We present here three new algorithms (one purely iterative and two DIIS-like [Direct Inversion in the Iteractive Subspace]) to compute maxima of homogeneous functions of orthogonal matrices. These algorithms revolve around the mathematical lemma that, given an invertible matrix A, the function f(U)=Tr(AU) has exactly one local (and global) maximum for U special orthogonal [i.e., UU(T)=1 and det...

A methodology is developed for the quantitative identification of the quasi-atomic orbitals that are embedded in a strongly correlated molecular wave function. The wave function is presumed to be generated from configurations in an internal orbital space whose dimension is equal to (or slightly larger) than that of the molecular minimal basis set. The quasi-atomic orbitals are found to have lar...

The basis for a quantum-mechanical description of matter is electron wave functions. For atoms and molecules, their spatial distributions and phases are known as orbitals. Although orbitals are very powerful concepts, experimentally only the electron densities and -energy levels are directly observable. Regardless whether orbitals are observed in real space with scanning probe experiments, or i...

In this design an optical ring resonator are embedded between two Horizontal input and output waveguides which has 4 orbitals around the center of the resonator so that each orbital consists of 8 rods with different size in which radius of larger orbitals rods are bigger than radius of smaller orbitals rods. The analysis of simulation results showed the proposed filter has the transmission effi...

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and ...

The experimental imaging of electronic orbitals has allowed one to gain a fascinating picture of quantum effects. We here show that the energetically high-lying orbitals that are accessible to experimental visualization in general differ, depending on which approach is used to calculate the orbitals. Therefore, orbital imaging faces the fundamental question of which orbitals are the ones that a...