Variational Perturbation Method Research Articles

Ab initio configuration interaction determination of the overtone vibrations of methyleneimine in the region 2800–3200 cm−1

Ab initio configuration interaction (CI) potential function calculated from a 6-311G** basis set at a MP2 level of theory is used to compute the vibrational energy levels of methyleneimine CH2NH between 2800 and 3200 cm−1. The most important configurations selected by an iterative process by means of a variational perturbational method are diagonalized. Results show a perfect agreement with the most reliable experimental values and predict the ν5+ν6, ν4+ν6, and ν4+ν5 unobserved combinations.

Interfacial behavior of phase separated asymmetric compressible binary polymer blends

Our theory for the interfacial properties of compressible binary polymer systems [J. Chem. Phys. 98, 8994 (1993)] is generalized to treat phase separated asymmetric binary blends. The theory is illustrated by using a Sanchez–Lacombe approximation for the homogeneous system free energy and a Cahn–Hilliard–de Gennes expression for the square gradient contribution. These two ingredients enable the same theory to describe both the compositions of the coexisting phases and the interfacial properties. The coupled equations for the two concentration profiles are numerically unstable, and our perturbation–variational method for symmetric blends is extended to treat blends with asymmetry due to differing polymerization indices and/or interaction parameters. The zeroth order approximation, which uses a hyperbolic tangent interpolation between the generally different densities in the coexisting phases, is found to be extremely accurate in predicting the interfacial tensions and widths. Illustrations of the theory are provided for systems with upper and with lower critical solution temperatures, as well as with hour-glass miscibility gap type phase diagrams. The higher order perturbation–variation contributions mainly affect the total density variation through the interface, exhibiting several different patterns of density redistributions to lower the interfacial free energy. Computations are also provided for the pressure dependence of the interfacial properties.

Calculation of the Partition Function of a Double Minimum Oscillator from a Modified Variation Perturbation Method

Abstract The partition function of a double minimum oscillator is evaluated by means of variation perturbation theory. For low temperatures, the method cannot be applied in the usual way. Even for a symmetric double minimum potential VDM(x), the shift of the harmonic reference oscillator is not always zero as expected, but its minimum is near one of the minima of VDM(x) at low temperatures. The partition function thus calculated is only half the correct value. For sufficiently high temperature, the method works normally. The anomaly in the low temperature region is investigated in detail, and a modification of the variation perturbation method is suggested which eliminates most of the problems.

Variational calculation of the dynamic third-order susceptibility of water

We present the variation-perturbation method for calculating dynamic third-order molecular hyperpolarizabilities. After a summary of the general theory, we report calculations on the water molecule, using the CNDO approximation with an extended basis set, and a truncated expansion of the trial second-order wavefunction that includes only singlyexcited Slater determinants. In the static limit, the results are found to compare well with the best ab initio values. The dispersion of the cubic hyperpolarizability tensor is also calculated.

Effects of electron-phonon interaction on exciton binding energy in a quantum well

Using Lee-Low-Pines transformation and perturbative variational method, the effects of electron-phonon interaction on the exciton binding energy in a Ga 1− x Al x As quantum well can be solved analytically. Our results show that the phonon effect on binding energy of heavy-hole exciton is always larger than that of light-hole exciton and the correction of polaron effect on the exciton binding energy in a quantum well cannot be neglected.

Calculation of positronium compounds, PsLi, PsF, and PsCl, by second-order variational perturbation method

Correlation, positron ionization, and positronium (Ps) binding energies for the ground state ( 2,1S) of PsLi, PsF, and PsCl together with the excited state ( 2,1P) of PsF and PsCl are calculated by the second-order variational perturbation method with partial wave expansion. Estimated positronium binding energies for PsLi( 2,1S), PsF( 2,1S), PsCl( 2,1S), PsF( 2,1P), and PsCl( 2,1P) are −2.19, 2.24, 1.62, −0.16, and −0.05 eV, respectively. The Ps binding energies of PsF( 2,1S) and PsCl( 2,1S) are in good agreement with the ones estimated by quantum Monte Carlo calculation and also with experimental ones.

