State-to-state reactive scattering in six dimensions using reactant-product decoupling: OH + H2 → H2O + H (J = 0)

We extend to full dimensionality a recently developed wave packet method [M. T. Cvitas? and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)] for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions and also increase the computational efficiency of the method. This is done by introducing a new set of product coordinates, by applying the Crank-Nicholson approximation to the angular kinetic energy part of the split-operator propagator and by using a symmetry-adapted basis-to-grid transformation to evaluate integrals over the potential energy surface. The newly extended method is tested on the benchmark OH + H(2) → H(2)O + H reaction, where it allows us to obtain accurately converged state-to-state reaction probabilities (on the Wu-Schatz-Fang-Lendvay-Harding potential energy surface) with modest computational effort. These methodological advances will make possible efficient calculations of state-to-state differential cross sections on this system in the near future.     

Steps towards molecular parity violation in axially chiral molecules. I. Theory for allene and 1,3-difluoroallene

In view of exploring possibilities for an experimental investigation of molecular parity violation we report quantum-chemical calculations of the parity-conserving and parity-violating potentials in the framework of electroweak quantum chemistry in allene C3H4 and 1,3-difluoroallene C3H2F2, which is nonplanar and axially chiral in the electronic ground state but expected to be nearly planar and achiral in several electronically excited states. The parity-violating potentials Epv for allene and 1,3-difluoroallene calculated with the multiconfiguration linear-response (MC-LR) approach of Berger and Quack [J. Chem. Phys. 112, 3148 (2000)] show qualitatively similar behavior as a function of torsional angle tau with maximum values of about 0.5 pJ mol(-1) for C3H4 and 2 pJ mol(-1) for C3H2F2. However, in the latter case they are asymmetrically shifted around tau=90 degrees , with a nonzero value at the chiral equilibrium geometry resulting in a parity-violating energy difference between enantiomers DeltapvE=Epv(P)-Epv(M)=1.2 pJ mol(-1) (equivalent to about 10(-13) cm(-1)). The calculated barrier heights corresponding to the nonrigid (multiple, and in part chiral) transition states in 1,3-difluoroallene fall in the range of 180-200 kJ mol(-1). These high barriers result in hypothetical tunneling splittings much smaller than DeltapvE and thus parity violation dominates over tunneling for the stereomutation dynamics in 1,3-difluoroallene. Therefore, DeltapvE is predicted to be a spectroscopically measurable energy difference. Two of the lower excited electronic states of C3H2F2 (1A and 3A) are calculated to be planar or quasiplanar, allowing, in principle, for spectroscopic state selection of states of well-defined parity. The results are discussed in relation to possible schemes of measuring parity violation in chiral molecules.     

Quantum dynamics study of H+NH3-->H2+NH2 reaction

We report in this paper a quantum dynamics study for the reaction H+NH3-->NH2+H2 on the potential energy surface of Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The quantum dynamics calculation employs the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] and time-dependent wave packet method to propagate the wave function. Initial state-specific reaction probabilities are obtained, and an energy correction scheme is employed to account for zero point energy changes for the neglected degrees of freedom in the dynamics treatment. Tunneling effect is observed in the energy dependency of reaction probability, similar to those found in H+CH4 reaction. The influence of rovibrational excitation on reaction probability and stereodynamical effect are investigated. Reaction rate constants from the initial ground state are calculated and are compared to those from the transition state theory and experimental measurement.     

Herman-Kluk semiclassical dynamics of molecular rotations in laser fields

The action-angle mapping algorithm [R. Saha and M. Ovchinnikov, J. Chem. Phys. 124, 204112 (2006)] is utilized to provide a Herman-Kluk semiclassical initial value representation (SC-IVR) treatment of quantum dynamics of systems with non-Cartesian degrees of freedom. The non-Cartesian system under investigation is a linear rotor molecule in static electric and pulsed laser field. The results demonstrate that the SC-IVR procedure described in this work provides an accurate representation of quantum rotational dynamics of the system.     

