Theory of ultrafast nonresonant multiphoton transitions in polyatomic molecules: basics and application to optimal control theory

A systematic approach is presented to describe nonresonant multiphoton transitions, i.e., transitions between two electronic states without the presence of additional intermediate states resonant with the single-photon energy. The method is well suited to describe femtosecond spectroscopic experiments and, in particular, attempts to achieve laser pulse control of molecular dynamics. The obtained effective time-dependent Schrodinger equation includes effective couplings to the radiation field which combine powers of the field strength and effective transition dipole operators between the initial and final states. To arrive at time-local equations our derivation combines the well-known rotating wave approximation with the approximation of slowly varying amplitudes. Under these terms, the optimal control formalism can be readily extended to also account for nonresonant multiphoton events. Exemplary, nonresonant two- and three-photon processes, similar to those occurring in the recent femtosecond pulse-shaping experiments on CpMn(CO)(3), are treated using related ab initio potential energy surfaces.     

High-conversion polymerization. I. Theory and application to methyl methacrylate

The concept of polymer entanglements has been applied in conjunction with classical free-radical kinetics to describe vinyl polymerizations carried to high conversion. A kinetic model has been developed on the assumption that two populations of radicals exist in a high-conversion polymerization system: those radicals whose chain lengths are long enough to become entangled with neighboring molecules and have, therefore, a restricted mobility; and those shorter radicals whose mobilities are not strongly affected by diffusional effects. It has also been assumed that the kinetic rate constant for the termination step between entangled radicals is inversely proportional to the mean entanglement density. The model contains only two parameters in addition to the kinetic rate constants required to describe low-conversion polymerizations. One of these parameters can be determined, at least in principle, from measurements of solution properties of the polymer-monomer mixtures. The model so developed has been tested against experimental data obtained from the literature on the bulk polymerization of methyl methacrylate. The agreement between predicted and experimental monomer conversions and molecular weight averages is found to be satisfactory.     

Theory of diffusion-controlled reaction between non-simple molecules. I

A new vibrational principle is presented for reaction rates of diffusion-controlled chemical reaction. The variational principle is obtained by a modification of the closure approximation of Wilemski and Fixman. The closure approximation is found to correspond to a special choice of the trial function in this formation and to yield a lower bound of the reaction rate. This formulation is found to be especially useful for the analysis of reaction between non-simple molecules, such as macromolecules.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Molecular diffusion in liquid crystals and chiral discrimination. I. Theory

The possibility of using cholesteric phases for discriminating enantiomers of a chiral solute on the basis of their different transport properties, motivates the investigation of the translational diffusion by taking fully into account the roto-translational coupling. In this article a detailed theoretical analysis is presented for the transport properties evaluated according to the asymptotic limit of the mean-squared displacement. A general relation is derived for the transport coefficients, having as main ingredients the mean-field potential due to the mesophase, and the diffusion tensor with its purely translational and rotational components, and with the blocks describing the roto-translational coupling. The application of the theory to nematic phases shows that the roto-translational coupling generates a dynamical contribution reducing the transport coefficients evaluated by taking into account only the translational diffusion components in the center of diffusion. The theory is also specialized to a cholesteric phase with a given helical pitch for the director arrangement, in a form which is suitable for calculations of model systems of chiral solutes to be presented in a forthcoming paper.     

Electrochemical manipulation of localised pH: application to electroanalysis

The electrochemical manipulation of the local pH at a polymer functionalised electrode has been achieved in order to enhance the electrochemical response to cationic analytes. The changes in pH have been shown to provide a method for significantly enhancing the analytical signal towards the model compounds, dopamine and p-aminophenol. The procedure was found to operate irrespective of the electrical properties of the film. The main requirement for this electroanalytical system is that the film contains acidic groups within the polymer backbone. In the carboxylic acid functionalised polypyrrole film studied here, the performance was found to be greatest when the bulk solution pH was less than the pK_a of the acid groups. The mechanism attributed to the enhanced response is elucidated and the limitations of the technique are assessed.     

