Cluster method for the calculation of the electronic density and the ground-state energy of an insulator: Application to solid helium

Summary We propose a new method based on small clusters with the constraint of periodic symmetry to compute electron density and ground-state electronic energy of solids. Calculations are carried out on h.c.p. solid helium, and the Hartree-Fock density is shown to differ from the sum of atomic densities. The correlation energy is responsible for the existence of a small attractive energy per atom, which depends on the lattice parameters. The binding energy per atom cannot be expressed as the sum of two-atom interatomic potentials, but interatomic interactions to higher order must be included. Their effect is to decrease the Van der Waals attraction and to increase the hard-core repulsion.

---

Riassunto Si propone di calcolare la densità elettronica e l’energia dello stato fondamentale dei solidi con un nuovo metodo che utilizza un piccolo numero di atomi e impone la simmetria propria del cristallo attorno all’atomo centrale. Si eseguono calcoli sull’elio solido nella simmetria esagonale compatta. La densità elettronica del metodo Hartree-Fock differisce dalla somma delle densità atomiche. L’attrazione tra gli atomi è dovuta esclusivamente all’energia di correlazione e non può essere espressa come somma dei potenziali tra due atomi; essa contiene termini di ordine superiore, che tendono a diminuire l’attrazione di Van der Waals.

---

Резюме Для вычисления электронной плотности и энергии основного состояния твердого тела предлагается новый метод, при котором испольсуется небольшое число атомов при собственной симметрии кристалла вокруг центральноого атома. Проводятся вычисления в случае твердого гелия при шестиугольной компактной симметрии. Электронная плотность метода Гартпии-Фока (Hartree-Fock) отличается от суммы атомных плотностей. Притяжение между атомами обусловлено только энергией корреляции и не выразимо через сумму потенциалов между двумя атомами. В ней имеются слагаемые высшего порядка при которых уменьшается притяжение Ван дер Ваалса (Van der Waals).

     

A diagram method for the anderson model

Summary A diagram method to treat the Anderson model has been introduced. By applying this technique to the study of chemisorption phenomena, the density of states of adatom electrons has been calculated at finite temperature. Comparison with the results obtained in the symmetric limit atT=0 is given.

---

Riassunto Un metodo diagrammatico è stato introdotto per studiare il modello di Anderson. Applicando questa tecnica al problema del chemisorbimento, è stata calcolata la densità degli stati elettronici localizzati a temperatura finita. è inoltre riportato un confronto con risultati ottenuti aT=0 nel limite simmetrico.

---

Резуме Вводится диаграммный метод для рассмотрения модели Андерсона. Предложенная техника применяется для исследоваия явлений хемосорбции. При конечных температурах вычисляется плотность состояний электронов адатома. Проводится сравнение с результатами, полученными в симметричном пределе приT=0.

     

An inverse-scattering approach to the physics of transition metals

Summary A method is developed for the deduction of a transition metal ion potential from a knowledge of the phase-shift_ηl (k). The method used is based on the distorted plane-wave scattering approximation for the deduction of nonsingular potentials from scattering phase shifts in an inverse-scattering approach. The resulting electron-ion potential obtained is a finite Dirichlet series sum of short-range exponential functions. The Fourier transform of the potential is obtained for applications in the area of transition metal solid-state physics.

---

Riassunto Si sviluppa un metodo per la deduzione di un potenziale di ione metallico di transizione dalla conoscenza dello spostamento di fase_ηl (k). Il metodo usato è basato sull'approssimazione distorta dello scattering di onda piana per la deduzione di potenziali non singolari per spostamenti di fase di scattering in un approccio di scattering inverso. Il potenziale elettrone-ione risultante ottenuto è una somma di serie di Dirichlet finita di funzioni esponenziali a corto raggio. La trasformazione di Fourier del potenziale è ottenuta dalle applicazioni nell'area della fisica dello stato solido dei metalli di transizione.

