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The unconventional carbon dioxide insertion reaction of a gold-aluminyl [tBu3PAuAl(NON)] complex has been recently shown to be related to the electron-sharing character of the Au-Al bond that acts as a nucleophile and stabilizes the insertion product through a radical-like behavior. Since a gold-diarylboryl [IPrAuB(o-tol)2] complex with similar reactivity features has been recently reported, in this work we computationally investigate the reaction of carbon dioxide with [LAuX] (L = phosphine, N-heterocyclic carbene (NHC); X = Al(NON), B(o-tol)2) complexes to get insights into the Al/B anionic and gold ancillary ligand effects on the Au-Al/B bond nature, electronic structure, and reactivity of these compounds. We demonstrate that the Au-Al and Au-B bonds possess a similar electron-sharing nature, with diarylboryl complexes displaying a slightly more polarized bond as Au(δ+)-B(δ-). This feature reduces the radical-like reactivity toward CO2, and the Al/B anionic ligand effect is found to favor aluminyls over boryls, despite the greater oxophilicity of B. Remarkably, the ancillary ligand of gold has a negligible electronic trans effect on the Au-X bond and only a minor impact on the formation of the insertion product, which is slightly more stable with carbene ligands. Surprisingly, we find that the modification of the steric hindrance at the carbene site may exert a sizable control over the reaction, with more sterically hindered ligands thermodynamically disfavoring the formation of the CO2 insertion product.

Anionic aluminum(I) anions (“aluminyls”) are the most recent discovery along Group 13 anions, and the understanding of the unconventional reactivity they are able to induce at a coordinated metal site is at an early stage. A striking example is the efficient insertion of carbon dioxide into the Au–Al bond of a gold–aluminyl complex. The reaction occurs via a cooperative mechanism, with the gold–aluminum bond being the actual nucleophile and the Al site also behaving as an electrophile. In the complex, the Au–Al bond has been shown to be mainly of an electron-sharing nature, with the two metal fragments displaying a diradical-like reactivity with CO2. In this work, the analogous reactivity with isostructural Au–X complexes (X = Al, Ga, and In) is computationally explored. We demonstrate that a kinetically and thermodynamically favorable reactivity with CO2 may only be expected for the gold–aluminyl complex. The Au–Al bond nature, which features the most (nonpolar) electron-sharing character among the Group 13 anions analyzed here, is responsible for its highest efficiency. The radical-like reactivity appears to be a key ingredient to stabilize the CO2 insertion product. This investigation elucidates the special role of Al in these hetero-binuclear compounds, providing new insights into the peculiar electronic structure of aluminyls, which may help for the rational control of their unprecedented reactivity toward carbon dioxide., The reactivity of gold−aluminyl, −gallyl, and −indyl complexes with carbon dioxide is predicted to be favorable only for gold−aluminyl complexes. The increased polarity of the Au−Ga and Au−In bonds makes these compounds weaker nucleophiles in a radical-like reaction mechanism.

Aluminyls and carbenes as coordination ligands, although sharing similar electronic properties, reveal fundamental differences in their tunability, bonding to gold and reactivity of their complexes with carbon dioxide.

Nucleophilic formal gold(-i) and gold(i) complexes are investigated via Intrinsic Bond Orbital analysis and Energy Decomposition Analysis, based on density functional theory calculations. The results indicate gold(0) centres engaging in electron-sharing bonding with Al- and B- based ligands. Multiconfigurational (CASSCF) calculations corroborate the findings, highlighting the gap between the electonic structures and the oxidation state formalism.

In this work, the mechanism of the insertion reaction of 3-hexyne into Cu-Al and Au-Al bonds in M-aluminyl (M = Cu, Au) complexes is computationally elucidated. The mechanism is found to be radical-like, with the Cu-Al and Au-Al bonds acting as nucleophiles toward the alkyne, and predicts a less efficient reactivity for the gold-aluminyl complex. The proposed mechanism well rationalizes the kinetic (or thermodynamic) control on the formation of the syn (or anti) insertion product into the Cu-Al bond (i.e., dimetallated alkene) which has been recently reported. A comparative analysis of the electronic structure reveals that the reduced reactivity at the gold site─usually showing higher efficiency than copper as a "standard" electrophile in alkyne activation─arises from a common feature, i.e., the highly stable 6s Au orbital. The relativistic lowering of the 6s orbital, making it more suitable for accepting electron density and thus enhancing the electrophilicity of gold complexes, in the gold-aluminyl system is responsible for a less nucleophilic Au-Al bond and, consequently, a less efficient alkyne insertion. These findings demonstrate that the unconventional electronic structure and the electron-sharing nature of the M-Al bond induce a paradigm shift in the properties of coinage metal complexes. In particular, the peculiar radical-like reactivity, previously shown also with carbon dioxide, suggests that these complexes might efficiently insert/activate other small molecules, opening new and unexplored paths for their reactivity.

