Hartree-Fock level INDEX

To define Kab and more general multicenter indices at a post Hartree-Fock level, one must invoke more sophisticated techniques [64-67]. We follow our work [36] in which the full Cl and some approximated models were considered in detail. The conventional definition of the generalized bond index is based on identification of Kab with a charge density fluctuation measured via the second-order joint statistical moment [64] (generally, the joint cumulant) ... 

The number of electrons delocalization (shared) between atomic basins Q,- and Dj can be measured by the delocalization index (Dl), 8(Q,-,Q ). For a closed-shell molecule, the DI at the Hartree-Fock level of theory is defined [19] ... 

Besides the elementary properties of index permutational symmetry considered in eq. (7), and intrinsic point group symmetry of a given tensor accounted for in eqs. (8)-(14), much more powerful group-theoretical tools [6] can be developed to speed up coupled Hartree-Fock (CHF) calculations [7-11] of hyperpolarizabilities, which are nowadays almost routinely periformed in a number of studies dealing with non linear response of molecular systems [12-35], in particular at the self-consistent-field (SCF) level of accuracy. 

A theoretical evaluation of the aromaticity of the pyrones pyromeconic acid, maltol, and ethylmaltol along with their anions and cations was carried out at several levels (Hartree-Fock, SVWN, B3LYP, and B1LYP) using the 6-311++G(d,p) basis set <2005JP0250>. The relative aromaticity of these compounds was evaluated by harmonic oscillator model of aromaticity (HOMA), nucleus-independent chemical shifts (NICSs), and /6 indexes and decreases in the order cation > neutral molecule > anion. 

It has also been shown that for a series of benzene rings in paracyclophanes" and in benzenoid hydrocarbons," a very good correlation exists between the geometry-based index HOMA and the Hartree—Fock energy (HF) at the 6-3IG level of theory. It is clear that in all these cases the selection process favors a projection from a multidimensional space to a lower... 

Here, the general index j [i = 1,..., M M = n 2N + l) ]oftheCOshas been replaced by double indexing (for future convenience), where h denotes the band indices and p the levels inside the bands. The subscript 2 at the bracket indicates that integration must be performed over the coordinates of the second electron while Pn is the exchange operator. The detailed form of the relativistic Hartree-Fock equation for a crystal involves the definitions of the Dirac matrices in the form... 

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