Quasirelativistic method

The quasirelativistic (QR) PP of Hay and Wadt [61] use two-component wave functions, but the Hamiltonian includes the Darwin and mass-velocity terms and omits the spin-orbit effects. The latter are then included via the perturbation operator after the wave functions have been obtained. The advantage of die method is the possibility to calculate quite economically rather large systems. The method is implemented in the commercial system Gaussian 98 It has extensively been applied to calculations of transition-element and actinide systems [62],... 

The non-relativistic PolMe (9) and quasirelativistic NpPolMe (10) basis sets were used in calculations reported in this paper. The size of the [uncontractd/contracted] sets for B, Cu, Ag, and Au is [10.6.4./5.3.2], [16.12.6.4/9.7.3.2], [19.15.9.4/11.9.5.2], and [21.17.11.9/13.11.7.4], respectively. The PolMe basis sets were systematically generated for use in non-relativistic SCF and correlated calculations of electric properties (10, 21). They also proved to be successful in calculations of IP s and EA s (8, 22). Nonrelativistic PolMe basis sets can be used in quasirelativistic calculations in which the Mass-Velocity and Darwin (MVD) terms are considered (23). This follows from the fact that in the MVD approximation one uses the approximate relativistic hamiltonian as an external perturbation with the nonrelativistic wave function as a reference. At the SCF and CASSCF levels one can obtain the MVD quasi-relativistic correction as an expectation value of the MVD operator. In perturbative CASPT2 and CC methods one needs to use the MVD operator as an external perturbation either within the finite field approach or by the analytical derivative schems. The first approach leads to certain numerical accuracy problems. 

The AIMP method in its present form starts from a quasirelativistic all-electron Hartree-Fock calculation for the atom under consideration in a suitable electronic state and approximates the operators on the left-hand side of Equation (3.10) for an atomic core X as described in the following. 

The indices i and j denote electrons, X and ju nuclei. is the charge of the nucleus X. For the one- and two-particle operators h and g various expressions can be inserted (e.g., relativistic, quasirelativistic or nonrelativistic all-electron or valence-only). The basic goal of quantum chemical methods is usually the approximate solution of the time-independent Schrodinger equation for a specific Hamiltonian, the system being in the state 7, i.e.. 

Table 3 presents relativistic effects on several properties calculated as the difference (A) obtained in calculations which included the quasirelativistic correction, and corresponding calculations that excluded the correction, and used Hartree-Fock-Slater core orbitals rather than Dirac-Slater. The method finds significant relativistic Pt-C bond shortening, and little effect on the CO bond. The effect on adsorption energy is dramatic. Eads increases by about 50% when relativity is included. There is also an increase in the Pt-C force constant and frequency. The shortened Pt-C bond results in an increase in CO frequency through a wall effect, a Pauli repulsion effect. Ref. 34 ascribed the anomalously small shift in CO frequency from gas phase to adsorbed on Pt to the relativistic effect. 

The Amsterdam Density Functional (ADF) method [118,119] was used for calculations of some transactinide compounds. In a modem version of the method, the Hamiltonian contains relativistic corrections already in the zeroth order and is called the zero-order regular approximation (ZORA) [120]. Recently, the spin-orbit operator was included in the ZORA Fock operator [121]. The ZORA method uses analytical basis fimctions, and gives reliable geometries and bonding descriptions. For elements with a very large SO splitting, like 114, ZORA can deviate from the 4-component DFT results due to an improper description of the pi/2 spinors [117]. Another one-component quasirelativistic scheme [122] applied to the calculations of dimers of elements 111 and 114[116,117]isa modification of the ZORA method. 

A comparison of results from different relativistic density functional calculations gives some information on whether quasirelativistic treatments are good enough to describe the system under consideration. To assess the accuracy of the density functional results on the other hand requires comparison with experimental of high-level ab initio data. Only results from coupled cluster or Cl-type ab initio calculations are reported here. Although these methods are among the most accurate quantum chemical approaches, there is some variance in the quality of the results reported in the literature. This becomes evident by the substantial scatter sometimes shown by the ab initio results. Within this chapter, the quality of the ab initio results cannot be discussed extensively. We will just point out two possible sources of error ... 

Methods DHF, Dirac-Hartreer-Fock DHFS, Dirac-Hartree-Fock-Slater HF, Hartree-Fock OCE, one-center expansion MS, multiple-scattering DV, discrete-variational QR, quasirelativistic INDO, intermediate neglect of differential overlap WHT, Wolfsberg-Helmholz QR-EHT, quasirelativistic two-component extended Httckel EHT, extended Hllckel. 

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