A PPP-investigation of Structural Isomerism in Infinite Polyenes

1982 ◽  
Vol 37 (1) ◽  
pp. 28-32 ◽  
Author(s):  
Peter Karadakov ◽  
Obis Castaño
Keyword(s):  
Bond Order ◽  
Analytical Form ◽  
The Other ◽  
Nearest Neighbour ◽  
Bond Orders ◽  
Coulomb Interactions ◽  
Hartree Fock ◽  
Structural Isomerism ◽  
Bond Alternation ◽  
Self Consistent

Abstract It is shown on the grounds of a semiempirical PPP-treatment that for the equidistant eistrans infinite polyene two types of Hartree-Fock solutions are possible-one yielding a cis-transoid and the other a trans-cisoid distribution of nearest-neighbour bond-orders. Relaxing the nuclear framework according to bond-order magnitudes for the bond-alternation wave (BAW) in the equidistant all-trans polyene, resp. for the two solutions for the equidistant cis-trans polyene mentioned above and using repeatedly the Coulson-Golebiewski formula, realistic self-consistent values of bond lengths have been obtained. The calculated energy differences between the investigated isomers are small, predicting almost equal probabilities. The expressions for the PPPwavefunctions are presented in analytical form suitable for further applications. Long-range Coulomb interactions have been accounted for up to convergence of the groundstate energies.

Use of a Lowest Intensity 241Am Compton Spectrometer for the Measurement of Directional Compton Profiles of ZnSe

2006 ◽  
Vol 61 (7-8) ◽  
pp. 364-370 ◽  
Author(s):  
Babu Lal Ahuja ◽  
Narayan Lal Heda
Keyword(s):  
Bond Length ◽  
Theoretical Calculations ◽  
The Other ◽  
Energy Bands ◽  
Electron Momentum ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Self Consistent ◽  
Scattering Technique ◽  
Small Disc

In this paper we report on electron momentum densities in ZnSe using Compton scattering technique. For the directional measurements we have employed a newly developed 100 mCi 241Am Compton spectrometer which is based on a small disc source with shortest geometry. For the theoretical calculations we have employed a self-consistent Hartree-Fock linear combination of atomic orbitals (HF-LCAO) approach. It is seen that the anisotropy in the measured Compton profiles is well reproduced by our HF-LCAOcalculation and the other available pseudopotential data. The anisotropy in the Compton profiles is explained in terms of energy bands and bond length. - PACS numbers: 13.60.Fz, 78.70. Ck, 78.70.-g

VERTEX CORRECTIONS IN THE NUCLEAR SCHWINGER–DYSON FORMALISM

2002 ◽  
Vol 11 (04) ◽  
pp. 321-333 ◽  
Author(s):  
MASAHIRO NAKANO ◽  
HIROYUKI MATSUURA ◽  
TAISUKE NAGASAWA ◽  
KEN-ICHI MAKINO ◽  
NOBUO NODA ◽  
...  
Keyword(s):  
Field Theory ◽  
Correlation Energy ◽  
Mean Field Theory ◽  
Mean Field ◽  
The Other ◽  
Vertex Correction ◽  
Hartree Fock ◽  
Vertex Corrections ◽  
Negative Correlation Energy ◽  
Self Consistent

We develop the Nuclear Schwinger–Dyson (NSD) formalism to include the effects of ladder diagrams by modifying the vertex. In this extension, the NSD equation sums up both ring diagrams and ladder diagrams self-consistently. The results are compared with mean field theory, Hartree Fock and bare-vertex NSD calculations. It is shown that the vertex correction is important from the following viewpoints. First, the vertex correction greatly modifies the meson propagators, and we can avoid the ghost-pole from meson propagators in a self-consistent way. Secondly, it gives a large negative correlation-energy compared with the other calculations; as a result, it gives a softer equation of state which is preferable according to the experimental data.

Some consequences of bond alternation in long polyenes

1961 ◽  
Vol 57 (2) ◽  
pp. 353-363 ◽  
Author(s):  
L. Salem
Keyword(s):  
Power Series ◽  
Bond Order ◽  
Diamagnetic Susceptibility ◽  
Series Expansions ◽  
Bond Orders ◽  
Bond Alternation ◽  
Asymptotic Expressions ◽  
Electron Contribution ◽  
Power Series Expansions

ABSTRACTThe effect of a twofold bond alternation on the bond orders and and on the π-electron contribution to the diamagnetic susceptibility of a cyclic even hydrocarbon polyene is investigated. Power series expansions and asymptotic expressions are given for and χπ in terms of the parameter t2 (0 ≤ t2 < 1) which characterizes the amount of bond alternation. It is found that bond alternation reduces both bond order and χπ strongly, the effect being more drastic the greater the bond alternation (t2→0).

