Center for Molecular Modeling - K. Peirs

Self-consistent solution of Dyson's equation up to second order for closed- and open-shell atomic systems

wim — Fri, 30 Sep 2011 11:02:34 +0000

K. Peirs, D. Van Neck, M. Waroquier

International Journal of Quantum Chemistry

91 (2), 113-118

2003

Abstract

Green's function techniques offer new methods based upon perturbation theory to study many-body systems. The computational cost in these schemes is substantially higher than in density functional theory (DFT), but they offer a clear picture of the nature of correlations included in the calculations. In this way, a connection between the Green's function scheme and DFT can learn more about the underlying mechanisms of the latter. Therefore, we need the correlated density of some carefully selected systems. In this work, a numerical scheme is presented to solve the Dyson equation up to second order self-consistently for a few closed-shell (He, Be, Ne, Mg, and Ar) and open-shell (B, C, N, O, and F) atoms in coordinate space. A detailed discussion is held on the reproduction of total binding energies, ionization energies, electron affinities, and spectral strength distributions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

DOI

http://dx.doi.org/10.1002/qua.10405

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03 int. j. quantum chem 91(2)113 peirs.pdf

Algorithm to derive exact exchange-correlation potentials from correlated densities in atoms

wim — Fri, 30 Sep 2011 10:51:01 +0000

K. Peirs, D. Van Neck, M. Waroquier

Physical Review A

67 (1), 012505

2003

Abstract

A simple algorithm is presented to derive accurately the exchange-correlation potential in the density functional theory (DFT) from the electron density. The method, which can be used with any physically acceptable density as input, is applied here to the densities in atoms obtained from high-level Green’s function calculations. The resulting potentials show the correct asymptotic behavior and the characteristic intershell peaks. We illustrate the possible use of these potentials in fitting procedures for new functionals, by investigating the HCTH functional [F. A. Hamprecht, A. J. Cohen, D. J. Tozer, and N. C. Handy, J. Chem. Phys. 109, 6264 (1998)]. The potentials derived from Green’s function one-body densities provide a microscopic foundation for present-day functionals in DFT, and may therefore be helpful in the ultimate goal of constructing functionals on a fully ab initio basis.

DOI

http://dx.doi.org/

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03 physrev A 67(1)012505 peirs.pdf

Maximum occupation number for composite boson states

wim — Fri, 30 Sep 2011 10:36:01 +0000

S. Rombouts, D. Van Neck, K. Peirs, L. Pollet

Modern Physics Letters A (MPLA)

17 (29), 1899-1907

2002

Abstract

One of the major differences between fermions and bosons is that fermionic states have a maximum occupation number of one, whereas the occupation number for bosonic states is in principle unlimited. For bosons that are made up of fermions, one could ask the question to what extent the Pauli principle for the constituent fermions would limit the boson occupation number. Intuitively one can expect the maximum occupation number to be proportional to the available volume for the bosons divided by the volume occupied by the fermions inside one boson, though a rigorous derivation of this result has not been given before. In this letter we show how the maximum occupation number can be calculated from the ground-state energy of a fermionic generalized pairing problem. A very accurate analytical estimate of this eigenvalue is derived. From that a general expression is obtained for the maximum occupation number of a composite boson state, based solely on the intrinsic fermionic structure of the bosons. The consequences for Bose–Einstein condensates of excitons in semiconductors and ultra cold trapped atoms are discussed.

DOI

http://dx.doi.org/10.1142/S0217732302008411

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02 modern phys. lett. A 17(29)1899 rombouts.pdf

Self-consistent solution of Dyson's equation up to second order for closed- and open-shell atomic systems

