Field Wave Functions Research Articles

Enhancement of the Light Hole Character in Semiconductor Quantum Rings

We show that the repulsive core of semiconductor quantum rings enhances the heavy hole-light hole mixing. Calculations for InAs/GaAs quantum rings show that the light hole character of the valence band ground state increases at least by a factor of two as compared to that of quantum dots. The light-hole character becomes comparable to the heavy hole one in quasi-1 D rings. Biaxial strain reduces the light hole influence, but it is still larger than in quantum dots. The effect of strain on the magnetic field response and wave function localization is studied.

The Jaynes–Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties

In this paper, we investigate various dynamical properties of the Jaynes–Cummings (JC) model beyond the rotating wave approximation (RWA). We first show that in the absence of the RWA, the JC Hamiltonian can be transformed into an intensity-dependent Hamiltonian. Corrections produced by the counter-rotating terms (CRTs) appear in the first order as the intensity-dependent detuning, i.e. the dynamical Stark shift and in the second order as the intensity-dependent atom–field coupling. Then, by determining the atom–field wavefunction evolution, we study the effects of CRTs on various dynamical properties of the JC model, including the atomic population inversion, atomic dipole squeezing, atomic entropy squeezing, photon counting statistics, quadrature field squeezing, field entropy squeezing and quantum phase properties of the cavity field.

The predicted spectrum of the hypermetallic molecule MgOMg

The present study of MgOMg is a continuation of our theoretical work on Group 2 M(2)O hypermetallic oxides. Previous ab initio calculations have shown that MgOMg has a linear (1)Σ(g)+ ground electronic state and a very low lying first excited triplet electronic state that is also linear; the triplet state has (3)Σ(u)+ symmetry. No gas phase spectrum of this molecule has been assigned, and here we simulate the infrared absorption spectrum for both states. We calculate the three-dimensional potential energy surface, and the electric dipole moment surfaces, of each of the two states using a multireference configuration interaction (MRCISD) approach based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions with a cc-pCVQZ basis set. A variational MORBID calculation using our potential energy and dipole moment surfaces is performed to determine rovibrational term values and to simulate the infrared absorption spectrum of the two states. We also calculate the dipole polarizability of both states at their equilibrium geometry in order to assist in the interpretation of future beam deflection experiments. Finally, in order to assist in the analysis of the electronic spectrum, we calculate the vertical excitation energies, and electric dipole transition matrix elements, for six excited singlet states and five excited triplet states using the state-average full valence CASSCF-MRCISD/aug-cc-pCVQZ procedure.

Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field

To reduce the basis set incompleteness of the complete-active-space self-consistent field (CASSCF) wave function and energy we develop a second-order perturbation correction due to single excitations to complete set of unoccupied states. Other than the one- and two-electron integrals, only one- and two-particle reduced density matrices are required to compute the correction, denoted as [2](S). Benchmark calculations on prototypical ground-state bond-breaking problems show that only the aug-cc-pVXZ basis is needed with the [2](S) correction to match the accuracy of CASSCF energies of the aug-cc-pV(X+1)Z quality.

Communication: Rotational g-factor and spin-rotation constant of CH+

The rotational g-factor and spin-rotation constants of the methylidynium ion CH(+) have been calculated for the first time with a large multiconfigurational self-consistent field wave function and at the coupled-cluster singles and doubles level augmented by a perturbative triples correction. The results for an equilibrium internuclear distance as well as for the v=0, J=1 vibration-rotational state are presented.

ChemInform Abstract: Vibrational Analysis and Calculation of Franck-Condon Factors for the Vinoxy Radical X(2A′′) and B(2A′′) States.

Vibrational analysis and calculation of Franck–Condon factors (FCF) of the vinoxy radical were performed for the two electronic states in the title. Multiconfigurational self‐consistent field (MCSCF) wave functions were used to calculate the optimized geometries and the energy gradients of both states. Vibrational analysis was carried out with the harmonic approximation, and FCFs were calculated taking into account the Duschinsky rotation. The features of the experimental absorption and laser‐induced fluorescence (LIF) spectra were reproduced with the calculated FCFs. Previous analyses of the experimental spectra based on an oversimplified model were critically discussed.

