One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Spurious Oscillations Caused by Density Functional Approximations: Who is to Blame? Exchange or Correlation?

We analyze the varying susceptibilities of different density functional approximations (DFAs) to present spurious oscillations on the profiles of several vibrational properties. Among other problems, these spurious oscillations cause significant errors in harmonic and anharmonic IR and Raman frequencies and intensities. This work hinges on a judicious strategy to dissect the exchange and correlation components of DFAs and pinpoint the origins of these oscillations. We identify spurious oscillations in derivatives of all energy components with respect to nuclear displacements, including those energy terms that do not involve numerical integrations. These indirect spurious oscillations are attributed to suboptimal electron densities resulting from a self-consistent field procedure using a DFA that exhibits direct spurious oscillations. Direct oscillations stem from inaccurate numerical integration of the exchange and correlation energy density functionals. A thorough analysis of direct spurious oscillations reveals that only a handful of exchange and correlation components are insensitive to spurious oscillations, giving rise to three families of functionals, BH&H, LSDA, and BLYP. Among the functionals in these families, we encounter four widespread DFAs: BLYP, B3LYP, LC-BLYP, and CAM-B3LYP. Certain DFAs like PBE appear less sensitive to spurious oscillations due to compensatory cancellations between their energy components. Additionally, we found non-negligible but small oscillations in PBE and TPSS, which could be safely employed provided a sufficiently large integration grid is used in the calculations. These findings hint at the key components of current approximations to be improved and emphasize the necessity to develop accurate DFAs suitable for studying molecular spectroscopies.

Pitfall in simulations of vibronic TD-DFT spectra: diagnosis and assessment

In this Communication, we study the effect of spurious oscillations in the profiles of energy derivatives with respect to nuclear coordinates calculated with density functional approximations (DFAs) for formaldehyde, pyridine, and furan in their ground and electronic excited states. These spurious oscillations, which can only be removed using extensive integration grids that increase enormously the CPU cost of DFA calculations, are significant in the case of third- and fourth-order energy derivatives of the ground and excited states computed by M06-2X and ωB97X functionals. The errors in question propagate to anharmonic vibronic spectra computed under the Franck-Condon approximation, i.e., positions and intensities of vibronic transitions are affected to a large extent (shifts as significant as hundreds of cm-1 were observed). On the other hand, the LC-BLYP and CAM-B3LYP functionals show a much less pronounced effect due to spurious oscillations. Based on the results presented herein, we recommend either LC-BLYP or CAM-B3LYP with integration grids (250, 974) (or larger) for numerically stable simulations of vibronic spectra including anharmonic effects.

Ti(III) Catalysts for CO2/Epoxide Copolymerization at Unusual Ambient Pressure Conditions

Titanium compounds in low oxidation states are highly reducing species and hence powerful tools for the functionalization of small molecules. However, their potential has not yet been fully realized because harnessing these highly reactive complexes for productive reactivity is generally challenging. Advancing this field, herein we provide a detailed route for the formation of titanium(III) orthophenylendiamido (PDA) species using [LiBHEt3] as a reducing agent. Initially, the corresponding lithium PDA compounds [Li2(ArPDA)(thf)3] (Ar = 2,4,6-trimethylphenyl (MesPDA), 2,6-diisopropylphenyl (iPrPDA)) are combined with [TiCl4(thf)2] to form the heterobimetallic complexes [{TiCl(ArPDA)}(μ-ArPDA){Li(thf)n}] (n = 1, Ar = iPr 3 and n = 2, Ar = Mes 4). Compound 4 evolves to species [Ti(MesPDA)2] (6) via thermal treatment. In contrast, the transformation of 3 into [Ti(iPrPDA)2] (5) only occurs in the presence of [LiNMe2], through a lithium-assisted process, as revealed by density functional theory (DFT). Finally, the Ti(IV) compounds 3-6 react with [LiBHEt3] to give rise to the Ti(III) species [Li(thf)4][Ti(ArPDA)2] (Ar = iPr 8, Mes 9). These low-valent compounds in combination with [PPN]Cl (PPN = bis(triphenylphosphine)iminium) are proved to be highly selective catalysts for the copolymerization of CO2 and cyclohexene epoxide. Reactions occur at 1 bar pressure with activity/selectivity levels similar to Salen-Cr(III) compounds.

