A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH4 dissociative adsorption on Ir~111! and H2 on Si~100! using plane wave based density functional theory are presented. © 2000 American Institute of Physics. @S0021-9606~00!71246-3#

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A climbing image nudged elastic band method for finding saddle points and minimum energy paths

The phenomenon of growth, decline and death—aging—has been the source of considerable speculation (1, 8, 10). This cycle seems to be a more or less direct function of the metabolic rate and this in turn depends on the species (animal or plant) on which are superimposed the factors of heredity and the effects of the stresses and strains of life—which alter the metabolic activity. The universality of this phenomenon suggests that the reactions which cause it are basically the same in all living things. Viewing this process in the light of present day free radical and radiation chemistry and of radiobiology, it seems possible that one factor in aging may be related to deleterious side attacks of free radicals (which are normally produced in the course of cellular metabolism) on cell constituents.* Irradiation of living things induces mutation, cancer, and aging (9). Inasmuch as these also arise spontaneously in nature, it is natural to inquire if the processes might not be similar. It is believed that one mechanism of irradiation effect is through liberation of OH and HO 2 radicals (12). There is evidence, although indirect, that these two highly active free radicals are produced normally in living systems. In the first place, free radicals are present in living cells; this was recently demonstrated in vivo by a paramagnetic resonance absorption method (3). Further, it was shown that the concentration of free radicals increased with increasing metabolic activity in conformity with the postulates set forth some years ago that free radicals were involved in biologic oxidation-reduction reactions (11, 13). Are some of these free radicals OH and/or HO2, or radicals of a similar high order of reactivity, and where might they arise in the cell? The most likely source of OH and HO2 radicals, at least in the animal cell, would be the interaction of the respiratory enzymes involved

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Aging: A Theory Based on Free Radical and Radiation Chemistry

/pdf/brownian-motion-in-a-field-of-force-and-the-diffusion-model-2nbbzrdubb.pdf

Brownian motion in a field of force and the diffusion model of chemical reactions

Stanford Moore, William Stein, and Anfinsen were awarded the Nobel Prize in Chemistry in 1972 for \"their contribution\n to the understanding of the connection between chemical structure and catalytic activity of the active center of the ribonuclease\n molecule.\" In his Nobel Lecture, Anfinsen provided a sketch of the rich history of research that provided the foundation\n for his work on protein folding and the \"Thermodynamic Hypothesis,\" and outlined potential avenues of current and\n future scientific exploration.

https://web.iitd.ac.in/~amittal/1973_Anfinsen_Science.pdf

Principles that Govern the Folding of Protein Chains

We demonstrate in this work that the surface tension, water-organic solvent, transfer-free energies and the thermodynamics of melting of linear alkanes provide fundamental insights into the nonpolar driving forces for protein folding and protein binding reactions. We first develop a model for the curvature dependence of the hydrophobic effect and find that the macroscopic concept of interfacial free energy is applicable at the molecular level. Application of a well-known relationship involving surface tension and adhesion energies reveals that dispersion forces play little or no net role in hydrophobic interactions; rather, the standard model of disruption of water structure (entropically driven at 25 degrees C) is correct. The hydrophobic interaction is found, in agreement with the classical picture, to provide a major driving force for protein folding. Analysis of the melting behavior of hydrocarbons reveals that close packing of the protein interior makes only a small free energy contribution to folding because the enthalpic gain resulting from increased dispersion interactions (relative to the liquid) is countered by the freezing of side chain motion. The identical effect should occur in association reactions, which may provide an enormous simplification in the evaluation of binding energies. Protein binding reactions, even between nearly planar or concave/convex interfaces, are found to have effective hydrophobicities considerably smaller than the prediction based on macroscopic surface tension. This is due to the formation of a concave collar region that usually accompanies complex formation. This effect may preclude the formation of complexes between convex surfaces.

Protein folding and association: insights from the interfacial and thermodynamic properties of hydrocarbons.

The calculation of absolute reaction rates is formulated in terms of quantities which are available from the potential surfaces which can be constructed at the present time. The probability of the activated state is calculated using ordinary statistical mechanics. This probability multiplied by the rate of decomposition gives the specific rate of reaction. The occurrence of quantized vibrations in the activated complex, in degrees of freedom which are unquantized in the original molecules, leads to relative reaction rates for isotopes quite different from the rates predicted using simple kinetic theory. The necessary conditions for the general statistical treatment to reduce to the usual kinetic treatment are given.

The Activated Complex in Chemical Reactions

Since to form a hole the size of a molecule in a liquid requires almost the same increase in free energy as to vaporize a molecule, the concentration of vapor above the liquid is a measure of such ``molecular'' holes in the liquid. This provides an explanation of the law of rectilinear diameters of Cailletet and Mathias. The theory of reaction rates yields an equation for absolute viscosity applicable to cases involving activation energies where the usual theory of energy transfer does not apply. This equation reduces to a number of the successful empirical equations under the appropriate limiting conditions. The increase of viscosity with shearing stress is explained. The same theory yields an equation for the diffusion coefficient which when combined with the viscosity and applied to the results of Orr and Butler for the diffusion of heavy into light water gives a satisfactory and suggestive interpretation. The usual theories for diffusion coefficients and absolute electrical conductance should be replaced by those developed here when ion and solvent molecule are of about the same size.

Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates

Conformation Changes of Proteins

been of fundamental importance in the development of present-day physical theories. As has been stated so many times, the general problem is now solved "in principle" by the quantum mechanics, but the application of the theory to only the simplest systems has been practicable.l, 2 In recent years a very large amount of data has been accumulated on the "mass spectra" resulting from the bombardment of molecules by electrons of energy 50 and 70 volts.3 There is also a significant amount of data on special aspects of the mass spectra of a few polyatomic molecules. A reasonably exact analysis of a mass spectrum would require detailed knowledge of all the electronic states both of the molecule and of all the ions formed from it by removal of electrons and by removal and rearrangement of nuclei. In this paper we present a statistical approach to the problem. Necessarily, assumptions and approximations are required. 'While this theory is in no way complete, we believe it permits the discussion and coordination of a large amount of the available data in terms of the structure of molecules and ions. Knowledge of the effect of low-voltage electron bombardment on molecules, besides being of interest in its own right, has varied applications. It has bearing on the relation of molecular structure to chemical reactivity. It is well known that the major fraction of the effect of high energy radiation on matter, including living systems, is due to the low energy secondary electrons.4 The rate theory presented here should also be applicable to other problems involving isolated systems having a large but finite number of degrees of freedom. The ionization and dissociation of diatomic molecules by electron impact has by now become quite well understood. Hagstrum5 has recently discussed in great detail the mass spectra of a number of diatomic molecules, explaining the formation of the several ions and their kinetic energies in terms of Franck-Condon transitions to the various electronic states of the diatomic ions. Another discussion is that of Stevenson6 who calculated the relative abundance ratios H+/H2+ and D+/D2+ in the mass spectra of hydrogen and deuterium, again using the picture of Franck-Condon transitions to known electronic states. While any discussion of large polyatomic molecules mass spectra must be in accord with these discussions, the direct application of the same methods is impossible.

https://www.pnas.org/content/pnas/38/8/667.full.pdf

Henry Eyring

Papers

The Activated Complex in Chemical Reactions

Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates

Conformation Changes of Proteins

Absolute Rate Theory for Isolated Systems and the Mass Spectra of Polyatomic Molecules.

The Viscous Flow of Large Molecules