Double Bond Migration Mechanism in Allyl Systems Involving the Hydroxide Ion. 2. Polarizable Continuum Model (PCM)

Isomerization processes of a double bond site in propene and methylthiopropene molecules with the hydroxide ion were studied in the framework of the RHF/6-31+G*, MP2/6-31+G*, and B3LYP/6-31+G* (density functional) ab initio methods. The solvent effect was taken into account using PCM in its IEFPCM and SCIPCM versions. It is shown that to construct a reaction profile for propene rearrangement, it suffices to perform geometry optimization of stationary points within the Born–Onsager model with further refinement of the energy using IEFPCM. The reaction profiles obtained display that the multiple bond migration mechanism involving the hydroxide ion proton is energetically preferable to the two-stage mechanism forming a solvated carbanion for the propene molecule and for the methylthiopropene molecule that forms a much more stable carbanion.     

Unrestricted Hartree-Fock based on the fragment molecular orbital method: Energy and its analytic gradient

A consideration of the surrounding environment is necessary for a meaningful analysis of the reaction activity in large molecular systems. We propose an approach to perform unrestricted Hartree-Fock (UHF) calculations within the framework of the fragment molecular orbital (FMO) method (FMO-UHF) to study large systems with unpaired electrons. Prior to an energy analysis one has to optimize geometry, which requires an accurate analytic energy gradient. We derive the FMO-UHF energy and its analytic gradient and implement them into GAMESS. The performance of FMO-UHF is evaluated for a solvated organic molecule and a solvated metal complex, as well as for the active part of a protein, in terms of energy, gradient, and geometry optimization.     

The dependence of electrostatic solvation energy on dielectric constants in Poisson-Boltzmann calculations

The Poisson-Boltzmann equation gives the electrostatic free energy of a solute molecule (with dielectric constant epsilon(l)) solvated in a continuum solvent (with dielectric constant epsilon(s)). Here a simple formula is presented that accurately predicts the electrostatic free energy for all combinations of epsilon(l) and epsilon(s) from the calculation on a single set of epsilon(l) and epsilon(s) values.     

The fast multipole boundary element method for molecular electrostatics: An optimal approach for large systems

We propose a fast implementation of the boundary element method for solving the Poisson equation, which approximately determines the electrostatic field around solvated molecules of arbitrary shape. The method presented uses computational resources of order O(N) only, where N is the number of elements representing the dielectric boundary at the molecular surface. The method is based on the Fast Multipole Algorithm by Rokhlin and Greengard, which is used to calculate the Coulombic interaction between surface elements in linear time. We calculate the solvation energies of a sphere, a small polar molecule, and a moderately sized protein. The values obtained by the boundary element method agree well with results from finite difference calculations and show a higher degree of consistency due to the absence of grid dependencies. The boundary element method can be taken to a much higher accuracy than is possible with finite difference methods and can therefore be used to verify their validity. © 1995 by John Wiley & Sons, Inc.     

Solvent‐assisted planar structure of a stilbene‐based salicylhydrazone compound: crystal structure,solvent‐ and aggregation‐induced emission,and switchable luminescence colouration

A novel stilbene‐based salicylhydrazone compound {systematic name: (E)‐4,4′‐(ethene‐1,2‐diyl)bis[(N′E)‐N′‐(2‐hydroxybenzylidene)benzohydrazide] dimethyl sulfoxide disolvate, C₃₀H₂₄N₄O₄·2C₂H₆OS or L·2DMSO} was synthesized and characterized by single‐crystal X‐ray diffraction, powder X‐ray diffraction and luminescence spectroscopy. The title compound crystallizes in the monoclinic space group P2₁/c, with half a symmetry‐independent L molecule and one dimethyl sulfoxide (DMSO) solvent molecule in the asymmetric unit. The L molecule adopts an almost planar structure, with a small dihedral angle between the planes of the stilbene and salicylhydrazone groups. There are multiple π–π stacking interactions between adjacent L molecules. The DMSO solvent molecules act as proton donors and acceptors, forming hydrogen bonds of various strengths with the L molecules. In addition, the geometry optimization of a single molecule of L and its luminescence properties either in solution, as a solvated solid or as a desolvated solid were studied. The compound shows an aggregation‐induced emission (AIE) effect and exhibits switchable luminescence colouration in the solid state by the simple removal or re‐addition of the DMSO solvent.     