Full-dimensional quantum calculations of vibrational spectra of six-atom molecules. I. Theory and numerical results

Two quantum mechanical Hamiltonians have been derived in orthogonal polyspherical coordinates, which can be formed by Jacobi and/or Radau vectors etc., for the study of the vibrational spectra of six-atom molecules. The Hamiltonians are expressed in an explicit Hermitian form in the spatial representation. Their matrix representations are described in both full discrete variable representation (DVR) and mixed DVR/nondirect product finite basis representation (FBR) bases. The two-layer Lanczos iteration algorithm [H.-G. Yu, J. Chem. Phys. 117, 8190 (2002)] is employed to solve the eigenvalue problem of the system. A strategy regarding how to carry out the Hamiltonian-vector products for a high-dimensional problem is discussed. By exploiting the inversion symmetry of molecules, a unitary sequential 1D matrix-vector multiplication algorithm is proposed to perform the action of the Hamiltonian on the wavefunction in a symmetrically adapted DVR or FBR basis in the azimuthal angular variables. An application to the vibrational energy levels of the molecular hydrogen trimer (H2)3 in full dimension (12D) is presented. Results show that the rigid-H2 approximation can underestimate the binding energy of the trimer by 27%. Finally, it is demonstrated that the two-layer Lanczos algorithm is also capable of computing the eigenvectors of the system with minor effort.     

Internal dynamics of nonrigid molecules. I. Application to acetone

The group theory for nonrigid molecules is used for studying the internal dynamics of the two equivalent C_3v rotor “bent” molecules. Special emphasis is given to the deduction of the symmetry basis vectors which represent in box form the Hamiltonian operator. It is shown that these basis vectors may be advantageously employed in order to simplify the resolution of the two-rotor equation. The procedure is applied to the acetone molecule. It is found that the lowest solutions are clustered into groups of four. The four lowest levels are related to vibrational states, the upper 64 to vibro–rotational states, in which the rotors are rotating in a restricted manner. Only few states show some cogwheel effect. Internal rotation contributions to the principal thermodynamic parameters of acetone are also computed.     

Determination of the charge distribution in nonmetallic crystals. I. Theory and application to tetrahedrally coordinated solids

A SCF method using localized molecular orbitals which are built up on hybrid atomic orbitals is proposed to obtain the charges in infinite crystals. Hybrid orbitals are built up on a minimal STO basis set. The formalism has been adapted in order to take into account the periodicity of the system and its infinite size by introducing the Madelung constant. The total energy is given by an infinite sum of terms each corresponding to the energy of a bond in the crystal field. Minimizing this bond energy with respect to eigenvectors it is straightforward to obtain the electronic charges, whence the polarity, i.e., the ionicity, of bonds. In this first paper, we study and discuss the polarity of bonds in zincblende and wurtzite-type compounds built up on first and second row elements. Our values are coherent between themselves and in agreement with other authors' results. The connection with electronegativity and polarizability is discussed.     

Nanostructure manipulation device for transmission electron microscopy: application to titania nanoparticle chain aggregates.

Experimental difficulties in studying nanostructures stem from their small size, which limits the use of traditional techniques for measuring their physical properties. We have developed a nanostructure manipulation device to apply tension to chain aggregates mounted in a transmission electron microscope. A 1-mm-long slit was cut in the center of a lead-tin alloy disc, measuring 3 mm in diameter and 200 microm in thickness. The disc was heated to about 140 degrees C before it was pressed between two quartz slides. The disc was then thinned by mechanical dimpling and ion milling until holes developed around the slit. The edges of the slit were 0.2 to 3 microm in thickness while the gap between them was up to a few microns. This disc was bonded to the two plates of a cartridge. The slit could be widened or narrowed at controlled speeds of 0.5 to 300 nm/s. The system was tested using titania (TiO2) nanoparticle chain aggregates (NCA) deposited across the slit. The ends of the NCA remained attached to the edges of the slit, which was widened at about 0.7 nm/s. In this way, the NCA was stretched up to 176% of its initial length before breaking.     