The computational study of an unprecedented reactivity of coinage metal-aluminyl complexes with dihydrogen is reported. In close resemblance to Group 14 dimetallenes and dimetallynes, the complexes are predicted to activate H2 under mild conditions. Two different reaction pathways are found disclosing a common driving force, i.e., the nucleophilic behavior of the electron-sharing M-Al (M = Cu, Ag, Au) bond, which enables a cooperative and diradical-like mechanism. This mode of chemical reactivity emerges as a new paradigm for dihydrogen activation and calls for an experimental feedback.

Frozen density embedding (FDE) represents an embedding scheme in which environmental effects are included from first-principles calculations by considering the surrounding system explicitly by means of its electron density. In the present paper, we extend the full four-component relativistic Dirac-Kohn-Sham (DKS) method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme (DKS-in-DFT FDE). The implementation, based on the auxiliary density fitting techniques, has been enormously facilitated by BERTHA's python API (PyBERTHA), which facilitates the interoperability with other FDE implementations available through the PyADF framework. The accuracy and numerical stability of this new implementation, also using different auxiliary fitting basis sets, has been demonstrated on the simple NH

Helium chemistry is notoriously very impervious. It is therefore certainly no surprise that, for example, beryllium and helium atoms, in their ground state, do not bind. Full configuration-interaction calculations show that the same turns out to be true, save for a long-range shallow attraction, for the Be

Using computational approaches, we qualitatively and quantitatively assess the bonding components of a series of experimentally characterized Au(I) diarylallenylidene complexes (N.Kim, R.A.Widenhoefer, Angew. Chem. Int. Ed. 2018, 57, 4722-4726). Our results clearly demonstrate that Au(I) engages only weakly in pi-backbonding, which is, however, a tunable bonding component. Computationally identified trends in bonding are clearly correlated with the substitution patterns of the aryl substituents in the Au(I) diarylallenylidene complexes and good agreement is found with the previously reported experimental data, such as IR spectra, C-13 NMR chemical shifts and rates of decomposition together with their corresponding barrier heights, further substantiating the computational findings. The description of the bonding patterns in these complexes allow predictions of their spectroscopic features, their reactivity and stability.

We have carried out molecular-beam scattering experiments and high-level ab initio investigations on the potential energy surfaces of a series of noble-gas-Cl 2 adducts. This effort has permitted the construction of a simple, reliable and easily generalizable analytical model potential formulation, which is based on a few physically meaningful parameters of the interacting partners and transparently shows the origin, strength, and stereospecificity of the various interaction components. The results demonstrate quantitatively beyond doubt that the interaction between a noble-gas (Ng) atom-even He-and Cl 2 in a collinear configuration is characterized by weak halogen bond (XB) formation, accompanied by charge transfer (CT) from the Ng to chlorine. This characteristic, which stabilizes the adduct, rapidly disappears on going towards the T-shaped configuration, dominated by pure van der Waals (vdW) forces. Similarly, a pure vdW interaction takes place-with no CT component in any configuration-if Cl 2 is present in the lowest π g ∗ → σ u ∗ excited state, because the change in electron density that accompanies the excitation eliminates the Cl 2 polar flattening and σ hole, making the XB interaction inaccessible.

The coordination ability of the [(ppy)Au(IPr)]2+ fragment [ppy = 2-phenylpyridine, IPr = 1,3-bis(2,6-di-isopropylphenyl)-imidazol-2-ylidene] towards different anionic and neutral X ligands (X = Cl−, BF4−, OTf−, H2O, 2-butyne, 3-hexyne) commonly involved in the crucial pre-equilibrium step of the alkyne hydration reaction is computationally investigated to shed light on unexpected experimental observations on its catalytic activity. Experiment reveals that BF4− and OTf− have very similar coordination ability towards [(ppy)Au(IPr)]2+ and slightly less than water, whereas the alkyne complex could not be observed in solution at least at the NMR sensitivity. Due to the steric hindrance/dispersion interaction balance between X and IPr, the [(ppy)Au(IPr)]2+ fragment is computationally found to be much less selective than a model [(ppy)Au(NHC)]2+ (NHC = 1,3-dimethylimidazol-2-ylidene) fragment towards the different ligands, in particular OTf− and BF4−, in agreement with experiment. Effect of the ancillary ligand substitution demonstrates that the coordination ability of Au(III) is quantitatively strongly affected by the nature of the ligands (even more than the net charge of the complex) and that all the investigated gold fragments coordinate to alkynes more strongly than H2O. Remarkably, a stabilization of the water-coordinating species with respect to the alkyne-coordinating one can only be achieved within a microsolvation model, which reconciles theory with experiment. All the results reported here suggest that both the Au(III) fragment coordination ability and its proper computational modelling in the experimental conditions are fundamental issues for the design of efficient catalysts.

With the aim of rationalizing the experimental counterion- and solvent-dependent reactivity in the gold(i)-catalyzed Meyer-Schuster rearrangement of 1-phenyl-2-propyn-1-ol, a computational mechanistic study unraveled the unexpected formation of a gold-oxetene intermediate via commonly unfavorable 4-endo-dig cyclization triggered by the counterion in low polarity solvents.

