The talk will be divided into two parts. In the first part, I shall present
a simple method for estimating electron removal energies from ground-state
density functional computations [1]. Moreover, I shall discuss the relation
of the proposed method with previous schemes, like the self-interaction
correction, the Slater transition state method, and a semi-empirical scheme
proposed by S.~B.~Trickey in 1986 [2]. The comparison of the results obtained
with the new scheme with experimental data for atoms and molecules shows
that the proposed method corrects most of the error present in the single
electron eigenvalues of density functional theory.\\
In the second part of the talk, I shall discuss the advantages and limitations of quantum Monte Carlo methods in the evaluation of excitation energies, focusing mainly on collective excitations.
[1] M.~Harris, and P.~Ballone, Chem.~Phys.~Lett. {\bf 303}, 420 (1999)
[2] S.~B.~Trickey, Phys.~Rev.~Lett. {\bf 56}, 881 (1986).
Friedhelm Bechstedt
Friedrich-Schiller-Universitaet, Max-Wien-Platz 1, 07743 Jena Germany
We present two examples for a reasonable description of optical properties
of systems with extremely large unit cells. (i) The first example concerns
polar InP and GaP(001)2x4 surfaces, which are represented by slabs containing
more than 100 atoms. An approximate description of the self-energy and
excitonic effects is combined with a real-space multigrid approach. (ii)
In the framework of extremely softened non-normconserving Vanderbilt pseudopotentials
we are able to treat supercells with at least 216 atoms. Unfortunately
there are no complete wave functions. However, we show how momentum-matrix
elements can be obtained within the projector augmented-wave method.
George F. Bertsch
Niigata University
University of Washington
We have been surveying the applicability of the time-dependent local density approximation as a theory of electronic excitations, calculating various clusters and molecules. The real-time method allows us to compute the entire response at once, which is advantageous in treating response in the UV domain. The systems we have considered are:
Our experience is that the TDLDA reproduces the strong transitions rather well, getting the frequencies to about 10% accuracy and the oscillator strengths to 25%. This is very encouraging to try to apply the TDLDA to more ambitious questions. Concerning the chiroptical response, the circular dichroism in the cases we studied is only reproduced to a factor of 3, and the low-frequency optical rotatory power seems beyond the accuracy of the TDLDA.
[1] K. Yabana and G.F. Bertsch, Phys. Rev. B54 4484 (1996).
[2] " ", Z. Phys. D42 219 (1997).
[3] " ", Int. Journ. Quantum Chemistry 75, in press; physics/9808015.
[4] " ", physics/9903041.
[5] " ", Phys. Rev. A60, in press; physics/9812019.
WWW home page: www.phys.washington.edu/~bertsch
Peter Bobbert
Eindhoven University of Technology, The Netherlands
Twente University, The Netherlands
We calculate the one- and two-particle excitations in polythiophene
by using the GW approximation and solving the Bethe-Salpeter equation,
respectively. The screening of the Coulomb interaction plays a crucial
role in both kinds of excitations. We study the effects of intra- and interchain
screening separately. The first kind of screening is treated in an ab-initio
manner. The second kind of screening is obtained from a model in which
the polymer chains are treated as polarizable line objects. From this model
we obtain the frequency-dependent dielectric tensor for an experimentally
determined crystal structure, which is then used to describe the interchain
screening. It turns out that the fundamental gap as well as the exciton
binding energy are very much affected by the interchain screening. However,
the optical gap, i.e. the difference of the two former quantities, is hardly
affected. Only by including the interchain screening we obtain agreement
with various electro-optical experiments. We expect our conclusions to
be valid for conjugated polymers in general.
A method is presented to write the solution of equations involving functional
derivatives as a recursive sum indexed by planar binary trees. The method
is applied to quantum field theory. Each tree represents the sum of a number
of Feynman diagrams. The formulas are explicit and the diagram multiplicities
are generated automatically. The method is applied to the example of quantum
electrodynamics.
