We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well a...

These notes describe the multiconfigurational self-consistent-field (MCSCF) method, which is a general approach for describing chemical systems in which a single electron configuration is no longer an adequate description of the electronic structure. This commonly happens in reactions that break or form chemical bonds, diradicals, and metals of the first transition row. A single-determinant, re...

Atom centred ab initio Hartree-Fock is introduced for periodic systems with helical symmetry. Such a structure is decomposed as a product of two crystal sub-groups, one of which being cyclic. This enables the Fock matrix of a finite cluster of cells to be Fourier transformed into a block diagonal form. The diagonalisation is performed on the sub-matrices and the mean field experienced by the ce...

In this proceedings a particular example from [KMPY] is presented: the construction of the level 2 Fock space of Uq(ŝl2). The generating ideal of the wedge relations is given and the wedge space defined. Normal ordering of wedges is defined in terms of the energy function. Normally ordered wedges form a base of the wedge space. The q-deformed Fock space is defined as the space of semi-infinite ...

Nanopartmles have been used as an approach to improve the pharmacodynamic and phannacokinetie propertiesof various drues. Amino acids have been considered to be useful to make such nano particles because ofthocompatithe and biodegradable characteristic. The quantum mechanical method that was chosen to analyze inethio hexa peptide nano ring]. The structure of some peptide nanorrigs as well as th...

The role of power corrections and higher Fock-state contributions to exclusive charmonium decays will be discussed. It will be argued that the J/ψ (ψ′) decays into baryon-antibaryon pairs are dominated by the valence Fock-state contributions. P -wave charmonium decays, on the other hand, receive strong contributions from the ccg Fock states since the valence Fock-state contributions are suppres...

Abstract The quantum electron spin structure and the photon dressed energy spectrum problem are reanalyzed in framework of Fock many-temporal parameter approach. There is analyzed its dependence on symmetry properties related representations basic Clifford algebra, generated by creation-annihilation operators. self-interaction phenomenon discussed within renormalized Lorenz constraint a suitabl...

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagato...

Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in [Formula: see text] lattice, we depart from well-known Araki–Evans index for quasi-free fermion states and rewrite it terms rather than basis projections. Furthermore, reformulate results that relate equivalences Fock representations to parity into Gel’fand–Naimark–Segal associated parity.