Jerzy Cioslowski

Endohedral complexes : atoms and ions inside the C60 cage

The results of ab initio electronic structure calculations on the C60 cage and its endohedral (‘‘inside‐the‐cage’’) complexes with F−, Ne, Na+, Mg2+, and Al3+ are presented. Placing the ions at the center of the cage results in a net stabilization and screening of the charges. The ionic guests either decrease (F−) or increase (Na+, Mg2+, and Al3+ ) the cage radii. The complexes with the ions at the cage center are local maxima with respect to the displacement of the guests. The C60⋅Ne complex, which is destabilized by ca. 0.4 kcal/mol relative to the separated components, is an energy minimum. In the C60⋅Na+ complex, the energy minimum (which lies only 0.8 kcal/mol below the maximum) corresponds to the Na atom displaced by 0.66 A from the cage center. The calculated properties of the endohedral complexes are easily rationalized with a model involving a double‐layer polarizable C60 cage affected by the electrostatic potential produced by the enclosed guests.

Many-electron densities and reduced density matrices

Preface. I: Properties of Reduced Density Matrices. 1. RDMs: How Did We Get Here? A.J. Coleman. 2. Some Theorems on Uniqueness and Reconstruction of Higher-Order Density Matrices M. Rosina. 3. Cumulant Expansions of Reduced Densities, Reduced Density Matrices, and Greens Functions P. Ziesche. 4. On Calculating Approximate and Exact Density Matrices R. Erdahl, B. Jin. II: The Contracted Schroedinger Equation. 5. Density Equation Theory in Chemical Physics H. Nakatsuji. 6. Critical Questions Concerning Iterative Solution of the Contracted Schroedinger Equation C. Valdemoro, L.M. Tel, E. Perez-Romero 7. Cumulants and the Contracted Schroedinger Equation D.A. Mazziotti.. III: Density Matrix Functional Theory. 8. Natural Orbital Functional Theory S. Goedecker, C.J. Umrigar. 9. The Pair Density in Approximate Density Functional Theory: The Hidden Agent N.T. Maitra, K. Burke. 10. Functional N-representability in Density Matrix and Density Functional Theory: An Illustration for Hookes Atom E.V. Ludena, V. Karasiev, A. Artemiev, D. Gomez.. IV: Electron Intracule and Extracule Densities. 11. Intracule and Extracule Densities: Historical Perspectives and Future Prospects E. Valderrama, J.M. Ugalde, R.J. Boyd. 12. Topology of Electron Correlation J. Cioslowski. 13. Electron-Pair Densities of Atoms T. Koga. Index.

Rapid evaluation of atomic properties with mixed analytical/numerical integration

Abstract A novel approach to computation of atomic properties is presented. The new algorithm, which takes advantage of analytical radial integration used in conjunction with efficient thresholding, makes it possible to calculate properties of atoms in molecules with 12–120 nuclei 3.5–9.0 times faster than the previously published program VECAIM. Analysis of the new algorithm shows that its computational cost is independent of molecular size and can be as small as a few minutes of CPU time per atom on the CRAY Y-MP supercomputer.

An observable-based interpretation of electronic wavefunctions: application to “hypervalent” molecules

Abstract The quantum-mechanical definition of observables is extended to all properties that can be derived from experimentally measurable quantities with the help of universal operators. Even such an extended definition, however, does not cover several commonly used concepts such as atomic orbitais in molecules or Mulliken atomic charges. Principles of an observable-based interpretation of electronic wavefunctions are outlined. Such an approach avoids ill-defined properties and concepts, therefore minimizing arbitrariness inherent in the interpretation process. Currently known atomic and bond quantities that are observable are reviewed and applied to four “hypervalent” molecules containing sulfur atoms. It is found that the S-O bonds in the molecules under study have highly ionic character and bond orders close to unity. This clear-cut analysis demonstrates that the octet rule is not violated in “hypervalent” compounds with one or two S-O bonds.

An efficient approach to calculation of zero‐flux atomic surfaces and generation of atomic integration data

A new robust method for variational determination of atomic zero‐flux surfaces is presented. The zero‐flux surface sheets are expressed in terms of variational trial functions in prolate spheroidal coordinates. The trial functions are optimized with a Newton procedure to satisfy the zero‐flux condition on a grid. The data required for radial integrations are generated by an adaptive quadrature procedure that employs model electron densities and utilizes an original third‐order algorithm for linear search. Results of test calculations involving variational determination of atomic surfaces are presented for a representative set of 20 molecules. The new approach is both less time consuming and substantially more accurate than the previously published algorithms.

