Additivity in kramers pairs symmetry: Multiplets with up to four unpaired electrons

Many fermions Kramers pairs formalism is considered from the prospective of the sum of individual single fermion time‐reversal operators. The obtained many fermions “pseudo Kramers pairs operator” ( ), as well as its square ( ), have formally the same structure as the many fermion spin operators and . Nevertheless, the shape of eigenfunctions with respect to and is different. Herein all Kramers adapted eigenfunctions of for cases of up to four unpaired fermions are compiled, and their properties with respect to further advocated. It will be shown that degeneracy of the multiplets recovers the proper behavior with respect to Pascal's triangle. A projection operator for obtaining the “high spin” Kramers adapted eigenfunctions is suggested. Noncommutation of with spin and angular momentum operators and degeneracy is discussed at last. © 2016 Wiley Periodicals, Inc.     

The “bound wavefunction” on the repulsive excited ( ) state of the HD+ molecule

The time‐independent Schrödinger equation for the HD+ molecule is solved beyond the Born–Oppenheimer (B‐O) approximation. In the adiabatic representation, the wavefunction of the ground vibrational eigenstate is found to contain two parts: One is on the ground ( ) state which is dominant, and the other is on the repulsive excited ( ) state in the range from R = 0.0 to R = 5.0 Bohr. This is because the nonadiabatic coupling between the ground ( ) and excited ( ) states is strong in that region. The influences of the nonadiabatic coupling on the vibrational eigenfunctions are discussed in detail.     

Geometry of the canonical Van Vleck transformation

Bloch's transformation from the zeroth‐order space for a perturbation problem to the corresponding space of exact eigenvectors, was found as a geometrically defined alternative to the algebraically constructed Van Vleck transformation. Klein's theorem of uniqueness transferred some of this geometrical interpretation to its canonical form . Quite recently Kvaal has taken a large step further by writing as a product of commuting planar rotations, obtained by describing and in terms of certain principal vectors and canonical angles. Kvaal's approach is now developed further, using a new commutation relation which simplifies algebraic manipulations substantially. It allows for a simple definition of an operator for the angle between and which has Kvaal's vectors and angles as eigenvectors and eigenvalues. Klein's theorem is refined in various ways. The impact of the approach on a number of previous results is considered. © 2015 Wiley Periodicals, Inc.     

Study of adiabatic connection in density functional theory with an accurate wavefunction for two‐electron spherical systems

An accurate semianalytic wavefunction is proposed for the Hookium and two‐electron atoms for varying strength of where is the strength parameter and is coulomb interaction between two electrons. The wavefunction leads to energies that are as accurate as those from the Coupled cluster singles and doubles (CCSD) calculations. Using this wavefunction, we construct the external potential such that the density of the system remains unchanged as is varied. The work thus gives a unified picture of adiabatic connection for these systems based on an easy to use wavefunction and complements the past investigations done in this direction. Using the potential obtained, we explicitly calculate the energy of the corresponding positive ions and show that the chemical potential—calculated as the difference between the energies of the two‐electron system and its positive ion—is equal to the experimental ionization energy and remains unchanged as is varied. Furthermore, using total energies of these systems as a function of , we provide a new perspective into a variety of hybrid functionals.     

The H,H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

The one electron systems H, H , and HeH confined by an impenetrable spheroidal cavity are revisited in the frame of the Lagrange‐mesh method. The Born–Oppenheimer approximation where the nuclei are clamped at the foci is considered. Benchmark results of the total energy are obtained as a function of the interfocal distance R and the eccentricity of the cavity . Dipole oscillator strengths are calculated for the molecular ions H and HeH .     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.     

