Spin–orbit DFT with analytic gradients and applications to heavy element compounds

A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.

Size-controlled excitonic effects on electronic and optical properties of Sb2S3 nanowires

In this work, the electronic and optical properties of one-dimensional (1D) Sb2S3 nanowires (NWs) with different sizes are investigated using first-principles calculations. The indirect-direct band transition of Sb2S3 NWs can be tuned effectively by the NW size and various uniaxial strains. In the Sb2S3 NWs, the quantum confinement effects result in wider bandgaps while the significantly enhanced electron-hole interaction that is expected to produce excitonic bound states generates a bandgap narrowing. The exciton binding energies for the Sb2S3 NWs are predicted by the effective masses of electrons and holes to lie in the range of 0-1 eV, which are larger than that of bulk Sb2S3, suggesting that excitons in Sb2S3 NWs may bind possible defects to promote luminescence. The size-controlled absorption edge blueshift and redshift of Sb2S3 NWs suggest that Sb2S3 NWs may be promising in the applications of nanoscale light emitting devices.

Spin-orbit coupling from a two-component self-consistent approach. I. Generalized Hartree-Fock theory

Formal and computational aspects are discussed for a self-consistent treatment of spin-orbit coupling within the two-component generalization of the Hartree-Fock theory. A molecular implementation into the CRYSTAL program is illustrated, where the standard one-component code (typical of Hartree-Fock and Kohn-Sham spin-unrestricted methodologies) is extended to work in terms of two-component spinors. When passing from a one- to a two-component description, the Fock and density matrices become complex. Furthermore, apart from the αα and ββ diagonal spin blocks, one has also to deal with the αβ and βα off-diagonal spin blocks. These latter blocks require special care as, for open-shell electronic configurations, certain constraints of the one-component code have to be relaxed. This formalism intrinsically allows us to treat local magnetic torque as well as noncollinear magnetization and orbital current-density. An original scheme to impose a specified noncollinear magnetization on each atomic center as a starting guess to the self-consistent procedure is presented. This approach turns out to be essential to surpass local minima in the rugged energy landscape and allows possible convergence to the ground-state solution in all of the discussed test cases.

Fundamental Role of Fock Exchange in Relativistic Density Functional Theory

We perform a formal analysis of relativistic density functional theory for the treatment of spin-orbit coupling (SOC), noncollinear magnetization (NCM), and orbital current density (OCD). We identify specific components of the spinors (namely, those mapped onto imaginary diagonal spin-blocks of the density matrix) that arise from the SOC operator and define the OCD. We show that these pieces of the spinors only enter in the bielectronic part of the potential through the exact Fock exchange (FE) operator. The lack of FE therefore leads to a correspondingly incorrect physical description of SOC, NCM, and OCD. This analysis is complemented with an illustrative example, where we show that, while in the absence of FE, the theory fails even at reproducing the expected right-hand relationship between the NCM and OCD, its inclusion provides results that match those from a reference SOC configuration-interaction calculation.

Nitrogen Reduction by Multimetallic trans-Uranium Actinide Complexes: A Theoretical Comparison of Np and Pu to U

There is recent interest in organometallic complexes of the trans-uranium elements. However, preparation and characterization of such complexes are hampered by radioactivity and chemotoxicity issues as well as the air-sensitive and poorly understood behavior of existing compounds. As such, there are no examples of small-molecule activation via redox reactivity of organometallic trans-uranium complexes. This contrasts with the situation for uranium. Indeed, a multimetallic uranium(III) nitride complex was recently synthesized, characterized, and shown to be able to capture and functionalize molecular nitrogen (N₂) through a four-electron reduction process, N₂ → N₂^4-. The bis-uranium nitride, U-N-U core of this complex is held in a potassium siloxide framework. Importantly, the N₂^4- product could be further functionalized to yield ammonia (NH₃) and other desirable species. Using the U-N-U potassium siloxide complex, K₃U-N-U, and its cesium analogue, Cs₃U-N-U, as starting points, we use scalar-relativistic and spin-orbit coupled density functional theory calculations to shed light on the energetics and mechanism for N₂ capture and functionalization. The N₂ → N₂^4- reactivity depends on the redox potentials of the U(III) centers and crucially on the stability of the starting complex with respect to decomposition into the mixed oxidation U(IV)/U(III) K₂U-N-U or Cs₂U-N-U species. For the trans-uranium, Np and Pu analogues of K₃U-N-U, the N₂ → N₂^4- process is endoergic and would not occur. Interestingly, modification of the Np-O and Pu-O bonds between the actinide cores and the coordinated siloxide framework to Np-NH, Pu-NH, Np-CH₂, and Pu-CH₂ bonds drastically improves the reaction free energies. The Np-NH species are stable and can reductively capture and reduce N₂ to N₂^4-. This is supported by analysis of the spin densities, molecular structure, long-range dispersion effects, as well as spin-orbit coupling effects. These findings chart a path for achieving small-molecule activation with organometallic neptunium analogues of existing uranium complexes.