Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session K27: Density Functional Theory |
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Sponsoring Units: DCOMP Chair: Kieron Burke, Rutgers University Room: Baltimore Convention Center 324 |
Tuesday, March 14, 2006 2:30PM - 2:42PM |
K27.00001: Long-range excitations in time-dependent density functional theory David G. Tempel, Neepa T. Maitra Within TDDFT linear response, an adiabatic approximation such as ALDA to the exchange correlation kernel is most often used. It is local in time, or when considered in the frequency domain, frequency independent. We show that this neglected frequency dependence leads to drastic consequences for all excitations of a heteroatomic molecule composed of two open shell fragments at large separation. Strong frequency dependence of the kernel is needed for excitations of both local and charge transfer character. The needed frequency dependence arises from static correlation due to the step in the Kohn Sham potential between the fragments. An approximate kernel is derived to undo the static correlation and restore excited molecular dissociation curves at large separation. Leading order polarization and local dynamic correlation effects are also included. Future challenges for TDDFT will be discussed including molecular Feshabch resonances in stretched systems. [Preview Abstract] |
Tuesday, March 14, 2006 2:42PM - 2:54PM |
K27.00002: A physical interpretation of the Kohn-Sham energy in time-dependent current-density functional theory Roberto D'Agosta, Giovanni Vignale It is well known that in static density functional theory the Kohn-Sham energy plays a fundamental role because it gives, by construction, the ground state energy of the system under study. In time-dependent density functional theory, it is not possible to attach to the Kohn-Sham energy the same physical interpretation. For example we know that for an isolated system the Kohn-Sham energy can be ``dissipated'' while the total energy of the real system is conserved.$^{1}$ However, the Kohn-Sham energy can be given a new physical interpretation as the maximum work that can be extracted from the system and it is related to the production of entropy during the time evolution of the system.$^{1}$ Project supported by NFS Grant No. DMR-0313681\\ $^{1}$R. D'Agosta and G. Vignale, accepted by Phys. Rev. Lett., cond-mat/0508175 [Preview Abstract] |
Tuesday, March 14, 2006 2:54PM - 3:06PM |
K27.00003: Memory and exact exchange in time-dependent density-functional theory Harshani O. Wijewardane, Carsten A. Ullrich Most applications in time-dependent density-functional theory
(TDDFT) are being carried out using adiabatic approximations,
such as the ALDA, for the exchange-correlation potential $V_
{\rm xc}(r,t)$ at time $t$. In these approximations, the
previous history of the system at times $t' |
Tuesday, March 14, 2006 3:06PM - 3:18PM |
K27.00004: The Generating-Coordinate Method in Static and Time-Dependent Density Functional Theory Ednilsom Orestes, A. B. F. Da Silva, Klaus Capelle, Carsten A. Ullrich The generating-coordinate method represents a many-body wave function as a superposition of non-orthogonal Kohn-Sham Slater determinants arising from different Hamiltonians. This method provides additional variational degrees of freedom in the calculation of static and dynamical properties of electronic systems. We present results for atomic ground- and excited- state energies for various choices of generating coordinates. We then apply our variational approach to discuss a particularly challenging problem in TDDFT, the calculation of correlated double-ionization processes. We present results for single- and double-ionization probabilities of a strongly driven two-electron Hooke’s atom. [Preview Abstract] |
Tuesday, March 14, 2006 3:18PM - 3:30PM |
K27.00005: The quantum defect: the true measure of TDDFT results for atoms Meta van Faassen, Kieron Burke We apply quantum defect theory to (time-dependent) density-functional calculations of Rydberg series for some closed shell atoms. We will compare several potentials by considering the quantum defect instead of the excitation energies. The quantum defect has the property of amplifying errors, allowing us to show that results that seem accurate from tables of excitation energies are not always so, especially for larger values of the principle quantum number $n$. In this way the quantum defect provides the appropriate tool for comparing time-dependent density-functional results for atoms. [Preview Abstract] |
