Orthogonal atomic orbitals

One widely used valence bond theory is the generalised valence bond (GVB) method of Goddard and co-workers [Bobrowicz and Goddard 1977]. In the simple Heitler-London treatment of the hydrogen molecule the two orbitals are the non-orthogonal atomic orbitals on the two hydrogen atoms. In the GVB theory the analogous wavefunction is written ... 

Size consistency The DMRG ansatz is size-consistent when using a localized basis (e.g., orthogonalized atomic orbitals) in which the wave function for the separated atoms can be considered to factorize into the wave functions for the individual atoms expressed in disjoint subsets of the localized basis. To see this in an informal way, let us assume that we have two DMRG wave functions Pa) and I Pg) for subsystems A and B separately. Both Pa and VPB have a matrix product structure, that is... 

Therefore a plot of the radial probability for a given orthogonalized atomic orbital, n, will 3 3... 

Fischer-Hjalmars, I., Deduction of the zero differential overlap approximation from an orthogonal atomic orbital basis, J. Chem. Phys., 42, 1962-1972, 1965. 

Of comparable or better accuracy, but much faster, is the PRDDO (Partial Retention of Diatomic Differential Overlap) method proposed by Halgren and Lipscomb.66 This method uses the exact one-electron matrix over STOs transformed to an orthogonal atomic orbital (OAO) basis.66 Electron-repulsion integrals are systematically approximated using exact values of some integrals over the original STO basis. The method recognizes three basis sets ... 

LCOAO linear combination of orthogonalized atomic orbitals... 

In order to avoid the overlap partitioning problem while extending this concept to more elaborated wave-functions, one may use the natural populations defined from Lowdin s orthogonalized atomic orbitals [25] which diagonalize the first-order density matrix ... 

Orthogonalized atomic orbitals as they are defined in this chapter were first suggested by P. O. Lowdin in J. Chem. Phys. 18, 365 (1959). 

Natural bond orbital (NBO) analysis The NBO analysis transforms the canonical delocalized Hartree-Fock (HF) MOs and non-orthogonal atomic orbitals (AOs) into the sets of localized natural atomic orbitals (NAOs), hybrid orbitals (NHOs), and bond orbital (NBOs). Each of these localized basis sets is complete, orthonormal, and describes the wavefunction with the minimal amount of filled orbitals in the most rapidly convergent fashion. Filled NBOs describe the hypothetical, strictly localized Lewis structure. NPA charge assignments based on NBO analysis correlate well with empirical charge measures. ... 

Then one may introduce orthogonal atomic orbitals oj and b , which are excited atomic orbitals of A and B orthogonalized to a and b, and one will generate single and double excitations towards these virtual MOs from either neutral (0i, 2) or ionic (< 3, valence determinants. 

The repulsive potential rep(rab) varies exponentially with distance Tab between atoms a and b. is the energy of a molecular orbital, built as a linear combination of Nf non-orthogonal atomic orbitals ... 

The Cl formalism in semiempirical methods is in principal the same as in ab initio methods. The MOs xj/-, are obtained as linear combinations of orthogonalized atomic orbitals (OAOs) A. (equation 1). 

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