Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (II): The restricted open‐shell approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent two‐component relativistic calculations, termed the Kramers‐restricted open‐shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time‐reversal symmetry and quaternion algebra, based on the Kramers‐unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi: 10.1002/qua.25356 ). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans' theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006 , 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin's canonicalization procedure correctly gives physical spinor energies within the frozen‐orbital approximation under spin–orbit interactions.     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Coupled‐perturbed Hartree–Fock theory for quasi–one‐dimensional periodic systems: Calculation of static and dynamic nonlinear optical properties of model systems

An alternative method to solve the coupled‐perturbed Hartree–Fock (CPHF) equations for infinite quasi–one‐dimensional systems is presented. The new procedure follows a proposal made by Langhoff, Epstein, and Karplus to obtain perturbed wavefunctions free from arbitrary phase factors in each order of perturbation. It is based on the intermediate orthonormalization of the perturbed wavefunctions (which is different from the usual one) and a corresponding selection of the Lagrangian multipliers. In this way it is possible to incorporate the orthonormalization conditions into the set of CPHF equations. Moreover, a new, advantageous procedure to determine the derivatives of the wavefunction with respect to the quasimomentum k is presented. We report calculations of the dipole moment, the polarizability α, and the first hyperpolarizability β for different polymers (poly‐HF, poly‐H₂O, trans‐polyacetylene, polyyne, and polycarbonitrile) for different frequencies. These results are extensively compared with oligomer calculations. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 251–268, 2003     

An instability condition for the Hartree–Fock solution of the infinite one‐dimensional system with two‐crossing bands. I. Singlet‐instability check of metallic carbon nanotube

An instability condition is derived for the Hartree–Fock solution so that it can be applied to the system in which the highest occupied and the lowest unoccupied bands cross at the in‐between point in the Brillouin zone. The instability check developed here is further applied to a metallic single‐walled carbon nanotube having the two‐crossing bands toward prediction of its instability. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 574–582, 2000     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999     

Stereochemical behavior of geminal and vicinal 77Se–13C spin–spin coupling constants studied at the SOPPA(CC2) level taking into account relativistic corrections

A systematic theoretical study of geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants in the series of the open‐chain selenides and selenium‐containing heterocycles revealed that relativistic effects play an essential role in the selenium–carbon coupling mechanism, especially when the coupling pathway includes a triple bond, contributing to about 10–15% of their total values and noticeably improving the agreement of the calculated couplings with experiment. Both geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants show marked stereochemical behavior as documented by their calculated dihedral angle dependence that could be used as a practical guide in stereochemical studies of organoselenium compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

Solution of periodic Poisson's equation and the Hartree–Fock approach for solids with extended electron states: Application to linear augmented plane wave method

We formulate a Hartree–Fock‐LAPW method for electronic band structure calculations. The method is based on the Hartree–Fock–Roothaan approach for solids with extended electron states and closed core shells where the basis functions of itinerant electrons are linear augmented plane waves. All interactions within the restricted Hartree–Fock approach are analyzed and in principle can be taken into account. In particular, we obtained the matrix elements for the exchange interactions of extended states and the crystal electric field effects. To calculate the matrix elements of exchange for extended states, we first introduce an auxiliary potential and then integrate it with an effective charge density corresponding to the electron exchange transition under consideration. The problem of finding the auxiliary potential is solved by using the strategy of the full potential LAPW approach, which is based on the general solution of periodic Poisson's equation. Here, we use an original technique for the general solution of periodic Poisson's equation and multipole expansions of electron densities. We apply the technique to obtain periodic potentials of the face‐centered cubic lattice and discuss its accuracy and convergence in comparison with other methods. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

First example of the correlated calculation of the one‐bond tellurium–carbon spin–spin coupling constants: Relativistic effects,vibrational corrections,and solvent effects