scholarly journals Bond lengths in naphthalene and anthracene

1951 ◽  
Vol 207 (1090) ◽  
pp. 306-320 ◽  
Keyword(s):  
Aromatic Hydrocarbon ◽  
Bond Length ◽  
Configuration Interaction ◽  
Bond Order ◽  
Bond Orders ◽  
Bond Lengths ◽  
Self Consistent ◽  
Hydrocarbon Molecules ◽  
Experimental Values ◽  
Correction Terms

An extremely careful inquiry is made into the possibility of predicting bond lengths in condensed aromatic hydrocarbon molecules. Agreement with the best experimental values, such as those of Robertson, Abrahams, White, Mathieson and Sinclair, is fairly easily obtained to an accuracy of about 0.02Å. This shows that the concept of fractional bond order may quite properly be used to infer bond lengths. Both the molecular-orbital and resonance methods are equally good for this purpose. Predictions to within less than 0.02Å require the introduction of new factors usually neglected. No less than five such factors are discussed: ( а ) electrostatic forces, arising from possible differences in electronegativity of the various carbon atoms, ( b ) changes of bond orders due to electronegativity differences, ( c ) variation of resonance integrals with bond length, ( d ) obtaining a self-consistent set of resonance integrals, ( e ) inclusion of configuration interaction. Correction terms which result from these improvements lie between 0 and 0.015Å, and are not all of the same sign. It is unlikely therefore that this type of analysis will be able to give confident predictions of bond lengths to less than 0.01Å.

A Correlation between Bond Length and Ionic Bond Order. Application to the Ylide–Ylene Problem

1975 ◽  
Vol 53 (20) ◽  
pp. 3040-3043 ◽  
Author(s):  
Myung-Hwan Whangbo ◽  
Saul Wolfe ◽  
Fernando Bernardi
Keyword(s):  
Bond Length ◽  
Bond Order ◽  
The Other ◽  
Atomic Charges ◽  
Bond Orders ◽  
Ionic Bond ◽  
Molecular Systems ◽  
Bond Lengths ◽  
Coulombic Repulsion ◽  
Overlap Population

The C—O and C—S bond lengths of the cations, radicals, and anions CH3O, CH3S, CH2OH, and CH2SH have been found not to correlate with the overlap populations of the C—X bonds. On the other hand, very satisfactory linear relations are observed with the ionic bond orders of the C—X bonds. It is suggested that, in certain molecular systems, it may be more meaningful to associate shortening of a bond A—B with greater coulombic attraction (or smaller coulombic repulsion) between the two point charges represented by the net atomic charges on the atoms A and B than with an increase in the overlap population between these atoms. It is noted that such an interpretation can account for the short C—P bond in a phosphonium ylide without resort to (p → d)π conjugation.

The electronic structure of N2O4. I. σ-Electron delocalization study

1965 ◽  
Vol 18 (8) ◽  
pp. 1115 ◽  
Author(s):  
RD Brown ◽  
RD Harcourt
Keyword(s):  
Electronic Structure ◽  
Molecular Orbital ◽  
Bond Order ◽  
The Other ◽  
Electron Delocalization ◽  
Special Consideration ◽  
Bond Orders ◽  
Bond Properties ◽  
Classical Structure ◽  
Molecular Orbital Study

A detailed molecular orbital study of the σ- and π-electrons of N2O4 is described. Special consideration is given to possible types of oxygen σ-electron delocalization into antibonding NK and KO orbitals which are vacant in the classical structure. Of these, only depopulation of oxygen 2pπ-orbitals into the antibonding NN σ-orbital seems to be of overall importance for interpreting the NN and NO bond properties. The other oxygen a-electron delocalizations are small, and their contributions to the NO bond orders (although sometimes significant), appear largely to cancel. The possibility that our VESCF procedure may yield an overestimate in the magnitude of the calculated NN σ-bond-order is discussed. A distinction is made between the nature of molecular orbitals arising from combination of π-orbitals on oxygen with the antibonding NN and the antibonding NO orbitals respectively.

Self-consistent tensor effects on nuclear matter systems within a relativistic Hartree-Fock approach

2015 ◽  
Vol 91 (2) ◽  
Author(s):  
Li Juan Jiang ◽  
Shen Yang ◽  
Jian Min Dong ◽  
Wen Hui Long
Keyword(s):  
Nuclear Matter ◽  
Hartree Fock ◽  
Self Consistent

Correlation in the Ground State of He Atom

1981 ◽  
Vol 36 (3) ◽  
pp. 272-275 ◽  
Author(s):  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Ground State ◽  
Zero Order ◽  
Consistent Variation ◽  
Hartree Fock ◽  
Perturbation Procedure ◽  
Self Consistent ◽  
He Atom ◽  
Atomic Parameters

It is possible to reproduce the entire results of Pekeris et al. of different atomic parameters for the He atom by introducing (ll) type correlation in a self consistent variation perturbation procedure using the Hartree-Fock (HF) wavefunction as the zero-order wavefunction

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