The potential energy surfaces in gas phase and in aqueous solution for the nitration of benzene, chlorobenzene, and phenol have been elucidated with density functional theory at theM06-2X/6-311G(d,p) level combined with the polarizable continuum solvent model (PCM). Three reaction intermediates have been identified along both surfaces: the unoriented pi-complex (I), the oriented reaction complex (II), and the sigma-complex (III). In order to obtain quantitatively reliable results for positional selectivity and for modeling the expulsion of the proton, it is crucial to take solvent effects into consideration. The results are in agreement with Olah's conclusion from over 40 years ago that the transition state leading to (II) is the rate-determining step in activated cases, while it is the one leading to (III) for deactivated cases. The simplified reactivity approach of using the free energy for the formation of (III) as a model of the rate-determining transition state has previously been shown to be very successful for halogenations, but problematic for nitrations. These observations are rationalized with the geometric and energetic resemblance, and lack of resemblance respectively, between (III) and the corresponding rate determining transition state. At this level of theory, neither the sigma-complex (III) nor the reaction complex (II) can be used to accurately model the rate-determining transition state for nitrations.

The halogenation of monosubstituted benzenes in aqueous solvent was studied using density functional theory at the PCM-M06-2X/6-311G(d,p) level. The reaction with Cl-2 begins with the formation of C atom coordinated pi-complex and is followed by the formation of the sigma-complex, which is rate-determining. The final part proceeds via the abstraction of the proton by a water molecule or a weak base. We evaluated the use of the sigma-complex as a model for the rate-determining transition state (TS) and found that this model is more accurate the later the TS comes along the reaction coordinate. This explains the higher accuracy of the model for halogenations (late TS) compared to nitrations (early TS); that is, the more deactivated the substrate the later the TS. The halogenation with Br-2 proceeds with a similar mechanism as the corresponding chlorination, but the bromination has a very late rate-determining TS that is similar to the sigma-complex in energy. The iodination with ICl follows a different mechanism than chlorination and bromination. After the formation of the pi-complex, the reaction proceeds in a concerted manner without a sigma-complex. This reaction has a large primary hydrogen kinetic isotope effect in agreement with experimental observations.

Using local DFT-based probes for electrostatic as well as charge transfer/polarization interactions, we are able to characterize Lewis basic and acidic sites on copper, silver and gold nanoparticles. The predictions obtained using the DFT-probes are compared to the interaction energies of the electron donating (CO, H2O, NH3 and H2S) and the electron accepting (BH3, BF3, HCl [H-down] and Na+) compounds. The probes include the local electron attachment energy [E(r)], the average local ionization energy [Ī(r)], and the electrostatic potential [V(r)] and are evaluated on isodensity surfaces located at distances corresponding to typical interaction distances. These probes have previously been successful in characterizing molecular interactions. Good correlations are found between Lewis acidity and maxima in V(r), appearing as a consequence of σ-holes, as well as minima in E(r), of the noble metal nanoparticles. Similarly are Lewis basic sites successfully described by surface minima in V(r) and Ī(r); the former are indicative of σ-lumps, i.e. regions of enhanced σ-density. The investigated probes are anticipated to function as reliable tools in nanoparticle reactivity and interaction characterization, and may act as suitable descriptors in large-scale screenings for materials of specific properties, e.g. in heterogeneous catalysis. Because of the similarity between the noble metal nanoparticle's interactions with Lewis bases and the concepts of halogen and hydrogen bonding, a new class of bonds is introduced-regium bonds-taking place between a σ-hole of a Cu, Ag or Au compound and an electron donor.

The initial steps of Cu₂O sulphidation to Cu₂S have been studied using plane-wave density functional theory at the PBE-D3+U level of sophistication. Surface adsorption and dissociation of H₂S and H₂O, as well as the replacement reaction of lattice oxygen with sulphur, have been investigated for the most stable (111) and (100) surface facets under oxygen-lean conditions. We find that the (100) surface is more susceptible to sulphidation than the (111) surface, promoting both H₂S adsorption, dissociation and the continued oxygen–sulphur replacement. The results presented in this proceeding bridge previous results from high-vacuum experiments on ideal surface to more realistic corrosion conditions and set the grounds for future mechanistic studies. Potential implications on the long-term final disposal of spent nuclear fuel are discussed.

Adsorption and desorption of methanol on the (111) and (100) surfaces of  Cu2O have been studied using high-resolution photoelectron spectroscopy in the temperature range 120–620 K, in combination with density functional theorycalculations and sum frequency generation spectroscopy. The bare (100) surfaceexhibits a (3,0; 1,1) reconstruction but restructures during the adsorption process into a Cu-dimer geometry stabilized by methoxy and hydrogen binding in Cu-bridge sites. During the restructuring process, oxygen atoms from the bulk that can host hydrogen appear on the surface. Heating transforms methoxy to formaldehyde, but further dehydrogenation is limited by the stability of the surface and the limited access to surface oxygen. The (√3 × √3)R30°-reconstructed (111) surface is based on ordered surface oxygen and copper ions and vacancies, which offers a palette of adsorption and reaction sites. Already at 140 K, a mixed layer of methoxy, formaldehyde, and CHxOy is formed. Heating to room temperature leaves OCH and CHx. Thus both CH-bond breaking and CO-scission are active on this  surface at low temperature. The higher ability to dehydrogenate methanol on (111) compared to (100) is explained by the multitude of adsorption sites and, in particular, the availability of surfaceoxygen.

