Crystal orbital method, systems with

In contrast to the case of an isolated molecule, calculation of the force constants of a polymer is only possible if a further approximation is introduced. By definition, the crystal orbital method can only be applied to systems with perfect periodic symmetry. Energy surfaces were hence computed with all unit cells moving in phase. The force constants /y obtained by the fitting procedure thus correspond formally to the infinite sums... 

The last system investigated by the deformation-potential method is a member of the large family of charge-transfer molecular crystals containing as anion the tetracyanoquinodimethane (TCNQ) molecule. The K TCNQ" salt as well as the other TCNQ crystals consist of columns of stacked TCNQ molecules coordinated by similar columns of the cations. The energy band structures of the stack have been calculated earlier with the help of Pariser-Parr-Pople parametrization of the unrestricted Hartree-Fock crystal-orbital method The last two columns of Table 9.10 show that this material behaves again as a normal... 

The availability of detailed information about the electronic states of PDAs makes them ideal systems to test molecular quantum mechanical theories. The earliest calculation for a model PDA chain with simple sidegroups gave rather poor values for the band-gap, see (7). In most of these calculations Coulomb correlations were neglected so that only band structures were deduced. Further work along these lines has included the use of an ab initio crystal orbital method [105), studies of the ground state geometries [106), a priori Hartree Fock crystal orbital calculations (107) and a non-empirical effective Hamiltonian technique [108). These show... 

The SCF method for molecules has been extended into the Crystal Orbital (CO) method for systems with ID- or 3D- translational periodicityiMi). The CO method is in fact the band theory method of solid state theory applied in the spirit of molecular orbital methods. It is used to obtain the band structure as a means to explain the conductivity in these materials, and we have done so in our study of polyacetylene. There are however some difficulties associated with the use of the CO method to describe impurities or defects in polymers. The periodicity assumed in the CO formalism implies that impurities have the same periodicity. Thus the unit cell on which the translational periodicity is applied must be chosen carefully in such a way that the repeating impurities do not interact. In general this requirement implies that the unit cell be very large, a feature which results in extremely demanding computations and thus hinders the use of the CO method for the study of impurities. 

In tune with the above introductory remarks, we have arranged this review in the following way Section II deals with the oriented gas model that employs simple local field factors to relate the microscopic to the macroscopic nonlinear optical responses. The supermolecule and cluster methods are presented in Section III as a means of incorporating the various types of specific interactions between the entities forming the crystals. The field-induced and permanent mutual (hyper)polarization of the different entities then account for the differences between the macroscopic and local fields as well as for part of the effects of the surroundings. Other methods for their inclusion into the nonlinear susceptibility calculations are reviewed in Section IV. In Section V, the specifics of successive generations of crystal orbital approaches for determining the nonlinear responses of periodic infinite systems are presented. Finally,... 

In summary, the calculations on this special impurity system, with only one open-shell electron and simple manifolds, in which the assigmnents of the 5/<-> 6d absorption/emission bands were specially clear, even though not complete, and where absorption/emission bands built on a single origin and recorded with an extremely hi resolution exist, allow to be initially optimistic in the evaluation of the applicability of present day ab initio methods of the Quantum Chemistry in structural and spectroscopic studies of actinide ion impurities in ionic crystals. The quality of the approximate Hamiltonians and of the approximate procedures for decoupling the treatment of electron correlation and spin-orbit seems to be acceptable. The performance in other impurities with several open-shell electrons and large manifolds will be presented in the next two sections. 

J. C. Slater together with G. F. Koster developed a method called the Slater-Koster tight-binding method, which builds directly on Figure 16.1. This tight-binding model is a simplified MO model where the crystal orbitals are expressed in terms of atomic functions, as in the Hiickel model. Later, basis sets of the same type as in quantum chemical calculations on finite systems have also come to be used in infinite systems. 

The Fenske-Hall method is a modification of crystal held theory. This is done by using a population analysis scheme, then replacing orbital interactions with point charge interactions. This has been designed for the description of inorganic metal-ligand systems. There are both parameterized and unparameterized forms of this method. 

The proper way of dealing with periodic systems, like crystals, is to periodicize the orbital representation of the system. Thanks to a periodic exponential prefactor, an atomic orbital becomes a periodic multicenter entity and the Roothaan equations for the molecular orbital procedure are solved over this periodic basis. Apart from an exponential rise in mathematical complexity and in computing times, the conceptual basis of the method is not difficult to grasp [43]. Software for performing such calculations is quite easily available to academic scientists (see, e.g., CASTEP at www.castep.org CRYSTAL at www.crystal.unito.it WIEN2k at www.wien2k.at). 

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