An energy decomposition analysis method is implemented for the analysis of both covalent bonds and intermolecular interactions on the basis of single-determinant Hartree-Fock ͑HF͒ ͑restricted closed shell HF, restricted open shell HF, and unrestricted open shell HF͒ wavefunctions and their density functional theory analogs. For HF methods, the total interaction energy from a supermolecule calculation is decomposed into electrostatic, exchange, repulsion, and polarization terms. Dispersion energy is obtained from second-order Møller-Plesset perturbation theory and coupled-cluster methods such as CCSD and CCSD͑T͒. Similar to the HF methods, Kohn-Sham density functional interaction energy is decomposed into electrostatic, exchange, repulsion, polarization, and dispersion terms. Tests on various systems show that this algorithm is simple and robust. Insights are provided by the energy decomposition analysis into H 2 , methane C-H, and ethane C-C covalent bond formation, CH 3 CH 3 internal rotation barrier, water, ammonia, ammonium, and hydrogen fluoride hydrogen bonding, van der Waals interaction, DNA base pair formation, BH 3 NH 3 and BH 3 CO coordinate bond formation, Cu-ligand interactions, as well as LiF, LiCl, NaF, and NaCl ionic interactions.

Triple bonding is conventionally considered to be the limit for multiply bonded main group elements, despite higher metal-metal bond orders being frequently observed for transition metals and lanthanides/actinides. Here, using high-level theoretical methods, we show that C(2) and its isoelectronic molecules CN(+), BN and CB(-) (each having eight valence electrons) are bound by a quadruple bond. The bonding comprises not only one σ- and two π-bonds, but also one weak 'inverted' bond, which can be characterized by the interaction of electrons in two outwardly pointing sp hybrid orbitals. A simple way of assessing the energy of the fourth bond is proposed and is found to be ~12-17 kcal mol(-1) for the isoelectronic species studied, and thus stronger than a hydrogen bond. In contrast, the analogues of C(2) that contain higher-row elements, such as Si(2) and Ge(2), exhibit only double bonding.

National Natural Science Foundation of China[20873106]; Ministry of Science and Technology[2011CB808504]; Israel Science Foundation[ISF 53/09

Mechanochemistry offers exciting opportunities for molecular-level engineering of stress-responsive properties of polymers. Reactive sites, sometimes called mechanophores, have been reported to increase the material toughness, to make the material mechanochromic or optically healable. Here we show that macrocyclic cinnamate dimers combine these productive stress-responsive modes. The highly thermally stable dimers dissociate on the sub-second timescale when subject to a stretching force of 1–2 nN (depending on isomer). Stretching a polymer of the dimers above this force more than doubles its contour length and increases the strain energy that the chain absorbs before fragmenting by at least 600 kcal per mole of monomer. The dissociation produces a chromophore and dimers are reformed upon irradiation, thus allowing optical healing of mechanically degraded parts of the material. The mechanochemical kinetics, single-chain extensibility, toughness and potentially optical properties of the dissociation products are tunable by synthetic modifications.

The ab initio VB study for the electronic structure of the C2 molecule in the ground state is presented in this work. VB calculations involving 78 chemically relevant VB structures can predict the bonding energy of C2 quite well. Sequentially, a VBCIS calculation provides spectroscopic parameters that are very close to full CI calculated values in the same basis set. Furthermore, the analysis of the bonding scheme shows that a triply bonded structure is the major one in terms of weights, and the lowest in energy at the equilibrium distance. The second structure in terms of weights is an ethylene-like structure, displaying a σ + π double bond. The structure with two suspended π bonds but no σ bond contributes only marginally to the ground state. This ordering of weights for the VB structures describing the C2 molecule is shown to be consistent with the shape of the molecular orbitals and with the multireference character of the ground state. With the triply bonded bonding scheme, the natures of the π and σ bonds are investigated, and then the corresponding "in situ" bond strengths are estimated. The contribution of the covalent-ionic resonance energy to π and σ bonding is revealed and discussed.

In this paper, a new energy decomposition analysis scheme based on the generalized Kohn-Sham (GKS) and the localized molecular orbital energy decomposition analysis (LMO-EDA) scheme, named GKS-EDA, is proposed. The GKS-EDA scheme has a wide range of DFT functional adaptability compared to LMO-EDA. In the GKS-EDA scheme, the exchange, repulsion, and polarization terms are determined by DFT orbitals; the correlation term is defined as the difference of the GKS correlation energy from monomers to supermolecule. Using the new definition, the GKS-EDA scheme avoids the error of LMO-EDA which comes from the separated treatment of EX and EC functionals. The scheme can perform analysis both in the gas and in the condensed phases with most of the popular DFT functionals, including LDA, GGA, meta-GGA, hybrid GGA/meta-GGA, double hybrid, range-separated (long-range correction), and dispersion correction. By the GKS-EDA scheme, the DFT functionals assessment for hydrogen bonding, vdW interaction, symmetric radical cation, charge-transfer, and metal-ligand interaction is performed.

Rigorously continuous and smooth potential energy surfaces, as well as exact analytic gradients, are obtained for a conductorlike screening solvation model ͑CPCM, a variant of the general COSMO͒ with Hartree-Fock ͑RHF, ROHF, UHF, and MCSCF͒ and density functional theory ͑R-DFT, RO-DFT, and U-DFT͒ methods using a new tessellation scheme, fixed points with variable areas ͑FIXPVA͒. In FIXPVA, spheres centered at atoms are used to define the molecular cavity and surface. The surface of each sphere is divided into 60, 240, or 960 tesserae, which have positions fixed relative to the sphere center and areas scaled by switching functions of their distances to neighboring spheres. Analytic derivatives of the positions and areas of the surface tesserae with respect to atomic coordinates can be obtained and used to evaluate the solvation energy gradients. Due to the accurate analytic gradients and smooth potential energy surface, geometry optimization processes using these methods are stable and convergent.

Hydrogen abstraction reactions of the type X(*) + H-H' --> X-H + H'(*) (X = F, Cl, Br, I) are studied by ab initio valence bond methods and the VB state correlation diagram (VBSCD) model. The reaction barriers and VB parameters of the VBSCD are computed by using the breathing orbital valence bond and valence bond configuration interaction methods. The combination of the VBSCD model and semiempirical VB theory leads to analytical expressions for the barriers and other VB quantities that match the ab initio VB calculations fairly well. The barriers are influenced by the endo- or exothermicity of the reaction, but the fundamental factor of the barrier is the average singlet-triplet gap of the bonds that are broken or formed in the reactions. Some further approximations lead to a simple formula that expresses the barrier for nonidentity and identity hydrogen abstraction reactions as a function of the bond strengths of reactants and products. The semiempirical expressions are shown to be useful not only for the model reactions that are studied in this work, but also for other nonidentity and identity hydrogen abstraction reactions that have been studied in previous articles.