Determining excited state properties of atomic clusters is a challenging problem for several reasons. In general, ground state structural properties are unknown and not subject to direct experimental probes. Without knowledge of the ground state structural properties, it is not possible to predict accurate excited state properties such as optical excitations. We present a real space method to determine the structural properties of semiconductor clusters and the corresponding optical properties. A combination of higher-order finite difference techniques and ab initio pseudopotentials constructed within density functional theory is used to compute quantum interatomic forces. These forces can be used to perform simulated annealing to determine the structural properties of clusters. Real space approaches have several advantages in this procedure. For example, the ``basis'' is unbiased, charged clusters can be easily accommodated and the algorithm is suitable for implementation on parallel platforms. Once the structural properties have been determined, we use the time dependent local density approximation (TDLDA) to extract the excited state properties of clusters. We demonstrate that TDLDA can yield accurate optical properties via a comparison to experiment. TDLDA is very efficient and easily added on top of electronic structure programs. Also, we will compare the results of TDLDA to other theoretical approaches such as solutions of the Bethe-Salpeter equations for confined systems.
I. Vasiliev, S. Ougut and J.R. Chelikowsky, Phys. Rev. Lett.78, 4805 (1997); 82, 1919 (1999).
Supported by the National Science Foundation and the Minnesota Supercomputing Institute
WWW home page: www.jrc.cems.umn.edu
We present calculations of the one and two particle excitations in silicon
nanocrystallites. The one-particle properties are handled in the GW approximation
while the magnitude of the electron-hole interaction is obtained from the
solutions of the corresponding Bethe-Salpeter equation. We develop a simplified
tight-binding version of these methods allowing us to treat large clusters
(up to 200 atoms) which cannot be treated by ab-initio methods. We show
that the self energy and Coulomb corrections obey simple physical laws
and almost exactly cancel each other for crystallites with radius larger
than 0.6 nm. The result of this cancellation is that simple one-particle
calculations (corrected LDA, empirical tight-binding or pseudopotentials)
give quite accurate values for the excitonic gap of crystallites in the
most studied range of sizes.
We report about the lifetimes of hot electrons in crystalline Aluminum and in copper and Silver. For Aluminum the results agree quantitavely with the experimental data. For Cu we get good agreement for quasiparticle energies in the (110) direction above 2eV. For Ag the theoretical results are in good agreement with available experimental data for all energies [in (110) direction].
The calcultions were performed within the shielded interaction aproximation
(SIA or GWA) using a plane wave basis set. We show that for Cu and Ag this
basis leads to equally good results as the more demanding LAPW basis.
I will review my calculations of the electronic structure of II-VI semiconductors,
done with various methods. Because of an interplay of the localized semi-core
states with the valence states in IIb-VI compounds, these materials play
important role as a test case for theoretical approaches.
The current approximations for the exchange and correlation energy in Density-Functional Theory fail to describe many important aspects of some complex systems, such as the barrier heights of several chemical reactions [1]. In Many-Body Theory, the exchange and correlation energy is treated from a fundamental point of view, using the self-energy operator $\Sigma$. However, calculating $\Sigma$ for real materials is computationally very expensive and in many cases not feasible.
We propose a new method for calculating total energies of interacting systems, in which the self-energy operator is modelled in a simple way [2] that nevertheless retains the main features of the exact operator. The total energy is calculated by means of the Galitskii-Migdal total energy formula that appears in Many-Body Theory. In this way, the major part of the exchange and correlation energy is treated in a much more realistic way than in traditional density functional theories, while the small remaining part is approximated locally so that our approach is exact in the limit of homogenous densities. The method has been tested to calculate total energies of the imhomogenous electron gas and of bulk silicon.
[1] J.C Grossman and L. Mitas, PRL {\bf 79} 4353 (1997).
