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Advances in quantum chemistry

Reduced density-matrix treatment of spin-spin interaction terms in many-electron systems

Rossen L. Pavlov, Alexander I. Kuleff, P. Tz. Yotov, J. Maruani

Published Jan 1, 2001• 1 citation
Publisher
DOI
10.1016/s0065-3276(05)39017-4

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The Journal of Chemical Physics•Sep 22, 2025•1 citation
In the formalism of reduced density matrices and functions, using the irreducible tensor-operator technique and the space-spin separation scheme, the matrix elements of one of the main spin-relativistic corrections of the Breit-Pauli Hamiltonian, the spin-orbit interactions, are expressed in a form suitable for numeric implementation. A comparison with other methods is made and the advantages of such an approach are discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties.
This work extends the variational determination of two-electron reduced density matrices to the generalized spin formulation within the doubly occupied configuration interaction treatment. We describe electronic states of N-electron systems by means of variational evaluation of the corresponding two-electron reduced density matrix elements, subject to determined N-representability conditions, arising from the restricted, unrestricted, and generalized spin approaches. The results are compared with those predicted by the counterpart treatments involving wave functions. We report potential energy curves for a series of hydrogen atom clusters with different geometries in the presence of an external uniform magnetic field. These results allow us to analyze and discuss crossings between potential energy curves involving transitions between electronic states of different spin multiplicities. The predictions provided by these methods have been contrasted with the results arising from the full configuration interaction procedure, confirming changes of ⟨Ŝ2⟩ and ⟨Ŝz⟩ expectation values.