Complex Hermite-Gaussians Behaving Badly

A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians.

Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresp...

Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the β-Hermite and β-Laguerre ensembles, using the matrix models we described in [5], in the limit as β → ∞. We find that the fluctuations are described by Gaussians of variance O(1/β), centered at the roots of a corresponding Hermite (Laguerre) polynomial. We also show that the approximation is very good, even for sma...

Consumers behaving badly: deviation or innovation? A conceptual exploration of empowered communications online-The case of consumer- producer relationships on the web

Numerical fitting of molecular properties to Hermite Gaussians.

A procedure is presented to fit gridded molecular properties to auxiliary basis sets (ABSs) of Hermite Gaussians, analogous to the density fitting (DF) method (Dunlap; et al. J. Chem. Phys. 1979, 71, 4993). In this procedure, the ab initio calculated properties (density, electrostatic potential, and/or electric field) are fitted via a linear- or nonlinear-least-squares procedure to auxiliary ba...

The Fast Gauss Transform

Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes it very expensive to carry out such calculations on a large scale. In this paper, an algorithm is presented which evaluates the sum of N Gaussians at M arbitrarily distributed points in C. (N + M) work, ...