D. Van Neck

On the thermal stability of vacancy–carbon complexes in alpha iron

D. Terentyev, G. Bonny, A. Bakaev, D. Van Neck
Journal of Physics: Condensed Matter
24, 385401
2012
A1

Abstract 

In this work we have summarized the available ab initio data addressing the interaction of carbon with vacancy defects in bcc Fe and performed additional calculations to extend the available dataset. Using an ab initio based parameterization, we apply object kinetic
Monte Carlo (OKMC) simulations to model the process of isochronal annealing in bcc Fe doped with carbon to compare with experimental data. As a result of this work, we clarify that a binding energy of ~0.65 eV for a vacancy–carbon (V–C) pair fits the available experimental
data best. It is found that the V2–C complex is less stable than the V–C pair and its dissociation with activation energy of 0.55 + 0.49 eV also rationalizes a number of experimental data where the breakup of V–C complexes was assumed instead. From the summarized ab initio data, the subsequently obtained OKMC results and critical discussion, provided here, we suggest that the twofold interpretation of the V–C binding energy, which is believed to vary between 0.47 and 0.65 eV, depending on the ab initio approximation, should be removed. The stability and mobility of small and presumably immobile SIA clusters formed at stage II is also discussed in the view of experimental data.

Self-consistent methods constrained to a fixed number of particles in a given fragment and its relation to the electronegativity equalization method

A. Cedillo, D. Van Neck, P. Bultinck
Theoretical Chemistry Accounts
131(6), 1227
2012
A1

Abstract 

The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the
electronegativity equalization method.

Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions

B. Verstichel, H. van Aggelen, W. Poelmans, D. Van Neck
Physical Review Letters
108 (21), 213001
2012
A1

Abstract 

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J.R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.

Open Access version available at UGent repository

Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations

S. Wouters, P.A. Limacher, D. Van Neck, P.W. Ayers
Journal of Chemical Physics
136, 134110
2012
A1

Abstract 

We have implemented the sweep algorithm for the variational optimization of SU(2) x U(1) (spin and particle number) invariant matrix product states (MPS) for general spin and particle number invariant fermionic Hamiltonians. This class includes non-relativistic quantum chemical systems within the Born-Oppenheimer approximation. High-accuracy ab-initio finite field results of the longitudinal static polarizabilities and second hyperpolarizabilities of one-dimensional hydrogen chains are presented. This allows to assess the performance of other quantum chemical methods. For small basis sets, MPS calculations in the saturation regime of the optical response properties can be performed. These results are extrapolated to the thermodynamic limit.

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

Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods

P. Bultinck, D. Van Neck, G. Acke, P.W. Ayers
Physical Chemistry Chemical Physics (PCCP)
14, 2408-2416
2012
A1

Abstract 

The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.

Faddeev random phase approximation for molecules

M. Degroote, D. Van Neck, C. Barbieri
Computer Physics Communications
182 (9) 1995-1998
2011
A1

Abstract 

This paper presents the problem of Molecular Beam Epitaxy and Reflection High-Energy Electron Diffraction with the help of a unified, modern MDA approach. Model-Driven Architecture (MDA) constitutes a modern and unusually efficient method of improving the process of generating software. It was created at the beginning of the twenty-first century by the Object Management Group as an element of Model-Driven Development, a highly promoted trend in software engineering. In MDA a viewpoint on a system is a technique for abstraction using a selected set of architectural concepts and structuring rules, in order to focus on particular concerns within a system. In MDA, system design begins with defining the problem domain. Next, at a highly abstract level independent of the system and programming platform a Platform-Independent Model (PIM) is constructed as well as a general system specification. This specification is created with the help of Unified Modeling Language. The real implementation of the system is performed through the transformation of PIM to Platform-Specific Model (PSM). The essence of Model-Driven Architecture is the replacement of the twentieth century approach to programming, calling that "everything is an object, to the modern "everything is a model". (C) 2011 Elsevier B.V. All rights reserved.

Open Access version available at UGent repository

Considerations on describing non-singlet spin states in variational second order density matrix methods

H. van Aggelen, B. Verstichel, P. Bultinck, D. Van Neck, P.W. Ayers
Journal of Chemical Physics
136, 014110
2012
A1

Abstract 

Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions. In pursuit of a consistent description of spin in second order density matrix theory, we propose and evaluate two main approaches: we consider constraints derived from a pure spin state and from an ensemble of spin states. This paper makes a comparative assessment of the different approaches by applying them to potential energy surfaces for different spin states of the oxygen and carbon dimer. We observe two major shortcomings of the applied spin constraints: they are not size consistent and they do not reproduce the degeneracy of the different states in a spin multiplet. First of all, the spin constraints are less strong when applied to a dissociated molecule than when they are applied to the dissociation products separately. Although they impose correct spin expectation values on the dissociated molecule, the dissociation products do not have correct spin expectation values. Secondly, both under “pure spin state conditions” and under “ensemble spin state” conditions is the energy a convex function of the spin projection. Potential energy surfaces for different spin projections of the same spin state may give a completely different picture of the molecule's bonding. The maximal spin projection always gives the most strongly constrained energy, but is also significantly more expensive to compute than a spin-averaged ensemble. In the dissociation limit, both the problem of nondegeneracy of equivalent spin projections, size-inconsistency and unphysical dissociation can be corrected by means of subspace energy constraints.

Fast density matrix-based partitioning of the energy over the atoms in a molecule consistent with the hirshfeld-I partitioning of the electron density

D. Vanfleteren, D. Ghillemijn, D. Van Neck, P. Bultinck, M. Waroquier, P.W. Ayers
Journal of Computational Chemistry
32 (16), 3485–3496
2011
A1

Abstract 

For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree–Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren et al., J Chem Phys 2010, 132, 164111). Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. As the Hartree–Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads to a corresponding partitioning of the Hartree–Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011

Nuclear equation of state and the structure of neutron stars

A.E.L. Dieperink, D. Van Neck, Y. Dewulf, V. Rodin
Nato Science series: Superdense QCD Matter and Compact Stars
20 (1), 1742-6588 | ISSN 1742-6588 (Print) ISSN 1742-6596 (Online)
2006
A2

Abstract 

The hadronic equation of state for a neutron star is discussed with a particular emphasis on the symmetry energy. The results of several microscopic approaches are compared and also a new calculation in terms of the self-consistent Green function method is presented. In addition possible constraints on the symmetry energy coming from empirical information from the neutron skin of finite nuclei are considered. | Invited talk presented at the Advanced Research Workshop on "Superdense QCD Matter and Compact Stars", Yerevan, Armenia, Sep 27 2003

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