Molecular integrals of relativistic effects with gaussian-type orbitals

A mathematical analysis is presented of molecular integrals of relativistic interactions in molecules. The integrals are based on Gaussian-type orbitals and include those arising from variation of electron mass with velocity, one-electron Fermi contact interaction, electron spin-same-orbit interaction, electron spin-nuclear spin interaction, electron spin-spin contact interaction, electron spin-other-orbit interaction, electron spin-spin dipolar interaction and electron orbit-orbit interaction. The integrals are expressed in suitable forms for use in computer. It is also pointed out that the integrals are written essentially in terms of the overlap, nuclear attraction, electron repulsion, or field integrals.     

AB initio calculations of the electronic structure and doubling parameters of BS

Ab initio calculations have been performed to understand the influence of spin—orbit interaction upon the fine structure of the observed valence doublet states of the BS molecules: spin—orbit splittings, γ-type and Λ-type doublings. Configuration interaction is shown to be an essential feature in order to account for the observed data. Other properties of the electronic states (transition energies) have also been calculated.     

Spin-aligned CN(X2Σ+) from the photodissociation of ICN and BrCN

We report the first observation of a nascent photodissociation product of ²Σ symmetry, whose electron spin is aligned preferentially relative to the fragment rotational angular momentum. Spin—orbit interaction can align spins during the dissociation process, and electron correlation can couple this spatial information to the ²Σ species.     

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.     

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.     

Magnetic field effects due to spin—orbit coupling in transient intermediates

The effects of anisotropic spin—orbit coupling on the radical yield and CIDEP in chemical reactions of short-lived triplet intermediate are treated in the density matrix formalism. Analytical expressions for the magnetic field effect (MFE) on the lifetime of the triplet precursor and electron spin polarization are obtained in terms of the molecular parameters, reorientational correlation time, and magnetic field strength.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

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.     

The zero-field splitting tensors of dimeric bis(dialkyldithiocarbamato)-copper(II) and -silver(II)

The zero-field splitting tensor of dimeric bis(dialkyldithiocarbamato)-copper(II) is separated into a dipolar and a spin—orbit part, which both have been calculated using the results of an extended Hückel molecular orbital calculation. It has been established that the zero-field splitting tensor of the corresponding Ag dimer is determined by spin—orbit interactions.     

Origin of the variation with vibrational and rotational state of the fine-structure constants in O2, SO and S2

Calculations of the spin—orbit part λ_SO of the fine-structure parameter λ have been performed at several internuclear distances for the molecules O₂, SO and S₂ in their ground (X ³Σ^?) states. Only the interaction with the lowest ¹Σ⁺ state was considered and two-centre integrals were neglected. λ_SO is found to make the dominant contribution to λ. The variation of the matrix elements in λ_SO with internuclear distance has been derived and when combined with expressions for the variation of the energy denominator in λ_SO enables the coefficients for the vibrational and rotational dependence of λ to be estimated. Excellent agreement with experiment is found.     

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     

Electronic-to-vibrational energy transfer from Br (42P12 to HF

Room temperature experiments have measured the rate of electronic-to-vibrational energy transfer between spin—orbit excited Br(4²P_{$\text{1}\text{2}$}) and HF. The Br^* + HF quenching rate is very fast, (1.1 ± 0.2) × 10⁶ s^?1 torr^?1, due to a near resonance between the spin—orbit splitting and the vibrational spacing. The majority of the Br^* spin—orbit energy goes directly into HF vibration.     

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.     

Can AuF be synthesized? A theoretical study using relativistic configuration interaction and plasma modeling techniques

Theoretical studies using spin—orbit averaged relativistic configuration interaction and plasma modeling techniques indicate AuF to be a stable gas-phase compound and the dominant gas-phase species in the reaction of gold with O₂ and CF₄ between 1000 and 2700 K. Accurate spectroscopic properties are predicted and a synthesis for AuF is proposed.     

Optically detected zero field magnetic resonance in the lowest triplet nπ* state of p-benzoquinone

Optically detected magnetic resonance (ODMR) techniques are used to determine the orbital assignment of the phosphorescent triplet state of p-bezonquinone in the condensed phase. The principal spin—orbit coupling routes are discussed in terms of the observed spin—vibronic activity.     

Fluorescence spectra of matrix isolated silver atoms

Silver atoms isolated in noble gas matrices show fluorescence spectra with large Stokes shifts, when optically excited via the 5P ← 5S transition which is three-fold split in the matrix by spin—orbit and crystal field interaction. The shifts are explained by the formation of an excimeric bond between the excited metal atom and the noble gas cage. For Ag in Kr it is demonstrated, that most of the Stokes shift arises from the ground state repulsion.     

ChemInform Abstract: Interplay of Orbital and Relativistic Effects in Bismuth Oxyhalides: BiOF,BiOCl, BiOBr,and BiOI.

Study by using hybrid DFT with explicit treatment of spin—orbit coupling effects and dispersion interactions.     

Position dependent heavy atom effect in physical triplet quenching by electron donors

The radical yields and rate constants in the quenching reaction of thionine triplet with the complete series of monohalogen substituted anilines as electron donors were determined by flash spectroscopy. Whereas the quenching rate constants show little and unsystematic variation, the radical yields decrease with increasing spin—orbit coupling constant of the halogen substituent. This effect is very sensitive to the position of the halogen in the donor. The results are explained in terms of a heavy atom effect on the intersystem crossing rate constant in a triplet exciplex.     

Relativistic molecular orbital theory of zero-field splittings in triplets

A method of calculating matrix elements of 1/r₁₂ in a basis of Dirac scattered-wave (DSW) orbitals is outlined. In the limit c → ∞, this method reduces to that described by Cook and Karplus for non-relativistic orbitals. For triplet states that can be described by a single configuration with two unpaired electrons, the relativistic exchange integrals give not only the singlet—triplet splittings (as in non-relativistic theory), but also the spin—orbit contributions to the triplet zero-field splittings. Results are reported for the ³ (n → π*) excited state of γ-thiopyrone (4H-pyran-4-thione), which has a very large value of D (calc. ?31 cm^?1, exp. ?24 to ?28 cm^?1).