arXiv subjects

Amlan K. Roy

Publications and source records attributed to Amlan K. Roy.

At least 37 records · Page 2Linked to original sources

arXiv2021

Analysis of Compton profile through information theory in H-like atoms inside impenetrable sphere

Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a \emph{hard} spherical enclosure, as well as in \emph{free condition}. Some exact analytical relations for the CP's of circular or nodeless states of free atom is presented. By means of a scaling idea, this has been further extended to the study of an H-like atom trapped inside an impenetrable cavity. The accuracy of these constructed CP has been confirmed by computing various momentum moments. Apart from that, several information theoretical measures, like Shannon entropy ($S$) and Onicescu energy ($E$) have been exploited to characterize these profiles. Exact closed form expressions are derived for $S$ and $E$ using the ground state CP in free H-like atoms. A detailed study reveals that, increase in confinement inhibits the rate of dissipation of kinetic energy. At a fixed $\ell$, this rate diminishes with rise in $n$. However, at a certain $n$, this rate accelerates with progress in $\ell$. A similar analysis on the respective free counterpart displays an exactly opposite trend as that in confined system. However, in both free and confined environments, CP generally gets broadened with rise in $Z$. Representative calculations are done numerically for low-lying states of the confined systems, taking two forms of position-space wave functions: (a) exact (b) highly accurate eigenfunctions through a generalized pseudospectral method. In essence, CPs are reported for confined H atom (and isoelectronic series) and investigated adopting an information-theoretic framework.

quant-ph↗

arXiv2021

Excitation energies through Becke's exciton model within a Cartesian-grid KS DFT

Photon-induced electronic excitations are ubiquitously observed in organic chromophore. In this context, we present a simple, alternative time-independent DFT procedure, for computation of single-particle excitation energies, in particular, the lower bound excited singlet states, which are of primary interest in photochemistry. This takes inspiration from recently developed Becke's exciton model, where a key step constitutes the accurate evaluation of correlated singlet-triplet splitting energy. It introduces a non-empirical model, both from "adiabatic connection theorem" and "virial theorem" to analyze the role of 2e$^-$ integral in such calculations. The latter quantity is efficiently mapped onto a real grid and computed accurately using a purely numerical strategy. Illustrative calculations are performed on 10 $π$-electron organic chromophores within a Cartesian-grid implementation of pseudopotential Kohn-Sham (KS) DFT, developed in our laboratory, taking SBKJC-type basis functions within B3LYP approximation. The triplet and singlet excitation energies corresponding to first singly excited configuration, are found to be in excellent agreement with TD-B3LYP calculations. Further, we perform the same for a set of larger molecular systems using the asymptotically corrected LC-BLYP, in addition to B3LYP. A systematic comparison with theoretical best estimates demonstrates the viability and suitability of current approach in determining optical gaps, combining predictive accuracy with moderate computational cost.

physics.chem-ph↗

arXiv2019

Critical parameters and spherical confinement of H atom in screened Coulomb potential

Critical parameters in three screened potentials, namely, Hulthén, Yukawa and exponential cosine screened Coulomb potential are reported. Accurate estimates of these parameters are given for each of these potentials, for all states having $n \leq 10$. Comparison with literature results is made, wherever possible. Present values compare excellently with reference values; for higher $n,\ell$, our results are slightly better. Some of these are presented for first time. Further, we investigate the spherical confinement of H atom embedded in a dense plasma modeled by an exponential cosine screened potential. Accurate energies along with their variation with respect to box size and screening parameter are calculated and compared with reference results in literature. Sample dipole polarizabilities are also provided in this case. The generalized pseudospectral method is used for accurate determination of eigenvalues and eigenfunctions for all calculations.

physics.chem-ph↗

arXiv2019

Static polarizability and hyperpolarizability in atoms and molecules through a Cartesian-grid DFT

