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

A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.

General atomic and molecular electronic structure system

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

Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.

A New Mixing of Hartree-Fock and Local Density-Functional Theories

Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

The influence of polarization functions on molecular orbital hydrogenation energies

Analytical self‐consistent field (SCF) functions for the neutral atoms and positive ions isoelectronic series of 2 to 10 electrons up to Z=36 are presented. These computations deal with the lowest electronic configuration ground states and excited states. The basis set of Slater‐type orbitals (STO) is fully optimized with respect to the orbital exponent, and considerable effort was given to obtain a short expansion. A maximum of nine STO's were considered sufficient for the largest expansion. The total energies of each isoelectronic series are collected in simple series expansions in power of Z. For the 444 computed SCF functions here reported, only the most important features are discussed.

Analytical Self‐Consistent Field Functions for Positive Ions. I. Isoelectronic Series with 2 to 10 Electrons

In this paper we have summarized the complete multiconfiguration self‐consistent‐field theory (CMC SCF LCAO MO or CMC for short) as given from the analysis of Veillard and the author (published elsewhere).In the analysis of the CMC theory it is shown that the CMC technique allows determination of the pair and pair—pair correlation energy and retains the physical simplicity of the Hartree—Fock functions. The CMC theory differs from usual many‐body techniques in so far as it does not take the Hartree—Fock energy as zero‐order energy. It has been shown that the CMC wavefunction can be cast in the form of a new type of ``single determinant'' (the ``CMC determinant'') with elements which are different from the standard elements of the Slater determinant. The existence of the CMC determinant provides the formal justification for the use of a single determinant in semiempirical work aiming at exact prediction.The analysis of the CMC wavefunctions is then continued in terms of a population analysis which to a lar...

Study of the Electronic Structure of Molecules. I. Molecular Wavefunctions and Their Analysis

The usual way to compute Hartree-Fock type functions for molecules is by an expansion of the one-electron functions (molecular orbitals) in a linear combination of analytical functions (LCAO-MO-SCF, linear combination of atomic orbitals—Molecular Orbital—Self Consistent field). The expansion coefficients are obtained variationally. This technique requires the computation of several multicenter two-electron integrals (representing the electron-electron interaction) proportional to the fourth power of the basis set size. There are several types of basis sets; the Gaussian type introduced by S. F. Boys is used herein. Since it requires from a minimum of 10 (or 15) Gaussian-type functions to about 25 (or 30) Gaussian functions to describe a second-row atom in a molecule, the fourth power dependency of the basis set has been the de facto bottleneck of quantum chemical computations in the last decade. 

In this paper, the concept is introduced of a “dynamical” basis set, which allows for drastic computational simplifications while retaining full numerical accuracy. Examples are given that show that computational saving in computer time of more than a factor of one hundred is achieved and that large basis sets (up to the order of several hundred Gaussian functions per molecule) can be used routinely. 

It is noted that the limitation in the Hartree-Fock energy (correlation energy error) can be easily computed by use of a statistical model introduced by Wigner for solid-state systems in 1934. 

Thus, large molecules can now be simulated by computational techniques without reverting to semi-empirical parameterization and without requiring enormous computational time and storage.

https://www.pnas.org/content/pnas/69/10/2942.full.pdf

Computation of large molecules with the hartree-fock model.

I. Structure of Macromolecules.- Conformational Analysis of Polypeptides and Proteins for the Study of Protein Folding, Molecular Recognition, and Molecular Design.- Conformation of Non-Crystalline Proteins Viewed by NMR.- Structures and Superstructures in Periodical Polynucleotides.- Conformational Peculiarities and Biological Role of Some Nucleotide Sequences.- Multifrequency ESR of an Isotopically Enriched Copper System in the Immobilized Phase: A Monte Carlo Approach.- Neutron Scattering from Agarose Gels.- Non-Empirical Pair Potentials for the Interaction Between Amino Acids.- II. Dynamics of Macromolecules.- Molecular Dynamics of Proteins.- Proton NMR Studies of Protein Dynamics and Folding: Applications of Magnetization Transfer NMR.- Distributions and Fluctuations of Protein Structures Investigated by X-Ray Analysis and Mossbauer Spectroscopy.- Rotational Motions of Tryptophan and Tyrosine Residues in Proteins.- Protein Fluctuations and Hemeprotein Affinity for Ligand.- Cytochrome Oxidase in Energy Transduction.- Proteins and Glasses.- III. Solvation of Macromolecules.- Global Ab Initio Simulations: Study of a Liquid as an Example.- Proton Conductivity of Hydrated Lysozyme Powders, Considered Within the Framework of Percolation Theory.- Molecular Dynamics Simulations of Biomolecules in Water.- Low Frequency Coherent Vibrations of DNA: The Role of the Hydration Shell and Phosphate-Phosphate Interactions.- IV. Components of Larger Systems.- Elasticity, Structure and Dynamics of Cell Plasma Membrane and Biological Functions.- Neuronal Signaling. A Simple Thermodynamic Process Involving Complex Membrane Proteins.- Panel Discussions: Session 1. Understanding Brain Mechanisms and the Challenge of Artificial Intelligence Machines: An Interdisciplinary Approach Session 2. Sixth Generation Computers: A Sketch.- Physicists Explore Human and Artificial Intelligence.- Recognition Automata Based on Selective Neural Networks.- A Neural Theory of Preattentive Visual Information Processing: Emergent Segmentation, Cooperative-Competitive Computation, and Parallel Memory Storage.- Large-Scale Computations on a Scalar, Vector and Parallel "Supercomputer".

Structure and Dynamics of Nucleic Acids, Proteins, and Membranes

The two‐body Hartree‐Fock potential for water‐water interactions previously used to describe small water clusters and used in Monte Carlo studies of liquid water has been used to assess the effect of neglecting the correlation energy correction. A number of semiempirical corrections based on the London, Kirkwood, and Wigner formulas were used. They have an energy spread such that they encompass the expected magnitude of the exact correlation energy correction. Short range correlation interactions were included using a modification of the functional of density proposed by Wigner and the corresponding long range interactions were given by a term proportional to r−6 with coefficients due to both London and Kirkwood. After adding the corrections to the Hartree‐Fock potential the various potentials were compared by generating a number of potential energy surfaces. Following this the water‐water potentials were used in a Monte Carlo simulation of liquid water to calculate thermodynamic and structural data. Afte...

Study of the structure of molecular complexes. VII. Effect of correlation energy corrections to the Hartree‐Fock water‐water potential on Monte Carlo simulations of liquid water

Enrico Clementi

Papers

Analytical Self‐Consistent Field Functions for Positive Ions. I. Isoelectronic Series with 2 to 10 Electrons

Study of the Electronic Structure of Molecules. I. Molecular Wavefunctions and Their Analysis

Computation of large molecules with the hartree-fock model.

Structure and Dynamics of Nucleic Acids, Proteins, and Membranes

Study of the structure of molecular complexes. VII. Effect of correlation energy corrections to the Hartree‐Fock water‐water potential on Monte Carlo simulations of liquid water