Density Functional Theory -- an introduction

Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often considered too lengthy to be included in various curricula. An alternative introduction to DFT is presented here, drawing on ideas which are well-known from thermodynamics, especially the idea of switching between different independent variables. The central theme of DFT, i.e. the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is presented as a straightforward generalization of the familiar Legendre transform from the chemical potential (\mu) to the number of particles (N). This approach is used here to introduce the Hohenberg-Kohn energy functional and to obtain the corresponding theorems, using classical nonuniform fluids as simple examples. The energy functional for electronic systems is considered next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchange-correlation hole. A very brief survey of various applications and extensions is included.Comment: Substantially revised to improve pedagogical value; explicit examples added. 14 twocolumn pages, 4 figures, American Journal of Physics (in press

Novel experimental design for high pressure - high temperature electrical resistance measurements in a 'Paris-Edinburgh' large volume press

We present a novel experimental design for high sensitivity measurements of the electrical resistance of samples at high pressures (0-6GPa) and high temperatures (300-1000K) in a 'Paris-Edinburgh' type large volume press. Uniquely, the electrical measurements are carried out directly on a small sample, thus greatly increasing the sensitivity of the measurement. The sensitivity to even minor changes in electrical resistance can be used to clearly identify phase transitions in material samples. Electrical resistance measurements are relatively simple and rapid to execute and the efficacy of the present experimental design is demonstrated by measuring the electrical resistance of Pb, Sn and Bi across a wide domain of temperature-pressure phase space and employing it to identify the loci of phase transitions. Based on these results, the phase diagrams of these elements are reconstructed to high accuracy and found to be in excellent agreement with previous studies. In particular, by mapping the locations of several well-studied reference points in the phase diagram of Sn and Bi, it is demonstrated that a standard calibration exists for the temperature and pressure, thus eliminating the need for direct or indirect temperature and pressure measurements. The present technique will allow simple and accurate mapping of phase diagrams under extreme conditions and may be of particular importance in advancing studies of liquid state anomalies.Comment: 8 pages, 12 figure

Robust Bayesian Analysis of Loss Reserves Data Using the Generalized-t Distribution

This paper presents a Bayesian approach using Markov chain Monte Carlo methods and the generalized-t (GT) distribution to predict loss reserves for the insurance companies. Existing models and methods cannot cope with irregular and extreme claims and hence do not offer an accurate prediction of loss reserves. To develop a more robust model for irregular claims, this paper extends the conventional normal error distribution to the GT distribution which nests several heavytailed distributions including the Student-t and exponential power distributions. It is shown that the GT distribution can be expressed as a scale mixture of uniforms (SMU) distribution which facilitates model implementation and detection of outliers by using mixing parameters. Different models for the mean function, including the log-ANOVA, log-ANCOVA, state space and threshold models, are adopted to analyze real loss reserves data. Finally, the best model is selected according to the deviance information criterion (DIC).Bayesian approach; state space model; threshold model; scale mixtures of uniform distribution; device information criterion

