Effective Core Potential-Based Method

The relativistic effective potential 17 is the j (total angular momentum) dependent core potential fit to the large component of the Dirac four-component wave functions. The average relativistic effective potential is the average relativisitic potential of the j states, given as 

Because u is constructed from a potential fit to the Dirac fovu-component wave functions, it contains all relativisitic effects, except for spin-orbit coupling. The spin-orbit coupling operator for the effective core potential is then given as the difference between the relativistic effective potential, and the averaged relativistic effective potential, 

The spin-orbit operator, Eq. [72], is constructed from the effective core potentials. 

The spin-orbit coupling is incorporated into the calculations at the post-Hartree-Fock level, particularly with CL This is generally referred to as spin-orbit CL The core potential and associated basis sets for Li—Kr, including the spin-orbit operator, have been published. ° Implementation of the spin-orbit Cl method has been discussed by Pitzer and co-workers. It has also been reported that the spin-orbit Cl code has been adapted to a parallel computing enviroment.  

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Ab initio methods for lanthanide and actinide molecules are mostly based on the effective core potential (ECP) method, especially if the molecules in question have several heavy atoms. The philosophy of the ECP method is to replace the chemically unimportant core electrons by an effective core potential and treat the remaining valence electrons explicitly. There are several techniques to derive RECPs which we now briefly describe and refer to the reviews by Christiansen et al. (1985), Krauss and Stevens (1984), Balasubramanian and Pitzer (1987) for further details. 

The only calculation we found for CdH is the work of Balasubramanian [68], using Cl with relativistic effective core potentials. The coupled-cluster results are presened in Table 6. Calculated values for R , cOg and Dg agree very well with experiment. Relativity contracts the bond by 0.04 and reduces the binding energy by 0.16 eV. The one- and two-component DK method reproduce the relativistic effects closely. Similar trends are observed for the excited states (Tables 7-9). Comparison with experiment is difficult for these states, since many of the experimental values are based on incomplete or uncertain data [65]. Calculated results for the CdH anion are shown in Table 10. The... 

The results presented here show that quantum-chemistry methods, whose accuracy and sophistication continue to increase, are capable of providing thermochemical data of practical value for modehng organometallic tin chemistry. In particular, the relativistic effective core potential used here appears to provide an adequate description of the electronic structure at tin, based on the favorable comparisons between experimental heats of formation and values predicted by the ECP/BAC-MP4 method. Trends in heats of... 

Model potential methods and their utilization in atomic structure calculations are reviewed in [139], main attention being paid to analytic effective model potentials in the Coulomb and non-Coulomb approximations, to effective model potentials based on the Thomas-Fermi statistical model of the atom, as well as employing a self-consistent field core potential. Relativistic effects in model potential calculations are discussed there, too. Paper [140] has examples of numerous model potential calculations of various atomic spectroscopic properties. 

Before any computational study on molecular properties can be carried out, a molecular model needs to be established. It can be based on an appropriate crystal structure or derived using any technique that can produce a valid model for a given compound, whether or not it has been prepared. Molecular mechanics is one such technique and, primarily for reasons of computational simplicity and efficiency, it is one of the most widely used technique. Quantum-mechanical modeling is far more computationally intensive and until recently has been used only rarely for metal complexes. However, the development of effective-core potentials (ECP) and density-functional-theory methods (DFT) has made the use of quantum mechanics a practical alternative. This is particularly so when the electronic structures of a small number of compounds or isomers are required or when transition states or excited states, which are not usually available in molecular mechanics, are to be investigated. However, molecular mechanics is still orders of magnitude faster than ab-initio quantum mechanics and therefore, when large numbers of... 

Two levels of theory are commonly used in the design of the nickel-based catalysts shown in Figure 11 Density Functional Theory (B3LYP functional used with effective core potentials for Ni and 6-3IG for everything else in the complex) and molecular mechanics (both the UFF (4) and reaction force field, RFF (85,86) are used) (87). All these methods are complementary, and the experiments are guided from the results of several calculations using different molecular modeling techniques. 

A further reduction of the computational effort in investigations of electronic structure can be achieved by the restriction of the actual quantum chemical calculations to the valence electron system and the implicit inclusion of the influence of the chemically inert atomic cores by means of suitable parametrized effective (core) potentials (ECPs) and, if necessary, effective core polarization potentials (CPPs). Initiated by the pioneering work of Hellmann and Gombas around 1935, the ECP approach developed into two successful branches, i.e. the model potential (MP) and the pseudopotential (PP) techniques. Whereas the former method attempts to maintain the correct radial nodal structure of the atomic valence orbitals, the latter is formally based on the so-called pseudo-orbital transformation and uses valence orbitals with a simplified radial nodal structure, i.e. pseudovalence orbitals. Besides the computational savings due to the elimination of the core electrons, the main interest in standard ECP techniques results from the fact that they offer an efficient and accurate, albeit approximate, way of including implicitly, i.e. via parametrization of the ECPs, the major relativistic effects in formally nonrelativistic valence-only calculations. A number of reviews on ECPs has been published and the reader is referred to them for details (Bala-subramanian 1998 Bardsley 1974 Chelikowsky and Cohen 1992 Christiansen et... 

In the calculations based on effective potentials the core electrons are replaced by an effective potential that is fitted to the solution of atomic relativistic calculations and only valence electrons are explicitly handled in the quantum chemical calculation. This approach is in line with the chemist s view that mainly valence electrons of an element determine its chemical behaviour. Several libraries of relativistic Effective Core Potentials (ECP) using the frozen-core approximation with associated optimised valence basis sets are available nowadays to perform efficient electronic structure calculations on large molecular systems. Among them the pseudo-potential methods [13-20] handling valence node less pseudo-orbitals and the model potentials such as AIMP (ab initio Model Potential) [21-24] dealing with node-showing valence orbitals are very popular for transition metal calculations. This economical method is very efficient for the study of electronic spectroscopy in transition metal complexes [25, 26], especially in third-row transition metal complexes. 

To conclude this section, we mention an article [68] that discusses desirable features for next-generation NDDO-based semiempirical methods. Apart from orthogonalization corrections and effective core potentials that are already included in some of the more recent developments (see above) it is proposed that an implicit dispersion term should be added to the Hamiltonian to capture intramolecular dispersion energies in large molecules. It is envisioned that dispersion interactions can be computed self-consistently from an additive polarizability model with some short-range scaling [68]. 

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