Magnetic Anisotropy of Small Ir<Subscript>n</Subscript> Clusters (n = 2–5)

We employ a noncollinear implementation of density functional theory (DFT) including spin–orbit coupling (SOC) interaction to calculate the magnetic properties of Ir_n (n = 2–5) clusters. The impact of the magnetic anisotropy on the geometric structures and magnetic properties has been analyzed. SOC leads to formation of large orbital moment and a mixing of different spin states, but does not affect the relative stability of different structural isomers for a given cluster. In order to measure the SOC effect, we further define the spin–orbit energy (E_so) and compute the exact values. Magnetic anisotropy energies (MAEs) obtained from DFT calculations are further supported by the results of torque approach. We find that MAEs of Ir₂ and Ir₃ in ground state configurations are 40.6 and 28.5 meV respectively, while the MAE decreases to 9 meV for Ir₄. For Ir₅, MAE for its ground state structure increases to 38.3 meV.     

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–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     

Spin–orbit coupling in the intersystem crossing of the ring-opened oxirane biradical

The intersystem crossing (ISC ) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin–orbit coupling (SOC ) in oxirane biradicals (?R′R″—CRR*—?) is stressed through calculations where the spin–orbit matrix elements over the full Breit–Pauli SOC operator has been obtained in the singlet–triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin–orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin–orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(³P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.     

Ab initio surface hopping excited-state molecular dynamics approach on the basis of spin–orbit coupled states: An application to the A-band photodissociation of CH3I

Ab initio molecular dynamics approach has been extended to multi-state dynamics on the basis of the spin–orbit coupled electronic states that are obtained through diagonalization of the spin–orbit coupling matrix with the multi-state second-order multireference perturbation theory energies in diagonal elements and the spin–orbit coupling terms at the state-averaged complete active space self-consistent field level in off-diagonal elements. Nonadiabatic transitions over the spin–orbit coupled states were taken into account explicitly by a surface hopping scheme with utilizing the nonadiabatic coupling terms calculated by numerical differentiation of the spin–orbit coupled wavefunctions and analytical nonadiabatic coupling terms. The present method was applied to the A-band photodissociation of methyl iodide, CH₃I + hv → CH₃ + I (²P_3/2)/I* (²P_1/2), for which a pioneering theoretical work was reported by Amatatsu, Yabushita, and Morokuma. The present results reproduced well the experimental branching ratio and energy distributions in the dissociative products. © 2018 Wiley Periodicals, Inc.     

Spin uncoupling in ethylene activation by palladium and platinum atoms

Spin‐dependent effects in complex formation reactions of the ethylene molecule with palladium and platinum atoms were studied by electron correlation calculations with account of spin–orbit coupling. Simple correlation diagrams illustrating spin‐uncoupling mechanisms were obtained, showing that the low spin state of the transition‐metal atom or the transition‐metal atom complex is always more reactive than are the high spin states because of the involvement of the triplet excited molecule in the chemical activation. Spin–orbit coupling calculations of the reaction between a platinum atom and ethylene explain the high‐spin Pt(³D) reactivity as due to an effective spin flip at the stage of the weak triplet complex formation. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 581–596, 1999     

Carbynes phonons: a tight binding force field

Modeling the vibrational structure of linear carbon chains has proved to be a difficult task with present first-principles calculations. This limits their applicability for the interpretation of experimental data, such as Raman scattering experiments on linear carbon chains within nanotubes. These limitations can be overcome by means of a simple tight binding scheme for pi-electrons. In this work a force field for the calculation of longitudinal phonon dispersion branches is built on the basis of bond-bond polarizabilities and just three parameters. The so obtained phonon dispersion branches are in very good agreement with the experimental data on carbynes in different environments and polyynes of any length. The model is discussed in relation to the importance of long range vibrational interactions in carbynes. The physical phenomena affecting their vibrational properties (i.e., Kohn anomaly, electron-phonon coupling) can be accurately and analytically described by the present approach.     

Geometric approximation to nuclear spin–spin coupling constants in the water molecule

The geometric aproximation is used within the framework of triple perturbation theory to evaluate the contributions to nuclear spin–spin coupling constants in the water molecule provided by the Fermi contact, the spin–orbit, and the spin–dipolar interactions. The results, obtained with SCF wave functions expanded over Gaussian basis sets of increasing quality, are compared with corresponding coupled Hartree–Fock estimates. The limits of the geometric approximation to coupling constants are discussed.     

Quantum chemical topology at the spin–orbit configuration interaction level: Application to astatine compounds

We report a methodology that allows the investigation of the consequences of the spin–orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the “state-specific” natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin–orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = At F) and trihalide anions (IAtI⁻ , BrAtBr⁻ , and IAtBr⁻ ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin–orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin–orbit couplings.     

Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin–orbit couplings in Π electronic states of linear tetra‐atomic molecules

Avariational and a perturbative approach are developed to handle the combined effect of the vibronic and spin–orbit couplings in Π electronic states of tetra‐atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin–orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth‐order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second‐order formulae when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin–orbit structure in the X²Π electronic state of HCCS by employing the ab initio‐computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The modified all-valence INDO method with the inclusion of spin–orbit coupling

The all-valence INDO method has been modified for the inclusion of spin–orbit coupling effects. In the method presented, the Hamiltonian includes spin–orbit coupling and the basis set constitutes the singlet and triplet determinental wave functions constructed from molecular orbitals resulting from nonrelativistic calculations. Eigenvectors obtained are later used for the evaluation of transition probabilities among different states. The results presented include lifetimes of different states of organic molecules and transition energies for halogen molecules and they are in a good agreement with experimental results. © 1992 John Wiley & Sons, Inc.     

Noncollinear magnetization density in VAu4

The spin and orbital magnetic moments of VAu₄ have been calculated using a first principles method that allows for noncollinear magnetic ordering. The large spin–orbit coupling of the Au atom is argued to induce large noncollinear components of the magnetization density as well as a parallel coupling between spin and orbital moments of the V atom, in contrast to expectations from Hund's third rule. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Semiempirical spin–orbit coupling calculations. I. Theory and method. Benzophenone as a test case

The molecular spin–orbit coupling operator is brought into a simplified form through a convenient choice of origin for the orbital angular momentum operator. The eigenvalue problem of the Hamiltonian that includes the spin–orbit (SOC ) operator as a perturbation is solved by means of a linear variational procedure in the basis of the spin-pure molecular eigenstates. Test calculations on benzophenone are presented and the results are compared to experiment. We discuss the minimal size of the spin-pure variational basis needed to achieve stable results as well as the amount of single-excitation configurational mixing needed to describe the spin-pure molecular eigenstates.     

Relativistic Spin–Orbit Electronegativity and the Chemical Bond Between a Heavy Atom and a Light Atom

Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-element compounds. In this work, we introduce the concept of spin–orbit (SO) electronegativity of a heavy atom, as reflected by an SO-induced change in the interatomic distance between the heavy atom (HA) and a neighboring light atom (LA). We provide a transparent interpretation of these SO effects by using the concept of spin–orbit electron deformation density (SO-EDD). Spin–orbit coupling at the HA induces rearrangement of the electron density for the scalar-relativistically optimized geometry that, in turn, exerts a new force on the LA. The resulting expansion or contraction of the HA−LA bond depends on the nature and electron configuration of the HA. In addition, we quantify the change in atomic electronegativity induced by SO coupling for a series of hydrides, thereby complementing the SO-EDD picture. The trends in the SO-induced electronegativity and the HA−LA bond length across the periodic table of elements are demonstrated and interpreted, and also linked, intuitively, with the SO-induced NMR shielding at the LA.     

Enhancing Intersystem Crossing in Phenotiazinium Dyes by Intercalation into DNA

Phenothiazinium dyes are used as photosensitizers in photodynamic therapy. Their mode of action is related to the generation of triplet excited states by intersystem crossing. Therefore, rationalizing the factors that influence intersystem crossing is crucial to improve the efficacy of photodynamic therapy. Here we employ quantum mechanics/molecular mechanics calculations to investigate the effect of aqueous and nucleic acid environments on the intersystem crossing mechanism in methylene blue. We find that the mechanism by which the triplet states are generated depends strongly on the environment. While intersystem crossing in water is mediated exclusively by vibronic spin–orbit coupling, it is enhanced in DNA due to a second pathway driven by electronic spin–orbit coupling. Competing charge‐transfer processes, which are also possible in the presence of DNA, can therefore be suppressed by a suitable structural functionalization, thereby increasing the efficacy of photodynamic therapy.     

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.     

Relativistic theory for indirect nuclear spin–spin couplings within the polarization propagator approach

We present a relativistic theory for the nuclear spin–spin coupling tensor within the polarization propagator approach using the particle-hole Dirac–Coulomb–Breit Hamiltonian and the full four-component wave function. We give explicit expressions for the coupling tensor in the random-phase approximation, neglecting the Breit interaction. A purely relativistic perturbative electron–nuclear Hamiltonian is used and it is shown how the single relativistic contribution to the coupling tensor reduces to Ramsey's three second-order terms (Fermi contact, spin–dipole, and paramagnetic spin–orbit) in the nonrelativistic limit. The principal propagator becomes complex and the leading property integrals mix atomic orbitals of different parity. The well-known propagator expressions for the coupling tensor in the nonrelativistic limit is obtained neglecting terms of the order c^?n (n ? 1). © 1993 John Wiley & Sons, Inc.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Molecular orbital calculation of spin-orbit splittings in some halogeno-compounds

CNDO and INDO calculations incorporating the spin—orbit operator in the Hamiltonian have been carried out to obtain the spin—orbit splittings of ionization potentials of some halogen compounds. Two sets of spin—orbit coupling constants were tested. The calculated splittings are compared with photoelectron spectroscopy experimental results from the literature.     

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin‐orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree–Fock (CAHF) algorithm for the determination of 4f quasi‐atomic active orbitals common to all multi‐electron spin manifolds contributing to the ground spin‐orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi‐Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem‐specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state–of–the–art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres , represents a more time‐efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non‐perturbative spin‐orbit coupling effects. © 2017 Wiley Periodicals, Inc.