Diffusion Monte Carlo Studies on the Detection of Structural Changes in the Water Hexamer upon Isotopic Substitution

Implementation of the self-consistent phonons method with ab initio potentials (AI-SCP)

The self-consistent phonon (SCP) method allows one to include anharmonic effects when treating a many-body quantum system at thermal equilibrium. The system is then described by an effective temperature-dependent harmonic Hamiltonian, which can be used to estimate its various dynamic and static properties. In this paper, we combine SCP with ab initio (AI) potential energy evaluation in which case the numerical bottleneck of AI-SCP is the evaluation of Gaussian averages of the AI potential energy and its derivatives. These averages are computed efficiently by the quasi-Monte Carlo method utilizing low-discrepancy sequences leading to a fast convergence with respect to the number, S, of the AI energy evaluations. Moreover, a further substantial (an-order-of-magnitude) improvement in efficiency is achieved once a numerically cheap approximation of the AI potential is available. This is based on using a perturbation theory-like (the two-grid) approach in which it is the average of the difference between the AI and the approximate potential that is computed. The corresponding codes and scripts are provided.

Isotope Effects in the Zundel-Eigen Isomerization of H+(H2O)6

The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer was investigated using high-level ab initio calculations including a treatment of zero-point corrections. On the basis of these calculations, the Zundel-Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel-Eigen isomerization. Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H⁺(H₂O)₆ and D⁺(D₂O)₆ have well-defined structures. The energetic ordering of the three isomers changes upon deuteration. The implications of these results for the vibrational spectra of H⁺(H₂O)₆ and D⁺(D₂O)₆ are also discussed.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H₂O, CH₅⁺, and (H₂O)₂. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH₅⁺ and (H₂O)₂. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.

A path integral ground state approach for asymmetric top rotors with nuclear spin symmetry: Application to water chains

A path integral ground state (PIGS) approach for the simulation of asymmetric top rotors is presented. The method is based on Monte Carlo sampling of angular degrees of freedom. A symmetry-adapted rotational density matrix is used to account for nuclear spin statistics. To illustrate the method, ground-state properties of collections of para-water molecules confined to a one-dimensional lattice are computed. Those include energetic and structural observables. An advantage of the PIGS method is that expectation values can be obtained directly since the square of the wavefunction is sampled during a simulation. To benchmark the method, ground state energies and orientational distributions are computed using exact diagonalization for a single para-water molecule in an external field using a finite basis of symmetric top eigenfunctions. Benchmark results are also provided for N = 2 para-water molecules pinned to lattice sites at various distances to sample the crossover from hydrogen bonding to the dipole-dipole interaction regime. Excellent agreement between the PIGS results and the finite basis set calculations is observed. A thorough analysis of the convergence in terms of the imaginary time propagation length and systematic Trotter error is performed. The PIGS approach is then applied to a chain of N = 11 water molecules, and an equation of state is constructed in terms of the intermolecular separation. Ordering effects are also studied, and a transition between hydrogen bonding to dipole-dipole alignment is observed. The method is scalable and can also be applied in higher dimensions.