The ETS-NOCV bond analysis has been exploited to quantitatively estimate donation and back-donation properties of [(η5-C5H5)]−, CO, and FeI in the cis-/trans-[(η5-C5H5)Fe(η1-CO)(μ-CO)]2 (cis-I/trans-I) tautomers. Theoretical outcomes indicate that the Fe-CO bond, regardless to the CO monoapto (η1-) or bridging (μ-) coordination, has a sizeable π Fe → CO back-bonding contribution, which is stronger in trans-I than in cis-I. Moreover, [(η5-C5H5)]− has the weakest back-donation acceptor capability. The back-bonding behaviour of the Fe → η1-CO interaction well agrees with the experimental symmetric/antisymmetric infrared νCO (sνηjavax.xml.bind.JAXBElement@fc12185-CO/aνηjavax.xml.bind.JAXBElement@4c260f05-CO) trend for cis-I and trans-I and further confirms the infrared classical behaviour of the η1-CO group in this class of complexes.

For the first time, NHC-Au-X [NHC = (1,3-bis(2,6-di-isopropylphenyl)-imidazol-2-ylidene, X− = BF4−, OTf−, OTs−, TFA−] catalysts were tested in the cycloisomerization of N-(prop-2-yn-yl)benzamide to 2-phenyl-5-vinylidene-2-oxazoline in a wide set of green solvents. We found that most of these solvents (cyclohexanone, isopropyl acetate, MIBK, ethyl lactate, furfuryl alcohol, γ-valerolactone, propylene carbonate and propionic acid) are comparable or better solvents with respect to traditional VOS. Furthermore, the catalyst activity is related to the basic strength of the anion and the performances of the catalysts decrease gradually with increasing basicity and hydrogen-bond acceptor power of X−. Kinetic experiments and DFT calculations seem to indicate that both the characteristic of the solvent and counterion should be taken into account.

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn‐Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2‐xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019, 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid‐GGA exchange‐correlation functional (PBEh‐3c) paired with a double‐ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis., Rapid tool: An efficient computational protocol for the rapid evaluation of the viability of proposed mechanistic pathways in the field of gold catalysis is described. The combination of the tight binding GFN2‐xTB method for obtaining geometrical parameters and DFT (e. g. PW6B95‐D3(BJ)) for evaluating electronic energies is recommended.

A gold-aluminyl complex has been recently reported to feature an unconventional gold nucleophilic center, which was revealed through reactivity with carbon dioxide leading to the Au-CO2 coordination mode. In this work, we computationally investigate the reaction mechanism, which is found to be cooperative, with the gold-aluminum bond being the actual nucleophile and Al also behaving as electrophile. The Au-Al bond is shown to be mainly of an electron-sharing nature, with the two metal fragments displaying a diradical-like reactivity with CO2.

With the aim of rationalizing the experimental counterion- and solvent-dependent reactivity in the gold(I)-catalyzed Meyer–Schuster rearrangement of 1-phenyl-2-propyn-1-ol, a computational mechanistic study unraveled the unexpected formation of a gold-oxetene intermediate via commonly unfavorable 4-endo-dig cyclization triggered by the counterion in low polarity solvents.

Photoelectron spectroscopy (PES) is a well-known technique which provides unique information about the electronic structure of anionic and neutral species of simple molecules containing heavy elements; however, the detailed interpretation of the resulting experimental spectra can be very complex and theoretical support is mandatory. In this work, based on the available vibrationally resolved PES experiments for gold dihydride (Liu, H.-T. et al., Chem. Sci., 2012, 3, 3286), we have employed several relativistic theoretical approaches with the aim of reproducing experimental photoelectron Detachment Energies (DEs) of AuH2- to give a neutral open-shell molecule, AuH2. The results are discussed in terms of relativistic effects, orbital relaxation and electron correlation. In order to reproduce accurate DEs it has been necessary to include all these effects in a consistent manner at a high degree of accuracy, by means of the equation-of-motion coupled-cluster theory (EOM-IP-CCSD) based on the relativistic exact two-component Hamiltonian (Shee A. et al. J. Chem. Phys., 2018, 174113). This method has also been applied for investigating the ground and low-lying electronic potential energy surfaces of the neutral open shell AuH2 species. The equilibrium geometry of the AuH2 ground state is found to be bent, which is fully consistent with the experimental findings, while all the excited states, including the first, which was previously suggested to have a slightly bent structure, are found to be linear. In the linear centrosymmetric nuclear configuration (which corresponds to the equilibrium geometry of the anion, AuH2-), we find that the first excited state and ground state are very close in energy and the ground state is characterized by an unexpected symmetry breaking in the direction of the asymmetric stretching, due to the pseudo-Jahn-Teller effect. This effect depends on the energy difference between these two electronic states and disappears when the spin-orbit coupling is neglected. The picture that emerges here is intriguing and demonstrates that the interpretation, for which the vibronic transitions that were previously assigned to a slightly bent structure of the first excited state needs to be revised and that a full rationalization of the PES spectra would require the explicit inclusion of the nuclear dynamical effects, beyond the Born-Oppenheimer (BO) approximation. From a methodological point of view, the relativistic EOM-IP-CCSD method results are highly accurate and capable of giving a well-balanced description of the anionic and neutral species, which is a key aspect for the interpretation of the PES spectra in open-shell heavy element compounds.