Tuesday, March 14, 2006 3:30PM - 3:42PM |
K27.00006: Atom-Atom Scattering with TDDFT - Beyond the Born-Oppenheimer Approximation. Ryan M. Hatcher, Alan R. Tackett, Matthew J. Beck, Sokrates T. Pantelides We report results of calculations of atom-atom scattering going beyond the Born-Oppenheimer (B-O) approximation. We use time-dependent density functional theory with an adiabatic approximation to the scalar exchange-correlation potential in the local-density approximation. We use pseudopotentials, keeping the nearest approach larger than the core radius. The ions are treated as classical particles while the electrons have full freedom to evolve off their instantaneous ground state. If radiative energy loss is not included, energy is conserved; part of the initial ion kinetic energy is transferred to electrons and stays there after separation, a clear sign of effects beyond the B-O approximation. Results of treating radiative losses at two levels of approximation will be discussed. Further results of ongoing calculations of scattering of a Si atom by a solid Si matrix will be described. [Preview Abstract] |
Tuesday, March 14, 2006 3:42PM - 3:54PM |
K27.00007: Effects of core-valence interaction in the screened-exchange density functional method Byounghak Lee, Lin-Wang Wang We present a new development for the screened-exchange (sX) density functional method using a planewave basis. In the screened-exchange density functional method, an explicit screened exchange interaction term is included in the total energy expression. When implemented with a planewave basis, the LDA derived norm-conserving pseudopotentials have usually been used without any change for the sX calculation. While this works well for valence $s$ and $p$ orbitals with the same quantum numbers, we found that there is a problem when $d$ orbitals with a different quantum number are included. This is due to an error in the exchange integral between $d$ and $s$, $p$ orbitals stemming from the use of pseudowavefunctions. As a result, the calculated bulk electronic structures have much smaller band gaps compared to all electron sX calculations and experiments. We propose a scheme to correct the $d$-$s$/$p$ exchange integrals using atomic orbital projection operators. We test our scheme on ZnTe, CdSe, and GaAs, and discuss the effects of shallow core states in comparison with other implementations such as the full potential linearized augmented planewave method. We will also compare our scheme with other Hartree-Fock pseudopotentials. [Preview Abstract] |
Tuesday, March 14, 2006 3:54PM - 4:06PM |
K27.00008: Non-Uniqueness of Local Effective Potential Energy in Density Functional Theory Viraht Sahni, Xiao-Yin Pan, Marlina Slamet As a consequence of the first Hohenberg-Kohn (HK) theorem, in the mapping from a \emph{ground} state of an interacting system to an S system of noninteracting fermions with equivalent density, the effective potential energy of the latter is \emph{unique}. But it is so \emph{only} if these fermions are in their \emph{ground} state. It can be shown via Quantal Density Functional Theory,\footnote{\emph{Quantal Density Functional Theory}, V. Sahni (Springer-Verlag, 2004)} that the \emph{ground} state density of an interacting system can also be reproduced by S systems that are in an \emph{excited} state. Hence, in principle, there are an infinite number of functions that can reproduce a \emph{ground} state density. Similarly, in the mapping from an \emph{excited} state of the interacting system to an S system with equivalent density, the state of the latter is \emph{arbitrary}. Hence, there are an infinite number of functions that can reproduce the excited state density. The latter proves the lack of a first HK theorem for \emph{excited }states. The difference between the potential energy functions in either case is due solely to Correlation-Kinetic effects. [Preview Abstract] |
Tuesday, March 14, 2006 4:06PM - 4:18PM |
