Molecular DHF calculations

The number of reported molecular DHF calculations is sufficiently small that a fairly complete account is possible. The cases which have been studied in the DHF model all involve small molecules, or molecules which exhibit high spatial symmetry. Larger molecules have been studied using more approximate schemes, ranging from semi-empirical and pseudopotential methods to Dirac-Fock-Slater and density functional methods. These are discussed elsewhere in this book. 

One-centre expansions Pyykkb and Desclaux performed ab initio one-centre expansions of the molecular spinors of small molecular species using finite difference methods. These studies included diatomic hydrides [191,192] and systematic investigations of chemical trends in the properties of hydrides which placed the heavy central atom in tetrahedral [193] and octahedral [194] environments. These calculations were amongst the first to enable the invesiga-tion of the likely chemical properties of some of the superheavy elements at a plausible level of theory. 

Finite difference methods Benchmark calculations have been performed for a number of diatomic species containing heavy elements, for one-electron systems [195-197], and in the Dirac-Fock-Slater approximation [198,199]. 

Physical applications An early application of relativistic molecular theory was to heavy atom collisions, and the production of supercritical fields involving highly stripped ions [234-237]. Studies have been made of parity- and time-reversal symmetry violation in diatomic molecules [74,238,239], and of parity violation in small chiral molecules [240-242]. 

HMQ wishes to acknowledge the support of the Victorian Partnership for Advanced Computing (VPAC) and the School of Chemistry (University of Melbourne). 

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Explicit inclusion of relativistic effects in valence-only calculations has been by far less frequently attempted. Datta, Ewig and van Wazer [135] used a Phillips-Kleinman PP in a study of PbO, whereas Ishikawa and Malli [136] tested PPs of semilocal form in four-component atomic DHF finite difference calculations. This work was extended by Dolg [137] to four-component molecular DHF calculations with a subsequent correlation treatment. In addition a complicated form of Vcv based on the Foldy-Wouthuysen transformation [138] was derived by Pyper [139] and applied in atomic calculations [140]. For all these approaches the computational effort is significantly higher than for the implicit treatment of relativity, and the gain of computational accuracy is not obvious at all. 

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