Compact and Flexible Basis Functions for Quantum Monte Carlo Calculations

Molecular calculations in quantum Monte Carlo frequently employ a mixed basis consisting of contracted and primitive Gaussian functions. While standard basis sets of varying size and accuracy are available in the literature, we demonstrate that reoptimizing the primitive function exponents within quantum Monte Carlo yields more compact basis sets for a given accuracy. Particularly large gains are achieved for highly excited states. For calculations requiring non-diverging pseudopotentials, we introduce Gauss-Slater basis functions that behave as Gaussians at short distances and Slaters at long distances. These basis functions further improve the energy and fluctuations of the local energy for a given basis size. Gains achieved by exponent optimization and Gauss-Slater basis use are exemplified by calculations for the ground state of carbon, the lowest lying excited states of carbon with $^5S^o$, $^3P^o$, $^1D^o$, $^3F^o$ symmetries, carbon dimer, and naphthalene. Basis size reduction enables quantum Monte Carlo treatment of larger molecules at high accuracy.Comment: 8 Pages, 2 Figures, 9 Table

Approaching Chemical Accuracy with Quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.Comment: 6 pages, 5 figure

Semistochastic Projector Monte Carlo Method

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.Comment: 5 pages, 5 figure

First-Principles Modeling of Non-Covalent Interactions in Supramolecular Systems: The Role of Many-Body Effects

Supramolecular host-guest Systems play an important role for a wide range of applications in chemistry and biology. The prediction of the stability of host-guest complexes represents a great challenge to first-principles calculations Clue to, an interplay of a ride variety of covalent and noncovalent interactions in these systems. In particular van der Waals (vdW) dispersion interactions frequently play a prominent role in determining the structure, stability, and function of supramolecular systems. On the basis of the widely used benchmark case of the buckyball catcher complex (C-60@C60H28), we assess the feasibility of computing the binding energy of supramolecular host-guest complexes from first principles. Large-scale diffusion Monte Carlo (DMC) calculations are carried out to accurately determine the binding energy for the C-60@C60H28 complex (26 +/- 2 kcal/mol). On the basis of the DMC reference, we assess the accuracy of widely used and efficient density-functional theory (DFT) methods with dispersion interactions. The inclusion of vdW dispersion interactions in DFT leads to a large stabilization of the C-60@C60H28 complex. However, DFT methods including pairwise vdW interactions overestimate the stability of this complex by 9-17 kcal/mol compared to the DMC reference and the extrapolated experimental data. A significant part of this overestimation (9 kcal/mol) stems from the lack of dynamical dielectric screening effects in the description of the molecular polarizability in pairwise dispersion energy approaches. The remaining overstabilization. arises from the isotropic treatment of atomic polarizability tensors and the lack of Many-body dispersion interactions. A further; assessment of a different supramolecular system - glycine anhydride interacting with an amide macrocycle - demonstrates that both the dynamical screening and the many-body dispersion energy are complex contributions that are very sensitive to the underlying molecular geometry and type of bonding. We discuss the required improvements in theoretical methods for achieving ``chemical accuracy'' in the first-principles modeling of supramolecular systems

Molecular Electrical Properties from Quantum Monte Carlo Calculations: Application to Ethyne

We used Quantum Monte Carlo (QMC) methods to study the polarizability and the quadrupole moment of the ethyne molecule using the Jastrow-Antisymmetrised Geminal Power (JAGP) wave function, a compact and strongly correlated variational ansatz. The compactness of the functional form and the full optimization of all its variational parameters, including linear and exponential coefficients in atomic orbitals, allow us to observe a fast convergence of the electrical properties with the size of the atomic and Jastrow basis sets. Both variational results on isotropic polarizability and quadrupole moment based on Gaussian type and Slater type basis sets are very close to the Lattice Regularized Diffusion Monte Carlo values and in very good agreement with experimental data and with other quantum chemistry calculations. We also study the electronic density along the C 61C and C\u2013H bonds by introducing a generalization for molecular systems of the small-variance improved estimator of the electronic density proposed by Assaraf et al. (Assaraf, R.; Caffarel, M.; Scemama, A. Phys. Rev. E, 2007, 75, 035701)