Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol^?1 and R ² = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol^?1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol^?1, R ² = 0.999 98 and MAD = 7.2 kcal mol^?1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol^?1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.     

Thermochemistry of the reactions between CN+ and H2O in the gas phase

The [H₂, C, N, 0]⁺ potential energy surface (PES) has been explored by means of high-level ab initio calculations, carried out in the framework of the G2 theory. From this survey we concluded that the predominant products of the CN⁺ + H₂O reaction are the result of the dissociation of HNCOH⁺ species and to a much lesser extent of the CNHOH⁺ cation to yield CNH⁺ + OH. According to our results HCN⁺ should not be a product of this reaction because all pathways leading to its formation are unfavourable with regards to other competitive processes. Other reactive channels lead to the formation of the H₂ONC⁺ structure which dissociates into CN + H₂O⁺. The loss of NH(3σ) and O(³P) seems to take place following spin-forbidden reaction paths through an intersystem crossing between the singlet and the triplet PESs. The global minimum of the PES, H₂NCO⁺ is easily accessible and should lead to the loss of carbon monoxide which has not been experimentally observed in CN⁺ + H₂O reactions. We cannot offer a clear explanation for this disagreement between theory and experiment.     

A MODEL FOR ESTIMATING PREMIUMS TO REDUCE IRRIGATION ON FARMS

Abstract This paper aims to determine the minimum agri‐environmental premium per hectare that farmers should receive to reduce crop irrigation. To this end, the authors develop a mixed‐integer quadratic model using a new methodology based on traditional positive mathematical programming, which allows the inclusion in the model of crop variants that are not present in the baseline situation of the farms. What is shown is that the results obtained with this new methodology, using the cost average approach of calibration, are the same as those obtained with an empirical method, when there is no change of crop distribution after the changeover from irrigated to nonirrigated farms. The theoretical results are compared with those obtained using the calibration with exogenous elasticities and are illustrated numerically for a representative farm of an area around Spain's Tablas de Daimiel in which the use of groundwater for crop irrigation has led to the ongoing deterioration of wetlands that depend on the same source of water, endangering the region's environmental sustainability.     

Self-assembled growth of nanostructural Ge islands on bromine-passivated Si(111) surfaces at room temperature

We have deposited relatively thick (∼60 nm) Ge layers on Br-passivated Si(111) substrates by thermal evaporation under high vacuum conditions at room temperature. Ge has grown in a layer-plus-island mode although it is different from the Stranski-Krastanov growth mode observed in epitaxial growth. Both the islands and the layer are nanocrystalline. This appears to be a consequence of reduction of surface free energy of the Si(111) substrate by Br-passivation. The size distribution of the Ge nanoislands has been determined. The Br-Si(111) substrates were prepared by a liquid treatment, which may not produce exactly reproducible surfaces. Nevertheless, some basic features of the nanostructural island growth are reasonably reproducible, while there are variations in the details of the island size distribution.     

The reactions of Cl+ (3P) and Cl+ (1D) with hydrogen sulphide. A G2 molecular orbital study

G2 ab initio molecular orbital calculations have been performed to study the potential energy surfaces (PESs) associated with the reactions of Cl⁺ in its ³P ground state and in its ¹D first excited state with hydrogen sulphide. [H₂, Cl, S]⁺ singlet and triplet state cations present very different bonding characteristics. The latter are systematically ion-dipole or hydrogen-bonded weakly bound species, while the former are covalent molecular ions. As a consequence, although the Cl⁺(³P) is 34.5 kcal mol^?1 more stable than Cl⁺(¹D), the global minimum of the singlet PES lies 37.3 kcal mol^?1 below the global minimum of the triplet PES. Both singlet and triplet potential energy surfaces show significant differences with respect to those associated with Cl⁺ + H₂O reactions as well as with SH₂ reactions with F⁺. In both cases, the major product should be SH⁺ ₂; SH⁺ and HCl⁺ being the minor products, in agreement with the experimental evidence. The estimated heat of formation for the most stable H₂SCl⁺ singlet state species is 198 ± 1 kcal mol^?1.     

Gas-phase reactivity of lactones: structure and stability of their Cu+ complexes

The structure and relative stability of different lactone-Cu⁺ complexes, including cycles changing from four to six-membered rings, have been investigated through the use of density functional theory methods. The geometries and vibrational frequencies were calculated at the B3LYP/6-311G(d,p) level. Final energies were obtained in single point calculations carried out at the B3LYP/6-311+G(2df,2p) level of theory. Upon interaction with Cu⁺ in the gas phase, lactones behave in a rather similar way as they do in protonation processes. Systematically the global minimum of the potential energy surface corresponds to the attachment of the metal cation to the carbonyl oxygen cis with respect to the ether-like oxygen. Also, similarly to proton affinities, the calculated Cu⁺ binding energies increase with the size of the system. The unsaturated compounds are found to be only slightly more basic than the saturated counterparts. Cu⁺ attachment leads to significant bond activation and bond reinforcement effects, reflected in redshiftings and blueshiftings of the stretching frequencies, respectively. Cu⁺ is able to form agostic bonds with some of the CH² groups of the lactone moiety. These agostic complexes can be good precursors for the unimolecular loss of H², which very likely should be observed in the mass spectra.