[2] R.W. Godby, M. Schluter and L.J. Sham, PRB {\bf 37} 10159 (1988)
WWW home page: www-users.york.ac.uk/~psf100
Hedin's $GW$ approximation has been extensively used to calculate the one-electron excitation spectra of a wide variety of systems.[1] However, there are not many results concerning the ground state properties, such density[2] or total energy[3,4], obtained from the one-particle Green's function $G$ which arises after a $GW$ calculation. Obviously, the main reason is the routine use of the Density Functional Theory (DFT) as a practical tool for such ground state calculations. However, the most popular implementations of the DFT (LDA or GGA) lack predictive accuracy in many cases. An alternative approach to ground state calculations is based on many-body perturbation theory. In this context, Hedin's original {\em self-consistent} $GW$ approximation can be viewed as a $\Phi $-derivable model (in the Baym-Kadanoff sense). Hence, the {\em self-consistent} Green's function verifies exactly particle number and energy conservation laws.[4,5] In this work we present fully self-consistent $GW$ results for simple electron systems (the homogeneous 2D and 3D electron gases, and jellium slabs), and the corresponding ground state properties. Note that whereas self-consistent $GW$ calculations for inhomogeneous systems have been already performed,[6] these standard $GW$ methods are not able to give a Green's function with the minimum level of accuracy to obtain meaningful ground state properties. Careful analysis of asymptotic behaviours of Green's function as well as the use of the space time method developed by Rojas {\em et al.}[7] allow us to obtain $G$ with the desired precision.
[1] L. Hedin, Phys. Rev {\bf 139}, A796 (1995). F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys. {\bf 61}, 237 (1998).
[2] M. M. Rieger and R. W. Godby, Phys. Rev. B {\bf 58}, 1343 (1998).
[3] E. L. Shirley, Phys. Rev. B {\bf 54}, 7758 (1996).
[4] B. Holm and U. von Barth, Phys. Rev. B {\bf 57}, 2108 (1998).
[5] A. G. Eguiluz and W. Ku, {\em Proceedings of the International Workshop on Electron Correlations and Materials Properties}, A. Gonis and N. Kioussis eds., Plenum (New York, 1999) and references therein
[6] W. D. Sch\"{o}ne and A. G. Eguiluz, Phys. Rev. Lett. {\bf 81}, 1662 (1998).
[7] H. N. Rojas, R. W. Godby and R. J. Needs, Phys. Rev. Lett {\bf 74},
1827 (1995). M. M. Rieger {\em et al.}, Computer Physics Communications
{\bf 117}, 211 (1999).
The triplet self-trapped excitons (STE) in alkali-halide crystals are the prototype systems for studies of exciton self-trapping phenomena in insulators. Despite being a subject of intense experimental and theoretical studies, many features of the STE structure and dynamics remain unclear. Previous first principles calculations of the STE suffered from small model systems, restricted basis sets, and little or no account of electron correlation. These limitations can be partially lifted by the use of the plane wave spin polarised density functional techniques implemented on massively parallel computers. We present the first such calculations of the STE in NaCl which were performed using the VASP code [1], implementing the gradient corrected density functional with non-local pseudo-potential. The adiabatic potential energy surfaces and charge/spin densities of the crystal in the singlet and triplet states (which are the lowest energy states for the corresponding total spin quantum numbers) were calculated within the periodic cells of up to 72 NaCl molecules. Based of this results we predict the photoluminescence energies as well as frequencies of certain local vibrational modes. We discuss the convergence of the results for different multiplets with respect to a cell size and a Brillouin zone mesh.
We also analyse the role of the correlation effects in the STE dynamics and discuss the applicability of the method to the studies of localised electronic excitations.
1. G. Kresse and J. Hafner, Phys. Rev. B 47, RC558 (1993)
G. Kresse and J. Furthm\"uller, Phys. Rev. B 54, 11169, (1996)
I shall describe recent developments of the space-time method [1,2], and
applications including the quasiparticle band structure of gallium nitride.
