Felipe A. Bulat

Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies

AbstractWe 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. FigureCalculated electrostatic potential (left) and average local ionization energy (right) on the molecular surface of Tetryl. Yellow and black circles indicate the positions of the local minima and maxima, respectively.

Density-functional theory (hyper)polarizabilities of push-pull π-conjugated systems: Treatment of exact exchange and role of correlation

The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.

Optimized effective potentials in finite basis sets

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.

A donor-nanotube paradigm for nonlinear optical materials.

Studies of the nonlinear electronic response of donor/acceptor substituted nanotubes suggest a behavior that is both surprising and qualitatively distinct from that in conventional conjugated organic species. We find that the carbon nanotubes serve as both electronic bridges and acceptors, leading to a donor-nanotube paradigm for the effective design of large first hyperpolarizabilities. We also find that tuning the donor orientation, relative to the nanotube, can significantly enhance the first hyperpolarizability.

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains : Treatment of exact exchange and role of correlation

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.

Hydrogenation and Fluorination of Graphene Models: Analysis via the Average Local Ionization Energy

We have investigated the use of the average local ionization energy, I[combining overline](S)(r), as a means for rapidly predicting the relative reactivities of different sites on two model graphene surfaces toward the successive addition of one, two, and three hydrogen or fluorine atoms. The I[combining overline](S)(r) results were compared with directly computed interaction energies, at the B3LYP/6-311G(d,p) level. I[combining overline](S)(r) correctly predicts that the edges of graphene sheets are more reactive than the interior portions. It shows that added hydrogens activate the adjoining (ortho) sites and deactivate those that are separated by one site (meta). Overall, I[combining overline](S)(r) is effective for rapidly (single calculations) estimating the relative site reactivities of these large systems, although it reflects only the system prior to an interaction and cannot take into account postinteraction factors, e.g., structural distortion.

Optimized effective potentials from electron densities in finite basis sets

The Wu-Yang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its ill-posed nature, as recently done for the direct minimization method for OEPs from a given orbital functional [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the Kohn-Sham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the ill-posed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.

Average Local Ionization Energies as a Route to Intrinsic Atomic Electronegativities

Historically, two important approaches to the concept of electronegativity have been in terms of: (a) an atom in a molecule (e.g., Pauling) and (b) the chemical potential. An approximate form of the latter is now widely used for this purpose, although it includes a number of deviations from chemical experience. More recently, Allen introduced an atomic electronegativity scale based upon the spectroscopic average ionization energies of the valence electrons. This has gained considerable acceptance. However it does not take into account the interpenetration of valence and low-lying subshells, and it also involves some ambiguity in enumerating d valence electrons. In this paper, we analyze and characterize a formulation of relative atomic electronegativities that is conceptually the same as Allens but avoids the aforementioned problems. It involves the property known as the average local ionization energy, I̅(r), defined as [Formula: see text], where ρi(r) is the electronic density of the i(th) orbital, having energy εi, and ρ(r) is the total electronic density. I̅(r) is interpreted as the average energy required to remove an electron at the point r. When I̅(r) is averaged over the outer surfaces of atoms, taken to be the 0.001 au contours of their electronic densities, a chemically meaningful scale of relative atomic electronegativities is obtained. Since the summation giving I̅(r) is over all occupied orbitals, the issues of subshell interpenetration and enumeration of valence electrons do not arise. The procedure is purely computational, and all of the atoms are treated in the same straightforward manner. The results of several different Hartree-Fock and density functional methods are compared and evaluated; those produced by the Perdew-Burke-Ernzerhof functional are chemically the most realistic.

The average local ionization energy as a tool for identifying reactive sites on defect-containing model graphene systems

AbstractIn a continuing effort to further explore the use of the average local ionization energy