Heavy-atom molecules Dirac-Fock

The twin facts that heavy-atom compounds like BaF, T1F, and YbF contain many electrons and that the behavior of these electrons must be treated relati-vistically introduce severe impediments to theoretical treatments, that is, to the inclusion of sufficient electron correlation in this kind of molecule. Due to this computational complexity, calculations of P,T-odd interaction constants have been carried out with relativistic matching of nonrelativistic wavefunctions (approximate relativistic spinors) [42], relativistic effective core potentials (RECP) [43, 34], or at the all-electron Dirac-Fock (DF) level [35, 44]. For example, the first calculation of P,T-odd interactions in T1F was carried out in 1980 by Hinds and Sandars [42] using approximate relativistic wavefunctions generated from nonrelativistic single particle orbitals. 

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

Any realistic description of molecules containing heavy atoms has to take into account relativistic effects (13,41). Attempts to use the algebraic approach to solve the Dirac-Hartree-Fock (DHF) equations are now well advanced (42-45). The difficulties encountered axe much greater than in the nonrelativistic case since the basis sets used have to be larger and have to fulfil the kinetic balance criterion to guarantee the proper description of the large and small components of the molecular orbitals (46-49). 

The last decade has seen a vast amount of method and algorithm development to set up computer programs that can be used for efficient four-component calculations of the electronic structure of molecules. These calculations need incredibly large computer resources even for standard noncorrelated methods like Dirac-Hartree-Fock applied to molecules with only one heavy atom. 

Dirac-Fock calculations were the standard four-component method for electronic structure calculations on molecules during the last decade. However, they are still very demanding or completely infeasible if applied to large unsymmetric molecules with several heavy atoms. In addition, taking properly care of electron correlation increases the computational effort tremendously. Future work will certainly continue the development of relativistic correlation methods, which will be far less expensive. 

All-electron Dirac-Fock relativistic calculations on molecules containing heavy atoms such as Au or U are very time-consuming. A commonly used approach is to do... 

Spin-dependent operators are required when we wish to account for relativistic effects in atoms and molecules [118, 119]. These effects can roughly be classified as strong and weak ones. The relativistic corrections are especially important in heavy atoms where they play a particularly significant role when describing the inner shells. In those cases, they have to be accounted for from the start, usually relying on Dirac-Hartree-Fock method. Fortunately, in most chemical phenomena, only valence electrons play a decisive role and are satisfactorily... 

Desclaux s (1975) numerical Dirac-Fock implementation in a computer is widely used to generate relativistic numerical all-electron wavefu notions for almost any atom in the periodic table. This appears to be one starting point for ab initio relativistic quantum computations of molecules containing very heavy atoms. 

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