BERTHA: Implementation of a four-component Dirac-Kohn-Sham relativistic framework.

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.

Orbital Decomposition of the Carbon Chemical Shielding Tensor in Gold(I) N-Heterocyclic Carbene Complexes.

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.

Leading Interaction Components in the Structure and Reactivity of Noble Gases Compounds.

The nature, strength, range and role of the bonds in adducts of noble gas atoms with both neutral and ionic partners have been investigated by exploiting a fine-tuned integrated phenomenological-theoretical approach. The identification of the leading interaction components in the noble gases adducts and their modeling allows the encompassing of the transitions from pure noncovalent to covalent bound aggregates and to rationalize the anomalous behavior (deviations from noncovalent type interaction) pointed out in peculiar cases. Selected adducts affected by a weak chemical bond, as those promoting the formation of the intermolecular halogen bond, are also properly rationalized. The behavior of noble gas atoms excited in their long-life metastable states, showing a strongly enhanced reactivity, has been also enclosed in the present investigation.

The Chemical Bond and s-d Hybridization in Coinage Metal(I) Cyanides.

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]+/0 of 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.

Alkyne Activation with Gold(III) Complexes: A Quantitative Assessment of the Ligand Effect by Charge-Displacement Analysis.

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.

Insight into the halogen-bond nature of noble gas-chlorine systems by molecular beam scattering experiments, ab initio calculations and charge displacement analysis.

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-Cl2 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 Cl2 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 Cl2 is present in the lowest πg* → σu* excited state, because the change in electron density that accompanies the excitation eliminates the Cl2 polar flattening and σ hole, making the XB interaction inaccessible.

Chemical Bond Mechanism for Helium Revealed by Electronic Excitation.

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+ + He system. However, quite astonishingly, when one electron is re-added to Be+ in an excited 2pπ or 3s orbital (Be 1P or 1S), a bound adduct with He is formed, at an interatomic separation as short as 1.5 Å. Understanding why this happens reveals an unsuspected chemical mechanism that stabilizes helium compounds at the molecular level.

The Halogen-Bond Nature in Noble Gas-Dihalogen Complexes from Scattering Experiments and Ab Initio Calculations.

In order to clarify the nature of the halogen bond (XB), we considered the prototype noble gas-dihalogen molecule (Ng-X2) systems, focusing on the nature, range, and strength of the interaction. We exploited data gained from molecular beam scattering experiments with the measure of interference effects to obtain a suitable formulation of the interaction potential, with the support of high-level ab initio calculations, and charge displacement analysis. The essential interaction components involved in the Ng-X2 adducts were characterized, pointing at their critical balance in the definition of the XB. Particular emphasis is devoted to the energy stability of the orientational Ng-X2 isomers, the barrier for the X2 hindered rotation, and the influence of the X2 electronic state. The present integrated study returns reliable force fields for molecular dynamic simulations in Ng-X2 complexes that can be extended to systems with increasing complexity and whose properties depend on the selective formation of XB.

Selective Emergence of the Halogen Bond in Ground and Excited States of Noble-Gas-Chlorine Systems.

Molecular-beam scattering experiments and theoretical calculations prove the nature, strength, and selectivity of the halogen bonds (XB) in the interaction of halogen molecules with the series of noble gas (Ng) atoms. The XB, accompanied by charge transfer from the Ng to the halogen, is shown to take place in, and measurably stabilize, the collinear conformation of the adducts, which thus becomes (in contrast to what happens for other Ng-molecule systems) approximately as bound as the T-shaped form. It is also shown how and why XB is inhibited when the halogen molecule is in the 3 Πu excited state. A general potential formulation fitting the experimental observables, based on few physically essential parameters, is proposed to describe the interaction accurately and is validated by ab initio computations.

Spin-Forbidden Reactions: Adiabatic Transition States Using Spin-Orbit Coupled Density Functional Theory.

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.

Modelling Charge Transfer in Weak Chemical Bonds: Insights from the Chemistry of Helium.

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(1 D) (1s2 2s2 →1s2 2s0 2p2 ) excited state is involved, with a binding energy of as much as 10.2 kcal/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.

Ligand Effect on Bonding in Gold(III) Carbonyl Complexes.

We quantitatively assess the Dewar-Chatt-Duncanson (DCD) components of the Au(III)-CO bond and the charge density polarization at the CO, in a series of neutral, cationic, and dicationic bis- and monocyclometalated gold(III) complexes via charge-displacement (CD) analysis. A striking feature concerns the very small net electron charge flux from CO to the metal fragment which is unexpectedly stable toward both the charge of the complex and the oxidation state of gold (I, III). All systems exhibit a similar trend for the σ charge rearrangement in the region of the carbonyl bond, where, by contrast, the π back-donation trend variation is large, which is strictly correlated to the change in CO bond distance and the shift in CO stretching frequencies, in close analogy with the gold(I) carbonyl complexes. In the whole series of gold(III) compounds, a large Au(III) ← CO σ donation is measured (from 0.19 to 0.31 electrons), as well as a significant Au(III) → CO π back-donation (from -0.09 to -0.22 electrons), which however is not generally able to completely balance the polarization of the CO π electrons in the direction from oxygen to carbon (C ← O) induced by the presence of the metal fragment [LAu(III)]0/+1/+2. Surprisingly, all the gold(III) complexes in the series are characterized by a very small anisotropy in the Au(III) → CO in-plane and out-of-plane π back-donation components, in sharp contrast with the marked anisotropy found before for the experimentally characterized [(C^N^C)Au(III)CO]+ complex. A first attempt to figure out a rationale on the bonding/reactivity relationship for Au(III)-CO is made by performing a comparative study with an isostructural [(N^N^C)Pt(II)CO]+ complex in a model water-gas shift (WGS) reaction.