Crystalline surfaces of gold are chemically inert, whereas nanoparticles of gold are excellent catalysts for many reactions. The catalytic properties of nanostructured gold have been connected to increased binding affinities of reactant molecules to low-coordinated Au atoms. Here we show that the high reactivity at these sites is a consequence of the formation of σ-holes, i.e. maxima in the surface electrostatic potential (Vs,max) due to the overlap of mainly the valence s-orbitals when forming the bonding σ-orbitals. The σ-holes are binding sites for Lewis bases, and binding energies correlate with magnitudes of the Vs,max. For symmetrical Au clusters, of varying size, the most positive Vs,max are found at corners, edges, and surfaces (facets) and decreasing in that order. This is in agreement with the experimentally and theoretically observed dependence of catalytic activity on local structure. The density of σ-holes can explain the increasing catalytic activity with decreasing particle size also for other transition metal catalysts, such as platinum.

Transition metal oxide nanoparticles are common materials in a multitude of applications including heterogeneous catalysis, solar energy harvesting, and energy storage. Understanding the particles' interplay with their surroundings is key to their efficient usage and design. Herein two DFT-based descriptors are used to study local reactivity on (TiO2)(n) (n = 7-10) nanoparticles. The local electron attraction energy [E(r)] and the electrostatic potential [V(r)], evaluated on isodensity surfaces, are able to identify and rank Lewis acidic sites on the particles with high accuracy when compared to the interaction energies of the Lewis bases H2O, H2S, NH3, and CO. These interactions are characterized as mainly electrostatically controlled. Given the local character, low computational cost, and excellent performance of the E-s(r) and V-s(r) descriptors, they are anticipated to find widespread use in nanoparticle research and development.

A local multiorbital electrophilicity descriptor, the local electron attachment energy [E(r)], is used to study the nucleophilic aromatic substitution reactions of SNAr and VNS (vicarious nucleophilic substitution). E(r) considers all virtual orbitals below the free electron limit and is determined on the molecular isodensity contour of 0.004 atomic units. Good (R-2 = 0.83) to excellent (R-2 = 0.98) correlations are found between descriptor values and experimental reactivity data for six series of electron deficient arenes. These include homo- and heteroarenes, rings of five to six atoms, and a variety of fluorine, bromine, and hydride leaving groups. The solvent, temperature, and nucleophile are in addition varied across the series. The surface E(r) [E-s(r)] is shown to provide reactivity predictions better than those of transition-state calculations for a concerted SNAr reaction with a bromine substantially stronger than those of LUMO energies, and is overall more reliable than the molecular electrostatic potential. With the use of E-s(r), one can identify the various electrophilic sites within a molecule and correctly predict isomeric distributions. Since the calculations of E-s(r) are computationally inexpensive, the descriptor offers fast but accurate reactivity predictions for the important nucleophilic aromatic substitution class of reactions. Applications in, e.g., drug discovery, synthesis, and toxicology studies are envisaged.

In this work, sampled-current voltammetry performed on a series of aryldiazonium, diaryliodonium, and triarylsulfonium salts allows the determination of the reduction potential of aryl radicals in acetonitrile. Specifically, this is accomplished by measuring the number of electrons consumed in the reduction process as a function of the applied potential. For the phenyl, 4-bromophenyl, and 4-nitrophenyl radicals, the reduction potential is found to be -0.91 +/- 0.06, -0.90 +/- 0.10, and -0.98 +/- 0.06 V vs. SCE, respectively. Furthermore, from measurements on an extended series of substituted compounds, it is concluded that the substituent effect on the reduction potential is small, which can be explained by the sigma nature of the aryl radical as evidenced from theoretical calculations. At the same time this yields a mean value for the reduction potential of the aryl radical of -0.87 V +/- 0.03 V vs. SCE. Determination of the intrinsic barrier and the standard potential from the data obtained are more uncertain since it is unknown to which extent the competing reference reaction, the electrochemical grafting reaction, is affected by the applied potential. From calculations using density functional theory, the intrinsic barrier for the reduction of the phenyl radical is determined to be 0.32 eV.

Understanding the molecular interaction behavior of transition metal nanoclusters lies at the heart of their efficient use in, e.g., heterogeneous catalysis, medical therapy and solar energy harvesting. For this purpose, we have evaluated the applicability of the surface electrostatic potential [VS(r)] and the local surface electron attachment energy [ES(r)] properties for characterizing the local Lewis acidity of a series of low-energy TM13 transition metal nanoclusters (TM = Au, Cu, Ru, Rh, Pd, Ir, Pt, Co), including also Pt7Cu6. The clusters have been studied using hybrid Kohn–Sham density functional theory (DFT) calculations. The VS(r) and ES(r), evaluated at 0.001 a.u. isodensity contours, are used to analyze the interactions with H2O. We find that the maxima of VS(r), σ-holes, are either localized or diffuse. This is rationalized in terms of the nanocluster geometry and occupation of the clusters’s, p and d valence orbitals. Our findings motivate a new scheme for characterizing σ-holes as σs (diffuse), σp (localized) or σd (localized) depending on their electronic origin. The positions of the maxima in VS(r) (and minima in ES(r)) are found to coincide with O-down adsorption sites of H2O, whereas minima in VS(r) leads to H-down adsorption. Linear relationships between VS,max (and ES,min) and H2O interaction energies are further discussed.