1. "The GWspace-time method for the self-energy of large systems", Martin M. Rieger, L. Steinbeck, I.D. White, H.N. Rojas and R.W. Godby, Computer Physics Communications 117 211-228 (1999). Abstract
2. "Enhancements to the GW space-time method", L. Steinbeck, A. Rubio, L. Reining, M. Torrent, I. D. White and R. W. Godby, submitted
Specific matrix elements of exchange and correlation kernels in time-dependent
density-functional theory are computed. The knowledge of these matrix elements
not only constraints approximate time-dependent functionals, but also allows
to link different practical approaches to excited states, either based
on density-functional theory, or on many-body perturbation theory, despite
the approximations that have been performed to derive them [published in
Phys.Rev.Lett.{\bf 82}, 4416 (1999)]
The usefulness of Time-Dependent Density Functional Theory (TD-DFT) for the computation of excitation energies of atoms, molecules and clusters, has been demonstrated recently [1-4]. Here this formalism is applied to the computation of excited state potential energy surfaces. For the (HeH)$^+$ system, we investigate the ground state as well as the 5 lower-lying singlet and triplet states, for a series of internuclear distances. We work both in the Local Density Approximation (TDLDA) and in the exchange-only Optimized Effective Potential approximation (TDOEP). For this system, comparison with Configuration Interaction (CI) data shows that TDLDA is insufficient. TDOEP gives much better results, especially for the position of the avoided crossings between the different curves. The good approximation to the exact exchange-correlation potential provided by the OEP partly explains this observation. Surprisingly, for some of the singlet excited states, the straight OEP Kohn-Sham eigenvalue differences, that constitute the starting point of TDOEP, are in even better agreement with CI data. We also compute excited state energies within the $Delta$SCF approach, using both LDA and GGA. In general, TDOEP and $Delta$SCF results show comparable accuracy.
[1] M. Petersilka, U.J. Gossman and E.K.U. Gross, Phys. Rev. Lett. {\bf 76}, 1212 (1996).
[2] M.E. Casida {\it et al}, J. Chem. Phys.{\bf 108}, 4439 (1998), and references therein.
[3] S.J.A. van Gisbergen {\it et al}, Phys. Rev. A {\bf 57}, 2556 (1998).
[4] I. Vasiliev, S. \"Og\"ut, and J.R. Chelikowski, Phys.
Rev. Lett. {\bf 82}, 1919 (1999).
How do excited electrons behave in superconductors? To investigate this question we study the phenomenon of dichroism, i.e., the fact that under certain circumstances the power absorption of left-handed circularly polarized light differs from the power absorption of right-handed circularly polarized light. In normalconducting metals dichroism is observed if a static magnetic field (either external or internal, due to ferromagnetic order) is present in addition to the external light source. Theoretical investigations have demonstrated that this phenomenon is a relativistic effect: Without spin-orbit coupling there is no dichroism in normalconducting metals.
To study dichroism in superconductors we therefore will first present a relativistic generalization of the Bogolubov-de Gennes equations where the particle and hole amplitudes are Dirac spinors [1,2]. In the weakly relativistic limit one obtains, besides the usual spin-orbit, Darwin and kinetic energy corrections, an additional ``spin-orbit'' and an additional ``Darwin'' term [1,3]. The latter terms are present in superconductors only and involve the pairing field in place of the electrostatic potential. On the basis of these equations we then identify four distinct mechanisms for dichroism in superconductors [4,5]. Two are modifications of mechanisms known from the normal state, and two are novel mechanisms found in superconductors only. We solve the equations for a simple model superconductor and find a variety of new effects, not known from dichroism in the normal state.
[1] K. Capelle and E.K.U. Gross, Phys. Lett. A {\bf 198}, 261 (1995).
[2] K. Capelle and E.K.U. Gross, Phys. Rev. B {\bf 59}, 7140 (1999).
[3] K. Capelle and E.K.U. Gross, Phys. Rev. B {\bf 59}, 7155 (1999).
[4] K. Capelle, E.K.U. Gross and B.L. Gy\"orffy, Phys. Rev. Lett. {\bf 78}, 3753 (1997).
[5] K. Capelle, E.K.U. Gross and B.L. Gy\"orffy, Phys. Rev. B {\bf 58}, 473 (1998).
The one-electron spectral function is an important ingredient in all electron spectroscopies. It has a quasi-particle peak of strength Z(k), and a satellite structure of strength 1-Z(k), where k is the electron momentum. The function Z(k) is typically 0.6-0.8 for k smaller than the Fermi momentum kF. As shown by B. I. Lundqvist already in 1969 Z(k) has an anomalous behaviour and can drop to quite small values when k approaches kF+qc, where qc is the momentum where Landau damping of plasmons sets in. At larger k-values Z(k) slowly approaches 1. The effect of correlation on x-ray absorption is analyzed by using an expansion in fluctuation potentials as proposed by Bardyszewski and Hedin in 1987. We find strong interference effects for energies just above the Fermi energy, before the anomalous region is reached. For higher energies the intrinsic effects dominate, and the spectrum becomes a convolution of the core-electron spectrum and the usual one-electron expression, as predicted by Rehr and collaborators in 1978.
