We describe a procedure for performing quantitative analyses of fields f(r) on molecular surfaces, including statistical quantities and locating and evaluating their local extrema. Our approach avoids the need for explicit mathematical representation of the surface and can be implemented easily in existing graphical software, as it is based on the very popular representation of a surface as collection of polygons. We discuss applications involving the volumes, surface areas and molecular surface electrostatic potentials, and local ionization energies of a group of 11 molecules.

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The average local ionization energy I(r) is the energy necessary to remove an electron from the point r in the space of a system. Its lowest values reveal the locations of the least tightly-held electrons, and thus the favored sites for reaction with electrophiles or radicals. In this paper, we review the definition of I(r) and some of its key properties. Apart from its relevance to reactive behavior, I(r) has an important role in several fundamental areas, including atomic shell structure, electronegativity and local polarizability and hardness. All of these aspects of I(r) are discussed.

We report the first observation of the n-type nature of hydrogenated graphene on SiO(2) and demonstrate the conversion of the majority carrier type from electrons to holes using surface doping. Density functional calculations indicate that the carrier type reversal is directly related to the magnitude of the hydrogenated graphene's work function relative to the substrate, which decreases when adsorbates such as water are present. Additionally, we show by temperature-dependent electronic transport measurements that hydrogenating graphene induces a band gap and that in the moderate temperature regime [220-375 K], the band gap has a maximum value at the charge neutrality point, is tunable with an electric field effect, and is higher for higher hydrogen coverage. The ability to control the majority charge carrier in hydrogenated graphene, in addition to opening a band gap, suggests potential for chemically modified graphene p-n junctions.

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of unbalanced, and thus unsuitable, basis sets. A modified functional incorporating a regularizing smoothness measure of the OEP is introduced. This provides a condition on balanced basis sets for the potential, as well as a method to determine the most appropriate OEP and energy from calculations performed with any finite basis set.