Photodetachment of hydrogen negative ion near inelastic surfaces: Arbitrary laser polarization direction

The photodetachment of hydrogen negative ion near different inelastic surfaces is investigated by the semiclassical closed orbit theory for arbitrary laser polarization direction . A two‐term formula of photodetachment cross section consisting of a smooth background term and an oscillatory term is derived. The oscillatory term contains an extra angular factor that describes the dependence of oscillations in total cross section on the laser polarization direction. It is observed that the amplitude of oscillations in cross section reaches maximum at when laser polarization is parallel to the z‐axis and it approaches zero as the laser polarization direction becomes perpendicular to the z‐axis. It is also observed that as the reflection coefficient , which accounts for the inelastic behavior of the surfaces, increases the amplitude of oscillation also increases. © 2015 Wiley Periodicals, Inc.     

Theoretical prediction of the optical rotation of chiral molecules in ordered media: A computational study of (Ra)‐1,3‐dimethylallene, (2R)‐2‐methyloxirane,and (2R)‐N‐methyloxaziridine

A theoretical procedure has been developed and implemented to calculate the optical rotation of chiral molecules in ordered phase via origin‐independent diagonal components , of the optical activity tensor and origin‐independent components , for , of the mixed electric dipole‐electric quadrupole polarizability. Origin independence was achieved by referring these tensors to the principal axis system of the electric dipole dynamic polarizability at the same laser frequency ω. The approach has been applied, allowing for alternative quantum mechanical methods based on different gauges, to estimate near Hartree–Fock values for three chiral molecules, (2R)‐N‐methyloxaziridine C₂NOH₅, (2R)‐2‐methyloxirane (also referred to as propylene oxide) C₃OH₆, and ( )‐1,3‐dimethylallene C₅H₈, at two frequencies. The theoretical predictions can be useful for an attempt at measuring correspondent experimental values in crystal phase. © 2015 Wiley Periodicals, Inc.     

Quantum control of electron‐proton symmetry breaking in dissociative ionization of H2 by intense laser pulses

Forward and backward electron/proton ionization/dissociation spectra from one‐dimensional non‐Born‐Oppenheimer H₂ molecule exposed to ultrashort intense laser pulses ( W/cm², λ = 800 nm) have been computed by numerically solving the time‐dependent Schrödinger equation. The resulting above‐threshold ionization and above‐threshold dissociation spectra exhibit the characteristic forward‐backward asymmetry and sensitivity to the carrier‐envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H₂ has been established. It is found that the symmetry breaking of electron‐proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.     

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two‐electron ions in states has been performed. The energy values of 1sns [ ] ( ) states of helium‐like ions ( ) are estimated within the framework of Ritz variational method using explicitly correlated Hylleraas‐type basis sets. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. A comparative study between the singlet and triplet states originating from a particular electronic configuration shows incidental degeneracy and the subsequent level‐crossing phenomena. The thermodynamic pressure felt by the ion inside the sphere pushes the energy levels toward continuum. Critical pressures for the transition to strong confinement regime (where the singly excited two‐electron energy levels cross the corresponding one‐electron threshold) as well as for the complete destabilization are also estimated.     

Rovibrational spectra of bounded diatomic molecules

Spectra of a bounded diatomic molecule is studied numerically. Shifted Deng–Fan oscillator potential has been used to model the molecule. The accurate five‐point finite difference method has been used to solve the Schrödinger equation for rovibrational motion of the molecule. The energies of the bound states as well as free states of the molecule have been calculated. In addition, radial matrix elements like , n = 1, 2, and 3 have been calculated. These have been used to calculate the ‐pole static polarizabilities. The variation of bound state energies, matrix elements and ‐pole static polarizabilities with the boundary radius has also been studied. The Stark effect in case of this bounded system has also been investigated.     

Information‐entropic measures in free and confined hydrogen atom

Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T), Fisher information (I), and Onicescu energy (E) have been explored extensively in both free H atom (FHA) and confined H atom (CHA). For a given quantum state, accurate results are presented by employing respective exact analytical wave functions in r space. The p‐space wave functions are generated from respective Fourier transforms—for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. Exact mathematical expressions of , are derived for circular states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n, l, and with confinement radius (r_c) for the latter. In a CHA, at small r_c, kinetic energy increases, whereas decrease with growth of n, signifying greater localization in high‐lying states. At moderate r_c, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.     

