DIRAC program system

Another option that reduces the number of functions, particularly when heavy atoms are involved, is the replacement of inner shell electrons by effective (or pseudo) potentials. Such procedures have been incorporated into many ab initio program systems including ACES II. Since the core electrons are not explicitly considered, effective potentials can drastically reduce the computational effort demanded by the integral evaluation. However, because the step is an inexpensive part of a correlated calculation, the role of effective potentials in correlated calculations is less important, due to the fact that dropping orbitals is tantamount to excluding them via effective potentials. An exception occurs when relativistic effects are important, as they would be in a description of heavy atom systems. Most such chemically relevant effects are due to inner shell elearons their important physical effects, like expanding the Pt valence shell, can be introduced via effective potentials that are extracted from Dirac-Fock or other relativistic calculations on atoms. ° Similarly, some effeaive potentials introduce some spin-orbital effects as well. Thus, besides simplifying the computation, effective potential calculations could include important physical effects absent from the ordinary nonrelativistic methods routinely applied. 

In these methods, calculations of two-electron integrals require large disk space and computational time. They are, therefore, still too computer time intensive and not sufficiently economical to be applied to the heaviest elements in a routine manner, especially to complex systems studied experimentally. Mostly small molecules, like hydrides or fluorides were studied with their use. The main aim of those works was investigation of the influence of relativistic and correlation effects on properties of model systems. One of successful implementations of this group of methods is a part of the DIRAC program package [50]. 

The l/REP(r), U ARKP(r), and terms At/f EP(r) in 11s0 of Eqs. (23), (31), and (34) or Eq. (6), respectively, are derived in the form of numerical functions consistent with the large components of Dirac spinors as calculated using the Dirac-Fock program of Desclaux (27). These operators have been used in their numerical form in applications to diatomic systems where basis sets of Slater-type functions are employed (39,42,43). It is often more convenient to represent the operators as expansions in exponential or Gaussian functions (32). The general form of an expansion involving M terms is... 

Dreams is a program that has evolved as a Dirac-Fock code (Dyall 1994c Dyall et al. 1991a) and has been extended to the RMP2 approach for the estimation of correlation energies for closed and open-shell systems (Dyall 1994a). 

The programs described so far use basis-set expansions for the one-electron spinors. The fully numerical approach, which is still a challenging task for general molecules in nonrelativistic theory (Andrae 2001), has also been tested for Dirac-Fock calculations on diatomics (DtisterhOft etal. 1994,1998 Kullie etal. 1999 Sundholm 1987,1994 Sundholm et al. 1987 v. Kopylow and Kolb 1998 v. Kopylow et al. 1998 Yang et al. 1992). The finite-element method (FEM) was tested for Dirac-Fock and Kohn—Sham calculations by Kolb and co-workers in the 1990s. However, this approach has not yet been developed into a general method for systems with more than two atoms only test systems, namely few-electron linear molecules at some fixed intemuclear distance, have been studied with the FEM. Nonetheless, these numerical techniques are able to calculate the Dirac-Fock limit and thus yield reference data for comparisons with more approximate basis-set approaches. The limits of the numerical techniques are at hand ... 

But the most important feature for practical purposes comes with a certain approximation, which is the scalar-relativistic variant of DKH. This one-component DKH approximation, in which all spin-dependent operators are separated by Dirac s relation and then simply omitted, is particularly easy to implement in widely available standard nonrelativistic quantum chemistry program packages, as Figure 12.4 demonstrates. Only the one-electron operators in matrix representation are modified to account for the kinematic or (synonymously) scalar-relativistic effects. The inclusion of the spin-orbit terms requires a two-component infrastructure of the computer program. The consequences of the neglect of spin-orbit effects have been investigate in pilot studies such as those reported in Refs. [626,655] and, naturally, the accuracy depends on the systems under consideration (see also section 14.1.3.2 and chapter 16 for further discussion). 

---