Density-based methods Gaussian functions

FIGURE 20 Density-based methods individual and cumulative potentials in the univariate case when (A) triangular or (B) Gaussian functions are used. 

A computer program for the theoretical determination of electric polarizabilities and hyperpolarizabilitieshas been implemented at the ab initio level using a computational scheme based on CHF perturbation theory [7-11]. Zero-order SCF, and first-and second-order CHF equations are solved to obtain the corresponding perturbed wavefunctions and density matrices, exploiting the entire molecular symmetry to reduce the number of matrix element which are to be stored in, and processed by, computer. Then a /j, and iap-iS tensors are evaluated. This method has been applied to evaluate the second hyperpolarizability of benzene using extended basis sets of Gaussian functions, see Sec. VI. 

One aspect of the approximations to the density functional theory is that some of the integrals required to solve the above equation can not be evaluated in closed form even for the gaussian-orbital basis functions used in this work. Therefore some numerical work is required to solve the above equations. An extensive literature on our gaussian-orbital-based methods exists and the interested readers are referred to Refs. [48-56] for a more detailed discussion of the numerical methods used here. Here we provide a brief discussion on some of these algorithms. 

In the solution of the electronic Schrodinger equation via wavefunction-based methods, there are two major sources of error fhaf musf be considered. One is fhe expansion of fhe many-elecfron wavefuncfion in terms of Slafer deferminanfs (fhe "mefhod") and fhe ofher is fhe represenfafion of the 1-particle orbitals by a suitable basis set, typically consisting of Gaussian-fype functions, from which fhese defer-minants are constructed. In general, similar considerations also apply in common implementations of density functional theory (DFT), however the first approximation then involves the chosen form of the correlation and exchange functionals. In any event, each of these two expansions, except in very special cases, are necessarily incomplete and they separately impact the final accuracy of an electronic... 

Abstract The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation. 

Ab-initio CAChe features all of the above plus ab-initio and density functional methods. This program requires a workstation (Windows NT minimum or SGI and IBM unix-based machines) and can be used to build and visualize results from ab-initio programs (e.g., Gaussian, see description under Gaussian, Inc.). Also, CAChe directly interfaces to Dgauss , a computational chemistry package that uses density functional theory to predict molecular structures, properties, and energetics. 

Sim, F., Salahub, D.R., and Chin, S. (1992) The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods. Int. J. Quantum Chem., 43 (4), 463-479. 

Illas et al. compared in detail the MEP maps calculated by ab initio method using a variety of Gaussian basis sets [36] with those obtained by the MNDO method [37], Since the MNDO method is based on the ZDO approximation, in accordance with the previously published results [22, 27], the ZDO molecular electron density function was used for generating the MEP maps after inverse Lowdin s transformation (deorthogonalization). It was found that, whereas the MNDO MEP maps could reproduce the main characteristics of the HF/6-31G MEP maps, the position of the MNDO minima were too close to the molecules and they were deeper than the corresponding ab initio ones. Fortunately, the ratios of the HF/6-31G and MNDO MEP minima energies are constant, and therefore the MNDO MEP minima energies can be scaled to reproduce the... 

---