B. M. Deb

Developments in excited-state density functional theory

Abstract This article discusses the reasons behind the apparent lack of success of density functional theory (DFT), during the past three decades, with excited states of many-electron systems. It describes various variational and non-variational approaches developed so far for dealing with this problem. Those include Theophilou’s equiensemble approach, extended to unequally weighted ensembles by Gross et al., Fritsche’s wavefunction partitioning approach, local scaling transformation theory by Kryachko et al., the work-function formalism developed by Harbola and Sahni, etc. Through intimate connections between time-dependence and excited states, under a perturbation, various time-dependent (TD) DFT approaches to excited states, e.g., a quantum fluid dynamical approach, a TD density-functional response theory and a TD optimized effective potential approach, are also reviewed.

Stability analysis of finite difference schemes for quantum mechanical equations of motion

For a pdf involving both space and time variables, stability criteria are presently shown to change drastically when the equation contains i, as in the quantum-mechanical equations of motion. It is further noted that the stability of finite difference schemes for quantum-mechanical equations of motion depends on both spatial and temporal zoning. It is possible to compare a free particle Greens function to the solution of a simple diffusion equation, and the quantum-mechanical motion of a free particle to Fresnel diffraction in optics.

Direct ab initio calculation of ground-state electronic energies and densities for atoms and molecules through a time-dependent single hydrodynamical equation

By using an imaginary-time evolution technique, coupled with the minimization of an expectation value, ground-state electron densities and energies have been directly calculated for six atomic and molecular systems (He, Be++, Ne, H2, HeH+, He2++), from a single time-dependent (TD) quantum fluid dynamical equation of motion whose real-time solution yields the TD electron density. For all the systems, a local Wigner-type correlation functional has been employed. For Ne, a local exchange functional is used while, for all the other systems, the exchange energy is calculated exactly. The static (ground-state) results are of beyond-Hartree–Fock quality for all the species.

Direct calculation of ground-state electronic densities and properties of noble gas atoms through a single time-dependent hydrodynamical equation

Ground-state electronic densities and properties of noble gas atoms (He, Ne, Ar, Kr and Xe) have been calculated through a single time-dependent quantum fluid dynamical equation of motion. The equation has been transformed through imaginary time into a diffusion equation which is then numerically solved in order to reach a global minimum. The present results compare favourably with other available values.

Quantum fluid density functional theory of time-dependent phenomena: Ion-atom collisions

Abstract Using a recently proposed kinetic energy density functional and an amalgamation of density functional theory with quantum fluid dynamics, a time-dependent Kohn-Sham-type equation in three-dimensional space, which is a new non-linear Schrodinger equation, has been derived. The equation is also derived through the stochastic interpretation of quantum mechanics. A molecular “thermodynamic” viewpoint is suggested in terms of space-time-dependent quantities. Numerical solution of the above equation yields the time-dependent charge density, current density, effective potential and chemical potential. Perspective plots of these quantities for the proton-neon 25 keV head-on collision are presented.

Density functional calculation for doubly excited autoionizing states of helium atom

Several doubly excited autoionizing states of He have been calculated within the density functional framework by employing the Harbola–Sahni exchange potential. Correlation effects have been incorporated in the total effective potential through a Wigner‐type correlation potential. Although continuum functions are not explicitly incorporated into these calculations, resonance energies of these states are in satisfactory agreement with other theoretical results.

Electron in one-dimensional symmetric and asymmetric double-well potentials under intense/superintense laser fields: A numerical study based on time-dependent Schrödinger equation

The responses of an electron moving in one-dimensional symmetric and asymmetric double-well oscillator (DWO) potentials respectively are analyzed under intense and superintense laser fields by numerically solving the time-dependent Schrodinger equation and evolving the systems for 96 fs at λ=1064 nm as well as different laser intensities. Emphasis is placed on the study of only those features which can arise from the response of a single system. A detailed investigation of multiphoton processes such as high harmonics generation and the energy spectrum (obtained by fast fourier transform of the autocorrelation function) is made. The applicability of these DWOs as model systems for the generation of attosecond pulses is examined. Furthermore, a comparison is made with atoms and molecules under similar conditions, thereby establishing a qualitative parallelism in the behavior of real atoms/molecules and these model DWO systems.

Density-functional calculations for doubly excited states of He, and

More than 200 low-lying and moderately high-lying doubly excited states of He-isoelectronic systems (Z = 2 - 5) have been studied in the nonrelativistic Hohenberg - Kohn - Sham density-functional framework by incorporating the nonvariational work-function exchange potential suggested by Harbola and Sahni and a simple parametrized local Wigner-type correlation functional. In essence, a Kohn - Sham-type equation has been solved numerically. Our results on excited-state energies, excitation energies and differences between excitation energies are in good agreement with available experimental and theoretical results. In 50% of cases, the percentage deviation in the calculated excitation energy is less than unity. The estimates of the relatively small distances (0.02 - 0.1 au) of the He states below the corresponding N = 2, 3, 4 ionization thresholds are in error by 0.5 - 34.9%, indicating that the Wigner correlation functional needs to be improved for greater accuracy. The excited radial densities display expected structures. Some new states are reported.

One-dimensional multiple-well oscillators: a time-dependent quantum mechanical approach

Time-dependent Schr ̈ odinger equation (TDSE) is solved numerically to calculate the groundand first three excited-state energies, expectation values hx2 j i; j = 1;2; : : : ;6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.

Helium atom in intense and superintense laser fields: A new theoretical approach

A quantum hydrodynamical study is made of the dynamical changes of a helium atom interacting with lasers of two different intensities, but having the same frequency. Under the intense laser field, electron density oozes out of the helium atom by absorbing laser photons and getting promoted to higher excited states including the continuum. Under the superintense field, electron density partly moves away from the helium nucleus but remains in the “quasi-bound” dressed states along with the laser field, thus suppressing ionization.