A semiclassical hybrid approach to many particle quantum dynamics

We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys. 62, 1544 (1975)]. A first application of this hybrid approach to the well studied Secrest-Johnson [J. Chem. Phys. 45, 4556 (1966)] model of atom-diatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical Herman-Kluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.     

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.     

On the precision of quasi steady state assumptions in stochastic dynamics

Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)]. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.     

Isotopic replacement in ionic systems: the 4He2+ + 3He-->3He 4He+ + 4He reaction

Full quantum dynamics calculations have been carried out for the ionic reaction (4)He(2) (+)+(3)He and state-to-state reactive probabilities have been obtained using both time-dependent and time-independent approaches. An accurate ab initio potential-energy surface has been employed for the present quantum dynamics and the two sets of results are shown to be in agreement with each other. The results for zero total angular momentum suggest a marked presence of atom exchange (isotopic replacement) reaction with probabilities as high as 60%. The reaction probabilities are only weakly dependent on the initial vibrational state of the reactants, while they are slightly more sensitive to the degree of rotational excitation. A brief discussion of the results for selected higher total angular momentum values is also presented, while the l-shifting approximation [S. K. Gray et al., Phys. Chem. Chem. Phys. 1, 1141 (1999)] has been used to provide estimates of the total reaction rates for the title process. Such rates are found to be large enough to possibly become experimentally accessible.     

Wave packet dynamics of H2(v1=8-14)+H2(v2=0-2): the role of the potential energy surface on different reactive and dissociative processes

A time-dependent wave packet method has been used to study different competing products of H(2)+H(2) collisions: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. A three-degree-of-freedom reduced dimensionality model has been used for five different geometries of the colliding complex (parallel H, crossed X, collinear L, and two T-shaped geometries T(I) and T(II)), with reactants in selected vibrational states with one diatom vibrationally "hot" and the other one vibrationally "cold." Product probabilities have been calculated using two potential energy surfaces [J. Chem. Phys. 101, 4004 (1994); J. Chem. Phys. 116, 666 (2002)] in order to compare their performance in the dynamics. The regions of the potential energy surfaces responsible of the threshold behavior of the probabilities have been identified. Overall, we have found that the most recent potential energy surface is less anisotropic, provides a smaller propensity for insertion-type processes, and gives lower energy thresholds.     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Quantum control of internal conversion in 24-vibrational-mode pyrazine

Quantum control of the S(2)-->S(1) internal conversion in a complete 24-mode dimensionality model of pyrazine is demonstrated. The fully quantum mechanical study makes use of the recently developed "QP algorithm" for performing accurate computations of projected quantum dynamics and the role of overlapping resonances in control. The results are extremely encouraging, demonstrating active control over internal conversion so as to almost completely suppress the process over time scales of approximately 50-100 fs [well in excess of the natural internal conversion times (approximately 20 fs)] or to accelerate it to complete internal conversion in less than 5 fs. A number of new diagnostics are introduced to demonstrate the significance of overlapping-resonance contributions to control. Control is far better than for a reduced dimensionality model of pyrazine, presumably because of the increased degree of overlap between bound state resonances existing in the full dimensionality case.     

Long-time and unitary properties of semiclassical initial value representations

We numerically compare the semiclassical "frozen Gaussian" Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the "thawed Gaussian" propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear one-dimensional potentials. The reasons for the lack of long-time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy.     

A Hierarchical-Equation-of-Motion Based Semiclassical Approach to Quantum Dissipation?

We present a semiclassical (SC) approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion (HEOM) formalism. The dynamical components considered in the developed SC-HEOM are wavepackets' phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators (ADOs) of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effects of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation[J. Chem. Phys. 131 , 214111 (2009)] and numerically demonstrated on linear spectra of anharmonic oscillators.     

