Atomic orbitals valence

Split-Valence Basis Sets. In split-valence basis sets, inner or core atomic orbitals ar e represented by one basis function and valence atomic orbitals are represented by two. The carbon atom in methane is represented by one Is inner orbital and 2(2s, 2pj., 2py, 2pj) = 8 valence orbitals. Each hydrogen atom is represented by 2 valence orbitals hence, the number of orbitals is... 

Valence Atomic Orbitals on Neighboring Atoms Combine to Form Bonding, Non-Bonding and Antibonding Molecular Orbitals... 

A minimal basis in which the number of STO or CGTO orbitals is equal to the number of core and valence atomic orbitals in the atom. 

Appearance of the metallic structure of CNT is based on the crossing of the highest occupied (HO) and the lowest unoccupied (LU) bands (see, e.g.. Fig. 3), each accompanying pseudo rt-type crystal orbital. Note that pseudo n-type orbital, particularly when all the valence atomic orbitals (AO) are taken into consideration, implies that its main AO component is normal to the cylindrical CNT surface. The band crossing mentioned above is possible when these two... 

The valence atomic orbitals which are available to form the orbitals of a CC single bond, directed along the x axis, are the 2s and 2px atomic orbitals on each carbon atom. Their admixture—in proportions which depend on the number of neighbors at each carbon and on the subsequent hybridization—creates two (s, p ) hybrids on each atom. One of these hybrids points away from the other atom and can be used for bonding to additional atoms. The pair of hybrids which point at each other overlap and interact in the conventional fashion [we symbolize the non-interacting orbitals by an interruption of the bond axis (Fig. 1)]. The two bond orbitals which are formed in this manner both have [Pg.3]

The appropriate valence atomic orbitals which must be considered are 2s, 2pj., 2p, on carbon, and the Is orbitals lsH and Ish. The orbital 2py is clearly nonbonding (n) relative to the carbon-hydrogen interactions and need not be considered further. The hydrogen orbitals can be combined into a (lsH + Ish) combination of a symmetry and a (lsH — ls ) combination of 7r symmetry. (Fig. 5). Although there are three available basic cr orbitals, only two of these belong to the C1H2 group proper. We can first eliminate the ( out )... 

When N valence atomic orbitals overlap, they form N molecular orbitals. The ground-state electron configuration of a molecule is deduced by using the building-up principle to accommodate all the valence electrons in the available molecular orbitals. The bond order is the net number of bonds that hold the molecule together. 

Atoms of Period 1 elements (H and He) have one valence atomic orbital each, and atoms of Period 2 and Period 3 elements (Li through Ne, Na through Ar) have four (one s and three p). 

The complex contains 72 atoms with 244 valence electrons distributed in 226 valence atomic orbitals. In order to reduce the computational effort, and to assess the contribution of the ligand 7r-orbitals to the overall spectrum, we examined a "reduced" model, see Figure 2, in which the benzene rings of the ligands are replaced by -HC=CH- groups. This model compound consists of... 

The number of valence orbitals generated by the hybridization process equals the number of valence atomic orbitals participating in hybridization. 

The classic case distinguishes between an atomic core, which is essentially unperturbed by bonding, and a valence shell whose content may be accessible to bond formation. Since we suppose this simplifying assumption to be maintained in the MO treatment, an atomic orbital belonging to the valence shell will be termed a valence atomic orbital (VAO). For the construction of MOs, we utilize the following general results of the MO/LCAO model ... 

A local frontier orbital (LFO) study involving the variational method to analytically find appropriate combinations of valence atomic orbitals giving the maximum and minimum energies of the occupied and unoccupied LFOs, respectively, was employed to find the acidities of the conjugate cation of 1,2,5-thiadiazole 1 <1997PCA5593>. A later study adopted a projected reactive orbital (PRO) approach, which describes local reactivity better than frontier orbital theory in high-symmetry systems to predict the basicity of 1,2,5-thiadiazole 1 <2005PCA7642>. 

Figure 1.2 (a) Lowest s- and p-type valence atomic orbitals of rare-gas atoms, showing radial profiles (left) and contour plots (right). (Each plot is 3 A wide, and only the four outermost contours are plotted see note 26.) (b) Similar to Fig. 1.2(a), for valence 4s, 4p, and 3d atomic orbitals of Kr, corresponding directly to the surface plots of Fig. 1.1. 

An important advantage of ECP basis sets is their ability to incorporate approximately the physical effects of relativistic core contraction and associated changes in screening on valence orbitals, by suitable adjustments of the radius of the effective core potential. Thus, the ECP valence atomic orbitals can approximately mimic those of a fully relativistic (spinor) atomic calculation, rather than the non-relativistic all-electron orbitals they are nominally serving to replace. The partial inclusion of relativistic effects is an important physical correction for heavier atoms, particularly of the second transition series and beyond. Thus, an ECP-like treatment of heavy atoms is necessary in the non-relativistic framework of standard electronic-structure packages, even if the reduction in number of... 

Based on equations (2-5) with initial data calculated with quantum-mechanical techniques [6-8], the values of P0-parameters of the majority of elements being tabulated constant values for each valence atom orbital were calculated. Mainly covalent radii were applied as a dimensional characteristic for calculating PE-parameter - by main type of chemical bond of interactions considered (table 1). For hydrogen atom also the value of Bohr radius and value of atomic ( metal ) radius were applied. 

Equation (11.8) reads The average of the expectation values of r — for the various valence AOs of atom I, weighted by the rations of the orbital populations to the total atomic population of atom I equals the inverse of the — / distance. For all their their simplicity, Eqs. (11.7) and (11.8) cannot be tested numerically by direct calculation. The reason is linked to the difficulty of partitioning the total electron density into atomic contributions, in spite of an important conceptual step forward due to Parr [219]. A practical step in the same direction is in the construction of suitable in situ valence atomic orbitals (VAO) from accurate ab initio computations [143], as advocated long ago by Mulliken [220] and discussed by Del Re [221]. As will be seen, such in situ VAOs do provide useful information, but they are of no help in solving the additional problem of assigning suitable populations to the orbitals and of dividing overlap populations into atomic contributions. In view of this situation, we take Eqs. (11.5) and (11.8) as statements whose validity rests on experimental evidence, at least for saturated hydrocarbons. 

A split-valence basis set represents core atomic orbitals by one set of functions and valence atomic orbitals by two sets of functions. Hydrogen is provided by two s-type functions, and main-group elements are provided two sets of valence s and p-type functions. 

In the simplest picture of chemical bonding, the valence molecular orbitals (ftj are constructed as linear combinations of valence atomic orbitals X x according to the LCAO-MO formula ... 

A double-zeta (DZ) basis in which twice as many STOs or CGTOs are used as there are core and valence atomic orbitals. The use of more basis functions is motivated by a desire to provide additional variational flexibility to the LCAO-MO process. This flexibility allows the LCAO-MO process to generate molecular orbitals of variable diffuseness as the local electronegativity of the atom varies. Typically, double-zeta bases include pairs of functions with one member of each pair having a smaller exponent (C, or a value) than in the minimal basis and the other member having a larger exponent. 

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