Perturbation theory of liquid helium-4 at zero temperature

The formal pertubation theory of a Bose liquid, due to Beliaev, Hugenholtz, Pines, Gavoret, and Nozieres, is carefully examined in an effort to surmount the limitations of the Brueckner-Sawada theory of liquid He⁴. In order to make the formal results as directly relevant as possible for Brueckner-theoretic calculations, all of the basic results are rederived by time-independent and number-conserving methods, starting from a linked-cluster expansion for bosons which is the exact analog of the Goldstone expansion for normal fermion systems. The analogy between the ground state and collective excitations of liquid He⁴, and those of a normal Fermi liquid, is emphasized and explored in detail. Several aspects of the difficult problem of convergence are discussed. A specific partial summation procedure is recommended, the compact-cluster scheme, to deal with the short-range correlations within clusters of more than two particles. It is then argued that the very strong depletion of the condensate would lead to an extremely slow convergence for the most obvious class of approximations, and a remedy for this difficulty is proposed. The possibility of establishing a fairly detailed correspondence between the perturbation-theoretic wavefunction and the Jastrow wavefunction, including Feenberg-CBF extensions of the latter, is also pointed out.     

Density functional theory for chiral nematic liquid crystals

ABSTRACT

In this note, the density functional theory for chiral nematic liquid crystals is expressed in terms of rotational invariant expansion coefficients of the pair-excluded area at fixed separation. This modification from the standard approach, without making any additional assumptions, yields a more efficient procedure for minimising the free energy, as well as providing insight into the origins of the effect away from the long-pitch limit.     

Density functional theory for a model of nonuniform liquid metal in partially ionized states

Summary The problem of the electronic, ionic and atomic density profiles in a nonuniform liquid metal which can locally exist in partially ionized states is examined using the density functional formalism. Ions and electrons are allowed to bind into atoms through a ?reaction? governed by the mass action law. Formally exact equations for the density profiles are given in terms of the inverse response matrix of the nonuniform system, which consists of two terms: the first corresponding to to a mixture of ions, electrons and structureless atoms and the other to the atomic internal degrees of freedom. Approximate schemes are proposed for both contributions, stressing, in partieular, i) how ionization of the atoms arises with increasing density and the relation with Mott’s criterion for the metal-insulator transition, and ii) the usefulness of a weak-coupling assumption for interspecies correlations. This formalism used together with properly parametrized trial functions for the density profiles should be particularly useful for studying the liquid-vapour interface of alkali metals.

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Riassunto Il lavoro usa il formalismo del funzionale di densità per discutere la determinazione dei profili di densità in un fluido non omogeneo che può trovarsi localmente in stati di ionizzazione parziale. Con riferimento specifico ai metalli alcalini, la formazione di atomi per legame di ioni ed electtroni è descritta come una ?reazione? governata dalla legge di azione di massa. Le condizioni di equilibrio microscopico del fluido sono espresse tramite una matrice di risposta in cui appaiono due contributi, associati rispettivamente ai gradi di libertà interni degli atomi e ad una miscela di tre specie di particelle senza struttura interna. Si propongono quindi schemi approssimati per il calcolo di questi due contributi, con attenzione particolare all’uso di teorie perturbative e alla relazione tra grado di ionizzazione locale e densità localle, in connessione col criterio di Mott per la transizione isolante-metallo. Il formalismo proposto è in particolare appropriato per lo studio dell’interfaccia liquido-vapore in metalli alcalini.

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Резюме Используя функционала плотности, исследуется проблема профилей электронной, ионной и атомой ллотностей В неоднодном зидком металле, которий мозет локалщно существоватщ в частично иониэированных состояних. Ионы и электроны могут şвяэыватщся в атомщ череэ ?реакцию, определяемую эаконом дейşтвуюших масс. Приводятся формалщно точные уравнения для профнлеи плотности в термина⇆ обратной матрици отклика для неоднородной системы, которая состоит иэ двух чуленов: первий соответствует ссмеси ионов, электронов и бесстрктурных атмов и второй член соответствует атомным внутренним степеням свобды. Предлагаются приближенные схемы для обоых вкладов, обрашая особое бнмание, в частности, 1) как иониэация атомов воэликает бри увеличени влотности, на свяэы с критерием Мота для берехода ?металл-иеолятор?, и 2) на полеэносты предположения слабой свяэи для межвидовых кореляций. Предложенный Формалиэм, исполыеовалный вместе с параметриэованными пробными функциями для профилей плотнорти, окаэываетця оробенне полеэным для исследования грраницы ?жидкостъ-пар? в шелочлых металлах.

