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.     

Local vertex corrections from exchange-correlation kernels with a discontinuity

The fundamental gap of an interacting many-electron system is given by the sum of the single-particle Kohn-Sham gap and the derivative discontinuity. The latter can be generated by advanced approximations to the exchange-correlation (XC) energy and is the key quantity to capture strong correlation with density functional theory (DFT). In this work we derive an expression for the derivative discontinuity in terms of the XC kernel of time-dependent density functional theory and demonstrate the crucial role of a discontinuity in the XC kernel itself. By relating approximate XC kernels to approximate local vertex corrections we then generate beyond-GW self-energies that include a discontinuity in the local vertex function. The quantitative importance of this result is illustrated with a numerical study of the local exchange vertex on model systems.     

Implication of the Electron Exchange-Correlation on Fully Nonlinear Quantum Dust Ion-Acoustic Solitons

We examine the effect of the electron exchange-correlation on weak and arbitrary amplitude quantum dust ion-acoustic(QDIA) solitons.The reduced quantum hydrodynamic(QHD) model is used.Carrying out a fully nonlinear analysis,it is found that the effect of the exchange-correlation on the main quantities for solitary-wave propagation can be quite important.In particular,it may be noted that the arbitrary amplitude QDIA soliton experiences a spreading as the phenomenon of exchange-correlation becomes effective.Furthermore,our results show that the exchange-correlation effects inhibit the formation of the flat-bottomed solitons and do not favor their emergence.It turns out that exchangecorrelation and quantum diffraction may act concurrently to set up the conditions for the existence of the QDIA solitary waves.Our results complement and provide new insight into our previously published work on this problem.     

Weak interactions between tetraphenylporphyrin dimers: A Wannier orbitals study

We investigate the weak interactions taking place in the tetraphenylporphyrin dimers by using Wannier orbitals and DFT. The Van der Waals interaction energies for various geometric configurations of the dimers are then compared to the differences between the total DFT energies of dimers and those of sums over the energies of monomers. The comparison allows us to estimate the weight of the Van der Waals contribution to the total interaction energy since the DFT values include all contributions such as weak chemical interaction or Pauli repulsion to the binding energy. We show that the interaction energy computed with vdW-DF-cx exchange-correlation functional is almost identical with the one computed using Wannier orbitals. By analyzing the properties of Wannier orbitals in monomer and dimer structures, we check the fact the Van der Waals energy can be accurately calculated by using only the orbitals corresponding to the single molecule, which is useful from a practical perspective.     

含温有界原子理论体系下电子状态方程不确定度的量化计算

通过含温有界原子模型,给出基于35种交换关联势形式,计算等离子体电子状态方程不确定度的方法.设计一种快速粗估不确定度的方法,并在TF模型中进行检验.以金为例,计算温度从1.0 eV~10 000.0 eV、密度为1.0、10.0、100.0 g·cm^-3的电子总能量、压强、离化度的不确定度和拟真值.计算结果可为工程设计提供参考.     

A coupled cluster treatment of intramonomer electron correlation within symmetry-adapted perturbation theory: benchmark calculations and a comparison with a density-functional theory description

Symmetry-adapted perturbation theory (SAPT) with intramonomer electron correlation described by coupled cluster theory limited to single and double excitations was applied to 21 noncovalent complexes in their minimum geometries. The resulting benchmark contributions to the interaction energy were utilized to examine the accuracy of a more approximate variant of the SAPT method, where interacting molecules are described by density functional theory (DFT) with different functionals, like LDA, PBE, B3LYP, PBE0, M05, M05-2X, M06, and M06-2X (in all cases the asymptotic correction for the exchange-correlation functional has been utilized). Average errors for individual energy components of SAPT(DFT) are not larger than 10% for best functionals under study. Among the tested functionals PBE0, M05, and B3LYP should be especially recommended for the SAPT(DFT) approach. The M06 functional gives the largest errors with respect to SAPT(CCSD) and should not be used for describing intramonomer correlation in SAPT.     

Parametric instabilities in quantum plasmas with electron exchange-correlation effects

Parametric instabilities induced by the nonlinear interaction between high frequency quantum Langmuir waves and low frequency quantum ion-acoustic waves in quantum plasmas with the electron exchange-correlation effects are presented.By using the quantum hydrodynamic equations with the electron exchange-correlation correction,we obtain an effective quantum Zaharov model,which is then used to derive the modified dispersion relations and the growth rates of the decay and four-wave instabilities.The influences of the electron exchange-correlation effects and the quantum effects on the existence of quantum Langmuir waves and the parametric instabilities are discussed in detail.It is shown that the electron exchange-correlation effects and quantum effects are strongly coupled.The quantum Langmuir wave can propagate in quantum plasmas only when the electron exchange-correlation effects and the quantum effects satisfy a certain condition.The electron exchange-correlation effects tend to enhance the parametric instabilities,while quantum effects suppress the instabilities.     

