Classical Monte Carlo simulations have been carried out for liquid water in the NPT ensemble at 25 °C and 1 atm using six of the simpler intermolecular potential functions for the water dimer: Bernal–Fowler (BF), SPC, ST2, TIPS2, TIP3P, and TIP4P. Comparisons are made with experimental thermodynamic and structural data including the recent neutron diffraction results of Thiessen and Narten. The computed densities and potential energies are in reasonable accord with experiment except for the original BF model, which yields an 18% overestimate of the density and poor structural results. The TIPS2 and TIP4P potentials yield oxygen–oxygen partial structure functions in good agreement with the neutron diffraction results. The accord with the experimental OH and HH partial structure functions is poorer; however, the computed results for these functions are similar for all the potential functions. Consequently, the discrepancy may be due to the correction terms needed in processing the neutron data or to an effect uniformly neglected in the computations. Comparisons are also made for self‐diffusion coefficients obtained from molecular dynamics simulations. Overall, the SPC, ST2, TIPS2, and TIP4P models give reasonable structural and thermodynamic descriptions of liquid water and they should be useful in simulations of aqueous solutions. The simplicity of the SPC, TIPS2, and TIP4P functions is also attractive from a computational standpoint.

Comparison of simple potential functions for simulating liquid water

CHARMM (Chemistry at HARvard Macromolecular Mechanics) is a highly flexible computer program which uses empirical energy functions to model macromolecular systems. The program can read or model build structures, energy minimize them by first- or second-derivative techniques, perform a normal mode or molecular dynamics simulation, and analyze the structural, equilibrium, and dynamic properties determined in these calculations. The operations that CHARMM can perform are described, and some implementation details are given. A set of parameters for the empirical energy function and a sample run are included.

CHARMM: A program for macromolecular energy, minimization, and dynamics calculations

A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation‐reduction reactions involving electron transfer in solution is presented. The assumption of "slight‐overlap" is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction.

This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over‐all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.

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On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I

