Characterization and Quantification of Polyradical Character

The decomposition of ⟨<i>Ŝ</i>²⟩ into atomic and diatomic contributions (local spin analysis) is used to detect and quantify the polyradical character of molecular systems. A model triradical system is studied in detail, and the local spin analysis is used to distinguish several patterns of local spin distributions and spin–spin interactions that can be found for different electronic states. How close a real molecular system is to an ideal system of <i>k</i> perfectly localized spin centers is utilized to define a measure of its <i>k</i>-radical character. The spin properties and triradical character of the lowest-lying electronic states of a number of all σ, all π, and σ–π organic triradicals are discussed in detail. The local spin contributions exhibit good correlation with experimental triradical stabilization energies

Oxidation States from Wave Function Analysis

We introduce a simple and general scheme to derive from wavefuntion analysis the most appropriate atomic/fragment electron configurations in a molecular system, from which oxidation states can be inferred. The method can be applied for any level of theory for which the first-order density matrix is available, and unlike others, it is not restricted to transition metal complexes. The method relies on the so-called spin-resolved effective atomic orbitals which for the present purpose is extended here to deal with molecular fragments/ligands. We describe in detail the most important points of the new scheme, in particular the hierarchical fragment approach devised for practical applications. A number of transition metal complexes with different formal oxidation states and spin states and a set of organic and inorganic compounds are provided as illustrative examples of the new scheme. Challenging systems such as transition state structures are also tackled on equal footing

Comprehensive Kinetic and Mechanistic Analysis of TiO₂ Photocatalytic Reactions According to the Direct–Indirect Model: (I) Theoretical Approach

The photocatalytic oxidation kinetics of organic species in semiconductor (sc) gas phase and liquid semiconductor suspensions, strongly depends on the electronic interaction strength of substrate species with the sc surface. According to the Direct–Indirect (D-I) model, developed as an alternative to the Langmuir–Hinshelwood (L-H) model (Salvador, P. et al. <i>Catalysis Today</i> <b>2007</b>, <i>129</i>, 247), when chemisorption of dissolved substrate species is not favored and physisorption is the only existing adsorption mechanism, interfacial hole transfer takes place via an indirect transfer (IT) mechanism, the photo-oxidation rate exponentially depending on the incident photon flux (<i>V</i>_ox = <i>V</i>_ox^IT ∝ ρ^<i>n</i>), with <i>n</i> = 1/2 under high enough photon flux (standard experimental conditions), whatever the dissolved substrate concentration, [(RH₂)_liq]. In contrast, under simultaneous physisorption and chemisorption of substrate species, hole capture takes place via a combination of an indirect transfer (IT) and a direct transfer (DT) mechanism (<i>V</i>_ox = <i>V</i>_ox^IT + <i>V</i>_ox^DT), with <i>V</i>_ox^DT ∝ ρ^<i>n</i> and <i>n</i> = 1 for low enough ρ values, as long as adsorption–desorption equilibrium conditions existing in the dark are not broken under illumination, and monotonically decreasing toward <i>n</i> = 0 as ρ increases and adsorption–desorption equilibrium becomes broken. This behavior invalidates the frequently invoked axiom that the reaction order (exponent <i>n</i>) exclusively depends on the photon flux intensity, being in general <i>n</i> = 1 and <i>n</i> = 1/2 under low and high illumination intensity, respectively, independent of the nature of the sc-substrate electronic interaction. On the basis of a detailed analysis of the parameter defined as <i>a</i> = (<i>V</i>_ox)²/2­[(RH₂)_liq]­ρ, an experimental test able to determine the influence of both interfacial hole transfer mechanisms, DT and IT, in the photo-oxidation kinetics, is presented. A simple method allowing the estimation of the photon flux critical value where adsorption–desorption equilibrium of chemisorbed substrate species is broken and the reaction order starts to decreases from <i>n</i> = 1 toward <i>n</i> = 0, is described

Bonding Quandary in the [Cu₃S₂]³⁺ Core: Insights from the Analysis of Domain Averaged Fermi Holes and the Local Spin

The electronic structure of the trinuclear symmetric complex [(tmedaCu)₃S₂ ]³⁺, whose Cu₃S₂ core represents a model of the active site of metalloenzymes involved in biological processes, has been in recent years the subject of vigorous debate. The complex exists as an open-shell triplet, and discussions concerned the question whether there is a direct S–S bond in the [Cu₃S₂]³⁺ core, whose answer is closely related to the problem of the formal oxidation state of Cu atoms. In order to contribute to the elucidation of the serious differences in the conclusions of earlier studies, we report in this study the detailed comprehensive analysis of the electronic structure of the [Cu₃S₂]³⁺ core using the methodologies that are specifically designed to address three particular aspects of the bonding in the core of the above complex, namely, the presence and/or absence of direct S–S bond, the existence and the nature of spin–spin interactions among the atoms in the core, and the formal oxidation state of Cu atoms in the core. Using such a combined approach, it was possible to conclude that the picture of bonding consistently indicates the existence of a weak direct two-center–three-electron (2c–3e) S–S bond, but at the same time, the observed lack of any significant local spin in the core of the complex is at odds with the suggested existence of antiferromagnetic coupling among the Cu and S atoms, so that the peculiarities of the bonding in the complex seem to be due to extensive delocalization of the unpaired spin in the [Cu₃S₂]³⁺ core. Finally, a scrutiny of the effective atomic hybrids and their occupations points to a predominant formal Cu^II oxidation state, with a weak contribution of partial Cu^I character induced mainly by the partial flow of electrons from S to Cu atoms and high delocalization of the unpaired spin in the [Cu₃S₂]³⁺ core

