M. Yoshimine

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.

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.

Theory of Molecular Polarizabilities

Buckinghams theory of the interaction between a polarizable charge distribution and an external electric field is presented and extended in a unified way. Transformations of components of the molecular polarizability tensors under change of the coordinate origin are derived. Relationships between tensor components in systems of axial and spherical symmetry are given.

Computed Ground‐State Properties of FH and CH

The accuracy of existing comprehensive calculations of wavefunctions of first‐ and second‐row hydrides in close to the Hartree—Fock approximation is confirmed by performing test calculations, with larger Slater‐function basis sets, on FH and ClH.Dipole moments, quadrupole moments, magnetic susceptibilities, rotational g factors, forces on the nuclei, field gradients at the nuclei, and polarizabilities are then discussed and estimated from either computation alone, or by combining computed expectation values with observed properties. Excellent agreement between computation and observation is demonstrated for the quadrupole coupling constant for 35Cl and 37Cl nuclei in ClH. The following estimates of molecular properties not available elsewhere are made: rotational g factor is −0.033 for 19FH and +0.006 for 35ClH; diamagnetic anisotropy (ξ∥−ξ⊥) is −2.1 × 10−6 erg/G2·mole for FH, and −3.3 × 10−6 erg/G2·mole for ClH; eqQ(2H) = 0.34 Mc/sec in FH and 0.18 Mc/sec in ClH. For FH the axial components of the molecu...

The alchemy configuration interaction method. I. The symbolic matrix method for determining elements of matrix operators

The symbolic matrix method which gives compact representation and efficient determination of expressions for the Hamiltonian and other matrix operators arising in configuration interaction (CI) calculations is presented. With this method, the computing and storage requirements for matrix expressions become insignificant compared to the total requirements of a CI calculation. The efficiency is achieved by taking advantage of analogies between expressions of different matrix elements to reduce drastically the number of expressions determined explicitly. The symbolic matrix method is completely general, unrestricted by the type of operators considered, or by the choice of n‐particle basis. It can take full advantage of any point group symmetry, and the ordered interacting spaces to reduce the dimension of the n‐particle basis. In addition, the method provides a basis for a general direct CI method which will be presented in a forthcoming paper. A comparison with the graphical unitary group approach is provided.

The binding energy of the ground state of Be2

Two convergent sequences of multiconfiguration self‐consistent field and configuration interaction (CI) calculations have confirmed the predictions of a previous interacting correlated fragments (ICF) calculation and given best values for the De and Re of Be2(X 1Σ+) of 2.04±0.21 kcal/mol and 4.73±0.03a0, respectively. These calculations used a 6s/4p/3d/1f Slater basis set on each atom and correlated only the four 2s electrons. They were shown computationally to be free from basis set superposition and size‐consistency errors. A large second order CI calculation yielded a rigorous lower bound to the full four‐electron CI binding energy of 1.87 kcal/mol within the present basis set. Arguments are presented that the 1s electronic correlation effect on the binding energy is less than 0.2 kcal/mol. The earlier ICF calculation on Be2 has been repeated and extended to a higher level of fragment correlation using the current basis set. The best ICF results are in close agreement with the second order CI calculati...

Band strengths for electric dipole transitions from ab initio computation: Lio (X 2Π −X 2Π), (A 2Σ+−A 2Σ+), (X 2Π − A 2Σ+); AlO (X 2Σ+−X 2Σ+), (A 2Π −A 2Π), (X 2Σ+−A 2Π), (B 2Σ+−B 2Σ+), (X 2Σ+−B 2Σ+)

Intensity relations in diatomic molecule spectra are reviewed and computationally useful expressions given for band strengths and band oscillator strengths in terms of electronic expectations values, which are the normal output of ab initio calculation. Calculations of these properties are reported for 7Li16O and 27Al16O. With very accurate X 2Π and A 2Σ+ LiO wavefunctions, band strengths and band oscillator strengths for all transitions involving ν,′ ν″ up to four are given, both within and between the electronic states. Results, given as band strengths (band oscillator strengths), are X 2Π −X 2Π 0–1 band, 0.038 a.u. (2.4× 10−6). A 2Σ+ −A 2Σ+ 0–1 band, 0.029 a.u. (3.7× 10−5); and X 2Π −A 2Σ+ 0–0 band, 6.4× 10−4a.u. (1.1× 10−6). Similar data are presented for the X 2Σ+ and A 2Π states of 27Al16 0 using wavefunctions of comparable quality. The dipole moment in the X 2Σ+ state is shown to be essentially constant over the range of nuclear vibration in the lowest vibrational levels. Results, given as band str...

Ab initio study of the X2Π and A2Σ+ states of OH. I. Potential curves and properties

Accurate ab initio CI potential curves and molecular properties are presented for the X2Π and A2Σ+ states of OH. Results with known experimental values in parentheses are Re(X2Π) = 1.841(1.834) bohr, Re(A2Σ+) = 1.906(1.913) bohr, De(X2Π) = 4.43(4.63) eV, De(A2Σ+) = 2.29(2.53) eV, μ(OH,X2Π,ν=0) = 1.634(1.668) D, and μ(OD,A2Σ+,ν=0) = 1.861(1.72±0.10) D. Spectroscopic constants calculated from the theoretical potential curves are in satisfactory agreement with experimental results. Other molecular properties studied include quadrupole moments and the electric field gradient at the nuclei.

Accurate Potential Curves and Properties for the X2π and A2Σ+ States of LiO

Ab initio calculations have been performed to determine potential curves and molecular properties for the X 2π and A 2Σ+ states of the LiO molecule. The calculations use a conventional configuration interaction (CI) method in which the Hartree‐Fock configuration is taken as reference configuration and only valence shells are correlated. The molecular orbital (MO) basis set used in the CI calculations is composed of the Hartree‐Fock orbitals and additional MOs. These additional MOs are formed by truncating a set of pseudonatural orbitals (PSNOs) obtained as the natural orbitals of a CI calculation on a single pair of valence electrons. The main results are Re=1.695 A, De0=3.37 eV, ωe=851.5 cm−1 (7Li16O), μ=6.76 D for the X 2π state; and Re=1.599 A, De0=4.90 eV, ωe=866.8 cm−1 (7Li16O), μ=5.96 D for the A 2Σ+ state. The computed De0(X 2Π)=3.37 eV is in good agreement with the observed value of 3.39± 0.26 eV. The other results are also believed to be accurate to within a few percent. The computed term ener...

On the dissociation energy of Mg2

The bonding in the X 1Σ+g state of Mg2 is investigated using near‐complete valence one‐particle Slater and Gaussian basis sets containing up to h functions. Full configuration interaction (FCI) calculations are used to calibrate four‐electron correlation treatments. We show that the four‐electron complete CI limit can be approached using a sequence of either second‐order CI (SOCI) or interacting correlated fragment (ICF) calculations. At the valence level, our best estimate of the dissociation energy (De) is 464 cm−1. We show that this is a lower limit and probably within 5 cm−1 of the complete basis value. The inclusion of core–valence correlation using a model operator approach decreases De by about 35 cm−1 and increases the bond length by 0.03 a0, thereby yielding spectroscopic constants in good agreement with experiment. Attempts to compute the core–valence effect accurately by expanding the CI treatment were unsuccessful.