Modulating the Bonding Properties of N-Heterocyclic Carbenes (NHCs): A Systematic Charge-Displacement Analysis.

In view of their intensive use as ligands in many reactions catalyzed by transition-metal complexes, modulation of the bonding properties of N-heterocyclic carbenes (NHCs) on a rational basis is highly desirable, which should enable optimization of current applications or even promote new functions. In this paper, we provide a quantitative analysis of the chemical bond between a metal fragment AuCl and a series of 29 different NHCs in [(NHC)AuCl] complexes. NHCs electronic properties are modified through: i) variation of the groups attached to the NHC nitrogen atoms or backbone; ii) change of unsaturation/size of the NHC ring; iii) inclusion of paracyclophane moieties; or iv) heteroatom substitution on the NHC ring. For evaluating the donation and back-donation components of the Dewar-Chatt-Duncanson (DCD) model in the NHC-AuCl bond, we apply the charge-displacement (CD) analysis within the NOCV (natural orbitals for chemical valence) framework, a methodology that avoids the constraint of using symmetrized structures. We show that modulation of the NHC bonding properties requires substantial modification of their structure, such as, for instance, insertion of two ketone groups into the NHC backbone (which enhances the π back-donation bond component and introduces an effective electronic communication within the NHC ring) or replacement of a nitrogen atom in the ring with an sp3 or sp2 carbon atom (which increases and decreases the π back-donation bond component, respectively). We extend our investigation by quantitatively comparing the NHC electronic structures for a subset of 13 NHCs in [(NHC)PPh] adducts, the 31 P NMR chemical shift values of which are experimentally available. The latter have been considered as a suitable tool for measuring the NHCs π acceptor properties [Bertrand et al., Angew. Chem. Int. Ed. 2013, 52, 2939-2943]. We show that information obtained using the metal fragment can be transferred to the PPh moiety and vice versa. However, the 31 P NMR chemical shift values only qualitatively correlate with the π acceptor properties of the NHCs, with the stronger π acidic carbenes as the most outliners.

13 C†NMR Spectroscopy of N-Heterocyclic Carbenes Can Selectively Probe σ Donation in Gold(I) Complexes.

The Dewar-Chatt-Duncanson (DCD) model provides a successful theoretical framework to describe the nature of the chemical bond in transition-metal compounds and is especially useful in structural chemistry and catalysis. However, how to actually measure its constituents (substrate-to-metal donation and metal-to-substrate back-donation) is yet uncertain. Recently, we demonstrated that the DCD components can be neatly disentangled and the π back-donation component put in strict correlation with some experimental observables. In the present work we make a further crucial step forward, showing that, in a large set of charged and neutral N-heterocyclic carbene complexes of gold(I), a specific component of the NMR chemical shift tensor of the carbenic carbon provides a selective measure of the σ donation. This work opens the possibility of 1) to characterize unambiguously the electronic structure of a metal fragment (LAu(I)n+/0 in this case) by actually measuring its σ-withdrawing ability, 2) to quickly establish a comparative trend for the ligand trans effect, and 3) to achieve a more rigorous control of the ligand electronic effect, which is a key aspect for the design of new catalysts and metal complexes.

Ultrafast Molecular Three-Electron Auger Decay.

Three-electron Auger decay is an exotic and elusive process, in which two outer-shell electrons simultaneously refill an inner-shell double vacancy with emission of a single Auger electron. Such transitions are forbidden by the many-electron selection rules, normally making their decay lifetimes orders of magnitude longer than the few-femtosecond lifetimes of normal (two-electron) Auger decay. Here we present theoretical predictions and direct experimental evidence for a few-femtosecond three-electron Auger decay of a double inner-valence-hole state in CH_{3}F. Our analysis shows that in contrast to double core holes, double inner-valence vacancies in molecules can decay exclusively by this ultrafast three-electron Auger process, and we predict that this phenomenon occurs widely.

π Activation of Alkynes in Homogeneous and Heterogeneous Gold Catalysis.

The activation of alkynes toward nucleophilic attack upon coordination to gold-based catalysts (neutral and positively charged gold clusters and gold complexes commonly used in homogeneous catalysis) is investigated to elucidate the role of the σ donation and π back-donation components of the Au-C bond (where we consider ethyne as prototype substrate). Charge displacement (CD) analysis is used to obtain a well-defined measure of σ donation and π back-donation and to find out how the corresponding charge flows affect the electron density at the electrophilic carbon undergoing the nucleophilic attack. This information is used to rationalize the activity of a series of catalysts in the nucleophilic attack step of a model hydroamination reaction. For the first time, the components of the Dewar-Chatt-Duncanson model, donation and back-donation, are put in quantitative correlation with the kinetic parameters of a chemical reaction.

