Biomedical subjects

Jerzy Cioslowski

Publications and source records attributed to Jerzy Cioslowski.

9 recordsLinked to original sources

PubMed2006

Wigner molecules: natural orbitals of strongly correlated two-electron harmonium.

Explicit asymptotic expressions for natural orbitals and their occupancies are derived for the harmonium atom at the strong-correlation limit at which the confinement strength omega tends to zero. Unlike in systems with moderate correlation effects, the occupancies at the omega-->0 limit (derived from occupation amplitudes with alternating sign patterns) are vanishingly small and asymptotically independent of the angular momentum, forming a geometric progression with the scale factor proportional to omega(1/3) and the common ratio of ca. 0.0186. The radial components of the natural orbitals are given by products of polynomials and Gaussian functions that, as expected, peak at approximately half of the equilibrium interelectron distance.

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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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PubMed2005

Simple approximants for natural orbitals of harmonium.

Simple approximations to the natural orbitals (NOs) of harmonium with enforced correct short- and long-range asymptotics yield accurate bounds for the NO occupancies. In particular, expressions involving Pade approximants with just one variational parameter are capable of producing the largest NO occupancies with accuracy better than 10(-4). The comparison of two cases with different coupling strengths omega (1.948 51<n<1.948 60 for omega=12 and 1.821 24<n<1.821 29 for omega=110) indicates that the bounds actually become tighter with the increasing extent of correlation. The expressions derived for the most strongly occupied NOs can be readily generalized to all natural orbitals of harmonium.

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PubMed2005

New constraints upon the electron-electron repulsion energy functional of the one-electron reduced density matrix.

Three strict constraints upon the electron-electron repulsion energy functional of the one-electron reduced density matrix (the 1-matrix) are obtained by combining its invariance and stationary properties with the extended Koopmans' theorem. The constraints relate the quantities derived from the functional pertaining to an N-electron system with those of its (N-1)-electron congener. Together with the N-representability requirement for the 1-matrix of the congener, identities involving the electron-electron repulsion energies of the two systems and their derivatives with respect to the 1-matrices seriously narrow down the choices for potential approximate density-matrix functionals. This fact is well illustrated in the case of two-electron systems, where the validity of the new constraints is confirmed and found to originate from a nontrivial cancellation among different terms. Thus, the constraints provide a new tool for the construction and testing of new functionals that complements the previously known conditions such as the reproduction of the homogeneous gas energies and momentum distributions, convexity, and the N-representability of the associated 2-matrices.

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PubMed2005

Collective natural orbital occupancies of harmonium.

In the harmonium atom, the collective occupancies {n(l)} of natural orbitals with different angular momenta l can be rigorously studied for those values of the confinement strength omega that lead to ground-state wave functions with correlation factors given by polynomials of kth order. Analysis of two such cases, with omega equal to 12 (k=1) and 110 (k=2), uncovers some interesting properties of {n(l)}, which turn out to be given by rational functions of pi(12) with simple coefficients. In particular, contrary to naive expectations, the collective occupancies for l>2 actually decrease upon strengthening of correlation. The explicit formulas for l-matrices and {n(l)} can be readily utilized in testing, calibration, and benchmarking of approximate implementations of the density matrix functional theory (DMFT).

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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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PubMed2002

Electronic structures and energetics of [5,5] and [9,0] single-walled carbon nanotubes.

Standard enthalpies of formation, ionization potentials, electron affinities, and band gaps of finite-length [5,5] armchair and [9,0] zigzag single-walled carbon nanotubes (SWNTs) capped with C(30) hemispheres obtained by halving the C(60) fullerene have been computed at the B3LYP/6-311G* level of theory. Properties of SWNTs are found to depend strongly on the tube length and, in the case of the [9,0] zigzag species, on the relative orientation of the caps. The metallic character of an uncapped infinite-length [5,5] armchair SWNT manifests itself in the oscillatory dependence of the properties of capped finite-length tubes on their size. An infinite-length [9,0] zigzag SWNT is predicted to be a semiconductor rather than a metal irrespective of the presence of caps. The present results underscore the slow convergence of SWNT properties with respect to the tube length and uncover small but significant radial distortions along the long axes of SWNTs.

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PubMed1996

Nonclassical Aryl Radicals: Intermediates or Transition States for the Hydrogen Shift Reactions?

Electronic properties of aryl radicals obtained by removing single hydrogen atoms from the sterically congested regions of benzo[c]phenanthrene, biphenyl, triphenylene, phenanthrene, and perylene are studied at the UBLYP/6-311G level of theory. Two structures are considered by each radical, the classical one involving a C-H.C arrangement of atoms and the nonclassical one possessing a three-center C-H-C linkage. The five nonclassical radicals under study are found to be transition states for degenerate 1,4- and 1,5-hydrogen shift reactions that interconvert the classical species. However, the results of the present calculations indicate that the nonclassical structures with the C-H distances in the C-H-C linkages shorter than 1.34 Å should be energy minima representing potentially observable chemical systems. The predicted energy barrier to the 1,5-hydrogen shift in the 1-benzo[c]phenanthrenyl radical is only 9.3 kcal/mol (6.1 kcal/mol with the zero-point energies included), making the hydrogen migration in this system facile at relatively low temperatures. Rigorous analysis of the computed electronic wave functions provides a clear-cut picture of bonding in both the classical and nonclassical aryl radicals.

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