wim — Fri, 30 Sep 2011 09:50:53 +0000

K. Peirs, D. Van Neck, M. Waroquier

Journal of Chemical Physics

117(9), 4095-4105

2002

Abstract

Green’s function techniques are powerful tools for studying interacting many-fermion systems in a structural and diagrammatical way. The central equation in this method is the Dyson equation which determines, through an approximation for the self-energy, the Green’s function of the system. In a previous paper [J. Chem. Phys. 115, 15 (2001)] a self-consistent solution scheme of the Dyson equation up to second order in the interaction, the Dyson(2) scheme, has been presented for closed-shell atoms. In this context, self-consistency means that the electron propagators appearing in a conserving approximation for the self-energy are the same as the solutions of the Dyson equation, i.e., they are fully dressed. In the present paper this scheme is extended to open-shell atoms. The extension is not trivial, due to the loss of spherical symmetry as a result of the partially occupied shells, but can be simplified by applying an appropriate angular averaging procedure. The scheme is validated by studying the second-row atomic systems B, C, N, O, and F. Results for the total binding energy, ionization energy and single-particle levels are discussed in detail and compared with other computational tools and with experiment. In open-valence-shell atoms a new quantity—the electron affinity—appears which was not relevant in closed-shell atoms. The electron affinities are very sensitive to the treatment of electron correlations, and their theoretical estimate is a stringent test for the adequacy of the applied scheme. The theoretical predictions are in good agreement with experiment. Also, the Dyson(2) scheme confirms the nonexistence of a stable negative ion of N. The overall effect of the self-consistent Dyson(2) scheme with regard to the Dyson(1) (i.e., Hartree–Fock) concept, is a systematic shift of all quantities, bringing them closer to the experimental values. The second-order effects turn out to be indispensable for a reasonable reproduction of the electron affinity. © 2002 American Institute of Physics.

DOI

http://dx.doi.org/10.1063/1.1497682

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02 j. chem. phys. 117(9)4095 peirs.pdf

v-representability of one-body density matrices

wim — Fri, 30 Sep 2011 09:10:03 +0000

D. Van Neck, M. Waroquier, K. Peirs, V. Van Speybroeck

Physical Review A

64 (4), 042512

2001

Abstract

We consider low-dimensional model systems with a fixed two-body interaction and a variable (nonlocal) one-body potential. It is shown explicitly that an extended domain of allowed (N-representable) one-body density matrices cannot be generated in this way, the excluded domain depending on the two-body interaction under consideration. This stands in contrast to the behavior of the diagonal part of the density matrix.

Open Access version available at UGent repository

DOI

http://dx.doi.org/10.1103/PhysRevA.64.042512

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01 phys. rev. A 64(4)042512 van neck.pdf

Self-consistent solution of Dyson’s equation up to second order for atomic systems

wim — Fri, 30 Sep 2011 09:08:09 +0000

D. Van Neck, K. Peirs, M. Waroquier

Journal of Chemical Physics

115 (1), 15-25

2001

Abstract

In this paper, the single-particle Green’s function approach is applied to the atomic many-body problem. We present the self-consistent solution of the Dyson equation up to second order in the self-energy for nonrelativistic spin-compensated atoms. This Dyson second-order scheme requires the solution of the Hartree–Fock integro-differential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a basis set). To cope with the huge amount of poles generated in the iterative approach to tackle Dyson’s equation in second order, the BAGEL (BAsis GEnerated by Lanczos) algorithm is employed. The self-consistent scheme is tested on the atomic systems He, Be, Ne, Mg, and Ar with spin-saturated ground state 1S0. Predictions of the total binding energy, ionization energy, and single-particle levels are compared with those of other computational schemes [density functional theory, Hartree–Fock (HF), post-HF, and configuration interaction] and with experiment. The correlations included in the Dyson second-order algorithm produce a shift of the Hartree–Fock single-particle energies that allow for a close agreement with experiment. © 2001 American Institute of Physics.

DOI

http://dx.doi.org/10.1063/1.1376126

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01 j. chem. phys. 115(1)15 van neck.pdf

Solution of the Dyson equatios in atomic systems

wim — Tue, 18 Oct 2011 08:59:52 +0000

K. Peirs, D. Van Neck, M. Waroquier

Poster

Conference / event / venue

DFT2000: Satellite Symposium of the 10th international Congress of Quantum Chemistry

Menton, France

Wednesday, 14 June, 2000

Self-consistent solution of Dyson's equation up to second order: closed and open shell atoms

wim — Tue, 18 Oct 2011 08:53:11 +0000

K. Peirs, D. Van Neck, M. Waroquier

Poster

Conference / event / venue

9th International Conference on the Applications of the Density Functional Theory in Chemistry and Physics

Madrid, Spain

Monday, 10 September, 2001 to Friday, 14 September, 2001

Self-consistent solution of Dyson's equation up to second order for atomic systems

wim — Mon, 17 Oct 2011 12:10:15 +0000

K. Peirs

Talk

Conference / event / venue

Summer School on Density Functional Theory

Caramulo, Portugal

Tuesday, 28 August, 2001 to Saturday, 1 September, 2001

Self-consistent solution of Dyson's equation up to second order for atomic systems

wim — Mon, 17 Oct 2011 12:07:48 +0000

K. Peirs

Talk

Conference / event / venue

Contact Forum WOG-Density Functional Theory

Leuven, Belgium

Monday, 17 September, 2001