol agrees well with the experimental value of -4.4 kcal/mol, although the corresponding activation free-energy estimate is still high at 21 ± 2 kcal/mol compared with the experimental value of 13.4 kcal/mol. The results are less supportive of the ionized Asp27 model, which gives rise to a much higher activation barrier and favors the reverse reaction.

A two-dimensional Born–Oppenheimer treatment of intramolecular electron transfer reactions

Abstract The Born–Oppenheimer (BO) formulation of polar solvation is developed and implemented at the semiemperical (PM3) configuration interaction (CI) level, yielding estimates of electron transfer (ET) coupling elements ( V 0 ) for intramolecular ET in several families of radical ion systems. In contrast to the traditional treatment based on a single solvent coordinate and a fixed gas-phase coupling element, the present treatment yields a self-consistent characterization of kinetic parameters in a 2-dimensional solvent framework which includes an exchange coordinate. The dependence of V 0 on inertial solvent contributions and on donor/acceptor separation ( r DA ) is discussed.

Semiempirical modeling free energy surfaces for proton transfer in polar aprotic solvents

Abstract A method of calculation of a free-energy surface (FES) of the proton transfer (PT) reaction in a polar aprotic solvent is developed. This is based on the two-state (valence bond) VB description of the solute combined with recent continuum medium models. Its essential new feature is an explicit quantum-chemical treatment of VB wave functions, including internal electronic structure of a chemical subsystem. The FES includes a pair of intrasolute coordinates, R, the distance between hydrogen-bonded atoms and s, the proton coordinate, together with the collective medium polarization mode. Two hydrogen-bonded systems immersed in a polar solvent (Freon) were considered. The first one is the H5O2+ ion, a model system which was used as a benchmark testifying the validity of our semiempirical calculations. The second system is the neutral (CN)(CH3)N–H⋯N(CH3)3 complex in Freon. PT for this system has been studied experimentally. The dependencies of basic parameters controlling FES properties (the overlap integral, the coupling matrix element and the reorganization energy Er) on intrasolute coordinates R and s are evaluated and discussed. In particular, for the neutral complex, Er depends on s linearly, and its dependence on R is weak. The FES, for the neutral system, has two potential wells separated by the energy barrier of ∼7 kcal/mol. Quantum-mechanical averaging over the proton coordinate, s, reduces the barrier from 7.0 to 1.2 kcal/mol. The value of the nonadiabatic parameter on the averaged FES is equal to 0.13. This implies that the PT in the second system corresponds to an intermediate dynamic regime and that proton tunneling effects are hardly significant for this reaction.

Advanced dielectric continuum models of solvation, their connection to microscopic solvent models, and application to electron transfer reactions

Some recent advances in dielectric continuum models for static and dynamic aspects of molecular solvation are discussed, and connections with molecular-level solvent models are noted. The traditional Born-Onsager-Kirkwood (BKO) model is compared to a more flexible model (the so-called frequency-resolved cavity model (FRCM)) which assigns distinct inner and outer solute cavities in accommodating, respectively, the inertialess (optical) and inertial solvent response. Sample calculations of solvent reorganization energy (λs) are presented for various thermal and optical electron transfer (ET) processes, based on self-consistent reaction field models using molecular orbital (MO) or configuration interaction (CI) solvent wave functions.

A correlated ab initio quantum chemical study of the interaction of the Na+, Mg2+, Ca2+ and Zn2+ ions with the tautomers of cytosine in the presence of polar solvent.

The interactions of the metal ions Na(+), Mg(2+), Ca(2+) and Zn(2+) with cytosine have been investigated with inclusion of solvent effects. Computations have been performed at the density functional and Møller-Plesset levels of theory within the IEFPCM solvent model. It has been found that the inclusion of the solvent environment is essential for giving more biologically realistic results. Earlier gas-phase findings of the stabilisation of rare tautomeric forms by the metal ions have been reproduced, with the presence of the solvent further affecting the relative stabilities.

Erratum to “A two-dimensional Born–Oppenheimer treatment of intramolecular electron transfer reactions”: [Journal of Electroanalytical Chemistry 450 (1998) 69–82]

On p. 71, the expression for p in Eq. (8) should read p=2[C2]. On p. 72, Eq. (18) should read s=2 V0 /Es. On p. 73, Eqs. (30) and (31), the symbol d should be replaced by b. On p. 74, Eq. (38) should read la(a−2m)−2mnl sign V+ (a−m)−n=0. On p. 76, right-hand column, line 2 from bottom, the phrase ‘functions Qn ’ should read ‘functions Q9n ’. On p. 80, the third column of numbers in Table 4 (DU) should be replaced by the following entries: 0.0092, 0.013, 0.014, 0.024, 0.031, 0.035.