E. Clementi

Atomic Screening Constants from SCF Functions

The self‐consistent‐field function for atoms with 2 to 36 electrons are computed with a minimal basis set of Slater‐type orbitals. The orbital exponent of the atomic orbitals are optimized as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1s, 2s, 3s, 4s, 2p, 3p, 4p, and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need of accounting for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the groundstate configuration and to the positive ions.

CI study of the water dimer potential surface

The potential energies for the water dimer in various geometrical configurations have been calculated with a configuration–interaction method. The computed dimerization binding energies corresponding to the potential minima for the linear, cyclic, and bifurcated configurations are −5.6, −4.9, and −4.2 kcal/mol, respectively; the correlation effects account for −1.1, −1.2, and −0.9 kcal/mol, respectively, of the total binding energy for these three dimeric forms. The correlation effects for the entire potential surface have been analyzed in terms of inter‐ and intramolecular effects; the substantial coupling found between these effects, particularly in the vicinity of equilibrium position, is discussed. The computational technique employed, in particular an analysis on the selection criteria for the configuration state functions, is discussed, and its reliability is assessed. Two analytical expressions for the water dimer potential surface obtained by fitting the calculated energies are presented. The potential surface given here is being used to determine the structure of liquid water (in the pairwise approximation and with Monte Carlo techniques); this latter work will be reported elsewhere.

ATOMIC SCREENING CONSTANTS FROM SCF FUNCTIONS. II. ATOMS WITH 37 TO 86 ELECTRONS.

Minimal basis‐set atomic functions for the ground‐state atoms from Rb(Z=37) to Rn(Z=86) are presented. These functions are analyzed in order to obtain systematic data for the screening constants and atomic radii following the work initiated by Slater.

The Perfect Club Benchmarks: Effective Performance Evaluation of Supercomputers

This report presents a methodology for measuring the performance of supercomputers. It includes 13 Fortran programs that total over 50,000 lines of source code. They represent applications in several areas of engi neering and scientific computing, and in many cases the codes are currently being used by computational re search and development groups. We also present the PERFECT Fortran standard, a set of guidelines that allow portability to several types of machines. Furthermore, we present some performance measures and a method ology for recording and sharing results among diverse users on different machines. The results presented in this paper should not be used to compare machines, except in a preliminary sense. Rather, they are presented to show how the methodology has been applied, and to encourage others to join us in this effort. The results should be regarded as the first step toward our objec tive, which is to develop a publicly accessible data base of performance information of this type.

Ab initio analytic polarizability, first and second hyperpolarizabilities of large conjugated organic molecules: Applications to polyenes C4H6 to C22H24

The static dipole polarizability and second hyperpolarizability tensors are calculated for polyene systems via ab initio coupled‐perturbed Hartree–Fock theory. The effect of basis set augmentation on the calculated properties is explored for C4H6 and example basis sets are used to calculate the polarizability and second hyperpolarizability for the longer polyenes: C6H8, C8H10, C10H12, C12H14, C14H16,C16H18, C18H20, C20H22, C22H24. Results for the finite polyenes are extrapolated to predict the unit‐cell polarizability and second hyperpolarizability of infinite polyacetylene. The working equations which take advantage of the 2n+1 theorem of perturbation theory for calculating up to the second hyperpolarizability are given, and their implementation is briefly discussed. In particular it is shown that the implementation is readily amenable to parallel processing.

Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree‐Fock density and its application to the hydrides of the second row atoms

A semiempirical functional of the Hartree‐Fock density is presented for estimates of the correlation energy correction. The functional is similar to the one proposed by Gombas and is (a) parametrized with reference to few atomic systems, and (b) is modified as to reproduce the atomic correlation correction not only for closed but also for open shell systems. The functional is then applied to the ground state function of the hydrides LiH(1Σ+), BeH(2Σ+), BH(1Σ+), CH(2Π), NH(3Σ−), OH(2Π), and HF(1Σ+). Several internuclear distances have been considered for each hydride, scanning the potential energy curve from the repulsive region to the dissociation products (∼ 10 a.u.). For these points a simple multiconfigurational function (consisting of no more than three configurations) was computed to obtain Hartree‐Fock functions with proper dissociation behavior (H‐F‐P‐D functions). The semiempirical functional was applied both to the traditional H‐F functions and the H‐F‐P‐D functions in order to study how to selec...

Study of the structure of molecular complexes. IV. The Hartree‐Fock potential for the water dimer and its application to the liquid state

The Hartree‐Fock energy of the water dimer has been computed for 216 different nuclear configurations using the basis set given in the first paper of this series. Near the equilibrium configuration, a calculation was carried out using a large Gaussian basis set with optimized orbital exponents for the oxygen 3d ‐ and 4f ‐type and hydrogen 2p ‐ and 3d ‐type functions in order to get results close to the Hartree‐Fock limit. In the vicinity of the equilibrium configuration the mechanism for binding of the dimer is analyzed with the help of the bond energy analysis formalism. The importance of polarization (internal charge transfer), as pointed out previously by a number of authors, is clearly evident. The computed energies have been used to derive a simple analytical expression that reproduces the Hartree‐Fock potential energy surface to a high degree of accuracy. This analytical potential is compared with the empirical effective pair potentials proposed by Rowlinson and Ben‐Naim and Stillinger for the descr...

Study of the structure of molecular complexes. XIII. Monte Carlo simulation of liquid water with a configuration interaction pair potential

A water–water interaction potential obtained from configuration interaction calculations has been used to simulate liquid water, at 25 °C, by a Monte Carlo technique. The resulting radial distribution functions and x‐ray and neutron scattering intensities are compared with experiment and found to be in satisfactory agreement. Some thermodynamic properties are also computed and discussed. The overall agreement seems to indicate that many‐body effects contribute little in determining the structure of liquid water, although they seem to be important for an accurate simulation of internal energy and related quantities.

Study of the Structure of Molecular Complexes. I. Energy Surface of a Water Molecule in the Field of a Lithium Positive Ion

In the Introduction we have outlined the technique adopted in this paper (and in others of this series to follow) in order to elucidate the structure and energetics of water molecules around positive ions. The raw data to be analyzed are obtained from the Hartree‐Fock model. We have started by considering the H2O molecule making use of the bond energy analysis formalism. Next we report Hartree‐Fock data for the Li+–H2O energy surface keeping the H2O geometry rigid. These data are analyzed in the same way as for the H2O molecule. In addition, the energy of rotation of the H2O molecule for a fixed Li–O distance has been studied in detail. Analytical expressions aimed at reproducing the energy surface data in a very simple and condensed form are presented. Finally, the effect of complete optimization of the geometry and use of a large basis set for Li+–H2O energy calculations is discussed. The most stable configuration for the Li+–H2O complex is planar and is predicted to have the following geometry: The Li–...

Correlation Energy for Atomic Systems

The correlation energies are estimated for the isoelectronic series of atoms with 2 to 10 electrons in the ground state and in the excited states of the lowest electronic configuration. The obtained values of the correlation energy point out clearly the importance of precorrelation energy, i.e., the energy difference between Hartree and Hartree—Fock energies, the quasi‐additivity of 1s, 2s, 2‐, ··· intra‐ and intershell correlation, the relative importance of spin‐multiplicity correlation and total angular‐momentum correlation, and the Z effects on correlation. The estimate of the correlation energy makes use of energy data for the relativistic energy: the accuracy of the relativistic energy computations is discussed. The 2 to 10 electron correlation energies were used as a basis to estimate the 11 to 18 electron correlation energies and to draw general conclusions on the value of the correlation energy for any atomic system.