     

Luttinger liquid in the core of a screw dislocation in helium-4

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp 4He crystal features a superfluid (at T-->0) core. This is the first example of a regular quasi-one-dimensional supersolid--the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid H2 is insulating.     

Density functional theory of fermion condensation

A density functional formulation of the fermion condensation is presented. It is demonstrated that the standard Kohn-Sham scheme is not valid beyond the fermion condensation phase transition since the functional starts to depend on the quasiparticle density matrix. Our consideration also furnishes an opportunity to calculate the real single particle excitation spectra of superconducting systems within the density functional theory.     

Density functional theory of heterogeneous crystallization

This mini-review summarizes recent progress in describing heterogeneous crystallization processes and microstructure formation within microscopic classical density functional theory (DFT). After outlining the basic features of DFT, we discuss several applications ranging from the structure and thermodynamics of fluid-crystal interfaces for hard sphere and Yukawa systems to dynamical phenomena such as crystal growth on structured substrates and induced by externally imposed seeds.     

Density functional theory: Foundations reviewed

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N$N$-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N$N$-representability conditions on the 2-RDM have recently been attained.     

Si_4N_4团簇结构与性质的密度泛函理论研究(英文)

用密度泛函理论(DFT)中的杂化密度泛函B3LYP方法,在6-31G(d)的水平上对Si4N4团簇的可能结构进行了几何结构优化和电子结构计算,得到了可能的17个异构体.Si4N4团簇的最稳定结构是有8个Si-N键的平面结构.用自然键轨道(NBO)方法分析了成键性质.计算结果表明,Si-N键中Si原子向N原子有较大的电荷转移,因此Si-N原子间有较强的电相互作用;最强的IR和Raman谱峰分别位于1387.64cm-1和1415.05cm-1处;并计算了Si4N4团簇的最稳定结构的极化率和超极化率.     

Density functional theory of single-file classical fluids

An overcomplete density functional formalism is derived to represent the thermal behaviour of confined classical fluids under single-file conditions. Strictly one-dimensional hard rod systems are reanalysed from this viewpoint, and the context is then broadened to encompass hard spheres in cylindrical enclosures. Applications to non-single-file conditions, modulated enclosures, and confined polymers are mentioned.     

Density functional theory study of doping effects in monoclinic clinobisvanite BiVO4

The doping effects of several transition metal impurities for monoclinic BiVO₄ are studied by DFT calculations. The results indicated that transition metal doping could reduce the effective mass of holes on the top of valence band, except Zr doping. In particular, we found the “e” states of impurities have significant influence on the photophysical properties of BiV_1 − xM_xO₄ under visible-light irradiation.     

HCOOH在Pd-Fe(111)(nPd:nFe=1:1)表面吸附的密度泛函理论研究

采用密度泛函理论与周期性平板模型相结合的方法,对HCOOH在Pd(111)表面top, fcc, hcp, bridge 四个吸附位和Pd-Fe(111)表面Pd-top, Fe-top, PdPd-bridge, PdFe-bridge, FeFe-bridge, Pd2Fe-hcp, PdFe2-hcp, Pd2Fe –fcc, PdFe2-fcc等9个吸附位的13种吸附模型进行了能量计算、构型优化,得到了HCOOH较有利的吸附位;并对清洁表面进行能带分析。结果表明：掺杂Fe后,Pd催化剂对HCOOH催化活性增强;HCOOH在Pd(111)表面的最稳定吸附位fcc的吸附能是-41.8kJ•mol-1,在Pd-Fe(111)表面的最稳定吸附位Pd2Fe-hcp的吸附能是-126.5 kJ•mol-1,而且HCOOH在金属表面属于化学吸附。     