Theoretical investigation on dual fluorescence and intramolecular charge transfer of 5-phenyl-5H-phenanthridin-6-one

Quantum-chemical calculations with the time-dependent density function theory (TDDFT) have been carried out for 5-phenyl-5H-phenanthridin-6-one (PP). For this molecule, dual fluorescence and in- tramolecular charge transfer (ICT) were experimentally observed. The B3LYP functional with 6-311 G (2d, p) basis set has been used for the theoretical calculations. The solvent effects have been described within the polarizable continuum model (PCM). Ground-state geometry optimization reveals that the phenyl/phenanthridinone dihedral angle equals 90.0°, a nearly perpendicular structure. Vertical ab- sorption energy calculations characterize the lower singlet excited states both in gas phase and in solvents. It can be found that the lower excited states have locally excitation (LE) feature. Through constructing the potential energy curves of both isolated and solvated systems describing the LE→ICT reaction and fluorescence emission, we obtain the enthalpy difference ΔH between the LE and ICT states, energy barrier Ea, and energy difference δEFC, indicating the structural changes taking place during the ICT reaction. Potential curve and calculated emission energies for both isolated and sol- vated systems show a dual fluorescence phenomenon, consisting of a LE emission band and a red-shifted ICT band. Our calculations including the solvent effects indicate that the dual fluorescence is brought about by the change in molecular structure connected with the planarization of the twisted N-phenylphenanthridinone during the ICT reaction.     

An energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

Energy decomposition analysis for intramolecular non-covalent interaction in solvated environment

In this work, the intra-EDA method, which is a recently developed energy decomposition analysis scheme for intramolecular non-covalent interaction is extended from gas phase to solvated environment. It is the first analysis scheme that performs analysis for intramolecular interaction in solution. By fragmentation scheme, a molecule is divided into intramolecular interacting fragments and environmental fragments via single bond homolysis breaking. The solvent effect is taken into account by implicit solvation model. Intramolecular interaction free energy is estimated as the separated treatment of inter-fragment interactions in dielectric environment. The analysis results highlight the importance of solvent effects to intramolecular non-covalent interaction.     

New data on the solubility of amorphous silica in organic compound-water solutions and a new model for the thermodynamic behavior of aqueous silica in aqueous complex solutions

Experimental solubilities of amorphous silica in several aqueous electrolyte solutions and in aqueous solutions of organic compounds, and theoretical considerations concerning cavity formation, electrostriction collapse, ion solvation, and long- and short-range interaction of the solvated ions with one another⁽¹⁾ permit the calculation of the partial excess free energies and the activity coefficients of aqueous silica. It is shown that, in the case of non-dissociated aqueous organic solutions, the variation of log m (SiO₂) with the reciprocal of the dielectric constant of the solution is described by a single linear equation independent of the nature of the organic compound. For aqueous electrolyte solutions, a specific linear relationship between log m (SiO₂) and the reciprocal of the dielectric constant occurs for each electrolyte. The success of the equation in reproducing the experimental solubilities of amorphous silica in aqueous solutions of electrolytes and organic compounds supports previous evidence indicating a polar charge distribution in the solvated SiO₂ molecule. Our data permit the calculation of the effective local charge of dissolved SiO₂ molecules and of the short-range interaction parameters between SiO₂ and various ions. The proposed equation of state can be used to calculate the affinity of reactions among SiO₂ minerals and complex aqueous solutions.     

Effect of polyion conformation on dye binding. IV. Fluorescence of auramine O in relation to its binding to synthetic polyacids

The effect of polymer conformation, polymer concentration, and added salt concentration on the quantum yield ? of Auramine O (AuO) is discussed in connection with dialysis equilibrium data. The quantum yield per bound dye molecule (?/q) assumes different values which are related principally to solvation changes in the environment of the binding sites. Binding to globular compact a states results in high ?/q, whereas low ?/q (of the order of magnitude of ? of free AuO) are observed for the binding to expanded solvated b states. The quantum yield of bound AuO is therefore affected by the organic nature of the environment, but shows little or no relation to the amount of bound dye molecules.     

Intra‐ and intermolecular interactions in crystals of polar molecules. A study by the mixed quantum mechanical/molecular mechanical SCMP‐NDDO method

Stabilization energies of crystals of polar molecules were calculated with the recently developed NDDO‐SCMP method that determines the wave function of a subunit embedded in the symmetrical environment constituted by the copies of the subunit. The total stabilization energies were decomposed into four components. The deformation energy is the difference between the energy of the molecule in the geometries adopted in the crystal on the one hand, and in vacuo, on the other hand. Further energy components are derived from the molecular geometry found in the crystal phase. The electrostatic component is the interaction energy of the molecule with the crystal field, corresponding to the charge distribution obtained in vacuo. The polarization component is the energy lowering resulted in the self‐consistent optimization of the wave function in the crystal field. The rest of the stabilization energy is attributed to the dispersion–repulsion component, and is calculated from an empirical potential function. The major novelty of this decomposition scheme is the introduction of the deformation energy. It requires the optimization of the structural parameters, including the molecular geometry, the intermolecular coordinates, and the cell parameters of the crystal. The optimization is performed using the recently implemented forces in the SCMP‐NDDO method, and this new feature is discussed in detail. The calculation of the deformation energy is particularly important to obtain stabilization energies for crystals in which the molecular geometry differs considerably from that corresponding to the energy minimum of the isolated molecule. As an example, crystals of diastereoisomeric salts are investigated. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1679–1690, 2001     

