The phenomena of bond alternation and bond equalisation in conjugated hydrocarbons are studied using dynamic orbital forces (DOF) which provide an index of intrinsic CC binding, with its sigma and pi components. Some linear polyenes, polyynes and cumulenes have been analysed. Dealing with linear polyenes and polyynes, it is shown that sigma bonds can be considered as weak "inverted" ones in formally multiple bonds and strong "superdirect" ones in formally single ones. This alternance in sigma bonding partly compensates and, in some cases, overcome the alternance in pi binding. Moreover, it was shown from a panel of seven aromatic annulenes and allyl compounds that the bond equalization is favoured by sigma bonding. It can be unfavoured or favoured by the pi binding according to the system and the nature of its deformation into a bond alternant structure.

Water ice plays an important role in reactions taking place on the surface of interstellar ice grains, ranging from catalytic effects that reduce reaction barrier heights to effects that stabilize the reaction products and intermediates formed, or that favor one reaction pathway over another, passing through water-involvement in the reaction to produce more complex molecules that cannot be formed without water or water-derived fragments H, O and OH. In this context, we have combined experimental and theoretical studies to investigate ketene (CH2CO) + H solid-state reaction at 10 K in the presence and absence of water molecules under interstellar conditions, through H-bombardment of CH2CO and CH2CO/H2O ices. We show in the present study that with or without water, the ketene molecule reacts with H atoms to form four reaction products, namely CO, H2CO, CH4 and CH3CHO. Based on the amounts of CH2CO consumed during the hydrogenation processes, the CH2CO + 2H reaction appears to be more efficient in the presence of water. This underlines the catalytic role of water ice in reactions occurring on the surface of interstellar ice grains. However, if we refer to the yields of reaction products formed during the hydrogenation of CH2CO and CH2CO/H2O ices, we find that water molecules favor the reaction pathway to form CH3CHO and deactivate that leading to CH4 and H2CO. These experimental results are in good agreements with the theoretical predictions that highlight the catalytic effect of H2O on the CH2CO + H reaction, whose potential energy barrier drops from 4.6 kcal mol(-1) (without water) to 3.8 and 3.6 kcal mol(-1) with one and two water molecules respectively.

Context. Formamide is one of the possible precursors of life because it has a bond analogous to the peptide bond. Aims. In this work, we examine the reaction pathways that lead from HCN or HNC and OH to formamide. Both HCN and HNC are present in the interstellar medium, while OH could be present in interstellar water ice, which under the effect of cosmic rays, partially decomposes into H and OH. Methods. We carried out first principles calculations. We represented the solid state either by a model of clusters or by a model of slabs that takes into account periodicity. The confrontation of these two models and with the reaction in the gas phase enabled us to find reactivity trends. Results. For HCN, the formation of the C-N bond presents an energy barrier that cannot be overcome in the interstellar medium. The presence of water ice grains does not catalyze this step. The formation of the same bond from HNC is spontaneous, even without the presence of the solid. The second step of the pathway is a transposition of H. This step requires the presence of water ice for the barrier to allow the reaction to take place in the interstellar medium. The last step is a hydrogenation of a barrier-free radical. Our work therefore concludes that the synthesis of formamide can take place in the interstellar medium through water ice, which not only catalyzes the reaction but also constitutes a reservoir of OH.

Observational data show complex organic molecules in the interstellar medium (ISM). Hydrogenation of small unsaturated carbon double bond could be one way for molecular complexification. It is important to understand how such reactivity occurs in the very cold and low-pressure ISM. Yet, there is water ice in the ISM, either as grain or as mantle around grains. Therefore, the addition of atomic hydrogen on double-bonded carbon in a series of seven molecules have been studied and it was found that water catalyzes this reaction. The origin of the catalysis is a weak charge transfer between the π MO of the unsaturated molecule and H atom, allowing a stabilizing interaction with H2O. This mechanism is rationalized using the non-covalent interaction and the quantum theory of atoms in molecules approaches.

