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

An open‐shell Hartree–Fock (HF) theory for spin‐dependent, two‐component relativistic calculations, termed the Kramers‐unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time‐reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin‐orbit interactions. In addition, KUHF can improve the self‐consistent field convergence behavior in spin‐dependent calculations, for example, for f‐block elements.     

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.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF,DFT, and CI approaches

We present ab initio methods to determine the Dzyaloshinskii–Moriya (DM) parameter, which provides the anisotropic effects of noncollinear spin systems. For this purpose, we explore various general spin orbital (GSO) approaches, such as Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI), with one‐electron spin–orbit coupling (SOC1). As examples, two simple D_3h‐symmetric models, H₃ and B(CH₂)₃, are examined. Implications of the computational results are discussed in relation to as isotropic and anisotropic interactions of molecular‐based magnets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

NMR spin–spin coupling constants in hydrogen‐bonded glycine clusters

The influence of the hydrogen bond formation on the NMR spin–spin coupling constants (SSCC), including the Fermi contact (FC), the diamagnetic spin‐orbit, the paramagnetic spin‐orbit, and the spin dipole term, has been investigated systematically for the homogeneous glycine cluster, in gas phase, containing up to three monomers. The one‐bond and two‐bond SSCCs for several intramolecular (through covalent bond) and intermolecular (across the hydrogen‐bond) atomic pairs are calculated employing the density functional theory with B3LYP and KT3 functionals and different types of extended basis sets. The ab initio SOPPA(CCSD) is used as benchmark for the SSCCs of the glycine monomer. The hydrogen bonding is found to cause significant variations in the one‐bond SSCCs, mostly due to contribution from electronic interactions. However, the nature of variation depends on the type of oxygen atom (proton‐acceptor or proton‐donor) present in the interaction. Two‐bond intermolecular coupling constants vary more than the corresponding one‐bond constants when the size of the cluster increases. Among the four Ramsey terms that constitute the total SSCC, the FC term is the most dominant contributor followed by the paramagnetic spin‐orbit term in all one‐bond interaction.     

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     

Spin–other–orbit and spin–orbit interactions in ƒ2 and ƒ3 electron configurations

Expressions of the matrix elements of the spin–other–orbit and spin–orbit interactions for the various multiplets of all the states of ?²- and ?³-electron configurations are reported and used to evaluate the Hartree–Fock values of these interactions in the neutral atoms Ce(4?²), Pr(4?³), Ho(4?¹¹) and Er(4?¹²). The required values of the spin–spin parameters M, and the spin-orbit parameter ζ for these atoms were obtained using numerical Hartree–Fock wave functions.     

Si-H, P-H 和 S-H 键离解能Alfa取代基效应研究

CBS-Q and G3 methods were used to generate a large number of reliable Si--H, P---H and S--H bond dissociation energies （BDEs） for the first time. It was found that the Si--H BDE displayed dramatically different substituent effects compared with the C--H BDE. On the other hand, the P---H and S--H BDE exhibited patterns of substituent effects similar to those of the N--H and O--H BDE. Further analysis indicated that increasing the positive charge on Si of XSiH3 would strengthen the Si--H bond whereas increasing the positive charge on P and S of XPH2 and XSH would weaken the P---H and S--H bonds. Meanwhile, increasing the positive charge on Si of XSiH2^＋ stabilized the silyl radical whereas increasing the positive charge on P and S in XPH＂ and XS＊ destabilized P- and S-centered radicals. These behaviors could be reasonalized by the fact that Si is less electronegative than H while P and S are not. Finally, it was demonstrated that the spin-delocalization effect was valid for the Si-, P- and S-centered radicals.     

Spontaneous Phosphorus‐Halogen Bond Cleavage in N‐Heterocyclic Halogenophosphanes Revisited: The Case of P–Br and P–I Bonds

P‐bromo‐ and P‐Iodo‐substituted N‐heterocyclic phosphanes (NHP) were synthesized by halogen exchange starting from the P‐chloro compound and characterized by spectroscopic data and X‐ray diffraction studies. Whereas the Br‐NHP still forms a molecular crystal, the solid‐state structure of the I‐derivative consists of ion‐pairs which assemble via secondary P···I interactions to form one‐dimensional coordination polymers. Computational studies indicate that the bond dissociation is due to a combination of intramolecular stabilisation (aromatisation of the phosphenium cation formed) and intermolecular Lewis‐acid/base interactions. Reaction of the I‐NHP with I₂ proceeded under complete P–I bond cleavage to give an ionic phosphenium triiodide whose single‐crystal X‐ray diffraction study revealed a unique supramolecular structure.     

Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

Intermolecular interactions in uracil–nitrous acid complexes: structures,binding energy,topological properties,and nuclear magnetic resonance study

Molecular interactions between uracil and nitrous acid (U–NA) [C₄N₂O₂H₄? NO₂H] have been studied using B3LYP, B3PW91, and MP2 methods with different basis sets. The optimized geometries, harmonic vibrational frequencies, charge transfer, topological properties of electron density, nucleus‐independent chemical shift (NICS), and nuclear magnetic resonance one‐ and two‐bonds spin–spin coupling constants were calculated for U–NA complexes. In interaction between U and NA, eight cyclic complexes were obtained with two intermolecular hydrogen bonds N(C)HU…N(O) and OH_NA…O_U. In these complexes, uracil (U) simultaneously acts as proton acceptor and proton donor. The most stable complexes labeled, UNA1 and UNA2, are formed via NH bond of U with highest acidity and CO group of U with lowest proton affinity. There is a relationship between hydrogen bond distances and the corresponding frequency shifts. The solvent effect on complexes stability was examined using B3LYP method with the aug‐cc‐pVDZ basis set by applying the polarizable continuum model (PCM). The binding energies in the gas phase have also been compared with solvation energies computed using the PCM. Natural bond orbital analysis shows that in all complexes, the charge transfer takes place from U to NA. The results predict that the Lone Pair (LP)(O)_U → σ*(O? H) and LP(N(O)_NA → σ*(N(C)? H)_U donor–acceptor interactions are most important interactions in these complexes. Atom in molecule analysis confirms that hydrogen bond contacts are electrostatic in nature and covalent nature of proton donor groups decreases upon complexation. The relationship between spin–spin coupling constant (^1hJ_H…_Y and ^2hJ_H…_Y) with interaction energy and electronic density at corresponding hydrogen bond critical points and H‐bonds distances are investigated. NICS used for indicating of aromaticity of U ring upon complexation. © 2013 Wiley Periodicals, Inc.     

EHF theory of chemical reactions V. Nature of manganese–oxygen bonds by hybrid density functional theory (DFT) and coupled‐cluster (CC) methods

Hybrid density functional theory (DFT) and post‐Hartree–Fock methods are compared by depicting potential energy curves of the O–O dissociation of hydroperoxide and the M–O dissociation of transition‐metal oxides. The former approach includes BLYP, B2LYP, B3LYP, and more general hybrid DFT methods, while the unrestricted Hartree–Fock (UHF) coulpled‐cluster (UCC) SD(T) method is considered as the latter approach. The hybrid DFT methods can reproduce the potential curve of the O–O dissociation process and the dissociation energy of HOOH by UCCSD(T). The methods are also useful for depicting potential curves of copper oxide (CuO) and manganese oxide (MnO), and reproduce the experimental M–O binding energies. The nature of Mn–O bonds in the naked Mn–O, Mn–O porphyrine system and model complexes, XH₃Mn(IV)O₂Mn(IV)H₃Y (X,Y=O,H), are examined in relation to the possible mechanisms of oxygenation reactions. It is found that the radical character of Mn–O bonds increases with the increase of the oxidation number of the Mn ion in these systems. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ab initio calculation of spin–orbit interaction in polyatomic molecules using Gaussian-type wavefunctions

A set of programs has been developed to calculate molecular spin–orbit interaction with Gaussian-type wavefunctions in connection with the popular GAUSSIAN 76 program. The spin–orbit contributions to the fine structure of O₂ (X³∑_g^?), NH (X³∑^?), and CH₂ (X³B₁) are evaluated with the standard STO -3G and 6-31G basis sets; for NH the influence of bond functions added to the latter basis set is also investigated. The results are compared to values previously obtained with other types of basis sets.     

Heats of formation for Fe(CO)n(n=1–4)

The dissociation energies of Fe(CO)_n (n=2–4) are computed using correlation consistent basis sets and the CCSD(T) approach. The dissociation energies are extrapolated to the CBS limit and are corrected for core–valence (CV), scalar relativistic, spin–orbit, zero-point, and thermal effects. Our iron carbonyl bond strengths agree with experiment within the respective error bars. We use our dissociations energies at 298 K to obtain the heats of formation of Fe(CO)_n (n=1–4).     