Einkristall-Strukturen eines Donator-Akzeptor-substituierten Cyclopentadiens,seines Kations und seines dimeren Anions: Verschiedenartige Störungen eines Kohlenstoff-Fünfringes

Single-Crystal Structures of a Donor-Acceptor-Substituted Cyclopentadiene, Its Cation and Its Anion Dimer: Different Distortion of a Five-Membered Carbon Ring 1,4-Dimethyl-2,3,4,6-tetrahydro-1 H-cyclopentapyrazine-5,7-dicarbonitrile, its molecular cation, and its dimer dianion, generated by hydride abstraction or deprotonation, and crystallized, differ remarkably in their structures: the five-membered ring in the neutral compound is of (Z)-butadiene-type, whereas, in the tetrafluorborate salt, a peripheric NCCCCCN⊕ cyanine distortion occurs and in the sodium derivatives, solvated by either one or two 1,2-dimethoxyethane molecules, a cyclopentadienyl anion is formed. The structural perturbations induced by changing molecular charges are rationalized by extensive MNDO calculations, which on geometry optimization, reproduce the experimental structures and, in addition, provide charge distributions, further confirming the n_N/π and π/π interactions already recognizable from the structural parameters.     

Influence of 1,4‐dioxane solvent inclusion on the crystal structure of 5,5′‐diphenyl‐2,2′‐(p‐phenylene)di‐1,3‐oxazole (POPOP)

Crystallization of 5,5′‐diphenyl‐2,2′‐(p‐phenylene)di‐1,3‐oxazole (POPOP), C₂₄H₁₆N₂O₂, from chloroform or 1,4‐dioxane yielded crystals in pure and solvated forms, respectively. The solvated crystals of POPOP were found to contain 1,4‐dioxane in a strict 1:2 compound–solvent stoichiometry, C₂₄H₁₆N₂O₂·C₄H₈O₂, thus being a defined solvent‐inclusion compound. The crystal system is monoclinic in both cases and the asymmetric unit of the cell contains only half of the molecule (plus one dioxane molecule in the case of the solvated structure), owing to the centrosymmetry of the di‐1,3‐oxazole molecule.     

Isomeric active ends of growing chains in the cationic polymerization of 4-methyl-1-pentene

Quantum chemical investigation of the relative stabilities of carbenium ions modelling the end units of growing chains in the cationic polymerization of 4-methyl-1-pentene has been carried out. The investigation was performed by the CNDO/2 method and by partial optimization of geometry. It is shown that the polymer chain can be adequately modelled by a methyl group. The calculated values of relative energies ΔE, geometric parameters and charge distribution are given for free cations, ion-pairs and for the cation-electron donor and cation-electron acceptor systems (H₂O, HCN and NO₂). All the additives show donor behaviour with respect to cations. The differences in the energies of secondary and tertiary cations decrease on going from free ions to ion-pairs or cation-additive molecule system.     

Lattice sum calculations for 1/rp interactions via multipole expansions and Euler summation

A method is developed here for doing multiple calculations of lattice sums when the lattice structure is kept fixed, while the molecular orientations or the molecules within the unit cells are altered. The approach involves a two‐step process. In the first step, a multipole expansion is factored in such a way as to separate the geometry from the multipole moments. This factorization produces a formula for generating geometry constants that uniquely define the lattice structure. A direct calculation of these geometry constants, for all but the very smallest of crystals, is computationally impractical. In the second step, an Euler summation method is introduced that allows for efficient calculation of the geometry constants. This method has a worst case computational complexity of O(( log N)²/N), where N is the number of unit cells. If the lattice sum is rapidly converging, then the computational complexity can be significantly less than N. Once the geometry constants have been calculated, calculating a lattice sum for a given molecule becomes computationally very fast. Millions of different molecular orientations or molecules can quickly be evaluated for the given lattice structure. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 208–215, 2001     

A molecule on the surface or inside a spherical nanoparticle: the computation of the interaction energy in terms of the dielectric continuum model

The electrostatic interaction energy between a charged or polar molecule and a spherical polarizable nanoparticle is studied within the advanced dielectric continuum model proposed previously. The molecule can be located either inside or outside the nanoparticle or in the vicinity of its boundary surface. The nanoparticle and its environment are considered as a polarizable medium and described in terms of a nonuniform dielectric continuum approximation with a position-dependent dielectric permittivity function e(r) \varepsilon (r) , where r is the position vector. A special construction of this function accounts for the proper treatment of sophisticated boundary effects. Test computations are performed for a number of sample molecules.     

Non-empirical LCAO-MO-SCF calculations of the electronic structure of SiF2

Non-empirical LCAO-MO-SCF calculations on SiF₂ using two Gaussian basis sets are reported. The larger basis set gives a calculated geometry in good agreement with experiment. The effect on the energy and population analysis of optimization of the Si 3d exponent was investigated. 3d orbitals are found to be much less important in the bonding than in the isoelectronic molecule SO₂.