Terms Of Wave Functions Research Articles

Evaluation of Coulomb Energy Difference for Light Mirror Nuclei Using Slater-Type Orbitals

Behavior of the Coulomb energy difference for light nuclei is explained in terms of the different values of the average Coulomb interaction between two particles. Coulomb energy difference according to shell model of light mirror nuclei in the Coulomb and exchange integrals in the formula can be explained with exponential-type wavefunctions. In this study, using the one-center expansion of exponential-type wavefunctions in terms of Slater-type orbitals with the same center, we derived formula for Coulomb energy difference of light mirror nuclei.

The Wigner representation of classical mechanics, quantization and classical limit

Starting from the Liouvillian formulation of classical physics, it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanics. The importance of this new representation lies in the fact that it turns out to be the suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Brownian particle with non-linear friction in the Markovian approximation—the thermal bath may be quantum or classical—, thus when the bath is classically described we obtain a master equation which reduces to the Caldeira–Leggett equation (vide, A.O. Caldeira and A.J. Leggett, Physica A 121 (1983) 587) for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. (Phys. Rev. A 40 (1989) 3438). By neglecting the environmental influence, we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrödinger–Langevin equation and equations of the Caldirola–Kanai type. Finally, to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method ℏ→0.

The selective population of the vibrational levels of thioformaldehyde

The simulation of the selective excitation of the vibrational levels of the electronic ground state of H2CS by femtosecond coherent light pulses was investigated. The simulation model was based on the development of the time-dependent wavefunction in terms of the stationary vibrational eigenstates. The dipole moment and the potential energy functions were obtained ab initio and approximated by polynomial expansions. Chirped and non-chirped linear polarized pulses were tried as well as circularly polarized pulses. If the target vibrational level was not involved in resonances a selectivity of more than 60% was achieved. In several cases the target state was 100% populated. Different ways of achieving the population were investigated.

Gravity and duality between coordinates and matter fields

We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metric in this later reparametrization.

Orbital transformations and configurational transformations of electronic wavefunctions

Transformations among molecular orbitals are often expedient or illuminating, and sometimes essential in quantum chemical contexts. In order to express the many-electron wavefunction in terms of the corresponding transformed configurations, full CI calculations used to be repeated in the transformed orbital basis. The configurational transformations can however be obtained directly, as shown by Malmqvist, by a factorization into single orbital transformations. In the present paper, a direct transformation method is presented that is based on the factorization of orbital transformations in terms of Jacobi rotations. Compared to the repetition of a CI calculation, both direct re-expansion methods drastically reduce the computational effort and increase the numerical accuracy. They are, moreover, applicable to wavefunctions whose original construction is not accessible.

Methanol conversion to hydrocarbons over zeolite catalysts: comments on the reaction mechanism for the formation of the first carbon–carbon bond

The reaction mechanism for the conversion of methanol to hydrocarbons using zeolite catalysts is discussed. In particular, the mechanism of the formation of the initial carbon–carbon bond is considered in terms of the reaction of a surface ylide intermediate with adsorbed methanol. It is suggested that the formation of the initial carbon–carbon bond involves the interaction of the surface-bound ylide intermediate and its associated Brønsted acid site with a methanol molecule. This leads to the formation of a surface ethoxy group from which ethene can be formed by β-elimination. α-Elimination will lead to a higher carbon nucleophile for further reaction with methanol or dimethyl ether. To investigate the suggested scheme, density functional theory calculations are used to discern the nature of the surface ylide species and its interaction with adsorbed methanol. We find that the surface ylide formation step actually results in the insertion of a CH 2 group into the Al–O bond of the cluster representing the zeolite surface. Simple analysis of the wavefunction in terms of atomic charges and bond orders indicates that this CH 2 group has the required nucleophilic character to react with a methanol carbon atom. On the formation of a surface ethoxy group, we find that the Al–O bond is reformed and so the reaction appears to proceed by the formation of transient defects in the zeolite framework. We also suggest that this C–C bond formation will be more facile for clusters of methanol molecules at the active site.

