Gaussian basis functions Hartree-Fock energies

G. A Split-Valence Basis Set in which each Core Basis Function is written in terms of three Gaussians, and each Valence Basis Function is split into two parts, written in terms of two and one Gaussians, respectively. 3-2IG basis sets have been determined to yield the lowest total Hartree-Fock Energies for atoms. 

It has been demonstrated[81] that a sufficiently large and flexible universal even-tempered basis set of Gaussian primitive functions can support a total matrbc Hartree-Fock energy for the gas phase CO molecule of —112.7909045 Hartree for a nuclear separation of 2.132 Bohr. This differs from the finite difference Hartree-Fock energy by 2.8 jiHartree. 

The second approximation in HF calculations is due to the fact that the wave function must be described by some mathematical function, which is known exactly for only a few one-electron systems. The functions used most often are linear combinations of Gaussian-type orbitals exp(—nr ), abbreviated GTO. The wave function is formed from linear combinations of atomic orbitals or, stated more correctly, from linear combinations of basis functions. Because of this approximation, most HF calculations give a computed energy greater than the Hartree-Fock limit. The exact set of basis functions used is often specified by an abbreviation, such as STO—3G or 6—311++g. Basis sets are discussed further in Chapters 10 and 28. 

The Hartree-Fock ground state of the F anion is described by orbitals of s Emd of p symmetry. In the first part of this study, attention was restricted to the convergence of the second order many-body perturbation theory component of the correlation energy for stematically constructed even-tempered basis sets of primitive Gaussian-typ>e functions of s and p symmetry. 

The accurate description of correlation effects requires the inclusion of functions of higher symmetry than those required for the matrix Hartree-Fock model. The most important of these functions for the F anion are functions of d-type. In this section, the convergence of the total energy through second order and the second order correlation energy component for a systematic sequence of even-tempered basis sets of Gaussian functions of s-, p-and d-type is investigated. 

---