Extended Huckel EH

As applied to CPs, the EH method takes a set of basis orbitals for the atomic constituents of a unit cell, x, and forms the set of Bloch basis functions  

The corresponding eigenvalues e (4) and coefficients C ( ) are obtained from the eigenvalue equation 

Equation 7.1 indicates that each Bloch basis bjjc) consists of the atomic orbitals Z (r-R ) located at the various unit cells /, and each of them carries the phase factor Thus the nodal properties of a crystal orbital V (A ) at a specific value of k are constructed once the expansion coefficient C k) is known for each bjik). 

The one-electron, non-empirical VEH method first developed by Nicolas and Durand and adapted to CPs by Br6das and others [240, 241], considers only the valence electrons explicitly, with Gaussian functions of appropriate orbital symmetry typically used for the C and H valence electrons. Coulomb interactions are simulated implicitly. In this, effective Fock operators contain the kinetic term and a sum of atomic potentials  

The atomic potential parameters are the linear coefficients, Cg, and nonlinear exponents i, which are optimized for each atomic potential type on model molecules, thus explicitly including the effects of the chemical environment. 

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FIG. 1. Potential-energy curves calculated for Ag2 curve A-extended Huckel (EH) calculations, K = 1.3 curve B-EH, Eq. (8) curve C-complete neglect of differential overlap. 

TTie three methods that have been most widely adopted to calculate DOS curves for clusters are (/) the semi-empirical extended-Huckel (EH) method, (n) the complete-neglect-of-differential-overlap (CNDO) method, and iii) the self-consistent-field Xa scattered-wave (Xa-SW) method. Calculations of electronic structures of many transition- and noble-metal clusters have been reported over the last decade. No attempt is made to summarize them all, because there appears to be a disparity of view among the expert practitioners as to the validities of the various methods of calculation. However, the story to date is as follows. 

On the other hand, the excited energy state diagrams of porphyrins with transition metals are rather complicated when the d orbitals of metal intervene between the n and n orbitals of the porphyrin system. The d d, n d, and d tf states are drawn over the normal porphyrin itstate. The relative positioning is complicatedly dependent on metal atoms, substituents, and axial ligands. Extended Huckel (EH) MO calculation has suggested that the lowest excited states should have a d d nature for Ni" [32-34], Co [36,37] n d... 

EH-extended HUckel (calculations) CNDO-complete neglect of differential overlap. ... 

Molecular-orbital theory has taken many forms and has been dealt with by many approximations. In 1963 Hoffmann S presented a formalism which he referred to as extended Hiickel (EH). In the 1930 s, however, this formalism would simply have been called molecular-orbital, since it is a straightforward application of molecular-orbital (MO) theory, using a one-electron Hamiltonian. Hoffmann referred to it as extended Hiickel because it did not limit itself to 7r-electron systems and was able to deal with saturated molecules by including all overlap integrals. In these respects it did extend the usual, or simple Huckel, method, which was customarily applied to 7T-electrons, and assumed complete tt — a separability. 

Extended Huckel theory is well-known for its flexibility and the ease with which its results lend themselves to chemical interpretation, no matter whether the objects of study are molecules or solids, and a plethora of chemical (bonding) information has been deduced from it, at least qualitatively, and in many cases semiquantitatively. EH theory, however, is not at all made for total-energy calculations or structure optimizations because the electronic potential is too primitive to yield acceptable molecular geometries the latter weakness may be cured, though [114]. 

The quantum chemical calculations differ as to the relative magnitude of AV(cis) and AV(trans). AV(cis)< AV(trans) was obtained by semiempirical methods using the experimentally determined geometry. AV(cis)> AV(trans) follows from ab initio calculations and also from the CNDO/2 and the MINDO methods if the energy is minimized with respect to the residual geometric parameters (EH = extended Huckel calculation) ... 

The input of the problem requires total analytically measured concentrations of the selected components. Total concentrations of elements (components) from chemical analysis such as ICP and atomic absorption are preferable to methods that only measure some fraction of the total such as selective colorimetric or electrochemical methods. The user defines how the activity coefficients are to be computed (Davis equation or the extended Debye-Huckel), the temperature of the system and whether pH, Eh and ionic strength are to be imposed or calculated. Once the total concentrations of the selected components are defined, all possible soluble complexes are automatically selected from the database. At this stage the thermodynamic equilibrium constants supplied with the model may be edited or certain species excluded from the calculation (e.g. species that have slow reaction kinetics). In addition, it is possible for the user to supply constants for specific reactions not included in the database, but care must be taken to make sure the formation equation for the newly defined species is written in such a way as to be compatible with the chemical components used by the rest of the program, e.g. if the species A1H2PC>4+ were to be added using the following reaction ... 

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