Can One Assess the π Character of a C–C Bond with the Help of the NMR Spin–Spin Coupling Constants?

Measured one‐bond spin–spin coupling constants (SSCC) ¹J(CC) can be used to describe the nature of the C–C bond, provided one is able to separate the various coupling mechanisms leading to ¹J(CC). The Fermi‐contact (FC) term probes the first‐order density at the positions of the coupling nuclei, whereas the noncontact terms (the paramagnetic spin orbit (PSO) and the spin–dipole (SD) terms) probe the π character of the C–C bond (the diamagnetic spin orbit (DSO) term can mostly be neglected). A model is tested, in which the value of the FC(CC) term is estimated with the help of measured SSCCs ¹J(CH). The difference between the measured J(CC) and the estimated FC(CC) values, Δ(CC)=PSO(CC)+SD(CC)+DSO(CC), provides a semiquantitative measure of the π character of a C–C multiple bond. The applicability and limitations of this approach are discussed by partitioning the four Ramsey terms of the SSCC ¹J(CC) into one‐ and two‐orbital contributions. The FC, PSO, and SD terms of ¹J(CC) are explained and analyzed with regard to their relationship to other C–C bond properties. It is shown that empirical relationships between measured SSCCs and the s character of a bond need reconsideration.     

Borane–Lewis Base Complexes as Homolytic Hydrogen Atom Donors

Radical stabilization energies (RSE)s have been calculated for a variety of boryl radicals complexed to Lewis bases at the G3(MP2)‐RAD level of theory. These are referenced to the B? H bond dissociation energy (BDE) in BH₃ determined at W4.3 level. High RSE values (and thus low BDE(B? H) values) have been found for borane complexes of a variety of five‐ and six‐membered ring heterocycles. Variations of RSE values have been correlated with the strength of Lewis acid–Lewis base complex formation at the boryl radical stage. The analysis of charge‐ and spin‐density distributions shows that spin delocalization in the boryl radical complexes constitutes one of the mechanisms of radical stabilization.     

Spin–orbit and correlation effects in platinum hydride (PtH)

The low-lying electronic states of PtH were studied by all-electron one- and two-component variational calculations on the multireference CI levels. The orbital optimization is performed within a one-component formalism, whereas the further refinement of the wave functions follows two different schemes: The most demanding approach introduces spin–orbit coupling in the CI optimization step, giving a simultaneous treatment of electron correlation and spin–orbit coupling. The second, considerably less demanding approach, corresponds almost to a perturbational treatment, introducing spin–orbit coupling as a final step after the CI optimization by diagonalizing the resulting Hamiltonian matrix over CI states. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 53–64, 1998     

Theory of chemical bonds in metalloenzymes III: Full geometry optimization and vibration analysis of ferredoxin‐type [2Fe–2S] cluster

The nature of chemical bonds in a ferredoxin‐type [2Fe–2S] cluster has been investigated on the basis of natural orbitals and several bond indices developed in Parts I and II of this study. The broken‐symmetry hybrid density functional theory (BS‐HDFT) with spin projection approach has been applied to elucidate the natural orbitals and occupation numbers for a model compound [Fe₂S₂(SCH₃)₄] (1), which is used to calculate the indices. The molecular structure, vibration frequencies, electronic structures, and magnetic properties in both oxidized and reduced forms of 1 have been calculated and compared with the experimental values. The optimized molecular structures after approximate spin projection have been in good agreement with experimental data. The structure changes upon one‐electron reduction have been slight (<0.1 Å) and only limited around one side of the Fe atom. Raman and infrared (IR) spectra have been calculated, and their vibration modes have been assigned using the bridging ³⁴S isotope substitution. Their magnetic properties have been examined in terms of spin Hamiltonians that contain exchange interactions and double exchange interactions. The BS‐HDFT methods have provided the magnetic parameters; i.e., effective exchange integral (J) values and valence delocalization (B) values, which agree with the experimental results. It is found that large charge transfer (CT) from the bridging sulfur to the iron atoms has led to the strong antiferromagnetic interactions between iron atoms. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007