Algebraic formulae of matrix elements between valence-bond determinants for periodic systems: The one-band linear case

1992 ◽  
Vol 43 (2) ◽  
pp. 281-300
Author(s):  
Alessandro Fortunelli
Keyword(s):  
Valence Bond ◽  
Linear Case ◽  
Periodic Systems ◽  
Matrix Elements ◽  
The One

The shift lattice: an interpretation of some infinitely adaptive structures

1993 ◽  
Vol 440 (1908) ◽  
pp. 23-36 ◽  
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Periodic Systems ◽  
Adaptive Structures ◽  
One Dimensional ◽  
Modulated Structures ◽  
Simple Generalization ◽  
The One

The structures of various ordered, but non-periodic, systems have been investigated and exhibit features which can be directly described by means of a construction which the authors call the shift lattice , which is a simple generalization of the concept of the lattice. This paper is devoted to a description of the properties of the one-dimensional shift lattice and its Fourier transform. Its applications to the phases related to L–Ta 2 O 5 and some Bi 2 TeO 5 -related systems are outlined and its relation to the theory of modulated structures and their Fourier transforms is briefly discussed.

Electron Correlation Effects on the Lattice Dynamics of Sodium and Potassium

1975 ◽  
Vol 53 (16) ◽  
pp. 1507-1512 ◽  
Author(s):  
V. K. Jindal
Keyword(s):  
Dielectric Function ◽  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Matrix Elements ◽  
Correlation Effects ◽  
Phonon Dispersion Curves ◽  
Electron Correlation Effects ◽  
Experimental Values ◽  
The One ◽  
Sodium And Potassium

The phonon dispersion curves for sodium and potassium have been calculated using the one OPW (orthogonalized plane wave) bare electron matrix elements and the dielectric function of Vashishta and Singwi. Results are compared with experimental results as well as with similar calculations using the dielectric function of Geldart and Taylor. It is found that the screening function of Vashishta and Singwi gives at least as good an agreement with experimental values as obtained from the screening function of Geldart and Taylor. The interionic potentials for these metals have also been calculated and compared with similar calculations done previously. The reason for the appreciable difference between the potentials is discussed.

Collective motion in the nuclear shell model III. The calculation of spectra

1963 ◽  
Vol 272 (1351) ◽  
pp. 557-577 ◽  
Keyword(s):  
Shell Model ◽  
Collective Motion ◽  
Mass Region ◽  
Wave Functions ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
One Dimensional ◽  
The One ◽  
Nuclear Shell ◽  
Main Pattern

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

Heavy-ion reactions as spin probes

1987 ◽  
Vol 65 (6) ◽  
pp. 609-613 ◽  
Author(s):  
Sam M. Austin ◽  
N. Anantaraman ◽  
J. S. Winfield
Keyword(s):  
Cross Sections ◽  
Reaction Mechanisms ◽  
Heavy Ion ◽  
Spin Transfer ◽  
Calibration Function ◽  
Matrix Elements ◽  
Heavy Ion Reactions ◽  
One Step ◽  
The One ◽  
Gamow Teller

Heavy-ion reactions can be powerful probes for spin-transfer strength in nuclei, provided their reaction mechanism is simple so that a correlation can be established between cross sections and the relevant matrix elements. We discuss the desirable features of heavy-ion reactions in general and a series of tests of reaction mechanisms that have been carried out for two of the most favorable reactions; (6Li, 6He) and (12C, 12N). We establish that the (6Li, 6He) reaction is one-step in nature above 25 MeV∙nucleon−1 and establish a calibration function relating cross sections and Gamow–Teller matrix elements. We also find that the (12C, 12N) reaction is likely to be dominated by the one-step process above about 50 MeV∙nucleon−1.

Dipole transition-matrix elements of the one-electron heterodiatomic quasimolecules

2005 ◽  
Vol 71 (2) ◽  
Author(s):  
A. Devdariani ◽  
T. M. Kereselidze ◽  
I. L. Noselidze ◽  
E. Dalimier ◽  
P. Sauvan ◽  
...  
Keyword(s):  
Transition Matrix ◽  
Dipole Transition ◽  
Matrix Elements ◽  
Transition Matrix Elements ◽  
The One

ELECTRONIC DELOCALIZATION: A QUANTITATIVE STUDY FROM MODERN AB INITIO VALENCE BOND THEORY

2002 ◽  
Vol 01 (01) ◽  
pp. 137-151 ◽  
Author(s):  
YIRONG MO ◽  
LINGCHUN SONG ◽  
WEI WU ◽  
ZEXING CAO ◽  
QIANER ZHANG
Keyword(s):  
Ab Initio ◽  
Valence Bond ◽  
Free Valence ◽  
Matrix Elements ◽  
Resonance Theory ◽  
Valence Bond Theory ◽  
Quantitative Level ◽  
Electronic Delocalization ◽  
Bond Theory ◽  
Overlap Matrix

An ab initio spin-free valence bond code called Xiamen-99 has been developed based on an efficient algorithm called paired-permanent-determinant approach, where Hamiltonian and overlap matrix elements are expressed in terms of paired-permanent-determinants. With this tool, we probed the electronic delocalization phenomenon in a few typical examples including benzene, formamide and ethane. Our computations revealed that ab initio valence bond methods are able to estimate the energetic contribution from the delocalization effect to the stabilization of molecules, thus pave the way to illuminate the resonance theory at the quantitative level. In particular, we analyzed the cyclic electronic delocalization in benzene and showed that different understandings on the resonance may originate from the different usage of one-electron orbitals in the valence bond theory. Our investigation into the hyperconjugative interaction in ethane demonstrated that the hyperconjugation effect is not the dominating factor in the preference of the staggered conformer of ethane.

Polar structures in the theory of conjugated molecules. II. Symmetry properties and matrix elements for polar structures

1950 ◽  
Vol 200 (1062) ◽  
pp. 390-401 ◽  
Keyword(s):  
Valence Bond ◽  
Matrix Elements ◽  
Conjugated Molecules ◽  
Energy Calculations ◽  
Valence Bond Theory ◽  
Energy Parameters ◽  
Symmetry Properties ◽  
The Matrix ◽  
Bond Theory ◽  
Usual Formalism

The inclusion of polar structures in the valence-bond theory of π-electrons entails some additions to the usual formalism, and these are given in this part. The symmetry properties of sets of structures, both non-polar and polar, and the matrix elements that come into energy calculations, are dealt with. Using the work of part I, and the conclusions of this part, the energy parameters for work with polar structures are evaluated.

Sign in / Sign up

Export Citation Format

Share Document