Semileptonic and rare B-meson transitions in a QCD relativistic potential model

Using a QCD relativistic potential model, previously applied to the calculation of the heavy meson leptonic constants, we evaluate the form factors governing the exclusive decays $B\to\rho\ell\nu$, $B\to K^*\gamma$ and $B\to K^*\ell^+\ell^-$. In our approach the heavy meson is described as a $Q\bar q$ bound state, whose wave function is solution of the relativistic Salpeter equation, with an instantaneous potential displaying Coulombic behaviour at small distances and linear behaviour at large distances. The light vector meson is described by using a vector current interpolating field, according to the Vector Meson Dominance assumption. A Pauli-Villars regularized propagator is assumed for the quarks not constituting the heavy meson. Our procedure allows to avoid the description of the light meson in terms of wave function and constituent quarks, and consequently the problem of boosting the light meson wave function. Assuming as an input the experimental results on $B\to K^*\gamma$, we evaluate all the form factors describing the $B\to \rho, K^*$ semileptonic and rare transitions. The overall comparison with the data, whenever available, is satisfactory.

A simple method for polarizabilities and hyperpolarizabilities of alkali isoelectronic systems

A pseudopotential is introduced to make it possible to express the multipolar perturbed wavefunctions in terms of closed elementary functions. This pseudopotential is slightly different from the asymptotic Coulomb potential. This difference is accounted for in the final results with an interpolation procedure. Polarizabilities and hyperpolarizabilities of Li, Na, K, Rb, Cs, Be +, Mg +, Ca +, Sr + and Ba + are calculated with this method and are shown to be highly accurate. Particularly noteworthy is the simplicity of the third-order calculations which give the hyperpolarizabilities of the alkali series beyond Li.

First-principles study of piezoelectricity in tetragonal PbTiO3

The e 33 component of the piezoelectric strain tensor in tetragonal PbTiO3 was studied by an allelectron ab initio method, and was found to be in good agreement with the experimental piezoelectric stress constant of high quality twin-free single PbTiO3 crystals. Equations of the density functional theory were solved within the general gradient approximation (GGA) using the general potential linearized augmented plane-wave local orbital (LAPW + LO) method. Macroscopic polarization values necessary to calculate the piezoelectric coefficient and elements of the Born effective charge tensors were determined via finite differences using the geometric phase formulation. In this approach, bulk quantities are expressed as the property of the phase of the wavefunction in terms of a Berry connection. The e 33 component of the piezoelectric tensor, i.e. the change in polarization with strain, was extracted from results of groundstate Berry's phase calculations performed on units cells of different strains and volumes. We found that in PbTiO3 the large intrinsic piezoelectric response is mainly due to strong coupling between macroscopic strain and internal microscopic strain, giving the value of 3.23 C/m2 for the e 33 modulus.

Nanoscopic tunneling contacts on mesoscopic multiprobe conductors

We derive Bardeen-like expressions for the transmission probabilities between two multi-probe mesoscopic conductors coupled by a weak tunneling contact. We emphasize especially the dual role of a weak coupling contact as a current source and sink and analyze the magnetic field symmetry. In the limit of a point-like tunneling contact the transmission probability becomes a product of local, partial density of states of the two mesoscopic conductors. We present expressions for the partial density of states in terms of functional derivatives of the scattering matrix with respect to the local potential and in terms of wave functions. We discuss voltage measurements and resistance measurements in the transport state of conductors. We illustrate the theory for the simple case of a scatterer in an otherwise perfect wire. In particular, we investigate the development of the Hall-resistance as measured with weak coupling probes.

Vibrational Properties of Liquid Crystal Molecules from AB Initio Computer Simulation

We determine the molecular vibrational frequencies and displacement patterns for the 4–4′ pentyl-cyanobiphenyl (5CB) molecule by first principles density functional theory. All dynamic properties of the isolated molecule are obtained directly by diagonalisation of the dynamical matrix, the elements of which are determined from Hetlmann-Feynman Forces. Periodic boundary conditions are used which allow for the expansion of the molecular electronic wavefunction in terms of a delocalised plane wave basis set. These calculations are in excellent agreement with the results of vibrational spectroscopy and they provide a reliable means of predictive modelling of molecular properties and can be applied to as yet unsynthesised molecules.

