Density-functional and hydrodynamical approach to ion-atom collisions through a new generalized nonlinear Schrödinger equation

Conceptual density functional theory based electronic structure principles

In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.

Reactivity Dynamics

The chemical reactivity of a molecule as a whole or of an atom in a molecule varies during a chemical reaction. A variation of global and local reactivity descriptors in the course of a physicochemical process was studied within a quantum fluid density functional theory framework. Effects of a physical confinement and the electronic excitation therein were studied. In this Perspective, we also highlight the direction of a spontaneous chemical reaction in the light of the dynamical variants of the conceptual density functional theory-based electronic structure principles. An exhaustive state-of-the-art dynamical study is warranted in order to understand a chemical reaction from a reactivity perspective augmenting the associated molecular reaction dynamics analysis.

An investigation into possible quantum chaos in the H2 molecule under intense laser fields via Ehrenfest phase space (EPS) trajectories

By employing the Ehrenfest "phase space" trajectory method for studying quantum chaos, developed in our laboratory, the present study reveals that the H₂ molecule under intense laser fields of three different intensities, I = 1 × 10¹⁴ W/cm², 5 × 10¹⁴ W/cm², and 1 × 10¹⁵ W/cm², does not show quantum chaos. A similar conclusion is also reached through the Loschmidt echo (also called quantum fidelity) calculations reported here for the first time for a real molecule under intense laser fields. Thus, a long-standing conjecture about the possible existence of quantum chaos in atoms and molecules under intense laser fields has finally been tested and not found to be valid in the present case.

Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system

Regular to chaotic transition takes place in a driven van der Pol oscillator in both classical and quantum domains.

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

He 2++ molecular ion in a strong time-dependent magnetic field: a current-density functional study

The He 2++ molecular ion exposed to a strong ultrashort time-dependent (TD) magnetic field of the order of 10(9) G is investigated through a quantum fluid dynamics (QFD) and current-density functional theory (CDFT) based approach using vector exchange-correlation (XC) potential and energy density functional that depend not only on the electronic charge-density but also on the current density. The TD-QFD-CDFT computations are performed in a parallel internuclear-axis and magnetic field-axis configuration at the field-free equilibrium internuclear separation R = 1.3 au with the field-strength varying between 0 and 10(11) G. The TD behavior of the exchange- and correlation energy of the He 2++ is analyzed and compared with that obtained using a [B-TD-QFD-density functional theory (DFT)] approach based on the conventional TD-DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge-density alone. The CDFT based approach yields TD exchange- and correlation energy and TD electronic charge-density significantly different from that obtained using the conventional TD-DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT-based approach is traced to the TD current-density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He 2++ molecular ion is elucidated by treating electronic charge density as an electron-"fluid" in the terminology of QFD.

Hydrodynamic tensor density functional theory with correct susceptibility

In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory [J. Chem. Phys. 124, 024105 (2006)]. The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix. A basic ingredient in the theory is how to truncate the series of equation of motion for the moments. In the original work the authors assumed that the cumulants vanish above a certain order (N). Here the authors show how to modify this assumption to obtain the correct susceptibilities. This is done for N=3, a level above the previous study. At the desired truncation level a few relevant terms are added, which, with the right combination of coefficients, lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system. The approach is also powerful away from linear response, as demonstrated in a nonperturbative study of a jellium with a repulsive core, where excellent matching with Kohn-Sham simulations is obtained, while the Thomas-Fermi and von Weiszacker methods show significant deviations. In addition, time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.

Orbital-free tensor density functional theory

We propose a family of time-dependent orbital-free density-based theories that go beyond the usual current-density description of electrons or other particles. The theories deal with physical quantities that characterize the one-particle density matrix and consequently the kinetics of the particles. We analyze the first two theories in the family. The "lowest-order" theory is quantum hydrodynamics. The second one yields not only the longitudinal plasmon collective excitations, but also the transverse phonon modes that are associated with elementary excitations in Fermi liquids. The theories should make it feasible to do large orbital-free simulations of time-dependent and stationary systems.

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

HSAB principle applied to the time evolution of chemical reactions

Time evolution of various reactivity parameters such as electronegativity, hardness, and polarizability associated with a collision process between a proton and an X- atom/ion (X = He, Li(+), Be(2+), B(3+), C(4+)) in its ground ((1)S) and excited((1)P,(1)D,(1)F) electronic states as well as various complexions of a two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion and a proton to give rise to an XH(+) molecule. A favorable dynamical process is characterized by maximum hardness and minimum polarizability values according to the dynamical variants of the principles of maximum hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid, gradually prefers less to interact with X as has been discerned through the drop in maximum hardness value and the increase in the minimum polarizability value when the actual chemical process occurs. Among the noble gas elements, Xe is the most reactive. During the reaction: H(2) + H(+) --> H(3)(+) hardness maximizes and polarizability minimizes and H(2) is more reactive in its excited state. Regioselectivity of proton attack in the O-site of CO is clearly delineated wherein HOC(+) may eventually rearrange itself to go to the thermodynamically more stable HCO(+).

Solution of the quantum fluid dynamical equations with radial basis function interpolation

The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation psi = exp(R + iS)/[symbol: see text]. The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density rho = magnitude of psi 2 and on the structure of R = [symbol: see text]/2 ln rho generally being simpler and smoother than rho. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase for higher dimensional systems to provide a practical computational tool.