K27.00009: Dynamical exchange-correlation potentials beyond the local density approximation Jianmin Tao, Giovanni Vignale Approximations for the static exchange-correlation (xc) potential of density functional theory (DFT) have reached a high level of sophistication. By contrast, time-dependent xc potentials are still being treated in a local (although velocity-dependent) approximation [G. Vignale, C. A. Ullrich and S. Conti, PRL {\bf 79}, 4879 (1997)]. Unfortunately, one of the assumptions upon which the dynamical local approximation is based appears to break down in the important case of d.c. transport. Here we propose a new approximation scheme, which should allow a more accurate treatment of molecular transport problems. As a first step, we separate the exact adiabatic xc potential, which has the same form as in the static theory and can be treated by a generalized gradient approximation (GGA) or a meta-GGA. In the second step, we express the high-frequency limit of the xc stress tensor (whose divergence gives the xc force density) in terms of the exact static xc energy functional. Finally, we develop a perturbative scheme for the calculation of the frequency dependence of the xc stress tensor in terms of the ground-state Kohn-Sham orbitals and eigenvalues. [Preview Abstract] |
Tuesday, March 14, 2006 4:18PM - 4:30PM |
K27.00010: Beyond the LDA in density functional theory: empirical Laplacian-based models for the exchange-correlation energy. Antonio C. Cancio, M.Y. Chou We report recent work in developing a simple GGA-level density functional theory using primarily the Laplacian of the density $\nabla^2 n$ as an input beyond the LDA, obtained by a fit to the exchange-correlation energy density of the Si crystal and atom\footnote{A.~C.~Cancio and M.~Y.~Chou, cond-mat/ 0506462.}. Preliminary tests of this model with LDA pseudopotentials for several solids and molecules show a modestly improved treatment of structural properties over that of conventional GGA's, particularly for covalently bonded systems. We discuss an all-electron generalization of our model constructed by fitting to all-electron data for the energy density and potential of closed-shell first row atoms (He, Be, Ne)~\footnote{C.~J.~Umrigar and X.~Gonze, Phys.\ Rev.\ A \textbf{50}, 3827 (1994).}. The use of $\nabla^2 n$ trivially avoids the singularity in the Kohn-Sham potential that gradient-based models suffer due to the cusp in electron density at the nucleus. Using an expansion in $1/\nabla^2 n$ we are able to fit exchange energy densities in the cusp region with a great degree of accuracy, while obtaining reasonable potentials. [Preview Abstract] |
Tuesday, March 14, 2006 4:30PM - 4:42PM |
K27.00011: Local self-interaction correction in LSMS. Markus Eisenbach, G. M. Stocks While local density approximation (LDA) calculations have proven to be exceptionally successful for performing first principles calculations materials generally thought of as being strongly correlated (e.g. transition metal oxides) are poorly described. However, for many of these systems, it is now clear that an important factor in this failure is the self-interaction error that results in an unphysical Coulomb interaction of an electron with itself. This error can be readily accounted for by use of self-interaction corrected (SIC) LDA [1,2]. Here we report on our implementation of the recently developed local SIC (L-SIC) formulation developed by L\"uders et al. [3] and which is particularly well suited to multiple scattering theory based electronic structure methods. Here we will describe the implementation of L-SIC in our order-N locally self-consistent multiple scattering (LSMS) code as well results for example applications f-electron and TMO systems. 1. J. P. Perdew \& A. Zunger, PRB 23, 5048 (1981). 2. Z. Szotek et al., J. Phys.:CM 16, S5587-S5600 (2004). 3. M. L\"uders et al., PRB 71 205109 (2005). This research is sponsored by DOE-OS, BES-DMEP under contract number DE-AC05-00OR22725 with UT-Battelle LLC. [Preview Abstract] |
Tuesday, March 14, 2006 4:42PM - 4:54PM |
