Path-integral molecular dynamics

Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

Martyna, G.J. Adiabatic path integral molecular dynamics methods. I. Theory. J. Chem. Phys. 104 (1996) 2018-2027. 

Figure 6.6 (a) Dihydrogen-bonded complex system NH4+- H-Be-H represented by the optimized equilibrium geometry, and (b) the ab initio path integral molecular dynamics simulation (representative snapshot of configuration). (Reproduced with permission from ref. 12.)... 

Using a plane wave representation for the electron wavefunction with 163 grid points and approximately 800 independent electronic and molecular configurations from the path integral molecular dynamics trajectories, we have also computed the density of states for the electron under different supercritical conditions of the solvents and the corresponding steady-state optical absorption spectra. The latter were computed within the dipolar approximation from the following expression within the Frank-Condon approximation ... 

D. Marx and M. Parrinello, Ab initio path-integral molecular dynamics, Z. Phys. B Condens. Matter, 95 (1994), 143-144. 

P. Minary, G. J. Martyna, and M. E. Tuckerman (2003) Algorithms and novel applications based on the isokinetic ensemble. 1. Biophysical and path integral molecular dynamics. J. Chem,. Phys. 118, p. 2510... 

We did not address also other extensions of first-principle MD to free-energy Density Functional Theory for metals [145,256,257], simulations with a variable number of electrons [11,14,67,258-260] (fixed electron chemical potential) or otherwise path-integral Molecular Dynamics in the Car-Parrinello framework [27,43,51,80,81,208,261-268]. We hope however that the present introduction on first-principle MD will give the reader both the background and the enthusiasm to look in this vast literature. 

S. Miura, M. Tuckerman, and M. Klein (1998) An ab initio path integral molecular dynamics study of double proton transfer in the formic acid dimer. J. Chem. Phys. 109, p. 5290... 

In a path-integral Monte Carlo (PIMC) calculation, the centroid force can readily be calculated from Eq. (3.64) by using the importance sampling function exp[-5p(q,. . . , qp) h] and pairwise MC moves to enforce the centroid constraint. For a path-integral molecular dynamics (PIMD) calculation [71], one defines fictitious momenta p, for each of the quasiparticles q and then runs an MD simulation with Hamilton s... 

Two routes are available to obtain such quantum mechanical description a simulation can be realised with the path integral molecular dynamics method (PIMD), recently applied to liquid water (Billeter, King and van Gunsteren, 1994), or a classical dynamics simulation can be realised, with an a posteriori corrections of the results (Berens, Mackay, White and Wilson, 1983 Berens and Wilson, 1981). The latter choice has been made for the calculation of gaseous CO spectra in liquid argon (Berens and Wlson, 1981). 

Ab Initio Path Integral Molecular Dynamics Simulations of F2H and F2H3... 

Variational Path Integral Molecular Dynamics Study of Small Para-Hydrogen Clusters... 

In this section, we briefly describe the variational path integral molecular dynamics method. We start to consider a system consisting of N identical particles whose coordinates are collectively represented to be i . The Hamiltonian of the system is written by H = f + V where f and V are the kinetic and potential energy operators, respectively. The system is assumed to be well described by a trial wavefunction exact ground state of the system, 4 o), can be obtained using the trial wavefunction 7 ) by the following relation [1,4]... 

Future applications by the VPIMD method include vibrational fluctuations of molecular clusters such as hydrogen bonded clusters. Molecular clusters characterized by weak intermolecular interactions are expected to have large anharmonicity of the potential energy surfaces. As demonstrated in the present study, the VPIMD method properly handles the anharmonicity including the case of multiple minima. Another important point is on the description of the adiabatic potential energy surfaces of molecular clusters. An improvement can be achieved by combining the VPIMD method with electronic structure calculations as in the case of the finite temperature path integral molecular dynamics [30-32], These issues will be addressed in the near future. 

---