Precision is given to the concept of electronegativity. It is the negative of the chemical potential (the Lagrange multiplier for the normalization constraint) in the Hohenberg–Kohn density functional theory of the ground state: χ=−μ=−(∂E/∂N)v. Electronegativity is constant throughout an atom or molecule, and constant from orbital to orbital within an atom or molecule. Definitions are given of the concepts of an atom in a molecule and of a valence state of an atom in a molecule, and it is shown how valence-state electronegativity differences drive charge transfers on molecule formation. An equation of Gibbs–Duhem type is given for the change of electronegativity from one situation to another, and some discussion is given of certain relations among energy components discovered by Fraga.

Computations at the Hartree-Fock level on ammonia and ethane verify the principle of maximum hardness as developed by Parr and Chattaraj. The point groups of the molecules are determined by maximum hardness. However, the equilibrium bond angles and distances are determined by the electrostatic Hellman-Feynman theorem.

Exact numerical calculations are made for the scattering of quantum mechanical particles from a square two-dimensional potential barrier. This treatment is an exact analog of both frustrated total reflection of perpendicularly polarized light and the longitudinal Goos-Hänchen shift. Quantum mechanical streamlines (which are analogous to either classical mechanical trajectories or optical rays) are plotted. These streamlines are smooth, continuous, and have continuous first derivatives even through the classically forbidden region. The streamlines form quantized vortices surrounding each of the nodal points (which result from interference between the incident and reflected waves). Similar vortices occur in reactive collisions of H + H2 (McCullough and Wyatt; Kuppermann, Adams, and Truhlar) and undoubtedly play an important role in molecular collision dynamics. The theory for these vortices is given in a companion paper. A comparison is given between our numerical calculations and the stationary phase approximation (SPA). Although our incident wave packet has a half-width of more than one de Broglie wavelength in contrast to the SPA which replaces the diffuse beams by rays with delta function profiles, the agreement was surprisingly good for both the Goos-Hänchen shifts and for the reflection coefficients. However, we found that the Goos-Hänchen shift for the transmitted beam is significantly smaller than for the reflected beam, although in the stationary phase approximation these two shifts are equal. Furthermore, we found that the scattering from the potential barrier has very little effect on the shape of the wave packets. The power series expansion of the incident Debye-Picht wave packet ψI has an extremely small radius of convergence, whereas the power series for ψI*ψI has a radius of convergence of more than two de Broglie wavelengths. The imaginary velocity viis introduced into the Madelung-Landau-London hydrodynamical formulation of quantum mechanics. The corresponding imaginary streamlines will be considered in a forthcoming paper. The time-independent Schrödinger equation for real wavefunctions is reduced to solving the nonlinear first order partial differential equation: ℏ▿·vi = 2(E − V) + vi2. Here, vi is irrotational. This equation may lead to interesting new methods of solving the Schrödinger equation. It does lead to a generalization of the Prager-Hirschfelder perturbation scheme which invokes an electrostatic analogy. The philosophical implications of the hydrodynamical formulation of quantum mechanics are discussed. Penetration of a one-dimensional square potential barrier is used to demonstrate exactly how tunneling occurs by particles ``riding over the barrier'' à la Bohm. Cases are cited where quantum and classical mechanical motions are identical.

The Cu(1) tetranuclear cluster Cu414py4 (I, py = pyridine), together with several analogues of general formula Cu414L4, presents remarkable photophysical properties, which have been attributed to two poorly coupled emissive excited states of different orbital parentages2 Ab initio calculations at the restricted HartreeFock self-consistent field level on this and related systems have been used to complement the results of the experimental spectroscopic studies. The outcome indicates an iodinatepyridine charge transfer nature for the state(s) responsible for the high-energy emission band of I. In contrast, the low-energy emission band is assigned to a transition with both iodine-to-copper charge transfer and metal centered 3d -4s promotion within the Cu414 cluster core; thus this band is labelled a cluster-centered (CC) transition. The lack of communication between the two excited states is explained by different respective distortions relative to the ground state, as indicated by excitation-induced changes in the calculated bond orders. Calculations are also described for the hypothetical cluster Cu414(NH,),, as a model for compounds like Cu414pip4 (pip = the saturated amine piperidine) for which only CC emission has been observed.

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