Rapid topography mapping of scalar fields: Large molecular clusters

The following article appeared in Journal of Chemical Physics 137.7 (2012): 074116 and may be found at http://scitation.aip.org/content/aip/journal/jcp/137/7/10.1063/1.4746243An efficient and rapid algorithm for topography mapping of scalar fields, molecular electron density (MED) and molecular electrostatic potential (MESP) is presented. The highlight of the work is the use of fast function evaluation by Deformed-atoms-in-molecules (DAM) method. The DAM method provides very rapid as well as sufficiently accurate function and gradient evaluation. For mapping the topography of large systems, the molecular tailoring approach (MTA) is invoked. This new code is tested out for mapping the MED and MESP critical points (CP's) of small systems. It is further applied to large molecular clusters viz. (H 2O) 25, (C 6H 6) 8 and also to a unit cell of valine crystal at MP26-31G(d) level of theory. The completeness of the topography is checked by extensive search as well as applying the Poincaré-Hopf relation. The results obtained show that the DAM method in combination with MTA provides a rapid and efficient route for mapping the topography of large molecular systemsAuthors thank the Center for Development of Advanced Computing (C-DAC), Pune for financial and computational support. S.R.G. is grateful to the Department of Science and Technology (DST) for the award of J. C. Bose National Fellowship. R. López acknowledges partial funding from the CAM (S2009_PPQ-1545, LIQUORGAS) and MICINN (CTQ2010-19232). Authors are also thankful to Dr. Graeme M. Day, University of Cambridge, for providing the coordinates of unit cell of valine crystal and to Dr. V. Subramanian, CLRI, Chennai for providing some test run

Complexity analysis of Klein-Gordon single-particle systems

The Fisher-Shannon complexity is used to quantitatively estimate the contribution of relativistic effects to on the internal disorder of Klein-Gordon single-particle Coulomb systems which is manifest in the rich variety of three-dimensional geometries of its corresponding quantum-mechanical probability density. It is observed that, contrary to the non-relativistic case, the Fisher-Shannon complexity of these relativistic systems does depend on the potential strength (nuclear charge). This is numerically illustrated for pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is analysed in various ground and excited states. It is found that the relativistic effects enhance when n and/or l are decreasing.Comment: 4 pages, 3 figures, Accepted in EPL (Europhysics Letters

Universal trend of the information entropy of a fermion in a mean field

We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $\Lambda$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \ln (\mu E +\nu)$. This relation holds for all the systems under consideration.Comment: 9 pages, latex, 6 figure

Information entropy as a measure of the quality of a nuclear density distribution

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various microscopic mean field approaches are also employed. It turns out that the entropy increases on going from crude phenomenological models to more sophisticated (microscopic) ones. It is concluded that the larger the information entropy, the better the quality of the nuclear density distribution. An alternative approach is also examined: the net information content i.e. the sum of information entropies in position and momentum space $S_{r}+S_{k}$. It is indicated that $S_{r}+S_{k}$ is a maximum, when the best fit to experimental data of the density and momentum distributions is attained.Comment: 12 pages, LaTex, no figures, Int. J. of Mod. Phys. E in pres

Enabling rapid and accurate construction of CCSD(T)-level potential energy surface of large molecules using molecular tailoring approach

The construction of the potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is an arduous task due to the high computational cost. In this Letter, we report the possibility of efficient construction of such a PES employing the molecular tailoring approach (MTA) on off-the-shelf hardware. The full calculation (FC) as well as MTA energies at CCSD(T)/aug-cc-pVTZ level for three test molecules, viz. acetylacetone, N-methyacetamide, and tropolone are reported. All the MTA energies are in excellent agreement with their FC counterparts (typical error being sub-millihartree) with a time advantage factor of 3 to 5. The energy barrier from the ground- to transition-state is accurately captured. Further, the accuracy and efficiency of the MTA method for estimating energy gradients at CCSD(T) level are demonstrated. This work brings out the possibility of the construction of PES for large molecules using MTA with the computational economy at a high level of theory and/or basis set

Co-operative electrostatics for understanding crown ether hydration patterns

A prototype problem in supramolecular chemistry is: Would it be possible to understand qualitative trends in hydration preocess of crown ether from simple considerations at the molecular levels? An answer is offered for the hydration of 18-crown-6 in terms of co-operative electrostatic effects. These effects are monitored by mapping the molecular electrostatic potential topography of 18-crown-6 as well as various interemediate hydrated species, followed by electrostatic modelling. All model calculations have been done at ab-initio HF/6-31G** level. The trends of these hydration patterns are in good agreement with the corresponding fully optimized ab-initio ones. Final structure of 18C6·4H2O is quite similar to the corresponding experimental crystal structure. Such an electrostatics-based method seems to be an excellent general tool for understanding weak interactions in supramolecular chemistry

Electron momentum distributions and compton profiles of some molecules with FSGO model

The electron momentum distributions and the Compton profiles (within the impulse approximation) of H2, LiH, methane, water, acetylene, ethylene, ethane cyclopropane and cyclobutane have been calculated using the floating spherical Gaussian orbital (FSGO) wavefunctions. The agreement of the single-FSGO Compton profiles with the corresponding experimental or the Hartree-Fock (HF-SCF) theoretical ones is fairly good in most of the cases examined. The advantages and drawbacks of using the FSGO model for the calculation of Compton profiles are discussed

Quantum-information entropies for highly excited states of single-particle systems with power-type potentials

The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k→∞ (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states

An ab initio topographical investigation on the molecular electrostatic potential of some chemical mutagens

A detailed topographical investigation on the molecular electrostatic potentials (MESPs) of different conformers of acetaldehyde, nitrous acid and hydroxylamine has been carried out at the ab initio SCF level using TZ2p, 6-31G* and STO-3G basis sets. In general, large regions of negative potential have been observed. An attempt has been made to correlate these potentials with biological activities of the molecules. Mutagenic and toxicological properties appear to be related to the presence of these large negative zones

Free expansion of impenetrable bosons on one-dimensional optical lattices

We review recent exact results for the free expansion of impenetrable bosons on one-dimensional lattices, after switching off a confining potential. When the system is initially in a superfluid state, far from the regime in which the Mott-insulator appears in the middle of the trap, the momentum distribution of the expanding bosons rapidly approaches the momentum distribution of noninteracting fermions. Remarkably, no loss in coherence is observed in the system as reflected by a large occupation of the lowest eigenstate of the one-particle density matrix. In the opposite limit, when the initial system is a pure Mott insulator with one particle per lattice site, the expansion leads to the emergence of quasicondensates at finite momentum. In this case, one-particle correlations like the ones shown to be universal in the equilibrium case develop in the system. We show that the out-of-equilibrium behavior of the Shannon information entropy in momentum space, and its contrast with the one of noninteracting fermions, allows to differentiate the two different regimes of interest. It also helps in understanding the crossover between them.Comment: 21 pages, 14 figures, invited brief revie