The Vlasov equation for Coulomb systems and the Husimi picture

AbstractWe explore the validity of the Vlasov equation as a semi‐classical approximation of time‐dependent Hartree‐Fock and time‐dependent LDA theories. We discuss the h → 0 limit for the propagation of quantal wavefunctions in terms of classical densities. The h → 0 limit is studied formally by means of its Wigner and Husimi phase‐space representations. We consider an application to the valence electron cloud of metal clusters and show a comparison between quantal and Vlasov dynamics in this case.

Magneto-optical absorption spectra of periodic superlattices under in-plane magnetic fields

An extensive theoretical study of the magneto-optical absorption spectra of periodic GaAs - (Ga, Al)As superlattices under magnetic fields parallel to the heterostructure interfaces is presented within the framework of the effective-mass approximation. The absorption coefficient associated with interband transitions between valence-hole and conduction-electron magnetic levels is calculated by considering an expansion of the envelope wavefunctions in terms of sine functions and by adopting a parabolic-band model for both electrons and holes. Results for the theoretical magneto-optical interband absorption spectra for varying in-plane magnetic fields compare qualitatively well with various experimental measurements. We present a detailed analysis of the effects of off-diagonal interband transitions involving conduction and valence Landau levels n and , respectively, with , and it is unambiguously shown that off-diagonal transitions may introduce significant contributions and extra features in the magneto-optical absorption spectra.

Use of quark wave functions in the calculation of structure functions of mesons.

In the description of deep-inelastic scattering the most extensively used model is the parton model. However, there has been an ongoing effort to understand structure functions of nucleons and mesons in terms of wave functions of quarks. Calculations made using the constituent quark model usually do not fit the experimental data. It has been argued that such calculations refer to some low-momentum scale parameterized by {ital Q}{sup 2}{sub 0}. The calculated distribution is then evolved up to a large scale, {ital Q}{sup 2}, by perturbative QCD evolution. The change needed if the distribution is to fit the data is quite large and, therefore, the scale {ital Q}{sup 2}{sub 0} is taken to be quite small. The large changes required for the distribution makes this procedure suspect. In this work we introduce a class of wave functions that are meant to apply at the scale {ital Q}{sup 2}, so that evolution is not required. These wave functions describe the motion of a current quark, or parton, relative to a residual system. (In order to calculate a cross section the residual system is placed on mass shell in the calculation.) Our procedure is inherently asymmetric in the description of the struck particlemore » and the residual system. We show how we are able to fit the (valence) structure function of the pion at {ital Q}{sup 2}=20 GeV{sup 2} (without QCD evolution) using our scheme. {copyright} {ital 1996 The American Physical Society.}« less

Q analogs of the radial Schrödinger equation in N space dimensions.

Transparent closed forms of the radial ${\mathrm{SO}}_{\mathit{q}}$(N) Schr\"odinger equation acting on the noncommutative quantum Euclidean space are written both for l=0 and l\ensuremath{\ne}0. Starting from the s-wave equation leads to the derivation of an alternative q analog of the radial Schr\"odinger equation in N space dimensions exhibiting a modified symmetry, now in terms of wave functions depending on the radial coordinate only. The harmonic oscillator and the Coulomb system are treated as concrete examples. These results open the way to the derivation of q-deformed (1/N)-energy formulas for arbitrary spherically symmetrical potentials. Comparisons with exact ${\mathrm{SO}}_{\mathit{q}}$(N) results, as well as further interpretations, have also been made.

