LCAO SCF molecular orbitals

Single determinant ab initio LCAO-SCF molecular orbital theory is used throughout this study (6,7), Molecular geometries were optimized with the minimal STO-3G basis set (8,9), and where possible the energy of the final structure was recalculated with the extended 4-31G basis set (9,10), Such a procedure has been shown to provide a reasonable description of the structures and energies of neutral organic molecules (11) and carbocations (12), The potential surface for the concerted elimination of hydrogen chloride from ethyl chloride also has been studied successfully (13) with this technique. 

Table 17, LCAO coefficients and energies for SCF molecular orbitals in the azide ion, NaNt,N ... 

The second step determines the LCAO coefficients by standard methods for matrix diagonalization. In an Extended Hiickel calculation, this results in molecular orbital coefficients and orbital energies. Ab initio and NDO calculations repeat these two steps iteratively because, in addition to the integrals over atomic orbitals, the elements of the energy matrix depend upon the coefficients of the occupied orbitals. HyperChem ends the iterations when the coefficients or the computed energy no longer change the solution is then self-consistent. The method is known as Self-Consistent Field (SCF) calculation. 

The molecular orbital methods which have been employed for such studies include extended Hiickel theory (EHT), CNDO, and ab initio LCAO-SCF. 

Within the SCF-CI method a fixed set of molecular orbitals is used. This means that during the calculation (leading to slow convergence) the individual molecular orbitals remain unchanged. A method where the linear expansion coefficients and the LCAO coefficients are optimized simultaneously is the multi-configuration SCF (MCSCF). 

Vibrational 57) and F NMR 68) spectroscopy were used to establish for CIF3O2 the following structure of symmetry C v, which according to semi-empirical linear combination of atomic orbitals-molecular orbitals (LCAO-MO) self-consistent field (SCF) calculations 239) is most stable ... 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Steiger et al. (205) suggested the Coni-02- structure based on femtosecond dynamics. Molecular orbital diagrams (24,25) and earlier LCAO-MO-SCF calculations (29) support this assignment. No ab initio or DFT results on the electronic structure of CoP-02 have been reported so far. 

Hartree-Fock-Roothaan SCF theory, using molecular orbitals expanded as linear combinations of atomic orbital basis functions (LCAO-MO theory)... 

DFT = Density Functional Theory DSD = Diamond-Square-Diamond HOMO = Highest Occupied Molecular Orbital IR = Irreducible Representation LCAO = Linear Combination of Atomic Orbitals Ph = Phenyl PSEPT = Polyhedral Skeletal Electron Pair Theory SCF = Self-Consistent-Field SDDS = Square-Diamond, Diamond-Square TSH = Tensor Surface Harmonic. 

We use standard ab initio self-consistent field (SCF) linear combination of atomic orbitals (LCAO) molecular orbital (MO) theory in this work. Xhe molecular orbitals ipi) are written as linear combinations of basis functions n)... 

In the present paper, first we investigate the photoionization cross sections for atomic orbitals calculated with different scaling parameters of exchange-correlation potential, and for those of different oxidation states, namely different charge densities. We discuss the effect of the variation of the spatial extension of the atomic orbital on the photoionization cross section. Next we make LCAO (linear combination of atomic orbitals) molecular orbital (MO) calculations for some compounds by the SCF DV-Xa method with flexible basis functions including the excited atomic orbitals. We calculate theoretical photoelectron spectrum using the atomic orbital components of MO levels and the photoionization cross sections evaluated for the flexible atomic orbitals used in the SCF MO calculation. The difference between the present result and that calculated with the photoionizaion cross section previously reported is discussed. 

---