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Among the simplest split-valence basis sets are 3-21G and 6-31G. Each core atomic orbital in the 3-21G basis set is expanded in terms of three Gaussians, while basis functions representing inner and outer components of valence atomic orbitals are expanded in terms of two and one Gaussians, respectively. 6-31G basis sets are similarly constructed, with core orbitals represented in terms of six Gaussians and valence orbitals split into three and one Gaussian components. Additional valence-shell splitting should lead to even greater flexibility.

Unoccupied molecular orbtials electron promotion occupied molecular orbtials Conceptually, the most straightforward approach is the so-called full configuration interaction model. Here, the wavefunction is written as a sum, the leading term of which, Ψo, is the Hartree-Fock wavefunction, and remaining terms, Ψs, are wavefunctions derived from the Hartree-Fock wavefunction by electron promotions. Ψ = aoΨo + Σa Ψ s (26) s s>o The unknown linear coefficients, as, are determined by solving equation 27.

Thus, the energies of two helium atoms treated separately and two helium atoms at infinite separation will be different. Møller-Plesset Models6 Another practical correlation energy scheme is the second-order Møller-Plesset model, or MP2. This is the simplest member of the class of so-called Møller-Plesset models, the basis of which is the recognition that, while the Hartree Fock wavefunction Ψ0 and groundstate energy E0 are approximate solutions to the Schrödinger equation, they are exact solutions to an analogous problem involving the ˆ 0, in place of the “exact” Hamiltonian, Hartree-Fock Hamiltonian, H ˆ Assuming that the Hartree-Fock wavefunction Ψ and energy are, H.

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