In this talk, I will briefly review a first-principles approach [1,2] to the optical properties of materials based on making the GW approximation to the quasiparticle self energy and solving the two-particle Bethe-Salpeter equation for the optically excited states. In particular, we examine the validity of this approach to the optical absorption of various systems. In many cases, an accurate determination of the quasiparticle wavefunctions by solving fully the Dyson's equation is found to be necessary for accurate results. That is, the quasiparticle wavefunctions can be significantly different from the LDA or GGA Kohn-Sham eigenfunctions, and these differences can strongly affect the calculated quasiparticle energies, exciton energies, and optical spectra. We present results from calculations on atoms, clusters, and crystals. For atoms and small clusters, our results are compared with best available results from quantum chemistry methods including the quantum Monte Carlo method. As a specific example of crystals, we discuss our results for SiO2 and try to resolve some of the long-standing issues regarding the optical spectrum of this important insulator.
[1] M. Rohlfing and S. G. Louie, "Excitonic Effects and Optical Absorption Spectrum of Hydrogenated Si Clusters," Phys. Rev. Lett. 80, 3320 (1998).
[2]M. Rohlfing and S. G. Louie, "Electron-hole Excitations in Semiconductors and Insulators," Phys. Rev. Lett. 81, 2312 (1998).
The late transition--metal monoxides (MnO, FeO, CoO, NiO) have the rocksalt
structure in their paramagnetic phase, while below the Neel temperature
a weak structural distortion accompanies an AFM ordering of type II. Therefore,
it is generally assumed that most {\it nonmagnetic} ({\it i.e.} spin--integrated)
crystalline properties are essentially cubic: we give here convincing evidence
of the contrary. We focus\footnote{S. Massidda et al., Phys. Rev. Lett.,
{\bf 82}, 430 (1999)} on the half--filled $d$ shell oxide MnO as the most
suitable case study, on which we perform accurate ab--initio, all--electron
calculations, within different one--particle schemes. In order to study
the symmetry lowering due to AFM ordering, we assume an ideal cubic geometry
throughout. The calculated TO frequencies and Born effective charge tensor
do not have cubic symmetry. The standard LSD severely exaggerates the deviations
from cubic symmetry, confirming its unreliability for calculating properties
of insulating AFM oxides, while a model self--energy correction scheme\footnote{S.
Massidda {\it et al.}, Phys. Rev. B {\bf 55}, 13494 (1997).} reduces considerably
the anisotropy. We also explain the origin and the magnitude of this effect
in terms of the mixed charge--transfer/Mott--Hubbard character of MnO.\\
The role of including explicitly the geometric structure in the calculation of the photo-absorption process in simple metal clusters is investigated. Quantitative agreement with recent low-temperature experiments on charged clusters is obtained by means of a simple theory in which the role played by the ionic skeleton becomes particularly transparent.
The many--body Green's function embeds by construction the complete information about the (N+1)-particle and (N-1)-particle excitations of a given sistem: it also provides some partial information about the N-particle ground state. In particular, knowledge of the many-body Green's function is enough to recover the one-body reduced density matrix and the ground-state energy: other observables, like two-body (and higher order) correlation functions are instead not accessible.
Berry phases occur in many fields of physics: they are a kind of "exotic" observable, which cannot be cast as the expectation value of any operator, being instead a gauge-invariant phase of the wavefunction [1]. Here I focus on a generic Berry phase in a many-electron system: two simple examples are the Aharonov-Bohm phase [2], and the phase generated by a conical intersection in a molecule [3]. In order to evaluate a Berry phase, one needs in principle the full N-body wavefunction: since many-particle wavefunctions are nasty objects, carrying redundant information, it is worthwhile to assess whether the many-body Berry phase can be expressed in terms of simpler quantities.
