Vibrational analysis of L-serine using the density functional theory

In this paper, we present a computational study of L-serine using ab initio molecular dynamics simulation based on density functional theory (DFT) within the ultrasoft pseudopotentials and generalized-gradient approximation. Taking into account the intermolecular interactions, we can indeed simulate the features of the experimental results very well for L-serine zwitterions in its solid state. The vibrational spectrum of L-serine performed by DFT was in excellent agreement with our previous inelastic incoherent neutron scattering spectra measured at 20K for L-serine in the 10--200meV region on HET spectrometers at ISIS, Rutherford Appleton Laboratory.     

On the density functional theory

Based on the theoretical analysis of the Kohn Nobel lecture, three important analytical observations regarding the fundamental statements of the density functional theory are presented. It is also noted that the Kohn-Sham equation formally coincides with the Hartree-Fock-Slater equation: both equations have a single-particle character and differ from each other only by additions to the Hartree potential.     

特丁基对苯二酚的光谱及密度泛函研究

特丁基对苯二酚是重要的食品抗氧化剂.理论上,基于密度泛函理论,采用B3LYP泛函及6-311G(d,p)基组在气相环境下优化分子的结构并进行频率计算.在此基础上,基于含时密度泛函理论,选用SMD(solvation model based on density)溶剂模型,利用B3LYP泛函并结合def2-TZVP基组计...     

Kinetic theory of photon density waves

A kinetic equation is obtained for the modulated intensity of multiply scattered light, which generalizes the known Bethe-Salpeter equation. An asymptotic solution is found in the P ₁ approximation, which takes into account the anisotropy of single scattering within the average cosine of the scattering angle. The parameters of the photon density wave are calculated from this solution. It is shown that the relative phase shift and modulation degree calculated for modulation frequencies exceeding several gigahertz noticeably differ from the values predicted by the radiation transfer equation.     

Nuclear density functional theory

An understanding of atomic nuclei is crucial for a complete nuclear theory, for the nuclear astrophysics, for performing new experimental tasks, and for various other applications. Within a density functional theory, the total binding energy of the nucleus is given by a functional of the nuclear density matrices and their derivatives. The variation of the energy density functional with respect to particle and pairing densities leads to the Hartree-Fock-Bogoliubov equations. The “Universal Nuclear Energy Density Functional” (UNEDF) SciDAC project to develop and optimize the energy density functional for atomic nuclei using state-of-the-art computational infrastructure, is briefly described. The ultimate goal is to replace current phenomenological models of the nucleus with a well-founded microscopic theory with minimal uncertainties, capable of describing nuclear data and extrapolating to unknown regions.     

Improving band gap prediction in density functional theory from molecules to solids

A novel nonempirical scaling correction method is developed to tackle the challenge of band gap prediction in density functional theory. For finite systems the scaling correction largely restores the straight-line behavior of electronic energy at fractional electron numbers. The scaling correction can be generally applied to a variety of mainstream density functional approximations, leading to significant improvement in the band gap prediction. In particular, the scaled version of a modified local density approximation predicts band gaps with an accuracy consistent for systems of all sizes, ranging from atoms and molecules to solids. The scaled modified local density approximation thus provides a useful tool to quantitatively characterize the size-dependent effect on the energy gaps of nanostructures.     

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.     

Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate exchange-correlation functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large and bulk systems. Functionals whose energy is convex for fractional charges such as the local density approximation display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an apparent paradox and identifies the physical nature of the error to be addressed to obtain accurate band gaps from density functional theory.     

基于密度泛函理论的单层氢化石墨烯特性分析

本文采用密度泛函理论的第一性原理方法,研究了不同尺寸H-graphene的稳定性、HOMO-LU-MO能隙以及电子激发态.研究结果表明,对于C_(16)H_(10)、C_(30)H_(14)、C_(48)H_(18)、C_(70)H_(22)、C_(96)H_(26)、C_(126)H_(30)计算的比结合能,C_(126)H_(30)相比C_(16)H_(10)的比结合能增长23.9%,且比结合能随着H-graphene尺寸扩大而增加,意味着稳定性不断提高.通过对HOMO-LUMO能隙分析发现,在较小尺寸的H-graphene中,由于量子效应起主要作用,因此出现了较大的HOMO-LUMO能隙,且随着H-graphene团簇尺寸的增加,能隙逐渐缩小可以看出,对于无限大的H-graphene团簇中,HOMO-LUMO能隙无限趋近于零(相当于零带隙),其电子性质与纯石墨烯相似.通过分析C_(16)H_(10)、C_(30)H_(14)、C_(48)H_(18)、C_(70)H_(22)激发态以及了吸收光谱,发现随着尺寸的扩大,吸收光谱发生红移,为石墨烯在电子器件领域的应用提供理论基础.     

Developments in excited-state density functional theory

This article discusses the reasons behind the apparent lack of success of density functional theory (DFT), during the past three decades, with excited states of many-electron systems. It describes various variational and non-variational approaches developed so far for dealing with this problem. Those include Theophilou’s equiensemble approach, extended to unequally weighted ensembles by Gross et al., Fritsche’s wavefunction partitioning approach, local scaling transformation theory by Kryachko et al., the work-function formalism developed by Harbola and Sahni, etc. Through intimate connections between time-dependence and excited states, under a perturbation, various time-dependent (TD) DFT approaches to excited states, e.g., a quantum fluid dynamical approach, a TD density-functional response theory and a TD optimized effective potential approach, are also reviewed.     

Memory in time-dependent density functional theory

Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all initial-state dependence is a dependence on a pseudo-prehistory, providing a route to excited-state densities from time-dependent density functional theory.     

Derivative discontinuities in density functional theory

Fifty years after the original formulation of density functional theory (DFT), subtle consequences of the mathematical mappings underlying its formalism continue to merit new views. In this article, we discuss the origin, the importance, and the challenges associated with finding the derivative discontinuity of the exchange-correlation (XC) energy of DFT at integer–electron numbers. We show how even the energy of a quantum electron gas with finite volume and number of electrons displays such derivative discontinuities, but continuous density functional approximations to the XC functional miss them entirely. We discuss some of the practical problems that arise due to this lack of derivative discontinuities in standard functionals, and explain new ways to recover them.     

Quantal density functional theory of excited states

We explain by quantal density functional theory the physics of mapping from any bound nondegenerate excited state of Schr?dinger theory to an S system of noninteracting fermions with equivalent density and energy. The S system may be in a ground or excited state. In either case, the highest occupied eigenvalue is the negative of the ionization potential. We demonstrate this physics with examples. The theory further provides a new framework for calculations of atomic excited states including multiplet structure.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

Single-particle energies and density of states in density functional theory

Time-dependent density functional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn– Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange– correlation functional has no dependence on the superfluid density. The Kohn– Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of density functionals specifically targeted at accurate single-particle eigenvalues and bandgaps.     

Development of electron-proton density functionals for multicomponent density functional theory

We present a strategy for the development of electron-proton density functionals in multicomponent density functional theory, treating electrons and selected nuclei quantum mechanically without the Born-Oppenheimer approximation. An electron-proton functional is derived using an explicitly correlated electron-proton pair density. This functional provides accurate hydrogen nuclear densities, thereby enabling reliable calculations of molecular properties. This approach is potentially applicable to relatively large molecular systems with key hydrogen nuclei treated quantum mechanically.     

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.