We introduce here the spin-resolved version of the charge displacement function, which is applied to two competing pathways of proton-coupled electron transfer in oxidation catalysis (hydrogen-atom transfer, concerted proton-coupled electron transfer). The difference in charge displacement between the two mechanisms is directly observable and can be translated to electron flow using this new analysis tool.

While since mid-seventies it has been clearly shown that relativistic effects play a crucial role for the complete understanding of the chemistry of molecules especially when heavy elements are involved, still nowadays in most of the case the relativistic effects are introduced via approximate methods. The main motivation behind the introduction of such approximation, respect to the natural and most rigorous component (4c) formalism derived from the Dirac equation, is the computational burden. In the present paper we are proposing a review of the BERTHA code that, together with the recently introduced Python bindings, represents the state of the art for full 4c calculations both in term of performances as well as in terms of code usability.

We studied the nature of the interaction of the weakly bound Be-He adduct by means of an integrated theoretical approach based on high-level quantum chemical calculations for the characterization of the potential energy surfaces and charge displaced upon adduct formation, together with the development of a semi-empirical analytical formulation of the interaction potential. Our results show that Be is able to form a stable adduct with He when the Be(D-1) (1s(2)2s(2)1s(2)2s(0)2p(2)) excited state is involved, with a binding energy of as much as 10.2kcal/mol, an astonishingly large value for He in neutral systems. The analysis of the leading interaction components in the Be*-He adduct proves the relevance of the charge transfer to the overall stability, which contributes to decreasing the intermolecular distance, thus strengthening the induction-energy component.

A spin-forbidden chemical reaction involves a change in the total electronic spin state from reactants to products. The mechanistic study is challenging because such a reaction does not occur on a single diabatic potential energy surface (PES), but rather on two (or multiple) spin diabatic PESs. One possible approach is to calculate the so-called "minimum energy crossing point" (MECP) between the diabatic PESs, which however is not a stationary point. Inclusion of spin-orbit coupling between spin states (SOC approach) allows the reaction to occur on a single adiabatic PES, in which a transition state (TS SOC) as well as activation free energy can be calculated. This Concept article summarizes a previously published application in which, for the first time, the SOC effects, using spin-orbit ZORA Hamiltonian within density functional theory (DFT) framework, are included and account for the mechanism of a spin-forbidden reaction in gold chemistry. The merits of the MECP and TS SOC approaches and the accuracy of the results are compared, considering both our recent calculations on molecular oxygen addition to gold(I)-hydride complexes and new calculations for the prototype spin-forbidden N2 O and N2 Se dissociation reactions.

Spin-forbidden reactions are frequently encountered when transition metal oxo species are involved, particularly in oxygen transfer reactivity. The computational study of such reactions is challenging, because reactants and products are located on different spin potential energy surfaces (PESs). One possible approach to describe these reactions is the so-called minimum energy crossing point (MECP) between the diabatic reactants and products PESs. Alternatively, inclusion of spin-orbit coupling (SOC) effects allows to locate a saddle point on a single adiabatic PES (TS SOC). The TS SOC approach is rarely applied because of its high computational cost. Recently evidence for a TS SOC impact on significantly lowering the activation barrier in dioxygen addition to a carbene-gold(I)-hydride complex reaction (Chem. Sci. 2016, 7, 7034-7039) or even on predicting a qualitatively different reaction mechanism in mercury methylation by cobalt corrinoid (Angew. Chem. Int. Ed. 2016, 55, 11503-11506) has been put forward. Using MECP and TS SOC approaches a systematic analysis is provided here of three prototypical transition metal oxo spin-forbidden processes to investigate their implications on reactivity. Cycloaddition of ethylene to chromyl chloride (CrO2 Cl2 +C2 H4 ), iron oxide cation insertion into the hydrogen molecule (FeO+ +H2 ) and H-abstraction from toluene by a MnV -oxo-porphyrin cation (MnOP(H2 O)+ +C6 H5 CH3 ) are case studies. For all these processes the MECP and TS SOC results are compared, which show that the spin-forbidden reactivity of transition metal oxo species can be safely described by a MECP approach, at least for the first-row transition metals investigated here, where the spin-orbit coupling is relatively weak. However, for the Mn-oxo reactivity, the MECP and TS SOC have been found to be crucial for a correct description of the reaction mechanism. In particular, the TS SOC approach allows to straightforwardly explore detailed features of the adiabatic potential energy surface which in principle could affect the overall reaction rate in cases where the involved diabatic PESs are tricky. ispartof: CHEMISTRY-A EUROPEAN JOURNAL vol:26 issue:14 pages:3080-3089 ispartof: location:Germany status: published

