Atomic orbital resolution

Aryl vinyl sulphones, reactions of 646 Aryl vinyl sulphoxides 620 optical resolution of 287 reactions of 354, 355, 360, 361, 621 Asscher-Vofsi reaction 189 Asymmetric induction 625 Asymmetric oxidation 72-78 Asymmetric reduction 78, 79 Asymmetric synthesis 824-846 Atomic orbitals 2, 3 Azetidinones 790, 791 ot-Azidoaldehydes, synthesis of 811 Azidosulphones, photolysis of 883, 884 Azosulphones, photolysis of 879 Azoxysulphones, photolysis of 879 1-Azulyl sulphoxides, synthesis of 265... 

R.F. Nalewajski, Orbital resolution of molecular information channels and stockholder atoms, Mol. Phys. 104 (2006) 2533. 

The upper limit of CCI mode resolution is determined by the characteristics of the STM tip, assuming that a surface contour map is indeed produced. Where the tip is a semiconductor material, tip-to-surface interactions are presumed to be mediated by a single p orbital. Where the tip is a d-band metal then interactions are presumed to be mediated by a single frontier dz orbital. In either case, single-orbital-mediated interactions should lead to at least atomic-level resolution of surface features. 

An original and complete solution of that problem has been offered by Komorowski and Lipinski [30,31]. Their analysis is based on the resolution of the Hartrec-Fock eigcnproblem for a molecule on the basis of atomic orbitals. If Fu denote elements of the energy matrix, Su arc overlap integrals and P stand for the elements of the bond order matrix, the following results for atomic electronegativity and hardness are obtained. 

In usual MO calculations with the ZORA Hamiltonian, the atomic orbital integrals derived from the ZORA Hamiltonian are simple and are evaluated numerically in direct space. In our study, however, we use the resolution of identity (RI) approximation with finite basis functions to evaluate them. To this end we use the relation. 

Lee AM, Handy NC, Colwell SM (1995) The density functional calculation of nuclear shielding constants using London atomic orbitals. J ChemPhys 103 10095-10109 Lippmaa,E, Magi M, Samoson A, Engelhard G, Grimmer,A-R (1980) Structural studies of silicates by solid-state high-resolution Si NMR. J Am Chem Soc 102 4889-4893 Lipscomb WN (1966) The chemical shift and other second-order magnetic and electric properties of small molecules. In Adv Mag Reson, Vol. 2, p 137-176... 

The computational cost of the transformation in Eq. (9) is negligible compared to the cost of calculating the generalized polarizabilities, a. Compared to the method used by Geerlings et al. [29], the advantage of our method is that its resolution, i.e., the size of the sine basis, can be defined by the user and is not given by the atomic orbital basis set. The main features of the DRE do not require high resolution. The number of the expansion (sine) basis is proportional to the molecular volume and at a constant resolntion scales linearly with molecular size. This quantity determines the main computational cost, the calculation of the first-order perturbed wavefunctions by the CPHF or CPKS procedure... 

Figure 2 Contents at higher resolution of the dark square in Figure I labeled by kernel 7. The elements in the squares are functions of the coefficients of the orbitals associated with the atoms that label the squares. The contents of the square labeled by N7 are shown in Figure 3 at orbital resolution...

The resulting operators are products of algebraic functions (square root expressions) of p and are usually not evaluated analytically in the framework of a basis set in the LCAO (linear combination of atomic orbitals) approximation. Rather, a matrix technique employing the approximate resolution of the identity is used to evaluate the operators. ... 

The spatial localization of specific bonds presents another challenging problem to be tackled by this novel treatment of molecular systems. Another diagnostic problem in the theory of molecular electronic structure deals with the shell structure and electron localization in atoms and molecules. The nonadditive Fisher information in the Atomic Orbital (AO) resolution has been recently used as the Contra-Gradience (CG) criterion for localizing the bonding regirais in molecules [10-14, 26-28], while the related information density in the Molecular Orbital (MO) resolution has been shown [9, 29] to determine the vital ingredient of the Electron-Localization Function (ELF) [30-32]. 

Despite its success in reproducing the hydrogen atom spectmm, the Bolir model of the atom rapidly encountered difficulties. Advances in the resolution obtained in spectroscopic experiments had shown that the spectral features of the hydrogen atom are actually composed of several closely spaced lines these are not accounted for by quantum jumps between Bolir s allowed orbits. However, by modifying the Bolir model to... 

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