Dynamic Orbital Forces (DOF) and Non-Covalent Interactions (NCIs) allow an analysis of the attractive/repulsive interactions whose variations lead to the staggered preference of ethane and some related compounds. In ethane, it is found that CH3···CH3 attractive interactions are predominant in the staggered preference with respect to adiabatic eclipsed conformation, with an important  contribution. On the contrary, vertical eclipsed ethane is destabilized almost only by repulsive  interactions. Weak long-range H···H repulsions favor the staggered conformation. From the sum of DOFs, the energy barrier can be decomposed into C-H and C-C bond energies. It is found due to the weakening of the C-C bond (ca. 7 kcal/mol), moderated by a strengthening of C-H ones (ca. 4 kcal/mol) arising from the decrease of hyperconjugation with respect to the staggered conformation. In the compounds CH3-SiH3, SiH3-SiH3, CH3-CF3 and CF3-CF3, the conformational preference is predominantly or exclusively due to repulsive interactions, with respect as well to adiabatic as to vertical eclipsed structures.

The bond energy (BE) of CC in CH3-CH3 with respect to geometry frozen fragments follows a sigmoidal increase as a function of the θ = HCC pyramidalization angle. Using dynamic orbital forces as a BE index, the same behaviour as a function of a unique 〈θ〉 parameter, mean angle of the substituents, is found for 24 single CC bonds in various hydrocarbons. Thus the 〈θ〉 parameter appears as a straightforward and robust index of the geometrical constraints which can either strengthen or weaken a bond. This way, CC sigma bonds can be easily classified into weak "inverted" bonds for 〈θ〉 <90° (eg. in [1 1 1]propellane and bicyclobutane), "direct" (or "normal") bonds for 90° < 〈θ〉 < 120° (eg. ethane), and strong "superdirect" bonds for 〈θ〉 > 120° (eg. in tetrahedryl-tetrahedrane and butadiyne).

The reaction of ketene (H2CCO) with hydrogen atoms has been studied under interstellar conditions through two different experimental methods, occurring on the surface and in the bulk of H2CCO ice. We show that ketene interaction with H-atoms at 10 K leads mainly to four reaction products, carbon monoxide (CO), methane (CH4), formaldehyde (H2CO) and acetaldehyde (CH3CHO). A part of these results shows a chemical link between a simple organic molecule such as H2CCO and a complex one such as CH3CHO, through H-addition reactions taking place in dense molecular clouds. The H-addition processes are very often proposed by astrophysical models as mechanisms for the formation of complex organic molecules based on the abundance of species already detected in the interstellar medium. However, the present study shows that the hydrogenation of ketene under non-energetic conditions may also lead efficiently to fragmentation processes and the formation of small species such as CO, CH4 and H2CO, without supplying external energy such as UV photons or high energy particles. Such fragmentation pathways should be included in the astrophysical modeling of H2CCO + H in the molecular clouds of the interstellar medium. To support these results, theoretical calculations have explicitly showed that, under our experimental conditions, H-atom interactions with the CC bond of ketene lead mainly to CH3CHO, CH4 and CO. By investigating the formation and reactivity of the reaction intermediate H3C-CO radical, our calculations demonstrate that the H3C-CO + H reaction evolves through two barrierless pathways to form either CH3CHO or CH4 and CO fragments.

The C-C dissociation energy with respect to geometry frozen fragments (BE) has been calculated for C2H6 as a function of  = H-C-C angles. BE decreases rapidly when  decreases from its equilibrium value to yield the so-called “inverted bonds” for  < 90°; on the contrary BE increaseswhen  increases to yield somehow “superdirect” bonds, following a sigmoidal variation. The central bond in Si2H6, Ge2H6 and N 2H4 as well as the C-H bond in CH3-H behaves similarly. The concept of “invertedness”/”directedness” is generalized to any CC sigma bond in hydrocarbons and characterized by the mean angle value <> of substituents. Using dynamic orbital forces (DOF) as indices, the intrinsic  bond energies are studied as a function of <> for formally single bonds in apanel of 22 molecules. This energy decreases from the strongest “superdirect” bonds in butadiyne, (<> = 180°) or tetrahedrylacetylene to the weakest “inverted bond” in cyclobutene, tetrahedrane, bicyclobutane and [1.1.1]propellane (<> = 60°), according to a sigmoidal variation. The <> parameter appears as a crude, but straightforward and robust, index of strain in cyclic molecules. Sigma bonds in multiple bonds of a panel of 11 molecules have most of time <> values less than 90°and are significantly weaker than standard single bonds. Thus they can be considered as formally inverted or near inverted.

