An improved ab initio relativistic zeroth-order regular approximation correct to order 1/c2

Combining Time-Dependent Density Functional Theory and the ΔSCF Approach for Accurate Core-Electron Spectra

Spectroscopies that probe electronic excitations from core levels into unoccupied orbitals, such as X-ray absorption spectroscopy and electron energy loss spectroscopy, are widely used to gain insight into the electronic and chemical structure of materials. To support the interpretation of experimental spectra, we assess the performance of a first-principles approach that combines linear-response time-dependent density (TDDFT) functional theory with the Δ self-consistent field (ΔSCF) approach. In particular, we first use TDDFT to calculate the core-level spectrum and then shift the spectrum such that the lowest excitation energy from TDDFT agrees with that from ΔSCF. We apply this method to several small molecules and find encouraging agreement between calculated and measured spectra.

How Does the Redox State of Polyoxovanadates Influence the Collective Behavior in Solution? A Case Study with [I@V18O42] q- ( q = 3, 5, 7, 11, and 13)

A series of stable reduction-oxidation states of the cagelike [I@V^IV _xV^V_{18- x}O₄₂]^{5- x} polyoxovanadate (POV) with x = 8, 10, 12, 16, and 18 were studied with density functional theory and molecular dynamics to gain insight into the structural and electron distribution characteristics of these metal-oxo clusters and to analyze the charge/redox-dependent assemblage processes in water and acetonitrile (MeCN) solutions. The calculations show that the interplay between the POV redox state (molecular charge) and the solvent polarity, countercation size, and hydrophilicity (or hydrophobicity) controls the POV agglomeration phenomena, which substantially differ between aqueous and MeCN media. In MeCN, agglomeration is more pronounced for intermediate-charged POVs, whereas in water, the lowest-charged POVs and organic countercations tend to agglomerate into a microphase. Tests made on wet MeCN show diminished agglomeration with respect to pure MeCN. Simulations with alkali countercations in water show that only the highest-charged POV can form agglomerates. The herein presented theoretical investigation aims to support experimental studies of POVs in the field of functional nanomaterials and surfaces, where controlled molecular deposition from the liquid phase onto solid substrates requires knowledge about the features of these metal-oxo clusters in discrete solutions.

Decoding the role of encapsulated ions in the electronic and magnetic properties of mixed-valence polyoxovanadate capsules {X@V22O54} (X = ClO4-, SCN-, VO2F2-): a combined theoretical approach

The electronic structure and magnetism of mixed-valence, host-guest polyoxovanadates {X@VO₅₄} with diamagnetic (X =) ClO₄^- (T_d, 1) and SCN^- (C_∞v, 2) template anions are assessed by means of two theoretical methods: density functional theory and effective Hamiltonian calculations. The results are compared to those obtained for another member of this family with X = VO₂F₂^- (C_2v, 3) (see P. Kozłowski et al., Phys. Chem. Chem. Phys., 2017, 19, 29767-29771), for which complementary data are also acquired. It is demonstrated that the X guest anions strongly influence the electronic and magnetic properties of the system, leading to various valence states of vanadium and modifying V-O-V exchange interactions. Our findings are concordant with and elucidate the available experimental data (see K. Y. Monakhov et al., Chem. - Eur. J., 2015, 21, 2387-2397).

Bicapped Keggin polyoxomolybdates: discrete species and experimental and theoretical investigations on the electronic delocalization in a chain compound

Monomeric and 1D reduced Keggin polyoxometalates have been isolated as black crystals soluble in DMSO; DFT calculations allowed the explanation of the magnetic behavior.

A Quasirelativistic Two-component Density Functional and Hartree-Fock Program

This work describes the implementation of an efficient two-component quasirelativistic density functional and Hartree-Fock program. The fact that the basis functions are real can be exploited if a special internal representation of operators and density matrices is used. This also leads to a considerable reduction of the effort in the closed shell case. While in most applications to open shell molecules, the noncollinear approach to define a relativistic spin density is preferable, the collinear approach finds its application in the calculation of magnetic anisotropy energies. Linear algebra steps in the SCF procedure have a higher relative weight compared to the nonrelativistic case, therefore some care was necessary to make them fast when parallelizing the code. The quasirelativistic Hamiltonians that have been implemented are the ´zeroth-order regular approximation´ (ZORA) Hamiltonian, the Douglas-Kroll-Hess Hamiltonian up to the sixth order, together with an accurate approximation to treat the picture change effect of the electron interaction, and effective core potential (ECP) matrix elements. Geometry gradients are available for the ZORA and ECP methods.

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer, is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X=F, Cl, Br, I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.

Density functional calculations of molecular parity-violating effects within the zeroth-order regular approximation

A (quasirelativistic) two-component density functional theory (DFT) approach to the computation of parity-violating energy differences between enantiomers is presented which is based on the zeroth-order regular approximation (ZORA). This approach is employed herein to compute parity-violating energy differences between several P and M conformations of dihydrogen dichalcogenides (H2X2 with X=O, S, Se, Te, Po), of which some compounds have recently been suggested as potential molecular candidates for the first experimental measurement of parity-violating effects in chiral molecules. The DFT ZORA results obtained in this work with "pure" density functionals are anticipated to deviate by well less than 1% from data that would be computed within related (relativistic) four-component Dirac-Kohn-Sham-Coulomb schemes. In our implementation of the ZORA slightly larger relative deviations are expected for hybrid functionals, depending on the amount of "exact" exchange. For B3LYP (20% exact exchange) differences are estimated to amount to at most 3% in hydrogen peroxide, 2% in disulfane, and 1% or less for the heavier homologs. Thus, the present two-component approach is expected to perform excellently when compared to four-component density functional schemes while being at the same time computationally more efficient. The ZORA approach will therefore be of particular interest for the prediction of parity-violating vibrational frequency shifts, for instance, in isotopomers of H(2)Se(2) and H(2)Te(2).