Biomedical subjects

Katarzyna Pernal

Publications and source records attributed to Katarzyna Pernal.

6 recordsLinked to original sources

PubMed2006

Wigner molecules: the strong-correlation limit of the three-electron harmonium.

At the strong-correlation limit, electronic states of the three-electron harmonium atom are described by asymptotically exact wave functions given by products of distinct Slater determinants and a common Gaussian factor that involves interelectron distances and the center-of-mass position. The Slater determinants specify the angular dependence and the permutational symmetry of the wave functions. As the confinement strength becomes infinitesimally small, the states of different spin multiplicities become degenerate, their limiting energy reflecting harmonic vibrations of the electrons about their equilibrium positions. The corresponding electron densities are given by products of angular factors and a Gaussian function centered at the radius proportional to the interelectron distance at equilibrium. Thanks to the availability of both the energy and the electron density, the strong-correlation limit of the three-electron harmonium is well suited for testing of density functionals.

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PubMed2006

Coupled-perturbed density-matrix functional theory equations. Application to static polarizabilities.

Starting from the variational equations for the natural occupation numbers and the recently proposed eigenequations for the natural spin-orbitals, we derive coupled-perturbed density-matrix equations that furnish a linear response of the one-electron reduced density matrix to a static perturbation when the total energy is a functional of the one-electron reduced density matrix. Cases when some occupation numbers achieve exactly 0 or 1 or when the total number of the particles in a system is not preserved are taken into consideration. The scheme is applied to computing static polarizabilities from two simple density-matrix functionals. The behavior of the functionals is erratic and they provide only little or no improvement over the coupled-perturbed Hartree-Fock results.

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PubMed2005

Effective potential for natural spin orbitals.

For the first time the explicit form of the effective nonlocal potential for the natural spin orbitals is derived and analyzed. It is shown that in the case of the degenerate one-electron reduced density matrix the potential is not unique. The knowledge of the effective potential allows one to establish one-electron equations for the natural spin orbitals that may be of great value for efficient density matrix functional theory calculations.

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PubMed2005

An improved density matrix functional by physically motivated repulsive corrections.

An improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB). The first correction C1 restores the repulsive exchange-correlation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density rho(2) for the limiting two-electron case. The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchange-type interaction. The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond. In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals). With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond. BBC greatly improves the quality of the BB potential energy curves for the prototype few-electron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves. The average error of the self-consistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca. 6%.

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PubMed2004

Size versus volume extensivity of a new class of density matrix functionals.

Despite being size-extensive, the "second-generation" 1-matrix functionals for the electron-electron repulsion energy V(ee) yield vanishing correlation energy for the homogeneous electron gas. This failure is directly related to the idempotency condition imposed upon an auxiliary matrix that enters the expression for V(ee). In particular, the recently proposed Kollmar-Hess functional is not volume-extensive and thus is incapable of properly describing any delocalized system at its thermodynamic limit.

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PubMed2004

Phase dilemma in density matrix functional theory.

For closed-shell systems, a particular parametrization of coefficients in a configuration interaction (CI) expansion provides a convenient formulation for the search over electronic wave functions constrained by a set of natural orbitals (NOs) and the corresponding occupation numbers that are invoked in every variational construction of the density matrix functional (DMF) V(ee)(Gamma) for the electron--electron repulsion energy. It produces an explicit expression for V(ee) in terms of the Coulomb and exchange integrals over NOs, and an idempotent matrix omega, diagonal elements of which equal the occupation numbers. At the same time, it reveals a very serious bottleneck affecting any rigorous approach to the DMF theory, namely the phase dilemma that stems from the necessity to carry out minimization over a large number of possible combinations of CI coefficient signs. While underscoring its lack of variational nature, a simple approximation for the phase factor products provides a strict derivation for the recently proposed Kollmar-Hess functional.

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