The importance of the asymptotic exchange-correlation potential in density functional theory

The importance to density functional theory (DFT) of the integer discontinuity in the exchange-correlation potential is reiterated and further examined. It follows that if generalized gradient approximation (GGA) functional are used, then the asymptotic value of the exchange-correlation potential must be a positive system-dependent constant. Our previously introduced asymptotic correction (AC), which forces the correct behaviour of the potential in the asymptotic region, is further discussed. Three examples are given that demonstrate the importance of the analysis; (i) HOMO eigenvalues lie well above the negative of the ionization energy when GGA functionals are used—this is not detrimental to GGA DFT; (ii) an independent calculation of the GGA asymptotic potentials for some molecules is presented, based on the determination of parametrized GGA functionals; (iii) Rydberg states of He⁺ and H⁺ ₂ are studied, demonstrating that essentially exact Rydberg potential energy curves can be determined if the AC is used, even though the valence curves may be incorrect.     

Density functional theory of transition metal phthalocyanines,II: electronic structure of MnPc and FePc—symmetry and symmetry breaking

We present a two-part systematic density functional theory (DFT) study of the electronic structure of selected transition metal phthalocyanines. We use a semi-local generalized gradient approximation (GGA) functional, as well as several hybrid exchange-correlation functionals, and compare the results to experimental photoemission data. Here, we study the intermediate spin systems MnPc and FePc. We show that DFT calculations of these systems are extremely sensitive to the choice of functional and basis set with respect to the obtained electronic configuration and to symmetry breaking. Interestingly, all simulated spectra are in good agreement with experiment despite the differences in the underlying electronic configurations.     

Calculation of the nonlinear susceptibilities of interacting homogeneous electron gas by the density functional method

The density functional method is used for the calculation of nonlinear susceptibilities of an interacting electron gas. It is shown that this approach leads to the expression for nonlinear susceptibilities which satisfy exactly the strict sum rules derived previously. By using the local densities approximation we obtain the expression for the exchange-correlation contribution in the first non-linear susceptibility of interacting electron gas. It is shown that such a contribution may have a noticeable effect on the binding energy and phonon spectrum of polivalent simple metals.     

交换关联泛函近似方法对Ru催化剂上甲烷和乙烷形成的影响

密度泛函理论作为多相催化研究中的一个强有力工具,常被用于获得催化过程中关键的热力学及动力学参数,如吸附能、反应焓、活化能垒和速率常数等. 理解密度泛函交换关联近似方法对于揭示催化剂的催化性能及机理至关重要. 本文报道了六种不同的交换关联泛函近似方法,包括PBE、RPBE、BEEF+vdW、optB86b+vdW、SCAN和SCAN+rVV10,对金属Ru(0001)和Ru(1011)表面上甲烷和乙烷形成过程中涉及到的中间体的吸附能、反应能和活化能垒的影响. 当基元反应中反应物和产物与表面的配位数不同时,理论计算的反应能大小强烈依赖于交换关联密度泛函的选择. 对于涉及多个基元步骤的总反应,反应能的计算偏差会逐渐累积,从而导致不同的交换关联泛函近似方法之间的巨大差异. 由于不同泛函对反应涉及到的中间体吸附能之间存在差异,交换关联泛函近似方法的选择显著地影响Ru(0001)表面上甲烷、乙烯和乙烷的选择性. 然而,不同泛函近似方法对于Ru(0001) 和Ru(1011)表面上基元反应的能垒以及结构敏感性影响不大. 本工作不仅揭示了交换关联密度泛函近似方法在理论计算研究催化领域的局限性,也强调了选择合适的交换关联泛函方法对于正确评估催化剂活性和选择性的重要性.     

Density functional theory versus quantum Monte Carlo simulations of Fermi gases in the optical-lattice arena

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via density functional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks–Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries.     

Exchange and correlation in inhomogeneous electron systems

An exchange-correlation functional with a nonlocal density dependence is proposed. It fulfills a sum rule stating that the exchange-correlation hole should contain on electron, atom. We have used this functional as well as an earlier proposed approximation to calculate the exchange energy of atoms. The errors in the local density approximation are reduced by an order of magnitude, indicating that these improved functionals should be very useful for more complicated systems.     

