Spin-orbit interactions from self consistent field wavefunctions

Effects of the spin-orbit Hamiltonian H_LS , including both the spin-same orbit and spin-other orbit terms, are studied at the self consistent field (SCF) level of theory. Separate calculations are carried out for each state considered, and biorthogonal orbitals are constructed for the evaluation of matrix elements. Doublet-doublet and singlet-triplet interactions are discussed. The evaluation of the Gaussian basis function integrals is described in a Cartesian component representation, these integrals being directly related to one and two electron second derivative integrals. This new SCF spin-orbit code is used to (i) determine the spatial dependence of the spin-orbit parameters for the Renner-Teller ²B₁, ²A₁ states of H₂O⁺, (ii) determine the spin-orbit splitting of the ²Π states of OH as a function of bond-length and (iii) calculate the radiative lifetime of the a ³Σ⁺ state of NO⁺. In each case these calculations are compared with more sophisticated configuration interaction studies, but it is found that the evaluation of these effects near equilibrium geometries at the SCF level is sufficiently accurate, provided that a large basis set is used.     

Calculation of harmonic force constants from Hartree-Fock-Roothaan wavefunctions

Some current methods of non-empirical computation of force constants are discussed; emphasis is given to the complete, analytical evaluation. It is shown that force constants evaluated to the Hartree-Fock limit are correct through first order in the error of the wavefunction. The consequences of using well-optimized wavefunctions are investigated in some detail. Some of the aspects are illustrated by exploratory calculations on H₂.     

Spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions

An efficient method for the calculation of Breit-Pauli spin-orbit matrix elements for internally contracted multireference configuration interaction wavefunctions is presented. Instead of taking all two-electron contributions of the wavefunction explicitly into account, the most important two-electron contributions of the spin-orbit operator are incorporated by means of an effective one-electron Fock operator. As a further refinement, explicit two-electron contributions can be reinstated for the dominant all-internal parts of the wavefunctions.     

Relative wavefunctions, vertex functions and coupling constants for the virtual decay of 4He

The d + d, t + p and h + n relative wavefunctions and their asymptotic normalizations are considered in the framework of the generator coordinate method (GCM) and compared with ATMS (amalgamation of two-body correlation into multiple scattering processes) method which used the realistic Reid soft core interaction. The asymptotic normalization of relative wavefunctions provide various coupling constants, the cluster probability amplitude (the so-called Z ^1/2-factor) and matter RMS radii. These wavefunctions are also used to obtain ⁴He − d − d, ⁴He − t − p and ⁴He − h − n vertex functions in the virtual decay of ⁴He. The extrapolation of vertex functions for negative values of q ² upto the corresponding poles provide the vertex constants which are comparable with other estimates. It is noticed that in GCM the coupling constants C ² for ⁴He − d − d vertex is less than 2 as has been obtained in the forward dispersion relation technique.     

Spin-orbit coupling in Σ-hypernuclei

Single-particle energies of Σ-hyperons in _Σ¹⁶O are calculated within a relativistic mean-field theory. This model predicts a small spin-orbit splitting for Σ-hyperons in _Σ¹⁶O compared to ordinary nucleons in nuclei. Half of the small spin-orbit splitting is due to the anomalous magnetic moment of the Σ-hyperon. K and K¹ exchange terms are negligible. This is to be seen in contrast to a previous quark-model prediction of a strong spin-orbit splitting for hyperons.     

Spin-orbit coupling in the chlorobenzene molecule

The possible ways of drawing of the intensity of the S₀ T* transition in the chlorobenzene molecule are investigated. The effective spin-orbit coupling of either S* or S* states with the T* state leads to the out-of-plane polarized component of phosphorescence in the chlorobenzene. The in-plane polarized component cannot be explained by the mechanism under consideration — by drawing of intensity of the S₀ S₀* transitions through spin-orbit coupling of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 134–138, August, 1974.     

Spin-orbit coupling in interacting quasi-one-dimensional electron systems

We present a new model for the study of spin-orbit coupling in interacting quasi-one-dimensional systems and solve it exactly to find the spectral properties of such systems. We show that the combination of spin-orbit coupling and electron-electron interactions results in the replacement of separate spin and charge excitations with two new kinds of bosonic mixed-spin-charge excitation, and a characteristic modification of the spectral function and single-particle density of states. Our results show how manipulation of the spin-orbit coupling, with external electric fields, can be used for the experimental determination of microscopic interaction parameters in quantum wires.     

Spin-orbit coupling and dissociation of CO2 molecules

Potential surfaces of the CO₂ molecule for the ground and excited ³ B ₂, ¹ B ₂ electronic states are calculated by quantum chemistry methods. The calculation of the spin-orbit coupling in the molecule shows a large the matrix element, which removes the prohibition for the dissociation-recombination process CO₂(X ¹Σ) + M ? CO(X ¹Σ) + O(³ P) + M. The barrier on the potential curve for ³ B ₂, the energy of which exceeds the limit of dissociation into components in the ground states, explains the data on the dissociation and recombination energies measured in experiments with shock tubes. The absorption cross section of CO₂ molecules in the UV spectral region measured at high temperatures allowed us to plot branches of potential curves near their minima for two upper singlet states assigned to the ¹ B ₂ and ¹ A ₂ symmetry.     