The effect of stochastic barrier fluctuation on semiclassical transmission probability and Shannon entropy of a symmetric double well potential

Stochastic fluctuation of barrier height and width of a symmetric double well plays a very significant role in the corresponding dynamics by increasing the semiclassical transmission probability and Shannon entropy of the system. The population of the system has been observed to be spread into several under barrier states starting from the or [, where and are the wave functions describing the two lowest degenerate states] in presence of the stochastic fluctuation. This distribution over several states is manifested by steady increase in Shannon entropy. However, any arbitrary value of the stochastic fluctuation cannot increase the populations of the upper energy states and consequently no gain in the net value of Shannon entropy results. There is an optimum frequency for which the Shannon entropy passes through a maximum, which is also found out in this work. We have also calculated the semiclassical WKB like transmission probability as a function of time and it is clear that the random fluctuation of barrier causes the transmission probability to increase to a significant amount. As the total energy of the system remains below the potential barrier, this transmission probability is equivalent to tunneling probability. It has been clearly shown that if the fluctuation is made to be periodic (without changing the frequency and magnitude of the fluctuation) it cannot effect any significant change in the overall dynamics.     

and Au6 clusters: Superatomic molecules bearing an SP3‐hybrid Au6 core

The octahedral Au₆ core is explored for the formation of novel SP³‐hybrid superatomic molecules by considering and Au₆ clusters (X= F, Cl, Br, I). The bonding between the four capping atoms and the Au₆ core requires a combination of 1S and 1P shells of the core leading to a set of four equivalent hybrid orbitals. Thus, combining the superatom concept with both the Lewis structure model and VSEPR theory contributes to the rationalization of structure and bonding in metal clusters. For example, our results consider the Au₆ clusters as analogues of the simplest perhalogenated hydrocarbon, CX₄.     

Presentation of a new index for estimation of aromaticity in halo‐ and cyanobenzenes: The role of potential energy in aromaticity

A linear correlation has been obtained between average values of Hamiltonian kinetic energy ( ) and potential energy ( ) calculated at the bond critical points using atoms in molecules method. This relation was used to introduce a new index ( ) for estimation of aromaticity in halo‐ and cyanobenzenes. Potential energy has different terms such as attraction between nuclei and electrons, also repulsion of electrons which affect the inertia and mobility of electrons, respectively. Therefore, contribution of potential energy in this relation must be controlled. Contribution of potential energy in aromaticity has been managed using a fitting parameter. This parameter was obtained by fitting the aromaticity stabilization energy data with values of aromaticity calculated by index for halo‐ and cyanobenzenes. The contribution of potential energy in index is complete when molecule is nonaromatic and is negligible when molecule is antiaromatic. Indeed, molecule is aromatic when contribution of potential energy in index lies between above limits. © 2013 Wiley Periodicals, Inc.     

Simulated annealing‐based optimal control over tunneling process through SDWP and Eckart barrier: A momentum basis representation

For a reaction to proceed via tunneling mechanism, it is essential that the reactants will cross the potential barrier (E_P), where its initial energy (E₀) is below the potential barrier E_P. Tunneling probability τ is defined as the probability of having momentum higher than k_m, where . In the momentum basis representation, τ can be directly calculated by integrating from the limit k_m to infinity, where is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as . Our target here is to increase this τ by applying a polychromatic field, so that the reaction rate can be enhanced. By applying Simulated Annealing technique we have designed some polychromatic electric fields, spatially symmetric and asymmetric type, which enhances the tunneling rate in symmetric double well system and Eckart barrier confined in an infinite well.     

