Optimization of quantum Monte Carlo wave functions by energy minimization

We study three wave function optimization methods based on energy minimization in a variational Monte Carlo framework: the Newton, linear, and perturbative methods. In the Newton method, the parameter variations are calculated from the energy gradient and Hessian, using a reduced variance statistical estimator for the latter. In the linear method, the parameter variations are found by diagonalizing a nonsymmetric estimator of the Hamiltonian matrix in the space spanned by the wave function and its derivatives with respect to the parameters, making use of a strong zero-variance principle. In the less computationally expensive perturbative method, the parameter variations are calculated by approximately solving the generalized eigenvalue equation of the linear method by a nonorthogonal perturbation theory. These general methods are illustrated here by the optimization of wave functions consisting of a Jastrow factor multiplied by an expansion in configuration state functions (CSFs) for the C2 molecule, including both valence and core electrons in the calculation. The Newton and linear methods are very efficient for the optimization of the Jastrow, CSF, and orbital parameters. The perturbative method is a good alternative for the optimization of just the CSF and orbital parameters. Although the optimization is performed at the variational Monte Carlo level, we observe for the C2 molecule studied here, and for other systems we have studied, that as more parameters in the trial wave functions are optimized, the diffusion Monte Carlo total energy improves monotonically, implying that the nodal hypersurface also improves monotonically.     

The first three anisotropy constants of nickel

The technique of ferromagnetic resonance at 23 GHz has been used to determine the first three anisotropy constants of pure Ni down to 4.2K. A temperature and orientation dependent linewidth has also been observed.     

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

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 multiconfigurational 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.     

Alleviation of the Fermion-sign problem by optimization of many-body wave functions

We present a simple, robust, and highly efficient method for optimizing all parameters of many-body wave functions in quantum Monte Carlo calculations, applicable to continuum systems and lattice models. Based on a strong zero-variance principle, diagonalization of the Hamiltonian matrix in the space spanned by the wave function and its derivatives determines the optimal parameters. It systematically reduces the fixed-node error, as demonstrated by the calculation of the binding energy of the small but challenging C(2) molecule to the experimental accuracy of 0.02 eV.