---

Резюме Развивается метод для определения ионного потенциала переходного металла с использованием фазового сдвига_ηl (k). Предложенный метод предполагает использование искаженных плоских волн в процессе рассеяния для получения несинтуляторных потенциалов из фазовых сдвигов рассеяния в подходе обратного рассеяния. Полученный электрон-ионный потенциал представляет конечную сумму ряда Дирихле коротко-действующих экспоненциальных функций. Получается фурье-преобразование потенциала для использования в физике твердого тела переходных металлоб.

     

Electronic structure ofCuNi,CuCo andAgNi alloys

Summary The pseudo Green's function theory for dilute alloys ofd-band metals is used to study the electronic structure ofCuNi,CuCo andAgNi alloys. The calculated densities of state are found in agreement with other available results. The virtual bound states with double-hump structure are found at 0.514, 0.54 and 0.4 Ryd forCuNi,CuCo andAgNi alloys, respectively.

---

Riassunto La teoria della pseudo funzione di Green per leghe diluite di metalli nella bandad è usata per studiare la struttura elettronica delle legheCuNi,CuCo eAgNi. Si trova che le densità di stato calcolate sono in accordo con altri risultati disponibili. Gli stati legati virtuali con struttura a doppia sporgenza si trovano a 0.514, 0.54 e 0.4 Ryd per leghe diCuNi,CuCo eAgNi.

---

Резуме Используется теория псевдо-гриновских функций для разбавленных сплавов металловd-зоны, чтобы исследовать злектронную структуруCuNi,CuCo иAgNi. Получено, что вычисленная плотность состояния согласуется с другими имеющимися результатами. Обнаружены виртуальные связанные состояния, имеюшие структуру с двойным максимумом, при 0.514, 0.54, 0.4 Ry соответственно для сплавовCuNi,CuCo иAgNi.

     

Electronic-structure calculations for complex crystals

Summary We discuss some new ideas for improving first-principle muffin-tin orbital-type electronic-structure calculations for complex crystals such as ternary and multinary compounds. The new ideas include construction of generalized muffin-tin orbitals and energy-dependent double MTO basis sets, cellular decomposition based on strongly overlapping atomic spheres and evaluation of matrix elements in the residual interstitial region by extrapolation. Supported in part by the Office of Naval Research, Contract Number N00014-79-C-0814.     

Electrostatic neutron-electron scattering

Summary We demonstrate that the electrostatic neutron-electron interaction, formed by the Schwinger and Foldy terms, leads to a cross-section in which the response function is the inverse dielectric function observed in X-ray scattering and electron loss experiments. The experimental conditions for scattering off the acoustic plasmon in metals are unobtainable at present and, at large scattering wave vectors, where the scattered intensity is proportional to the Compton profile, scattering is too weak to be useful. For intermediate scattering vectors, outside the first Brillouin zone, experimental restrictions are still severe although the experiment is feasible but we do not have relevant calculations of the dielectric function, for band structure models, from which to estimate the cross-section. Calculations available for the first Brillouin zone lead us to expect a significant and highly structured response.

---

Riassunto Si dimostra che l’interazione elettrostatica neutrone-elettrone, formata dai termini, di Schwinger e Foldy, porta ad una sezione d’urto nella quale la funzione di risposta è la funzione dielettrica inversa osservata nella diffusione dei raggi X e negli esperimenti di perdita degli elettroni. Le condizioni sperimentali per lo scattering fuori dal plasmone acustico nei metalli sono al momento inottenibili e, per vettori d’onda di scattering molto grandi, in cui l’intensità di diffusione è proporzionale al profilo di Compton, la diffusione è troppo debole per essere utile. Per vettori di diffusione intermedi, fuori dalla prima zona di Brillouin, le restrizioni sperimentali sono aconra notevoli anche se l’esperimento è, fattibile, ma non abbiamo calcoli rilevanti della funzione dielettrica, per modelli di struttura di banda, dai quali calcolare la sezione d’urto. I calcoli utilizzabili per la prima zona di Brillouin portano ad attendersi un responso significativo e altamente strutturato.