Interaction of O2 with CH4, CF4, and CCl4 by Molecular Beam Scattering Experiments and Theoretical Calculations.

Gas phase collisions of O2 by CH4, CF4, and CCl4 have been investigated with the molecular beam technique by measuring both the integral cross section value, Q, and its dependence on the collision velocity, v. The adopted experimental conditions have been appropriate to resolve the oscillating "glory" pattern, a quantum interference effect controlled by the features of the intermolecular interaction, for all the three case studies. The analysis of the Q(v) data, performed by adopting a suitable representation of the intermolecular potential function, provided the basic features of the anisotropic potential energy surfaces at intermediate and large separation distances and information on the relative role of the physically relevant types of contributions to the global interaction. The present work demonstrates that while O2-CH4 and O2-CF4 are basically bound through the balance between size (Pauli) repulsion and dispersion attraction, an appreaciable intermolecular bond stabilization by charge transfer is operative in O2-CCl4. Ab initio calculations of the strength of the interaction, coupled with detailed analysis of electronic charge displacement promoted by the formation of the dimer, fully rationalizes the experimental findings. This investigation indicates that the interactions of O2, when averaged over its relative orientations, are similar to that of a noble gas (Ng), specifically Ar. We also show that the binding energy in the basic configurations of the prototypical Ng-CF4,CCl4 systems [ Cappelletti , D. ; Chem. Eur. J. 2015 , 21 , 6234 - 6240 ] can be reconstructed by using the interactions in Ng-F and Ng-Cl systems, previously characterized by molecular beam scattering experiments of state-selected halogen atom beams. This information is fundamental to approach the modeling of the weak intermolecular halogen bond. On the basis of the electronic polarizability, this also confirms [ Aquilanti , V. ; Angew. Chem., Int. Ed. 2005 , 44 , 2356 - 2360 ] that O2 can be taken as a proper reference partner for simulating the behavior of some basic noncovalent components of the interactions involving water. Present results are of fundamental relevance to build up the force field controlling the hydrophobic behavior of prototypical apolar CX4 (X = H, F, Cl) molecules.

Selectively measuring π†back-donation in gold(I) complexes by NMR spectroscopy.

Even though the Dewar-Chatt-Duncanson model has been successfully used by chemists since the 1950s, no experimental methodology is yet known to unambiguously estimate the constituents (donation and back-donation) of a metal-ligand interaction. It is demonstrated here that one of these components, the metal-to-ligand π back-donation, can be effectively probed by NMR measurements aimed at determining the rotational barrier of a C-N bond (ΔHr (≠) ) of a nitrogen acyclic carbene ligand. A large series of gold(I) complexes have been synthesized and analyzed, and it was found that the above experimental observables show an accurate correlation with back-donation, as defined theoretically by the appropriate charge displacement originated upon bond formation. The proposed method is potentially of wide applicability for analyzing the ligand effect in metal catalysts and guiding their design.

Experimental evidence of chemical components in the bonding of helium and neon with neutral molecules.

The complexes of helium and neon with gaseous neutral molecules are generally perceived to be van der Waals adducts held together by physical (non-covalent) forces, owing to the combination of size (exchange) repulsion with dispersion/induction attraction. Molecular beam experiments confirm that this is the case for He-CF4 , Ne-CF4 adducts, but revealed that the interaction of He and Ne with CCl4 features an appreciable contribution of chemical components that arise from the anisotropy of the electron density of CCl4 that enhances a charge transfer from Ng (Ng=He, Ne). These findings furnish a novel assay of the bonding capabilities of helium and neon, and invite to revisit the neutral complexes of these elements as systems of chemical relevance. The CCl4 -Ng are also peculiar examples of halogen bonds, a group of interactions of major current concern. Finally, this investigation is a prelude to the development of semi-empirical models for force fields aimed to the unified description of static and dynamical properties of systems of comparable or higher complexity.

H2O-CH4 and H2S-CH4 complexes: a direct comparison through molecular beam experiments and ab initio calculations.

New molecular beam scattering experiments have been performed to measure the total (elastic plus inelastic) cross sections as a function of the velocity in collisions between water and hydrogen sulfide projectile molecules and the methane target. Measured data have been exploited to characterize the range and strength of the intermolecular interaction in such systems, which are of relevance as they drive the gas phase molecular dynamics and the clathrate formation. Complementary information has been obtained by rotational spectra, recorded for the hydrogen sulfide-methane complex, with a pulsed nozzle Fourier transform microwave spectrometer. Extensive ab initio calculations have been performed to rationalize all the experimental findings. The combination of experimental and theoretical information has established the ground for the understanding of the nature of the interaction and allows for its basic components to be modelled, including charge transfer, in these weakly bound systems. The intermolecular potential for H2S-CH4 is significantly less anisotropic than for H2O-CH4, although both of them have potential minima that can be characterized as 'hydrogen bonded'.