Density profiles and solvation force for a liquid in a slit

Computer simulations and density functional theory results are reported for a Lennard-Jones liquid in a slit or pore formed by two parallel hard walls. Both density profiles and solvation forces are computed. Two classes of calculation are performed. In the first class, a high bulk density is selected and, starting from a high temperature, the temperature is reduced until the temperature corresponding to bulk liquid—vapour coexistence is reached. For small slit widths or exceedingly large widths, the density in the slit decreases continuously until the slit is virtually empty or ‘dry’. When the slit width is somewhat larger than a molecular diameter, but still finite, the density in the slit decreases continuously as the temperature is decreased until there is an abrupt change in the density in the slit. Below this temperature, the density is smaller. Further decreases in the temperature, result in a continuous decrease in the slit density until the slit is virtually empty. In the second class, the density and temperature for bulk coexistence are chosen and the bulk density is increased. At the temperature and bulk density for bulk coexistence, the slit is virtually empty and remains so for all widths that we consider. As the bulk density is increased at constant temperature, the slit remains empty as the width is increased until some specific width is reached and then starts to fill abruptly. The agreement of the density functional and simulation results is qualitative but good.     

Molecular structure and IR spectra of bromomethanes by DFT and post-Hartree-Fock MP2 and CCSD(T) calculations

The molecular parameters (geometries, rotational constants, dipole moments) and vibrational IR spectra (harmonic wavenumbers, absolute intensities) of bromomethanes (CH₃Br, CH₂Br₂, CHBr₃, CBr₄) are predicted by a density functional theory with the hybrid Becke3-LYP functional (DFT) and post-Hartree-Fock methods (MP2, CCSD(T)) using a 6-311G(2d,2p)-type basis set. The MP2 calculations are carried out with different numbers of frozen core orbitals to find how the number of bromine orbitals used for electron correlation influences the predicted molecular parameters and IR spectra of the species in question. Three options were used: (a) all electrons (full), with both the core and valence orbitals considered; (b) partial frozen core option (pfc), when the orbitals up to 3p of bromine were frozen; and (c) full frozen core option (ffc), when all core orbitals up to 3d were frozen. The CCSD(T) calculations for geometric parameters were carried out with both the pfc and ffc options, while for the prediction of the IR spectra only the ffc option was used. In addition, the calculations at the DFT and MP2(pfc) levels with inclusion of f functions on carbon and bromine atoms in bromomethanes (and also the CCSD(T)(pfc) calculations for CH₃Br) were carried out to predict the changes in the geometric parameters and/or vibrational IR spectra of the molecules upon inclusion of f functions The geometries of bromomethanes (particularly the CBr bond lengths) are predicted better by the DFT and CCSD(T) calculations when the f functions (in particular on bromine atom) are included, while the MP2 calculations without f functions are good enough for correct predictions of the molecular geometries. The molecular parameters and vibrational IR spectra of bromomethanes in question and their deuterated species predicted by the DFT, MP2(ffc) and CCSD(T)(ffc) with the 6-311G(2d,2p) basis set agree well with the available experimental data.     

Controllability of second-order infinite-dimensional systems

In the paper, the approximate controllability of linear abstractsecond-order infinite-dimensional dynamical systems is considered.Using the frequency-domain method, it is proved that approximatecontrollability of such a system follows from that of a suitablydefined first-order system. The general results are then appliedto investigating the approximate controllability of a vibratorydynamical system modelling a flexible mechanical structure.Some special case are also considered. Moreover, remarks andcomments on the relationships between different concepts ofcontrollability are given. The paper generalizes earlier resultson second-order abstract dynamical systems.     

Conformations and thermodynamic properties of sulphur homocycles. II. The fluxional S+ 8 radical cation

According to both UB3LYP/6-311G* and UMP2/6-311G* calculations, the lowest energy conformer of the S⁺ ₈ radical cation possesses C_s symmetry. However, there are three other structures with low relative energies that do not exceed 6.5 kcal mol^?1. These conformers, which are found to be very prone to pseudorotation, are predicted to interconvert readily. The fluxional nature of S⁺ ₈ is expected to facilitate its reactions with organic species where a specific conformation is demanded by steric constraints, which may explain its high reactivity towards PAHs with crowded hydrogen atoms.     

