Quasi-periodic stability of normally resonant tori

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.     

Wave-packet continuum discretization for quantum scattering

A general approach to a solution of few- and many-body scattering problems based on a continuum-discretization procedure is described in detail. The complete discretization of continuous spectrum is realized using stationary wave packets which are the normalized states constructed from exact non-normalized continuum states. Projecting the wave functions and all scattering operators like t$t$-matrix, resolvent, etc. on such a wave-packet basis results in a formulation of quantum scattering problem entirely in terms of discrete elements and linear equations with regular matrices. It is demonstrated that there is a close relation between the above stationary wave packets and pseudostates which are employed often to approximate the scattering states with a finite L₂$L_2$ basis. Such a fully discrete treatment of complicated few- and many-body scattering problems leads to significant simplification of their practical solution. Also we get finite-dimensional approximations for complicated operators like effective interactions between composite particles constructed via the Feshbach-type projection formalism. As illustrations to this general approach we consider several important particular problems including multichannel scattering and scattering in the three-nucleon system within the Faddeev framework.     

Theoretical Insights into Intermolecular Hydrogen-Bonding Strengthening in Fluorenone-Methanol Complexes Induced by Electronic Excitation and Bulk Solvent Effect

This work presents a theoretical insight into the variation of the site-specific intermolecular hydrogen-bonding （HB）, formed between C=O group of fluorenone （FN） and O-H groups of methanol （MeOL） molecules, induced by both the electronic excitation and the bulk solvent effect. Through the calculation of molecular ground- and excited-state properties, we not only demonstrate the characters of HB strengthening induced by electronic excitation and the bulk solvent effect but also reveal the underlying physical mechanism which leads to the HB variation. The strengthening of the intermolecular HB in electronically excited states and in liquid solution is characterized by the reduced HB bond-lengths and the red-shift IR spectra accompanied by the increasing intensities of IR absorption corresponding to the characteristic vibrational modes of the O-H and C--O stretching. The HB strengthening in the excited electronic states and in solution mainly arises from the charge redistribution of the FN molecule induced by the electronic excitation and bulk solvent instead of the intermolecular charge transfer. The charge redistribution of the solute molecule increases the partial dipole moment of FN molecule and the FN-MeOL intermolecular interaction, which subsequently leads to the HB strengthening. With the bulk solvent effect getting involved, the theoretical IR spectra of HBed FN-MeOL complexes agree much better with the experiments than those of gas-phase FN-MeOL dimer. All the calculations are carried out based on our developed analytical approaches for the first and second energy derivatives of excited electronic state within the time-dependent density functional theory.     

First-principles characterization of formate and carboxyl adsorption on stoichiometric CeO2(111) and CeO2(110) surfaces

Molecular adsorption of formate and carboxyl on stoichiometric CeO₂(111) and CeO₂(110) surfaces was studied using periodic density functional theory (DFT+U) calculations. Two distinguishable adsorption modes (strong and weak) of formate are identified. The bidentate configuration is more stable than the monodentate adsorption configuration. Both formate and carboxyl bind at the more open CeO₂(110) surface are stronger. The calculated vibrational frequencies of two adsorbed species are consistent with the experimental measurements. Finally, the effects of U parameters on the adsorption of formate and carboxyl over both CeO₂ surfaces were investigated. We found that the geometrical configurations of two adsorbed species are not affected by different U parameters (U = 0, 5, and 7). However, the calculated adsorption energy of carboxyl pronouncedly increases with the U value while the adsorption energy of formate only slightly changes (<0.2 eV). The Bader charge analysis shows the opposite charge transfer occurs for formate and carboxyl adsorption where the adsorbed formate is negatively charge while the adsorbed carboxyl is positively charged. Interestingly, with the increasing U parameter, the amount of charge is also increased.     

Adatom Defect Induced Spin Polarization of Asymmetric Structures

The spin polarization of carbon nanomaterials is crucial to design spintronic devices. In this paper, the first-principles is used to study the electronic properties of two defect asymmetric structures, Cap-(9, 0)-Def [6, 6] and Cap-(9, 0)-Def [5, 6]. We found that the ground state of Cap-(9, 0)-Def [6, 6] is sextet and the ground state of Cap-(9, 0)-Def [5, 6] is quartet, and the former has a lower energy. In addition, compared with Cap-(9, 0) CNTs, the C adatom on C₃₀ causes spin polarization phenomenon and Cap-(9, 0)-Def [6, 6] has more spin electrons than Cap-(9, 0)-Def [5, 6] structure. Moreover, different adsorb defects reveal different electron accumulation. This finding shows that spin polarization of the asymmetric structure can be adjusted by introducing adatom defects.     

Exploration of carbonic anhydrase inhibition of bioactive metabolites from Pistacia integerrima by molecular docking and first-principles investigations

Bioassay guided fractionation of Pistacia integerrima crude methanolic extract gave Pistacide-A (1) and Pistacide-B (2), along with ten known phytochemicals (3–12). Biochemical analysis of crude plant extract, in-vitro and in-silico carbonic anhydrase inhibitory potential of newly isolated compounds Pistacide-A (1) and Pistacide-B (2) were performed. The cytotoxicity of extract in methanol, ethylacetate and n-butanol against Artemia salina brine-shrimp was 34.98 g/ml, 160.81 g/ml, and 135.77 g/ml, respectively. The significant antimicrobial activity was exhibited by crude, ethyl acetate, and n-butanol fractions. Compounds 1 (IC₅₀ = 6.51 ± 0.42 mM) and 2 (IC₅₀ = 2.85 ± 0.09 mM) showed good carbonic anhydrase inhibition compared with standard zonisamide drug (IC₅₀ = 1.87 ± 0.003 mM). In addition, we have also clarified the electronic properties, absorption wavelengths, molecular electrostatic potential and Hirshfeld analysis by first-principles studies. The coherent intra-molecular charge transfer was seen from occupied to unoccupied molecular orbitals. The absorption wavelengths calculated at time dependent B3LYP/6-31G** level in methanol provided excellent accord with the experimental evidence. Molecular docking score revealed that Pistacide-B would be an efficient drug than its other counterpart that is rational to the experimental data.     

Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems

Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga–Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.     

Recent Progress in the Simulation of Chiral Systems with Real Time Propagation Methods

In this brief review, an overview about recent efforts to simulate the spectroscopic signatures of chiral molecules is given with focus on real time propagation approaches to solve the time-dependent Schrödinger equation. In particular the simulation of electric circular dichroism spectra and vibrational Raman optical activity is discussed. In comparison to linear absorption spectra, where only the response of the electric dipole moment is necessary, the response of the magnetic dipole moment and electric quadrupole moment is more intricate. Issues such as gauge origin dependence, basis set dependence, non-local potentials and the dipole approximation are addressed.