Some recent developments in quantum Monte Carlo for electronic structure: Methods and application to a bio system

Review of Feynman’s Path Integral in Quantum Statistics: from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

“…Similar to the complementary interplay between the rapidly growing quantum Monte Carlo simulations [146][147][148][149] and the well-established ab initio or density-functional theories (DFT) for electronic structure calculations [4,5,[25][26][27]29], non-sampling/non-stochastic pathintegral methods can complement the conventional Fourier or discretized path-integral Monte-Carlo (PIMC) [131,136,[139][140][141] and molecular dynamics (PIMD) [87,88] [e.g., Eqs. (2.46) and (2.47)] simulations which have been widely used in condensed phases.…”

Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

“…/non-stochastic methods[118] to systematically (i.e., order by order) incorporate internuclear quantum-statistical effects[88] in condensed phase systems. Similar to the complementary interplay between the rapidly growing quantum Monte Carlo simulations[119][120][121][122] and the well-established ab initio or density-functional theories (DFT) for electronic structure calculations [25, 26, 78-80, 123], non-sampling/non-stochastic path-integral methods can complement the conventional Fourier or discretized path-integral Monte-Carlo (PIMC) [37-42] and molecular dynamics (PIMD) [43-45] simulations which have been widely used in condensed phases. For example, as opposed to estimating the error bars (or the precision) for simulations, one clear advantage for using a non-sampling/non-stochastic method is the calculated values can be as precise as (not as accurate as) the numerical precision of the computing machine.…”

Developing a Systematic Approach for Ab Initio Path-Integral Simulations

“…Similar to the complementary interplay between the rapidly growing quantum Monte Carlo simulations (Anderson 1975;Grossman and Mitas 2005;Lester and Salomon-Ferrer 2006;Wagner, Bajdich et al 2009) and the well-established ab initio or density-functional theories (DFT) for electronic structure calculations (Hehre, Radom et al 1986;Szabo and Ostlund 1996;Kohn 1999;Pople 1999;Helgaker, Jørgensen et al 2000;Springborg 2000), non-stochastic pathintegral methods can complement the conventional Fourier or discretized path-integral Monte-Carlo (PIMC) (MacKeown 1985;Coalson 1986;Ceperley 1995;Sauer 2001) and molecular dynamics (PIMD) (Cao and Voth 1994;Voth 1996) simulations which have been widely used in condensed phases.…”