Location of energy barriers. VIII. Reagent → product energy conversion on surfaces with sudden or gradual late-barriers

At energies well above the threshold for reaction, the effect of additional reagent vibration (ΔV′) and relative translation (ΔT′) on the product energy distribution (V,R,T,) has been examined on four different substantially endothermic potential-energy surfaces for two extreme mass combinations (LH + H $\text{endo}$ L + HH and HH + L $\text{endo}$ H + HL). As noted previously, additional reagent vibration tends to be retained as product vibration, ΔV′ → ΔV, and a similar approximate adiabaticity applies to translation, ΔT′ → ΔT + ΔR. The present work is concerned with the effect of potential-energy surface and extreme mass-combination on these generalizations. The surfaces examined had late barrier-crests, but surfaces designated S exhibited a sudden rise to the barrier-crest and G a gradual rise. The extent of adiabaticity was found to be significantly greater on the gradual (G-type) surfaces than on the sudden (S-type) ones. The mass-combination LH + H $\text{endo}$ L + HH (in which enhanced reagent orbital angular momentum correlates with enhanced product rotation) was anomalous in giving ΔT′ → ΔR.     

Location of energy barriers. VI. The dynamics of endothermic reactions,ab + c

A systematic 3D classical-trajectory study has been made of the effect of reagent energy distribution and mass combination on the dynamics of endothermic reaction. The potential-energy hypersurface was endothermic by 35.7 kcal mole^?1. Reagent translation, T′, and vibration, V′, was varied in the range up to T′ + V′ = 90 kcal mole^?. Among the principal findings for the equal-mass case were the following. (i) There is an orders-of-magnitude increase in reaction cross section when energy is transferred from T′ to V′, until an optimal distribution over T′ and V′ is achieved at V′ ?, T′. There is a qualitative difference between the forms of the reactive cross section dependences S(T′) V′ and S(V′)_T′. (ii) The greater efficacy of V′ than T′ in promoting endothermic reaction is marked even at total reagent energies ≈ 3 x the endothermic barrier height. (iii) The total reactive cross section for endothermic reaction increases to large values (≈ gas kinetic) as V′ increased to several times the barrier height. (iv) Reagent energy in excess of that required to cross the endothermic barrier is subject to the same “adiabatic” transformation into product energy as was previously observed for exothermic reactions: ΔT′ → ΔT + ΔR (where R is enhanced product rotational energy), and ΔV′ → ΔV. This is explained in terms of induced repulsive energy release in the former case, and induced attractive energy release in the latter. (v) The molecular product is backwards or sideways scattered. Enhanced V′ at constant T′ diminishes product repulsion, giving rise to more-forward scattering. (vi) These findings remain qualitatively unchanged when extreme mass combinations H H + L and L H + H (L = 1 amu, H = 80 amu) are substituted for the equal-mass combination, L L + L. Effects ascribable to a “late” barrier are accentuated for HH + L. and diminished for L H + H. (vii) The total reactive cross section at a given reagent energy increases in the sequence H H + L, L L + L, L H + H, for simple kinematic reasons. (viii) The dynamics on this endothermic potential-energy surface resemble, in all the points listed above, the dynamics on a thermoneutral surface which has its barrier crest in the coordinate of separation (surface II of part I of this series).     

Diffusion in channeled structures. II. Systems with large energy barriers

The methods developed in a previous paper (Phys. Rev. E.: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 046127) are used to calculate the permeability of argon in alpha-quartz, a system containing large energy barriers. The permeability is reported at three different temperatures and follows Arrhenius behavior. The permeabilities obtained from a hopping model combined with transition state theory closely follow our predicted values but are systematically lower. Lattice flexibility cannot be neglected in this system, and the energy-transfer between alpha-quartz and the argon atom through lattice vibrations occurs on a fast enough time scale such that it plays a role in the guest diffusive motion.     

The multiscale coarse-graining method. VII. Free energy decomposition of coarse-grained effective potentials

The potential of mean force (PMF) with respect to coarse-grained (CG) coordinates is often calculated in order to study the molecular interactions in atomistic molecular dynamics (MD) simulations. The multiscale coarse-graining (MS-CG) approach enables the computation of the many-body PMF of an atomistic system in terms of the CG coordinates, which can be used to parameterize CG models based on all-atom configurations. We demonstrate here that the MS-CG method can also be used to analyze the CG interactions from atomistic MD trajectories via PMF calculations. In addition, MS-CG calculations at different temperatures are performed to decompose the PMF values into energetic and entropic contributions as a function of the CG coordinates, which provides more thermodynamic information regarding the atomistic system. Two numerical examples, liquid methanol and a dimyristoylphosphatidylcholine lipid bilayer, are presented. The results show that MS-CG can be used as an analysis tool, comparable to various free energy computation methods. The differences between the MS-CG approach and other PMF calculation methods, as well as the characteristics and advantages of MS-CG, are also discussed.     

