Bound D‐states of helium atom under Debye screening

We have investigated the 1snd^1,3D (3 ≤ n ≤ 7) state energies of helium atom embedded in weakly coupled plasma environments using the Rayleigh–Ritz variational method. The effect of the plasma environment is taken care of using a Debye screening model. A correlated wave function involving exponential expansion has been used to represent correlation between the charge particles. The bound 1snd^1,3D (3 ≤ n ≤ 7) state energies of helium for various Debye lengths along with the excitation energies of few singlet and triplet states are reported. Our results are useful references to atomic physics, plasma physics, and astrophysics research communities. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Confinement effects on the electronic structure of M‐shell atoms: A study with explicitly correlated wave functions

The ground and some excited states of Na and Mg atoms confined at the center of a spherical box with impenetrable walls are studied. Variational wave functions including dynamic correlations and configuration mixing have been obtained. Level crossings induced by confinement have been analyzed in terms of the energy of the occupied orbitals of the M shell and the weight of the different configurations. Confinement effects on the correlation energy have been studied. The parameterized optimized effective potential and the variational Monte Carlo methods have been employed. A cut off‐factor has been included to account for the hard wall confinement.     

Bound states of oscillators in infinite and finite domains: A semiclassical study

By involving the uncertainty product along with a semiclassical requirement for observables, a simple variational scheme is employed to extract major features of bound states of systems in (?∞,∞) and the same of systems confined in (?L,L). Special attention is paid to perturbative studies on the asymptotic behavior of energies for oscillators in infinite domains and dependence of energy spectra of oscillators in finite domains on various system parameters. A corrected form of the virial theorem is obtained in the latter case. The governing equations for quantum isothermal and adiabatic processes, derived recently, are also shown to be modified for general confined oscillator systems and closed‐form expressions are found. These results are useful in dealing with the quantum Carnot cycles. Advantages of the present route over other semiclassical strategies are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavor under various situations. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Calculations of D‐wave bound states and resonance states of the screened helium atom using correlated exponential wave functions

We have investigated the effects of screened Coulomb (Yukawa) potentials on the bound ^1,3D states and the doubly excited ^1,3 D^e resonance states of helium atom using highly correlated exponential basis functions. The Density of resonance states are calculated using stabilization method. Highly correlated exponential basis functions are used to consider the correlation effect between the charged particles. A total of 18 resonances (nine each for ¹ D^e and ³ D^e states) below the n = 2 He ⁺ threshold has been calculated. For each spin states, this includes four members in the 2pnp series, three members in the 2snd series, and two members in 2pnf series. The resonance energies and widths for various screening parameters ranging from infinity to a small value for these ^1,3 D^e resonance states are reported along with the bound‐excited 1s3d ^1,3 D state energies. Overall behavior of the spectral profile of 1s3d ¹D state of helium atom due to electron‐electron and electron‐nucleus screening are also presented. Accurate resonance energies and widths are also reported for He in vacuum. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Nonsingular constraints in time‐dependent variational principle for parametrized wave functions

In this work, we consider two conditions required for the nonsingularity of constraints in the time‐dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second‐class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP‐parameters, the regularity and the second‐class conditions become equivalent. The second‐class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second‐class condition in an extended canonical phase‐space. © 2012 Wiley Periodicals, Inc.     

Variational problem for ground and excited rovibronic states on the basis of a molecular Hamiltonian in the principal central axes

A general scheme of realization of nonempirical methods for calculation of the ground and excited rovibronic states of flexible molecules is proposed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Bound states of helium atom in dense plasmas

We have obtained the bound 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies of helium atom in dense plasma environments in accurate variation calculations. A screened Coulomb potential to represent the Debye model is used for the interaction between the charged particles. A correlated wave function consisting of a generalized exponential expansion has been used to take care of the correlation effect. The 1s^{2 1}S, 1s2s ^1,3S, and 1s2p ^1,3P states energies along with the ionization potential, the energy splitting between the 1s2s ³S, and 1s2s ¹S states, transition energies between the ground state and low‐excited states of He estimated for various Debye lengths, are reported. The results show high degree of accuracy even under strong plasma conditions. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

