G R O U P theory tells us the conditions under which an energy level is invariant under changes of the co-ordinate system (rotations, etc.) which do not change the physical properties of the electron system considered. Thus, the (2L + l)-fold degeneracy of multiplet terms and (21 + l)-fold degeneracy of orbitals is closely connected with the assumption of spherical symmetry, surrounding a gaseo...

Using numerical calculations and analytic theory, we examine the convergence behavior of Gaussian expansions of several model orbitals. By following the approach of Kutzelnigg, we find that the errors in the energies of the optimal n-term even-tempered Gaussian expansions of s-type, p-type, and d-type exponential orbitals are εn s ∼ exp(−π(3n)), εn ∼ exp(−π(5n)), and εn ∼ exp(−π(7n)), respectiv...

The effective atomic orbitals have been realized in the framework of Bader's atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows tha...

A variational, self-consistent implementation of the Perdew-Zunger self-interaction correction (PZ-SIC), based on a unified Hamiltonian and complex optimal orbitals, is presented for finite systems and atom-centered basis sets. A simplifying approximation allowing the use of real canonical orbitals is proposed. The algorithm is based on two-step self-consistent field iterations, where the updat...

Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally ...

Through a basis-set-independent web of localizing orbital-transformations, the electronic wave function of a molecule is expressed in terms of a set of orbitals that reveal the atomic structure and the bonding pattern of a molecule. The analysis is based on resolving the valence orbital space in terms of an internal space, which has minimal basis set dimensions, and an external space. In the in...

ZnO has been extensively studied by virtue of its remarkably high piezoelectric responses, especially in nanowire forms. Currently, the high piezoelectricity of wurtzite ZnO is understood in terms of the covalent-bonding interaction between Zn 3d and O 2p orbitals. However, the Zn 3d orbitals are not capable of forming hybridized orbitals with the O 2pz orbitals since the Zn ion is characterize...

to investigate non-bonded interaction of phenanthrene and bn nanostructure, geometric structure of phenanthrene and b12n12 nano-ring with b3lyp method and 6-31g* basis set are optimized by using ab initio gaussian quantum chemical package. the main purpose of this study was to evaluate changes of electronic properties of aromatic compound in presences nano ring field. therefore reactivity and s...