Basis set for correlated wave functions

Krishnan R, Binkley J S, Seeger R and Popie J A 1980 Self-consistent molecular orbital methods XX. A basis set for correlated wave functions J. Chem. Phys. 72 650-4... 

Krishnan R, Binkley JS, Seeger R, Pople JA(1980) Self-consistent molecular-orbital methods. 20. Basis set for correlated wave-functions. J Chem Phys 72 650-654... 

R. Krishnan, J. S. Binkley, R. Seeger, and J. A. Pople,/. Chem. Phys., 72, 650 (1980). Self-Consistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. 

It is usually observed that the CP correction for methods including electron correlation is larger and more sensitive to the size of the basis set, than that at the HE level. This is in line with the fact that the HE wave function converges much faster with respect to the size of the basis set tlian correlated wave functions. 

It is apparent that the Hartree-Fock level is characterized by an enormous average deviation from experiment, but standard post-HF methods for including correlation effects such as MP2 and QCISD also err to an extent that renders their results completely useless for this kind of thermochemistry. We should not, however, be overly disturbed by these errors since the use of small basis sets such as 6-31G(d) is a definite no-no for correlated wave function based quantum chemical methods if problems like atomization energies are to be addressed. It suffices to point out the general trend that these methods systematically underestimate the atomization energies due to an incomplete recovery of correlation effects, a... 

Pierloot, K., Dumez, B., Widmark, P.-O., Roos, B.O. Density-matrix averaged atomic natural orbital (ANO) basis-sets for correlated molecular wave-functions. IV. Medium-size basis-sets for the atoms H-Kr. Theor. Chim. Acta 1995, 90, 87-114. 

Notice that we want to use 2 d-type functions in the basis. This is because for correlated wave functions the d-type functions serve two purposes, which cannot easily be accomplished by one basis function First they serve as polarization functions, polarizing the electron density in the bonding region, a feature that is especially important in 7t-bonded systems. Secondly, they give important contributions to the angular correlation effects, which is very important in linear molecules. Studies of the ANO s shows that the two properties of the d-type functions cannot be incorporated into one function. Hie polarization d is rather diffuse, while the correlating d is a much more contracted function. We therefore prefer to include two d-type functions in the basis set... 

In two previous papers [8,9] we have calculated the static polarizabilities and hyperpolarizabilities for ls3p Pj (J = 0, 2)-states of helium. The method was based on degenerate perturbation-theory expressions for these quantities. The necessary dipole matrix elements were found by using the high-precision wave function on framework of the configuration-interaction (Cl) method [10]. The perturbed wave functions are also expanded in a basis of accurate variational eigenstates [11]. These basis sets of the wave functions explicitly take account of electron correlation. To control the result we have also carried out similar calculations with Fues model potential method. 

In Section 8.3.2, we consider the use of atomic natural orbitals as basis functions for correlated wave functions. The atomic natural orbitals constitute a conceptually important class of atomic basis functions, useful for systematic investigations of molecular electronic structure at the correlated level. An alternative class of basis functions, perhaps somewhat more useful in practice, is provided by the correlation-consistem basis sets discussed in Section 8.3.3 (for valence correlation) and in Section 8.3.4 (for core and valence correlation). The correlation-consistent basis sets are used extensively in the remainder of this book. 

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