Decoding the infrared spectra changes upon formation of molecular complexes: the case of halogen bonding in pyridine⋯perfluorohaloarene complexes

A recently developed computational scheme is employed to interpret changes in the infrared spectra of halogen-bonded systems in terms of intermolecular interaction energy components (electrostatic, exchange, induction, dispersion) taking pyridine⋯perfluorohaloarene complexes as examples. For all complexes, we find a strong linear correlation between the different terms of the interaction-induced changes of the IR band associated with an intermolecular halogen bond stretching mode and the corresponding terms of the interaction energy, which implies that the interaction components play similar roles in both properties. This is not true for other vibrational modes localized in one of the monomers studied here, for which the corresponding interaction-induced changes in IR bands may present a completely different decomposition than the interaction energy.

Effect of external electric fields in the charge transfer rates of donor-acceptor dyads: A straightforward computational evaluation

We present a straightforward and low-cost computational protocol to estimate the variation of the charge transfer rate constant, kCT, in a molecular donor-acceptor caused by an external electric field. The proposed protocol also allows for determining the strength and direction of the field that maximize the kCT. The application of this external electric field results in up to a >4000-fold increase in the kCT for one of the systems studied. Our method allows the identification of field-induced charge-transfer processes that would not occur without the perturbation caused by an external electric field. In addition, the proposed protocol can be used to predict the effect on the kCT due to the presence of charged functional groups, which may allow for the rational design of more efficient donor-acceptor dyads.

Cost-Effective Simulations of Vibrationally-Resolved Absorption Spectra of Fluorophores with Machine-Learning-Based Inhomogeneous Broadening

The results of electronic and vibrational structure simulations are an invaluable support for interpreting experimental absorption/emission spectra, which stimulates the development of reliable and cost-effective computational protocols. In this work, we contribute to these efforts and propose an efficient first-principle protocol for simulating vibrationally-resolved absorption spectra, including nonempirical estimations of the inhomogeneous broadening. To this end, we analyze three key aspects: (i) a metric-based selection of density functional approximation (DFA) so to benefit from the computational efficiency of time-dependent density function theory (TD-DFT) while safeguarding the accuracy of the vibrationally-resolved spectra, (ii) an assessment of two vibrational structure schemes (vertical gradient and adiabatic Hessian) to compute the Franck-Condon factors, and (iii) the use of machine learning to speed up nonempirical estimations of the inhomogeneous broadening. In more detail, we predict the absorption band shapes for a set of 20 medium-sized fluorescent dyes, focusing on the bright ππ^★ S₀ → S₁ transition and using experimental results as references. We demonstrate that, for the studied 20-dye set which includes structures with large structural variability, the preselection of DFAs based on an easily accessible metric ensures accurate band shapes with respect to the reference approach and that range-separated functionals show the best performance when combined with the vertical gradient model. As far as band widths are concerned, we propose a new machine-learning-based approach for determining the inhomogeneous broadening induced by the solvent microenvironment. This approach is shown to be very robust offering inhomogeneous broadenings with errors as small as 2 cm^-1 with respect to genuine electronic-structure calculations, with a total CPU time reduced by 98%.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Characterization of a Ferryl Flip in Electronically Tuned Nonheme Complexes. Consequences in Hydrogen Atom Transfer Reactivity

Two oxoiron(IV) isomers (^R 2a and ^R 2b) of general formula [Fe^IV (O)(^R PyNMe₃ )(CH₃ CN)]²⁺ are obtained by reaction of their iron(II) precursor with NBu₄ IO₄ . The two isomers differ in the position of the oxo ligand, cis and trans to the pyridine donor. The mechanism of isomerization between ^R 2a and ^R 2b has been determined by kinetic and computational analyses uncovering an unprecedented path for interconversion of geometrical oxoiron(IV) isomers. The activity of the two oxoiron(IV) isomers in hydrogen atom transfer (HAT) reactions shows that ^R 2a reacts one order of magnitude faster than ^R 2b, which is explained by a repulsive noncovalent interaction between the ligand and the substrate in ^R 2b. Interestingly, the electronic properties of the R substituent in the ligand pyridine ring do not have a significant effect on reaction rates. Overall, the intrinsic structural aspects of each isomer define their relative HAT reactivity, overcoming changes in electronic properties of the ligand.

A new computational tool for interpreting infrared spectra of molecular complexes

The popularity of the Infrared (IR) spectroscopy is due to its high interpretive power. This study presents a new computational tool for analyzing the IR spectra of molecular complexes in...