This work reports on the comprehensive calculation of the NMR one‐bond spin–spin coupling constants (SSCCs) involving carbon and tellurium, ¹J(¹²⁵Te,¹³C), in four representative compounds: Te(CH₃)₂, Te(CF₃)₂, Te(C?CH)₂, and tellurophene. A high‐level computational treatment of ¹J(¹²⁵Te,¹³C) included calculations at the SOPPA level taking into account relativistic effects evaluated at the 4‐component RPA and DFT levels of theory, vibrational corrections, and solvent effects. The consistency of different computational approaches including the level of theory of the geometry optimization of tellurium‐containing compounds, basis sets, and methods used for obtainig spin–spin coupling values have also been discussed in view of reproducing the experimental values of the tellurium–carbon SSCCs. Relativistic corrections were found to play a major role in the calculation of ¹J(¹²⁵Te,¹³C) reaching as much as almost 50% of the total value of ¹J(¹²⁵Te,¹³C) while relativistic geometrical effects are of minor importance. The vibrational and solvent corrections account for accordingly about 3–6% and 0–4% of the total value. It is shown that taking into account relativistic corrections, vibrational corrections and solvent effects at the DFT level essentially improves the agreement of the non‐relativistic theoretical SOPPA results with experiment. © 2016 Wiley Periodicals, Inc.     

An assessment of pure,hybrid, meta,and hybrid‐meta GGA density functional theory methods for open‐shell systems: The case of the nonheme iron enzyme 8R–LOX

The performance of a range density functional theory functionals combined in a quantum mechanical (QM)/molecular mechanical (MM) approach was investigated in their ability to reliably provide geometries, electronic distributions, and relative energies of a multicentered open‐shell mechanistic intermediate in the mechanism 8R–Lipoxygenase. With the use of large QM/MM active site chemical models, the smallest average differences in geometries between the catalytically relevant quartet and sextet complexes were obtained with the B3LYP^* functional. Moreover, in the case of the relative energies between ⁴II and ⁶II , the use of the B3LYP^* functional provided a difference of 0.0 kcal mol^–1. However, B3LYP^± and B3LYP also predicted differences in energies of less than 1 kcal mol^–1. In the case of describing the electronic distribution (i.e., spin density), the B3LYP^*, B3LYP, or M06‐L functionals appeared to be the most suitable. Overall, the results obtained suggest that for systems with multiple centers having unpaired electrons, the B3LYP^* appears most well rounded to provide reliable geometries, electronic structures, and relative energies. © 2012 Wiley Periodicals, Inc.     

Dose‐, time‐and lipophilicity‐dependent silver(I)–N‐heterocyclic carbene complexes: Synthesis,characterization and interaction with plasmid and Aedes albopictus DNA

Four new Ag(I)–N‐heterocyclic carbene (NHC) complexes ( 5 – 8 ) bearing symmetrically substituted NHC ligands have been synthesized starting from the corresponding benzimidazolium bromide salts which are accessible in a single step from N ‐substituted benzimidazoles (N ‐alkyl and N ‐aryl) and subsequently reacted with the basic metal source Ag₂O in acetonitrile–methanol. These compounds were characterized using elemental analyses, ¹H NMR, ¹³C NMR, Fourier transform infrared and UV–visible spectroscopic techniques, and molar conductivity. Single‐crystal structural studies for complex 5 show that the Ag(I) centre has a perfectly linear C–Ag–C coordination, with quasi‐parallel pairs of aromatic benzimidazole planes. All the complexes interact with Aedes albopictus DNA via intercalation mode by a large hypochromicity of 22 and 27% and smaller hypochromicity of 16 and 19%. Furthermore, all complexes exhibit efficient DNA cleavage activity via a non‐oxidative mechanistic pathway. The DNase activities of the test compounds revealed a time‐ and concentration‐dependent activity pattern. The Ag(I)–NHC complexes showed considerably higher DNA cleavage activity compared to their respective benzimidazolium salts at a lower concentration. The DNA cleavage of these complexes changed from a moderate effect to a good one, corresponding to the increasing lipophilicity order of the complexes as 5  <  6  <  7  <  8 (1.02, 1.05, 1.78 and 2.06 for 5 – 8 , respectively). This order is further corroborated with the DNA binding study, but with the exception of complex 5 , which shows a better binding ability for DNA (K _b = 3.367 × 10⁶) than complexes 6 – 8 (6.982 × 10⁵, 8.376 × 10⁵ and 1.223 × 10⁶, respectively).     