[AuCl(NHC)(ppy)]Cl (1) and [AuCl(PPh3)(ppy)]OTf (2) complexes [ppy = 2-phenylpyridine, NHC = 1,3-bis(2,6-di-isopropylphenyl)-imidazol-2-ylidene] successfully catalyze the hydration of alkynes in γ-valerolactone (GVL), under acid-free conditions. The solution structure, reactivity, and catalytic properties of (1) and (2) were established by means of multinuclear NMR and computational (DFT) studies. Structural features of 1 during the catalysis, inferred by NMR spectroscopy, clearly indicate that complex 1 retains its square planar structure and no reduction to Au(I) and/or Au(0) nanoparticles was observed. The overall catalytic and kinetic investigations [kinetic isotopic effect (KIE), effect of acid additives, the order of reaction with respect to the catalyst, alkyne and nucleophile and the effect of the temperature] supported by computational results confirm that the pre-equilibrium step of the reaction mechanism is the RDS: water or counterion substitution by 3-hexyne in the first co-ordination sphere of Au(III) is the key step of the whole process. The description of the mechanism of the hydration of 3-hexyne catalyzed by 1 here reported appears therefore to be of high significance because comprehensive mechanistic studies of the Au(III)-catalyzed hydration reaction of the CC bond are scarce in the literature and generally lack experimental basis.

The self-assembling of the 10-methylacridinium perchlorate fluorophore and azathiocrown ether derivative receptor through sodium dodecyl sulfate (SDS) or sodium 4-octylbenzenesulfonate (SOBS) aggregates in water has allowed the realization of a new effective sensing system for Hg2+ ions. In the absence of metal ions, occurrence of the fluorophore-receptor interaction was signaled through the fluorescence quenching of acridinium. Upon addition of increasing quantities of Hg2+, fluorescence experiments pointed out an unusual further quenching of the acridinium fluorescence, followed by an emission enhancement with a switching point around 1 × 10−7 and 1 × 10−8 M in SDS and SOBS, respectively. Such a behavior was attributed to the formation of mercury-receptor complexes with different coordination number and accordingly with distinct redox activity. The stoichiometry of the mercury complexes was assessed by spectrophotometric titration, while insights into their structures were obtained with density functional theory (DFT) calculation. Hg2+ ions can be selectively detected in SDS solutions, and its concentration in the nanomolar range can be linearly determined. Altogether, this modular approach allows quick variation of the components, which makes the optimal tuning of the process up to its maximum efficiency level very easy.

A new OFF-ON fluorescent chemosensor for ions Hg2+ in water has been designed by associating fluorophore 10-methylacridinium perchlorate (MA+ClO4−) with a selective lipophilic sulfur-containing ligand, such as N,N-bis (2-hydroxyethylthio-1-ethyl)dodecyl amine (DBSO). The communication between the two subunits is only due to their spatial closeness, ensured by sodium dodecyl sulfate (SDS) micellar aggregates. The quenching of MA+ fluorescence is ascribed to a photoinduced electron-transfer from the ligand to the excited fluorophore, still the emission is quickly restored by addition of Hg2+ (as chloride salt) due to the complex formation between ligand and metal. The sensitivity of the system improves by decreasing the ligand concentration, as well as by changing the stoichiometry of the ligand-Hg2+ complex from 1:1 to 2:1. DFT calculations give interesting insights into the structures of the complexes and provide useful information on the sensorial activity experimentally observed. The replacement of MA+ClO4− with 9-cyanoanthracene, a fluorophore differently localized on the micellar aggregate, highlights the effect of Cl− coordination to the complexed Hg2+ on the operating mechanism of the sensor. These results demonstrate as the micellar aggregates provide for a straightforward means to regulate the response of the sensorial system without altering the recognition or reporter unit.

Group 11 dihydrides MH2– (M = Cu, Ag, Au, Rg) have been much less studied than the corresponding MH compounds, despite having potentially several interesting applications in chemical research. In this work, their main spectroscopic constants (bond lengths, dissociation energies, and force constants) have been evaluated by means of highly accurate relativistic four-component coupled cluster (4c-CCSD(T)) calculations in combination with large basis sets. Periodic trends have been quantitatively explained by the charge-displacement/natural orbitals for chemical valence (CD-NOCV) analysis based on the four-component relativistic Dirac–Kohn–Sham method, which allows a consistent picture of the nature of the M–H bond to be obtained on going down the periodic table in terms of Dewar–Chatt–Duncanson bonding components. A strong ligand-to-metal donation drives the M–H bond and it is responsible for the heterolytic (HM···H–) dissociation energies to increase monotonically from Cu to Rg, with RgH2– showing the strongest and most covalent M–H bond. The “V”-shaped trend observed for the bond lengths, dissociation energies, and stretching frequencies can be explained in terms of relativistic effects and, in particular, of the relativistically enhanced sd hybridization occurring at the metal, which affects the metal–ligand distances in heavy transition-metal complexes. The sd hybridization is very small for Cu and Ag, whereas it becomes increasingly important for Au and Rg, being responsible for the increasing covalent character of the bond, the sizable contraction of the Au–H and Rg–H bonds, and the observed trend. This work rationalizes the spectroscopic/bond property relationship in group 11 dihydrides within highly accurate relativistic quantum chemistry methods, paving the way for their applications in chemical bond investigations involving heavy and superheavy elements.