Carboxylic Acid Directed γ-Lactonization of Unactivated Primary C-H Bonds Catalyzed by Mn Complexes: Application to Stereoselective Natural Product Diversification

Reactions that enable selective functionalization of strong aliphatic C-H bonds open new synthetic paths to rapidly increase molecular complexity and expand chemical space. Particularly valuable are reactions where site-selectivity can be directed toward a specific C-H bond by catalyst control. Herein we describe the catalytic site- and stereoselective γ-lactonization of unactivated primary C-H bonds in carboxylic acid substrates. The system relies on a chiral Mn catalyst that activates aqueous hydrogen peroxide to promote intramolecular lactonization under mild conditions, via carboxylate binding to the metal center. The system exhibits high site-selectivity and enables the oxidation of unactivated primary γ-C-H bonds even in the presence of intrinsically weaker and a priori more reactive secondary and tertiary ones at α- and β-carbons. With substrates bearing nonequivalent γ-C-H bonds, the factors governing site-selectivity have been uncovered. Most remarkably, by manipulating the absolute chirality of the catalyst, γ-lactonization at methyl groups in gem-dimethyl structural units of rigid cyclic and bicyclic carboxylic acids can be achieved with unprecedented levels of diastereoselectivity. Such control has been successfully exploited in the late-stage lactonization of natural products such as camphoric, camphanic, ketopinic, and isoketopinic acids. DFT analysis points toward a rebound type mechanism initiated by intramolecular 1,7-HAT from a primary γ-C-H bond of the bound substrate to a highly reactive Mn^IV-oxyl intermediate, to deliver a carbon radical that rapidly lactonizes through carboxylate transfer. Intramolecular kinetic deuterium isotope effect and ¹⁸O labeling experiments provide strong support to this mechanistic picture.

Csp2-H Amination Reactions Mediated by Metastable Pseudo-Oh Masked Aryl-CoIII-nitrene Species

Cobalt-catalyzed C–H amination via M-nitrenoid species is spiking the interest of the research community. Understanding this process at a molecular level is a challenging task, and here we report a well-defined macrocyclic system featuring a pseudo-O_h aryl-Co^III species that reacts with aliphatic azides to effect intramolecular C_sp2–N bond formation. Strikingly, a putative aryl-Co=NR nitrenoid intermediate species is formed and is rapidly trapped by a carboxylate ligand to form a carboxylate masked-nitrene, which functions as a shortcut to stabilize and guide the reaction to productive intramolecular C_sp2–N bond formation. On one hand, several intermediate species featuring the C_sp2–N bond formed have been isolated and structurally characterized, and the essential role of the carboxylate ligand has been proven. Complementarily, a thorough density functional theory study of the C_sp2–N bond formation mechanism explains at the molecular level the key role of the carboxylate-masked nitrene species, which is essential to tame the metastability of the putative aryl-Co^III=NR nitrene species to effectively yield the C_sp2–N products. The solid molecular mechanistic scheme determined for the C_sp2–N bond forming reaction is fully supported by both experimental and computation complementary studies.

A well-defined pseudo-O_h aryl-Co^III species reacts with aliphatic azides to effect intramolecular C_sp2−N bond formation via a carboxylate masked-Co^III-nitrene, which serves as a shortcut to guide the reaction to productive C_sp2−N bond formation.

How Reliable Are Modern Density Functional Approximations to Simulate Vibrational Spectroscopies?

We show that properties of molecules with low-frequency modes calculated with density functional approximations (DFAs) suffer from spurious oscillations along the nuclear displacement coordinate due to numerical integration errors. Occasionally, the problem can be alleviated using extensive integration grids that compromise the favorable cost-accuracy ratio of DFAs. Since spurious oscillations are difficult to predict or identify, DFAs are exposed to severe performance errors in IR and Raman intensities and frequencies or vibrational contributions to any molecular property. Using Fourier spectral analysis and digital signal processing techniques, we identify and quantify the error due to these oscillations for 45 widely used DFAs. LC-BLYP and BH&H are revealed as the only functionals showing robustness against the spurious oscillations of various energy, dipole moment, and polarizability derivatives with respect to a nuclear displacement coordinate. Given the ubiquitous nature of molecules with low-frequency modes, we warrant caution in using modern DFAs to simulate vibrational spectroscopies.

Infrared Spectra of Hydrogen-Bonded Molecular Complexes Under Spatial Confinement

Infrared (IR) spectroscopy is commonly used in chemical laboratories to study the geometrical structure of molecules and molecular complexes. The analysis of experimental IR spectra can nowadays be reliably supported by the results of quantum-chemical computations as vibrational frequencies and corresponding vibrational transition intensities are routinely calculated using harmonic approximation by virtually all quantum chemistry packages. In the present study we combine the methodology of computing vibrational spectra using high-level electron correlation treatments with an analytical potential-based approach to take into account spatial confinement effects. Using this approach, we perform a pioneering analysis of the impact of the spatial confinement caused by a cylindrical harmonic oscillator potential on the harmonic vibrational transition intensities and frequencies of two hydrogen-bonded complexes: HCN…HCN and HCN…HNC. The emphasis is put on the largest-intensity bands, which correspond to the stretching vibrations. The obtained results demonstrate that embedding the molecular complexes in an external confining potential causes significant changes of transition intensities and vibrational frequencies.