IA Basic Concepts.- 1 The Importance of Hydrogen Bonds.- 1.1 Historical Perspective.- 1.2 The Importance of Hydrogen Bonds in Biological Structure and Function.- 1.3 The Role of the Water Molecules.- 1.4 Significance of Small Molecule Crystal Structural Studies.- 1.5 The Structural Approach.- 2 Definitions and Concepts.- 2.1 Definition of the Hydrogen Bond - Strong and Weak Bonds.- 2.2 Hydrogen-Bond Configurations: Two- and Three-Center Hydrogen Bonds Bifurcated and Tandem Bonds.- 2.3 Hydrogen Bonds Are Very Different from Covalent Bonds.- 2.4 The van der Waals Radii Cut-Off Criterion Is Not Useful.- 2.5 The Concept of the Hydrogen-Bond Structure.- 2.6 The Importance of ? and ? Cooperativity.- 2.7 Homo-, Anti- and Heterodromic Patterns.- 2.8 Hydrogen Bond Flip-Flop Disorder: Conformational and Configurational.- 2.9 Proton-Deficient Hydrogen Bonds.- 2.10 The Excluded Region.- 2.11 The Hydrophobic Effect.- 3 Experimental Studies of Hydrogen Bonding.- 3.1 Infrared Spectroscopy and Gas Electron Diffraction.- 3.2 X-Ray and Neutron Crystal Structure Analysis.- 3.3 Treatment of Hydrogen Atoms in Neutron Diffraction Studies.- 3.4 Charge Density and Hydrogen-Bond Energies.- 3.5 Neutron Powder Diffraction.- 3.6 Solid State NMR Spectroscopy.- 4 Theoretical Calculations of Hydrogen-Bond Geometries.- 4.1 Calculating Hydrogen-Bond Geometries.- 4.2 Ab-Initio Molecular Orbital Methods.- 4.3 Application to Hydrogen-Bonded Complexes.- 4.4 Semi-Empirical Molecular Orbital Methods.- 4.5 Empirical Force Field or Molecular Mechanics Methods.- 5 Effect of Hydrogen Bonding on Molecular Structure.- IB Hydrogen-Bond Geometry.- 6 The Importance of Small Molecule Structural Studies.- 6.1 Problems Associated with the Hydrogen-Bond Geometry.- 6.2 The Hydrogen Bond Can Be Described Statistically.- 6.3 The Problems of Measuring Hydrogen-Bond Lengths and Angles in Small Molecule Crystal Structures.- 7 Metrical Aspects of Two-Center Hydrogen Bonds.- 7.1 The Metrical Properties of O-H *** O Hydrogen Bonds.- 7.1.1 Very Strong and Strong OH *** O Hydrogen Bonds Occur with Oxyanions, Acid Salts, Acid Hydrates, and Carboxylic Acids.- 7.1.2 OH *** O Hydrogen Bonds in the Ices and High Hydrates.- 7.1.3 Carbohydrates Provide the Best Data for OH ... O Hydrogen Bonds: Evidence for the Cooperative Effect.- 7.2 N-H *** O Hydrogen Bonds.- 7.3 N-H *** N Hydrogen Bonds.- 7.4 O-H *** N Hydrogen Bonds.- 7.5 Sequences in Lengths of Two-Center Hydrogen Bonds.- 7.6 H/D Isotope Effect.- 8 Metrical Aspects of Three- and Four-Center Hydrogen Bonds.- 8.1 Three-Center Hydrogen Bonds.- 8.2 Four-Center Hydrogen Bonds.- 9 Intramolecular Hydrogen Bonds.- 10 Weak Hydrogen-Bonding Interactions Formed by C-H Groups as Donors and Aromatic Rings as Acceptors.- 11 Halides and Halogen Atoms as Hydrogen-Bond Acceptors.- 12 Hydrogen-Bond Acceptor Geometries.- II Hydrogen Bonding in Small Biological Molecules.- 13 Hydrogen Bonding in Carbohydrates.- 13.1 Sugar Alcohols (Alditols) as Model Cooperative Hydrogen-Bonded Structures.- 13.2 Influence of Hydrogen Bonding on Configuration and Conformation in Cyclic Monosaccharides.- 13.3 Rules to Describe Hydrogen-Bonding Patterns in Monosaccharides.- 13.4 The Water Molecules Link Hydrogen-Bond Chains into Nets in the Hydrated Monosaccharide Crystal Structures.- 13.5 The Disaccharide Crystal Structures Provide an Important Source of Data About Hydrogen-Bonding Patterns in Polysaccharides.- 13.6 Hydrogen Bonding in the Tri- and Tetrasaccharides Is More Complex and Less Well Defined.- 13.7 The Hydrogen Bonding in Polysaccharide Fiber Structures Is Poorly Defined.- 14 Hydrogen Bonding in Amino Acids and Peptides: Predominance of Zwitterions.- 15 Purines and Pyrimidines.- 15.1 Bases Are Planar and Each Contains Several Different Hydrogen-Bonding Donor and Acceptor Groups.- 15.2 Many Tautomeric Forms Are Feasible But Not Observed.- 15.3 ?-Bond Cooperativity Enhances Hydrogen-Bonding Forces.- 15.4 General, Non-Base-Pairing Hydrogen Bonds.- 16 Base Pairing in the Purine and Pyrimidine Crystal Structures.- 16.1 Base-Pair Configurations with Purine and Pyrimidine Homo-Association.- 16.2 Base-Pair Configurations with Purine-Pyrimidine Hetero-Association: the Watson-Crick Base-Pairs.- 16.3 Base Pairs Can Combine to Form Triplets and Quadruplets.- 17 Hydrogen Bonding in the Crystal Structures of the Nucleosides and Nucleotides.- 17.1 Conformational and Hydrogen-Bonding Characteristics of the Nucleosides and Nucleotides.- 17.2 A Selection of Cyclic Hydrogen-Bonding Patterns Formed in Nucleoside and Nucleotide Crystal Structures.- 17.3 General Hydrogen-Bonding Patterns in Nucleoside and Nucleotide Crystal Structures.