Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions.

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; 2015, 142, 154116].

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.

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] (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 -donor but may have a significant π-acceptor character. It turns out, however, that only the -donation bonding component strongly correlates with one specific component of the chemical shielding tensor.

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.

PyBERTHART: A Relativistic Real-Time Four-Component TDDFT Implementation Using Prototyping Techniques Based on Python.

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 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-X) 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-X adducts were characterized, pointing at their critical balance in the definition of the XB.

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.

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.

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.

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.

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 Π excited state.

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.

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( D) (1s 2s →1s 2s 2p ) 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.

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.

The ligand effect on the oxidative addition of dioxygen to gold(i)-hydride complexes.

The ligand effect on the recently uncovered feasible oxidative addition reaction of O on [LAuH] complexes has been investigated for a series of fifteen ligands. The activation barriers of this spin-forbidden reaction have been estimated at the minimum energy crossing points (MECP, relativistic scalar level) between the adiabatic triplet (reactants spin state) and singlet (product spin state) potential energy surfaces (PES) and calculated at the transition states by including Spin-Orbit Coupling (SOC) effects, as applied for the mechanistic study of this reaction in a previous study by us [Chem. Sci.

Helium Accepts Back-Donation In Highly Polar Complexes: New Insights into the Weak Chemical Bond.

We studied the puzzling stability and short distances predicted by theory for helium adducts with some highly polar molecules, such as BeO or AuF. On the basis of high-level quantum-chemical calculations, we carried out a detailed analysis of the charge displacement occurring upon adduct formation. For the first time we have unambiguously ascertained that helium is able not only to donate electron density, but also, unexpectedly, to accept electron density in the formation of weakly bound adducts with highly polar substrates.

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.

The gold(iii)-CO bond: a missing piece in the gold carbonyl complex landscape.

We investigate the Au(iii)-CO bond in the [(CNC)Au(iii)CO] complex via charge-displacement (CD) analysis, revealing surprising peculiarities with respect to the Au(i)-CO bond. It shows a large Au(iii) ← CO σ donation and, unexpectedly, an even larger Au(iii) → CO π back-donation. The overall bonding picture, including a marked anisotropy in the Au(iii) → CO in-plane and out-of-plane π back-donation components, is consistent with a CO carbon atom highly susceptible to nucleophilic attack.

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.

Dioxygen insertion into the gold(i)-hydride bond: spin orbit coupling effects in the spotlight for oxidative addition.

O insertion into a Au(i)-H bond occurs through an oxidative addition/recombination mechanism, showing peculiar differences with respect to Pd(ii)-H, for which O insertion takes place through a hydrogen abstraction mechanism in the triplet potential energy surface with a pure spin transition state. We demonstrate that the spin-forbidden Au(i)-hydride O insertion reaction can only be described accurately by inclusion of spin orbit coupling (SOC) effects. We further find that a new mechanism involving two O molecules is also feasible, and this result, together with the unexpectedly high experimental entropic activation parameter, suggests the possibility that a third species could be involved in the rate determining step of the reaction.

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.

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.

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.

How π back-donation quantitatively controls the CO stretching response in classical and non-classical metal carbonyl complexes.

The CO stretching response upon coordination to a metal M to form [(L) M(CO)] complexes (L is an auxiliary ligand) is investigated in relation to the σ donation and π back-donation components of the M-CO bond and to the electrostatic effect exerted by the ligand-metal fragment. Our analysis encompasses over 30 carbonyls, in which the relative importance of donation, back-donation and electrostatics are varied either through the ligand in a series of [(L)Au(CO)] gold(i) complexes, or through the metal in a series of anionic, neutral and cationic homoleptic carbonyls. Charge-displacement analysis is used to obtain well-defined, consistent measures of σ donation and π back-donation charges, as well as to quantify the σ and π components of CO polarization.

Advances in Charge Displacement Analysis.

We define new general density-based descriptors for the quantification of charge transfer and polarization effects associated with the interaction between two fragments and the formation of a chemical bond. Our aim is to provide a simple yet accurate picture of a chemical interaction by condensing the information on the charge rearrangement accompanying it into a few chemically meaningful parameters. These charge displacement (CD) parameters quantify the total charge displaced upon bond formation and decompose it into a charge transfer component between the fragments and charge rearrangements taking place within the fragments.