Basis set construction for molecular electronic structure theory: Natural orbital and Gauss-Slater basis for smooth pseudpotentials

A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation supplemented with primitive functions, chosen such that the asymptotics are appropriate for the potential of the system. Primitives are optimized for the homonuclear diatomic molecule to produce a balanced basis set. Two general features that facilitate this basis construction are demonstrated. First, weak coupling exists between the optimal exponents of primitives with different angular momenta. Second, the optimal primitive exponents for a chosen system depend weakly on the particular level of theory employed for optimization. The explicit case considered here is a basis set appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these pseudopotentials are finite at nuclei and have a Coulomb tail, the recently proposed Gauss-Slater functions are the appropriate primitives. Double- and triple-zeta bases are developed for elements hydrogen through argon. These new bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg bases at various levels of theory. Using a Gaussian expansion of the basis functions, these bases can be employed in any electronic structure method. Quantum Monte Carlo provides an added benefit: expansions are unnecessary since the integrals are evaluated numerically.Comment: 9 pages, 7 figure

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