Electronic structure methods periodic systems

In the last decade, quantum-chemical investigations have become an integral part of modern chemical research. The appearance of chemistry as a purely experimental discipline has been changed by the development of electronic structure methods that are now widely used. This change became possible because contemporary quantum-chemical programs provide reliable data and important information about structures and reactivities of molecules and solids that complement results of experimental studies. Theoretical methods are now available for compounds of all elements of the periodic table, including heavy metals, as reliable procedures for the calculation of relativistic effects and efficient treatments of many-electron systems have been developed [1, 2] For transition metal (TM) compounds, accurate calculations of thermodynamic properties are of particularly great usefulness due to the sparsity of experimental data. 

These properties of the d-shell chromophore (group) prove the necessity of the localized description of d-electrons of transition metal atom in TMCs with explicit account for effects of electron correlations in it. Incidentally, during the time of QC development (more than three quarters of century) there was a period when two directions based on two different approximate descriptions of electronic structure of molecular systems coexisted. This reproduced division of chemistry itself to organic and inorganic and took into account specificity of the molecules related to these classical fields. The organic QC was then limited by the Hiickel method, the elementary version of the HFR MO LCAO method. The description of inorganic compounds — mainly TMCs,— within the QC of that time was based on the crystal field... 

Within the tight-binding (TB) approach. Slater and Roster [64] described the linear combination of atomic orbitals (LCAO) method as an eflRcient scheme for calculation of the electronic structure of periodic solids. As this method is computationally much less demanding than other methods such as the plane-wave methods, it has been extensively employed to calculate electronic structures of various metals, semiconductors, clusters and a number of complex systems such as alloys and doped systems. The calculation of the electronic structure requires solving the Schrodinger equation with the TB Hamiltonian given by... 

Electronic structure methods provide detailed insight into optic and electronic properties and are useful in multiscale approaches. They are currently less suited for the simulation of filler materials and nanocomposites as the maximum feasible number of atoms (<10 ) and timescales (<10ps) are rather small. All-atom models on the basis of interatomic potentials (force fields) in combination with molecular dynamics (MD) are a powerful tool that allows the simulation of systems of lO-lOOnm size (up to 1(F atoms) for periods approaching microseconds. MD simulations rely on Newton s classical equations of motion ... 

We have extended the linear combination of Gaussian-type orbitals local-density functional approach to calculate the total energies and electronic structures of helical chain polymers[35]. This method was originally developed for molecular systems[36-40], and extended to two-dimensionally periodic sys-tems[41,42] and chain polymers[34j. The one-electron wavefunctions here are constructed from a linear combination of Bloch functions c>>, which are in turn constructed from a linear combination of nuclear-centered Gaussian-type orbitals Xylr) (in ihis case, products of Gaussians and the real solid spherical harmonics). The one-electron density matrix is given by... 

Sometimes the estimation of the electronic structures of polymer chains necessitates the inclusion of long-range interactions and intermolecular interactions in the chemical shift calculations. To do so, it is necessary to use a sophisticated theoretical method which can take account of the characteristics of polymers. In this context, the tight-binding molecular orbital(TB MO) theory from the field of solid state physics is used, in the same sense in which it is employed in the LCAO approximation in molecular quantum chemistry to describe the electronic structures of infinite polymers with a periodical structure -11,36). In a polymer chain with linearly bonded monomer units, the potential energy if an electron varies periodically along the chain. In such a system, the wave function vj/ (k) for electrons at a position r can be obtained from Bloch s theorem as follows(36,37) ... 

A physical approach to the electronic structure problems of solids contrasts sharply with the notion that local interactions dominate the structure and properties of molecular systems. Hence, it is very appealing to replace the infinite solid, which is difficult to treat quantum-chemically, by finite sites that can model considered species. Intuitively, cutouts from the bulk or the surface are made and treated like molecules. This type of method is called the cluster approach, and the models made as cutouts of the periodic structure are called cluster models [22]. 

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