Static electric response properties of atoms and molecules are reported within the real-space Cartesian grid implementation of pseudopotential Kohn-Sham (KS) density functional theory (DFT). A detailed systematic investigation is made for a representative set of atoms and molecules, through a number of properties like total ground-state electronic energies, permanent dipole moment ($\bmμ$), static average dipole polarizability ($\overlineα$). This is further extended to first-hyperpolarizability ($\bmβ$) in molecules. It employs a recently developed non-uniform grid-optimization technique, with a suitably chosen fixed initial applied field. A simple variant of the finite-field method, using a rational function fit to the dipole moment with respect to electric field, is adopted. We make use of Labello-Ferreira-Kurtz (LFK) basis set, which has performed quite well in these scenarios. To assess the efficacy and feasibility, four XC functionals such as LDA, BLYP, PBE and LBVWN are chosen. Present results are compared with available literature (both theoretical and experimental) values, whenever possible. In all instances, they show excellent agreement with the respective atom-centered-grid results, very widely used in many quantum chemistry programs. This demonstrates a viable alternative towards accurate prediction of response properties of many-electron systems in Cartesian coordinate grid.

physics.chem-ph↗

arXiv2019

Information entropy as a measure of tunneling and quantum confinement in a symmetric double-well potential

Information entropic measures such as Fisher information, Shannon entropy, Onicescu energy and Onicescu Shannon entropy of a symmetric double-well potential are calculated in both position and momentum space. Eigenvalues and eigenvectors of this system are obtained through a variation-induced exact diagonalization procedure. The information entropy-based uncertainty relation is shown to be a better measure than conventional uncertainty product in interpreting purely quantum mechanical phenomena, such as, tunneling and quantum confinement in this case. Additionally, the phase-space description provides a semiclassical explanation for this feature. Total information entropy and phase-space area show similar behavior with increasing barrier height.

quant-ph↗

arXiv2019

A density functional method for general excited states in atoms

This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more than one thresholds, degeneracy with more than one minima. Therefore these pose unusual challenges to both theoreticians and experimentalists. Our method uses a work-function-based exchange potential in conjunction with the popular gradient-corrected Lee-Yang-Parr correlation functional. The resulting Kohn-Sham equation, in the non-relativistic framework, is numerically solved accurately and efficiently by means of a generalized pseudospectral method through a non-uniform, optimal spatial discretization. This has been applied to a variety of excited states, such as low and high states; single, double, triple as well as multiple excitations; valence and core excitations; autoionizing states; satellites; hollow and doubly-hollow states; very high-lying Rydberg resonances; etc., of atoms and ions, with remarkable success. A thorough and systematic comparison with literature data reveals that, for all these systems, the exchange-only results are practically of Hartree-Fock quality; while with inclusion of correlation, this offers excellent agreement with available experimental data as well as those obtained from other sophisticated theoretical methods. Properties such as individual state energies, excitation energies, radial densities as well as various expectation values are studied. This helps us in predicting many states for the first time.

physics.chem-ph↗

arXiv2019

A general method for central potentials in quantum mechanics

We focus on a recently developed generalized pseudospectral method for accurate, efficient treatment of certain central potentials of interest in various branches in quantum mechanics, usually having singularity. Essentially this allows optimal, nonuniform spatial discretization of the pertinent single-particle Schrodinger equation satisfying Dirichlet boundary condition leading to standard diagonalization of symmetric matrices. Its validity and feasibility have been demonstrated for a wide range of important potentials such as Hulthén, Yukawa, generalized spiked harmonic oscillators, Hellmann, Coulomb potentials without/with various perturbations (for instance, linear and quadratic) etc. Although initially designed for singular potentials, this has also been remarkably successful for various other cases such as power-law, logarithmic, harmonic potentials containing higher order perturbations, 3D rational potentials as well as confinement studies. Furthermore, a large number of low-, moderately high-, high-lying multiply excited Rydberg states such as singly, doubly excited He as well as triply excited hollow $2l2l'2l'' (n \ge 2)$ and $3l3l'3l''$ doubly-hollow resonances in many-electron atoms have been treated by this approach within a KS DFT with great success. This offers very high-quality results for both ground and higher lying states for arbitrary values of potential parameters (covering both weak and strong coupling) with equal ease and efficacy. In all cases, excellent agreement with literature results are observed; in many cases this surpasses the accuracy of all other existing results while in other occasions our results are comparable to the best ones available in literature.