K27.00012: One-to-one Correspondence of the Normalization and Coulomb Hole Sum Rules for Approximate Wave Functions.$^{1}$ Xiao-Yin Pan, Viraht Sahni, Lou Massa For approximate wave functions, we prove the theorem that there is a one-to-one correspondence between the constraints of normalization, and of the Fermi-Coulomb and Coulomb hole sum rules. This correspondence is surprising because normalization depends on the probability of finding an electron at some position, whereas the Fermi-Coulomb/Coulomb hole sum rules depend on the probability of two electrons staying apart due to Pauli-Coulomb/Coulomb correlations. We demonstrate the theorem by example using wave function functionals${}^{2}$. The significance of the theorem for DFT lies in the fact that the extensively employed LYP correlation energy functional${}^{3}$ is based on a wave function (that of Colle-Salvetti${}^4$) which satisfies the Coulomb hole sum rule only approximately, and that wave function is therefore not normalized.\newline \newline 1 Supported by RF CUNY \\ 2 X.-Y. Pan\emph{ et al}, Phys. Rev. Lett. \textbf{93}, 130401 (2004) \\ 3 C. Lee \emph{et al}, Phys. Rev. B \textbf{37}, 785 (1988) \\ 4 R. Colle and O.Salvetti, Theor. Chim. Acta \textbf{37}, 329 (1975). [Preview Abstract] |
Tuesday, March 14, 2006 4:54PM - 5:06PM |
K27.00013: Wave Function Arbitrariness of Noninteracting Fermion Model in Quantal Density Functional Theory$^{1}$(QDFT) Marlina Slamet, Viraht Sahni In the QDFT mapping from a \emph{ground} or \emph{excited} state of the interacting system to one of noninteracting fermions in a particular \emph{excited} state with equivalent density, there is an arbitrariness in the wave function of the model system. For example, in the case of a two-electron atom, the mapping to the excited singlet $2^{1}S$ state of the model system, there are three wave functions that lead to the \emph{same} density: two single Slater determinants of the orbitals that are eigen functions of only $S_{z}$, and a linear combination of Slater determinants of these orbitals that is an eigen function of both $S_{z}$ and $S^{2}$. Neither of the wave functions is more appropriate than the other, since all three wave functions deliver the same density. However, based on the choice of wave function, the structure of the corresponding Fermi and Coulomb holes, and therefore the values of the resulting Pauli and Coulomb correlation energies, will differ. Their sum, the Fermi-Coulomb holes, and the Pauli-Coulomb energy, remains unchanged. The wave function arbitrariness will be demonstrated via the Hooke's atom.\\ \newline 1 \emph{Quantal Density Functional Theory}, V. Sahni (Springer-Verlag, 2004). [Preview Abstract] |
Tuesday, March 14, 2006 5:06PM - 5:18PM |
K27.00014: Rydberg transitions from the local density approximation Kieron Burke, Adam Wasserman Using quantum defect theory, we show how to extract accurate Rydberg transitions (both frequencies[1] and oscillator strengths[2]) from density functional calculations using the local density approximation, despite the short-ranged potential. For the case of He and Ne, the asymptotic quantum defects predicted by the calculations are in less than 5\% error, yielding transition frequency errors of less than 0.1 eV. \newline \newline [1]Rydberg transition frequencies from the Local Density Approximation A. Wasserman and K. Burke, Phys. Rev. Lett. 95, 163006 (2005). \newline [2]Accurate Rydberg Excitations from Local Density Approximation A. Wasserman, N.T. Maitra, and K. Burke, Phys. Rev. Lett. 91, 263001 (2003). [Preview Abstract] |
Tuesday, March 14, 2006 5:18PM - 5:30PM |
K27.00015: Ions on the verge of ionization Vazgen Shekoyan, Kieron Burke The behavior of negative ions on the verge of ionization is studied. Electron-electron correlation plays a significant role for negative ions, especially for the outermost electron. Answering questions such as what negative ions exist, what the behavior of its electronic density is at the ionization threshold or why negative ions are particularly hard to treat in Density Functional Theory(DFT) are important. A general formalism (a differential equation for the square root of the electronic density) has been developed to treat such systems. It has been applied on a 1-d model of 2-electron negative ion, and its behavior on the verge of ionization has been studied in detail. [Preview Abstract] |
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