A new robust algorithm for fully automated determination of attractor interaction lines in molecules

Abstract A new algorithm for locating bond critical points and attractor interaction lines in molecules is described. The drawbacks of the conventional algorithm, which include occasional divergence and the need for good starting coordinates, are completely eliminated. The new approach employs parametric equations to describe the attractor interaction lines. It requires only the electron density and the Cartesian coordinates of nuclei as input, meaning that all of the bond critical points can be located in a completely automated fashion. The performance of the new algorithm is demonstrated for several medium-size and large molecules.

The ground state of harmonium

A detailed analysis that benefits from a slate of new approximate numerical and exact asymptotic results produces highly accurate properties of the ground state of the harmonium atom as functions of the confinement strength ω and quantifies the domains of the weakly and strongly correlated regimes in this system. The former regime, which encompasses the values of ω greater than ωcrit≈4.011 624×10−2, is characterized by the one-electron density ρ(ω;r1) with a global maximum at r1=0. In contrast, the harmonium atom within the latter regime, which corresponds to ω<ωcrit, differs fundamentally from both its weakly correlated counterpart and Coulombic systems. Resembling a Wigner crystal of a homogeneous electron gas, it possesses a radially localized pair of angularly correlated electrons that gives rise to ρ(ω;r1) with a “fat attractor” composed of a cage critical point and a (1, −1) critical sphere. Allowing for a continuous variation in ω, the new compact representation of the ground-state wave function an...

A set of standard enthalpies of formation for benchmarking, calibration, and parametrization of electronic structure methods

A comprehensive set of 600 experimental standard enthalpies of formation (ΔHf0) is presented. With its diverse species, many possessing less usual geometries and bonding situations, this compilation is capable of uncovering deficiencies in approaches of quantum chemistry that are not detectable with smaller sets of ΔHf0 values. Its usefulness in benchmarking, calibration, and parametrization of new electronic structure methods is illustrated with the development of the B3LYP/6-311++G** bond density functional scheme. This scheme, which is sufficiently inexpensive in terms of computer time and memory to allow predictions even for molecules as large as the C60 fullerene, requires only single point calculations at optimized geometries. It yields values of ΔHf0 with the average absolute error of 3.3 kcal/mol, rivaling more expensive methods in accuracy (especially for larger systems). A list of species that are poorly handled by a typical hybrid density functional used in conjunction with a moderate-size basis set is given. This list is intended for rigorous testing of new density functionals.A comprehensive set of 600 experimental standard enthalpies of formation (ΔHf0) is presented. With its diverse species, many possessing less usual geometries and bonding situations, this compilation is capable of uncovering deficiencies in approaches of quantum chemistry that are not detectable with smaller sets of ΔHf0 values. Its usefulness in benchmarking, calibration, and parametrization of new electronic structure methods is illustrated with the development of the B3LYP/6-311++G** bond density functional scheme. This scheme, which is sufficiently inexpensive in terms of computer time and memory to allow predictions even for molecules as large as the C60 fullerene, requires only single point calculations at optimized geometries. It yields values of ΔHf0 with the average absolute error of 3.3 kcal/mol, rivaling more expensive methods in accuracy (especially for larger systems). A list of species that are poorly handled by a typical hybrid density functional used in conjunction with a moderate-size basi...

An efficient evaluation of atomic properties using a vectorized numerical integration with dynamic thresholding

Abstract A new efficient algorithm for the evaluation of atomic properties by means of numerical integration over atomic basins is described. The fully vectorized algorithm takes advantage of a dynamic thresholding technique which neglects the primitive Cartesian Gaussian functions that do not contribute significantly to the properties of a given atom. This results in a procedure with a computational effort that scales only linearly with the size of the molecule in question, as opposed to the quadratic size dependence of the traditional approach. The ensuing savings in CPU time, which vary between 90% and 99%, make the determination of the properties of atoms in such molecules as C 60 and C 60 H 60 routinely feasible. In the latter molecule, it is found that on average only ≈8% of the primitives survive the thresholding algorithm capable of reproducing the exact properties within 10 −6 au.

Electron flow and electronegativity equalization in the process of bond formation

Charge‐constrained calculations make it possible to rigorously analyze electron flow and electronegativity equalization in the process of bond formation. Such an analysis is performed for the prototypical H2, HF, and LiH molecules. As the bonds are stretched, the dependence of the electronegativity difference on the extent of charge transfer undergoes a transition from approximate linearity to a steplike discontinuous character. With the help of the second‐order perturbation theory, the bond hardness is related to the matrix elements of the fragment‐electron‐count operator and is shown to increase exponentially with the bond length R at the dissociation limit. For polar bonds, the magnitude of the in situ electronegativity difference ΔχAB decreases quickly with R due to the decreasing polarization of the fragments. However, ΔχAB levels off for large distances, and most of the reduction in charge transfer that accompanies bond dissociation can be attributed to the dramatic increase in the bond hardness. Th...