On bonding in the tetraphosphabicyclo[3.3.0]octa-1,4-diene-1,4-diolate dilithium structure

Bonding in tetraphosphabicyclo[3.3.0]octa-1,4-diene-1,4-diolate dilithium is investigated by means of ab initio calculations at the RHF level. A population analysis of the resulting wavefunction in terms of the natural bond populations indicates that 1. (a) the d-orbital population at phosphorus does not play a dominant role in the determination of bonding in the bicyclic system and 2. (b) there is a transfer of charge density from the bridgehead atoms to the oxygen atoms. This causes a shortening of the central PP bond and can be rationalized qualitatively within the model of Dewar-Chatt-Duncanson.

Rotation‐Vibrational States of H3+ using Hyperspherical Coordinates and Harmonics

AbstractA new method for calculating rotation‐vibrational states of triatomic molecules is presented. It is based on an expansion of the wavefunction in terms of hyperspherical harmonics, which cover five coordinates, and numerical integration of the resulting set of differential equations in the remaining coordinate, the hyperradius ρ. The method is applied to H3+. Here we compare the results for two electronic surfaces, the Meyer‐Botschwina‐Burton surface and the new surface by Kutzelnigg and coworkers.

Properties of wave functions in homogeneous anisotropic media.

The general solutions of the first, second, third, and fourth kinds to the wave equation in homogeneous anisotropic media are expressed by integrals over a finite range. The convergence of the series solution of wave functions in homogeneous anisotropic media [Phys. Rev. E 47, 664 (1993)] is discussed. The use of the wave functions in anisotropic media is demonstrated. The theory is expounded via an illustrative example of a two-dimensional scalar case. The analytical solution of plane-wave scattering by a conducting circular cylinder coated with anisotropic materials is formulated in terms of the series of wave functions for anisotropic media. Numerical results show that the solution in terms of wave functions of various kinds in anisotropic media gives essentially the same radar cross sections as obtained by Beker, Umashankar, and Taflove [Electromagnetics 10, 387 (1990)] using a different approach. Numerical results in the resonance region are presented for reference purposes. The analysis of this paper can be easily generalized to vector and tensor wave functions in homogeneous anisotropic media.

Computation of time-dependent transition probabilities in excimer molecules induced by femtosecond laser pulses

We have computed the time-dependent probabilities of exciting and deexciting the bound states of the excimer molecules NeH, ArH and HeF, via the interaction of these systems with femtosecond laser pulses. The method involves the expansion of the time-dependent wavefunction in terms of stationary states with time-dependent coefficients and complex energies, whose imaginary parts represent the lifetimes of the collision complex on the initial repulsive ground state and of the excited states which are coupled by the field. The resulting system of differential equations is solved by a Taylor series expansion method. We have studied the efficiency of laser-induced molecular formation (LIMP) from the ground repulsive surfaces as a function of frequency and intensity, for trapezoidal pulses. Given the shortness of the pulse and the characteristics of the spectra of these molecules, for reasons of economy the bulk of the calculations was carried out in a ‘frozen nuclei’ approximation. Additional calculations for NeH, using a wavepacket representation of the initial state on the repulsive curve produced similar results as regards the possibility of LIMF. Additional information has been obtained regarding transitions among excited states. For example, starting the photoreaction in HeF from the first excited repulsive state 1 2Π with a pulse frequency of 4 eV allows an experimentally verifiable probability of obtaining bound-continuum emission at about 1320 Å (9.4 eV). For resonance conditions, the probabilities are appreciable during the pulse and go through maxima as a function of intensity of the order of 1011 W/cm2-1014W/cm2.

Excited states of a hydrated electron and aqueous chloride by computer simulation

Results of adiabatic molecular dynamics simulations for a hydrated electron and the aqueous chloride anion are reported. A novel technical feature is the efficient representation of solute electronic wavefunctions in terms of floating spherical Gaussian orbitals. The simulations account for the coupling of the excess electron to the solvent electronic polarization in an explicit and self-consistent fashion. The computed electronic ground state absorption spectrum for e −/H 2O and the charge-transfer-to-solvent spectra for C1 −/H 2O are analyzed. The energetic aspects of the models and the short time solute electronic dynamics are discussed.