B. M. Deb

Bio: B. M. Deb is an academic researcher from Panjab University, Chandigarh. The author has contributed to research in topics: Excited state & Density functional theory. The author has an hindex of 24, co-authored 93 publications receiving 4959 citations. Previous affiliations of B. M. Deb include Indian Institute of Science Education and Research, Kolkata & Indian Institute of Science.

The Force Concept in Chemistry

Abstract: The applications, most of which have been developed in the last decade, of the Hellmann-Feynman (H-F) theorem in molecular quantum mechanics are reviewed. In general, the forces (on the nuclei of molecules) calculated with the use of this theorem provide great qualitative insight into the nature of the phenomena investigated; outstanding examples of these are in the concepts of chemical binding and molecular shapes. However, there are serious limitations in quantitative applications of the H-F theorem with approximate wave functions, since the calculated forces are extremely sensitive to small inaccuracies in the wave functions, especially near the nuclei of interest. Nevertheless, in view of the fact that it is difficult to discern general qualitative features in very accurate or ab initio molecular calculations, the H-F theorem is likely to be a highly useful tool for developing much needed qualitative chemical models which will be based on firm quantum mechanical foundations and will also remain open to quantitative extension, at least in principle.

Schrödinger fluid dynamics of many‐electron systems in a time‐dependent density‐functional framework

Abstract: For an N‐electron system, a connection is explored between density‐functional theory and quantum fluid dynamics, through a dynamical extension of the former. First, we prove the Hohenberg–Kohn theorem for a time‐dependent harmonic perturbation under conditions which guarantee the existence of the corresponding steady (or quasiperiodic) states of the system. The corresponding one‐particle time‐dependent Schrodinger equation is then variationally derived starting from a fluid‐dynamical Lagrangian density. The subsequent fluid‐dynamical interpretation preserves the ’’particle’’ description of the system in the sense that the N‐electron fluid has N components each of which is an independent‐particle Schrodinger fluid characterized by a density function ρj and an irrotational velocity field uj, j = 1,⋅⋅⋅,N. However, the mean velocity u of the fluid is not irrotational, in general. The force densities and the stress tensor occurring in the Navier–Stokes equation are physically interpreted. The present work is another step towards the interpretation of physicochemical phenomena in three‐dimensional space.

The role of single-particle density in chemistry

Abstract: The definition, properties, and applications of the single-particle (electron) density $\ensuremath{\rho}(\mathrm{r})$ are discussed in this review. Since the discovery of Hohenberg-Kohn theorem, which gave a theoretical justification for considering $\ensuremath{\rho}(\mathrm{r})$, rather than the wave function, for studying both nondegenerate and degenerate ground states of many-electron systems, $\ensuremath{\rho}(\mathrm{r})$ has been acquiring increasing attention. The quantum subspace concept of Bader et al. has further highlighted $\ensuremath{\rho}(\mathrm{r})$ since a rigorous decomposition of the three-dimensional (3D) space of a molecule into quantum subspaces or virial fragments is possible, the boundaries of such subspaces being defined solely in terms of $\ensuremath{\rho}(\mathrm{r})$. Further, $\ensuremath{\rho}(\mathrm{r})$ is a very useful tool for studying various chemical phenomena. The successes and drawbacks of earlier models, such as Thomas-Fermi-Dirac, incorporating $\ensuremath{\rho}(\mathrm{r})$ are examined. The applications of $\ensuremath{\rho}(\mathrm{r})$ to a host of properties---such as chemical binding, molecular geometry, chemical reactivity, transferability, and correlation energy---are reviewed. There has been a recent trend in attempting to bypass the Schr\"odinger equation and directly consider single-particle densities and reduced density matrices, since most information of physical and chemical interest are encoded in these quantities. This approach, although beset with problems such as $N$-representability, and although unsuccessful at present, is likely to yield fresh concepts as well as shed new light on earlier ideas. Since charge density in 3D space is a fundamental quantum-mechanical observable, directly obtainable from experiment, and since its use in conjunction with density-functional theory and quantum fluid dynamics would provide broadly similar approaches in nuclear physics, atomic-molecular physics, and solid-state physics, it is not unduly optimistic to say that $\ensuremath{\rho}(\mathrm{r})$ may be the unifying link between the microscopic world and our perception of it.

Multiwfn: a multifunctional wavefunction analyzer.

Abstract: Multiwfn is a multifunctional program for wavefunction analysis. Its main functions are: (1) Calculating and visualizing real space function, such as electrostatic potential and electron localization function at point, in a line, in a plane or in a spatial scope. (2) Population analysis. (3) Bond order analysis. (4) Orbital composition analysis. (5) Plot density-of-states and spectrum. (6) Topology analysis for electron density. Some other useful utilities involved in quantum chemistry studies are also provided. The built-in graph module enables the results of wavefunction analysis to be plotted directly or exported to high-quality graphic file. The program interface is very user-friendly and suitable for both research and teaching purpose. The code of Multiwfn is substantially optimized and parallelized. Its efficiency is demonstrated to be significantly higher than related programs with the same functions. Five practical examples involving a wide variety of systems and analysis methods are given to illustrate the usefulness of Multiwfn. The program is free of charge and open-source. Its precompiled file and source codes are available from http://multiwfn.codeplex.com.

All-atom empirical potential for molecular modeling and dynamics studies of proteins.

Abstract: New protein parameters are reported for the all-atom empirical energy function in the CHARMM program. The parameter evaluation was based on a self-consistent approach designed to achieve a balance between the internal (bonding) and interaction (nonbonding) terms of the force field and among the solvent−solvent, solvent−solute, and solute−solute interactions. Optimization of the internal parameters used experimental gas-phase geometries, vibrational spectra, and torsional energy surfaces supplemented with ab initio results. The peptide backbone bonding parameters were optimized with respect to data for N-methylacetamide and the alanine dipeptide. The interaction parameters, particularly the atomic charges, were determined by fitting ab initio interaction energies and geometries of complexes between water and model compounds that represented the backbone and the various side chains. In addition, dipole moments, experimental heats and free energies of vaporization, solvation and sublimation, molecular volume...

Chemistry with ADF

Abstract: We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Density-Functional Theory for Time-Dependent Systems

Abstract: The response of an interacting many-particle system to a time-dependent external field can usually be treated within linear response theory. Due to rapid experimental progress in the field of laser physics, however, ultra-short laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse one observes a wealth of new phenomena [1] which cannot be explained by traditional perturbation theory. The non-perturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. In principle, it requires a full solution of the time-dependent Schrodinger equation for the interacting many-body system, which is an exceedingly difficult task. In view of the success of density functional methods in the treatment of stationary many-body systems and in view of their numerical simplicity, a time-dependent version of density functional theory appears highly desirable, both within and beyond the regime of linear response.

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

Abstract: This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential