Multireference perturbation CI I. Extrapolation procedures with CAS or selected zero-order spaces

We discuss the “three class” approximation to full multireference perturbation CI, which greatly reduces the computational effort by restricting the summation of diagrams to determinants belonging to a subspace of the zero-order space. In the framework of the CIPSI algorithm, we propose a new extrapolation procedure allowing recovery of the full “two class” results. The new procedure is applied to complete active spaces (CAS) and to individually selected zero-order spaces. Comparison with a full two class calculation on a CAS shows a reduction of computer time of one or two orders of magnitude in the tests presented here, with an accuracy in the order of 0.1 kcal/mol. Our procedure can thus compete with the CASPT2 algorithm, specifically conceived to deal with CAS. In the case of selected zero-order spaces, the speed-up is less dramatic but the method still retains its advantages. Received: 12 June 1997 / Accepted: 31 July 1997     

Density and Volume Properties of Ethane-1,2-diol + 1,2-Dimethoxyethane + Water Ternary Mixtures from −10° to 80°

Thermodynamic interactions in the ethane-1,2-diol (1) + 1,2-dimethoxyethane(2) + water (3) ternary system have been investigated in terms of the excessmolar volume, derived from density measurements at 19 different temperaturesfrom –10;dg to 80;dgC. Fourteen three-component mixtures have been considered,covering the entire composition range. The excess molar volumes are discussedin terms of conformational changes induced in each component by the presenceof another one. The results obtained support the hypothesis of the absence of anythree-component complex adducts under all experimental conditions investigated.     

Regioselective carbon-carbon bond formation at C2 of 1,3-thiazole by reaction of n-ethoxycarbonylthiazolium chloride with C-nucleophiles

N-Ethoxycarbonylthiazolium chloride generated $\text{in situ}$ from 1,3-thiazole and ethyl chloroformate, treated with lithium carbanions of esters, Grignard reagents, silyl enol ethers and esters, undergo nucleophilic addition at C₂ affording the corresponding 2-substituted N-ethoxycarbonylthiazolines.     

A numerical integration scheme for the evaluation of correlation energy functionals

A numerical integration scheme is presented for three-dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density-functional expression. The scheme is based on the choice of density-based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C₆₀ molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.     

Recurrence relations for the evaluation of electron repulsion integrals over spherical Gaussian functions

Recurrence relations are derived for the evaluation of two-electron repulsion integrals (ERIs) over Hermite and spherical Gaussian functions. Through such relations, a generic ERI or ERI derivative may be reduced to “basic” integrals, i.e., true and auxiliary integrals involving only zero angular momentum functions. Extensive use is made of differential operators, in particular, of the spherical tensor gradient ??(?). Spherical Gaussians, being nonseparable in the x, y, and z coordinates, were not included in previous formulations. The advantages of using spherical Gaussians instead of Cartesian or Hermite Gaussians are briefly discussed. © 1993 John Wiley & Sons, Inc.     

Synthesis, structure and reactivity of homobimetallic Rh(I) and Ir(I) complexes of s- and as-indacene-diide

The Rh(COD) and Ir(COD) homobimetallic complexes of s-indacene-diide, 2,6-dimethyl-s-indacene-diide, as-indacene-diide, and 2,7-dimethyl-as-indacene-diide have been synthesized from the di-lithium salts of the dianions and metal dimers [M(μ-Cl)L₂]₂ (M = Rh, Ir; L₂ = COD, NBD, (ethylene)₂, (CO)₂ as mixtures of syn and anti isomers. The syn/anti ratio depends on the nature of the ancillary ligands at the metal and on the s or as geometry of the bridging ligand. In the reaction of the 2,7-dimethyl-as-indacene-diide-[M(COD)]₂ species with CO, the higher reactivity of the syn isomers has been justified on the basis of a greater instability of the ground state due to steric interactions between the COD groups. Bis-η¹ metal-bonded intermediates have been identified in the carbonylation of iridium derivatives; on the other hand, the formation of the bis-η⁵ mixed complexes syn and anti-{2,7-dimethyl-as-indacene-diide-[Rh(COD)][Rh(CO)₂]} and their reactivity strongly support the existence of metal---metal interaction in the rhodium derivatives.