Einstein A Coefficients,Oscillator Strengths,and Absolute Band Strengths for the First Negative System,and Franck-Condon Factors for the Second Negative System of

The Franck-Condon factors and r centroids for the first negative and the second negative band systems of the molecule, based on the Rydberg-Klein-Rees potential energy curves, have been computed. The variation of the electronic transition moment with the internuclear separation has been studied for the first negative bands and the Einstein A coefficients, the oscillator strengths, and the absolute band strengths for this system have been calculated by adopting the recent experimental data on the lifetimes of the various levels of the excited B state. On a calculé pour la molécule les facteurs de Franck-Condon et les r centroïds pour les deux premiers systèmes de bandes négatives avec des courbes de potential de Rydberg-Klein-Rees. On a étudié la variation du moment de transition éléctronique avec la séparation internucléaire pour les premières bandes négatives. Les constantes A d'Einstein, les forces d'oscillateur et les intensités absolues des bandes ont été calculé des données expérimentales récentes sur les durées de vie des niveaux différents de l'état excité B . Die Franck-Condon-Faktoren und die r-Zentroide der zwei ersten negativen Banden-systeme des -Moleküls, wurden mit den Rydberg-Klein-kees Potentialkurven berechnet. Die Variation des elektronischen Übergangsmoment mit dem Kernabstand würde für die ersten negativen Bänder studiert. Die Einsteinschen A-Koeffizienten, die Oszillatorstärken and die absoluten Bandenstärken wurden mit die neuen experimentellen Tatsachen über die Lebensdauern der verschiedenen Niveaus des angeregten B Zustands berechnet.     

Scaled AMO Calculations on the Hydrogen Molecule

The energy curve for the state of H₂ is calculated. An AMO treatment, where the alternant orbitals are differently scaled is used. The three parameters needed are completely varied, this gives satisfactory results. General features of the AMO method, shown up in the present work, are pointed out and connections with earlier calculations are discussed. On a calculé la courbe d'énergie potentielle de l'état de H₂ par la méthode AMO avec des “constantes d'échelle” différentes pour les deux orbitales alternantes. Les trois paramètres ont été complètement variés, ce qui donne des résultats satisfaisants. On discute quelques aspects généraux de la méthode AMO, qui se sont manifestés dans le présent calcul, ainsi que les rapports avec d'autres calculs. Die Potentialkurve für den Zustand des Wasserstoffmoleküls wurde mit der AMO Methode mit verschiedenen Koordinatenstreckungsfaktoren für die zwei alternierenden Orbitale berechnet. Die drei Parameter wurden vollständig variiert, was befriedigende Resultate gab. Allgemeine Züge der AMO-Methode, die in dieser Berechnung erschienen sind, and Verbindungen mit anderen Berechnungen wurden diskutiert.     

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.     

General build up of basis and matrix in the diagonalization approach. Determination of Kramers configuration state functions

Algorithms to build the basis and matrix representation to obtain the Kramers configuration space functions (KCSFs) via diagonalization will be formally generalized to an arbitrary number of unpaired (open shell) fermions. Effective build up of the matrix representation will be outlined (including threading and graphical processing unit parallelism) to subsequently obtain the KCSFs via calling external/numerical library routines for diagonalization. The effective build up of the matrix representation relays on a binary tree search algorithm to allow evaluation the action on a given basis vector. The binary tree search avoids the treatment of zero matrix elements which leads to an exponential acceleration. The implementation ( basis creation, matrix representation, and matrix diagonalization) will be done in an all in core and all at once manner, hence the available core memory sets the physical limits in practical applications. Memory limitations, sparsity of the matrix, general case of n fermions in m spinors, and the application of KCSFs will be put into further perspective.     

Full–dimensional quantum molecular dynamics calculations of the rovibrationally mediated X → 2 transition of nitrous oxide

A full dimensional time‐dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X → 2 bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 , 1 , and 2 states) of N₂O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N₂? O bending vibrations, whereas, at higher temperatures, the N₂? O and N? NO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N₂ product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N₂ at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N₂ from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 state in determining the final dissociation pathway of N₂ + O. © 2016 Wiley Periodicals, Inc.     

Explicitly correlated variational estimates of the energy levels of negative hydrogen ion under spatial confinement

Comprehensive investigations on the structural modifications of negative hydrogen ion within an impenetrable spherical domain has been performed in the framework of Ritz variational method. Electron correlation plays a major role in the formation of H^– ion. The Hylleraas‐type basis set expansion of wave function considered here incorporates the effect of electron correlation in an explicit manner. Energy values of and 1sn states of H^– ion within confined domain have been calculated. Although the singly excited states do not exist for a “free” H^– ion, well converged energy values of such states have been found within a wide range of confinement radius. The thermodynamic pressure felt by the ion inside the sphere is also estimated. The general trend shows successive destabilization of the excited energy levels with increase of pressure. The contribution of angular correlation in the energy values have been estimated. Evolution of and energy levels of H^– ion as quasi‐bound states are being reported.     