In this paper, we present and review the most recent computational advances in the BERTHA code. BERTHA can be regarded as the state of the art in fully relativistic four-component Dirac–Kohn–Sham (DKS) software. Thanks to the implementation of various parallelization and memory open-ended distribution schemes in combination with efficient “density fitting” algorithms, it greatly reduces the computational burden of four-component DKS calculations. We also report the newly developed OpenMP version of the code, that, together with the berthmod Python module, provides a significant leap forward in terms of usability and applicability of the BERTHA software. Some applications of the recently developed natural orbitals for chemical valence/charge displacement bonding analysis and the real-time time dependent DKS implementation are also reported.

We present a real-time time-dependent four-component Dirac-Kohn-Sham (RT-TDDKS) implementation based on the BERTHA code. This new implementation takes advantage of modern software engineering, including the prototyping techniques. The software design follows a three step approach: (i) the prototype implementation of a time-propagation algorithm in nonrelativistic real-time TDDFT within the Psi4NumPy framework, which provides a suitable environment for the creation of a clear, readable, and easy to test reference code in Python, (ii) the design of an original Python application programming interface for the relativistic four-component code BERTHA (PyBERTHA), which has an efficient computational kernel for relativistic integrals written in FORTRAN, and (iii) the porting of the time-propagation scheme enveloped within the Psi4NumPy framework to PyBERTHA. The propagation scheme consequently resides in a single readable Python computer code that is easy to maintain and in which the key quantities, such as the Dirac-Kohn-Sham and dipole matrices, can be accessed directly from the PyBERTHA module. For linear algebra operations (matrix-matrix multiplications and diagonalization) we use the highly optimized procedures implemented in the popular NumPy library. The overhead introduced by the Python interface to BERTHA is almost negligible (less than 1% evaluated on the SCF procedure), and the interoperability between different programming languages (FORTRAN, C, and Python) does not affect the numerical stability of the time-propagation scheme. Our new RT-TDDKS implementation has been employed to investigate the stability of the time-propagation procedure in combination with a density-fitting algorithm (both for the Coulomb and for the exchange-correlation matrix construction), which are employed in BERTHA to speed up the Dirac-Kohn-Sham matrix evaluation. On the basis of systematic calculations, employing several density-fitting basis sets of increasing accuracy, we showed that quantitative agreement can be achieved in combination with extended-fitting basis sets, with an error in the Coulomb energy below 1 μ-hartree. Convergence of the transition energies increasing of quality of the fitting basis sets has been also observed. Our data suggest that the error in the Coulomb energy may also represent a good estimate of the fitting basis set quality for real-time electron dynamics simulations. Further, we study the applicability of the RT-TDDKS method in combination with both weak- and extreme strong-field regime. Numerical results of excited-state transitions for the Group 12 atoms are reported and compared with a previous real-time Dirac-Kohn-Sham implementation (Repisky et al. J. Chem. Theory Comput. 2015, 11, 980-991). Finally, calculations of high harmonic generation in the hydrogen molecule and Au dimer have been also carried out. We were able to generate high harmonics with relatively well-defined peaks up to the 21st and 13th order in the case of H2 and Au2, respectively. Our findings show that the four-component structure of the Dirac-Kohn-Sham Hamiltonian provides a suitable theoretical framework, with no intrinsic unfavorable features, to study molecules in the strong-field regime.

The effect of spin–orbit coupling (SOC) on the halogen bond involving astatine has been investigated using state-of-the-art two- and four-component relativistic calculations. Adducts between Cl–X (X = Cl, Br, I and At) and ammonia have been selected to establish a trend on going down the periodic table. The SOC influence has been explored not only on the geometric and energetic features that can be used to characterize the halogen bond strength but also on the three main contributions to it that are the charge transfer, the “σ-hole” (i.e.the localized region with a net positive electrostatic potential at the halogen site) and the “polar flattening” (which is related to the effective shape of the halogen site). A surprisingly large increase of the Cl–At dipole moment, due to the inclusion of SOC, has been worked out using four-component CCSD(T) reference calculations, indicating that this bond is significantly more ionic than one may predict. Due to the SOC effect, which induces a peculiar charge accumulation on the At side in the Cl–At dimer, a weakening of the astatine-mediated halogen bond occurs arising from the (i) reduced amount of charge transfer, (ii) decrease of the polar flattening and (iii) lowering of the short-range Coulomb potential. The analysis of the electronic structure of the Cl–At moiety allows for a rationalization of the SOC effects on all the considered features of the halogen bond, including an unprecedented unsymmetrical charge back-donation from Cl–At to ammonia.

