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.     

Effect of boron and nitrogen co-doping on CNT's electrical properties: Density functional theory

In this work, we have theoretically studied the changes in electrical properties of three different geometrical structures of carbon nanotubes upon co-doping them with boron and nitrogen atoms. We applied different doping mechanisms to study band structure variations in the doped structures. Doping carbon nanotubes with different atoms will create new band levels in the band structure and as a consequence, a shift in the Fermi level occurs. Whereas, filling up the lowest conduction/ upper valence bands created an up/ downshift in the Fermi level. Moreover, dopants concentration and dopants position play a critical rule in defining the number of new band levels. These new band levels in the band gap region represented as new peaks appeared in the density of states. These new bands are solely attributed to co-doping carbon nanotubes with boron and nitrogen atoms.     

A novel bionanosensor for dopamine detection based on titanium doped single walled boron nitride nanotube: Density functional theory

The development of new generation of nanobiosensors and other nanomedicine devices are urgently needed. In this study, we used computer simulations to study the interaction of titanium doped boron nitride nanotubes with dopamine under vacuum and solvent conditions. Our results revealed that the interaction between dopamine and boron nitride nanotube can be tuned via Ti-atom doping, which in turn facilitates the development of new generation of nanomedicine devices. Despite the medium conditions, it was found that the Ti-doped configurations are more stable and more conductive compared to the un-doped configurations. The stability of the investigated configurations under solvent conditions provides an opportunity to investigate real cases in human body. Moreover, it was found that the energy gap of the investigated structures is crucially dependent on the dopamine orientation with respect to the doped nanotube. Our results are thus expected to be very useful for the development of the next generation of nanobiosensors.     

含空位二维六角氮化硼电子和磁性质的密度泛函研究

基于密度泛函理论的第一性原理计算, 研究了含B原子空位(V_B), N原子空位(V_N), 以及含B–N键空位 (V_B+N)缺陷的二维氮化硼(h-BN)的电子和磁性质. 在微观结构上, V_B体系表现为在空位附近的N原子重构成等腰三角形, V_N体系靠近空穴的B 原子形成等边三角形, V_B+N体系靠近空穴处的B和N原子在h-BN平面上重构为梯形. 三种空位缺陷都使h-BN的带隙类型从直接带隙转变为间接带隙. V_B体系的总磁矩为1.0 μ_B, 磁矩全部由N原子贡献. 其中空穴周围的三个N原子磁矩方向不完全一致, 存在着铁磁性和反铁磁性两种耦合方式. 对于V_N 体系, 整个晶胞内的总磁矩也为1.0 μ_B, 磁矩在空穴周围区域呈现一定的分布. 关键词： 二维h-BN 空位 电子结构 磁性     

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.     

Density functional theory for general hard-core lattice gases

We put forward a general procedure to obtain an approximate free-energy density functional for any hard-core lattice gas, regardless of the shape of the particles, the underlying lattice, or the dimension of the system. The procedure is conceptually very simple and recovers effortlessly previous results for some particular systems. Also, the obtained density functionals belong to the class of fundamental measure functionals and, therefore, are always consistent through dimensional reduction. We discuss possible extensions of this method to account for attractive lattice models.     

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.     

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 of freezing of a system of highly elongated ellipsoidal oligomer solutions

We have used the density functional theory of freezing to study the liquid crystalline phase behavior of a system of highly elongated ellipsoidal conjugated oligomers dispersed in three different solvents namely chloroform, toluene and their equimolar mixture. The molecules are assumed to interact via solvent-implicit coarse-grained Gay–Berne potential. Pair correlation functions needed as input in the density functional theory have been calculated using the Percus–Yevick (PY) integral equation theory. Considering the isotropic and nematic phases, we have calculated the isotropic–nematic phase transition parameters and presented the temperature–density and pressure–temperature phase diagrams. Different solvent conditions are found not only to affect the transition parameters but also determine the capability of oligomers to form nematic phase in various thermodynamic conditions. In principle, our results are verifiable through computer simulations.     