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.     

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.     

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.     

A theoretical study on the stability difference of the borane and carborane C2Bn−2Hn (5 ≤ n ≤ 7) clusters

In order to study the electronic structure and structural stability of borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters, especially the stability difference between the borane and carborane C₂B₃H₅. The frontier orbital energy levels of the borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters are calculated at CCSD(T)/aug‐cc‐pVXZ//B3LYP/def2‐TZVPP level. The results are further analyzed by qualitative frontier orbital method based on the cap–ring interaction. The results reveal that: (1) the larger E_gap(HOMO‐LUMO energy gap) of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than borane (5 ≤ n ≤ 7) clusters originates from the more effective cap–ring orbital overlap of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than that of borane (5 ≤ n ≤ 7) clusters; (2) the smallest E_gap of the borane results from the highest energy level of the ring symmetry‐adapted linear combination orbital of cluster; and (3) the largest E_gap of the carborane C₂B₃H₅ is induced by the most effective cap–ring orbital interaction of C₂B₃H₅ cluster. © 2014 Wiley Periodicals, Inc.     

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 .     

The nature of the chemical bond in borazine (B3N3H6), boroxine (B3O3H3), carborazine (B2N2C2H6), and related species

The bonding problem in borazine (B₃N₃H₆), boroxine (B₃O₃H₃), and carborazine (B₂N₂C₂H₆) is successfully addressed through the consideration of the excited states of the constituent fragments, namely BH( ), NH( ), and CH( ). We propose the participation of resonant structures for all three species that help to explain the experimental findings. A discussion on the chemical pattern of the parental molecule benzene (C₆H₆) helps to make coherent the whole bonding analysis on the titled species.     

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.     

Unexpected properties of non‐autoionizing doubly excited states of the H2 molecule

We present accurate calculations of the non‐autoionizing and doubly excited states of the H₂ molecule using full configuration interaction with Hartree–Fock molecular orbitals and Heitler–London atomic orbitals. We consider the united atom configurations from He(2p2p) up to He(2p8g) and dissociation products from H₂(2p + 2p) up to H₂(2p + 6?). Born–Oppenheimer calculations are carried out with extended and optimized Slater‐type orbitals for a total of 40 states, 10 for each symmetry, covering the internuclear distances from the united atom to dissociation, which, for some states, is reached beyond 100 a₀. Occurrences of repulsive states cleanly interlaced between bound states with many vibrational levels are reported. Some of the potential minima are deep enough to accommodate many vibrational levels (up to 50). Noteworthy large equilibrium minima, like R_eq = 46.0 a₀ in the state dissociating as (2p + 6h) and with 18 vibrational levels. The occurrence of vertical excitations from the singly excited manifolds is analyzed. Several states present double minima generated by avoided crossings, some with a strong ionic character. © 2016 Wiley Periodicals, Inc.     

(Rg = He ∼ Rn,n = 1–4): In quest of the potential trapping ability of the aromatic ring

A new series of divalent boron‐rare gas cations (Rg = He ∼ Rn, n = 1–4) have been predicted theoretically at the B3LYP, MP2, and CCSD(T) levels to present the structures, stability, charge distributions, bond natures, and aromaticity. The Rg B bond energies are quite large for heavy rare gases and increase with the size of the Rg atom. Because of steric hindrance new Rg atoms introduced to the B₄ ring will weaken the Rg B bond. Thus in the Rg B bond has the largest binding energy 90–100 kcal/mol. p‐ has a slightly shorter Rg B bond length and a larger bond energy than o‐ . NBO and AIM analyses indicate that for the heavy Rg atoms Ar ∼ Rn the B Rg bonds have character of typical covalent bonds. The energy decomposition analysis shows that the σ‐donation from rare gases to the boron ring is the major contribution to the Rg B bonding. Adaptive natural density partitioning and nuclear‐independent chemical shift analyses suggest that both and have obvious aromaticity.     

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.     

Geometric and electronic structures of silicon fluorides (N = 4 – 6) and potential energy surfaces for dissociation reactions → SiF4 + F– and → + F–

The geometric and electronic structures of a series of silicon fluorides (n = 4 ? 6) were computationally studied with the aid of density functional theory (DFT) method with B3LYP and M06‐2X functionals and coupled cluster (CCSD and CCSD(T)) methods with 6‐311++G(d,p) basis set. The nature of the Si‐F bonds in these compounds was analyzed in the framework of the natural bond orbital theory and natural resonance theory. Energy characteristics (heats of reactions and energy barriers) of the dissociation reactions → SiF₄ + F^– and → + F^– were calculated using the DFT and CCSD methods. The potential energy surface of elimination of a fluoride anion from has a specific topology with valley‐ridge inflection points corresponding to bifurcations of the minimal energy reaction path. © 2016 Wiley Periodicals, Inc.     

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.     

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.