Direct minimization of the energy functional in the LCAO-MO density matrix formalism

The previously proposed method of direct energy minimization by a gradient approach is here applied to the separated electronic pair functions (strongly orthogonal geminals). The minimization of the energy is achieved by an alternate iterative procedure in which the geminal occupation coefficients are optimized making each geminal self-consistent in the field of the others and the orbital forms are directly optimized using a sequence of orthogonal transformations of an arbitrary orthonormal basis set. The method is tested on H₂, He₂, LiH, NH₃ and H₂O molecules.

Possible generalizations of the formalism to other geminal models are briefly presented.     

Relativistic density functional calculation of the total energy and Fermi surface of gold

For fcc gold we have studied the total energy, equilibrium lattice constant, bulk modulus and Fermi surface with their dependence on pressure. The self-consistent calculation in the local-density and warped muffin-tin approximation applies the modified augmented-plane-wave band-method. The core levels are treated in a fully relativistic way and the valence levels in a quasirelativistic approximation on the basis of the Foldy-Wouthuysen transformation. Though the Fermi surface properties and especially the dependence of the extremal orbit areas on pressure are in good agreement with other calculations and experimental values, careful convergence tests offer the quasi-relativistic approximation as source of large errors in the properties which are derived from the total energy.     

Hund's rule and the Z expansion for the energy,electron repulsion and electron nuclear attraction

A Z expansion is derived for the expectation values of the interelectronic repulsion energy and the electron-nuclear attraction energy in atomic states. The formalism, which is based on a non-relativistic hamiltonian, is applied to excited states in iso-electronic sequences. It appears that there are many cases where the state of the highest multiplicity has the larger expectation value for the interelectronic repulsion energy although it has a lower total energy.     

Calculation of the formation energy of alloys using the method of the model functional of electron density

Calculation of the formation and ordering energies of the alloys Fe-V and V-Ti has been performed on the basis of the method of the electron-density functional. It is shown that alloys of the system V-Ti should be dissolvable, whereas in the system Fe-V the most favorable state is an ordered alloy state with CsCl structure. Estimates of dissolving and ordering temperatures are performed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 32–35, January, 1982.     

Lattice density functional theory for confined Ising fluids: comparison between different functional approximations in slit pore

ABSTRACT

In this paper, Lafuente and Cuesta's cluster density functional theory (CDFT) and lattice mean field approximation (LMFA) are formulated and compared within the framework of lattice density functional theory (LDFT). As a comparison, an LDFT based on our previous work on nonrandom correction to LMFA is also developed, where local density approximation is adopted on the correction. The numerical results of density distributions of an Ising fluid confined in a slit pore obtained from Monte Carlo simulation are used to check these functional approximations. Due to rational treatment on the coupling between site-excluding entropic effect and contact-attracting enthalpic effect by CDFT with Bethe-Peierls approximation (named as BPA-CDFT for short), the improvement of BPA-CDFT beyond LMFA is checked as expected. And it is interesting that our LDFT has a comparative accuracy with BPA-CDFT. Apparent differences between the profiles such as solvation force, excess adsorption quantity and interfacial tension from LMFA and non-LMFAs are found in our calculations. We also discuss some possible theoretical extensions of BPA-CDFT.     

Active minimization of acoustic potential energy in a two-dimensional multimode waveguide

Acoustical Physics - The nonlinear inverse problem of active sound control in a two-dimensional waveguide is addressed. To solve the problem, a numerical algorithm based on an exhaustive search for...     

Curvy steps for density matrix based energy minimization: tensor formulation and toy applications

A unitary transformation-based framework is explained for varying the one-particle density matrix in a non-orthogonal expansion basis while preserving both the idempotency and electron number constraints. The equations are presented in a compact tensor formulation that permits the use of any representation for the matrices. A connection with the LNV method is established. Curvy steps, which are high order line searches along a chosen descent direction, are defined. Calculations with two toy model systems are presented to illustrate the nature of the displacements in this approach.     

Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E(c) in terms of the first-order reduced density matrix (1-RDM) is presented. With the contracted Schr?dinger equation the principal dependence of E(c) on the natural occupation numbers n(i) is identified. Using the effective mass theory, E(c) is expressed as a functional of the local density and the local variable, J = SUM (i)[square root of (n(i)(1-n(i))] /phi(i)/(2), where phi(i) are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% of the correlation energies of atoms and molecules.     

On the semiconductor energy gap in density functional theory

The non-existence of the functional derivative of the Hohenberg-Kohn functional at the ground-state density of a semiconductor earlier discussed in the literature^2,3 is analyzed. Arguments are given that this non-existence is not connected with the discontinuity of the (ordinary) derivative of the functional with respect to the particle number N as discussed by Perdew and Levy².     

Measuring the energy level repulsion in quantum dots

Energy level repulsion is one of the remnants of classical chaos in quantum mechanics. Measurements of the distribution of nearest neighbor spacings in quantum dots reveal, in contrast to other classically chaotic systems, deviations from the predictions made by random matrix theory. Here, we survey possible contributions to these deviations from experimental peculiarities present in measurements on quantum dots, and discuss the methods to eliminate or reduce such distortions.     

Effects of spatial distribution of the electron density functional in crystals

The variational principle was used within the concept of quasiparticles to determine one-electron states, taking into account effects of nonlocality of the electron density functional in electromagnetic fields.     

Kinetic and potential energy of isoelectronic atomic ions from density functional theory compared with exact values

The performance of the Fock exchange and the two most common Becke exchange functionals, B88 and B3, in combination with Perdew and Wang's correlation functional (PW91) has been studied for highly charged atomic ions. The study focuses on the accuracy of the components of total energy: kinetic and potential energy. It is found that Becke's exchange functionals introduce a significant error in the kinetic and nuclear attraction energy for most ions studied, and the use of these exchange functionals might lead to inaccurate momentum distributions when their Kohn-Sham orbitals are transformed to momentum space.     

总变差约束的数据分离最小图像重建模型及其Chambolle-Pock求解算法

基于优化的迭代法,可以结合压缩感知和低秩矩阵等稀疏优化技术高精度地重建图像.其中,总变差最小（total variation minimization,TV）模型是一种简单有效的优化模型.传统的约束TV模型,使用数据保真项为约束项,TV正则项为目标函数.本文研究TV约束的、数据分离最小（TV constrained,data divergence minimization,TVcDM）新型TV模型及其求解算法.详细推导了TVcDM模型的Chambolle-Pock（CP）算法,验证了模型及算法的正确性;分析了算法的收敛行为;评估了模型的稀疏重建能力;分析了模型参数的选择对重建的影响及算法参数对收敛速率的影响.研究表明,TVcDM模型有高精度稀疏重建能力;TVcDM-CP算法确保收敛,但迭代过程中有振荡现象;TV限对重建有重要影响,参数值过大会引入噪声而过小会模糊图像细节;算法参数的不同选取会导致不同的收敛速率.     

Floating double probe in non‐Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non‐Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than –e(V_f ? V_p) from the I–V double probe characteristics. V_f and V_p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V_f ? V_p) allows the determination of the total electron density (n_e) and the mean electron energy (<?_e>). The method is detailed and tested in the case of a theoretical Maxwell–Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.