How Many Electrons Does a Molecular Electride Hold?

Electrides are very peculiar ionic compounds where electrons occupy the anionic positions. In a crystal lattice, these isolated electrons often form channels or surfaces, furnishing electrides with many traits with promising technological applications. Despite their huge potential, thus far, only a few stable electrides have been produced because of the intricate synthesis they entail. Due to the difficulty in assessing the presence of isolated electrons, the characterization of electrides also poses some serious challenges. In fact, their properties are expected to depend on the arrangement of these electrons in the molecule. Among the criteria that we can use to characterize electrides, the presence of a non-nuclear attractor (NNA) of the electron density is both the rarest and the most salient feature. Therefore, a correct description of the NNA is crucial to determine the properties of electrides. In this paper, we analyze the NNA and the surrounding region of nine molecular electrides to determine the number of isolated electrons held in the electride. We have seen that the correct description of a molecular electride hinges on the electronic structure method employed for the analyses. In particular, one should employ a basis set with sufficient flexibility to describe the region close to the NNA and a density functional approximation that does not suffer from large delocalization errors. Finally, we have classified these nine molecular electrides according to the most likely number of electrons that we can find in the NNA. We believe this classification highlights the strength of the electride character and will prove useful in designing new electrides.

Well-Defined Aryl-FeII Complexes in Cross-Coupling and C–H Activation Processes

Herein we explore the intrinsic organometallic reactivity of iron embedded in a tetradentate N₃C macrocyclic ligand scaffold that allows the stabilization of aryl-Fe species, which are key intermediates in Fe-catalyzed cross-coupling and C–H functionalization processes. This study covers C–H activation reactions using ^MeL_H and FeCl₂, biaryl C–C coupling product formation through reaction with Grignard reagents, and cross-coupling reactions using ^MeL_Br or ^HL_Br in combination with Fe⁰(CO)₅. Synthesis under light irradiation and moderate heating (50 °C) affords the aryl-Fe^II complexes [Fe^II(Br)(^MeL)(CO)] (1^Me) and [Fe^II(^HL)(CO)₂]Br (1^H). Exhaustive spectroscopic characterization of these rare low-spin diamagnetic species, including their crystal structures, allowed the investigation of their intrinsic reactivity.

Evaluation of charge-transfer rates in fullerene-based donor-acceptor dyads with different density functional approximations

The shift towards renewable energy is one of the main challenges of this generation. Dye-sensitized solar cells (DSSCs), based on donor-acceptor architectures, can help in this transition as they present excellent photovoltaic efficiencies yet cheap and simple manufacturing. For molecular heterojunction DSSCs, donor-acceptor pairs are linked in a covalent manner, which facilitates their tailoring and rational design. Nevertheless, reliable computational characterization of charge transfer rate constants (kCT) is needed to speed this development process up. In this context, the performance of time-dependent density functional theory for the calculation of kCT values in donor-acceptor fullerene-based dyads has not been benchmarked yet. Herein, we present a detailed analysis on the performance of seven well-known density functional approximations (DFAs) for this type of system, focusing on several parameters such as the reorganization energies (λ), electronic couplings (VDA), and Gibbs energies (ΔG0CT), as well as the final rate constants. The amount of exact exchange at short range (SR) and long range (LR) electron-electron distances (and the transition from the SR to LR) turned out to be key for the success of the prediction. The tuning of these parameters improves significantly the performance of current DFAs.

Origin-Independent Decomposition of the Static Polarizability

Real-space analysis tools afford additive and transferable contributions of atoms to molecular properties. In the case of the molecular (hyper)polarizabilities, the atomic contributions that have been derived so far include a charge-transfer term that is origin-dependent. In this letter, we present the first genuinely origin-independent energy-based (OIEB) methodology for the decomposition of the static (hyper)polarizabilities that benefits from real-space molecular energy decomposition schemes, focusing on the static polarizability and showing that extension to static hyperpolarizabilities is straightforward. The numerical realization of the OIEB method shows the expected origin independence, atomic additivity, and transferability of atomic and functional group polarizability tensors. Furthermore, the OIEB atomic (fragment) polarizability tensors are symmetric by definition.

