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.

In this report we treat reaction rates, equilibrium theory, and irreversible thermodynamics as different aspects of a single discipline. In biological reactions the rate is ultimately controlled by enzymes and other proteins of complex structure and high molecular weight. The needed formalism can be placed in one-to-one correspondence with appropriate electrical and mechanical networks. An enzyme molecule has zwitter ions anchored in the polypeptide chain, which enable it to distort the substrate by electrostatic polarization. Water weakens the induced or existing polar bonds and so speeds reaction. Several biological processes, such as luminescence, catalysis, nerve excitation, and anesthesia, in which enzymatic reactions play a major part are discussed from this point of view. We also have discussed the energy consumption and coupling effect in living systems. It is likely that a small fraction of bonds can become energy rich through the process of quenching and that unsymmetrical barriers in biological systems act like transistors in making the driving forces more efficient by a valve effect.

Reaction kinetics in living systems.

From the steady-state theory of mutation rates we have the probability, q, of the occurrence of a critical change at some site in a cell that leads to genetic alternation, and the probability, p = 1 - q, that the site either is not changed or that it has been repaired. In this paper the formal theory is extended to include survival of biological systems. Single and multiple mechanisms of nonsurvival, and multiple factors acting on a single mechanism, are considered. The number of sites that must be altered to lead to nonsurvival is examined and found to be greater than one. The effect of independent action on separate sets of sites, and the relationship between dose size and survival time are given.

The Dynamics of Life, III. Mechanisms of Nonsurvival and the Relation of Dose Size

For the present calculation of the mobile bond orders of para‐quaterphenyl and meta‐terphenyl molecules, Pople's simplified SCF—LCAO—MO theory for unsaturated hydrocarbon molecules in their ground states is utilized. The symmetry orbitals for these molecules are formulated in order to simplify the calculations by the use of group theory. The symmetry properties of these molecules and the pairing properties of the molecular orbitals are discussed. Planar configurations of both molecules are assumed as a first approximation. The unreasonable mobile bond orders calculated from the Huckel MO theory are improved in the present calculations. The results are discussed in connection with the recent experimental values of the bond lengths of biphenyl.

Mobile Bond Orders of Some Polyphenyls from SCF—LCAO—MO Theory

Significant structure liquid theory of the alkali metals over the normal melting to boiling range

Molecular energy calculations employing actual and approximate multicenter angular dependent integral evaluations are compared. Individual integral values for three‐center integrals used in calculations for the triangular H3+ ion as computed by exact methods and by the approximate formulas of Mulliken and of Rudenberg are given. The results indicate that angular and distance relations of the nuclear skeleton of this polyatomic ion are determinable at almost the identical ``best'' value found using the much more laborious exact integral calculations. The energies of the approximate evaluations, however, indicate that once these ``best'' parametric values are determined the more exact calculations must be used. The approximate evaluations of second angular derivatives of integrals that are dependent on the angular and distance relations of component molecular nuclei are also computed and compared. Use of such derivatives in determination of approximate zero point energies, vibrational frequencies, and force...

Henry Eyring

Papers

Reaction kinetics in living systems.

The Dynamics of Life, III. Mechanisms of Nonsurvival and the Relation of Dose Size

Mobile Bond Orders of Some Polyphenyls from SCF—LCAO—MO Theory

Significant structure liquid theory of the alkali metals over the normal melting to boiling range

Approximate Integral Evaluations Used in the Molecular Quantum Mechanics of Nonlinear Molecules