Revised self-consistent continuum solvation in electronic-structure calculations

The solvation model proposed by Fattebert and Gygi [J. Comput. Chem. 23, 662 (2002)] and Scherlis et al. [J. Chem. Phys. 124, 074103 (2006)] is reformulated, overcoming some of the numerical limitations encountered and extending its range of applicability. We first recast the problem in terms of induced polarization charges that act as a direct mapping of the self-consistent continuum dielectric; this allows to define a functional form for the dielectric that is well behaved both in the high-density region of the nuclear charges and in the low-density region where the electronic wavefunctions decay into the solvent. Second, we outline an iterative procedure to solve the Poisson equation for the quantum fragment embedded in the solvent that does not require multigrid algorithms, is trivially parallel, and can be applied to any Bravais crystallographic system. Last, we capture some of the non-electrostatic or cavitation terms via a combined use of the quantum volume and quantum surface [M. Cococcioni, F. Mauri, G. Ceder, and N. Marzari, Phys. Rev. Lett. 94, 145501 (2005)] of the solute. The resulting self-consistent continuum solvation model provides a very effective and compact fit of computational and experimental data, whereby the static dielectric constant of the solvent and one parameter allow to fit the electrostatic energy provided by the polarizable continuum model with a mean absolute error of 0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit experimental solvation energies on the same set with a mean absolute error of 1.3 kcal/mol. A detailed analysis of these results, broken down along different classes of chemical compounds, shows that several classes of organic compounds display very high accuracy, with solvation energies in error of 0.3-0.4 kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating species and strong hydrogen-bond-forming compounds.     

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. I. Theories

We have reformulated and generalized our recent work [J. Liu and W. H. Miller, J. Chem. Phys. 126, 234110 (2007)] into an approach for generating a family of trajectory-based dynamics methods in the phase space formulation of quantum mechanics. The approach (equilibrium Liouville dynamics) is in the spirit of Liouville's theorem in classical mechanics. The trajectory-based dynamics is able to conserve the quantum canonical distribution for the thermal equilibrium system and approaches classical dynamics in the classical (? → 0), high temperature (β → 0), and harmonic limits. Equilibrium Liouville dynamics provides the framework for the development of novel theoretical∕computational tools for studying quantum dynamical effects in large∕complex molecular systems.     

Self-trapping of the N-H vibrational mode in alpha-helical polypeptides

Recent calculations on the formation of self-trapped amide group vibrational states in alpha-helical polypeptides [J. Chem. Phys. 124, 134907 (2006)] are extended to the amide N-H normal mode vibrations. First, the adiabatic N-H vibrational single- and two-exciton states are examined by treating the longitudinal chain coordinates as parameters. Then, in using the multiconfiguration time-dependent Hartree method coupled exciton-chain vibrational quantum dynamics are accounted for. Based on the respective exciton-chain vibrational wave function propagation the infrared transient absorption related to a sequential pump-probe experiment is calculated. The modulation of local amide vibrational energies by the longitudinal chain coordinates is found to have a pronounced effect on the broadening of absorption lines. Moreover, the ultrafast exciton transfer in the system is studied in order to characterize the dynamics of the self-trapped single-exciton states on a time scale below 10 ps.     

Low temperature extension of the generalized Zusman phase space equations for electron transfer

In a previous paper [J. Chem. Phys. 119, 11864 (2003)], we derived a set of two coupled equations which describe electron transfer in the presence of dissipation at high temperature. Employing the low temperature extension of the Fokker-Planck operator, suggested by Haake and Reibold [Phys. Rev. A 32, 2462 (1985)] and Ankerhold [Europhys. Lett. 61, 301 (2003)], we show that one may extend the generalized Zusman equations in a similar manner to low temperature. Numerical simulation shows that addition of the temperature-dependent term which couples the coordinate and momentum causes an increase in the electron transfer rate as compared to the rate obtained from the previous high temperature equations. The increase in the rate comes from the increase in the equilibrium variances of the coordinate and momentum. The low temperature quantum theory allows for higher energy portions of phase space to contribute to the electron transfer rate where the rate is higher thus enhancing the overall rate.