No abstract

Spin contamination in density functional studies has been identified as a cause of discrepancies between theoretical and experimental spectra of metal oxide clusters such as MoNbO2. We perform calculations to simulate the photoelectron spectra of the MoNbO2 anion using broken-symmetry density functional theory incorporating recently developed approximate projection methods. These calculations are able to account for the presence of contaminating spin states at single-reference computational cost. Results using these new tools demonstrate the significant effect of spin-contamination on geometries and force constants and show that the related errors in simulated spectra may be largely overcome by using an approximate projection model.

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.

Broken symmetry solutions—solutions to the independent particle model that do not obey all symmetries required by the Hamiltonian—have attracted significant interest for capturing multireference properties with mean-field scaling. However, identification and optimization of broken-symmetry solutions is difficult owing to the non-linear nature of the self-consistent field (SCF) equations, particularly for solutions belonging to low-symmetry subgroups and where multiple broken symmetry solutions are sought. Linearization of SCF solution space results in the Lie algebra, which this work utilizes as a framework for elucidation of the set of solutions that exist at the desired symmetry. To demonstrate that searches constructed in the Lie algebra yield the set of broken symmetry solutions, a grid-based search of real-restricted, real-unrestricted, complex-restricted, paired-unrestricted, and real-general solutions of the C2v (nearly D4h) H4 molecule is performed.

A compact orbital representation of ionization processes is described utilizing the difference of calculated one-particle density matrices. Natural orbital analysis involving this difference density matrix simplifies interpretation of electronic detachment processes and allows differentiation between one-electron transitions and shake-up/shake-off transitions, in which one-electron processes are accompanied by excitation of a second electron into the virtual orbital space.

A spin projected double-hybrid density functional theory is presented that accounts for different scaling of opposite and same spin terms in the second order correction. This method is applied to three dissociation reactions which in the unprojected formalism exhibit significant spin contamination with higher spin states. This gives rise to a distorted potential surface and can lead to poor geometries and energies. The projected method presented is shown to improve the description of the potential over unprojected double hybrid density functional theory. Comparison is made with the reference states of the two double hybrid functionals considered here (B2PLYP and mPW2PLYP) in which the projected potential surface is degraded by an imbalance in the description of dynamic and static correlation.

Attempts to reconcile simulated photoelectron spectra of MoVO clusters are complicated by the presence of very low energy barriers in the potential energy surfaces (PESs) of the lowest energy spin states and isomers. Transition state structures associated with the inversion of terminal oxygen ligands are found to lie below, or close to, the zero point energy of associated modes, which themselves are found to be of low frequency and thus likely to be significantly populated in the experimental characterization. Our simulations make use of Boltzmann averaging over low-energy coordinates and full mapping of the PES to obtain simulations in good agreement with experimental spectra. Furthermore, molecular orbital analysis of accessible final spin states reveals the existence of low energy two-electron transitions in which the final state is obtained from a finite excitation of an electron along with the main photodetachment event. Two-electron transitions are then used to justify the large difference in intensity between different bands present in the photoelectron spectrum. Owing to the general presence of terminal ligands in metal oxide clusters, this study identifies and proposes a solution to issues that are generally encountered when attempting to simulate transition metal cluster photoelectron spectroscopy.

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.