Mechanistic Insights into the ortho-Defluorination-Hydroxylation of 2-Halophenolates Promoted by a Bis(μ-oxo)dicopper(III) Complex

C-F bonds are one of the most inert functionalities. Nevertheless, some [Cu₂O₂]²⁺ species are able to defluorinate-hydroxylate ortho-fluorophenolates in a chemoselective manner over other ortho-halophenolates. Albeit it is known that such reactivity is promoted by an electrophilic attack of a [Cu₂O₂]²⁺ core over the arene ring, the crucial details of the mechanism that explain the chemo- and regioselectivity of the reaction remain unknown, and it has not being determined either if Cu^II₂(η²:η²-O₂) or Cu^III₂(μ-O)₂ species are responsible for the initial attack on the arene. Herein, we present a combined theoretical and experimental mechanistic study to unravel the origin of the chemoselectivity of the ortho-defluorination-hydroxylation of 2-halophenolates by the [Cu₂(O)₂(DBED)₂]²⁺ complex (DBED = N,N'-di-tert-butylethylenediamine). Our results show that the equilibria between (side-on)peroxo (P) and bis(μ-oxo) (O) isomers plays a key role in the mechanism, with the latter being the reactive species. Furthermore, on the basis of quantum-mechanical calculations, we were able to rationalize the chemoselective preference of the [Cu₂(O)₂(DBED)₂]²⁺ catalyst for the C-F activation over C-Cl and C-H activations.

Bingel-Hirsch Addition of Diethyl Bromomalonate to Ion-Encapsulated Fullerenes M@C60 (M=Ø, Li+, Na+, K+, Mg2+, Ca2+, and Cl-)

In the last 30 years, fullerene-based materials have become popular building blocks for devices with a broad range of applications. Among fullerene derivatives, endohedral metallofullerenes (EMFs, M@C_x) have been widely studied owing to their unique properties and reactivity. For real applications, fullerenes and EMFs must be exohedrally functionalized. It has been shown that encapsulated metal cations facilitate the Diels-Alder reaction in fullerenes. Herein, the Bingel-Hirsch (BH) addition of ethyl bromomalonate over a series of ion-encapsulated M@C₆₀ (M=Ø, Li⁺, Na⁺, K⁺, Mg²⁺, Ca²⁺, and Cl^-; Ø@C₆₀ stands for C₆₀ without any endohedral metal) is quantum mechanically explored to analyze the effect of these ions on the BH addition. The results show that the incarcerated ion has a very important effect on the kinetics and thermodynamics of this reaction. Among the systems studied, K⁺@C₆₀ is the one that leads to the fastest BH reaction, whereas the slowest reaction is given by Cl^-@C₆₀.

Controlling Two-Photon Action Cross Section by Changing a Single Heteroatom Position in Fluorescent Dyes

The optimization of nonlinear optical properties for "real-life" applications remains a key challenge for both experimental and theoretical approaches. In particular, for two-photon processes, maximizing the two-photon action cross section (TPACS), the figure of merit for two-photon bioimaging spectroscopy, requires simultaneously controlling all its components. In the present Letter, a series of difluoroborates presenting various heterocyclic rings as an electron acceptor have been synthesized and their absorption, fluorescence, photoisomerization, and two-photon absorption features have been analyzed using both experimental and theoretical approaches. Our results demonstrate that the TPACS values can be fine-tuned by changing the position of a single heteroatom, which alters the fluorescence quantum yields without changing the intrinsic two-photon absorption cross section. This approach offers a new strategy for optimizing TPACS.

Partitioning of interaction-induced nonlinear optical properties of molecular complexes. II. Halogen-bonded systems

Following our study on hydrogen-bonded (HB) complexes [Phys. Chem. Chem. Phys., 2018, 20, 19841], the physical nature of interaction-induced (non)linear optical properties of another important class of molecular complexes, namely halogen-bonded (XB) systems, was analyzed in this study. The excess electronic and nuclear relaxation (hyper)polarizabilities of nine representative XB complexes covering a wide range of halogen-bond strengths were computed. The partitioning of the excess properties into individual interaction-energy components (electrostatic, exchange, induction, dispersion) was performed by using the variational-perturbational energy decomposition scheme at the MP2/aug-cc-pVTZ level of theory and further supported by calculations with the SCS-MP2 method. In the case of the electronic interaction-induced properties, the physical composition of Δαel and Δγel was found to be very similar for the two types of bonding, despite the different nature of the binding. For Δβel, the XB complexes exhibit a more systematic interplay of interaction-energy contributions compared to the HB systems studied in the previous work. Our analysis revealed that the patterns of interaction-energy contributions to the interaction-induced nuclear-relaxation contributions to the linear polarizability and the first hyperpolarizability are very similar. For both properties the exchange repulsion term is canceled out by the electrostatic and delocalization terms. The physical composition of these contributions is analogous to those observed for the HB complexes.