Electrostatic screening and energy barriers of ions in low-dielectric membranes

We present exact solutions of the linear Poisson-Boltzmann equation for several problems relevant for ion translocation across low-dielectric membranes. Our results are obtained for a finite Debye screening length, and they generalize the classical results for pure Coulombic electrostatics (Parsegian, A. Nature (London) 1969, 221, 844). We calculate the electrostatic self-energy of an ion in the middle of a low-dielectric slab, its energy inside a cylindrical high-dielectric pore, and its energy inside a high-dielectric spherical jacket. We consider also the influence of negative charges distributed on the walls of the cylindrical pore. We show that ion self-energy barriers are considerably reduced due to screening of electrolyte. We compare our results with some numerical results for screened electrostatics of ion channels and wide pores.     

Effective potential energy barriers and X-ray transitions of sulphate ion

X-ray transition energies and intensities of sulphate ion are computed from limited CI wavefunctions including singly excited configurations. The results are interpreted in terms of one-electron promotions by using the improved virtual orbitals introduced first by Hunt and Goddard III [11]. The effective potential for virtual orbitals shows a barrier at large distance from sulphur nucleus.     

Strain energy release and intrinsic barriers in internal nucleophilic reactions

This paper reports computational data for the energetics of internal attacks, both in ring-opening reactions (eq 3) where strain energy is released and in model, strain-free systems (eq 4). A comparison is drawn with the corresponding bimolecular processes. The exothermicity of three-membered ring-opening reactions is significantly larger than that of the four-membered ring systems. However, using the Marcus equation, it is shown that the higher reactivity of the three-membered rings is intrinsic to the system and does not stem only from a higher thermodynamic driving force. The intrinsic barriers for the strain-free reactions are shown to be dominated by the position of the nucleophilic and nucleofugic atoms in the periodic table, as in the bimolecular SN2 reactions, although a pi rather than a sigma bond is formed in these reactions.     

Determination of the rotational energy barriers of atropisomeric polychlorinated biphenyls

A spectrophotometric method for the simultaneous determination of Co, Cu, and Fe in ternary mixtures by means of 1,10-phenanthroline as a complexing agent was developed. The influence of chemical variables affecting the analytical reaction was evaluated. A principal component regression procedure was used to assess spectrophotometric data obtained from nineteen calibration solutions. The method was validated by applying it to the analysis of synthetic mixtures over the concentration ranges 0–407 μmol Co/L, 0–189 μmol Cu/L, and 0–143 μmol Fe/L. It was also successfully employed for the analysis of two cobalt magnetic alloys. The relative errors in the determinations were less than 7% in most cases.     

Overcoming free energy barriers using unconstrained molecular dynamics simulations

Association of unconstrained molecular dynamics (MD) and the formalisms of thermodynamic integration and average force [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)] have been employed to determine potentials of mean force. When implemented in a general MD code, the additional computational effort, compared to other standard, unconstrained simulations, is marginal. The force acting along a chosen reaction coordinate xi is estimated from the individual forces exerted on the chemical system and accumulated as the simulation progresses. The estimated free energy derivative computed for small intervals of xi is canceled by an adaptive bias to overcome the barriers of the free energy landscape. Evolution of the system along the reaction coordinate is, thus, limited by its sole self-diffusion properties. The illustrative examples of the reversible unfolding of deca-L-alanine, the association of acetate and guanidinium ions in water, the dimerization of methane in water, and its transfer across the water liquid-vapor interface are examined to probe the efficiency of the method.     

Probing inhomogeneous vibrational reorganization energy barriers of interfacial electron transfer

An atomic force microscopy (AFM) and confocal Raman microscopy study of the interfacial electron transfer of a dye-sensitization system, i.e., alizarin adsorbed upon TiO(2) nanoparticles, has revealed the distribution of the mode-specific vibrational reorganization energies encompassing different local sites ( approximately 250-nm spatial resolution). Our experimental results suggest inhomogeneous vibrational reorganization energy barriers and different Franck-Condon coupling factors of the interfacial electron transfer. The total vibrational reorganization energy was inhomogeneous from site to site; specifically, mode-specific analyses indicated that energy distributions were inhomogeneous for bridging normal modes and less inhomogeneous or homogeneous for nonbridging normal modes, especially for modes far away from the alizarin-TiO(2) coupling hydroxyl modes. The results demonstrate a significant step forward in characterizing site-specific inhomogeneous interfacial charge-transfer dynamics.     

Transition structures and energy barriers of pericyclic reactions in the CASSCF approach

Five energy hypersurfaces of the most examined pericyclic reactions have been investigated by using ab initio SCF , CASSCF , and the semiempirical AM 1 methods. The systems are H₄, H₆, C₃H₆, C₄H₄, and C₃OH₄. Stationary points and their sets of harmonic vibrational frequencies have been calculated by means of analytical gradient techniques in the frameworks of the respective approaches. ZPE corrected energy barriers are based on single-point calculations including dynamical correlation corrections by CAS -CI (SD )+DC , CASCEPA , or MP 2.     

VII. Technische Kolloidforschung

Colloid and Polymer Science -