The LEDO expansion for diatomic overlap densities: application to the density functional theory of molecules

The limited expansion of differential overlap (LEDO) approach for the expansion of diatomic overlap densities in terms of mono-centre densities is discussed in the context of density functional theory (DFT). It is shown that it leads to a particularly simple construction scheme for major parts of the secular matrix, i.e. the electron-electron interaction and the exchange-correlation potential: using the LEDO expansion coefficients, matrix elements between atomic orbitals located on different centres can be expressed in terms of the corresponding mono-centre elements, thus allowing the reduction of three-centre and four-centre integrals to two-centre integrals. This results in the first DFT method with formal N ² scaling for the construction of the secular matrix, with N being the dimension of the atomic orbital (AO) basis set. Test calculations show that numerical agreement with the results of conventional DFT calculations is excellent.     

Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations

A multiresolution solver for fully numerical linear response calculations of excitation states via the time-dependent Hartree–Fock and density functional theory (TD-HF/DFT) is presented. The linear response method Yanai et al. previously reported [J. Chem. Phys., submitted] was limited to the Tamm–Dancoff approximation and could only use the Hartree–Fock exchange and the local-spin density approximation (LSDA) with a crude asymptotic correction. The present development enables us to perform full TD-HF/DFT calculations employing generalized gradient approximation (GGA) exchange-correlation potentials as well as hybrid ones. The linear response of TD-HF/DFT is computed by means of iteratively solving the coupled integral equations with the Green's functions. In this study, Tozer and Handy's asymptotic correction (AC) is applied to existing DFT exchange-correlations, and is found numerically stable and efficient. Furthermore, the new hybrid exchange-correlation functional CAM-B3LYP, which was recently proposed by Yanai et al. [Chem. Phys. Lett. 393, 51 (2004)], is implemented. The implementation requires a new separated representation of the integral kernel for the Coulomb-attenuated potential. We demonstrate linear response calculations free of basis set error for the excited states of Be, N₂, C₂H₄ and C₆H₆ using LSDA, HCTH, CAM-B3LYP and PBE0 exchange-correlation functionals. The mean absolute errors of the C₆H₆ calculations with HCTH and CAM-B3LYP are 0.12 and 0.18?eV, respectively. The second derivative of exchange-correlation functionals is represented fully numerically at O(N) computation cost.     

Electron exchange-correlation effects on dispersion properties of electrostatic waves in degenerate quantum plasmas

Based on the quantum Magnetohydrodynamic (QMHD) model, the obliquely propagation of electrostatic waves in degenerate magnetized quantum plasmas with electron exchange-correlation effects are theoretically investigated. The modified linear dispersion relations of electrostatic waves are obtained and discussed in some specific cases. The analytical results clearly show that the dispersion properties of the high frequency electron waves (including the Langmuir wave and upper-hybrid wave) and the low frequency ion acoustic wave are modified by the quantum effects together with the electron exchange-correlation effects. The numerical results depict that the Langmuir wave and upper-hybrid wave can be unstable in the presence of the electron exchange-correlation effects, and it is also evidently indicated that the electron exchange-correlation effects can reduce the phase velocity of the waves, especially in the high wave number region. The corresponding results should be of relevance for identifying electrostatic fluctuations which transport in an inhomogeneous and magnetized quantum plasmas.     

One-body potential theory of molecules and solids modified semiempirically for electron correlation

The study of Cordero, March and Alonso (CMA) for four spherical atoms, Be, Ne, Mg and Ar, semiempirically fine-tunes the Hartree-Fock (HF) ground-state electron density by inserting the experimentally determined ionization potentials. The present Letter, first of all, relates this approach to the very recent work of Bartlett ‘towards an exact correlated orbital theory for electrons’. Both methods relax the requirement of standard DFT that a one-body potential shall generate the exact ground-state density, though both work with high quality approximations. Unlike DFT, the CMA theory uses a modified HF non-local potential. It is finally stressed that this potential generates also an idempotent Dirac density matrix. The CMA approach is thereby demonstrated to relate, albeit approximately, to the DFT exchange-correlation potential.     

Density functional theory simulation of the L<Subscript>2,3</Subscript> XANES spectra

A method for the theoretical simulation of X-ray absorption near edge structure (XANES) spectra at the Ru L_2,3 edges has been developed using relativistic density functional theory (DFT) calculations. The effect of the parameters of DFT calculations on the shape of theoretical curves has been comparatively analyzed for XANES spectra of a water oxidation catalyst and hexaammineruthenium complexes. Recommendations for the choice of the best parameters ensuring good agreement with the experimental data, including the most correct exchange-correlation potential, have been made.