The predicted infrared spectrum of the hyperberyllium molecule BeOBe in its [formula omitted] and [formula omitted] electronic states

Hypermetallation is a concept that applies to molecules having metal stoichiometries that exceed normal valence, and BeOBe is just one example of such a molecule. Previous ab initio calculations and spectroscopic studies have shown that BeOBe has a linear 1 Σ g + ground electronic state and a very low lying 3 Σ u + first excited electronic state. As the gas phase infrared spectrum of this molecule is unknown, we simulate such absorption spectra for both of these electronic states. To this end, we calculate the three-dimensional potential energy surfaces and the electric dipole moment surfaces of each of the two states using a multireference configuration interaction (MRCISD) approach based on full-valence complete active space self-consistent field (FV-CASSCF) wavefunctions. This is followed by variational MORBID calculations, using our potential energy and dipole moment surfaces, in order to determine rovibrational term values and to simulate the infrared absorption spectrum of both the singlet and triplet states. We also calculate the dipole polarizability for both states at their equilibrium geometry, as this is of interest for probing the molecule in future beam deflection experiments.

Excited-state polarizabilities of solvated molecules using cubic response theory and the polarizable continuum model

The theory and an implementation of the solvent contribution to the cubic response function for the polarizable continuum model for multiconfigurational self-consistent field wave functions is presented. The excited-state polarizability of benzene, para-nitroaniline, and nitrobenzene has been obtained from the double residue of the cubic response function calculated in the presence of an acetonitrile and dioxane solvent. The calculated excited-state polarizabilities are compared to results obtained from the linear response function of the explicitly optimized excited states.

Exact quantum scattering study of the Ne+H2+ reaction on a new ab initio potential energy surface

We present a new potential energy surface (PES) for the ground state (1(2)A(')) of the chemical reaction Ne+H(2) (+) from a set of accurate ab initio data, which were computed using highly correlated complete active space self-consistent field and multireference configuration interaction wave functions with a basis set of aug-cc-pV5Z. The quantum reactive scattering dynamics calculation was carried out over the collision energy (E(col)) range of 0.5-1.5 eV based on the new PES. In this work we have taken the Coriolis coupling (CC) effect into account. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC and the centrifugal sudden approximation calculation. The magnitude and profile of the CC total cross sections for v=0 and j=1 over the collision energy range of 0.5-1.5 eV are found to be in good agreement with the available experimental measurements obtained recently by Zhang et al. [J. Chem. Phys. 119, 10175 (2003)] after taking into account the experimental uncertainties.

Molecular dynamic simulations of OH-stretching overtone induced photodissociation of fluorosulfonic and chlorosulfonic acid

We investigate the OH-stretching overtone dynamics of fluorosulfonic acid (FSO(3)H) and chlorosulfonic acid (ClSO(3)H) using classical trajectory simulations. The initial nuclear coordinates and momenta for the trajectories are sampled from anharmonic correlation-corrected vibrational self consistent field (CC-VSCF) wavefunctions. We consider both OH-stretching overtone states and combination states containing a mix of OH-stretching overtones and SOH-bending or OSOH-torsional modes. Our molecular dynamics simulations confirm that photodissociation of these sulfonic acids to form the corresponding hydrogen halides and sulfur trioxide (HF + SO(3) and HCl + SO(3)), is possible via highly vibrationally excited states on a picosecond timescale. Hydrogen-hopping events are also observed in the trajectories whereby the hydrogen atom of the excited OH group is found to migrate to one of the adjacent S=O groups. The transition states, activation energies and dissociation dynamics of FSO(3)H and ClSO(3)H are found to be similar to those of H(2)SO(4). We suggest that these halogenated sulfonic acids should be suitable proxy molecules for an experimental investigation of the OH-stretching overtone induced photodissociation of H(2)SO(4) thought to be important in Earths' atmosphere.

Structural and optical properties of a neutral Nickel bisdithiolene complex: density functional versus ab initio methods

Density functional theory (DFT) and ab initio computations are applied to examine different properties of diamagnetic, square planar neutral nickel complexes that contain two bidentate ligands derived from bis ((ethylene)-1,2-dithiolato) ligands. Geometry, vibrational spectra (IR and Raman) are well reproduced in the density functional framework whereas TD-DFT methods are clearly insufficient to reproduce absorption properties. Multiconfigurational perturbation theory based on a complete active space self-consistent field wave function, i.e. MRPT2 and MRPT4 methods, reveal the pronounced multiconfigurational character of the ground state wave function. The singlet–triplet energy gap, the energy gained from symmetry breaking and the singlet diradical character are discussed in the DFT and ab initio frameworks. The complex of interest does not display a strong singlet diradical character. This molecule having a peculiar electronic structure; strong delocalization as shown by a new electron pair localization function analysis (EPLF); exemplifies the fragility of the TD-DFT method and thus, caution should be taken in the determination of the energetic properties of such compounds.

