Quadratic augmented plane wave method for self-consistent band structure calculations

Recently linearized versions of the augmented plane wave (APW) method have been introduced. The quadratic-APW (QAPW) method is presented which is a more general formulation of the linear-APW (LAPW) methods. Here the exact radial solution inside the muffin-tin (MT) sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term, i.e. with higher accuracy when compared with the standard LAPW method which uses only the linear term. The standard LAPW method is obtained as a special case from our formulation. Similarly to the standard LAPW method, the energy independent APW's are formed from approximate radial wave functions which lead to the secular equations linear in energy. The analysis of the solution inside the MT-sphere shows that the eigenvalue error is proportional to (E-E ₀)⁶ in the method suggested as compared with (E-E ⁰)⁴ for the standard LAPW method. As an application both non-self-consistent and self-consistent calculations are presented for the band structure of FCC copper metal.     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

High T c superconductors as ionic metals and the role of phonons in high T c superconductivity

We have investigated a number of zone center and zone boundary (X-point) modes in La₂CuO₄ using the full potential Linearized Augmented Plane Wave (LAPW) method and find excellent agreement with experiment for phonon frequencies, showing that the local density approximation (LDA) is an excellent approximation for the total energies, charge density, and static density response in high T _c superconductors. Results are compared with those of a non-empirical ionic model for La₂CuO₄ and YBa₂Cu₃O₇. Self-consistent calculations show that the ionic nature of these materials leads to large changes in the potential with atomic displacements. The ionic contributions to the electron-phonon matrix elements, which were neglected in previous studies, are large and possibly sufficient to explain high T _c .     

Inequalities of the electron density at the nucleus and radial expectation values of the ground state for the lithium isoelectronic sequence

The electron density at the nucleus, ρ(0), and the radial expectation values, (-2≤n≤10), of the ground state for the lithium isoelectronic sequence are calculated with a full core plus correlation (FCPC) wavefunctions. By using these obtained expectation values, the accurate inequalities of the electron density at the nucleus and the radial expectation values derived by Gálvez and Porras for these systems are examined and verified. The final results show that FCPC wavefunctions used in this work can give satisfactory results in full configuration space.     

Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential

We solve the Klein-Cordon equation with a new anharmonic oscillator potential and present the exact solutions. It is shown that under the condition of equal scalar and vector potentials, the Klein-Cordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions.     

Systematic reduction of the permanent exciton dipole for charged excitons in individual self-assembled InGaAs quantum dots

The nature of the few particle wavefunctions for neutral and positively charged excitons is probed in individual InGaAs quantum dots using Stark-effect perturbation spectroscopy. A systematic reduction of the vertical component of the permanent excitonic dipole (p_z) is observed as additional holes are added to the dot. A comparison with calculations reveals that this reduction (Δp_z/e15–20%) is accompanied by a significant lateral expansion of the hole (2 nm) and contraction (1 nm) of the electron wavefunctions. We suggest that this lateral redistribution of the charged exciton wavefunctions provides an optical means to probe the lateral composition profile of the dot.     

First principle study of the cation vacancy in anatase TiO2

Based on first principle FP‐LAPW calculations, we have studied the electronic and magnetic properties of anatase TiO₂ with Ti cation vacancy. We find that the Ti cation vacancy defect can induce a magnetic moment of about 4μ_B/supercell. The magnetic moment mainly comes from p‐orbitals of O atoms which surround the Ti vacancy. We also find that the two Ti vacancies in anatase always coupled ferromagnetically. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase-integral calculation of quantal matrix elements between unbound states,without the use of wavefunctions

The paper deals with the calculation of diagonal as well as off-diagonal matrix elements between unbound states pertaining to a radial Schrödinger equation. For the case that the effective potential, i.e. the potential with the centrifugal barrier included, is real and that only a single generalized classical turning point exists, we derive, on the basis of a phase-integral method, a new, general formula for the calculation of such matrix elements without the use of wavefunctions. The formula applies to an arbitrary order of the phase-integral approximations used. While conventional methods may present difficulties when the radial wavefunctions oscillate rapidly in space, this formula, in which the wavefunctions do not appear, is expected to be more accurate the more rapidly the wavefunctions oscillate. The formula is tested numerically for a Lennard-Jones potential and is found to yield extremely accurate results.

When specialized to the first-order approximation, our formula goes over into a formula derived previously by other authors. They derived the formula by introducing the first-order JWKB approximation for the wave-functions in the integral defining the matrix element and simplifying the resulting expression by using simple qualitative arguments. The remarkably good accuracy of this first-order formula has puzzled previous authors. So has also the fact that attempts to improve it, by including quantities neglected on the basis of the simple qualitative arguments, and by using Airy functions or uniform approximations for the wavefunctions through the turning points, have failed. Our derivation throws light on the question of the accuracy to be expected, and it explains why already the first-order formula is remarkably accurate and why no improvement is gained in the attempts mentioned.     