I start with the uncorrelated case, where the ground wavefunction is a determinant of single-particle orbitals: in this simple case, one can prove that the many-body Berry phase is just the sum of the individual Berry phases of each orbital [1]. Switching then the interaction on, the question is whether one may continue to express the many-body Berry phase in terms of the Feynman-Dyson amplitudes (despite the fact that the latter are not orthonormal). I conjecture that the answer is "yes". I will present a proof for the special case of the Aharonov-Bohm phase; the problems of a general proof will be outlined.
[1] R. Resta, "Berry Phase in Electronic Wavefunctions"; Lecture Notes for the Troisieme Cycle de la Physique en Suisse Romande (Lausanne, Switzerland 1996). Available online (194K) at the URL: http://www-dft.ts.infn.it/~resta/publ/notes_trois.ps.gz gzipped file
[2] R. P. Feynman, R. B. Leighton, and M. Sands, "The Feynman Lectures in Physics", Vol. 2 (Addison Wesley, Reading, 1964), Sect. 15-4.
[3] C.A. Mead, "The geometric phase in molecular systems",
Rev. Mod. Phys. 64, 51 (1992).
We discuss the parallelization of the algorithms used to compute the
quasiparticle energies within the GW approximation and to calculate the
optical excitations by solving the Bethe-Salpeter equation (BSE) to include
excitonic effects. For several stages of the GW calculation, including
the calculation of the RPA polarization, static dielectric matrix, and
self-energy operator, the most efficient parallel scheme consists simply
in distributing the conduction bands between the processors. Since the
number of conduction bands required for an actual calculation can be quite
large (typically 5-10 times the number of valence bands), this scheme is
suitable and quite efficient for most finite and infinite-periodic systems.
For the calculation of optical excitations, this simple and natural distribution
is no more possible since the number of conduction bands needed in the
Bethe-Salpeter matrix can be very small. Therefore, for the implemetation
of the BSE, we develop a scheme different from that used in the GW calculation.
For all these algorithms, we discuss the load balancing, scalability, memory
distribution, minimization of the I/O, as well as other technical issues.
Further developments and possible improvements of the programs are proposed.
Finally, we present some recent applications.
Types of effects on excitation spectra that may be expected in GW calculations of realistic quantum dots are studied on a simple model quantum dot. In particular the impact of the electrostatic image potential and the centrifugal potential, arising in our spherical dots, are taken into account. The electron-electron interaction and the confining potential are replaced by a model potential and the material's properties are represented by their dielectric constants
Three different changes have been observed. The potential and therefore the electron energies are shifted and the level spacing in the excitation spectrum changes. Additional one-electron energy levels occur and a continuum of infitesimally seperated levels establishes at the potential edge. An intrinsic barrier arises for angular momentum excitation that creates meta stable states.
All of these changes become more visible with shrinking dot size
We investigate excitons at the Si(111)-(2x1) surface and their optical spectrum from first principles. To this end, we first solve Dyson's equation for the one-particle Green's function, yielding the quasiparticle excitations of the system. The electronic self-energy operator is calculated within the GW approximation. Thereafter, we solve the Bethe-Salpeter equation for the two-particle Green's function of coupled electron-hole pairs, fully including the electron-hole interaction.
The optical spectrum of the Si(111)-(2x1) surface is dominated by a
surface exciton formed from the pi-bonded surface states. The excitonic
binding energy is more than one order of magnitude larger than in bulk
Si. The two-particle wave function of the exciton state is strongly localized
at the surface and exhibits distinct anisotropy due to the surface reconstruction.
WWW home page: www.fhi-berlin.mpg.de/th/member/schindlmayr_a.html
We present results for the lifetimes of excited (so-called ``hot'') electrons in infinite, periodic systems. The lifetimes are obtained by evaluating the one-electron Green's function within the GW approximation. From the width of the quasiparticle peak in the retarded Green's function the lifetime of the corresponding state is determined. We apply our method to the nearly free electron (NFE) metal Al and the noble metals Cu, Ag, and Au. Our theoretical results are compared to experimentally obtained lifetimes. In Al the agreement is very good. We are even able to identify the states (wave vector and band) of the hot electrons which lifetime were probed in the experimental work using a polycrystalline sample. The experiments on the noble metals were performed wave vector resolved so that we can compare our results with the experimental data in the (110) direction. The agreement is good. However, we find that the GW approximation is unable to explain the sharp increase of the lifetime of excited electrons in Cu and Au for energies smaller than 2 eV. We also discuss some open questions and give an outlook to future work. The poster concentrates on the technical details of our calculation and complements W. Ekardt's talk.
