Physical Review A

Accuracy of the Faddeev random phase approximation for light atoms

C. Barbieri, D. Van Neck, M. Degroote
Physical Review A
85 (1) 012501
2012
A1

Abstract 

The accuracy of the Faddeev random phase approximation (FRPA) method is tested by evaluating total and ionization energies in the basis-set limit. A set of light atoms up to Ar is considered. Comparisons are made with the results of coupled-cluster singles and doubles (CCSD), with third-order algebraic diagrammatic construction [ADC(3)], and with the experiment. It is seen that even for two-electron systems, He and Be(2+), the inclusion of RPA effects leads to satisfactory results, and therefore it does not overcorrelate the ground state. The FRPA becomes progressively better for larger atomic numbers, where it gives approximate to 5 mH more correlation energy, and it shifts ionization potentials by 2-10 mH with respect to the similar ADC(3) method. The ionization potentials from FRPA tend to reduce the discrepancies with the experiment.

Open Access version available at UGent repository

Variational determination of the second-order density matrix for the isoelectronic series of beryllium, neon, and silicon

B. Verstichel, H. van Aggelen, D. Van Neck, P.W. Ayers, P. Bultinck
Physical Review A
80 (3), 032508
2009
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Abstract 

The isoelectronic series of Be, Ne and Si are investigated using a variational determination of the second-order density matrix. A semidefinite program was developed that exploits all rotational and spin symmetries in the atomic system. We find that the method is capable of describing the strong static electron correlations due to the incipient degeneracy in the hydrogenic spectrum for increasing central charge. Apart from the ground-state energy various other properties are extracted from the variationally determined second-order density matrix. The ionization energy is constructed using the extended Koopmans' theorem. The natural occupations are also studied, as well as the correlated Hartree-Fock-like single particle energies. The exploitation of symmetry allows to study the basis set dependence and results are presented for correlation-consistent polarized valence double, triple and quadruple zeta basis sets.

Open Access version available at UGent repository

Characterization of the electron propagator with a GW-like self-energy in closed-shell atoms

S. Verdonck, D. Van Neck, P.W. Ayers, M. Waroquier
Physical Review A
74 (6), 062503
2006
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Abstract 

The electron propagator is calculated for a set of closed-shell atoms using GW-like self-energies that contain the coupling of single-particle degrees of freedom with excited states in the framework of the random phase approximation. The effect of including exchange diagrams is investigated. Calculations are performed in the Hartree-Fock (HF) basis of the neutral atom. The HF continuum is taken into account using a discretization procedure, and the basis set limit is estimated using a systematic increase of basis set size. We check the approximation of taking the self-energy diagonal in the HF basis, and to what extent the extended Koopman’s theorem is fulfilled using an approximate self-energy. Finally we try to model the information contained in the propagator in terms of a functional containing Hartree-Fock quantities and demonstrate the feasibility of simultaneously reproducing the correlation and ionization energy of an underlying ab initio model.

Quasiparticle properties in a density-functional framework

D. Van Neck, S. Verdonck, G. Bonny, P.W. Ayers, M. Waroquier
Physical Review A
74 (4), 042501
2006
A1

Abstract 

We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving a self-consistent set of single-particle equations. The method can be viewed as a nontrivial extension of the Kohn-Sham scheme (which is embedded as a special case). It is based on separating the Green’s function into a quasiparticle part and a background part, and expressing only the background part as a functional of the density matrix. The calculated single-particle energies and wave functions have a clear physical interpretation as quasiparticle energies and orbitals.

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

K. Peirs, D. Van Neck, M. Waroquier
Physical Review A
67 (1), 012505
2003
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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.

v-representability of one-body density matrices

D. Van Neck, M. Waroquier, K. Peirs, V. Van Speybroeck
Physical Review A
64 (4), 042512
2001
A1

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

Improved lower bounds for the ground-state energy of many-body systems

D. Van Neck, Y. Dewulf, M. Waroquier
Physical Review A
63, 062107
2001
A1

Abstract 

Alternative lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. These bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.

Electron penetration into the nucleus and its effect on the quadrupole interaction

K. Koch, K. Koepernik, D. Van Neck, H. Rosner, S. Cottenier
Physical Review A
81, 032507
2010
A1

Abstract 

series expansion of the interaction between a nucleus and its surrounding electron distribution provides terms that are well-known in the study of hyperfine interactions: the familiar quadrupole interaction and the less familiar hexadecapole interaction. If the penetration of electrons into the nucleus is taken into account, various corrections to these multipole interactions appear. The best known correction is a scalar term related to the isotope shift and the isomer shift. This paper discusses a related tensor correction, which modifies the quadrupole interaction if electrons penetrate the nucleus: the quadrupole shift. We describe the mathematical formalism and provide first-principles calculations of the quadrupole shift for a large set of solids. Fully relativistic calculations that explicitly take a finite nucleus into account turn out to be mandatory. Our analysis shows that the quadrupole shift becomes appreciably large for heavy elements. Implications for experimental high-precision studies of quadrupole interactions and quadrupole moment ratios are discussed. A literature review of other small quadrupole-like effects is presented as well (pseudoquadrupole effect, isotopologue anomaly, etc.).

Open Access version available at UGent repository

Faddeev random-phase approximation for molecules

M. Degroote, D. Van Neck, C. Barbieri
Physical Review A
83, 042517
2011
A1

Abstract 

The Faddeev random-phase approximation is a Green’s function technique that makes use of Faddeev equations to couple the motion of a single electron to the two-particle–one-hole and two-hole–one-particle excitations. This method goes beyond the frequently used third-order algebraic diagrammatic construction method: all diagrams involving the exchange of phonons in the particle-hole and particle-particle channel are retained, but the phonons are now described at the level of the random-phase approximation, which includes ground-state correlations, rather than at the Tamm-Dancoff approximation level, where ground-state correlations are excluded. Previously applied to atoms, this paper presents results for small molecules at equilibrium geometry. © 2011 American Physical Society

Open Access version available at UGent repository
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