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Parallel Computing

Centroid molecular dynamics: A quantum dynamics method suitable for the parallel computer

Marc Pavese, Soonmin Jang, Gregory A. Voth

Published Jul 1, 2000• 50 citations
Publisher
DOI
10.1016/s0167-8191(00)00025-9

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The Journal of Chemical Physics•Nov 1, 2001•28 citations
Numerical algorithms are developed for the centroid molecular dynamics (centroid MD) method to calculate dynamical time correlation functions for general many-body quantum systems. Approaches based on the normal mode path integral molecular dynamics and staging path integral Monte Carlo methods are described to carry out a direct calculation of the force on the centroid variables in the centroid MD algorithm. A more efficient, but approximate, scheme to compute the centroid force is devised which is based on the locally optimized harmonic approximation for the centroid potential. The centroid MD equations in the latter method can be solved with the help of an iterative procedure or through extended Lagrangian dynamics. A third algorithm introduces an effective centroid pseudopotential to approximate the full many-body centroid mean force potential by effective pairwise centroid interactions. Numerical simulations for both prototype models and more realistic many-body systems are performed to explore the feasibility and limitations of each algorithm.
We propose a method which uses centroid molecular dynamics (CMD) [J. Cao and G. A. Voth, J. Chem. Phys. 100, 5106 (1994)] real-time data in conjunction with the imaginary-time data generated using path integral Monte Carlo simulations in a numerical analytic continuation scheme based on the maximum entropy approach. We show that significant improvement is achieved by including short-time CMD data with the imaginary-time data. In particular, for a particle bilinearly coupled to a harmonic bath, these methods lead to significant improvements over previous calculations and even allow accurate determination of transport coefficients such as the diffusion coefficient and mobility for this system. In addition we show how maximum entropy method can be used to extract accurate dynamic information from short-time CMD data, and that this approach is superior to the direct Fourier transform of long-time data for systems characterized by broad, featureless spectral distributions.
This paper is devoted to the development of an operator formulation of the recent extension of the centroid molecular dynamics method [J. Chem. Phys. 110, 3647 (1999); 111, 5303 (1999)] to boson and fermion systems. An operator calculus is used to rederive the basic equations of centroid dynamics. The following generalization to the case of systems of many indistinguishable particles is based on the use of a projection operator. Two different definitions of the quasi-density operator for bosonic and fermionic systems are suggested. The first definition allows an exact evaluation of equilibrium properties for systems with exchange effects using classical-like molecular dynamics calculations. The second one provides a formal justification of Bose–Einstein/Fermi–Dirac centroid dynamics with the same set of approximations as for Boltzmann statistics, and can be used to extract quantum dynamical information. In this case, the corresponding centroid correlation function can be related to a double Kubo transformed quantum mechanical one.