NMR shielding constants of CuX,AgX, and AuX (X = F,Cl, Br,and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two‐component relativistic density functional theory (DFT) with the second‐order Douglas–Kroll–Hess (DKH2) one‐electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2‐DFT‐calculated shielding constants of I and Xe in HI, I₂, CuI, AgI, and XeF₂ agree well with those obtained by the four‐component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d‐components in the Au d_π –F p_π and Au sd_σ–F p_σ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sd_σ + F p_σ and Au sd_σ–F p_σ MOs. The second‐order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin‐orbit effect calculated by the Breit–Pauli magnetic operator. © 2013 Wiley Periodicals, Inc.     

Monoclinic‐to‐orthorhombic phase transition of the hexamethylenetetramine–2‐methylbenzoic acid (1/2) cocrystal with temperature‐dependent dynamic molecular disorder

As a function of temperature, the hexamethylenetetramine–2‐methylbenzoic acid (1/2) cocrystal, C₆H₁₂N₄·2C₈H₈O₂, undergoes a reversible structural phase transition. The orthorhombic high‐temperature phase in the space group Pccn has been studied in the temperature range between 165 and 300 K. At 164 K, a t₂ phase transition to the monoclinic subgroup P2₁/c space group occurs; the resulting twinned low‐temperature phase was investigated in the temperature range between 164 and 100 K. The domains in the pseudomerohedral twin are related by a twofold rotation corresponding to the matrix (100/00/00). Systematic absence violations represent a sensitive criterium for the decision about the correct space‐group assignment at each temperature. The fractional volume contributions of the minor twin domain in the low‐temperature phase increases in the order 0.259 (2) → 0.318 (2) → 0.336 (2) → 0.341 (3) as the temperature increases in the order 150 → 160 → 163 → 164 K. The transformation occurs between the nonpolar point group mmm and the nonpolar point group 2/m, and corresponds to a ferroelastic transition or to a t₂ structural phase transition. The asymmetric unit of the low‐temperature phase consists of two hexamethylenetetramine molecules and four molecules of 2‐methylbenzoic acid; it is smaller by a factor of 2 in the high‐temperature phase and contains two half molecules of hexamethylenetetramine, which sit across twofold axes, and two molecules of the organic acid. In both phases, the hexamethylenetetramine residue and two benzoic acid molecules form a three‐molecule aggregate; the low‐temperature phase contains two of these aggregates in general positions, whereas they are situated on a crystallographic twofold axis in the high‐temperature phase. In both phases, one of these three‐molecule aggregates is disordered. For this disordered unit, the ratio between the major and minor conformer increases upon cooling from 0.567 (7):0.433 (7) at 170 K via 0.674 (6):0.326 (6) and 0.808 (5):0.192 (5) at 160 K to 0.803 (6):0.197 (6) and 0.900 (4):0.100 (4) at 150 K, indicating temperature‐dependent dynamic molecular disorder. Even upon further cooling to 100 K, the disorder is retained in principle, albeit with very low site occupancies for the minor conformer.     

