We discuss the importance of the fermion nodes for the quantum Monte Carlo (QMC) methods and find two cases of the exact nodes. We describe the structure of the generalized pairing wave functions in Pfaffian antisymmetric form and demonstrate their equivalency with certain class of configuration interaction wave functions. We present the QMC calculations of a model fermion system at unitary limit. We find the system to have the energy of E=0.425Efree and the condensate fraction of α=0.48. Further we also perform the QMC calculations of the potential energy surface and the electric dipole moment along that surface of the LiSr molecule. We estimate the vibrationally averaged dipole moment to be 〈D〉ν=0=−0.4(2).
In recent years, there has been increasing interest in combining machine learning with computational chemistry. Many machine learning applications in theoretical chemistry have focused on the development of potential energy surfaces (PES) based on \emph{ab initio} data points\footnote{Manzhos, S.; Carrington, T. Chem. Rev. Article ASAP. https://doi.org/10.1021/acs.chemrev.0c00665}. Another computational resource that has gained popularity in recent years is the use of Graphics Processing Units (GPUs) to accelerate calculations such as molecular dynamics simulations \footnote{Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. SoftwareX 2015, 1–2, 19–25}. In this work, we take advantage of the knowledge gained from both of these areas, and apply these approaches to the evaluations of the potential energy for Diffusion Monte Carlo (DMC) calculations. Diffusion Monte Carlo is a stochastic simulation approach through which an ensemble of localized functions (walkers) converges to the ground state vibrational wave function at long propagation times. This is accomplished through the ensemble randomly sampling a potential energy surface. These calculations require on the order of 10
8 to 10
10 potential energy evaluations, making the call to a potential energy surface the most expensive part of these calculations. To this end, we have developed a general technique for “learning” already existing potential energy surfaces using neural networks, which can then easily be evaluated on GPUs using TensorFlow. The technique entails running a small-scale DMC simulation to collect training data, coordinates and energies, and using this data to fit a subspace of the potential energy surface that is relevant for the DMC simulations. We find that using the neural network potential energy surface maintains the fidelity of the wave function while also enabling the use of ensemble sizes orders of magnitude larger than previously used for the same amount of wall time. We test this method on small systems such as \chem{CH5+}, \chem{H2O}, and water dimer.
The solution mapping methodology is presented as a method of geometry optimization of molecules in the quantum Monte Carlo method. Applied to formaldehyde as a test system, this approach is found to yield optimized bond lengths and bond angle in the diffusion Monte Carlo method that lie within experimental error. The variational Monte Carlo optimized geometry also lies within experimental error, with the exception of the CH bond length, which is slightly underestimated. Additionally, the resulting quadratic representation of the potential energy surface in the region of the minimum is used to calculate three of the force constants and harmonic frequencies.