Imaginary time path integral Monte Carlo route to rate coefficients for nonadiabatic barrier crossing

1987 ◽  
Vol 87 (11) ◽  
pp. 6559-6561 ◽  
Author(s):  
Peter G. Wolynes
Keyword(s):  
Monte Carlo ◽  
Path Integral ◽  
Rate Coefficients ◽  
Imaginary Time ◽  
Path Integral Monte Carlo ◽  
Barrier Crossing ◽  
Time Path

ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS

1992 ◽  
Vol 03 (02) ◽  
pp. 337-346 ◽  
Author(s):  
D. MARX ◽  
P. NIELABA ◽  
K. BINDER
Keyword(s):  
Heat Capacity ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Path Integral ◽  
General Relation ◽  
Absolute Magnitude ◽  
Computational Effort ◽  
Imaginary Time ◽  
Time Dimension ◽  
Path Integral Monte Carlo

In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator has the advantage of being based directly on the energy estimatorand thus requires no extra computational effort and is suited for extensive phase diagramstudies. As an example, numerical results are presented for a two-dimensional fluid withinternal magnetic quantum degrees of freedom. We discuss in detail origin and consequences of the excess term. Due to the subtraction of two relatively large contributions ofsimilar absolute magnitude a large statistical effort would be necessary for very accurateheat capacity estimates.

scholarly journals A comparison of the efficiency of Fourier- and discrete time-path integral Monte Carlo

1998 ◽  
Vol 109 (6) ◽  
pp. 2123-2134 ◽  
Author(s):  
C. Chakravarty ◽  
M. C. Gordillo ◽  
D. M. Ceperley
Keyword(s):  
Monte Carlo ◽  
Discrete Time ◽  
Path Integral ◽  
Path Integral Monte Carlo ◽  
Time Path

Constructing accurate interaction potentials to describe the microsolvation of protonated methane by helium atoms

2017 ◽  
Vol 19 (12) ◽  
pp. 8307-8321 ◽  
Author(s):  
Dennis Kuchenbecker ◽  
Felix Uhl ◽  
Harald Forbert ◽  
Georg Jansen ◽  
Dominik Marx
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Ab Initio ◽  
Path Integral ◽  
Interaction Potential ◽  
Stationary Point ◽  
Path Integral Monte Carlo ◽  
Interaction Potentials ◽  
Helium Atoms

An ab initio-derived interaction potential is derived and used in path integral Monte Carlo simulations to investigate stationary-point structures of CH5+ microsolvated by up to four helium atoms.

Sign in / Sign up

Export Citation Format

Share Document