Scrutinizing the Noninnocence of Quinone Ligands in Ruthenium Complexes: Insights from Structural, Electronic, Energy, and Effective Oxidation State Analyses

The most relevant manifestations of ligand noninnocence of quinone and bipyridine derivatives are thoroughly scrutinized and discussed through an extensive and systematic set of octahedral ruthenium complexes, [(en)₂RuL]^<i>z</i>, in four oxidation states (<i>z</i> = +3, +2, +1, and 0). The characteristic structural deformation of ligands upon coordination/noninnocence is put into context with the underlying electronic structure of the complexes and its change upon reduction. In addition, by means of decomposing the corresponding reductions into electron transfer and structural relaxation subprocesses, the energetic contribution of these structural deformations to the redox energetics is revealed. The change of molecular electron density upon metal- and ligand-centered reductions is also visualized and shown to provide novel insights into the corresponding redox processes. Moreover, the charge distribution of the π-subspace is straightforwardly examined and used as indicator of ligand noninnocence in the distinct oxidation states of the complexes. The aromatization/dearomatization processes of ligand backbones are also monitored using magnetic (NICS) and electronic (PDI) indicators of aromaticity, and the consequences to noninnocent behavior are discussed. Finally, the recently developed effective oxidation state (EOS) analysis is utilized, on the one hand, to test its applicability for complexes containing noninnocent ligands, and, on the other hand, to provide new insights into the magnitude of state mixings in the investigated complexes. The effect of ligand substitution, nature of donor atom, ligand frame modification on these manifestations, and measures is discussed in an intuitive and pedagogical manner

Comprehensive Kinetic and Mechanistic Analysis of TiO₂ Photocatalytic Reactions According to the Direct–Indirect Model: (II) Experimental Validation

As a continuation of the Direct–Indirect (D-I) model theoretical approach presented in Part I of this publication, concerning the photocatalytic oxidation of organic molecules in contact with TiO₂ dispersions, a comparative photooxidation kinetic analysis of three model organic molecules, benzene (BZ) dissolved in acetonitrile (ACN), phenol (PhOH) dissolved in either water or acetonitrile, and formic acid (FA) dissolved in water, is presented to test the applicability of the D-I model under both equilibrium and nonequilibrium adsorption–desorption conditions. A previous analysis involving diffuse reflectance ultraviolet–visible (DRUVS) and Fourier transform infrared (FTIR) spectroscopy, combined with adsorption isotherm plots, shows that BZ chemisorption on the TiO₂ surface is not allowed, physisorption being in this case the only possible adsorption mode. In line with D-I model predictions, BZ photooxidation is observed to take place via an adiabatic indirect transfer (IT) mechanism, with the participation of photogenerated terminal −O_s^•– radicals as oxidizing agents. In contrast, because of their strong chemisorption, FA species dissolved in water are found to be mainly photooxidized via inelastic direct transfer (DT) trapping of photogenerated valence-band free holes (<i>h</i>_f⁺). Finally, when dissolved in water, PhOH chemisorption is not favored because of the strong electronic affinity of water molecules with the TiO₂ surface, while chemisorption strength considerably increases when PhOH is dissolved in ACN, as far as the electronic interaction of solvent molecules with the TiO₂ surface is negligible. Consequently, as predicted by the D-I model, PhOH dissolved in water is photooxidized via a combination of IT and DT mechanisms, the IT photooxidation rate (<i>v</i>_ox^IT) being about 1 order of magnitude higher than DT photooxidation rate (<i>v</i>_ox^DT). In contrast, when ACN is used as solvent, <i>v</i>_ox^IT remains practically unchanged, while <i>v</i>_ox^DT increases by about 2 orders of magnitude. These photooxidation results sustain the central D-I model hypothesis that the degree of substrate species interaction with the TiO₂ surface is a decisive factor determining the kinetics of photocatalytic reactions. The effect of adsorption–desorption equilibrium rupture on the photooxidation kinetics of dissolved substrate species, predicted by the D-I model, is analyzed for the first time from experimental kinetic data concerning the photooxidation of PhOH dissolved in water under high enough illumination intensity (ρ ≈ 10¹⁷ cm^–2 s^–1)

Analysis of the Relative Stabilities of Ortho, Meta, and Para MClY(XC₄H₄)(PH₃)₂ Heterometallabenzenes (M = Rh, Ir; X = N, P; Y = Cl and M = Ru, Os; X = N, P; Y = CO)

Density functional theory calculations of the relative stabilities of the ortho, meta, and para MClY­(XC₄H₄)­(PH₃)₂ heterometallabenzenes (M = Rh, Ir; X = N, P; Y = Cl and M = Ru, Os; X = N, P; Y = CO) have been carried out. The ortho isomer is the most stable for X = P, irrespective of the metal M. For X = N and M = Ir, Rh the meta is the lowest-lying isomer, whereas for M = Ru, Os the ortho and meta isomers are almost degenerate. The electronic structure and chemical bonding have been investigated with energy decomposition analyses of the interaction energy between various fragments, to discuss the origin of the differences observed. The values of the multicenter index of aromaticity and nucleus-independent chemical shifts indicate that the heterometallabenzenes studied should be classified as aromatic or slightly aromatic