A new tuned range-separated density functional for the accurate calculation of second hyperpolarizabilities

Among the nine functionals benchmarked, the most accurate γ are obtained by Tα-LC-BLYP, reducing about half the errors of LC-BLYP.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Partition of optical properties into orbital contributions

A new tool to analyze the response property through the partition of nonlinear optical properties in terms of orbital contributions (PNOC), valuable in the assessment of the electronic structure methods in the NLOPs computations, is presented.

Design of Iron Coordination Complexes as Highly Active Homogenous Water Oxidation Catalysts by Deuteration of Oxidation-Sensitive Sites

The nature of the oxidizing species in water oxidation reactions with chemical oxidants catalyzed by α-[Fe(OTf)₂(mcp)] (1α; mcp = N, N'-dimethyl- N, N'-bis(pyridin-2-ylmethyl)cyclohexane-1,2-diamine, OTf = trifluoromethanesulfonate anion) and β-[Fe(OTf)₂(mcp)] (1β) has been investigated. Mössbauer spectroscopy provides definitive evidence that 1α and 1β generate oxoiron(IV) species as the resting state. Decomposition paths of the catalysts have been investigated by identifying and quantifying ligand fragments that form upon degradation. This analysis correlates the water oxidation activity of 1α and 1β with stability against oxidative damage of the ligand via aliphatic C-H oxidation. The site of degradation and the relative stability against oxidative degradation are shown to be dependent on the topology of the catalyst. Furthermore, the mechanisms of catalyst degradation have been rationalized by computational analyses, which also explain why the topology of the catalyst enforces different oxidation-sensitive sites. This information has served in creating catalysts where sensitive C-H bonds have been replaced by C-D bonds. The deuterated analogues D₄-α-[Fe(OTf)₂(mcp)] (D₄-1α), D₄-β-[Fe(OTf)₂(mcp)] (D₄-1β), and D₆-β-[Fe(OTf)₂(mcp)] (D₆-1β) were prepared, and their catalytic activity has been studied. D₄-1α proves to be an extraordinarily active and efficient catalyst (up to 91% of O₂ yield); it exhibits initial reaction rates identical with those of its protio analogue, but it is substantially more robust toward oxidative degradation and yields more than 3400 TON ( n(O₂)/ n(Fe)). Altogether this evidences that the water oxidation catalytic activity is performed by a well-defined coordination complex and not by iron oxides formed after oxidative degradation of the ligands.

Mechanistic insights into the SN2-type reactivity of aryl-Co(iii) masked-carbenes for C-C bond forming transformations

Herein we describe the synthesis and characterization of a family of C-metalated aryl-Co(iii) enolates, which can be considered as masked-carbenes, using diazoacetates as coupling partners. These species have been proved to be necessary intermediates in the C(sp2)-C(sp3) bond forming event to obtain cyclic amides, taming the elusive Co(iii)-carbene species. The scope of diazoacetates has been exhaustively examined, varying the nature of the ester and the α-substitution, and a clear preference for electron-poor carbene precursors is observed. Exhaustive experimental and theoretical studies indicate that an unprecedented intramolecular SN2-type process governs the formation of the newly formed C-C bond. Furthermore, the key role of several Lewis acids as carboxylate-activating reagents is further explored by DFT calculations.

Quantum Mechanics/Molecular Mechanics Studies on the Relative Reactivities of Compound I and II in Cytochrome P450 Enzymes

The cytochromes P450 are drug metabolizing enzymes in the body that typically react with substrates through a monoxygenation reaction. During the catalytic cycle two reduction and protonation steps generate a high-valent iron (IV)-oxo heme cation radical species called Compound I. However, with sufficient reduction equivalents present, the catalytic cycle should be able to continue to the reduced species of Compound I, called Compound II, rather than a reaction of Compound I with substrate. In particular, since electron transfer is usually on faster timescales than atom transfer, we considered this process feasible and decided to investigate the reaction computationally. In this work we present a computational study using density functional theory methods on active site model complexes alongside quantum mechanics/molecular mechanics calculations on full enzyme structures of cytochrome P450 enzymes. Specifically, we focus on the relative reactivity of Compound I and II with a model substrate for O⁻H bond activation. We show that generally the barrier heights for hydrogen atom abstraction are higher in energy for Compound II than Compound I for O⁻H bond activation. Nevertheless, for the activation of such bonds, Compound II should still be an active oxidant under enzymatic conditions. As such, our computational modelling predicts that under high-reduction environments the cytochromes P450 can react with substrates via Compound II but the rates will be much slower.