Новый способ определения симметричных составляющих трехфазного напряжения

Стаття присвячена цифровому визначенню трифазних показників якості електроенергії — коефіцієнта асиметрії по зворотній послідовності, відхилення і коливання напруги основної частоти. Ці показники характеризуються напругою зворотної (НЗП) і прямої (НПП) послідовності основної частоти. Для визначення НЗП, після аналого-цифрового перетворення з підстроюванням частоти виміру миттєвих значень міжфазної напруги, можна скористатися двома лінійними операціями — виділенням міжфазної напруги основної частоти і виділенням вимірюваної послідовності. Традиційний підхід визначення НЗП використовує саме таку послідовність виконання операцій. При цьому вимоги до точності виділення міжфазної напруги основної частоти дуже високі. В отриманих кодах міжфазної напруги домінуючою і неінформативною є НПП основної частоти. Далі за досить складним алгоритмом з багаторозрядними обчисленнями отримують НЗП основної частоти. Тому для визначення НЗП основної частоти пропонується після аналого-цифрового перетворення спочатку послабити домінуючу і неінформативну НПП, використовуючи складання зі зрушенням кодів миттєвих значень міжфазних напруг. При цьому спрощується алгоритм, у 20—50 разів знижуються вимоги до точності подальшого виділення напруги основної частоти, практично зникають НПП основної частоти і вищих гармонік, НЗП основної частоти збільшується в 3 рази порівняно з вмістом її у міжфазній напрузі. Далі виділяється НЗП основної частоти. Пропонований спосіб визначення напруги симетричних складових характеризується простотою і підвищеною точністю.This article concerns the digital determination of three-phase quality indexes of electric power — coefficient of asymmetry on a negative sequence, rejection and oscillation of fundamental frequency voltage. These indexes are characterized by voltages of negative (VNS) and direct (VDS) sequences of fundamental frequency. For determination of VNS (after analog-digital transformation with tuning of frequency of measuring of instantaneous values of linear voltages) it is possible to take advantage of two linear operations — selection of linear voltages of fundamental frequency and selection of measurable sequence. Traditional approach of VNS measuring uses just the same sequence of implementation of operations. Thus, accuracy requirements of selection of linear voltages of fundamental frequency are very high. And in obtained codes of linear voltages codes of VDS of fundamental frequency are dominant and inconclusive. Fundamental frequency is obtained further using complicated algorithm with the multi-bits calculations. Crushing down dominant and inconclusive VNS using addition of codes of instantaneous values of linear voltages after analog-digital transformation is proposed for determination of VNS of fundamental frequency. An algorithm is thus simplified in 20—50 times, accuracy requirements of subsequent selection of voltage of fundamental frequency decrease, VDS of most ultraharmonics disappears almost completely. VNS of fundamental frequency increases in 3 times as compared to its in linear voltages. VNS of fundamental frequency is further distinguished. The offered method of determination of voltage of symmetric constituents is characterized by simplicity and increased accuracy.Статья посвящена цифровому определению трехфазных показателей качества электроэнергии — коэффициента асимметрии по обратной последовательности, отклонения и колебания напряжения основной частоты. Эти показатели характеризуются напряжением обратной (НОП) и прямой (НПП) последовательности основной частоты. Для определения НОП, после аналого-цифрового преобразования с подстраиванием частоты измерения мгновенных значений межфазного напряжения, можно воспользоваться двумя линейными операциями: выделением межфазного напряжения основной частоты и выделением измеряемой последовательности. Традиционный подход определения НОП использует именно такую последовательность выполнения операций. При этом требования к точности выделения межфазного напряжения основной частоты очень высоки. В полученных кодах межфазного напряжения доминирующей и неинформативной является НПП основной частоты. Далее по достаточно сложному алгоритму с многоразрядными вычислениями получают НОП основной частоты. Поэтому для определения НОП основной частоты предлагается после аналого-цифрового преобразования сначала ослабить доминирующую и неинформативную НПП, используя сложение со сдвигом кодов мгновенных значений межфазных напряжений. При этом упрощается алгоритм, в 20—50 раз снижаются требования к точности последующего выделения напряжения основной частоты, практически исчезают НПП основной частоты и большинства высших гармоник, НОП основной частоты увеличивается в 3 раза по сравнению с ним в межфазных напряжениях. Дальше выделяется НОП основной частоты. Предлагаемый способ определения напряжения симметричных составляющих характеризуется простотой и повышенной точностью

Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations

The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equal the configuration obtained from the spectroscopic term within the independent-electron approximation. It was shown that use of the latter configuration can prevent the energy-minimization process from converging to the global minimum, e.g. in lanthanides. The spin values calculated ab-initio fit the experiment for most atoms and are almost unaffected by the choice of the xc-functional. Among the systems with incorrectly obtained spin there exist some cases (e.g. V, Pt) for which the result is found to be stable with respect to small variations in the xc-approximation. These findings suggest a necessity for a significant modification of the exchange-correlation functional, probably of a non-local nature, to accurately describe such systems. PACS numbers: 31.15.