In a continuing effort to further explore the use of the average local ionization energy [Formula: see text] as a computational tool, we have investigated how well [Formula: see text] computed on molecular surfaces serves as a predictive tool for identifying the sites of the more reactive electrons in several nonplanar defect-containing model graphene systems, each containing one or more pentagons. They include corannulene (C20H10), two inverse Stone-Thrower-Wales defect-containing structures C26H12 and C42H16, and a nanotube cap model C22H6, whose end is formed by three fused pentagons. Coronene (C24H12) has been included as a reference planar defect-free graphene model. We have optimized the structures of these systems as well as several monohydrogenated derivatives at the B3PW91/6-31G* level, and have computed their I(r) on molecular surfaces corresponding to the 0.001 au, 0.003 au and 0.005 au contours of the electronic density. We find that (1) the convex sides of the interior carbons of the nonplanar models are more reactive than the concave sides, and (2) the magnitudes of the lowest I(r) surface minima (the I S, min) correlate well with the interaction energies for hydrogenation at these sites. These I S, min values decrease in magnitude as the nonplanarity of the site increases, consistent with earlier studies. A practical benefit of the use of I(r) is that a single calculation suffices to characterize the numerous sites on a large molecular system, such as graphene and defect-containing graphene models.
Electrons , Graphite/chemistry , Models, Molecular , Catalytic Domain , Computer Simulation , Surface Properties
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.
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.
Graphite/chemistry , Hydrogen/chemistry , Models, Chemical , Nanostructures/chemistry , Nanostructures/ultrastructure , Computer Simulation , Electron Transport , Materials Testing , Models, Molecular , Semiconductors
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 Allen's but avoids the aforementioned problems. It involves the property known as the average local ionization energy, IÌ (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. IÌ (r) is interpreted as the average energy required to remove an electron at the point r. When IÌ (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 IÌ (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 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.
Thermodynamics , Electrons , Hardness , Ions , Models, Molecular
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.
Molecular Conformation , Static Electricity , Dimethyl Sulfoxide/chemistry , Ions , Surface Properties , Thermodynamics
We explored the relative stability, structure, and conductance of crossed nanotube junctions with dispersion corrected density functional theory. We found that the most stable junction geometry, not studied before, displays the smallest conductance. While the conductance increases as force is applied, it levels off very rapidly. This behavior contrasts with a less stable junction geometry that show steady increase of the conductance as force is applied. Electromechanical sensing devices based on this effect should exploit the conductance changes close to equilibrium.
We explore the connection between average local ionization energies computed within the Hartree-Fock (HF) and the Kohn-Sham (KS) frameworks, focusing on exchange-only KS theory. We find that they are connected through a local quantity for which good approximations exist; I(HF)(r) = I(KS)(r) + DeltaV(X)(r). This allows determination of HF local ionization energies from exchange-only KS calculations without utilizing a nonlocal potential. We also suggest interesting research directions that emerge during our analysis.
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.
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 OEP's 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.
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.
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.
Several molecular descriptors, based on topological approaches as well as on a more traditional orbital-based decomposition, have been used to asses relations with hydrogen bond strengths in a series of formic acid dimers and its sulfur derivatives. Particular attention has been devoted to the analysis of the core-valence bifurcation topological index and to the bond order index. Their values are seen to be linearly related to bond energies estimated through a bond-energy-bond-order relationship; also, the mean value of the topological index appears to be related to the complexation energy computed by methods based on density functional theory. The dependence of the index upon the donor-acceptor couple in relation to its applicability is discussed.
Formates/chemistry , Sulfur Compounds/chemistry , Computer Simulation , Dimerization , Hydrogen Bonding , Models, Chemical
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.