On an application of the intermediate Hamiltonian method for molecular systems

An application of the intermediate Hamiltonian method is reported in estimation of the lower bounds to the potential energy curve of the hydrogen molecule ion. An improvement of the method and its limitation are also discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 101–107, 1999     

New bosonic excitation operators in many-electron wave functions

New excitation operators which have perfect bosonic symmetry are constructed for many-electron wave functions by regarding the system of many electrons as that of many species of bosons. Any electronic configurations can be generated by the new bosonic “void” operators. A coherent state is constructed with the bosonic operators and is adopted as a trial function for the time-dependent variational principle. The equation of motion which has exactly the same form as Hamilton's equation in classical mechanics is obtained with the complex variational parameters, the number of which is equal to the number of electrons. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 71–75, 1998     

Near‐exact supersymmetric partner potentials: Construction and exploitation

Precise supersymmetric (SUSY) partner potentials can be generated only for exactly solvable problems of the stationary Schrödinger equation. This is a severe restriction, as most problems are not amenable to exact solutions. We employ here a linear variational strategy to explicitly construct approximate SUSY partners of a few common, not exactly solvable potentials and subsequently examine their properties to explore the advantages in practical implementation. The efficacy of our proposed scheme is commendable. We demonstrate that, for symmetric potentials, the constructed partners may be so good that the overall recipe has the nicety of generating the whole eigenspectrum by employing only half of the full Hilbert space functions. A similar strategy is shown to work for the odd states too, with proper boundary conditions. Pilot calculations involve a number of low‐lying states of some mixed oscillator and double‐well potentials. Analysis of the results reveals a few interesting features of the problem of construction of approximate SUSY partners and their practical use. Particularly, we identify places where the operator‐level approximations are involved and how far they affect the bounding properties of energies that are obtained as eigenvalues of a matrix diagonalization problem associated with linear variations. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Deflation techniques in quantum chemistry: Excited states from ground states

Applications of deflation techniques to the study of excited states of quantum systems are analyzed. It is demonstrated how these methods allow us to transform the excited state problem of one Hamiltonian, into the ground state problem of an auxiliary one. As an example, potential application in the density functional treatment of excited states is discussed. The inclusion of approximations in this scheme, such as the solution of the proposed model within a finite basis set is discussed. An extension of the Hartree–Fock (HF) method to excited states is presented. This new treatment includes previous self consistent field extensions to excited states and provides us with a way to obtain the HF extension to excited states of any ground state method. These results make the excited states of a system accessible through all ground state theoretical techniques. © 2013 Wiley Periodicals, Inc.     

Intra- and Intermolecular Rovibrational States of HCl-H\begin{document}$ _\textbf{2} $\end{document}O and DCl-H\begin{document}$ _\textbf{2} $\end{document}O Dimers from Full-Dimensional and Fully Coupled Quantum Calculations

We report full-dimensional and fully coupled quantum bound-state calculations of the \begin{document}$ J $\end{document} = 1 intra- and intermolecular rovibrational states of two isotopologues of the hydrogen chloride-water dimer, HCl-H\begin{document}$ _2 $\end{document}O (HH) and DCl-H\begin{document}$ _2 $\end{document}O (DH). The present study complements our recent theoretical investigations of the \begin{document}$ J $\end{document} = 0 nine-dimensional (9D) vibrational level structure of these and two other H/D isotopologues of this noncovalently bound molecular complex, and employs the same accurate 9D permutation invariant polynomial-neural network potential energy surface. The calculations yield all intramolecular vibrational fundamentals of the HH and DH dimers and the low-energy intermolecular rovibrational states in these intramolecular vibrational manifolds. The results are compared with those of the 9D \begin{document}$ J $\end{document} = 0 calculations of the same dimers. The energy differences between the \begin{document}$ K $\end{document} = 1 and \begin{document}$ K $\end{document} = 0 eigenstates exhibit pronounced variations with the intermolecular rovibrational states, for which a qualitative explanation is provided.     