The good performance of N‐heterocyclic carbenes (NHCs), in terms of versatility and selectivity, has called the attention of experimentalists and theoreticians attempting to understand their electronic properties. Analyses of the Au(I)–C bond in [(NHC)AuL]+/0 (L stands for a neutral or negatively charged ligand), through the Dewar–Chatt–Duncanson model and the charge displacement function, have revealed that NHC is not purely a σ‐donor but may have a significant π‐acceptor character. It turns out, however, that only the σ‐donation bonding component strongly correlates with one specific component of the chemical shielding tensor. Here, in extension to earlier works, a current density analysis, based on the continuous transformation of the current density diamagnetic zero approach, along a series of [(NHC)AuL]+/0 complexes is presented. The shielding tensor is decomposed into orbital contributions using symmetry considerations together with a spectral analysis in terms of occupied to virtual orbital transitions. Analysis of the orbital transitions shows that the induced current density is largely influenced by rotational transitions. The orbital decomposition of the shielding tensor leads to a deeper understanding of the ligand effect on the magnetic response properties and the electronic structure of (NHC)‐Au fragments. Such an orbital decomposition scheme may be extended to other magnetic properties and/or substrate‐metal complexes., (NHC) carbon chemical shielding tensor decomposition into orbital contributions. The current density is largely influenced by rotational transitions involving occupied and virtual orbitals localized on the (NHC) carbon atom with a 1 and b 1 symmetries, respectively.John Wiley & Sons, Ltd.

We present a four-component relativistic density functional theory study of the chemical bond and s–d hybridization in the group 11 cyanides M–CN (M = Cu, Ag, and Au). The analysis is carried out within the charge-displacement/natural orbital for chemical valence (CD-NOCV) scheme, which allows us to single out meaningful contributions to the total charge rearrangement that arises upon bond formation and to quantify the components of the Dewar–Chatt–Duncanson bonding model (the ligand-to-metal donation and metal-to-ligand back-donation). The M–CN bond is characterized by a large donation from the cyanide ion to the metal cation and by two small back-donation components from the metal toward the cyanide anion. The case of gold cyanide elucidates the peculiar role of the relativistic effects in determining the characteristics of the Au–C bond with respect to the copper and silver homologues. In AuCN, the donation and back-donation components are significantly enhanced, and the spin–orbit coupling, removing the degeneracy of the 5d atomic orbitals, induces a substantial split in the back-donation components. A simple spatial analysis of the NOCV-pair density, related to the ligand-to-metal donation component, allows us to quantify, with unprecedented accuracy, the charge rearrangement due to the s–d hybridization occurring at the metal site. The s–d hybridization plays a key role in determining the shape and size of the metal; it removes electron density from the bond axis and induces a significant flattening at the metal site in the position trans to the ligand. The s–d hybridization is present in all noble metal complexes, influencing the bond distances, and its effect is enhanced for Au, which is consistent with the preference of gold to form linear complexes. A comparative investigation of simple complexes [AuL]+/0of Au+with different ligands (L = F–,N-heterocyclic carbene, CO, and PH3) shows that the s–d hybridization mechanism is also influenced by the nature of the ligand.

In this chapter, the role of ion pairing in the mechanism of the reactions promoted by gold(i) catalysts L–Au–X is elucidated by means of both experimental findings and theoretical calculations. The synergy of the approach allowed the full elucidation of the role of the counterion X−. The catalytic performance in the alkoxylation and hydration of alkynes promoted by gold(i) is influenced by the coordinating ability and basicity (proton affinity) of the counterion, the anion/cation relative orientation and the appropriate matching of X− and L. Finally, how the nature of the anion plays a fundamental role in solvent-, silver- and acid-free gold(i)-catalysed hydration of alkynes is highlighted.

Noncovalent interactions often provide the spine of biomolecular and material structures, and can therefore play a key role in biological and catalytic processes. Selectivity in chemical reactions, particularly in catalytic processes, is often an orchestral action of various noncovalent interactions occurring in intermediates and transition states. Although the role of hydrogen bonding is well explored in catalysis, the other types of weak interactions, namely cation–π, anion–π, π–π stacking, pseudo-agostic, halogen, chalcogen, pnictogen, tetrel and icosagen bonds, must also be considered. Naturally, the chemo-, regio- or stereoselectivity of a reaction depends on the stability of such noncovalent-interaction-supported species in catalytic systems. Therefore, an in-depth understanding of these weak interactions may be the key to designing new catalytic materials. Providing an overview of the role of these different types of noncovalent interactions in both homogenous and heterogeneous catalysis, this book is a valuable resource for synthetic chemists who are interested in exploring and further developing noncovalent-interaction-assisted synthesis and catalysis.

