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We derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the fourdimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes. [ABSTRACT FROM AUTHOR]

We analyze how the choice of the sampling weight affects efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. By contrast, it is shown that the computational cost of the 'standard' algorithm sampling from the phase-space density may scale exponentially with the number of degrees of freedom. Yet, for the stationary Gaussian distribution of harmonic systems and for the autocorrelation function of a linear function of phase-space coordinates, the computational cost of this standard algorithm is also independent of dimensionality. [ABSTRACT FROM AUTHOR]

We propose to measure nonadiabaticity of molecular quantum dynamics rigorously with the quantum fidelity between the Born-Oppenheimer and fully nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies in situations where other criteria, such as the energy gap criterion or the extent of population transfer, fail. We further propose to estimate this quantum fidelity efficiently with a generalization of the dephasing representation to multiple surfaces. Two variants of the multiple-surface dephasing representation (MSDR) are introduced, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics (LMFD). The LMFD can be interpreted as the Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used previously in the nonadiabatic semiclassical initial value representation. In addition to propagating an ensemble of classical trajectories, the MSDR requires evaluating nonadiabatic couplings and solving the Schrödinger (or more generally, the quantum Liouville-von Neumann) equation for a single discrete degree of freedom. The MSDR can be also used in the diabatic basis to measure the importance of the diabatic couplings. The method is tested on three model problems introduced by Tully and on a two-surface model of dissociation of NaI. [ABSTRACT FROM AUTHOR]

We propose an approximate method for evaluating the importance of non-Born–Oppenheimer effects on the quantum dynamics of nuclei. The method uses a generalization of the dephasing representation (DR) of quantum fidelity to several diabatic potential energy surfaces and its computational cost is the cost of dynamics of a classical phase space distribution. It can be implemented easily into any molecular dynamics program and also can utilize on-the-fly ab initio electronic structure information. We test the methodology on three model problems introduced by Tully and on the photodissociation of NaI. The results show that for dynamics close to the diabatic limit, the decay of fidelity due to nondiabatic effects is described accurately by the DR. In this regime, unlike the mixed quantum-classical methods such as surface hopping or Ehrenfest dynamics, the DR can capture more subtle quantum effects than the population transfer between potential energy surfaces. Hence we propose using the DR to estimate the dynamical importance of diabatic, spin-orbit, or other couplings between potential energy surfaces. The acquired information can help reduce the complexity of a studied system without affecting the accuracy of the quantum simulation. [ABSTRACT FROM AUTHOR]

We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantum-classical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with 'on-the-fly' computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH2NH2+ considering 20 electronic states and in the collision of F + H2 considering six electronic states. [ABSTRACT FROM AUTHOR]

A correction to the article "Path integral evaluation of equilibrium isotope effects," that was published in the July 28, 2009 issue is presented.

This work is focused on the computational studies of reactions of hydrated forms of cisplatin with sulphur-containing amino acids cysteine and methionine. First, the appropriate model for solvation of the examined complexes was searched for. The suggested procedure employs the B3LYP density functional, 6-311++G(2df,2pd) basis set with Stuttgart-Dresden pseudopotentials on heavy atoms, the D-PCM solvation model and the UAKS cavity which uses more realistic NPA partial charges instead of formal partial charges for platinum ligands. In the second part this model is applied to the evaluation of the Legendre transformed reaction Gibbs free energy of cisplatin with cysteine and methionine in solution at constant pH.

Interactions of hydrated cisplatin complexes cis-[Pt(NH(3))(2)Cl(H(2)O)](+) and cis-[Pt(NH(3))(2)(OH)(H(2)O)](+) with cysteine and methionine in an aqueous solution at constant pH were explored using computational methods. Thermodynamic parameters of considered reactions were studied in a broad pH range, taking up to 4 protonation states of each molecule into account. Reaction free energies at constant pH were obtained from standard Gibbs free energies using the Legendre transformation. Solvation free energies and pK(a) values were calculated using the PCM model with UAHF cavities, recently adapted by us for transition metal complexes. The root mean square error of pK(a) values on a set of model platinum complexes and amino acids was equal to 0.74. At pH 7, the transformed Gibbs free energies differ by up to 15 kcal mol(-1) from the Gibbs free energies of model reactions with a constant number of protons. As for cysteine, calculations confirmed a strong preference for kappaS monodenate bonding in a broad pH range. The most stable product of the second reaction step, which proceeds from monodentate to chelate complex, is the kappa(2)S,N coordinated chelate. The reaction with methionine is more complex. In the first step all three considered methionine donor atoms (N, S and O) are thermodynamically preferred products depending on the platinum complex and the pH. This is in accordance with the experimental observation of a pH dependent migration between N and S donor atoms in a chemically related system. The most stable chelates of platinum with methionine are kappa(2)S,N and kappa(2)N,O bonded complexes. The comparison of reaction free energies of both amino acids suggests, that the bidentate methionine ligand can be displaced even by the monodentate cysteine ligand under certain conditions.