quant-ph↗

arXiv2019

DFT calculations of atoms and molecules in Cartesian grids

Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a variational DFT method for atoms and molecules \emph{completely} in a Cartesian grid. The non-relativistic Kohn-Sham equation is solved by using an LCAO-MO ansatz. Atom-centered localized basis set, electron density, molecular orbitals, two-body potentials are directly constructed on the grid. We adopt a Fourier convolution method for classical Coulomb potentials by making an Ewald-type decomposition technique in terms of short- and long-range interactions. It produces quite accurate and competitive results for various properties of interest, such as component energy, total energy, ionization energy, potential energy curve, atomization energy, etc. Both local and non-local functionals are employed for pseudopotential as well as full calculations. While most results are offered in a \emph{uniform} grid, initial exploratory attempts are made in a \emph{non-uniform} grid, which can significantly reduce the computational overhead. This offers a practical, viable alternative to atom-centered grid-based implementations, currently exploited by the majority of programs available world-wide.

physics.chem-ph↗

arXiv2019

A new density functional method for electronic structure calculation of atoms and molecules

This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradient- and Laplacian-dependent functionals. A detailed, systematic analysis on obtained results relevant to quantum chemistry, are made, \emph{for the first time}, using CCG, which clearly illustrates the significance of this alternative method in the present context. Quantities such as component energies, total energies, ionization energies, potential energy curve, atomization energies, etc., are addressed for pseudopotential calculations, along with a thorough comparison with literature data, wherever possible. Finally, some words on the future and prospect of this method are mentioned. In summary, we have presented a new CCG-based \emph{variational} DFT method for accurate, dependable calculation of atoms and molecules.

physics.chem-ph↗

arXiv2019

Information-Entropic Measures in Confined Isotropic Harmonic Oscillator

Information based uncertainty measures like R{é}nyi entropy (R), Shannon entropy (S) and Onicescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic oscillator. The transformation of Hamiltonian in to a dimensionless form gives an idea of the composite effect of oscillation frequency ($ω$) and confinement radius ($r_{c}$). For a given quantum state, accurate results are provided by applying respective \emph{exact} analytical wave function in $r$ space. The $p$-space wave functions are produced from Fourier transforms of radial functions. Pilot calculations are done taking order of entropic moments ($α, β$) as $(\frac{3}{5}, 3)$ in $r$ and $p$ spaces. A detailed, systematic analysis is performed for confined harmonic oscillator (CHO) with respect to state indices $n_{r},l$, and $r_c$. It has been found that, CHO acts as a bridge between particle in a spherical box (PISB) and free isotropic harmonic oscillator (IHO). At smaller $r_c$, $E_{\rvec}$ increases and $R_{\rvec}^α, S_{\rvec}$ decrease with rise of $n_{r}$. At moderate $r_{c}$, there exists an interaction between two competing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of $n_{r}$ (delocalization). Most of these results are reported here for the first time, revealing many new interesting features.

cond-mat.stat-mech↗

arXiv2019

Quantum confinement in an asymmetric double-well potential through energy analysis and information entropic measure

Localization of a particle in the wells of an asymmetric double-well (DW) potential is investigated here. Information entropy-based uncertainty measures, such as Shannon entropy, Fisher information, Onicescu energy, etc., and phasespace area, are utilized to explain the contrasting effect of localization-delocalization and role of asymmetric term in such two-well potentials. In asymmetric situation, two wells behaves like two different potentials. A general rule has been proposed for arrangement of quasi-degenerate pairs, in terms of asymmetry parameter. Further, it enables to describe the distribution of particle in either of the deeper or shallow wells in various energy states. One finds that, all states eventually get localized to the deeper well, provided the asymmetry parameter attains certain threshold value. This generalization produces symmetric DW as a natural consequence of asymmetric DW. Eigenfunctions, eigenvalues are obtained by means of a simple, accurate variationinduced exact diagonalization method. In brief, information measures and phase-space analysis can provide valuable insight toward the understanding of such potentials.

quant-ph↗

arXiv2019

Information entropic measures of a quantum harmonic oscillator in symmetric and asymmetric confinement within an impenetrable box

Information-based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of \emph{symmetric and asymmetric} confinement in a quantum harmonic oscillator. Also, the transformation of Hamiltonian into a dimensionless form gives an idea of the composite effect of force constant and confinement length ($x_c$). In symmetric case, a wide range of $x_{c}$ has been taken up, whereas asymmetric confinement is dealt by shifting the minimum of potential from origin keeping box length and boundary fixed. Eigenvalues and eigenvectors for these systems are obtained quite accurately via an imaginary time propagation scheme. For asymmetric confinement, a variation-induced exact diagonalization procedure is also introduced, which produces very high-quality results. One finds that, in symmetric confinement, after a certain characteristic $x_{c}$, all these properties converge to respective values of free harmonic oscillator. In asymmetric situation, excited-state energies always pass through a maximum. For this potential, the classical turning-point decreases, whereas well depth increases with the strength of asymmetry. Study of these uncertainty measures reveals that, localization increases with an increase of asymmetric parameter.

