Molecular orbitals combined with localized

Mixed labeling involving both x and a orbitals occurs in certain molecules the 5BU molecular orbitals of ra is-2-butene (III.78) and transoid 1,3-butadiene (III.65) are labeled ch3> ( cc) and 7rcn2> ( cc) because one lobe of the x orbital overlaps well with the adjacent CC bond-orbital to form a delocalized combination. In cisoid acrolein, orbitals 9A and 10A are labeled TCH2y nodal surfaces of the two localized orbitals coincide and allow for a delocalized combination (III.G8). 

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. 

Corresponding to this valence bond view is a molecular orbital picture. The three cr-orbitals of a CH3 group are regarded as a basis from which three group orbitals may be constructed. One of the possible combinations of the tr-orbitals has the same local symmetry as the vacant p-orbital on the cationic centre, and hence may overlap with it. Therefore, a withdrawal of electrons from the methyl group can take place. The orbital from which electron density... 

Essentially, the n ag, b u) and n b g, b2u) orbitals are the four symmetry-adapted combinations of the in-plane n orbitals of the CN groups. It is important to distinguish between the two n orthogonal orbitals of the CN group. They are degenerate for CN itself because of the cylindrical symmetry but become nondegenerate in TCNQ. Because of the symmetry plane of the molecule, the two formally degenerate orbitals lead to one in-plane tt orbital, denoted as a (nr), which is symmetrical with respect to the molecular plane even if locally it is a nr-type orbital, and one out-of-plane nr orbital, denoted as n n), which is anti-symmetrical with respect to the molecular plane and is locally a nr-type orbital. 

Graphical Models are introduced and illustrated in Chapter 4. Among other quantities, these include models for presentation and interpretation of electron distributions and electrostatic potentials as well as for the molecular orbitals themselves. Property maps, which typically combine the electron density (representing overall molecular size and shape) with the electrostatic potential, the local ionization potential, the spin density, or with the value of a particular molecular orbital (representing a property or a reactivity index where it can be accessed) are introduced and illustrated. 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

From a theoretical point of view XES furthermore provides a very strong basis for the evaluation of methods for population analysis, i.e., the decomposition of the molecular orbitals into atomic contributions [10]. Many different schemes subdividing the charge density into contributions assigned to respective atoms have been proposed, but the lack of means to directly measure the atomic populations in different orbitals has made all techniques somewhat arbitrary and a matter of taste. Due to the strongly localized character of the intermediate core-excited state, however, in combination with the direct dependence of the XES transition probability on the amount of local -population (assuming a Is core hole), XES provides a very sensitive tool to directly measure this atomic population. In all, we have an atom-specific tool, which can be used to address important questions regarding... 

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