Gaussian functions, electronic structure

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Gaussian and other ab initio electronic structure programs use gaussian-type atomic functions as basis functions. Gaussian functions have the general form ... 

There are two types of basis functions (also called Atomic Orbitals, AO, although in general they are not solutions to an atomic Schrodinger equation) commonly used in electronic structure calculations Slater Type Orbitals (STO) and Gaussian Type Orbitals (GTO). Slater type orbitals have die functional form... 

The electronic structure calculations were carried out using the hybrid density functional method B3LYP [15] as implemented in the GAUSSIAN-94 package [16], in conjunction with the Stevens-Basch-Krauss (SBK) [17] effective core potential (ECP) (a relativistic ECP for Zr atom) and the standard 4-31G, CEP-31 and (8s8p6d/4s4p3d) basis sets for the H, (C, P and N), and Zr atoms, respectively. 

The Gaussian orbitals are very important in practical applications. In spite of their wrong asymptotic behaviour at both r —> 0 and r —> °o, nearly all molecular electronic structure calculation programs have been constructed using Gaussian sets of one-electron functions. In this example the Gaussian basis has been selected as... 

Almost all contemporary ab initio molecular electronic structure calculations employ basis sets of Gaussian-type functions in a pragmatic approach in which no error bounds are determined but the accuracy of a calculation is assessed by comparison with quantities derived from experiment[l] [2]. In this quasi-empirical[3] approach each basis set is calibrated [4] for the treatment of a particular range of atoms, for a particular range of properties, and for a particular range of methods. Molecular basis sets are almost invariably constructed from atomic basis sets. In 1960, Nesbet[5] pointed out that molecular basis sets containing only basis sets necessary to reach to atomic Hartree-Fock limit, the isotropic basis set, cannot possibly account for polarization in molecular interactions. Two approaches to the problem of constructing molecular basis sets can be identified ... 

An important issue of the application of electronic structure theory to polyatomic systems is the selection of the appropriate basis set. As usual in quantum chemistry, a compromise between precision and computational cost has to be achieved. It is generally accepted that in order to obtain qualitatively correct theoretical results for valence excited states of polyatomic systems, a Gaussian basis set of at least double-zeta quality with polarization functions on all atoms (or at least on the heavy atoms) is necessary. For a correct description of Rydberg-type excited states, the basis set has to be augmented with additional diffuse Gaussian functions. Such basis sets were used in the calculations discussed below. 

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