quant-ph↗

arXiv2019

Information entropy and complexity measure in generalized Kratzer potential

Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed. \emph{Exact} analytical expression of $I_{\rvec}$ is derived for the arbitrary state, whereas the same could be done for $I_{\pvec}$ with $\{n,\ell,m=0\}$ state. It is found that shifting from neutral to the cationic system, $I_{\rvec}$ increases while $S_{\rvec}$ decreases, consistent with the interpretation of a localization in the probability distribution. Additionally, this study reveals that $C_{IS}$ increases with the number of nodes in a system.

quant-ph↗

arXiv2019

Fisher information in confined isotropic harmonic oscillator

Fisher information ($I$) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate $r$ and $p$ spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and respective free harmonic oscillator (FHO) is pursued with respect to energy spectrum and $I$. This reveals that, a CHO offers two exactly solvable limits, namely, a PISB and an FHO. Moreover, the dependence of $I$ on quantum numbers $n_{r}, l, m$ in FHO and CHO are analogous. The role of force constant is discussed. Further, a thorough systematic analysis of $I$ with respect to variation of confinement radius $r_c$ is presented, with particular attention on \emph{non-zero}-$(l,m)$ states. Considerable new important observations are recorded. The results are quite accurate and most of these are presented for the first time.

quant-ph↗

arXiv2019

Relative Fisher information in some central potentials

Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1D case, the $n=0$ state is chosen as reference, whereas for a central potential, the respective circular or node-less (corresponding to lowest radial quantum number $n_{r}$) state of a given $l$ quantum number, is selected. Starting from their exact wave functions, expressions of IR in both $r$ and $p$ spaces are obtained in closed analytical forms in all these systems. A careful analysis reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly with quantum number $n$. Likewise, for 3D QHO and PHP, it varies with single power of radial quantum number $n_{r}$ in both spaces. But, in H atom they depend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, at a fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ and then falls off; also for a given $n$, it always decreases with $l$.

quant-ph↗

arXiv2019

Quantum mechanical virial-like theorem for confined quantum systems

Confinement of atoms inside impenetrable (hard) and penetrable (soft) cavities has been studied for nearly eight decades. However, a unified virial theorem for such systems has not yet been found. Here we provide a general virial-like equation in terms of mean square and expectation values of potential and kinetic energy operators. It appears to be applicable in both free and confined situations. Apart from that, we have derived an equation using the time-independent Schrödinger equation, which can be treated as a sufficient condition for a given stationary quantum state. A change of boundary condition does not affect these virial equations. In the hard confining condition, the perturbing (confining potential) does not affect the expression; it merely shifts the boundary from infinity to a finite region. In the soft case, on the contrary, the final expression includes contributions from the perturbing term. These are demonstrated numerically for several representative enclosed systems like harmonic oscillators (one-dimensional and three-dimensional) and hydrogen atoms. Its applicability in various other confinements (including angular) has been discussed. In essence, a virial equation has been proposed for free and confined quantum systems, from simple arguments.

quant-ph↗

arXiv2019

Information-entropic measures for non-zero l states of confined hydrogen-like ions

quant-ph↗

arXiv2019

Some complexity measures in confined isotropic harmonic oscillator

Various well-known statistical measures like \emph{López-Ruiz, Mancini, Calbet} (LMC) and \emph{Fisher-Shannon} complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position ($r$) and momentum ($p$) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with Rényi entropy ($R$) is invoked here. The importance of scaling parameter in the exponential part is also investigated. $R$ is estimated considering order of entropic moments $α, β$ as $(\frac{2}{3},3)$ in $r$ and $p$ spaces respectively. Explicit results of these measures with respect to variation of confinement radius $r_c$ is provided systematically for first eight energy states, namely, $1s,~1p,~1d,~2s,~1f,~2p,~1g$ and $2d$. Detailed analysis of these complexity measures provides many hitherto unreported interesting features.

quant-ph↗