State-Interaction Approach for Evaluating g-Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks.

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the g-tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of g-tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models. A simplified and easier-to-implement approach is based on the state-interaction scheme, in which perturbation is included by considering a small number of states. We describe and benchmark the state-interaction approach using equation-of-motion coupled-cluster and restricted-active-space configuration interaction wave functions. The analysis confirms that this approach can deliver accurate results and highlights caveats of applying it, such as a choice of the reference state, convergence with respect to the number of states used in calculations, etc. The analysis also contributes toward a better understanding of challenges in calculations of higher-order properties using approximate wave functions.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians.

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Dynamic correlation for non-orthogonal reference states: Improved perturbational and variational methods.

The use of non-orthogonal orbitals allows the construction and use of more compact wave functions than offered by standard methods using orthogonal molecular orbitals; in particular, for molecules containing partly occupied atomic orbitals as present, for example, in transition metal complexes. With the purpose of developing efficient dynamic correlation methods, we discuss several new internal correlation methods employing a reference state containing non-orthogonal active orbitals. The non-orthogonal internally contracted perturbation theory approach is improved in several directions. The major improvements are the use of the Dyall Hamiltonian including two-electron interactions within the active space as the zero-order operator, the calculation of third-order energy-corrections, and the inclusion of excitations in the space of active orbitals. The latter improvement corrects for the use of an incomplete reference state. The improvements are tested for the nitrogen molecule and the challenging chromium dimer. The combined use of the improved zero-order Hamiltonian and the inclusion of active space excitations allow us to obtain potential curves for the chromium dimer that are close to those obtained using the larger complete active space reference wave function.

Non-orthogonal internally contracted multi-configurational perturbation theory (NICPT): Dynamic electron correlation for large, compact active spaces.

A computational method is presented for systems that require high-level treatments of static and dynamic electron correlation but cannot be treated using conventional complete active space self-consistent field-based methods due to the required size of the active space. Our method introduces an efficient algorithm for perturbative dynamic correlation corrections for compact non-orthogonal MCSCF calculations. In the algorithm, biorthonormal expansions of orbitals and CI-wave functions are used to reduce the scaling of the performance determining step from quadratic to linear in the number of configurations. We describe a hierarchy of configuration spaces that can be chosen for the active space. Potential curves for the nitrogen molecule and the chromium dimer are compared for different configuration spaces. Already the most compact spaces yield qualitatively correct potentials that with increasing size of configuration spaces systematically approach complete active space results.