Nonlocalized molecular orbitals

Several other molecular orbital models have been applied to the analysis of VCD spectra, primarily using CNDO wave functions. The nonlocalized molecular orbital model (NMO) is the MO analog of the charge flow models, based on atomic contributions to the dipole moment derivative (38). Currents are restricted to lie along bonds. An additional electronic term is introduced in the MO model that corresponds to s-p rehybridization effects during vibrational motion. 

Rotational and Dipole Strength Calculations for the CH-Stretching Vibrations of L-alanine Using the Localized Molecular Orbital, Nonlocalized Molecular Orbital, Atomic Polar Tensor, and Fixed Partial Charge Models ... 

Contrary to all former theories, in the theory of molecular orbitals the emphasis was on component (A), component (B) was adopted in a generalized form (many-center nonlocalized molecular orbitals), and component (C) was considered to be a mere incidental characteristic of chemical combination. Mulliken believed that the... 

Approximate models include the coupled oscillator (CO), the fixed partial charge (FPC), the chaige flow (CF), the ring current, the dynamic polarizability (DP), the bond dipole (BD), the localized molecular orbital (LMO) the nonlocalized molecular orbital (NMO), the atomic polar tensor (APT), and the locally distributed origins gauge... 

Tel. 612-683-3688, fax 612-683-3099, e-mail mcole cray.com DGauss for density functional theory calculations with nonlocal, SCF corrections, and geometry optimization. Cadpac 5.0 for ab initio calculations. MNDO90 for semiempirical molecular orbital calculations. A package with a graphics front end for structure input and visualizations of electron density, electrostatic potentials, and molecular orbitals. Silicon Graphics and Macintosh (under X-Windows) networked to a Cray. 

By diagonalizing the Fock matrix, the canonical MO coefficient matrix (C) is obtained (see Eq. [7]). However, we have seen in a previous section that almost all elements in the coefficient matrix are significant, which contrasts with the favorable behavior of the one-particle density matrix (P). The density matrix is conventionally constructed from the coefficient matrix by a matrix product (Eq. [8]). Although the Roothaan-Hall equations are useful for small-to medium-sized molecules, it makes no sense to solve first for a nonlocal quantity (C) and generate from this the local quantity (P) in order to compute the Fock matrix or the energy of a molecule. Therefore, the goal is to solve directly for the one-particle density matrix as a local quantity and avoid entirely the use of the molecular orbital coefficient matrix. 

AU these efforts point out how the GGA form is severely limited, and in practice some compromise must be done between molecular applications, which require more nonlocal functionals [57], and soUd-state uses, for which local functionals always provide good results [58]. One general way to go beyond the GGA is to construct a fiUly nonlocal density functional. This goal is quite ambitious and trials might lead to functionals useless for practical purpose [59]. A more practical way is to construct a functional casting additional semilocal information. This can be done, for instance, including the kinetic energy density of the occupied KS orbitals ... 

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