A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler᎐Lagrange equations for molecular fragments n described by internal parameters . An internal mode is localized in a molecular n fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k , adiabatic force constants. a Minimization of the kinetic energy of the vibrating fragment yields the adiabatic mass n Ž . m corresponding to 1rG of Wilson's G matrix and, by this, adiabatic frequencies . a n n aAdiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates.

We study the process of charged polymer translocation, driven by an external electric potential, through a narrow pore in a membrane. We assume that the number of polymer segments, m, having passed the entrance pore mouth, is a slow variable governing the translocation process. Outside the pore the probability that there is an end segment at the entrance pore mouth, is taken as the relevant parameter. In particular we derive an expression for the free energy as a function of m, F(m). F(m) is used in the Smoluchowski equation in order to obtain the flux of polymers through the pore. In the low voltage regime we find a thresholdlike behavior and exponential dependence on voltage. Above this regime the flux depends linearly on the applied voltage. At very high voltages the process is diffusion limited and the flux saturates to a constant value. The model accounts for all features of the recent experiments by Henrickson et al. [Phys. Rev. Lett. 85, 3057 (2000)] for the flux of DNA molecules through an α-hemolysin pore as a function of applied voltage.

Adiabatic internal frequencies are compared with c-vector frequencies and intrinsic frequencies. It is shown that c-vector modes are not suitable to characterize molecular fragments since they are not localized in and their definition leads to n n unreasonable frequency values. Intrinsic frequencies suffer from a strong dependence on the set of internal parameters chosen to describe the geometry of the molecule. Apart from this, they represent averaged frequencies, for which mass effects and electronic effects are not properly separated. Adiabatic frequencies are based on a dynamic principle, separate properly mass effects and electronic effects and do not depend in any Ž . way on the set of internal parameters. This is shown for HFr6-31G d, p vibrational frequencies of ethene, dichloroethene, benzene, the cyclooctatetraene dication, benzocyclobutadiene, and some of their isotopomers.

A unified reaction valley analysis (URVA) is presented to investigate the mechanism of the reaction CH 3 + H 2 f CH 4 + H at the UMP2/6-31G(d,p) level of theory. URVA is based on the reaction path Hamiltonian, the intrinsic reaction coordinate s, and the characterization of normal modes ω µ (s), reaction path vector η(s), and curvature vector K(s) in terms of generalized adiabatic modes a n g (s) associated with internal parameters that are used to describe the reaction complex. In addition, URVA combines the investigation of the harmonic reaction valley with the analysis of attractive and repulsive forces exerted on the nuclei by analyzing the electron density distribution F(r,s). It is shown that changes in F(r,s) reflect changes in the reaction valley and vice versa. Five reaction phases can be distinguished (reactant, reactant preparation, transition state (TS), product preparation, and product phase), of which the chemically relevant phases are indicated by small (reorganization of electron structure) and large curvature peaks (bond breaking or forming). Relatively large peaks of the adiabatic force constants indicate those positions at which the reaction is accelerated by appropriate electronic structure changes. Position and height of the curvature peaks in the TS region reflect the energetics of the reaction and the nature of the TS in the sense of the Hammond postulate: The reaction is exothermic with an early TS that is shifted by ∆s ) 0.3 amu 1/2 a 0 into the entrance channel.

Methods based on self-assembly, self-organization, and forced shape transformations to form synthetic or semisynthetic enclosed lipid bilayer structures with several properties similar to biological nanocompartments are reviewed. The procedures offer unconventional micro- and nanofabrication routes to yield complex soft-matter devices for a variety of applications for example, in physical chemistry and nanotechnology. In particular, we describe novel micromanipulation methods for producing fluid-state lipid bilayer networks of nanotubes and surface-immobilized vesicles with controlled geometry, topology, membrane composition, and interior contents. Mass transport in nanotubes and materials exchange, for example, between conjugated containers, can be controlled by creating a surface tension gradient that gives rise to a moving boundary or by induced shape transformations. The network devices can operate with extremely small volume elements and low mass, to the limit of single molecules and particles at a length scale where a continuum mechanics approximation may break down. Thus, we also describe some concepts of anomalous fluctuation-dominated kinetics and anomalous diffusive behaviours, including hindered transport, as they might become important in studying chemistry and transport phenomena in these confined systems. The networks are suitable for initiating and controlling chemical reactions in confined biomimetic compartments for rationalizing, for example, enzyme behaviors, as well as for applications in nanofluidics, bioanalytical devices, and to construct computational and complex sensor systems with operations building on chemical kinetics, coupled reactions and controlled mass transport.

ABSTRACT:A new way of analyzing measured or calculated vibrational spectra in terms of internal vibrational modes associated with the internal parameters used to describe geometry and conformation of a molecule is described. The internal modes are determined by solving the Euler᎐Lagrange equations for molecular fragments n described by internal parameters . An internal mode is localized in a molecular n fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, one can consider the new fragment motions as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. Because of this property, the internal modes are called adiabatic internal modes, and the associated force constants k , adiabatic force constants. a Minimization of the kinetic energy of the vibrating fragment yields the adiabatic mass n Ž . m corresponding to 1rG of Wilson's G matrix and, by this, adiabatic frequencies . a n n a Adiabatic modes are perfectly suited to analyze and understand the vibrational spectra of a molecule in terms of internal parameter modes in the same way as one understands molecular geometry in terms of internal coordinates.

The concept of characterizing normal vibrational modes l in terms of internal vibrational modes v typical of molecular fragments or structural subunits is n developed. Essential for this concept is the amplitude A A that provides the basis for a n quantitative comparison of modes l and v and, by this, facilitates the extraction of n chemical information out of vibrational spectra. Twelve possibilities of defining amplitude Ž . Ž . A A are tested with regard to a the physical basis of the definition of A A, b the dependence of A A on the set of internal parameters chosen to describe the molecule, and Ž . c the amount of chemical information transferred by A A. The two most promising candidates for a generally applicable amplitude A A are based on adiabatic internal modes and a comparison of l and v with the help of mass or force constant matrix. For the n practical testing of amplitude A A, three different criteria are developed.

ABSTRACT:The concept of characterizing normal vibrational modes l in terms of internal vibrational modes v typical of molecular fragments or structural subunits is n developed. Essential for this concept is the amplitude A A that provides the basis for a