Molecular alignment as a penalized permutation Procrustes problem

Molecular alignment is viewed as a permutation Procrustes problem, where the goal is to find the best assignment of points (or functional groups) in one molecule to the points in another molecule. A penalty function ensures that the optimal alignment respects the underlying connectivity between atoms/points. This method helps reveal why molecular alignment suffers from the curse of dimension.     

On the electronegativity nonlocality paradox

The electronegativity equalization principle states that, in its ground state, the electronegativity of every component in a system is the same. A paradox then arises: molecular fragments that are very far apart must still have the same electronegativity, which seems to contradict the common assumption that spatially separated molecular species can be described independently. Density-functional theory provides the tools needed to analyze this paradox at a fundamental level, and a resolution is found from the properties of the exact Hohenberg–Kohn functional. Specifically, there is no paradox because the electronegativity is not uniquely defined for separated systems. Instead, there is an “apparent electronegativity” that preserves locality. This may have implications for the treatment of charge-transfer excited states. A model for the energy as a function of the number of electrons is also presented. This model gives some insight into the utility of the grand canonical ensemble formulation (at nonzero temperature) and, unlike most previous models, this model recovers the appropriate behavior in the limits of infinitely separated and/or weakly interacting subsystems.     

Korrosion

Ohne Zusammenfassung     

Azido derivatives of low-valent group 14 elements: synthesis, characterization, and electronic structure of [(n-Pr)2ATI]GeN3 and [(n-Pr)2ATI]SnN3 featuring heterobicyclic 10-pi-electron ring systems

Treatment of THF solutions of [(n-Pr)2ATI]MCl (where [(n-Pr)2ATI]- = N-(n-propyl)-2-(n-propylamino)troponiminate; M = Ge and Sn) with sodium azide affords the compounds [(n-Pr)2ATI]MN3 in excellent yield. X-ray analyses revealed that these Ge(II) and Sn(II) compounds feature linear azide moieties and planar heterobicyclic C7N2M ring systems. Germanium and tin atoms adopt a pyramidal geometry. IR spectra of [(n-Pr)2ATI]GeN3 and [(n-Pr)2ATI]SnN3 display a nu asym(N3) band at 2048 and 2039 cm-1, respectively. DFT calculations on the corresponding methyl-substituted species demonstrate that the geometrical and electronic structure of these two species are very similar, and the dominant canonical form of the metal-azide moiety is M-N-N identical to N. The tin system is, as expected, slightly more ionic. A comparative CASSCF/DFT study on the model system H-Sn-N3 illustrates that the DFT approach is viable for the calculation of the structures of these species.     

Hamilton-Jacobi equation for the least-action/least-time dynamical path based on fast marching method

Classical dynamics can be described with Newton's equation of motion or, totally equivalently, using the Hamilton-Jacobi equation. Here, the possibility of using the Hamilton-Jacobi equation to describe chemical reaction dynamics is explored. This requires an efficient computational approach for constructing the physically and chemically relevant solutions to the Hamilton-Jacobi equation; here we solve Hamilton-Jacobi equations on a Cartesian grid using Sethian's fast marching method. Using this method, we can--starting from an arbitrary initial conformation--find reaction paths that minimize the action or the time. The method is demonstrated by computing the mechanism for two different systems: a model system with four different stationary configurations and the H+H(2)-->H(2)+H reaction. Least-time paths (termed brachistochrones in classical mechanics) seem to be a suitable chioce for the reaction coordinate, allowing one to determine the key intermediates and final product of a chemical reaction. For conservative systems the Hamilton-Jacobi equation does not depend on the time, so this approach may be useful for simulating systems where important motions occur on a variety of different time scales.     

The dependence on and continuity of the energy and other molecular properties with respect to the number of electrons

It was recently shown that the size consistency of the energy implies that, for any system with a rational number of electrons, the energy is given by the weighted average of the two systems with the nearest integer numbers of electrons. Specifically, E[N+P/Q] = (1−P/Q)E[N] + (P/Q)E[N+1]. This paper extends that analysis, showing that the same result holds for irrational numbers of electrons. This proves that the energy is a continuous function of the number of electrons, and justifies differentiation with respect to electron number, providing a rigorous justification or the density-functional theoretic approaches to chemical concepts like the electronegativity and the Fukui function. Similar results hold for properties other than the energy. Specific emphasis is placed on molecular response properties associated with the density-functional theory of chemical reactivity.     

Potential functionals: dual to density functionals and solution to the v-representability problem

A functional of external potentials and its variational principle for the ground-state energy is constructed. This potential functional formulation is dual to the density functional approach and provides a solution to the v-representability problem in the original Hohenberg-Kohn theory. A second potential functional for Kohn-Sham noninteracting systems establishes the foundation for the optimized effective potential approach and results in efficient approaches for ensemble Kohn-Sham calculations.     

Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.