The nuclear magnetic shielding and spin-rotation constants of the hydrogen molecule

The variation-perturbation method, employing an explicitly correlated basis set in the form of Gaussian functions with exponential correlation factors, has been used to calculate the paramagnetic component of the nuclear magnetic shielding and the electronic contribution to the spin-rotation constant for the hydrogen molecule in its ground state. The diamagnetic components of the shielding tensor have also been computed. The computations have been performed for three internuclear distances in the vicinity of equilibrium. A comparison of the calculated quantities, which are of high accuracy, with the experimental data reveals a small but significant discrepancy between theory and experiment.

Perturbative-variational approximation of the ground state of two-electron atoms

Here, we study the applicability of the perturbative variational method (PVM) to obtain the ground-state energy and wavefunction of the two-electron atoms. The convergence of the method has been studied with different bases and we have checked whether it is faster if we work with an orthogonal or quasi-orthogonal basis. We have focused our attention on the polynomial basis and our best results are very close to the best results provided for other calculations that include non-analytical terms in the basis. However, we have to use a number of states in a basis ten times larger than that used in other calculations.

Dipole polarizabilities for the ground states of lithium-like systems from Z=3 to 50

The dipole polarizabilities of the lithium-like ground states, 1s22s 2S, are calculated with the full-core plus correlation (FCPC) wavefunctions. The non-relativistic polarizabilities are obtained by using a variation-perturbation method. Based on the relativistic and QED corrections to the energy, the dipole polarizabilities are corrected using an oscillator strength formula. The results indicate that relativistic and QED effects on the dipole polarizability become very important for Z>or=15. The result for Li I, 164.08 a03, is in good agreement with a recent CI-Hylleraas calculation, 164.1 a03 and with the experiment, 164.0+or-3.4 a03. The calculated results of other lithium-like systems are compared with previous theoretical results in the literature.

A Method for the Prediction of the Transport Properties of Dense Fluids: Application to Liquid n-Alkanes

A new method is presented for the prediction of the transport properties (viscosity, thermal conductivity, and diffusion coefficient) of liquids. The method is based on the rough hard sphere theory of Chandler and incorporates the recent molecular dynamics results for Lennard-Jones fluids reported by Heyes. The Lennard-Jones parameters and the effective hard sphere diameter required in the calculations were determined from a knowledge only of the density-temperature behavior of the fluid at atmospheric pressure using the Ross variational perturbation method. Analytical expressions are presented for the transport properties of the n-alkanes, and comparisons are shown between calculations and experiment. The results generally agree with published results within experimental error

Effective oscillator strengths and transition energies for the hydrogen molecular ion

The variation-perturbation method using finite basis sets is applied to the hydrogen molecular ion H+ 2. Sets of ‘pseudostates’ consisting of N pairs of effective oscillator strengths and transition energies are determined and tabulations with N = 6, for both parallel and perpendicular electric dipole transitions, are presented over a range of internuclear distances. Various oscillator strength sums, including those involving the logarithms of the transition energies, and Rayleigh-Schrodinger perturbation theoretic expressions are evaluated. In particular, the isotropic and anisotropic components of the dipole-dipole dispersion energy between H+ 2 and each of a number of atoms, H2, and N2 are determined using published pseudostates.

Perturbation–variational methods revisited

AbstractWe describe a simple expansion of the Krylov type for the estimation of the electronic correlation energy of the ground state of closed‐shell systems and show its relationship with Brillouin–Wigner perturbation theory. We demonstrate the Brillouin–Wigner perturbation theory can be quickly solved in a noniterative fashion. Examples are presented using the intermediate neglect of the differential overlap model Hamiltonian (INDO/1), which indicates that this scheme captures well over 95% of the configuration interaction over double excitations method (CID) in a fraction of the computational effort. © 1993 John Wiley & Sons, Inc.

Centre-of-mass quantization of excitons in GaAs quantum boxes

By using a variational-perturbative method, the authors have studied the excitons confined in wide quantum boxes, i.e. the size quantization of the exciton centre-of-mass. The exciton energies are significantly shifted to high energy. The oscillator strength is enhanced with decreasing box size.

Effect of charge-carrier screening on the exciton binding energy in GaAs/AlxGa1-xAs quantum wells.