- III Hydrogen Bonding in Biological Macromolecules.- 18 O-H *** O Hydrogen Bonding in Crystal Structures of Cyclic and Linear Oligoamyloses: Cyclodextrins, Maltotriose, and Maltohexaose.- 18.1 The Cyclodextrins and Their Inclusion Complexes.- 18.2 Crystal Packing Patterns of Cyclodextrins Are Determined by Hydrogen Bonding.- 18.3 Cyclodextrins as Model Compounds to Study Hydrogen-Bonding Networks.- 18.4 Cooperative, Homodromic, and Antidromic Hydrogen-Bonding Patterns in the ?-Cyclodextrin Hydrates.- 18.5 Homodromic and Antidromic O-H *** O Hydrogen-Bonding Systems Analyzed Theoretically.- 18.6 Intramolecular Hydrogen Bonds in the ?-Cyclodextrin Molecule are Variable - the Induced-Fit Hypothesis.- 18.7 Flip-Flop Hydrogen Bonds in ?-Cyclodextrin * 11 H2O.- 18.8 From Flip-Flop Disorder to Ordered Homodromic Arrangements at Low lbmperature: The Importance of the Cooperative Effect.- 18.9 Maltohexaose Polyiodide and Maltotriose - Double and Single Left-Handed Helices With and Without Intramolecular O(2) *** O(3?) Hydrogen Bonds.- 19 Hydrogen Bonding in Proteins.- 19.1 Geometry of Secondary-Structure Elements: Helix, Pleated Sheet, and Turn.- 19.2 Hydrogen-Bond Analysis in Protein Crystal Structures.- 19.3 Hydrogen-Bonding Patterns in the Secondary Structure Elements.- 19.4 Hydrogen-Bonding Patterns Involving Side-Chains.- 19.5 Internal Water Molecules as Integral Part of Protein Structures.- 19.6 Metrical Analysis of Hydrogen Bonds in Proteins.- 19.7 Nonsecondary-Structure Hydrogen-Bond Geometry Between Main-Chains, Side-Chains and Water Molecules.- 19.8 Three-Center (Bifurcated) Bonds in Proteins.- 19.9 Neutron Diffraction Studies on Proteins Give Insight into Local Hydrogen-Bonding Flexibility.- 19.10 Site-Directed Mutagenesis Gives New Insight into Protein Thermal Stability and Strength of Hydrogen Bonds.- 20 The Role of Hydrogen Bonding in the Structure and Function of the Nucleic Acids.- 20.1 Hydrogen Bonding in Nucleic Acids is Essential for Life.- 20.2 The Structure of DNA and RNA Double Helices is Determined by Watson-Crick Base-Pair Geometry.- 20.3 Systematic and Accidental Base-Pair Mismatches: "Wobbling" and Mutations.- 20.4 Noncomplementary Base Pairs Have a Structural Role in tRNA.- 20.5 Homopolynucleotide Complexes Are Stabilized by a Variety of Base-Base Hydrogen Bonds - Three-Center (Bifurcated) Hydrogen Bonds in A-Tracts.- 20.6 Specific Protein-Nucleic Acid Recognition Involves Hydrogen Bonding.- IV Hydrogen Bonding by the Water Molecule.- 21 Hydrogen-Bonding Patterns in Water, Ices, the Hydrate Inclusion Compounds, and the Hydrate Layer Structures.- 21.1 Liquid Water and the Ices.- 21.2 The Hydrate Inclusion Compounds.- 21.3 Hydrate Layer Structures.- 22 Hydrates of Small Biological Molecules: Carbohydrates, Amino Acids, Peptides, Purines, Pyrimidines, Nucleosides and Nucleotides.- 23 Hydration of Proteins.- 23.1 Characterization of "Bound Water" at Protein Surfaces - the First Hydration Shell.- 23.2 Sites of Hydration in Proteins.- 23.3 Metrics of Water Hydrogen Bonding to Proteins.- 23.4 Ordered Water Molecules at Protein Surfaces - Clusters and Pentagons.- 24 Hydration of Nucleic Acids.- 24.1 Two Water Layers Around the DNA Double Helix.- 24.2 Crystallographically Determined Hydration Sites in A-, B-, Z-DNA. A Statistical Analysis.- 24.3 Hydration Motifs in Double Helical Nucleic Acids.- 24.3.1 Sequence-Independent Motifs.- 24.3.2 Sequence-Dependent Motifs.- 24.4 DNA Hydration and Structural Transitions Are Correlated: Some Hypotheses.- 25 The Role of Three-Center Hydrogen Bonds in the Dynamics of Hydration and of Structure Transition.- References.- Refcodes.

Hydrogen Bonding in Biological Structures

The Grotthuss mechanism

On the basis of the model of the water molecule derived from spectral and x-ray data and a proposed internal structure for water, the following properties of water and ionic solutions have been deduced quantitatively in good agreement with experiment. (1) The crystal structure of ice. (2) The x-ray diffraction curve for water. (3) The total energy of water and ice. (4) The degree of hydration of positive and negative ions in water. (5) The heat of solutions of ions. (6) The mobility of hydrogen and hydroxyl ions in water. And the following inferred in a qualitative way. (7) The density and density changes of water. (8) The explanation of the unique position of water among molecular liquids. (9) The dielectric properties of water and ice. (10) The viscosities of dilute ionic solutions. (11) The viscosities of concentrated acids.

R. H. Fowler

Papers

A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions