Hydrogen atom with split-basis sets

Split valence basis sets allow orbitals to change size, but not to change shape. Polarized basis sets remove this limitation by adding orbitals with angular momentum beyond what is required for the ground state to the description of each atom. For example, polarized basis sets add d functions to carbon atoms and f functions to transition metals, and some of them add p functions to hydrogen atoms. 

In the early calculations of IR spectra of molecules, small basis sets (e.g., STO-3G, 3-21G, or 4-31G) were used because of limitations of computational power. At present typically a basis set consists of split valence functions (double zeta) with polarization functions placed on the heavy atoms (i.e., non-hydrogens) of the molecule (the so-called DZ+P or 6-31 G basis set). Such basis sets have been... 

In the majority of current theoretical pubhcahons deahng with organocatalysis, Becke s [8a, b] three parameter hybrid functional B3 and the Lee, Yang, and Parr (LYP) correlahon functional [8c] are used in combinahon with standard split valence basis sets (e.g., 6-3IG). In most cases, polarization functions that allow a greater flexibiHty of angle are added (for example, [d,p] means addihonal d-functions for second-row atoms, and additional p-funchons for hydrogen atoms)... 

Basis sets for use in practical Hartree-Fock, density functional, Moller-Plesset and configuration interaction calculations make use of Gaussian-type functions. Gaussian functions are closely related to exponential functions, which are of the form of exact solutions to the one-electron hydrogen atom, and comprise a polynomial in the Cartesian coordinates (x, y, z) followed by an exponential in r. Several series of Gaussian basis sets now have received widespread use and are thoroughly documented. A summary of all electron basis sets available in Spartan is provided in Table 3-1. Except for STO-3G and 3 -21G, any of these basis sets can be supplemented with additional polarization functions and/or with diffuse functions. It should be noted that minimal (STO-3G) and split-valence (3-2IG) basis sets, which lack polarization functions, are unsuitable for use with correlated models, in particular density functional, configuration interaction and Moller-Plesset models. Discussion is provided in Section II. 

Unequivocally large basis sets would be triply-split valence shell sets with d and /functions on heavy atoms and p functions on hydrogen. At the smaller end of such sets is the 6-31 lG(df,p) basis, with five 3d s and seven 4/s on each heavy atom and three 2p s on each hydrogen and helium. For carbon this is Is... 

Two different basis sets were used (1) basis set I was medium size, and (2) split-valence basis set II taken from Huzinaga [24] (9s and 5p gaussian-type orbital contracted into [3s, lp] for the C,N,0 atoms). In basis set II, more flexibility has been allowed to the description of the valence shells by adapting a triple- contraction completed with one p type (for hydrogen) or one d type (for C,N,0) polarization function. Then two ab initio calculations were carried out (1) all atoms were described with basis set I, and (2) basis set II was used for all the atoms but those belonging to the methyl and phenyl substituents due to computer limitations. 

CAS SCF calculations were therefore performed with the split valence basis set incremented by a p polarisation function on the hydrogen atoms. Two different sets of active orbitals were considered. The first one was designed to account for the d - n back donation and was therefore restricted to the n type valence orbitals. The three 3d orbitals, which are strongly occupied, were each correlated by two weakly occupied orbitals, owing to the mixed 4d and tt o character of these weakly occupied orbitals. This 3 + 6 set of active orbitals referred to as CAS SCF-6 is populated by 6 electrons. The second set, hereafter referred as CAS SCF-12, took into account both a and n correlation eficcts. Twelve electrons were correlated and... 

The ab initio HF calculations reported below have been performed with the GAUSSIAN 76 [26] program package. The atomic basis sets applied are a minimal (STO-3G [26]) one, a split valence (6-31G [26]) one, a split-valence one plus a set of five d-functions on carbon (6-31G [26]), and one with an additional set of p-functions on hydrogen (6-31G [26]). The correlation energy has been computed using Mpller-Plesset many body perturbation theory of second order (MP2) [27], the linear approximation of Coupled Cluster Doubles theory (L-CCD)... 

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