A molecular orbital approach to electronegativity equalization

Baird, N. Colin; Sichel, J. M.; Whitehead, M. A.

doi:10.1007/bf00526067

Cited by 34 publications

(23 citation statements)

References 19 publications

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“…The total energy for integer occupation E(N) can be related to the eigenvalues for integer occupation; thus combining (1) and (11) by multiplying (11) (22) Now when non-integer occupancies are considered, (7) is used for E(Q). Paralleling equation (15), and from equation (7) E, can be expressed as…”

Section: Israel Journal Of Chemistry 19 1980 [ Ije Ij( Q ) ]mentioning

confidence: 99%

On the Dependence of Total Energy on Occupation Numbers

Gopinathan

Whitehead

1980

Israel Journal of Chemistry

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Abstract. An equation is developed for describing the pairwise interactions of q electrons, when q is integer or non-integer. This expression iscompared with the usual equation. It is found to give lower total energies, different ionization and transition energies in the Slater Transition State theory, different values for the atomic energies calculated by the Hyper-Hartree-Fock method, but numerically identical results for the Mulliken Electronegativity. APOLOGIAAs a entre remarked, "I am leary of attributing any physical meaning to E(N) no matter how the problem of non-integral occupancies is handled", and so are we in the precise physical and philosophical sense. It may even be that the recent work on the virial partitioning theory and catastrophe theory, ,-4and its applications to molecular systems,' wherein atomic regions of total integral occupances within the molecule are defined: may replace the current use of non-integral occupances in the analysis of molecular wavefunctions. However until this comes to pass, there will always be the need to attempt the accurate counting of non-integral occupancy interactions,' as in the recent and elegant formalism of density functionals," which even now is being extended to redefine electronegativity" as the chemical potential IL, expressed as (aE1an) where n is the occupancy. And it will always be more elegant, efficient and pleasing to produce the numerical results with a more direct algebraic formalism which avoids certain previously required assumptions. We feel that the present discussion gives an alternate interpolation formula which is theoretically sound within the limitations of using non-integer occupations.electrons were extended classical charge distributions, the total number of electron repulsions, including q.l2 self-repulsions, would be q:12.(3)An electron does not repel itself, quantum mechanically, so that the total number of repulsions reduces to (2).When cP' is an Hartree-Fock spin orbital, and q, is unity for all cPh (1) gives the Hartree-Fock energy, the coefficients q, (q, -1)/2 being zero.When cP' are for the Hyper-Hartree-Fock method, (1) gives the average energy of the multiplet states" because in the HHF method'" cP' represents a shell of (21, + 1) degenerate spin orbitals with (ii) and (ij) suitable averages."?" However, when (ii) and (ij) are suitable averages, the q, become non-integer, especially in calculating transition metal atom and ion ground state configurations. Similarly, in Slater's transition state calculations":" of excitation energies and ionization potentials, the q, becomes non-integer.In the current electronegativity theories.P" where the energy of an atom, or orbital, is assumed to be a differentiable quadratic function of the occupancy q, and where the electronegativity X is given by q is also allowed to be non-integer.The problem therefore arises, as to whether (1) is the best expression for E(N) when q is non-integer.

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Section: Israel Journal Of Chemistry 19 1980 [ Ije Ij( Q ) ]mentioning

confidence: 99%

On the Dependence of Total Energy on Occupation Numbers

Gopinathan

Whitehead

1980

Israel Journal of Chemistry

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“…According to the Hückel approximation, the total Hückel energy £ab (H) °f a two-center two-electron bond AB is given by: £ab(H) = 2 a ? aA + 4<ab ßAB + 2 b2 aB (4) where al symbols have their usual meanings and the MO is an LCAO of the form V>ab = «Va +…”

Section: Total Energy Minimization In the Simplementioning

confidence: 99%

“…This argument was already rejected by Baird et al 4 in their attempt to include molecular terms in the electronegativity-equalization formulae. The condition (see Introduction) that a convenient defi nition of electronegativity for atoms when forming molecules has to bear some initimate relationship with molecular terms is thus extremely well fulfilled.…”

Section: Total Energy Minimization In the Simplementioning

confidence: 99%

Electronegativity and Electron Affinity

Hooydonk¹

1973

Zeitschrift Für Naturforschung A

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Various consequences of the supposition that the value of the resonance integral /?ab depends on the nature of the bond are evaluated within the framework of the simple Hückel method. The resulting equation for /?aB in function of the polarity 1 of the AB bond is:/?AB = (1 -J2) -1/t [C+(V2) J" (aA-a B)d7] where ax is the Coulomb integral. A solution is proposed corresponding with /?ab = (ßAA' /?bb) Further elaboration then suggests that the simple Hückel method in this form is in favour of the ionic approximation to chemical bonding. The Coulomb integral turns out to be the electron affinity, which must now be considered as the electronegativity of elements when forming chemical bonds.

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“…The BEE method was developed [5] from the method of Hinze et al [7], where the total molecular electronic energy is expanded in terms of the energies of the atoms in the molecule [8] :…”

Section: Sigma Bondsmentioning

confidence: 99%