Bertha Code

The BERTHA package [50-54] builds on the principles and formalism described above. Its present core is a multi-centre DHFB self-consistent field code, with which the present chapter is concerned. The Fock matrix is constructed using direct methods that is to say molecular integrals are calculated as needed and are not retained in memory. The architecture of BERTHA aims at a transparent transcription of the mathematical formulae into simple and compact Fortran code. Modules for calculating molecular properties and for many-body calculations of correlation (2nd order MBPT) are available and more are planned, but these lie outside the scope of this chapter. Some of the calculations so far performed have been described in papers listed in the bibliography. 

The implementation follows current practices in nonrelativistic codes, but the internal structure, which has to carry relativistic spinor properties, is obviously different. However the computational overheads, which are much smaller than has usually been supposed, are offset by techniques to avoid calculating classes of integrals which make no detectable physical contribution and by improved representation of the physics. Some implementation issues are discussed in this section. 

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Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

By incorporating these symmetries in the 4-spinor basis functions, as we have done in our BERTHA code [50-54], we can make substantial computational economies in computing interaction integrals. The angular stracture of Dirac 4-spinors described here is also exploited by the major computer package TSYM, which utilizes projection operators to construct relativistic molecular symmetry orbitals for double valued representations of point groups [77-79]. 

Abstract. BERTHA is a 4-component relativistic molecular structure program based on relativistic Gaussian (G-spinor) basis sets which is intended to make affordable studies of atomic and molecular electronic structure, particularly of systems containing high-Z elements. This paper reviews some of the novel technical features embodied in the code, and assesses its current status, its potential and its prospects. 

The experience gained in these studies has been invaluable for the development of the BERTHA molecular code much of the material of the present article was first presented in [29] and [30], together with applications to the study of magnetic and hyperfine interactions in atoms and small molecules, NMR shielding constants for H2O and NH3, and P-odd interactions in chiral molecules such as CHBrClF. A detailed study of the water molecule [31] examined the convergence of the DHF and DHFB calculations with a series of uncontracted correlation consistent basis sets due... 

Finally the BERTHA technology has been applied to relativistic density functional theory by Quiney and Belanzoni [36]. This showed that the method works well for closed shell atoms as compared with benchmark calculations using finite difference methods, and there have been promising parallelization studies [37] which should in future greatly extend the range of application of the code. 

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