Spin-orbit coupling constants from semi-empirical wavefunctions

The problem of computing spin-orbit coupling constants from wave-functions of a semi-empirical variety are considered specifically for SCF wavefunctions with intermediate neglect of differential overlap. The incorporation of the 1s electrons into a ‘core’ should result in an effective nuclear charge of Z′ = Z - 2·5846 being used in one-electron terms, but for agreement with experiment the results have to be reduced by some 70 per cent. This reduction factor is different for ions. If the multiplicative factor is included good agreement between observed and calculated spin-orbit coupling constants is given.     

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.     

Spin-orbit interactions in semiconductor superlattice

The purpose of this paper is to theoretically investigate the spin-orbit interactions of common semiconductor superlattices. Spin splitting and spin-orbit interaction coefficients are calculated based on interactions between the interface-related-Rashba effect and Dresselhaus effect. Semiconductor superlattice shows a series of specific characteristics in spin splitting as follows. The spin splitting of the superlattice structure is greater than that of a single quantum well, contributing to significant spin polarization, spin filtering, and convenient manipulation of spintronic devices. The spin splitting of some superlattice structures does not change with variation of the size of some constituent quantum wells, reducing the requirements for accuracy in the size of quantum wells. The total spin splitting of lower sub-levels of some superlattice can be designed to be zero, realizing a persistent spin helix effect and long spin relaxation time, however, the total spin splitting of higher sub-levels is still appreciable, contributing to desirable spin polarization. These results demonstrate that one superlattice structure can realize two functions, acting as a spin field effect transistor and a spin filter.     

Spin-orbit interactions in heterocyclic analogues of fluorene

For carbazole, dibenzofuran, and dibenzothiophene—heterocyclic analogues of fluorene containing N-H, O, and S groups, respectively—the transition dipole moments P ₀₀ ⁱ for the transitions ³ B ₂→S ₀ and ³ A ₁→S ₀ from the sublevels i=z, y, x of the triplet electronic ππ* states, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The effect that the SO coupling between the S ₀ state and highest triplet states has on the calculation results is considered. The effects exerted on the value of P ₀₀ ⁱ by such specific features of the molecular structure as the position of a heteroatom on the symmetry axis, its valence, and different constants of SO coupling in heteroatoms are discussed. The reason for the weak influence of the quantity ?_HA on the rate constant of radiative deactivation of the lowest T state is ascertained.     

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.     

Double exchange models: self consistent renormalisation

We propose a scheme for constructing classical spin Hamiltonians from Hunds coupled spin-fermion models in the limit J_H/t →∞. The strong coupling between fermions and the core spins requires self-consistent calculation of the effective exchange in the model, either in the presence of inhomogeneities or with changing temperature. In this paper we establish the formalism and discuss results mainly on the “clean” double exchange model, with self consistently renormalised couplings, and compare our results with exact simulations. Our method allows access to system sizes much beyond the reach of exact simulations, and we can study transport and optical properties of the model without artificial broadening. The method discussed here forms the foundation of our papers [Phys. Rev. Lett. 91, 246602 (2003), and Phys. Rev. Lett. 92, 126602 (2004)].     

A self consistent technique for singular potentials

A technique used by Edwards and Singh [8] in the study of polymers is used to provide a simple analytic procedure for calculating the upper bound of the energies of a class of singular potentials. The accuracy of our procedure turns out to be better than 1%. Received 29 August 2002 / Received in final form 20 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: sumita@bose.res.in     

Investigation of analytic wavefunctions of two-electron systems in dynamic interactions with multiply charged ions and electromagnetic field ultrashort pulses

Coherence of various simple analytic wavefunctions of two-electron systems is investigated in with electromagnetic field ultrashort pulses. The coherence of wavefunctions in dynamic processes, for which cross sections (and probabilities) can be expressed only in terms of the ground-state wavefunctions, is determined. Direct recommendations given for using specific analytic wavefunctions can be helpful in simple calculations and estimation of dynamic processes.     

On spin three self interactions

In this paper we start the construction of a self interacting massless spin three field theory. The first order self interaction is constructed. The free field gauge invariance is modified by a term of first order in the coupling constant. Finally the abelian gauge transformation of the free Lagrangian is shown to become non-abelian.     

