There are three reasons for seeking an alternative density-based quantum mechanics of many-electron systems, incorporating both interpretive and basic quantum mechanical aspects: (i) failure of popularad hoc chemical concepts underab initio scrutiny; (ii) failure ofab initio calculations to provide simple concepts; and (iii) highly attractive concepts and pictures generated by the electron density in three-dimensional space. At present the three interlinked pillars for such a density mechanics (in contrast to wave mechanics) are: (a) density functional theory; (b) quantum fluid dynamics; and (c) property densities in three-dimensional space. This article describes several studies dealing with these aspects. Although a density mechanics may well be an impossible ideal to realize, the search for it is indeed rejuvenating the whole of quantum chemistry.

The lattice gas automata (LGA) technique as an alternative to the partial differential equation (PDE) approach for studying dynamical processes, including those in reaction-diffusion systems, is reviewed. The LGA approach gained significance after the simulation of Navier-Stokes equation by Hardyet al (1976). In this approach, the dynamics of a system are simulated by constructing a microlattice on each node of which Boolean bits are associated with the presence or absence of particles indistinct velocity states. A complete description involves the composition of anelastic collision operator, areactive collision operator and apropagation operator. The Hardy, de Pazzis and Pomeau (HPP) model does not have the desired isotropy, but its subsequent modification in 1986, known as the Frisch, Hasselacher and Pomeau (FHP) model (Frischet al 1986), has been applied to a variety of nonequilibrium processes. Reaction-diffusion systems have been simulated in a manner analogous to the master equation approach in a continuum framework. The Boltzmann kinetic equation as well as the expected complex features at the macroscopic level are obtained in LGA simulations. An increasing trend is to use real numbers instead of Boolean bits for the velocity states. This gives the lattice Boltzmann (LB) model which is not only less noisy than LGA but also numerically superior to finite-difference approximations (FDAs) to PDEs. The most significant applications of LGA appear to be in the molecular-level understanding of reactive processes.

Self-consistent density-functional calculations, in an exchange-only framework, are reported for the energies and moments of the 2³S excited states of the helium isoelectronic sequence, according to the prescription of Harbola and Sahni. The total energy values show excellent agreement with “exact” nonrelativistic values while the moments are also quite satisfactory.

A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining density functional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on the femtosecond dynamics of the electron density in the hydrogen molecule interacting with high-intensity laser fields. For this purpose, the GNLSE is solved numerically for many time-steps over a total interaction time of 100 fs, by employing a finite-difference scheme. Various time-dependent (TD) quantities, namely, electron density, ground-state survival probability and dipole moment have been obtained for two laser wavelengths and four different intensities. The high-order harmonics generation (HHG) is also examined. The present approach goes beyond the linear response formalism and, in principle, calculates the TD electron density to all orders of change.

By employing an intense microwave laser of wavelength 116.65 𝜇m with intensities $1 \times 10^{13}$ and $5 \times 10^{18}$Wcm⁻², respectively, the conclusion is reached theoretically and computationally that it is possible to dissociate the CO molecule, modelled as a Morse oscillator. It is predicted that for above-threshold dissociation (ATD), the molecule should absorb 1044 photons of the given wavelength in order to reach the lowest edge of the vibrational continuum. A consistent analysis of the predicted dissociation process is provided though the time-dependent probability density, dissociation probability, norm, potential function, HHG and ATD spectra, obtained by numerically solving the time-dependent vibrational Schödinger equation.