Steps towards molecular parity violation in axially chiral molecules. I. Theory for allene and 1,3-difluoroallene

In view of exploring possibilities for an experimental investigation of molecular parity violation we report quantum-chemical calculations of the parity-conserving and parity-violating potentials in the framework of electroweak quantum chemistry in allene C3H4 and 1,3-difluoroallene C3H2F2, which is nonplanar and axially chiral in the electronic ground state but expected to be nearly planar and achiral in several electronically excited states. The parity-violating potentials Epv for allene and 1,3-difluoroallene calculated with the multiconfiguration linear-response (MC-LR) approach of Berger and Quack [J. Chem. Phys. 112, 3148 (2000)] show qualitatively similar behavior as a function of torsional angle tau with maximum values of about 0.5 pJ mol(-1) for C3H4 and 2 pJ mol(-1) for C3H2F2. However, in the latter case they are asymmetrically shifted around tau=90 degrees , with a nonzero value at the chiral equilibrium geometry resulting in a parity-violating energy difference between enantiomers DeltapvE=Epv(P)-Epv(M)=1.2 pJ mol(-1) (equivalent to about 10(-13) cm(-1)). The calculated barrier heights corresponding to the nonrigid (multiple, and in part chiral) transition states in 1,3-difluoroallene fall in the range of 180-200 kJ mol(-1). These high barriers result in hypothetical tunneling splittings much smaller than DeltapvE and thus parity violation dominates over tunneling for the stereomutation dynamics in 1,3-difluoroallene. Therefore, DeltapvE is predicted to be a spectroscopically measurable energy difference. Two of the lower excited electronic states of C3H2F2 (1A and 3A) are calculated to be planar or quasiplanar, allowing, in principle, for spectroscopic state selection of states of well-defined parity. The results are discussed in relation to possible schemes of measuring parity violation in chiral molecules.     

The pyrolytic identification of organic molecules: I. The pyrolytic behavior of organic molecules

Results of a study on the pyrolysis of about 70 organic compounds of varied composition are presented and discussed. Identification of the volatile products formed was accomplished by mass spectrometry. It is shown how the pyrolytic patterns may be employed to distinguish one molecule from another. Some attention has been given to isomeric compounds and to aromatic structures containing one or more functional groups.     

Coherent control for spectroscopy and manipulation of biological dynamics.

Motivated originally by the goal of steering a photoreaction into desired product channels, the concept of coherent control is to adapt the spectral and temporal characteristics of the excitation light to the inherent molecular resonances and dynamics, such that these can be selectively addressed and manipulated. In the last decade, the ultrafast dynamics of many atomic and molecular quantum systems in the gas and condensed phase have been controlled successfully. Motivations in chemistry are now 1) to perform spectroscopy by coherent control, which requires a deeper understanding of control mechanisms, 2) to treat more complex, biological photoreactions, and 3) the pragmatic use of coherent control techniques, for example, for pulse compression or enhanced contrast in multiphoton microscopy. As examples for 1) and 2) we review here the combined effort and interplay of conventional spectroscopy and coherent control experiments, applied to the energy flow in the light-harvesting complex LH2 from bacterial photosynthesis. Closed-loop control experiments allowed the characteristic coupling frequency of internal conversion in the carotenoid in LH2 to be extracted. Open-loop three-pulse control experiments, on the other hand, could directly observe an anticipated Raman-excited carotenoid ground state. As a variant of difference spectroscopy, coherent control has thus served to gain complementary spectroscopic knowledge about the energy flow in carotenoids by comparing natural to manipulated dynamics. Finally, we propose future coherent control experiments on the electronic state structure of carotenoids and discuss prospects of coherent control for other biological chromophores.     