On symmetry preserving and symmetry broken bright,dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation

We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schrödinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT) method. We present explicit one and two bright soliton solutions and show that they exhibit stable structures only when we combine the field and parity transformed complex conjugate field. Further, we derive two dark/antidark soliton solution with the help of DT method. Unlike the bright soliton case, dark/antidark soliton solution exhibits stable structure for the field and the parity transformed conjugate field separately. In the dark/antidark soliton solution case we observe a contrasting behaviour between the envelope of the field and parity transformed complex conjugate envelope of the field. For a particular parametric choice, we get dark (antidark) soliton for the field while the parity transformed complex conjugate field exhibits antidark (dark) soliton. Due to this surprising result, both the field and PT transformed complex conjugate field exhibit sixteen different combinations of collision scenario. We classify the parametric regions of dark and antidark solitons in both the field and parity transformed complex conjugate field by carrying out relevant asymptotic analysis. Further we present 2N-dark/antidark soliton solution formula and demonstrate that this solution may have $2^{2N}\times 2^{2N}$ combinations of collisions.     

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.     

Laser welding of aluminium lightweight materials: problems,solutions, readiness for application

Using high-power CO₂ and Nd:YAG lasers of high beam quality, high process efficiencies and excellent seam qualities are achieved. A particular method for obtaining almost pore-free weld seams without blowholes is the combining of the beams of two CO₂ lasers. Without the need for filler material, crack-free welds can be produced in sheets of hot-crack susceptible, precipitation hardened alloys up to a welding speed of 5–7m min^-1 for full penetration and up to 3–4m min^-1 for partial penetration. In contrast, AlMg alloys containing more than 2.5wt% Mg and AlSi cast alloys are insensitive to hot-cracking even at high processing speeds. Laser welds possess much better static mechanical properties than gas tungsten arc (GTA) or gas metal arc (GMA) butt welds. For the alloys AlMgSi1 and AlMg5Mn the maximum static strength which can be achieved in laser welding is determined by the alloy type, i.e. the hardening mechanism and the heat-treated condition. Laser butt welded car body sheets without filler material exhibit the same load-bearing capacity under dynamical load as GMA welds with filler material. The latest research work has demonstrated that high-quality tailored blanks with good mechanical properties can also be made out of different aluminium plates.     

Ge(SiO2)n团簇结构和电子性质的密度泛函理论研究

采用密度泛函理论中的广义梯度近似(GGA)对Ge(SiO2)n (n = 1—7)团簇的几何构型进行优化,并对能量、频率和电子性质进行了计算。 结果表明,Ge(SiO2)n的最低能量结构是在(SiO2)n端位O原子以及近邻端位O原子的Si原子上吸附一个Ge原子优化得到;随着锗原子数的增加,增加的锗原子易与原来的锗原子形成锗团簇。掺杂锗原子后团簇的能隙比(SiO2)n团簇的能隙小,当多个Ge原子掺杂到(SiO2)3团簇时,其能隙随着Ge原子个数的增加出现了振荡,Gem(SiO2)3的能隙从可见光区到近红外光区变化。二阶能量差分、分裂能表明Ge(SiO2)2和Ge(SiO2)5团簇是稳定的。     

Accurate non-relativistic density functional theory predictions for 77Se NMR shielding parameters

A reoptimized density functional theory (DFT) hybrid functional gives orbitals and energies which when substituted into the uncoupled generalized gradient approximation (GGA) sum-over-states expressions gives NMR shielding constants of high accuracy for first- and second-row nuclei. This procedure is validated further and its performance compared against well established exchange-correlation (XC) functionals for the prediction of the third-row ⁷⁷Se NMR shielding constants, in a series of challenging molecules where both accurate theoretical and experimental data are available. The shielding parameters obtained from this new mixed hybrid GGA scheme provide a significant improvement over conventional XC functionals. and are competitive with the benchmark coupled-cluster singles and doubles (CCSD) methods. From these results together with previous studies it is now apparent that this new GGA shielding scheme provides high accuracy NMR shielding constants for first-, second-and third-row atoms (excluding transition-metal atoms) even in molecules exhibiting large correlation effects.     

Density functional theory study of structural stability for gas hydrate

Using the first-principles method based on the density functional theory(DFT),the structures and electronic properties of different gas hydrates(CO_2,CO,CH_4,and H_2) are investigated within the generalized gradient approximation.The structural stability of methane hydrate is studied in this paper.The results show that the carbon dioxide hydrate is more stable than the other three gas hydrates and its binding energy is-2.36 e V,and that the hydrogen hydrate is less stable and the binding energy is-0.36 e V.Water cages experience repulsion from inner gas molecules,which makes the hydrate structure more stable.Comparing the electronic properties of two kinds of water cages,the energy region of the hydrate with methane is low and the peak is close to the left,indicating that the existence of methane increases the stability of the hydrate structure.Comparing the methane molecule in water cages and a single methane molecule,the energy of electron distribution area of the former is low,showing that the filling of methane enhances the stability of hydrate structure.     