     

A mixed basis set of plane waves and Hermite Gaussian functions. Analytic expressions of prototype integrals

Summary Analytic expressions of prototype integrals for electronic-energy calculations involving plane waves and Hermite-Gaussian functions of every order are explicitly derived. A few notes on the use of such a mixed basis set in solid-state and molecular physics are given. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Electronic properties of multinary alloys

Summary A model version of the coherent-potential approximation (CPA) is outlined to evaluate the fundamental energy gapsΓ _15v -Γ _1c ′,Γ _15v -L _1c ,Γ _15v -X _1c of a multinary solid solution. A comparison of theoretical results with the transition energy values obtained from direct interpolation of the corresponding values of ternary alloys is presented for some composition of the solution Al_1−x−y Ga _x In _y As at fixed lattice constants (matching the lattice constants of InP and AlAs). Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Molecular orbital theory and tunnelling currents

Summary The parameters appearing in an effective tight-binding Hamiltonian are shown to be simply related to the tunnelling currents and the overlap between the different orbitals of the constituent atoms. Different systems are considered and the results show that our approach applies both to molecular and condensed-matter systems.

---

Riassunto Si mostra che i parametri presenti in una hamiltoniana efficace a legame forte sono correlati semplicemente alle correnti di tunnel e alla sovrapposizione tra i diversi orbitali degli atomi costituenti. Si considerano diversi sistemi e i risultati mostrano che il nostro approccio si applica sia a sistemi molecolari che di materia condensata.

---

Резюме ПоказЫвается, что параметрЫ, появляющиеср в эффективном Гамильтониане в приближении силъной связи, связнЫ с туннелънЫми токами и перекрЫтием между разяичнЫми орбиталями составляюших атомов. Рассматриваются различнЫе системЫ. ПолученнЫе результатЫ показЫвают, что наш подход применим к молекулярнЫм системам и к конденсироваииому веществу.

     

Matrix elements of the reduced Coulomb Green's function

Summary Using computer we tabulated matrix elements of the partial waves of the reduced Coulomb Green's functions forn=1, 2, 3, 4, 5 andl=0, 1, 2. They enable fast analytical evaluation of the second-order corrections to the bound energy levels for the perturbed hydrogenlike Hamiltonians. We also present the examples of their use for the effective-mass exciton Hamiltonian.

---

Riassunto Con l'uso del computer abbiamo tabulato elementi di matrice delle onde parziali delle funzioni di Green ridotte di Coulomb pern=1, 2, 3, 4, 5 el=0, 1, 2. Questi impediscono una rapida valutazione analitica delle correzioni di second'ordine ai livelli legati di energia per hamiltoniane perturbate del tipo idrogeno. Si presentano anche esempi del loro uso per l'hamiltoniana eccitonica della massa efficace.

---

Резюме Используя компьутер, мы табулируем матричные элементы парциальных волн приведенных кулоновских гриновских функций дляn=1, 2, 3, 4, 5 иl=0, 1, 2. Они позволяют получить аналитические оценки для поправок второго порядка к энергетическим уровням связанных состояний для возмущенных водородоподобных Гамильтонианов. Мы также приводим примеры использования полученных результатов для Гамильтониана экситонов с эффективной массой.

     

Effective resolvent applied to interacting resonances

The wave operator theory of quantum dynamics is applied to characterize coupled metastable states. The theory extends to quasi bound states methods which are standard for dealing with bound levels. It is shown that interacting resonances can be investigated by means of small-dimensional effective Hamiltonians containing all the significant information of intrinsic properties which drive the various dynamical processes taking place. The study of the vibrational predissociation of I₂Ne, mediated by intramolecular energy redistribution, illustrates the power of the method. In addition to its accuracy to determine spectroscopic profiles and survival probabilities, it results more efficient than usual energy or time-domain numerical calculations. Received 25 January 2001 and Received in final form 11 May 2001     

A new method for determining excited states of quantum systems

Summary A new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyE _t, we consider the auxiliary operatorA=(H−E _t)². We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Application of accelerated-convergence technique to modified Lanczos calculations

Summary The use of modified Lanczos procedure to obtain the ground-state eigenvalue and eigenvector of the Hamiltonians of physical systems and its subsequent modification for the determination of excited states has been revealed a very efficient and powerful procedure. Nevertheless, when implementing the method, one notices that the convergence of the algorithm is very slow, so that the calculation may become heavy from a computational point of view. The aim of this paper is the proposal of an accelerated-convergence technique (which has already been successfully used in density-of-states calculations), that allows to obtain a faster convergence of the modified Lanczos eigenvalues to the exact ones. The advantages of such a technique are shown through the discussion of some examples.     

