There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

Contracted Gaussian basis sets of triple zeta valence (TZV) quality are presented for Li to Kr. The TZV bases are characterized by typically including a single contraction to describe inner shells and three basis functions for valence shells. All parameters—orbital exponents and contraction coefficients—have been determined by minimization of atomic self‐consistent field ground state energies. Advantages and necessary modifications of TZV basis sets are discussed for simple test calculations of molecular energies and nuclear magnetic resonance (NMR) chemical shieldings in treatments with and without inclusion of electron correlation.

Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr

An ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory. The final magnetic shielding result is broken up into contributions which can be related to various features of electronic structure. Calculated magnetic shielding constants are presented using three sets of atomic orbitals, all of which are taken as contracted gaussian-type functions. The first two sets are minimal and the third is slightly extended. All three levels of theory give good descriptions of shielding at first row and hydrogen atoms. Carbon and hydrogen chemical shifts calculated at the extended level are in excellent agreement with experimental values.

Self-consistent perturbation theory of diamagnetism

Gas-phase 13C chemical shifts in the zero-pressure limit: refinements to the absolute shielding scale for 13C

Explicit expressions for the paramagnetic contribution σ(2) to the nuclear magnetic shielding are derived in the valence bond and the LCAO—MO framework including d as well as p orbitals on the atom in question. A survey of published experimental data reveals a periodic dependence of the range of chemical shifts on atomic number, which is explained in terms of the paramagnetic contribution to the chemical shift and its dependence on 〈1/r3〉 for the bonding electrons.A brief discussion is given of related but more complex periodicities in the electron coupling of nuclear spins, using the M—H coupling in Group IV hydrides as an example. It is suggested that the anisotropy in the nuclear shielding and internuclear coupling tensors may combine to give observable linewidth differences in the high‐resolution NMR spectra of directly bonded nuclei of large Z.

Calculation of Chemical Shifts. I. General Formulation and the Z Dependence

Unlike other chemical shifts in gaseous systems which have been found to have strictly linear dependence on density, we have found the 129Xe chemical shift in pure xenon gas to have a quadratic and cubic dependence in addition to the dominant linear dependence on density. This implies the importance of three or more body interactions in xenon. In mixtures of xenon with another gas (Ar, Kr, CO2, HCl, CH4, CH3F, CH2F2, CHF3, CF4), the dependence of the 129Xe chemical shift on the density of the other gas is found to be linear within experimental error, and varying from 2300–11 700 ppm/mol cc−1. These shifts are orders of magnitude greater than the reported H and F shifts in gases. Analysis of the results show that the density dependence cannot adequately be reproduced by the contributions, Σ1 = Σb − B〈e2〉 − B〈F2〉, which had been adequate for H and F shifts. The general formulation for calculation of the A and B parameters, the coefficients of the linear and quadratic electric field terms in the theory of ch...

Cynthia J. Jameson

Papers

Gas-phase 13C chemical shifts in the zero-pressure limit: refinements to the absolute shielding scale for 13C

Calculation of Chemical Shifts. I. General Formulation and the Z Dependence

Density Dependence of 129 Xe Chemical Shifts in Mixtures of Xenon and Other Gases

Gas-phase NMR spectroscopy

Absolute shielding scale for 31P from gas-phase NMR studies