Selected systems bearing carbon-chlorine (C Cl) bond and their complexes with two representative Lewis bases have been examined by means of quantum-chemistry DFT calculations to gain a deeper insight into the parameters affecting the halogen bond (XB) interaction. The dependence of the C hybridization (sp, sp2, sp3) and induction (by replacing the H atoms with the F electron-withdrawing atoms) on the polar flattening (PF), the σ-hole and the charge transfer (CT) in the XB complex has been unraveled.

A quantitative assessment of the Dewar-Chatt-Duncanson components of the Au(III)-alkyne bond in a series of cationic and dicationic bis- and monocyclometalated gold(III) complexes with 2-butyne via charge-displacement (CD) analysis is reported. Bonding between Au(III) and 2-butyne invariably shows a dominant σ donation component, a smaller, but significant, π back-donation, and a remarkable polarization of the alkyne CC triple bond toward the metal fragment. A very large net electron charge transfer from CC triple bond to the metal fragment results, which turns out to be unexpectedly insensitive to the charge of the complex and more strictly related to the nature of the ancillary ligand. The combination of σ donation, π back-donation, and polarization effects is in fact modulated by the different ligand frameworks, with ligands bearing atoms different from carbon in trans position with respect to the alkyne emerging as especially interesting for both imparting Au(III)-alkyne bond stability and inducing a more effective alkyne activation. A first attempt to figure out a rationale on the bonding/reactivity relationship for Au(III)-alkyne is made by performing a comparative study in a model nucleophilic attack of water to the alkyne triple bond. Smaller π back-donation facilitates alkyne slippage in the transition states, which is energetically less demanding for Au(III) than for Au(I), and suggests a greater propensity of Au(III) to facilitate the nucleophilic attack.

The Mn-oxo porphyrin (MnOP) mechanism for substrate hydroxylation is computationally studied with the aim to better understand reactivity in these systems. Theoretical studies suggest Mn(V)OP species to be very reactive intermediates with thermally accessible reaction barriers represented by low-spin/high-spin-crossover occurring in the Mn(V)OP oxidant, and kinetics for selected Mn(V)OP species indeed find high reactivity. On the other hand, MnOP complexes lead to modest yields in hydroxylation reactions of several different substrates, implying low rate constants and high reaction barriers. The resolution of this inconsistency is very important to understand the reactivity of Mn-oxo porphyrins and to improve the catalytic conditions. In this work we use the toluene hydroxylation by the Mn(V)OP(H2O)+ complex as a case study to gain deep insight into the reaction mechanism. Minimum energy crossing point (MECP) results on the H-abstraction process from toluene indicate a first crossover from a singlet to a triplet spin state of the Mn(V)OP(H2O)+ species with a thermally accessible barrier, followed by a very facile H-abstraction by the triplet complex. Issues concerning (i) the validation of the level of the density functional theory employed (BP86) to describe the singlet-triplet energy gap in the Mn(V)OP(H2O)+ system versus highly accurate DMRG-CASPT2/CC calculations, and (ii) the influence of the axial ligand (X = none, Cl-, CH3CN, OH-, and O2-) on MnOP reactivity, which models the different experimental conditions, are addressed. The ligand trans influence mainly controls the reactivity through the singlet-triplet energy gap modulation, with the porphyrin ruffling distortion also finely tuning it. Finally, a stepwise model for the H-abstraction process is proposed which allows a direct comparison between the calculated and experimentally measured Gibbs free activation energy barriers ( Zhang et al. J. Am. Chem. Soc. 2005 , 127 , 6573 - 6582 ). The low yields in catalysis are shown not to be due to low reactivity of Mn(V). ispartof: INORGANIC CHEMISTRY vol:58 issue:11 pages:7345-7356 ispartof: location:United States status: published

We have recently introduced a simple yet powerful tool for analyzing quantitatively the coordination bond in terms of the donation and back-donation constituents of the Dewar-Chatt-Duncanson model. Our approach is based on the decomposition, via natural orbitals for chemical valence (NOCV), of the so-called charge-displacement (CD) function into additive chemically meaningful components (Bistoni et al. J. Chem. Phys. 2015, 142, 084112 ). The method, referred to as NOCV/CD, provides clear-cut measures of donation and back-donation charge flows following bond formation, and its robustness has been demonstrated by a tight correlation of the related charge-transfer estimates with experimental observables. In this paper we extend the NOCV/CD analysis scheme to the four-component relativistic framework, which includes spin-orbit coupling variationally. This formalism is incorporated into a recently developed, highly efficient parallel version of the relativistic Dirac-Kohn-Sham (DKS) program BERTHA (Rampino et al. J. Chem. Theory Comput. 2014, 10, 3766-3776 ). We test the accuracy and numerical stability of this new implementation through the analysis of the convergence properties of the basis sets employed to expand the DKS spinor solution and those used to linearize the electronic density in the density-fitting algorithm speeding up the evaluation of the DKS matrix. An illustration of NOCV/CD analysis in the relativistic framework is also given through a study of the metal-carbonyl coordination bond in a series of [M-CO]+ (M = Cu, Ag, Au) complexes of group 11 metals, where relativistic effects, including spin-orbit coupling, are found to play an important role.