Energetics,electronic structures and geometries of didehydroazines

When calibrated against the available experimental data for didehydrobenzenes, RB3LYP/cc-pVTZ, QCISD/cc-pVTZ, CCSD(T)/cc-pVTZ, and G3 electronic structure calculations provide reliable predictions of standard enthalpies and singlet—triplet splittings in all possible isomers of didehydroazines that (with a possible exception of 2,6-didehydropyridine) possess singlet ground states. Singlet didehydroazines with larger numbers of nitrogen atoms turn out to be more prone to ring opening, as indicated by the fact that out of the 6, 11, 6 and 3 possible didehydropyridines, didehydrodiazines, didehydrotriazines, and didehydrotetrazines, respectively, 5, 7, 2 and none are actually found. Immediate proximity of the nitrogen atom to the formally triple carbon—carbon bond confers decreased thermodynamic stabilities and smaller singlet—triplet splittings on the species of the 1,2-didehydro type. Some of the aza analogues of singlet 1,3-didehydrobenzene are as stable as their 1,2-didehydro counterparts. The only existing aza analogue of singlet 1,4-didehydrobenzene is 2,5-didehydropyrazine, which is particularly stable and possesses a large singlet—triplet splitting, making it a feasible synthetic target. The present calculations indicate that the experimental standard enthalpies of formation of pyrimidine and pyrazine are in error.     

Constrained controllability of nonlinear systems

In the paper, infinite-dimensional dynamical systems describedby nonlinear abstract differential equations are considered.Using a generalized open-mapping theorem sufficient conditionsfor constrained exact local controllability are formulated andproved. It is generally assumed that the values of controlsare in a convex and closed cone with the vertex at zero. Asan illustrative example. the constrained exact local controllabilityproblem for nonlinear delayed dynamical system is solved indetail. Some remarks and comments on the existing results forcontrollability of nonlinear dynamical systems are also presented.     

Energetics,electronic structures and geometries of naphthalene,quinoline and isoquinoline analogues of 1,2-didehydrobenzene

B3LYP/cc-pVTZ electronic structure calculations employed in conjunction with additive corrections derived from experimental data for 1,2-didehydrobenzene predict the standard enthalpies of formation of 1,2- and 2,3-didehydronaphthalenes to be equal to 121.0 and 123.7 kcal mol^?1, respectively. The corresponding singlet-triplet splittings amount to 40.1 and 35.4 kcal mol^?1. The positional dependence of both of these quantities is preserved in those didehydroquinolines and didehydroisoquinolines in which the didehydrogenation sites are separated by at least one carbon from the heteroatoms. The effect of the adjacent heteroatoms on the singlet-triplet splittings is significantly more pronounced than that on the standard enthalpies of formation. Test G3 calculations on 2,3-didehydronaphthalene confirm the reliability of the additive correction scheme in the prediction of properties of annelated analogues of 1,2-didehvdrobenzene. Such a scheme opens an avenue to facile electronic structure calculations on didehydrogenation reactions of polycondensed heterocyclic compounds with six-membered rings.     

Theoretical thermochemistry of the C60F18, C60F36, and C60F48 fluorofullerenes

Relative energies of C₆₀F_N fluorofullerenes are reproduced reasonably well at the B3LYP/6- 311G** level of theory employed in conjunction with isodesmic transfluorination reactions, although overestimation of steric repulsions among non-bonded atoms is evident for species with larger values of N. On the other hand, the MNDO method is found to be less suitable for studies of fluorofullerene thermochemistry. The gas-phase standard enthalpy of formation of the C₆₀F₁₈ species is predicted to lie between ?1500 kJ mol^?1 and ?1400 kJ mol^?1.