Silacyclopropenylidene and Its Most Important SiC2H2 Isomers

In pioneering matrix isolation experiments, Maier and Reisenauer reported and identified infrared spectra for 1-silacyclopropenylidene and three of its isomers. These experiments were followed by microwave spectroscopy identification of two of the structures. Seven low-lying isomers of SiC2H2 are systematically investigated here using ab initio restricted Hartree−Fock (RHF), coupled cluster with single and double excitations (CCSD), and CCSD with perturbative triple excitations [CCSD(T)] methods and the correlation-consistent polarized valence cc-pVXZ/cc-pV(X+d)Z (X = D, T, and Q) basis sets. Full valence complete active space self-consistent field (CASSCF) wave functions are used for interpretation. All levels of theory employed in this study confirm the global minimum of the SiC2H2 potential energy surface (PES) to be 1-silacyclopropenylidene (1S). Among the seven singlet stationary points, six isomers are found to be minima, whereas one structure (6S) is a second-order saddle point. For the lowest-lyin...

Coexistence between checkerboarded charge and striped spin in two-dimensional Hubbard model

We have performed a variational Monte Carlo (VMC) simulation on a two-dimensional t–t′–t″–U Hubbard model to examine the stability of a 4×4 checkerboard state, which has been observed recently by scanning tunneling microscopy (STM) in Bi2Sr2CaCu2O8−δ and Ca2−xNaxCuO2Cl2 (Na–CCOC). In our VMC calculation, the checkerboard mean field wave function for the coexisting checkerboarded charge density wave in a striped spin density wave was used. We chose the transfer energies t′ and t″ suitable for Bi-based cuprate at the underdoping. The variational energy of the checkerboard state with 4×4 period comparable with that of the 4-period stripe state was obtained. It is important for stabilization of the checkerboard state that a Fermi surface around each of k=(π,0) and (0,π) points consists of two parallel flat section.

Is the Photoinduced Isomerization in Retinal Protonated Schiff Bases a Single- or Double-Torsional Process?

Nonadiabatic photodynamical simulations are presented for the all-trans and 5-cis isomers of the hepta-3,5,7-trieniminium cation (PSB4) with the goal of characterizing the types of torsional modes occurring in the cis-trans isomerization processes in retinal protonated Schiff base (RPSB), the rhodopsin and bacteriorhodopsin chropomhore. Steric hindrance of these processes due to environmental effects have been modeled by imposing different sets of mechanical restrictions on PSB4 and studying its response in the photodynamics. Both the mechanism toward the conical intersection and the initial phase of the hot ground state dynamics has been studied in detail. A total of 600 trajectories have been computed using a complete active space self-consistent field wave function. Careful comparison with higher level methods has been made in order to verify the accuracy of the results. The most important mechanism driving restricted PSB4 isomerization in the excited state is characterized by two concerted twist motions (bipedal and closely related to it nonrigid bipedal) from which only one torsion tends to be continued during the relaxation into the ground state. The one-bond-flip is found to be important for the trans isomer as well. The main isomerization trend is a torsion around C(5)C(6) (equivalent to C(11)C(12) in RPSB) in the case of the cis isomer and around C(3)C(4) (C(13)C(14) in RPSB) in the case of the trans isomer. The simulations show an initial 70 fs relaxation into twisted regions and give an average internal conversion time of 130-140 fs, timings that are fully compatible with the general picture described by femtosecond transient absorption spectroscopic studies.

C4ν Symmetry Crystal Field and Ground State Wavefunction of the VO2+ Ion

The spin-Hamiltonian parameters obtained from EPR studies of the VO2+ ion in different diamagnetic host lattices are used to estimate the ground state wave functions. These are of dxy type with admixture of the excited states dx2−y2, dyz and dxz. The hyperfine interaction parameter and Fermi contact term for the VO2+ doped crystals are determined using the coefficients of the ground state. The various parameters are correlated to the ligand properties of the complexes.

