Hierarchical Structure of the Atomic Orbital Wave Functions ofD-Dimensional Atom

1997 ◽  
Vol 101 (4) ◽  
pp. 418-421 ◽  
Author(s):  
Haruo Hosoya
Keyword(s):  
Hierarchical Structure ◽  
Atomic Orbital ◽  
Wave Functions

Optimum atomic orbital exponents for molecular wave functions

1970 ◽  
Vol 18 (4) ◽  
pp. 533-543 ◽  
Author(s):  
C.L. Silk ◽  
J.N. Murrell
Keyword(s):  
Atomic Orbital ◽  
Wave Functions ◽  
Orbital Exponents

Valence Bond Structures for the N3- Anion, the N3 Radical and the N6- Radical Anion

2012 ◽  
Vol 67 (9) ◽  
pp. 935-943 ◽  
Author(s):  
Richard D. Harcourta ◽  
Thomas M. Klapötke
Keyword(s):  
Radical Anion ◽  
Electron Pair ◽  
Atomic Orbital ◽  
Valence Bond ◽  
Wave Functions ◽  
The One ◽  
Lewis Structures ◽  
Increased Valence ◽  
Polarity Parameters

With Heitler-London atomic orbital-type formulations of the wave functions for (fractional) electron-pair πx(NN) and πy(NN) bonds, increased-valence structures for the N3- anion and N3- radical are equivalent to resonance between familiar standard Lewis structures and singlet diradical (or “long-bond”) Lewis structures. Theory is developed for the calculation of the polarity parameters that are associated with the one-electron πx(NN) and πy(NN) bonds in the increased-valence structures, and illustrative STO-6G estimates of their values are reported. They show that the πx and πy electrons of these bonds are strongly charge-correlated relative to each other. The increased-valence structures for the N3- anion and the N3- radical are used to help construct increased-valence structures for the N6- radical anion with C2h symmetry

scholarly journals High Harmonic Generation and the Role of Atomic Orbital Wave Functions

2007 ◽  
Vol 98 (18) ◽  
Author(s):  
J. Levesque ◽  
D. Zeidler ◽  
J. P. Marangos ◽  
P. B. Corkum ◽  
D. M. Villeneuve
Keyword(s):  
Harmonic Generation ◽  
Atomic Orbital ◽  
High Harmonic ◽  
High Harmonic Generation ◽  
Wave Functions

scholarly journals Multi-dimensional wavelets for scalable image decomposition: Orbital wavelets

2020 ◽  
Vol 18 (05) ◽  
pp. 2050038
Author(s):  
H. M. de Oliveira ◽  
V. V. Vermehren ◽  
R. J. Cintra
Keyword(s):  
Image Analysis ◽  
Atomic Orbital ◽  
Image Decomposition ◽  
Wave Functions ◽  
Still Images

Wavelets are closely related to Schrödinger’s wave functions and the interpretation of Born. Similar to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach allows the increase of the dimension of wavelets through this process. New orbital 2D-wavelets are introduced for the decomposition of still images, showing that it is possible to perform an analysis simultaneously in two distinct scales. An example of such an image analysis is shown.

Orthogonal effective atomic orbitais in the topological theory of atoms

1996 ◽  
Vol 74 (6) ◽  
pp. 939-942 ◽  
Author(s):  
I. Mayer
Keyword(s):  
Large Scale ◽  
Atomic Orbital ◽  
Molecular Fragment ◽  
Wave Functions ◽  
Actual State ◽  
Topological Theory ◽  
Hartree Fock ◽  
Maximal Weight ◽  
Simple Formalism ◽  
The Given

A simple formalism has been developed permitting us to extract, from the molecular wave functions, the effective orthogonal atomic orbitais characterizing the actual state of the atom in the molecule within the framework of Bader's topological theory of atoms. This may give important conceptual connections between the SCF wave functions obtained in the large-scale ab initio calculations, or even at the Hartree–Fock limit, and the traditional atomic orbital picture. The method is based on some partial orthogonality properties of the non-orthogonal localized molecular orbitais constructed by requiring a maximal weight in the given atomic domain, or in another selected molecular fragment. (The use of such localized orbitais may also be of independent interest.) Key words: effective atomic orbitais, atomic orbitais from molecular wave functions, non-orthogonal localized orbitais, topological theory of atoms, Bader's theory of atoms in molecules.

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