Table-configuration interaction

Callen, E., J. Chem. Phys. 23, 360, Configuration interaction applied to the hydrogen molecule." A useful table A list of investigations of the wave functions and binding energies of the H2" is also contained. 

Table 1. Configuration Interaction energy calculation with a minimal STO — 3G basis of the four lower singlet states of H2O.

Under these conditions, the 3-RDM of the three lower states of the Beryllium atom and the two lower ones of the Water molecule were determined [48] by taking as initial data the 2-RDM obtained in a Full Configuration Interaction. In Table 4 some of these results are given and as can be seen they are very satisfactory. 

The asymptotic energy values obtained by a configuration interaction calculation at 25 a.u. corrected by the coulombic repulsion term (the l/R" term has been neglected) are seen to be in quite good agreement with experiment (Table 3). 

The ideal calculation would use an infinite basis set and encompass complete incorporation of electron correlation (full configuration interaction). Since this is not feasible in practice, a number of compound methods have been introduced which attempt to approach this limit through additivity and/or extrapolation procedures. Such methods (e.g. G3 [14], CBS-Q [15] and Wl [16]) make it possible to approximate results with a more complete incorporation of electron correlation and a larger basis set than might be accessible from direct calculations. Table 6.1 presents the principal features of a selection of these methods. 

The oscillator strengths obtained for the different transitions studied in the present work with the RQDO methodology, and the use of the two forms of the transition operator, the standard one, and that corrected for core-valence polarization, are collected in Tables 1 to 8, where other data, from several theoretical and experimental sources, have been included for comparative purposes. The former comprise the large-scale configuration interaction performed with the use of the CIVS computer package [19] by Hibbert and Hansen [20] The configuration interaction (Cl) procedure of... 

Table 2. Configuration interaction expansion coefficients for the wavefunctions...

Finally, in order to illustrate the role of the 1-MZ purification procedure in improving the approximated 2-RDMs obtained by application of the independent pair model within the framework of the SRH theory, all the different spin-blocks of these matrices were purified. The energy of both the initial (non-purified) and updated (purified) RDMs was calculated. These energies and those corresponding to a full configuration interaction (full Cl) calculation are reported in Table 111. As can be appreciated from this table, the nonpurified energies of all the test systems lie below the full Cl ones while the purified ones lie above and very close to the full Cl ones. 

Here we examine the carbon net charges of ethane and ethylene, obtained from SCF and configuration interaction calculations, corrected by means of the appropriate p, determined for n = —4.4122. Remember that the same value of p applies to both ethane and ethylene, as n is solely determined by the effectiveness of the inductive effects. Equation (5.15) is used to get p, namely, p = 138.68 me in 4-31G + Cl calculations and thus, from Eq. (5.10), the corresponding carbon charges of ethane and ethylene (see Table 5.5). 

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. 

Structures were optimized at the theoretical level described in Table 1, footnote a. Final energies were obtained by using multi-reference configuration interaction (MRCI) wave functions including single and double excitations from die reference wave functions. cFrom Reference 8. 

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