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Energetics of two‐center two‐electron (2c–2e) systems carry challenges in theoretical understanding of Schrödinger equation (SE) for well‐known divergence of Coulomb interactions and nuclear separation (R) in modified H‐like AOs, Slater type orbitals (STOs), Gaussian type orbitals (GTOs), B‐spline, Sturmian function and etc. employed to VBT and MOT. Certain elegant computational and analytical techniques were developed for STO, GTO and other square integrable basis set within Born‐Oppenheimer (BO) approximation. STOs and GTOs have an essential limitation of absence of radial nodes. Thus, analytical treatment has become an urge for H‐like AOs. We have considered the diatomic molecules only for the sake of simplicity. Employing Sheffer identity in associated Laguerre polynomial/Whittaker‐M function forms of H‐like AOs and transforming integrals into elliptic coordinates with two nuclei on two foci furnishes exact, analytical and simple Coulomb integrals (Js) in terms of R. Lah number originated from Ln-1 ${L_n^{ - 1} }$ for nuclear coordinates only due to Sheffer identity shows that energetics of diatomic molecules can be anticipated as extremum function of R. Therefore, the optimization of potential energy surface (PES) of electrons as gradient of R may lead to σ‐bond formation. In this paper, we have developed diagonal Js for bound states of H2 molecule. [ABSTRACT FROM AUTHOR]

Theoretical studies of two-center one-electron (2c-1e) small microcluster are associated with hurdles in Schr o ¨ dinger equation (SE) born out of divergence of Coulomb interactions and nuclear separation (R). The SE deals with morphologically altered H-like AOs, Slater type orbitals (STO), Gaussian type orbitals (GTO), B-spline, Sturmian function and etc in both VBT and MOT calculations. Few elegant computational and analytical methods are available for STO, GTO and other square integrable trial wavefunction under Born-Oppenheimer approximation. Even so, analytical treatment for H-like AOs has become very necessary. Utilizing Sheffer identity in associated Laguerre polynomial/Whittaker-MH-like AOs and adopting elliptic coordinates provide exact, analytical and simple 2c-1e Coulomb exchange interactions (Ks) and overlap integrals as functions of R with different scaling factors associated with electrons. The energetics of diatomic molecule is evident to be the function of R with extrema as Lah number moderated L n - 1 for nuclear coordinates. Analytical and simple 2c-1e Coulomb exchange interactions (Ks) and overlap integrals (Ss) as functions of R are presented utilizing Sheffer identity in associated Laguerre polynomial/ Whittaker-MH-like AOs and adopting elliptic coordinates mediated through Lah number. The energetics of the diatomic molecule is evident to be the function of R. [ABSTRACT FROM AUTHOR]

As the density of electrons (N=2, 3, 4, 5, 6, 7, 8,.) increases, complexity arises due to coulomb interactions, inclusion of fermionic exchange symmetry and anisotropy. Consequently, Schrödinger equations of anisotropic quantum dots become non-trivial. Recasting such non-relativistic quantum equations into Whittaker-M basis functions unifies coulomb (exchange) correlation and antisymmetric nature of electrons in two-centered integrals of exact, finite, single-summed, terminated and simplest Lauricella functions (F2) via multi-pole expansion and the subsequent Chu-Vandermonde identity. Coulomb correlations interplay with in-plane and out-of-plane electrical and magnetic confinements in their moderate fields. On the other hand, full-scale fermionic exchange symmetry is incorporated through multiple number of Slater determinants, unlike Hartree-Fock method. In this context, both open-shell and restricted closed-shell configurations are considered for trial Hartree-products which are composed of the basis set of oscillator spin-orbitals. Thus optimized bound states can easily capture large number of mixed term symbols. Consequently, level clustering/accidental degeneracies occur in energy level diagram due to competition among strength of anisotropy in electrical confinements, magnetic field, mass of the carrier and dielectric constant. It brings about orbital induced paramagnetism (T∼(0-1)K), signature of fractional quantum Hall effect (FQHE) in chemical potential cusps (μ) and formation of different ′shell structures′ in capacitive energy respectively, spanning over wide dielectric range of materials (atomic like quantum dot, ZnO, GaAs, CdSe (Cadmium Chalcogenide) and PbSe (Lead Chalcogenide) etc). [ABSTRACT FROM AUTHOR]

A time-dependent quantum adiabatic switching algorithm is exploited to determine the eigenstates of 2-D quantum dots perturbed by a repulsive scatterer. Several forms of switching functions are explored and optimal forms are suggested. The switching paths are compared for a number of states, using overlap, information entropy and energy as descriptors for possible identification of the optimal switching function. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [ABSTRACT FROM AUTHOR]

The linear and non-linear optical response properties of 2-D quantum dots with two interacting carrier electrons having triplet coupling of spins are computed and compared with their singlet counterparts. The significant dependence of the response properties on the spin multiplicity in the high and low field regimes are sought to be rationalized. [ABSTRACT FROM AUTHOR]

We explore the pattern of evolution of energy levels and wavefunctions in a harmonically confined single electron artificial atom in 2 dimensions, in the presence of a perpendicular magnetic field and anharmonic perturbations. A configuration interaction (CI) type of approach in a basis of appropriate harmonic oscillator eigenfunctions is used, leading to a complex sparse hermitian matrix eigenvalue problem. We show that for a given strength of the confining potential descriptors like quantum information entropy, level spacing distribution, degree of localization of one electron density and probability current point to a threshold value for the cyclotron frequency (ωc), beyond which there appears to be a transition from a delocalized description rather than a localized one. No signature of quantum chaos is detected. [ABSTRACT FROM AUTHOR]