Quantum fluid dynamics approach for electronic structure calculation: application to the study of ground-state properties of rare gas atoms

Abstract

We explore the usefulness of a quantum fluid dynamics (QFD) approach for quantitative electronic structure calculations of many-electron systems. By combining QFD and density functional theory, a single time-dependent nonlinear QFD equation can be derived. The equation is further transformed into a diffusion-type form by an imaginary-time evolution method, whose asymptotic solution reaches a global minimum and the many-body ground-state wavefunction. The time-dependent generalized pseudospectral method is extended to solve the diffusion equation in spherical coordinates, allowing optimal and nonuniform spatial discretization and accurate and efficient solution of the diffusion function in space and time. The procedure is applied to the study of electronic energies, densities and other ground-state properties of noble gas atoms (He, Ne, Ar, Kr, Xe). The results are in good agreement with other best available values. The method offers a conceptually appealing and computationally practical procedure for the treatment of many-electron systems beyond the Hartree-Fock level.

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

“…Only the essential steps are given and the relevant details may be found elsewhere ( [34][35][36][37][38][39] and the references therein). Unless otherwise mentioned, atomic units are employed throughout this article.…”

“…In the past few years, the generalized pseudospectral (GPS) method has been proved to be a very powerful and efficient tool to deal with the static and dynamic processes of many-electron atomic/molecular systems characterized by the Coulomb singularities (see, for example, [34][35][36][37] and the references therein). Recently it has also been successfully applied to the power-law and logarithmic potentials [38], as well as the spiked harmonic oscillator with stronger singularity [39].…”

Ground and excited states of spherically symmetric potentials through an imaginary-time evolution method: application to spiked harmonic oscillators

“…Then eigenvalues are obtained by performing a Fourier transform of the auto-correlation function of propagated wave with the initial wave function. In yet another development, imaginary-time evolution technique was applied for direct calculation of ground-state densities and other properties of noble gas atoms, ions such as He, Be ++ , Ne, Ar, Kr, Xe, as well as molecules like H 2 , HeH + , He ++ 2 , from the solution of a single TD quantum fluid dynamical equation of motion [30][31][32]. Later, ground as well as excited-state energies, densities and other expectation values of 1D anharmonic and double-well [33], multiple-well [34] and self-interacting nonlinear [35] oscillators were obtained with impressive accuracy by transforming the relevant SE into a diffusion equation in imaginary time.…”

“…We follow the implementation used in [30][31][32][33][34][35][36] for this purpose. Note that, while for atoms and molecules in first three references, the diffusion equation originated from an amalgamation of quantum fluid dynamics and density functional theory, which eventually lead to a TD generalized non-linear SE, in the last four references, the same arose from a TDSE instead.…”

“…This method offered quite good results for ground and excited states of 1D and 2D potentials [33][34][35][36]. For spherically symmetric potentials (such as for atoms, as in [30][31][32]), however, only ground states were attempted using this approach. Here we include excited states in our study, that can extend its domain of applicability.…”