Quantum Thermal Bath for Molecular Dynamics Simulation

Molecular dynamics (MD) is a numerical simulation technique based on classical mechanics. It has been taken for granted that its use is limited to a large temperature regime where classical statistics is valid. To overcome this limitation, the authors introduce in a universal way a quantum thermal bath that accounts for quantum statistics while using standard MD. The efficiency of the new technique is illustrated by reproducing several experimental data at low temperatures in a regime where quantum statistical effects cannot be neglected.

Figure 1

QTB-MD simulation of a one-dimensional harmonic oscillator (HD molecule). The vibrational energies computed with the QTB and standard MD are compared to the expected energies given by $\theta (\omega ,T)$; ($\omega =6.84\times {10}^{14}\mathrm{rad}{\mathrm{s}}^{-1}$ [17]). It is seen that the QTB-MD allows to recover the quantum behavior at low temperature.

Figure 2

Influence of the effective frictional coefficient $\gamma$. We study the infrared absorption spectrum of a MgO bulk at $T=10\mathrm{K}$. Results were obtained by using a box of 64 atoms. The inset displays the imaginary part of the dielectric constant, ${\epsilon }_r$”, derived from the Fourier transform of the polarization correlation. The figure shows the FWHM (full width at half maximum) of the peak.

Figure 3

QTB-MD simulation of a MgO crystal. (a) Temperature dependence of the lattice parameter, $a$. The $a_0$ value is obtained by extrapolating, to 0 K, the linear behavior observed at high temperature. The QTB-MD reproduces the experimental data at low temperatures. (b) Temperature dependence of the heat capacity per molecule, $C_V$. The QTB values (obtained by differentiation of the mean energy) agree with the experimental data and the results derived using the harmonic density of vibrational states (DOS). The standard MD simulation gives reliable values only at temperatures higher than the Debye one (940 K) [19].

Figure 4

QTB-MD simulation of the nonsuperfluid liquid ${}^4\mathrm{He}$ at $T=2.5\mathrm{K}$. The feature of the radial distribution function, $g(r)$, allows to determine the phase of the simulated system: solid or liquid. $g(r)$ is calculated using both the QTB and standard MD. Results were obtained by using a box of 256 atoms. The QTB-MD predicts the experimentally observed liquid phase whereas the standard MD leads to a solid one.