Crystal orbitals, Hartree-Fock

Model Hartree-Fock calculations which include only the electrostatic interaction in terms of the Slater integrals F0, F2, F and F6, and the spin-orbit interaction , result in differences between calculated and experimentally observed levels596 which can be more than 500 cm-1 even for the f2 ion Pr3. However, inclusion of configuration interaction terms, either two-particle or three-particle, considerably improves the correlations.597,598 In this way, an ion such as Nd3+ can be described in terms of 18 parameters (including crystal field... 

In addition, ab initio Hartree-Fock crystal orbital calculations were performed upon 5,7-dimethylaminothieno[3,4-d]pyrimidine (90MI8). 

Suhai S, Bagus PS, Ladik J (1982) An error analysis for Hartree-Fock crystal orbital calculations. Chem Phys 68 467 171... 

The formalism to incorporate translational symmetry into the usual Hartree-Fock approach, the crystal orbital technique, is not new at all 74,75). Reviews of recent devel-opements and applications of the Hartree-Fock crystal orbital method may be found in refs. 76 79). However, only few investigations on the evaluation of equilibrium geometries and other properties derived from computed potential surfaces of one-dimensional infinite crystals or polymers have been reported. 

In Section 2 we briefly summarize the basic mathematical expressions of the LCAO Hartree-Fock crystal orbital method both in its closed-shell and DODS (different orbitals for different spin) forms and describe the difficulties encountered in evaluating lattice sums in configuration space. Various possibilities for calculating optimally localised Wannier functions are also presented. They can be efficiently used in the calculation of excited states and correlation effects discussed in Section 3. 

Hartree-Fock LCAO Crystal Orbital Method... 

The introduction of the concept of one-electron crystal orbitals (CO s) considerably reduces difficulties associated with the many-electron nature of the crystal electronic structure problem. The Hartree-Fock (HF) solution represents the best possible description of a many-electron system with a one-determinantal wavefunction built from symmetry-adapted one-electron CO s (Bloch functions). The HF approach is, of course, only a first approximation to the many-particle problem, but it has many advantages both from practical and theoretical points of view ... 

DOS = Density of states BO = Bloch orbital IBZ = Irreducible Brillouin zone BZ = Brillouin zone PZ = Primitive zone COOP = Crystal orbital overlap population CDW = Charge density wave MO = Molecular orbital DFT = Density functional theory HF = Hartree-Fock LAPW = Linear augmented plane wave LMTO = Linear muffin tin orbital LCAO = Linear combination of atomic orbitals. 

Hartree-Fock calculations on molecules commonly exploit the symmetry of the molecular point group to simplify calculations such studies on perfectly ordered bulk crystalline solids are possible if one exploits the translational symmetry of the crystalline lattice (see Ashcroft and Mermin, 1976) as well as the local symmetry of the unit cell. From orbitals centered on various nuclei within the unit cell of the crystal Bloch orbitals are generated, as given by the formula (in one dimension) ... 

Kertesz, M. Koller, J. Azman, A. Ab initio Hartree-Fock crystal orbital studies. J. Chem. Phys. 1978, 68, 2779-2782. 

In zeroth-order e is chosen to be diagonal and the result is the ordinary field-free Hartree-Fock crystal orbital equation. As usual C(k) is complex for arbitrary k. Apart from this aspect the most important difference between tlie crystal orbital and molecular TDHF perturbation equations is the presence of tlie dC/dk term in the former. Since dC/dk is multiplied by E, field-free derivatives of C(k) with respect to k appear for the first time in the first-order perturbation equations. These field-free... 

The electronic structure of (CH) has been studied using various approaches within the framework of the one-dimensional tight-binding crystal orbital (CO) method, that is, from the Hiickel to the ab initio Hartree-Fock level (see, e.g., Kertesz, 1982). Some of the calculated results of the energetic stability of the (CH), isomers in Fig. 1 are listed in Table I. 

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