Yolk–shell microspheres assembled from Preyssler‐type NaP5W30O11014− polyoxometalate and MIL‐101(Cr) metal–organic framework: A new inorganic–organic nanohybrid for fast and selective removal of cationic organic dyes from aqueous media

Novel inorganic–organic yolk–shell microspheres based on Preyssler‐type NaP₅W₃₀O₁₁₀^14? polyoxometalate and MIL‐101(Cr) metal–organic framework (P₅W₃₀/MIL‐101(Cr)) were synthesized by reaction of K_12.5Na_1.5[NaP₅W₃₀O₁₁₀], Cr(NO₃)₃·9H₂O and terephthalic acid under hydrothermal conditions at 200°C for 24 h. The as‐prepared yolk–shell microspheres were fully characterized using various techniques. All analyses confirmed the incorporation of the Preyssler‐type NaP₅W₃₀O₁₁₀^14? polyoxometalate into the three‐dimensional porous MIL‐101(Cr) metal–organic framework. The results revealed that P₅W₃₀/MIL‐101(Cr) demonstrated rapid adsorption of cationic methylene blue (MB) and rhodamine B (RhB) with ultrahigh efficiency and capacity, as well as achieving rapid and highly selective adsorption of MB from MB/MO (MO = methyl orange), MB/RhB and MB/RhB/MO mixtures. The P₅W₃₀/MIL‐101(Cr) adsorbent not only exhibited a high adsorption capacity of 212 mg g^?1, but also could quickly remove 100% of MB from a dye solution of 50 mg l^?1 within 8 min. The effects of some key parameters such as adsorbent dosage, initial dye concentration and initial pH on dye adsorption were investigated in detail. The equilibrium adsorption data were better fitted by the Langmuir isotherm. The adsorption kinetics was well modelled using a pseudo‐second‐order model. Also, the inorganic–organic hybrid yolk–shell microspheres could be easily separated from the reaction system and reused up to four times without any change in structure or adsorption ability. The stability and robustness of the adsorbent were confirmed using various techniques.     

Fabrication of covalently functionalized mesoporous silica core–shell magnetite nanoparticles with palladium(II) acetylacetonate: application as a magnetically separable nanocatalyst for Suzuki cross‐coupling reaction of acyl halides with boronic acids

We report the preparation of supported palladium(II) acetylacetonate, Pd(acac)₂, coordinated by pendant acac groups, by reacting palladium acetate with acac‐functionalized doubly silica‐coated magnetic nanoparticles. The solid support consists of an amorphous silica‐coated (as magnetite protecting layer) magnetite core and a mesoporous silica shell. The magnetically separable palladium nanocatalyst is active for Suzuki cross‐coupling reaction of acyl halides with boronic acids. The catalyst is simply isolated from the reaction mixture that allows fast and efficient isolation of product and catalyst compared to traditional methods that generally make use of time‐ and solvent‐consuming procedures. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of dppf‐Supported Nickel Precatalysts for the Suzuki–Miyaura Reaction: The Observation and Activity of Nickel(I)

Ni‐based precatalysts for the Suzuki–Miyaura reaction have potential chemical and economic advantages compared to commonly used Pd systems. Here, we compare Ni precatalysts for the Suzuki–Miyaura reaction supported by the dppf ligand in 3 oxidation states, 0, I and II. Surprisingly, at 80 °C they give similar catalytic activity, with all systems generating significant amounts of Ni^I during the reaction. At room temperature a readily accessible bench‐stable Ni^II precatalyst is highly active and can couple synthetically important heterocyclic substrates. Our work conclusively establishes that Ni^I species are relevant in reactions typically proposed to involve exclusively Ni⁰ and Ni^II complexes.     

Exploring the reaction dynamics of O(3P)+ (X2 )→OH+(X3Σ−)+ H(2S) reaction with time‐dependent wave packet method

The O(³P)+ reaction has been investigated by employing time‐dependent quantum wave packet with split operator method on potential energy surface of the doublet ground‐state H₂O⁺(1²A″). The reaction probabilities and integral cross sections are calculated using centrifugal sudden approximation, which basically agree with the quasi‐classical results of Paniagua et al. [Phys. Chem. Chem. Phys. 2014, 16, 23594]. Moreover, the effect of vibrational and rotational excitation of reactant is investigated. The results show that the vibrational and rotational excitation effects on the integral cross section are not obvious. The little differences between Coriolis coupling results and centrifugal sudden approximation ones show that the cheaper centrifugal sudden calculations here reported are effective for this reaction.