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

The electronic structure of several many‐electron atoms, confined within a penetrable spherical box, was studied using the Hartree–Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one‐electron equations. The resulting HF wave‐function was employed to evaluate the Shannon entropy, , in configuration space. Confinements imposed by impenetrable walls induce decrements on when the confinement radius, R_c, is reduced and the electron‐density is localized. For confinements commanded by penetrable walls, exhibits an entirely different behavior, because when an atom starts to be confined, delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many‐electron atoms, as the hydrogen atom confined in similar conditions.     

Mind the correct basis set: A case study for predicting gas phase acidities of small compounds using calculations from first principles

Some of the most popular computational methods have been utilized to determine a dependency of the acidity trend of the first‐row hydrides on a choice of basis set. For about three decades, methyl anion ( ) was known as the strongest base but after Tian et al. were able to produce the gas phase lithium monoxide anion (LiO–) they discovered it was a stronger base than (Tian et al., Proc Natl Acad Soc USA 2008, 105, 7647). Furthermore, the authors confirmed their experimental results using high‐level ab initio methods, namely W1 and W2C composite methods, as well as complete active space‐averaged quadratic coupled cluster and Brueckner Doubles with triple excitation contribution (BD(T)) within the aug‐cc‐pVQZ basis set. These methods are highly demanding in terms of the computational effort as well as a level of expertise needed from the user to correctly conduct such calculations. We have shown that the proper acidity trend, that is, , can be obtained with less expensive, ”black‐box” type methods if only the basis set is properly chosen. Our results prove that the diffuse augmented basis sets are absolutely necessary for appropriate predictions of acidities. Our calculations show that the correct order of is achieved by augmenting relatively small cc‐pVXZ (X = D,T) basis sets. A similar effect is observed for the family of Pople's basis sets. Our estimate for with CCSD(T)/aug‐cc‐pVTZ was 423.8 kcal/mol, which agrees very well with the experimental value 425.7 ± 6.1 kcal/mol. An important finding is that the proper acidity trend may be reversed if the basis sets are not correctly selected. © 2014 Wiley Periodicals, Inc.     

Discrete charge patterns in a Holstein‐SSH DNA lattice

DNA nonlinear charge transport is addressed in a combined Holstein–Su–Schrieffer–Heeger (HSSH) model. In the adiabatic approximation the dynamics of the system is shown to be governed by a modified discrete nonlinear Schrödinger (MDNLS) equation, where charge‐lattice coupling parameters are obvious. Attention is paid to the effective coupling parameter, , between charge and internal molecular vibrations, which importantly influences the stability/instability features of the plane wave, solution to the MDNLS equation. Region of instability are remarkably reduced, therefore predicting that increasing could progressively quench charge transport. This is confirmed by numerical simulations on the generic HSSH model, where only the charge density is excited and drives the dynamics of the global system. Polarons, as well as longitudinal and transversal nonlinear waves, are obtained and the dependence of charge transport on DNA conformation is discussed. Accordingly, the longtime evolution of the found polarons is studied and we observe a progressive extinction of its temporal evolution as increases. © 2014 Wiley Periodicals, Inc.     

Theoretical study of metal‐free organic dyes based on different configurations for efficient dye‐sensitized solar cells

Considering different solar dyes configuration, four novel metal‐free organic dyes based on phenoxazine as electron donor, thiophene and cyanovinylene linkers as the ‐conjugation bridge and cyanoacrylic acid as electron acceptor were designed to optimize open circuit voltage and short circuit current parameters and theoretically inspected. Density functional theory and time‐dependent density functional theory calculations were used to study frontier molecular orbital energy states of the dyes and their optical absorption spectra. The results indicated that D2‐4 dyes can be suitable candidates as sensitizers for application in dye sensitized solar cells and among these three dyes, D3 showed a broader and more bathochromically shifted absorption band compared to the others. The dye also showed the highest molar extinction coefficient. This work suggests optimizing the configuration of metal‐free organic dyes based on simple D‐ ‐A configuration containing alkyl chain as substitution, starburst conformation, and symmetric double D‐ ‐A chains would produce good photovoltaic properties.