An Objective Alternative to IUPAC's Approach To Assign Oxidation States

The IUPAC has recently clarified the term oxidation state (OS), and provided algorithms for its determination based on the ionic approximation (IA) of the bonds supported by atomic electronegativities (EN). Unfortunately, there are a number of exceptions and ambiguities in IUPAC's algorithms when it comes to practical applications. Our comprehensive study reveals the critical role of the chemical environment on establishing the OS, which cannot always be properly predicted using fix atomic EN values. By identifying what we define here as subsystems of enhanced stability within the molecular system, the OS can be safely assigned in many cases without invoking exceptions. New insights about the effect of local aromaticity upon OS are revealed. Moreover, we prove that there are intrinsic limitations of the IA that cannot be overcome. In this context, the effective oxidation state (EOS) analysis arises as a robust and general scheme to derive an OS without any external guidance.

Acid-Triggered O-O Bond Heterolysis of a Nonheme FeIII (OOH) Species for the Stereospecific Hydroxylation of Strong C-H Bonds

A novel hydroperoxoiron(III) species [Fe^III (OOH)(MeCN)(PyNMe₃ )]²⁺ (3) has been generated by reaction of its ferrous precursor [Fe^II (CF₃ SO₃ )₂ (PyNMe₃ )] (1) with hydrogen peroxide at low temperatures. This species has been characterized by several spectroscopic techniques and cryospray mass spectrometry. Similar to most of the previously described low-spin hydroperoxoiron(III) compounds, 3 behaves as a sluggish oxidant and it is not kinetically competent for breaking weak C-H bonds. However, triflic acid addition to 3 causes its transformation into a much more reactive compound towards organic substrates that is capable of oxidizing unactivated C-H bonds with high stereospecificity. Stopped-flow kinetic analyses and theoretical studies provide a rationale for the observed chemistry, a triflic-acid-assisted heterolytic cleavage of the O-O bond to form a putative strongly oxidizing oxoiron(V) species. This mechanism is reminiscent to that observed in heme systems, where protonation of the hydroperoxo intermediate leads to the formation of the high-valent [(Porph^. )Fe^IV (O)] (Compound I).

Partitioning of interaction-induced nonlinear optical properties of molecular complexes. I. Hydrogen-bonded systems

Interaction-induced electronic and vibrational (hyper)polarizabilities were decomposed into different interaction types (electrostatic, exchange, induction and dispersion).

Understanding light-driven H2 evolution through the electronic tuning of aminopyridine cobalt complexes

Electronic effects provide a general mechanistic scenario for rationalizing photocatalytic water reduction activity with aminopyridine cobalt complexes.

A new family of cobalt complexes with the general formula [Co^II(OTf)₂(^Y,XPy^Metacn)] (1^R, ^Y,XPy^Metacn = 1-[(4-X-3,5-Y-2-pyridyl)methyl]-4,7-dimethyl-1,4,7-triazacyclononane, (X = CN (1^CN), CO₂Et (1^CO2Et), Cl (1^Cl), H (1^H), NMe₂ (1^NMe2)) where (Y = H, and X = OMe when Y = Me (1^DMM)) is reported. We found that the electronic tuning of the ^Y,XPy^Metacn ligand not only has an impact on the electronic and structural properties of the metal center, but also allows for a systematic water-reduction-catalytic control. In particular, the increase of the electron-withdrawing character of the pyridine moiety promotes a 20-fold enhancement of the catalytic outcome. By UV-Vis spectroscopy, luminescence quenching studies and Transient Absorption Spectroscopy (TAS), we have studied the direct reaction of the photogenerated [Ir^III(ppy)₂(bpy˙^–)] (PS_Ir) species to form the elusive Co^I intermediates. In particular, our attention is focused on the effect of the ligand architecture in this elemental step of the catalytic mechanism. Finally, kinetic isotopic experiments together with DFT calculations provide complementary information about the rate-determining step of the catalytic cycle.