New algorithms to look for the most stable conformations of a molecule

Summary Some new algorithms useful for the study of the ≪low-energy conformational space≫ of a molecule are described, and in particular an algorithm which detects the most stable conformations through a random sampling of the energy hypersurface. An application of this algorithm to ethylmethylphosphate (a model molecule of the chain segment of nucleic acids between two furanose rings) is also shown. Presented in part at the Fourth Annual Montedison Chemistry Meeting (Milan, March 4, 1986).     

The continuum orbital problem in the calculation of auger decay rates: Application to Ne

Summary Described here are new computational procedures which have been developed for obtaining the continuum orbital in Auger problems. A Lippmann-Schwinger (LS) equation is solved for the inner, atomic or molecular region and in the asymptotic region the LS orbital is matched with the eigenfunctions of the long-range Hamiltonian. A detailed analysis of the form of the continuum orbital for various decay states of the KLL Auger spectrum of the neon atom is presented. Decay rates are given for the Ne and compared with previous results and with experiments.

---

Riassunto Si presenta una nuova tecnica per ottenere l'orbitale del continuo in problemi Auger. Essa consiste nella soluzione di un'equazione alla Lippmann-Schwinger (LS) per la regione atomica o molecolare e nel raccordo dell'orbitale cosí ottenuto con le autofunzioni dell'hamiltoniana contenente la parte asintotica del potenziale. Si effettua inoltre un'analisi dettagliata della forma dell'orbitale del continuo per vari possibili stati di decadimento Auger dell'atomo di Ne ionizzato nel guscio 1s e si interpreta lo spettro KLL di tale sistema in termini di energie di risonanza e velocitá di decadimento.

---

Резюме В работе описываются новые вычислительные процедуры, которые были развиты для получения непрерывной орбитали в Оже-проблемах. Решается уравнение Липмана-Мвнгера для внутренней атомной или молекулярной области. В асимптотической области орбиталь Липмана-Швингера согласуется с собственными функциями Гамильтониана. В работе проводится подробный анализ формы непрерывной орбитали для различных возможных состояниЙ Оже-распада атома Ne. Приводятся интенсивности распада для Ne и сравниваются с предыдущими результатами и данными экспериментов.

     

The Lippmann-Schwinger equation for obtaining the continuum orbital in Auger problems: Application to the KLL spectrum of atomic neon

Summary A new method is proposed for obtaining the continuum orbital representing the emitted electron in Auger problems through the use of a Lippmann-Schwinger equation. As a test of its accuracy, a comparison is made with previous calculations of the Auger spectrum of atomic Ne.     

On the relation between the connected-moments expansion and the Lanczos variational scheme

Summary The recently introduced Connected-Moments Expansion (CMX) is compared to a variational Lanczos scheme for estimating ground-state energies of many-body systems. A systematic approach is given for three quantum-mechanical systems: harmonic oscillator, anharmonic oscillator and the Kondo model. A second-order analysis is given in terms of particular ratios of moments of the Hamiltonian.     

Band effects on conduction electron density of states for the anderson model

Summary The effects of the shape of free conduction density of states on the physical quantities for the periodic Anderson model have been investigated.     

The electrical conductivity for inhomogeneous electric fields by the Liouville operator method

A derivation is given of the electrical conductivity for a metal in a space- and time-dependent electric field. Thereby it is assumed that the electrons are scattered elastically by randomly distributed impurities. The derivation starts from the Kubo-Nakajima formula and is based on a perturbation expansion with Liouville operators, where use is made of van Hove's diagonal singularity property of the scattering potential. The formulae obtained are compact and the method is simpler and more transparent than the perturbation formalism developed by van Hove. It is shown that the lowest order approximation corresponds to the Boltzmann equation for electrons in inhomogeneous electric fields.