This talk will focus on efforts to treat optical properties in metals in addition to insulators. Studying metals complicates matters because of the possibility of intra-band transitions. In addition, recent developments to treat non-zero momentum transfer will be discussed. These have permitted the interpretation of a wide variety of inelastic x-ray and electron scattering data.
Also, several algorithmic refinements have been made that better automate
and make more efficient earlier work. These refinements have permitted
more detailed zone sampling and extension of calculations to a greater
number of conduction bands, which permits replication of experimental absorption
features with remarkable fidelity and detail up to as far as 25 eV above
the absorption edge (with inclusion of even more bands possibly permitting
treatment of even wider spectral regions). With this, the goals of treating
practical optical materials with more complicated crystal structures and
of treating optical properties as a continuous function of strain have
been considered.
We recently found huge overestimations in LDA and GGA calculations on the (non)linear optical properties of finite molecular chains [1, 2]. Subsequent analysis showed this problem to be related to "Density-polarization functional theory" [3]. This extension of DFT for periodic systems has recently also been discussed by many other authors (Resta, Martin, Ortiz, Souza, Vanderbilt). It was shown that a linear term can exist in the exchange-correlation (xc) potential for polarized systems.
We analyze the consequences for finite molecular chains of varying size, for which the xc functionals do not need to depend on the polarization. For this analysis we use both "exact" xc potentials and the x-only Krieger-Li-Iafrate (KLI) potential [3, 4]. The results show that the linear term in the xc potential counteracts the externally applied electric field, and has its origin in the so-called "response" part [5] of the xc potential, not in the well-known potential of the xc hole.
A close analysis of the KLI potential reveals the mechanism through
which orbital-dependent functionals can generate such a counteracting term,
thus providing the "ultra nonlocal density dependence" which
is missing in LDA and GGA functionals (which lack the required linear term).
Such understanding should be the first step towards improved xc functionals.
[1] B. Champagne et al. J. Chem. Phys. 109, 10489 (1998) Abstract
[2] S.J.A. van Gisbergen, P.R.T. Schipper, O.V. Gritsenko, E.J. Baerends, J.G. Snijders, B. Champagne, and B. Kirtman, "Electric field dependence of the exchange-correlation potential in molecular chains", Phys. Rev. Lett., accepted. Abstract
[3] X. Gonze, Ph. Ghosez, and R.W. Godby, Phys. Rev. Lett. 74, 4035 (1995)
[4] O.V. Gritsenko, S.J.A. van Gisbergen, P.R.T. Schipper, E.J. Baerends, in preparation
[5] E.J. Baerends and O.V. Gritsenko, J. Phys. Chem. 101, 5383 (1997)
Many electronic-structure calculations in s-p bonded metals and in semi-conductors are carried out using pseudo-potentials and plane waves. In earlier work from 1995 we demonstrated that a straight- forward gradient expansion give exchange energies for the metallic pseudo systems that are accurate to within 1 mRy. There are reasons to believe that correlation energies can be obtained with similar accuracy from a new Meta-GGA by Perdew and coworkers. Unfortunately, the results for the s-p bonded semi-conductors are an order of magni- tude less accurate. This suggests two things: i) previous problems in obtaining accurate cohesive energies of s-p bonded metallic systems within DFT are mainly associated with the outskirts of the atoms, and ii) there is a definite problem with the GGA:s associated with the occurrence of a band-gap - an extremely non-local property. Recent investigations of the non-interacting kinetic energies of "pseudo" systems - perhaps the largest part of the total energies - again demonstrate the power of gradient expansions as long as exponentially decaying densities and band gaps are not considered. A solution to these two problems would open up the road to electronic structure calculations without the need for Schroedinger's equation.
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