Vibrational nonlinear optical properties of spatially confined weakly bound complexes

This study focuses on the theoretical description of the influence of spatial confinement on the electronic and vibrational contributions to (hyper)polarizabilities of two dimeric hydrogen bonded systems, namely HCNHCN and HCNHNC. A two-dimensional analytical potential is employed to render the confining environment (e.g. carbon nanotube). Based on the results of the state-of-the-art calculations, performed at the CCSD(T)/aug-cc-pVTZ level of theory, we established that: (i) the influence of spatial confinement increases with increasing order of the electrical properties, (ii) the effect of spatial confinement is much larger in the case of the electronic than vibrational contribution (this holds for each order of the electrical properties) and (iii) the decrease in the static nuclear relaxation first hyperpolarizability upon the increase of confinement strength is mainly due to changes in the harmonic term, however, in the case of nuclear relaxation second hyperpolarizability the anharmonic terms contribute more to the drop of this property.

Trifluoromethylation of a Well-Defined Square-Planar Aryl-NiII Complex involving NiIII /CF3. and NiIV -CF3 Intermediate Species

Ni-mediated trifluoromethylation of an aryl-Br bond in model macrocyclic ligands (L_n -Br) has been thoroughly studied, starting with an oxidative addition at Ni⁰ to obtain well-defined aryl-Ni^II -Br complexes ([L_n -Ni^II ]Br). Abstraction of the halide with AgX (X=OTf^- or ClO₄^- ) thereafter provides [L_n -Ni^II ](OTf). The nitrate analogue has been obtained through a direct C-H activation of an aryl-H bond using Ni^II salts, and this route has been studied by X-ray absorption spectroscopy (XAS). Crystallographic XRD and XAS characterization has shown a tight macrocyclic coordination in the aryl-Ni^II complex, which may hamper direct reaction with nucleophiles. On the contrary, enhanced reactivity is observed with oxidants, and the reaction of [L_n -Ni^II ](OTf) with CF₃⁺ sources afforded L_n -CF₃ products in quantitative yield. A combined experimental and theoretical mechanistic study provides new insights into the operative mechanism for this transformation. Computational analysis indicates the occurrence of an initial single electron transfer (SET) to 5-(trifluoromethyl)dibenzothiophenium triflate (TDTT), producing a transient L₁ -Ni^III /CF₃^. adduct, which rapidly recombines to form a [L₁ -Ni^IV -CF₃ ](X)₂ intermediate species. A final facile reductive elimination affords L₁ -CF₃ . The well-defined square-planar model system studied here permits to gain fundamental knowledge on the rich redox chemistry of nickel, which is sought to facilitate the development of new Ni-based trifluoromethylation methodologies.

Rationalizing the relative abundances of trimetallic nitride template-based endohedral metallofullerenes from aromaticity measures

The synthesis of endohedral metallofullerenes (EMFs) from a carbon soot sample of an arc discharge leads to a variety of EMFs that are obtained in different relative abundances. In the present work, we show that these abundances can be predicted from aromaticity calculations. In particular, we use the normalized Additive Local Aromaticity (ALAN) index. Our results show that the most abundant Sc3N-based and Y3N-based EMFs in fullerene soot are the most aromatic. This study reinforces the idea that aromaticity plays a key role in determining the stability of EMFs.

A CuI/CuIII prototypical organometallic mechanism for the deactivation of an active pincer-like CuI catalyst in Ullmann-type couplings

Decomposition pathways in Ullmann C–O couplings have been studied by helium tagging IRPD and DFT studies, supporting aryl–Cu^III intermediate species.

On the physical origins of interaction-induced vibrational (hyper)polarizabilities

This paper presents the results of a pioneering exploration of the physical origins of vibrational contributions to the interaction-induced electric properties of molecular complexes. In order to analyze the excess nuclear relaxation (hyper)polarizabilities, a new scheme was proposed which relies on the computationally efficient Bishop-Hasan-Kirtman method for determining the nuclear relaxation contributions to electric properties. The extension presented herein is general and can be used with any interaction-energy partitioning method. As an example, in this study we employed the variational-perturbational interaction-energy decomposition scheme (at the MP2/aug-cc-pVQZ level) and the extended transition state method by employing three exchange-correlation functionals (BLYP, LC-BLYP, and LC-BLYP-dDsC) to study the excess properties of the HCN dimer. It was observed that the first-order electrostatic contribution to the excess nuclear relaxation polarizability cancels with the negative exchange repulsion term out to a large extent, resulting in a positive value of Δα(nr) due to the contributions from the delocalization and the dispersion terms. In the case of the excess nuclear relaxation first hyperpolarizability, the pattern of interaction contributions is very similar to that for Δα(nr), both in terms of their sign as well as relative magnitude. Finally, our results show that the LC-BLYP and LC-BLYP-dDsC functionals, which yield smaller values of the orbital relaxation term than BLYP, are more successful in predicting excess properties.