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We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac–Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H2X2 (X = 17O, 33S, 77Se, 125Te, and 209Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin–orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H2Po2 enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only. [ABSTRACT FROM AUTHOR]

Accurate calculations of some response properties, like the NMR spectroscopic parameters, are quite exigent for the theoretical quantum chemistry models together with the computational codes that are written from them. They need to include a very good description of the electronic density in regions close to the nuclei. When heavy-atom containing systems are studied, those requirements become even higher. Given that relativistic effects must be included in one way or another on the calculation of response properties of heavy-atoms and heavy-atom containing molecules, different schemes were developed during the past decades to include them in as good as possible way. There are some four-component models, which include relativistic effects in a very compact way, although calculations have large time-consumption; one also needs to deal with new and unusual four-component operators. There are also two-component models, which in general may be less accurate, although their application to property calculations on medium-size and large-size molecules are feasible, and they maintain the application of usual operators. In this review, we give the fundamentals of the two-component linear response elimination of small component formalism, LRESC, together with some applications to few selected response properties. New physical insights do appear when the LRESC model is used to analyze the effect of the environment on magnetic shieldings, and when one search for the relativistic extension of well-known nonrelativistic relationships like Flygare's relation among the NMR magnetic shielding and the nuclear spin-rotation constant. A similar relationship is found for the g-tensor and the susceptibility tensor. [ABSTRACT FROM AUTHOR]

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree–Fock, Kohn–Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model. [ABSTRACT FROM AUTHOR]