Seogjoo Jang

A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables

Several methods to approximately evolve path integral centroid variables in real time are presented in this paper, the first of which, the centroid molecular dynamics (CMD) method, is recast into the new formalism of the preceding paper and thereby derived. The approximations involved in the CMD method are thus fully characterized by mathematical derivations. Additional new approaches are also presented: centroid Hamiltonian dynamics (CHD), linearized quantum dynamics (LQD), and a perturbative correction of the LQD method (PT-LQD). The CHD method is shown to be a variation of the CMD method which conserves the approximate time dependent centroid Hamiltonian. The LQD method amounts to a linear approximation for the quantum Liouville equation, while the PT-LQD method includes a perturbative correction to the LQD method. All of these approaches are then tested for the equilibrium position correlation functions of three different one-dimensional nondissipative model systems, and it is shown that certain quant...

Theory of coherent resonance energy transfer

A theory of coherent resonance energy transfer is developed combining the polaron transformation and a time-local quantum master equation formulation, which is valid for arbitrary spectral densities including common modes. The theory contains inhomogeneous terms accounting for nonequilibrium initial preparation effects and elucidates how quantum coherence and nonequilibrium effects manifest themselves in the coherent energy transfer dynamics beyond the weak resonance coupling limit of the Forster and Dexter (FD) theory. Numerical tests show that quantum coherence can cause significant changes in steady state donor/acceptor populations from those predicted by the FD theory and illustrate delicate cooperation of nonequilibrium and quantum coherence effects on the transient population dynamics.

Path integral centroid variables and the formulation of their exact real time dynamics

A formalism is presented in this paper which, for the first time, establishes the theoretical basis for the quantum time evolution of path integral centroid variables and also provides clear motivation for using these variables to study condensed phase quantum dynamics. The equilibrium centroid distribution is first shown to be a well-defined distribution function which is specific to the canonical density operator. A quantum mechanical quasi-density operator (QDO) is associated with each value of the distribution so that, upon application of the standard quantum mechanical formalism, the QDO can be used to provide a rigorous definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables are derived, including the perspective that the centroid constraint on the imaginary time paths introduces a nonstationarity in the equilibrium ensemble which, in turn, can be shown to yield information on the correlations of spontaneous fluctuations. The analytic solution for the harmonic oscillator and a numerical solution for a double well system are provided which illustrate the various aspects of the theory. The theory contained herein provides the basis for a derivation of Centroid Molecular Dynamics, as well as the systematic improvements of that theory.

Applications of higher order composite factorization schemes in imaginary time path integral simulations

Suzuki’s higher order composite factorization which involves both the potential and the force is applied to imaginary time path integral simulation. The expression is more general than the original version and involves a free parameter α in the range of [0, 1]. Formal expressions are derived for statistical averages, based on both thermodynamic and quantum operator identities. The derived expressions are then tested for one-dimensional model systems using the numerical matrix multiplication method, which involves no statistical error. When an optimum choice of α is made, the higher order factorization approach is shown to be more efficient than primitive factorization by about a factor of 4 and better than other existing higher order algorithms with similar character. Actual path integral simulation tests are then made for an excess electron in supercritical helium and for bulk water, and these generally demonstrate the efficiency of the higher order factorization approach.

A Feynman path centroid dynamics approach for the computation of time correlation functions involving nonlinear operators

The centroid dynamics formalism is extended to the calculation of time correlation functions of nonlinear operators. It is shown that centroid correlation functions can be related to quantum mechanical ones via higher order Kubo-type transforms. A key step is the construction of the correlation functions from a mixed classical/semiclassical centroid representation of the operators. A general methodology is developed to relate these Kubo-type transforms to the desired quantum correlation functions. The approach is tested using a one-dimensional anharmonic potential for which the 〈x2x2(t)〉 and the 〈x3x3(t)〉 correlation functions are computed. Applications of this new approach are also outlined.

Simple reversible molecular dynamics algorithms for Nosé–Hoover chain dynamics

Reversible algorithms for Nose–Hoover chain (NHC) dynamics are developed by simple extensions of Verlet-type algorithms: leap frog, position Verlet, and velocity Verlet. Tests for a model one dimensional harmonic oscillator show that they generate proper canonical distributions and are stable even with a large time step. Using these algorithms, the effects of the Nose mass and chain length are examined. For a chain length of two, the sampling efficiency is much more sensitive to the Nose mass than for a longer chain of length four. This indicates that the chain length in general should be longer than two. The noniterative nature of the algorithms allows them to be easily adapted for constraint dynamics. For the most general case where multiple NHC’s are coupled to a system with constraints, a correction of the first Nose acceleration is required, which is derived from the continuity equation on a constrained hypersurface of the phase space. Tests for model systems of two and three coupled harmonic oscilla...

Theory of multichromophoric coherent resonance energy transfer: a polaronic quantum master equation approach.

The approach of second order time local quantum master equation in the polaron picture, which has been employed for a theory of coherent resonance energy transfer, is extended for general multichromophore systems. Explicit expressions for all the kernel and inhomogeneous terms are derived, which can be calculated by any standard numerical procedure. The theory is then applied to a model of donor-bridge-acceptor system moderately coupled to bosonic bath. The results are compared with those based on the theory of Försters resonance energy transfer. It is shown that coherently coupled multichromophores can speed up the transfer of energy substantially and in a way insensitive to the disorder.

Theory of coherent resonance energy transfer for coherent initial condition

A theory of coherent resonance energy transfer [Jang et al., J. Chem. Phys. 129, 101104 (2008)] is extended for coherent initial condition. For the situation where the initial excitation is an arbitrary linear combination of donor and acceptor excitations, a second order time local quantum master equation combined with polaron transformation is derived. Inhomogeneous terms in the resulting equation have contributions not only from initial donor and acceptor populations but also from their coherence terms. Numerical tests are performed for general super Ohmic spectral density where the bath degrees of freedom coupled to donor and acceptor can be correlated with each other. Calculation results demonstrate sensitivity of early nonstationary population dynamics on the relative sign of initial donor and acceptor excitation states. It is shown that contribution of inhomogeneous terms is more significant for coherent initial condition than for localized one. The overall model calculations provide details of the interplay between quantum coherence and nonequilibrium/non-Markovian effects in the time dependent donor population dynamics.

Nonequilibrium generalization of Förster–Dexter theory for excitation energy transfer

Abstract Forster–Dexter theory for excitation energy transfer (EET) is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation–bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed.

Single complex line shapes of the B850 band of LH2

For a model of the B850 band in the light harvesting complex 2 of purple bacteria, the main quantum mechanical characteristics of the single complex line shapes are studied based on the theory of the preceding paper. The model consists of single exciton states coupled to harmonic oscillator bath, with the inclusion of both static and quasistatic disorder within the exciton Hamiltonian. A closed form line shape expression is derived that can account for the non-Markovian nature of the bath for a general spectral density. The calculation of the line shape only requires the inversion of a small matrix with dimension equal to the number of exciton levels, at each frequency. For two examples of site energy modulation with definite symmetries, we examine the dependencies of the line shape on the polarization of the radiation, on the type of exciton–bath coupling, and on temperature. For a plausible example of disorder, we simulate the line shapes of the ensemble and single complex spectroscopies. Simulation of single complex line shapes suggests that the quasistatic disorder is responsible for large spectral jumps (spectral diffusion) of the lowest exciton state and make the widths of the two brightest peaks comparable.