Spin-orbit coupling in nitrite ion and nitrite salts

The absorption intensity of the³B₁ ¹A₁ transition of nitrite salts of the non-transition metals is markedly dependent on the metal counterion and is causative of the yellow-orange colors of the heavier-metal salts. It is assumed that spin-orbit coupling is responsible for this phenomenon; this assumption is investigated here using semi-empirical one-electron calculations and is validated. The subjects of covalent bonding in metal salts, charge transfer transitions in such systems and the S _j S ₀ electronic spectroscopy of nitrite salts are also investigated.This work was supported by contracts between the United States Atomic Energy Commission — Biology Branch and the United States Air Force with the Louisiana State University.     

Spin-orbit coupling and spin current in mesoscopic devices

Recently,the spin-orbit coupling and spin current in nanodevice have been investigated extensively.In this paper,we review the recent progresses in this field.We introduce the real space Hamiltonian and the second quantization Hamiltonian of a typical quantum transport mesoscopic device,metal-QD-metal configuration,containing the spin-orbit interaction,e-e interactions,and magnetic field.Some noteworthy effects(e.g.,the spin-polarized current,spin accumulation,persistent spin current) originated from the spin-orbit interaction are reviewed,and the electric field induced by spin-current is mentioned.Lastly,we introduce some unsolved problems and prospects in this field.     

Spin-orbit coupling in oxygen near the dissociation limit

By using the method of configuration interactions in the valence basis with triple exponentials, the spectrum of the oxygen molecule is calculated in a range of internuclear distances from 1.2 to 2.45 Å, with the matrix of configuration interactions being diagonalized with regard to the spin-orbit coupling. The matrix elements of the spin-orbit coupling are presented, along with the spin splittings of triplet and quintet states. Particular attention is given to the intermediate range for the breaking of the O=O bond (1.8–2.45 Å), where the strong mixing of multiplets and rearrangement of the valence bonding to the atomic limit O(³ P)+O(³ P) occur. Other dissociation limits up to O(¹ D)+O(¹ D) are also taken into account. The results obtained are discussed in the context of the theory of the chemical bond, catalysis, radiation collisions, and the theory of spectral bands for high vibrational quantum numbers.     

Spin-orbit coupling effects in deuteron stripping angular correlations

Spin-orbit contributions in the DWBA analysis of particle-gamma angular correlations following deuteron stripping reactions have been investigated for several l=2 transitions. It is shown that in general these effects are quite large.     

Calculation of molecular geometries and force constants from CNDO wavefunctions by the force method

The semi-empirical quantum chemical calculation of molecular geometries and force constants by the usual energy hypersurface method rapidly becomes impractical as the size of the molecule increases. Here we show that the application of the force method to semi-empirical wavefunctions makes an economic and simple calculation of molecular geometries and force constants possible. Problems which are virtually insoluble by the classical method, such as full geometry optimization in large molecules, can be solved this way.

The calculation of forces as exact negative derivatives of the total SCF energy is given for CNDO wavefunctions. Two geometry optimization schemes are discussed ; it is concluded that a steepest descent method is the most practical in semi-empirical calculations. As an example the fully optimized equilibrium geometry of pyrrole has been determined. Except for the CH and NH bond lengths, the calculated geometry agrees almost perfectly with the experimental one.

The calculation of force constants from the forces is discussed. The force constants of CH₄ and H₂O have been determined, including the interaction ones. The signs and magnitudes of the stretch-bend interaction constants agree with experiment.     

Shielding and spin-spin coupling constants from gas-phase NMR

Intermolecular interactions modify nuclear magnetic resonance (NMR) chemical shifts and spin-spin coupling constants. The intermolecular effects can be determined if the NMR parameters for an isolated molecule are known. Gas-phase NMR spectroscopy offers such methods which allow one to measure the shielding and spin-spin coupling constants at the zero-density limit where the NMR parameters are free from intermolecular contributions. It is also shown that at present the multinuclear NMR spectra can easily be obtained for gaseous samples containing several micrograms of a solute compound.     

Spin-orbit coupling enhancement of 3d ions in metals

The interactions between localised 3d and itinerant electrons due to the Coulomb and exchange potential are shown to be responsible for the increase in magnitude of ionic spin-orbit coupling.     

Spin-orbit coupling in Bose-Einstein condensate and degenerate Fermi gases

We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and controlling the different frequency of two R,aman lasers to engineer the atom light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We, observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as halhnarks of SO coupling in a Fermi gas. To clearly reveal the, property of SO coupling Fermi gas, we also study the momentmn-resolved radio-frequency spectroscopy which characterizes the energy momentum dispersion and spin composition of the quantum states. We observe the change of errmion surfaces in different helieity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracoht Fermi gas.