Exciton binding energies of heavy- and light-hole excitons affected by charge-carrier screening in GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells are calculated by the variational-perturbation method. The exciton binding energies are found to decrease rapidly when the screening length is less than 30${\mathit{a}}_{\mathit{B}}^{\mathit{h}}$ (effective exciton Bohr radius). This screening length corresponds to a carrier density of 7.0\ifmmode\times\else\texttimes\fi{}${10}^{13}$/${\mathrm{cm}}^{3}$ at T=10 K. In the calculation, the Debye screening model is used for charge carriers. The exciton binding energies as functions of the screening length, carrier density, and quantum-well parameters have been calculated. The critical carrier densities, above which no excitons can be formed, are obtained at different well thickness. The effects of charge-carrier screening to the exciton photoluminescence are also discussed.

The bound states of the [formula omitted] relativistic quantum field models with weak coupling obtained by the variational perturbation method

The two-particle bound states of the simplest quantum field theory models with effective interaction, the weakly coupled P(ϕ) 2 models, are obtained by the variational perturbation method. This method leads to an eigenvalue equation for the bound state mass, which can be seen as a relativistic generalization of the Schrödinger equation, proposed by the P(ϕ) 2 models at first perturbation orders. Moreover it gives the zero-time eigenvectors of the bound states at first perturbation orders.

Binding energy spectra of ABC-excitons of CdS

A novel perturbative variational method was employed to calculate the exciton energy spectra of CdS. The band mixing effects were included by taking into account the detail feature of the valence bands. More extensive characteristics of the energy spectra of A-, B- and C-exciton, were identified. It is found that the binding energy of the ground state of a B-exciton is larger than that of an A-exciton, whilst the binding energy of the 2s state of a B-exciton is slightly lower than that of an A-exciton. Our results are compared with the previous theoretical values using the conventional perturbation method and the available experimental data. Better agreements between our results and the observed values are obtained.

The binding energy of hydrogenic impurities in quantum well structures under electric fields

The effect of an electric field on the hydrogenic impurity state in a quantum well is studied by using the variational-perturbative method. The variation of the binding energy as a function of the electric field with different well widths and impurity positions is calculated. We have also extended the calculation for the finite quantum well and some interesting points are discussed.

Electron-hole quantum-confined states affected by point charge in semiconductor crystallite

The effects of a point charge inside a semiconductor crystallite on the electron, hole and electron-hole (e-h) pair ground quantum-confined states have been studied under the effective-mass approximation by means of the variational-perturbation approach. The electron, hole and e-h pair ground quantum-confined state energy as functions of the crystallite radius, the charge position inside the crystallite have been obtained. The validity of the variational-perturbation method is presented. Effects of this point charge on the optical properties of the crystallite have also been discussed.

Nonadiabatic energy corrections for the vibrational levels of the B and B′ 1Σ+u states of the H2 and D2 molecules

The variation-perturbation method is used to calculate the nonadiabatic energy shifts of all bound vibrational levels of the B 1Σ+u and B′ 1Σ+u states of H2 and D2 from the best available ab initio wave functions. In H2 the nonadiabatic energy shifts lie between extremes of −0.31 cm−1 (B,v=0) and −5.07 cm−1 (B,v=30) and, as expected, the shifts in D2 are one half as large as the ones in H2 at the same vibrational energies. The resulting nonadiabatic vibronic term values of the B state lie ≂1.1±0.1 cm−1 above the experimental ones over a wide range of vibrational excitation energies, in H2 as well as in D2. This indicates that all nuclear-mass dependent contributions to the vibronic energies as well as the potential curve of the B state are now accounted for quite accurately. In the B′ state the remaining discrepancies with experimental term values depend markedly on vibrational excitation, and a large part of them is nuclear mass dependent, while the remaining error of the electronic energy calculation for the B′ state seems to be as small as the one for the B state.

Calculation of the exciton binding energies in type-II GaAs/AlAs quantum-well structures: Application of the perturbation-variational expansion method.

We report a calculation of the binding energies of both the heavy-hole and the light-hole excitons in type-II GaAs/AlAs quantum wells as a function of the size of the AlAs layer (or GaAs layer). We use a perturbation-variational expansion method to the first order in perturbation expansion. The exciton binding energies are calculated assuming infinite potential barriers and results thus obtained are compared with those of a published variational calculation. We find that the values of the exciton binding energies that we calculate are somewhat lower than those obtained using a variational calculation, even for small wells similar to the perturbation-variational method results in type-I quantum wells. An explanation of this behavior in terms of the average spatial separation of electrons and holes is given.