Molecular mechanics and molecular shape: Part VI. The response of simple molecules to bimolecular association

A molecular-mechanical force field, originally developed to calculate the structure and conformation of single molecules, has been applied to pairs of identical molecules lying at close proximity. The prototypes examined are very simple - short alkanes and short haloalkanes - but do include cases with conformational diversity and possible electrostatic effects. The optimized mutual orientations include the parallel alignment of linear alkanes, head-to-tail orientations of haloalkanes, as well as the head-to-head association, known from the crystallographic literature. The effect of aggregation on the conformation of the separate partners has been studied, and the intramolecular response characterized: in all cases examined, the partners contract. The computed energy gains are of the expected order of magnitude, the main contribution coming always from what molecular-mechanists label “non-bonded attraction”. Graphical representations of optimized orientations show the “protrusion-in-cleft” matching of molecular surfaces.     

Molecular orbital approach to odor molecules: Normal fatty acids and cyclamenaldehydes

Eight normal fatty acids and 24 cyclamenaldehydes were analyzed based on the molecular orbital theory using Computer-Aided Chemistry Programs (CAChe Programs) with PM3 parameters. We found reactive sites with high values of electrophilic frontier densities (EFDs) at appointed positions in both molecules. EFD is a theoretical index that predicts reactive sites acting as electron donors. A change in the values of EFDs in normal fatty acids would account for the selectivity in the response of a single olfactory receptor cell to the fatty acids. Changes in the values of EFDs at appointed positions of cyclamenaldehydes also correlated with their odor characteristics and intensities. This fact indicates that cyclamenaldehydes have common reactive sites that play a critical role in interactions with a receptor. Changes in their reactivities alter the odor characteristics and intensities of the molecules judged by perfumers, indicating that human discrimination of cyclamenaldehyde odor is determined at the stage of interaction between cyclamenaldehydes and an odor receptor. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 101–108, 2000     

A multi-configuration LCAO–MO study for complex unsaturated molecules. I. General theory and its application to the benzene anion

A multi-configuration LCAO –MO approach using a π-bond order–bond length linear relation is introduced to predict the geometrical structures for the electronic ground and excited states of unsaturated hydrocarbons. The procedure is designed to include configuration interaction in each iterative computation where the π-electron approximation is employed under the Pariser–Parr type semi-empirical treatment. The π-bond order–bond length relation is determined as r_pq = 1.523 – 0.193P_pq, when the bond lengths of ethylene, benzene and naphthalene are used and the groundstate functions including the singly and doubly excited configurations are taken into account to obtain the bond orders P_pq. The iterative calculation is applied to the ground state and the two lowest excited states of the benzene anion in both D_6h and D_2h molecular geometries. The geometrical structures and the π-electron energies are computed for the ground and excited states of the anion; for the latter, two types of configuration species are used. It is found that the first lowest excited state is not subjected to the Jahn–Teller effect and the calculated excited state energies do not agree with the observed values (c. 1.0 ～ 2.5 eV higher than the observed values). The latter point is discussed in detail. It is also found that the resultant ground state energy depression due to configuration mixing is not very large and the two types of configuration species used give different CI effects on the energy levels of the two lowest excited states of the anion. Finally, the stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the anion.     

Uptake of atmospheric molecules by ice nanoparticles: pickup cross sections

Uptake of several atmospheric molecules on free ice nanoparticles was investigated. Typical examples were chosen: water, methane, NO(x) species (NO, NO(2)), hydrogen halides (HCl, HBr), and volatile organic compounds (CH(3)OH, CH(3)CH(2)OH). The cross sections for pickup of these molecules on ice nanoparticles (H(2)O)(N) with the mean size of N≈260 (diameter ~2.3 nm) were measured in a molecular beam experiment. These cross sections were determined from the cluster beam velocity decrease due to the momentum transfer during the pickup process. For water molecules molecular dynamics simulations were performed to learn the details of the pickup process. The experimental results for water are in good agreement with the simulations. The pickup cross sections of ice particles of several nanometers in diameter can be more than 3 times larger than the geometrical cross sections of these particles. This can have significant consequences in modelling of atmospheric ice nanoparticles, e.g., their growth.