环形振子势的精确解

将环形振子势的Schrödinger方程在球坐标系中进行变量分离.然后求解了角向方程和径向方程,给出了精确的能谱方程.获得了用普遍的缔合Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数.     

On the path integrations for the Wood-Saxon and related potentials

It is demonstrated that the radial path integral for the Wood-Saxon potential for s-waves can be solved by using the path integration over the SU (2) manifold. The wavefunctions and the energy spectrum are obtained. It is shown that the path integrals for the Rosen-Morse and the Hulthén potentials are also solvable in a similar way.     

氢原子径向矩阵元及其递推关系

利用氢原子径向波函数的积分特性，导出了氢原子径向矩阵元〈ｎｌ’│ｒ＾ｋ│ｎｌ〉的一般计算式以及矩阵元之间的递推关系。     

The rotational Raman spectra and cross sections of H2O, D2O, and HDO

We report the experimental rotational Raman spectra of H₂O, and of a mixture of D₂O and HDO in the vapor phase at room temperature, and their interpretation in terms of rotational–vibrational energies, wavefunctions, and transition moments of the molecular polarizability. These transition moments are based on high-level ab initio calculations of the wavelength dependent polarizability surface, and on wavefunctions where the rotational–vibrational coupling is considered in detail. As a byproduct of this analysis several tables have been compiled including scattering strengths and assignments for individual rotational transitions of the three species. From these tables the rotational Raman spectra can be simulated over the range of temperatures up to 2000 K for H₂O, and up to 300 K for D₂O and HDO.     

低能电子与氢分子碰撞的振动激发积分散射截面的研究

采用振动密耦合方法,研究了低能电子与H₂分子碰撞的振动激发积分散射截面.研究表明,使用18个Morse振动波函数、5个分波和4个对称性可以得到收敛的0→0,0→1,0→2和0→3积分散射截面;而且振动波函数的性质和振动能级的精确性会直接影响振动激发散射势能和振动激发积分散射截面.计算结果与实验符合得很好. 关键词： 电子散射 振动激发 2分子')" href="#">H₂分子 积分截面     

Exact solutions of the radial Schrödinger equation for some physical potentials

By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.     

Magnetic form factor of Eu2+ in EuO

Polarized neutron measurements of the magnetic form factor of Eu²⁺ in EuO were made, to check for possible solid state effects on the radial extent of the 4f wavefunctions in this ferromagnetic insulator. Previous studies show good agreement between the magnetic form factors observed for the heavy rare earth metals and those calculated for the free ions using relativistic Dirac-Fock wavefunctions. However, the same comparison in this case shows an approximate 9% expansion of the 4f wavefunctions in EuO relative to that calculated for the Eu²⁺ ion. This apparent solid state effect has the same sign but twice the magnitude of that recently calculated by Byrom, Ellis and Freeman for (EuO₆)^?12 clusters.     

Generalized Parton Distributions of the Pion on the Transverse Lattice

The quark-generalized parton distributions of the pion are calculated from light-cone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite bound-state light-cone energy conditions, is given for the light-cone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.     

Makarov势的Dirac方程的束缚态解

给出了Makarov型标量势与矢量势相等条件下的Dirac方程的束缚态解. Dirac方程的角向方程用因子分解方法求解，在得出角向波函数的过程中，自然地得到了属于同一本征值的不同角向波函数间的递推操作. 径向束缚态波函数用合流超几何函数表示，束缚态的能量方程可由径向波函数满足的边界条件得到. 关键词： Makarov势 Dirac方程 束缚态 因子分解方法     

Superconducting instability in the large-U limit of the two-dimensional Hubbard model

We have investigated numerically the pairing instabilities of Gutzwiller wavefunctions. These are equivalent to a certain form of the resonant valence bond wavefunction. The case considered is a nearly half-filled two dimensional band with interactions given by a Hubbard model with large on-site Coulomb interactions. We find that the paramagnetic normal state is unstable tod-wave pairing but stable againsts-wave pairing. The antiferromagnetic state is marginally stable against both types of pairing. These results can be explained as an interference effect resulting in enhanced antiferromagnetic spin correlation in the paired state.     

The thermal metal-insulator phase transition in (EDO-TTF)2PF6

ABSTRACT

The thermal metal-insulator phase transition in the π-stacked (EDO-TTF)₂PF₆ charge transfer salt is of the Peierls type. It is related to geometrical reorganisations and charge ordering phenomena. We report that dimerising displacements are involved in the mechanism of this transition. By using periodic quantum chemical calculations, we find a double well potential in which dimerisation and charge localisation become manifest. By analysing the nuclear wavefunctions we discuss the mechanism of the phase transition in terms of thermal fluctuations.