Molecular Compton profiles from SCF-MO wavefunctions

This paper considers the dependence of Compton profiles calculated from molecular wavefunctions on the atomic basis set used. For fluoromethane there is no significant difference between profiles calculated with a Slater minimal basis set and with STO-3G, STO-4G and STO-5G sets. A Slater double-zeta set and Dunning's gaussian basis give essentially the same profile and the addition of polarization functions to the Dunning basis has little effect. For methanol, methylamine and ethane there is a significant difference between the STO-3G profiles and those calculated from extended basis sets but again the addition of polarization functions has little effect. The use of Dunning's basis would seem to be adequate for Compton profile calculations for molecules of medium size. As one goes along the series from ethane to fluoromethane the Compton profile becomes broader.     

Molecular Compton profiles from SCF-MO wavefunctions

Compton profiles are derived from ab initio SCF-MO wavefunctions calculated for cyclopropane, propene, aziridine, ethanimine, ethenamine, oxirane, acetaldehyde and formamide using Dunning's gaussian orbital basis. Good agreement with the experimental profile is found for formamide. The differences between the profiles for the cyclic and acyclic isomers are only slightly larger than the experimental accuracy that can presently be achieved. The cyclic compounds have slightly broader profiles and there are no significant differences arising from strain. Comparison with profiles derived from localized orbital contributions indicate that the localized orbital approach is essentially valid for these systems.     

On ground-state wavefunctions for Sutherland-Calogero systems in an external field

Conditions are considered under which the ground-state wavefunctions of quantum systems of interacting particles in an external field are factorizable and can be found explicitly. The corresponding classical systems of particles are completely integrable; in the quantum case an extra integral of motion is constructed for a two-particle system.     

Spin-orbit effects in a GaAs quantum dot in a parallel magnetic field

We analyze the effects of spin-orbit coupling on fluctuations of the conductance of a quantum dot fabricated in a GaAs heterostructure. Counterintuitively we argue that spin-orbit effects may become important in the presence of a large parallel magnetic field B( parallel), even if they are negligible for B( parallel) = 0. This should be manifest in the level repulsion of a closed dot, and in reduced conductance fluctuations in dots with a small number of open channels in each lead, for large B( parallel). Our picture is consistent with the experimental observations of Folk et al.     

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.     

A self consistent normalized calibration protocol for three dimensional magnetic resonance gel dosimetry

In a clinical setting, mixed and inconsistent results have been reported using Magnetic Resonance Relaxation imaging of irradiated aqueous polymeric gels as a three-dimensional dosimeter, for dose verification of conformal radiation therapy. The problems are attributed to the difficulty of identifying an accurate dose calibration protocol for each delivered gel at the radiation site in a clinical setting. While careful calibration is done at the gel manufacturing site in a controlled laboratory setting, there is no guarantee that the dose sensitivity of the gels remains invariant upon delivery, irradiation, magnetic resonance imaging and storage at the clinical site. In this study, we have compared three different dose calibration protocols on aqueous polymeric gels for a variety of irradiation scenarios done in a clinical setting. After acquiring the three-dimensional proton relaxation maps of the irradiated gels, the dose distributions were generated using the off-site manufacturer provided calibration curve (Cal-1), the on-site external tube gel calibration (Cal-2) and the new on-site internal normalized gel calibration (Cal-3) protocols. These experimental dose distributions were compared with the theoretical dose distributions generated by treatment-planning systems. We observed that the experimental dose distributions generated from the Cal-1 and Cal-2 protocols were off by 10% to 40% and up to 200% above the predicted maximum dose, respectively. On the other hand, the experimental dose distributions generated from the Cal-3 protocol matched reasonably well with the theoretical dose distributions to within 10% difference. Our result suggests that an independent on-site normalized internal calibration must be performed for each batch of gel dosimeters at the time of MR relaxation imaging in order to account for the variations in dose sensitivity caused by various uncontrollable conditions in a clinical setting such as oxygen contamination, temperature changes and shelf life of the delivered gel between manufacturing and MR acquisitions.