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Register a new userNuclear quantum effects in molecular dynamics simulations
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To take into account nuclear quantum effects on the dynamics of atoms, the path integral molecular dynamics (PIMD) method used since 1980s is based on the formalism developed by R. P. Feynman. However, the huge computation time required for the PIMD reduces its range of applicability. Another drawback is the requirement of additional techniques to access time correlation functions (ring polymer MD or centroid MD). We developed an alternative technique based on a quantum thermal bath (QTB) which reduces the computation time by a factor of ~20. The QTB approach consists in a classical Langevin dynamics in which the white noise random force is replaced by a Gaussian random force having the power spectral density given by the quantum fluctuation-dissipation theorem. The method has yielded satisfactory results for weakly anharmonic systems: the quantum harmonic oscillator, the heat capacity of a MgO crystal, and isotope effects in 7 LiH and 7 LiD. Unfortunately, the QTB is subject to the problem of zero-point energy leakage (ZPEL) in highly anharmonic systems, which is inherent in the use of classical mechanics. Indeed, a part of the energy of the high-frequency modes is transferred to the low-frequency modes leading to a wrong energy distribution. We have shown that in order to reduce or even eliminate ZPEL, it is sufficient to increase the value of the frictional coefficient. Another way to solve the ZPEL problem is to combine the QTB and PIMD techniques. It requires the modification of the power spectral density of the random force within the QTB. This combination can also be seen as a way to speed up the PIMD.
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Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency, but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating point operations. In spite of this, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on the tensor cores of a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.
Macroscopic parameters as well as precise information on the random force characterizing the Langevin type description of the nuclear fusion process around the Coulomb barrier are extracted from the microscopic dynamics of individual nucleons by exploiting the numerical simulation of the improved quantum molecular dynamics. It turns out that the dissipation dynamics of the relative motion between two fusing nuclei is caused by a non-Gaussian distribution of the random force. We find that the friction coefficient as well as the time correlation function of the random force takes particularly large values in a region a little bit inside of the Coulomb barrier. A clear non-Markovian effect is observed in the time correlation function of the random force. It is further shown that an emergent dynamics of the fusion process can be described by the generalized Langevin equation with memory effects by appropriately incorporating the microscopic information of individual nucleons through the random force and its time correlation function.
Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may distort such assumption. Fortunately, backward error analysis allows us to identify the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which coincides with the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refine
We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity $a=lambda/rho c_{rm V}$ of a quantum mechanical liquid such as para-hydrogen. Once $a$ has been calculated, the thermal conductivity can be obtained from $lambda=rho c_{rm V}a$, where $rho$ is the density of the liquid and $c_{rm V}$ is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity $c_{rm V}$, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to $lambda$ and then dividing this by the corresponding approximation to $rho c_{rm V}$. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures -- an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with experimental measurements for the thermal conductivity of normal liquid helium.
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