Hydrogen molecule ion: Path-integral Monte Carlo approach

Abstract

The path-integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born-Oppenheimer and nonadiabatic simulations, and inspecting projections of the full three-body dynamics onto the adiabatic Born-Oppenheimer approximation. Coupling of the electron and nuclear quantum dynamics is clearly seen. The nuclear pair correlation function is found to broaden by 0.040a 0 , and the average bond length is larger by 0.056a 0 . Also, a nonadiabatic correction to the binding energy is found. The electronic distribution is affected less than the nuclear one upon inclusion of nonadiabatic effects.

Thermal dissociation of dipositronium: Path-integral Monte Carlo approach

“…The positronium molecule, with all the four particles of the same mass, sets challenges to modeling, since quantum calculations are to be performed fully non-adiabatically [13]. This, however, can be realized with quantum Monte Carlo (QMC) methods [14,15,16]. It should be pointed out that also for other systems, approaches that are not restricted by the Born-Oppenheimer or other adiabatic approximations are gaining more attention [16,17,18,19,20,21,22,23].…”

“…This, however, can be realized with quantum Monte Carlo (QMC) methods [14,15,16]. It should be pointed out that also for other systems, approaches that are not restricted by the Born-Oppenheimer or other adiabatic approximations are gaining more attention [16,17,18,19,20,21,22,23].…”

Finite temperature quantum statistics of H3+ molecular ion

“…[14][15][16][17][18][19][20][21] For 0 K data with benchmark accuracies, however, the conventional quantum chemistry or other Monte Carlo methods, such as the diffusion Monte Carlo, 22 are more appropriate. [14][15][16][17][18][19][20][21] For 0 K data with benchmark accuracies, however, the conventional quantum chemistry or other Monte Carlo methods, such as the diffusion Monte Carlo, 22 are more appropriate.…”

“…The PIMC method is computationally expensive, but within the chosen models and numerical approximations it has been proven to be useful with exact correlations and finite temperature [14][15][16][17][18][19][20][21] . For zero Kelvin data with benchmark accuracies, however, the conventional quantum chemistry or other Monte Carlo methods, such as the diffusion Monte Carlo 22 , are more appropriate.…”

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing

“…There are many other approaches to treating non-adiabatic effects, such as path-integral molecular dynamics, [57][58][59][60][61][62][63] path-integral Monte-Carlo, [64][65][66] quantum Monte-Carlo 67,68 and wavepacket methods, [69][70][71][72][73] however, as they are not directly related to current work, we will not discuss them in detail.…”