Hyperfine-Coupling Tensors from Projected Hartree–Fock Theory

Abstract

We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree−Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO + , CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving S z symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin-and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.

Combining Complex Conjugation, Time-Reversal, and Spin-Flip Symmetry Projection of Coupled Cluster Wave Functions

“…Following the work of Ghassemi-Tabrizi and co-workers, 21 we could eliminate the phase in the projection operator by incorporating a phase into the optimized reference,…”

“…Following the work of Ghassemi-Tabrizi and co-workers, we could eliminate the phase in the projection operator by incorporating a phase into the optimized reference, | Φ̃ ⟩ = normale Z | Φ ⟩ . That is, if we write | 0 ⟩ = normale − i θ / 2 | Φ̃ ⟩ then we have .25ex2ex P K | Φ̃ ⟩ infix= P K normale i θ / 2 normale − i θ / 2 | Φ̃ ⟩ infix= P K normale i θ / 2 | 0 ⟩ infix= ( 1 + e i θ K ) normale i θ / 2 | 0 ⟩ infix= normale i θ / 2 | 0 ⟩ + normale …”

Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach

“…For a given grouping, the lowest variational energy is obtained when working with the largest symmetry group (PGSGHF). We do not include complex-conjugation symmetry [5,17] in the cPHF scheme, because this involves a more complicated formalism [6,18,19] and has comparatively small effects for Heisenberg systems [6].…”

“…Self-consistent field (SCF, [5,6,19,20]) and gradient-based optimization ( [12,21] and references cited therein) are two different strategies for the optimization of |Φ . In the SCF approach, the local cluster states |Φ i result from successively building and diagonalizing an effective Fock matrix for each cluster.…”

Dissecting the Molecular Origin of g-Tensor Heterogeneity and Strain in Nitroxide Radicals in Water: Electron Paramagnetic Resonance Experiment versus Theory

“…The field of theoretical spectroscopy has been very active in recent years (for reviews, see refs –) The challenges under investigation are manifold and include the explicit treatment of solvent effects for systems of nontrivial size, ,− the development and validation of improved density functionals − and correlated ab initio methods, ,,− the treatment of relativistic- , and vibronic- ,, effects as well as conceptual and algorithmic advances ,,− ,,,− to name only a few. The characterizing parameters of a nitroxide’s EPR spectrum, namely, the g - and A -tensors, are accessible at different levels of theory .…”