The main aim of this study is the calculation of acid dissociation constants of the products of cisplatin reaction with the amino acids cysteine and methionine. In the first step, a suitable procedure for the calculation of solvation Gibbs free energies is found, based on the comparison of the calculated and experimental pK(a)s of both amino acids and simple platinum complexes. The resulting approach combines the DFT/B3LYP density functional, 6-311++G(2df,2pd) basis set, the D-PCM formulation of the continuum solvation model, and modified UAHF cavities. Since the main area of applicability of the UAHF model is solvation of organic molecules, a minor modification of the UAHF algorithm was necessary to improve the accuracy when applying it to the transition metal complexes. Instead of the integer (or semi-integer) formal charges used in the original formulation, more realistic partial charges obtained from the electronic density using the NPA procedure are used to generate molecular cavity. All other parameters of the model remain unchanged. This simple modification of the UAHF model works markedly better than the original formulation. The root mean square error of calculated pK(a)s over a set of molecules including zwitterions and divalent diaquaplatinum cation is equal to 0.74. In the second step, pK(a)s of platinum amino-acid complexes with the total charge ranging from 0e to 2e were computed. It was found that the pK(a)s of all ionizable groups of both amino acids are highly variable among the complexes studied. They range from -5 (in complexes containing protonated thiol or carboxyl groups directly bonded to platinum) to 14 (in monodentate complexes containing a positively charged amino group, which is stabilized by intramolecular hydrogen bonds).

In this paper we explore cisplatin interactions with sulfur-containing amino acids in a polarizable continuum model. Two cisplatin hydrated complexes were considered as reactants (chloro complex, cis-[Pt(NH3)2Cl(H2O)]+; hydroxo complex, cis-[Pt(NH3)2(OH)(H2O)]+). We considered the following reaction mechanism: first step, substitution of the aqua ligand by amino acid; second step, dissociative chelate formation. For the optimized complex (at the B3LYP/6-31+G(d)/COSMO level), the energy profile was determined using the B3LYP/6-311++G(2df,2pd) level and two different PCM models-COSMO and UAKS/DPCM methods which were adapted for use on transition metal complexes. The results show thermodynamic preference for bonding by cysteine sulfur followed by the amino group nitrogen, methionine thioether sulfur, and carboxyl-group oxygen. Methionine slightly prefers the Pt-N(Met) coordination in the chloro complex, but in the hydroxo complex it prefers the Pt-S(Met) coordination. A similar trend follows from the bonding energies: BE(Pt-S(Cys)) = 80.8 kcal/mol and BE(Pt-N(Met)) = 76 kcal/mol. According to the experimental observations, the most stable structures found are kappa2(S,N) chelates. In the case of methionine, the same thermodynamic stability is predicted also for the kappa2(N,O) chelate. This differs from the gas-phase results, where kappa2(S,N) and even kappa2(S,O) were found to be more stable than kappa2(N,O) complex.

Three potential anticancer agents {trans-[PtCl(2)(NH(3))(thiazole)], cis-[PtCl(2)(NH(3))(piperidine)], and PtCl(2)(NH(3))(cyclohexylamine) (JM118)} were explored and compared with cisplatin and the inactive [PtCl(dien)](+) complex. Basic electronic properties, bonding and stabilization energies were determined, and thermodynamic and kinetic parameters for the aquation reaction were estimated at the B3LYP/6-311++G(2df,2pd) level of theory. Since the aquation process represents activation of these agents, the obtained rate constants were compared with the experimental IC(50) values for several tumor cells. Despite the fact that the processes in which these drugs are involved and the way in which they affect cells are very complex, some correlations can be deduced.