Mixed quantum-classical calculations

MIXED QUANTUM-CLASSICAL CALCULATIONS IN BIOLOGICAL SYSTEMS... 

Mixed Quantum-Classical Calculations in Biological Systems... 

Jansen, G., Colonna, F. and Angyan, J. G. Mixed quantum-classical calculations on the water molecule in liquid phase Influence of a polarizable environment on electronic properties, Int.J. Quantum Chem, in press (1995),... 

Theoretical calculations for ultrafast neat water spectroscopy are difficult to perform and difficult to interpret (because of the near-resonant OH stretch coupling). One classical calculation of the 2DIR spectrum even preceded the experiments [163] Torii has calculated the anisotropy decay [97], finding reasonable agreement with the experimental time scale. Mixed quantum/ classical calculations of nonlinear spectroscopy for many coupled chromo-phores is a daunting task. We developed the TAA for linear spectroscopy, and Jansen has very recently extended it to nonlinear spectroscopy [164]. We hope that this will allow for mixed quantum/classical calculations of the 2DIR spectrum for neat water and that this will provide the context for a molecular-level interpretation of these complex but fascinating experiments. 

In a mixed quantum-classical calculation the trace operation in the Heisenberg representation is replaced by a quantum-mechanical trace (tTq) over the quantum degrees of freedom and a classical trace (i.e., a phase-space integral over the initial positions xq and momenta Po) over the classical degrees of freedom. This yields... 

As a first example, let us consider the time-dependent mean position of a normal mode xj of the system. In a mixed quantum-classical calculation, this observable is directly given by the quasiclassical average over the nuclear trajectories x t), that is. 

Jansen, G., Colonna F. and Angyan J.G., Mixed Quantum-Classical Calculations on the Water Molecule in Liquid Phase Influence of a Polarizable Environment on Electronic Properties. Int. J. Quantum Chem. (1996) 58 251. 

Fig. 1. A Schematic illustration of the partitioning of a many-body system in mixed quantum/-classical calculations. The partitioning shows the division of the system into three regions the quantum motif, the classical region and the boundary region. This partitioning describes the division of the effective Hamiltonian given in Eq. (12)...

Haug, K., Metiu, H. A test of the possibility of calculating absorption spectra by mixed quantum-classical methods. J. Chem. Phys. 97 (1992) 4781-4791... 

A number of researchers [15, 38 40, 43, 113, 124 126, 128, 146] have used mixed quantum/classical models, mostly as described in Section III.A, to calculate vibrational line shapes for this system, and several are in fair agreement with experiment. Here we describe our latest work involving approaches discussed in Section III.C. Our theoretical line shapes are calculated as briefly described in previous sections and in published work [98]. From an MD simulation of SPC/E heavy water, we determine the electric field on each putative H atom. We then use electric field maps to determine the transition frequency and dipole derivative. The orientational contribution to mp(t) we... 

The goal of this chapter is twofold. First we wish to critically compare—from both a conceptional and a practical point of view—various classical and mixed quantum-classical strategies to describe non-Born-Oppenheimer dynamics. To this end. Section II introduces five multidimensional model problems, each representing a specific challenge for a classical description. Allowing for exact quantum-mechanical reference calculations, aU models have been used as benchmark problems to study approximate descriptions. In what follows, Section III describes in some detail the mean-field trajectory method and also discusses its connection to time-dependent self-consistent-field schemes. The surface-hopping method is considered in Section IV, which discusses various motivations of the ansatz as well as several variants of the implementation. Section V gives a brief account on the quantum-classical Liouville description and considers the possibility of an exact stochastic realization of its equation of motion. 

In a mixed quantum-classical simulation such as a mean-field-trajectory or a surface-hopping calculation, the population probability of the diabatic state v[/ t) is given as the quasiclassical average over the squared modulus of the diabatic electronic coefficients dk t) defined in Eq. (27). This yields... 

We have examined the proton transfer reaction AH-B A -H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. The intermolecular and the complex-solvent potentials have a Lennard-Jones and a Coulomb component as described in detail in the original papers. There have been other quantum studies of this system. Azzouz and Borgis performed two calculations one based on centroid theory and another on the Landau-Zener theory. The two methods gave similar results. Hammes-Schiffer and Tully used a mixed quantum-classical method and predicted a rate that is one order of magnitude larger and a kinetic isotope effect that is one order of magnitude smaller than the Azzouz-Borgis results. 

A similar translation scheme from the full quantum approach to a mixed quantum classical description has been used recently in Ref. [26-29] to calculate infrared absorption spectra of polypeptides within the amide I band (note that the translation scheme has been also used in the mentioned references to compute nonlinear response functions). 

The main goal in the development of mixed quantum classical methods has as its focus the treatment of large, complex, many-body quantum systems. While applications to models with many realistic elements have been carried out [10,11], here we test the methods and algorithms on the spin-boson model, which is the standard test case in this field. In particular, we focus on the asymmetric spin-boson model and the calculation of off-diagonal density matrix elements, which present difficulties for some simulation schemes. We show that both of the methods discussed here are able to accurately and efficiently simulate this model. 

In Fig. 2 we compare results using e = 0.4 for the two mixed quantum-classical methods outlined in this chapter with exact results obtained from MCTDH wavepacket dynamics calculations. To make a reliable comparison the approximate finite temperature calculations were performed at very low temperatures (/ = 25), though a product of ground state wave functions for the independent harmonic oscillator modes could have been used to make the initial conditions identical to those used in the MCTDH calculations. 

Theoretical modeling of the structure and reactivity of zeolitic materials, with special emphasis on the mechanism of catalytic reactions, has been the subject of several exhaustive review articles in the past decade. Theoretical approaches that have been used to describe such systems range from empirical molecular mechanics calculations to various ab initio methods as well as different variants of the mixed quantum/classical (QM/MM) algorithms. In the present contribution we focus our attention mainly on those studies which were accomplished by ab initio pseudopotential plane wave density functional methods that are able to treat three-dimensional periodic models of the zeolite catalysts. Where appropriate, we attempt a critical comparison of with other theoretical approaches. 

The multiple time step propagation scheme is expected to be useful whenever a mixed quantum-classical molecular simulation is performed where only a few degrees of freedom are necessarily described within quantum mechanics and the force calculations in the classical subsystem is the time-limiting step. These conditions hold, for example, in molecular dynamics simulations of electron-and/or proton-transfer processes in the complex photosynthetic centre or in liquid phase. Furthermore, since the RPS is time-reversible, it is possible to calculate quantum reaction rates by propagating mixed quantum-classical trajectories located on the transition state back and forward in time. This opens a wide range of applications. 

In recent work [16, 17] we presented a new mixed quantum-classical method, which we call LAND-Map (Linearized approach to non-adiabatic dynamics in the mapping formulation), for calculating correlation functions. The method couples the linearization ideas put forth by various workers [18-26] with the mapping description of non-adiabatic transitions [27-31]. 

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