The bonding and antibonding character of individual Molecular Orbitals has been previously shown to be related to their orbital energy derivatives with respect to nuclear coordinates, known as Dynamical Orbital Forces. Albeit usually derived from Koopmans' theorem, in this work we show a more general derivation from conceptual DFT, which justifies application in a broader context. The consistency of the approach is validated numerically for valence orbitals in Kohn-Sham DFT. Then, we illustrate its usefulness by showcasing applications in aromatic and antiaromatic systems and in excited state chemistry. Overall, Dynamical Orbital Forces can be used to interpret the results of routine ab initio calculations, be it wavefunction or density based, in terms of forces and occupations.

The A-A dissociation energy with respect to geometry frozen fragments (BE) of has been calculated for AHn-AHn models (C2H6, Si2H6, Ge2H6 and N2H4) as a function of  = H-A-A angles. Following a sigmoidal variation, BE decreases rapidly when  decreases to yield “inverted bonds” for  < 90° and finally nearly vanishes. On the contrary BE increases when  increases with respect to the equilibrium value; we propose the term of “superdirect” to qualify such bonds. This behaviour has been qualitatively interpreted in the case of C2H6 by the variation of the overlap of both s+p hybrids. The BE of one C-H bond in CH3 behaves similarly as function of its H-C-H angle with the other three hydrogen atoms. The concept of inverted/direct/superdirect bond is generalized to any CC sigma bond in hydrocarbons and can be characterized by the mean angle value <> of this bond with substituents (multiple-bonded substituents are considered as several substituents). This applies as well to formal single bonds as to sigma bonds in a formally multiple bond.

A simple numerical experiment is presented which allows tuning the lithium electrophilicity, a parameter strongly affected by the solvent and additives coordination. A series of coordination of Li+ to carbanions or polydentate nucleophiles is examined showing the potential and the limits of this approach. The results suggest that such a simple trick can be remarkably helpful to model and decipher the effects of solvation on the structure and properties of lithiated organometallic species.

This article dwells on the nature of “inverted bonds”, which make reference to the σ interaction between two s-p hybrids by their smaller lobes, and their presence in [1.1.1]propellane 1. Firstly we study H 3 C-C models of C-C bonds with frozen HCC angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane 1 and [1.1.1]bicyclopentane 2 are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic state of 1 species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non-bonding character of the σ central CC interaction in propellane. Within MO theory, this bonding is thus only due to π-type MOs (also called ‘banana’ MOs or ‘bridge’ MOs) and its total energy is evaluated to ca. 50 kcal/mol. In bicyclopentane 2, despite a strong σ-type repulsion, a weak bonding (15-20 kcal/mol) exists between both central CC, also due to π-type interactions, though no bond is present in the Lewis structure. Overall, the so-called ‘inverted’ bond, as resulting from a σ overlap of the two s-p hybrids by their smaller lobes, appears highly questionable.

The CC bonding is analyzed using dynamic orbital forces (DOF) in the series cyclopropane-ethane- benzene-ethylene-acetylene. The sum sigma(DOF)(t) of the DOF over occupied molecular orbitals (MOs) is found linearly correlated to bond energies and thus can be used as a tool for determination of CC bond strength. A partition of bonding into sigma and pi components indicates a weakening of the sigma bonding along the series, mainly due to the decrease of the bonding character of the highest sigma MO. For C-2 molecule, sigma(DOF) (t) was computed taking into account the four dominant configurations. On the basis of the preceding correlation, the C-2 bond was found about 15 kcal/mol weaker than that of acetylene, with a 25% sigma participation; the bond order of C-2 can be evaluated at about 2.8 if we assume bond orders of 3 for acetylene and 2 for ethylene. Some sila homologs of the preceding carbon compounds have been studied. They exhibit characteristics generally close to the carbon compounds. A quite good correlation between sigma(DOF)(t) and bond energies is also observed.