Localized orbitals in the coupled cluster singles and doubles model

In the vast majority of many-body perturbation theory and coupled-cluster method (MBPT/CCM) calculations, the self-consistent field (SCF) wavefunction is employed as the zeroth-order wave-function, and its associated canonical orbitals as the molecular orbital basis. The recent development of the coupled-cluster singles and doubles (CCSD) formalism provides an opportunity to explore alternative reference function and orbital choices, on a consistent basis. Here we examine, specifically, sets of orbitals that are more “localized” than the SCF orbitals. In particular, the bonding orbitals are selected to resemble traditional chemical bonds. CCSD calculations in the localized basis on methane employing a better than double-zeta basis set are performed and compared with conventional SCF basis results.

An improved MCSCF method

An improved scheme for calculating multiconfiguration self-consistent field wavefunctions has been developed. This scheme is powerful in its algebraic formulation and quadratic in its convergence behavior. Shell and wavefunction replacement operators are introduced to make equation manipulation more transparent and less tedious. The configuration state function coefficients as well as the orbital expansion coefficients are improved in each iteration by exponential unitary transformations. The symmetry properties of the wavefunctions are fully exploited. The present scheme should be convergent for a wider range of applications than currently available schemes.

Accelerating convergence in iterative solution for large‐scale complete active space self‐consistent‐field calculations

AbstractAn algorithm that accelerates the convergence of the iterative optimization of the complete active space self‐consistent field (CASSCF) wavefunction so as to find a optimum solution in fewer macroiterations is described. The algorithm is oriented to large‐scale CASSCF problems that are to be solved with a combination of density matrix renormalization group (DMRG) method for the configuration interaction (CI) process. The algorithm is based on the alternating (or two‐step) CASSCF optimization in which the CI and molecular orbital (MO) parameters are optimized separately. Convergence ratio is improved by finding further optimized MOs from a linear extrapolation of the MO sets of the iteration history. The acceleration results in fewer diagonalizations in a total CASSCF calculation to save a considerable computational cost. The convergence performance is examined in a couple of realistic applications on SiC3 and poly(phenyl)carbenes. For poly(phenyl)carbenes, the large‐size CASSCF calculations with CAS(30e,30o) that entails full π valence space as well as sp2 orbital space of carbenes are performed by using the practical implementation of DMRG‐CASSCF in conjunction with the acceleration technique. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

N= 8 superfield formulation of the Bagger-Lambert-Gustavsson model

We reformulate the Bagger-Lambert-Gustavsson model using an N = 8 superspace, thus making the full supersymmetry manifest. The formulation is based on appropriate ``pure spinor wave functions'' for the Chern-Simons and matter multiplets. The Lagrangian has an extremely simple structure, essentially containing a Chern-Simons-like term for the gauge field wave function and a minimally coupled matter wave function. No higher order interactions than cubic are present. The consistency of the setup relies on an interplay between the algebraic structures of the 3-algebra and of the pure spinors.

Theoretical investigation of anthracene‐9,10‐endoperoxide vertical singlet and triplet excitation spectra

The electronic absorption spectrum of anthracene-9,10-endoperoxide (APO) has been investigated by means of multiconfigurational multi-state second order perturbation theory on complete active space self-consistent field wavefunctions (MS-CASPT2/CASSCF) and two single reference methods: time-dependent density functional theory (TD-DFT) and coupled cluster of second order (CC2). After testing several active spaces and basis sets, a CAS (14,12) active space together with an ANO-S basis set was found an appropriate choice to describe the vertical singlet and triplet electronic states of APO. Unfortunately, TD-DFT and CC2 methods cannot reproduce the MS-CASPT2 and experimental spectrum. Our MS-CASPT2//CASSCF(14,12)/ANO-S calculations predict a predominant pi*(OO)sigma*(OO) character for the lowest singlet excited state S(1) at 3.85 eV. Accordingly, the lowest singlet state of APO should be responsible for homolysis of the endoperoxide group. The next two absorbing excited states, experimentally proposed to be responsible for singlet oxygen production and therefore connected to the biological interest of APO, have been computed vertically at 4.34 and 4.59 eV and assigned to pi(CC)pi*(CC) and pi*(OO)pi*(CC) transitions, respectively. The vertical triplet electronic spectrum follows the singlet vertical spectrum ordering. The high density of triplet and singlet excited states of different nature within few eV points to the possibility of intersystem crossings between potential energy surfaces of different multiplicity.