A singularity excluded approximate expansion scheme in relativistic density functional theory

 A singularity excluded approximate expansion (SEAX) scheme, which can be considered as one between Breit-Pauli expansion and RA expansion schemes, is proposed to expand the total energy of 4-component relativistic density functional theory. The one-electron equation can be derived variationally from the approximate total energy expression. The Hamiltonian of the one-electron equation is bounded from below and can be dealt with variationally, and the gauge dependency error in the ZORA method is essentially eliminated. It is easier to solve the SEAX equation than the IORA equation. The results related to the valence orbitals by solving the scalar SEAX equation agree very well with those by the scalar ZORA ESA method, and the results related to the inner-shell electrons of heavy elements by the two component SEAX calculations agree quite well with those by the 4-component relativistic density functional calculations. Received: 20 February 2002 / Accepted: 29 April 2002 / Published online: 8 July 2002     

A simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function

We devise and apply a simple computational scheme for obtaining localized bonding schemes and their weights from a CASSCF wave function. These bonding schemes are close to resonance structures drawn by chemists. Firstly, a CASSCF wave function is computed. Secondly, the CASSCF computation is repeated but now the delocalized complete active space MOs are substituted by Weinhold's localized natural atomic orbitals. In this way the original CASSCF wave function is represented by a sequence of Slater determinants composed of localized natural atomic orbitals. Thus, a standard CASSCF wave function can be reinterpreted in terms of a local picture. To test the method we obtain localized bonding schemes and their weights for the ground and the pi-pi* excited state of ethylene. Moreover, bonding schemes and their weights are derived for the ground, the 1(1)B(u), and the 2(1)Ag pi-pi* excited states of trans-butadiene. The large weight bonding schemes are shown to be a qualitative indicator for the known photochemistry of butadiene. The remarkable stability of the Arduengo carbene is discussed by obtaining bonding schemes that indicate a stabilizing delocalization of the pi electrons. We illustrate that the large weight bonding schemes are in line with the observed reactivity of the Arduengo carbene.     

Atop-the-barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

The spatio-temporal localization of a system in the presence of an oscillating electric field for a symmetric double-well potential is examined via numerical simulations of the time-dependent Schrödinger equation. For an initial state with equal probability densities in both the wells, stabilized localization atop the barrier can be achieved on a periodic high-frequency driving. The barrier localization is characterized using Shannon information entropies in position and momentum spaces, defined as S_ρ = − ∫ |ψ|² ln |ψ|² dx and S_γ = − ∫ |ϕ|² ln |ϕ|² dp , where ψ and ϕ refer to position and momentum space wave functions, respectively. The information entropy sum, S_ρ + S_γ, goes through a minimum indicating the formation of the barrier-localized state, when the peak intensity of the oscillating field is reached. The generalized uncertainty via the Białynicki-Birula-Mycielski inequality ( S_ρ + S_γ ≥ 1 + lnπ ) is saturated upon this minimization. This serves as a signature of the formation of the barrier-atop localized state, in terms of Shannon entropies of measurable densities.     

Photoionization cross sections with optimized orbital exponents within the complex basis function method

We show a new direction to expand the applicability of the complex basis function method for calculating photoionization cross sections through the imaginary part of the frequency-dependent polarizability. Based on the variational stability of the frequency-dependent polarizability, we made nonlinear optimizations of complex orbital exponents in basis functions representing continuum wave functions, and obtained fairly accurate results for H atom with only one or two complex basis functions particularly with dipole velocity gauge. Results were almost independent of whether Slater-type or Gaussian-type orbitals are used, implying the applicability to general many electron problems. The method was also applied to the (1)S (1s)(2) --> (1)P (1s)(1)(kp)(1) cross section of He atom and the optimized complex orbital exponents were related to those of H atom through the scaling property. The nonlinear optimizations have converged smoothly and the cross sections were in excellent agreement with experiment throughout wide photon energies, which suggest the effectiveness of the approach for many-electron systems.