Constant electronic energy trajectories in abstract nuclear charge space and level set topology

1987 ◽  
Vol 87 (10) ◽  
pp. 5882-5891 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Paul G. Mezey
Keyword(s):  
Level Set ◽  
Nuclear Charge ◽  
Electronic Energy ◽  
Charge Space

Lower bound energy calculations for

1966 ◽  
Vol 62 (4) ◽  
pp. 769-776 ◽  
Author(s):  
Mary Walmsley ◽  
C. A. Coulson
Keyword(s):  
Excited State ◽  
Lower Bound ◽  
Lower Bounds ◽  
Ground State ◽  
Nuclear Charge ◽  
Electronic Energy ◽  
Energy Calculations ◽  
First Excited State

AbstractTwo different calculations are made of lower bounds for the electronic energy of . In the first the method of truncated Hamiltonians due to Bazley and Fox is adapted in such a way that the nuclear charge rather than the energy becomes the eigenvalue. Lower bounds are calculated for the energies of the six lowest σg and six lowest σu states, as well as of the three lowest of both πg and πu symmetries. This approach gives better convergence than when the energy is used as eigenvalue. In the second calculation the method of Temple and Kato is shown to give a satisfactory value for the energy of the ground state, provided that some necessary knowledge of the energy of the first-excited state is available.

Charge distributions and chemical effects. XXV. On the homogeneity of total molecular energies and the relationships between electronic, orbital, and total energies

1981 ◽  
Vol 59 (7) ◽  
pp. 1074-1082 ◽  
Author(s):  
Sándor Fliszár ◽  
Marielle Foucrault ◽  
Marie-Thèrése Béraldin ◽  
Jacques Bridet
Keyword(s):  
Total Energy ◽  
Nuclear Charge ◽  
Homogeneous Function ◽  
Electronic Energy ◽  
Atomic Data ◽  
Average Deviation ◽  
Total Potential ◽  
Total Energies ◽  
Screening Factor ◽  
The Individual

With the definition of a "screening factor" σk transforming the nuclear charge Zk of an atom k into an "effective" nuclear charge Zk* = Zkσk, the total energy E = E(Zk*, Z*,...) of a molecule at equilibrium can be expressed as a homogeneous function of degree γ/α in Zk*, Zl*,..., i.e. E = −∑kZk*γ/α, where α is the average of the αk's(αk = ∂ ln Zkσk/∂ ln Zk) and γ = (Vne + 2Vnn)/E is a function of the nuclear-electronic, nuclear-nuclear, and total energies. Molecular energies calculated in this manner agree within 0.045% (average deviation) with their SCF counterparts. The sums of the orbital energies are correctly predicted from the equation [Formula: see text] A separation of the individual nuclear–electronic and nuclear–nuclear contributions to the total potential energy V(k, mol) of each nucleus k indicates that the Kkmol factors of the energy formula E = ∑kKkmolV(k, mol) are constant for each type of atom, thus stressing the basic homogeneity of the total energy rather than of the electronic energy only. The γ function, which is the inverse of the molecular average of the Kkmol's, can be estimated in a simple way from atomic data.

ELECTRONIC POTENTIAL SURFACES OF ACETYLENE IN LCAO/MO APPROXIMATION

1960 ◽  
Vol 38 (3) ◽  
pp. 365-372 ◽  
Author(s):  
G. W. King
Keyword(s):  
Nuclear Charge ◽  
Energy Levels ◽  
Electronic Energy ◽  
Potential Surfaces ◽  
Carbon Carbon Bond ◽  
Input Variables ◽  
Electronic Energy Levels ◽  
Electronic Transition Energies ◽  
Electronic Potential ◽  
Lcao Mo

A digital computer has been programmed to carry out 6-electron LCAO/ASMO calculations for linear and trans-bent acetylene, with the following input variables; coefficients of the LCAO/MOs, carbon–carbon bond length, and effective nuclear charge on the carbon atoms. The effect of varying these parameters upon the calculated electronic energy levels is discussed, and approximations to "best" MOs are obtained for various states of the molecule, leading to values of hybridization parameters for the carbon atoms. Certain assumptions enable the electronic energies to be related to the C—C—H bending angle; from this it is concluded the ground state is linear and the lowest Au excited state is bent, in accordance with experiment. Values are given for electronic transition energies and hydrogen-bending force constants.

The electronic energy spectrum of zero-gap semiconductors

1976 ◽  
Vol 120 (11) ◽  
pp. 337 ◽  
Author(s):  
B.L. Gel'mont ◽  
V.I. Ivanov-Omskii ◽  
I.M. Tsidil'kovskii
Keyword(s):  
Energy Spectrum ◽  
Electronic Energy ◽  
Electronic Energy Spectrum
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