The derivative of molecular orbitals (MO) energies with respect to a bond length (dynamic orbital force [DOF)) is used to estimate the bonding/antibonding character of valence MOs along this bond, with a focus on lone pair MOs, in a series of small molecules: AH (A = F, CI, Br), AH(2) (A = O, S. Se), AX(3) (A = N, P, As; X = H, F), and H2CO. The HOMO DOF agrees with the calculated variation of bond length and force constant in the corresponding ground state cation, and of bond length variation by protonation. These results also agree with available experimental data. It is worthy to note that the p-type HOMOs in AH and AH(2) are found bonding. The lone pair MO is bonding in NH3, while it is antibonding in PH3, AsH3, and AF(3).

The properties of the “inverted bond” in [1.1.1]propellane are investigated by two methods. Firstly we study H3C-C models of C-C bonds with frozen HCC angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate in-situ bond energies. Triplet state of propellane and cationic states of propellane and bicyclopentane are also considered to comfort the bonding/antibonding character of MOs in the parent molecules. Both approaches shows an essentially nonbonding or slightly repulsive character of the sigma central CC interaction in propellane: the so-called ‘inverted’ bond, as resulting from a sigma overlap of the two s-p hybrids by their smaller lobes, appears devoid of physical basis. The bonding of central CC in propellane is thus only due to pi-type MOs (also called ‘banana’ MOs or ‘bridge’ MOs) and its total energy is evaluated to ca. 60 kcal/mol. In bicyclopentane, despite a strong sigma-type repulsion, a weak bonding (20 kcal/mol) exists between both central CC, also due to pi-type interactions, though no formal bond is present

The derivative of the energy of a canonical molecular orbital (MO) [or dynamical orbital forces (DOFs)] with respect to a bond length provides a reliable index of the bonding/antibonding character of this MO on this bond. The DOFs of selected MOs as a function of the reaction coordinate were computed for a panel of model reaction mechanisms: [2+4] (Diels-Alder) cycloaddition, [2+2] cycloaddition, second-order nucleophilic substitution (SN 2), nucleophilic addition to a carbonyl group, and [1,2] hydrogen transposition. The results highlight the nature of the reorganization of the main MOs and the stage of the reaction coordinate (RC) at which it occurs. For instance, in the Diels-Alder reaction, one can identify a part of the reaction that is dominated by repulsive four-electron interactions and another part dominated by attractive two-electron interactions. Also, the shape of the DOF as a function of the reaction coordinate reveals the existence of avoided MO crossings and their location on the RC. Even for spontaneous reactions with monotonic variation in the potential energy, extrema of the MO energy and sudden electron rearrangements can be put into evidence. This study provides quantitative support to classical MO analyses of reactivity such as correlation diagrams and frontier approximation.

The detection of ArH(+) has revived the interest in the search for noble gas containing species. Despite helium being the second most abundant element in the universe (He/H ∼ 1/10), it has never been observed in any other form than that of a neutral/ionized atom in the interstellar medium. Because He is the "most noble" gas, its non-observation as part of neutral molecular systems is understandable. It is more surprising for charged species, especially HeH(+) whose spectral signatures are well documented in the laboratory. The purpose of this work was to find a simple positive ion containing He, and likely to be observed as an alternative to undetected HeH(+). Among the HeX(2+) diatomics formed with first row atoms, we focused on X = C because of both its relative abundance and the magnitude of its ionization potentials with respect to He. The formation of CHe(2+) by radiative association is the center of this study. The question was addressed by means of numerical simulations using high level ab initio calculations of the CHe(2+) potential surface, followed by a quantum chemical determination of the rate coefficients for the corresponding radiative association in the range of 10 to 1000K. The radiative association path shows a potential well deep enough to accommodate 20 vibrational levels, and no barrier to oppose the reaction. The rate coefficient varies from ∼4.5 × 10(-20) cm(3)s(-1) to ∼2.5 × 10(-22) cm(3)s(-1) for the temperatures considered. The present study suggests that the existence of this species has to be searched for mainly in highly irradiated regions.

•Good correlation between deformation force and binding energy for diatomics, but transition metal dimers.•Atomic densities and experimental bond lengths only can reproduce reasonable vibrational frequencies.•Derivatives of promolecular forces are sufficient.•Easy implementation and rapid evaluation even for large systems.