Density functional theory for dielectric properties of warm dense matter

ABSTRACT

Density functional theory (DFT) is applied for the calculation of the dielectric function (DF), reflectivity, conductivity, plasma frequency and effective free electron density of warm dense matter (WDM). Shock-compressed xenon plasma and warm dense hydrogen are considered. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the DF. The real part of the DF is calculated by means of the Kramers–Kronig transformation. Sum rule within the framework of the DFT is used for determination of the plasma frequency and effective free electron density. Corrections to the reflectivity are considered, which allow for the finite width of the transient layer (wave front) at the WDM border.     

Density functional theory for Baxter's sticky hard spheres in confinement

It has recently been shown that a free energy for Baxter's sticky hard-sphere fluid is uniquely defined within the framework of fundamental measure theory (FMT) for the inhomogeneous hard-sphere fluid, provided that it obeys scaled-particle theory and the Percus-Yevick (PY) result for the direct correlation function [H. Hansen-Goos and J. S. Wettlaufer, J. Chem. Phys. 134, 014506 (2011)]. Here, combining FMT weighted densities with a new vectorial weighted density, we regularize the divergences of the associated strongly confined limit. The free energy that emerges is exact in the zero-dimensional limit, leaves the underlying equation of state unaffected, and yields a direct correlation function distinct from that of PY. Comparison with simulation data for both the bulk pair-correlation function and the density profiles in confinement shows that the new theory is significantly more accurate than the PY-based results.     

Interaction between methanol and single-walled carbon nanotubes: Density functional theory study

Density functional calculations have been performed to investigate the dependence of methanol interaction with the side walls of single-walled carbon nanotubes (SWCNTs) on the nanotube's type, curvature and chirality. The author's results show that methanol prefers to be physically adsorbed on semiconducting CNTs in comparison with the metallic one. It was found that the binding energy of methanol is increased for adsorption on larger-diameter nanotubes. Furthermore, we find that when a methanol molecule was adsorbed on higher chiral angle nanotubes the binding energy was increased. The study of the electronic structures and Mulliken analysis indicate that the methanol and CNT are interacting rather weakly, consistent with recent experimental observation.     

Surfaces: a playground for physics with broken symmetry in reduced dimensionality

With our crystal ball in front of us, we attempt to articulate the opportunities and challenges for a surface physicist in the beginning of the new millennium. The challenge is quite clear: to use the unique environment of a surface or interface to do fascinating physics, while taking full advantage of the skills the community has developed over the last 30 years. The opportunities appear to be endless! In this age of Nanotechnology where the promise is to shape the world atom by atom, leading to the next industrial revolution [Nanotechnology: shaping the world atom by atom, National Science and Technology Council, Committee on Technology, 1999], surface science should be at the very forefront of both technological and scientific advances. The smaller objects become, the more important their surfaces become. In this article we focus on the role of a surface physicist in the emergence of nanoscale collective phenomena in complex materials.     

塞来昔布的密度泛函理论计算及光谱分析

塞来昔布(Celecoxib, CXB)是COX-2的高选择性抑制剂,经过20年的发展已经成为世界范围内使用最为广泛的一类处方药.本文基于密度泛函理论,使用B3LYP泛函,6-311++G(d, p)基组进行结构优化.在此工作上对该药物分子的结构、红外光谱、拉曼光谱、分子前线轨道、静电势和激发态性质做了一系列的研究.结果表明：CXB分子是一个稳定的非平面扭曲结构,此结构使得该药物分子在COX-2上的疏水通道中可以迅速通过,从而形成了一个可与苯磺酰胺片段结合的结合腔.对化合物进行频率计算,分别得到红外光谱和拉曼光谱,与实验采集的数据进行对比,呈现出较好的一致性.对分子的基态进行前线轨道和静电势的分析,磺酰胺基与COX-2易形成氢键作用.在CXB分子的激发态研究中发现,CXB分子的激发态性质主要由第1激发态、第3激发态和第6激发态共同决定.这为理解CXB的作用机理提供了重要的信息,也为后期扩展CXB衍生物提供了理论基础.