HCOOH在Pd-Fe(111)(nPd∶nFe=1∶1)表面吸附的密度泛函理论研究简

采用密度泛函理论与周期性平板模型相结合的方法,对HCOOH在Pd(111)表面top,fcc,hcp,bridge四个吸附位和Pd-Fe(111)表面Pd-top,Fe-top,PdPd-bridge,PdFe-bridge,FeFe-bridge,Pd2Fehcp,PdFe2-hcp,Pd2Fe-fcc,PdFe2-fcc等9个吸附位的13种吸附模型进行了能量计算、构型优化,得到了HCOOH较有利的吸附位;并对清洁表面进行能带分析.结果表明:掺杂Fe后,Pd催化剂对HCOOH催化活性增强;HCOOH在Pd(111)表面的最稳定吸附位fcc的吸附能是-41.8kJ·mol-1,在Pd-Fe(111)表面的最稳定吸附位Pd2Fe-hcp的吸附能是-126.5kJ·mol-1,而且HCOOH在金属表面属于化学吸附.     

Density functional theory for reactions of astrophysical interest

For astrophysical processes nuclear reactions close to the particle emission threshold are of particular importance. As representative examples we investigate pairing resonances and new low-energy multipole modes in light and heavy exotic nuclei with a large charge asymmetry. As a common theoretical background, density functional theory and Fermi Liquid Theory are used. In particular, we consider the spectroscopy particle unstable systems, carrying the properties of open quantum systems. Results for the continuum spectroscopy of ¹⁰Li, the neutron-rich carbon isotopes, and the electromagnetic response of Sn-isotopes ¹³⁸Ba are presented.     

O_2在FeN_4掺杂碳纳米管上氢化特性的密度泛函理论研究

因其速率快、稳定性高,非金属N与金属共掺杂的碳材料作为新型高效ORR催化剂而引起了人们的广泛关注.采用包含色散力校正的密度泛函理论方法系统地研究了氧分子在FeN_4掺杂的碳纳米管上的吸附、氢化特性.结果表明:(1)O_2倾向于以end-on模式吸附在Fe顶位,O-O键与衬底表面成一定角度,并指向五元环,对应的吸附能为1.62 e V.(2)O_2在FeN_4-CNTs上更倾向于直接氢化为OOH,然后解离为O+OH,整个路径的限速步为OOH的解离,对应的势垒为1.19 eV.     

Density functional resonance theory of unbound electronic systems

Density functional resonance theory (DFRT) is a complex-scaled version of ground-state density functional theory (DFT) that allows one to calculate the in-principle exact resonance energies and lifetimes of metastable anions. In this formalism, the energy and lifetime of the lowest-energy resonance of unbound systems is encoded into a complex "density" that can be obtained via complex-coordinate scaling. This complex density is used as the primary variable in a DFRT calculation, just as the ground-state density would be used as the primary variable in DFT. As in DFT, there exists a mapping of the N-electron interacting system to a Kohn-Sham system of N noninteracting particles. This mapping facilitates self-consistent calculations with an initial guess for the complex density, as illustrated with an exactly solvable model system.     

Computational studies of CO and CO: Density functional theory and time-dependent density functional theory

Potential energy curves, equilibrium interatomic distances, term energies and harmonic vibration frequencies for the 16 lowest states of neutral carbon monoxide and the six lowest states of singly ionized carbon monoxide are calculated by density functional theory (DFT) and linear-response time-dependent density functional (LR-TDDFT) theory. The results are compared with experimental data. The two theories, DFT and LR-TDDFT, are described briefly.     

CH4 dissociation on Ni surfaces: Density functional theory study

CH₄ dissociation on Ni surfaces, which is important in CH₄ reforming reactions, was discussed by using density functional theory. It was found that the CH_x species were changed to anions after chemisorption. The site preference of CH_x (x = 0-3) species on Ni(1 1 1), Ni(1 0 0) and Ni(1 1 0) was located on the basis of the computed chemisorption energies. Ni(1 0 0) is the most preferred surface for CH₄ dissociation, compared to Ni(1 1 0) and the widely investigated Ni(1 1 1).