π-Bonding and the Lone Pair Effect in Multiple Bonds between Heavier Main Group Elements

An Introduction to Coupled Cluster Theory for Computational Chemists

The fully relaxed single-bond torsional potentials in typical conjugated systems were evaluated with the aid of ab initio self-consistent-field and Moller−Plesset second-order calculations and, additionally, with several recently developed variants of the density functional theory. For this systematic investigation, 1,3-butadiene, styrene, biphenyl, 2,2‘-bithiophene, 2,2‘-bipyrrole and 2,2‘-bifuran have been selected as model molecules. As representative examples for nonconjugated systems, the molecules n-butane and 1-butene have been treated at the very same calculational levels. For all conjugated molecules, the electron correlation corrections to the self-consistent-field torsional potentials, as obtained with the density functional methods, are dramatically different from those resulting from the more conventional Moller−Plesset second-order approximation. For those cases where experimental data for torsional barriers are available, the self-consistent-field and the Moller−Plesset second-order results...

Single-Bond Torsional Potentials in Conjugated Systems: A Comparison of ab Initio and Density Functional Results

We describe an alternative procedure for obtaining approximate Brueckner orbitals in ab initio electronic structure theory. Whereas approximate Brueckner orbitals have traditionally been obtained by mixing the orbitals until the coefficients of singly substituted determinants in the many-electron wave function become zero, we remove singly substituted determinants at the outset and obtain orbitals which minimize the total electronic energy. Such orbitals may be described as variational Brueckner orbitals. These two procedures yield the same set of exact Brueckner orbitals in the full configuration interaction limit but differ for truncated wave functions. We consider the simplest variant of this approach in the context of coupled-cluster theory, optimizing orbitals for the coupled-cluster doubles (CCD) model. An efficient new method is presented for solving the coupled equations defining the energy, doubles amplitudes, and orbital mixing parameters. Results for several small molecules indicate nearly identical performance between the traditional Brueckner CCD method and the variational Brueckner orbital CCD approach. However, variational Brueckner orbitals offer certain advantages: they simplify analytic gradients by removing the need to solve the coupled-perturbed Brueckner coupled-cluster equations for the orbital response, and their straightforward extensions for inactive orbitals suggests possible uses in size-extensive models of nondynamical electron correlation. Application to O4+ demonstrates the utility of variational Brueckner orbitals in symmetry breaking cases.

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Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O4+

Twelve organic reactions (six closed shell and six radical) were studied using semiempirical, traditional ab initio and density functional methodologies. Full geometry optimizations of all species, both minima and transition states, were performed, and calculated geometries and barrier heights compared with experimental data. Our results demonstrate that although currently available density functionals tend to underestimate barrier heights, especially for radical reactions—in some cases reactions with low barriers are predicted to be essentially barrier free—they provide a significant improvement over standard methods. The adiabatic connection method recently proposed by Becke [J. Chem. Phys. 98, 5648 (1993)], in which a portion of the exact Hartree–Fock exchange is mixed in to the density functional, looks very promising.

Ian L. Alberts

Papers

Use of the molecular orbital Hessian for self-consistent-field (SCF) wavefunctions

The second stable conformer of 1,3-butadiene. Geometry optimizations with configuration interaction and coupled cluster methods

The boron—carbon triple bond (B̄C): Some theoretical predictions