Peter Pulay

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The general expression for the exact forces on the nuclei (negative derivatives of the total energy with respect to the nuclear coordinates) is applied for Hartree-Fock wavefunctions. It is suggested that force constants should be calculated by differentiating the forces numerically. This method, called the force method, is numerically more accurate and requires less computation than the customary one of differentiating the energy numerically twice. It permits the quick determination of the equilibrium geometry by relaxing the nuclear coordinates until the forces vanish. The unreliability of the methods using the Hellmann-Feynman forces is re-emphasized. The question of which force constants can be best calculated ab initio is discussed.

Convergence acceleration of iterative sequences. the case of scf iteration

Abstract Based on a recent method of Pople et al for the solution of large systems of linear equations, a procedure is given for accelerating the convergence of slowly converging quasi-Newton— Raphson type algorithms. This procedure is particularly advantageous if the number of parameters is so large that the calculation and storage of the hessian is no longer practical. Application to the SCF problem is treated in detail.

Can (semi)local density functional theory account for the London dispersion forces

Abstract The reproduction of the interatomic potential in He 2 , Ne 2 , and Ar 2 by Kohn-Sham theory is investigated using a density functional program which can perform counterpoise corrections for both basis sets and numerical integration. None of the functionals considered accounts successfully for the dispersion interaction. The Becke exchange and the Becke-Lee-Yang-Parr (B-LYP) exchange-correlation functionals yield a purely repulsive potential after counterpoise correction. The Dirac-Slater (D-S) functional gives minima which are too deep, at internuclear distances which are too short, particularly for He 2 and Ne 2 . The experimental repulsive potential is reproduced best by D-S calculations while the B-LYP results are close to the SCF ones.

Localizability of dynamic electron correlation

Abstract The convergence of the intrapair correlation energy for a localized internal orbital is investigated as the virtual subspace is enlarged. At variance with previous investigations of this kind, the virtual subspace is represented in atomic orbitals. This allows to define spatial relations between the orbitals involved. Typically, over 98% of the pair correlation energy is recovered by a small local basis set, consisting of the valence orbitals of the atoms with which the electron pair is associated. This opens the possibility of an efficient Cl procedure based on localized pairs.

Orbital-invariant formulation and second-order gradient evaluation in MOller-Plesset perturbation theory

Based on the Hylleraas functional form, the second and third orders of Møller-Plesset perturbation theory are reformulated in terms of arbitrary (e.g., localized) internal orbitals, and atomic orbitals in the virtual space. The results are strictly equivalent to the canonical formulation if no further approximations are introduced. The new formalism permits the extension of the local correlation method to Møller-Plesset theory. It also facilitates the treatment of weak pairs at a lower (e.g., second order) level of theory in CI and coupled cluster methods. Based on our formalism, an MP2 gradient algorithm is outlined which does not require the storage of derivative integrals, integrals with three external MO indices, and, using the method of Handy and Schaefer, the repeated solution of the coupled-perturbed SCF equations.

Geometry optimization by direct inversion in the iterative subspace

Abstract A version of the direct inversion in the iterative subspace (DIIS) algorithm (ref.8) adopted to geometry optimization is presented. Comparison with the most widely used variable metric methods indicate that this novel technique is very efficient.

Fourth‐order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method

Fourth‐order Mo/ller–Plesset perturbation theory (MP4) is formulated for localized internal orbitals of closed‐shell systems. Unlike previous localized perturbation theories, our formulation is strictly identical with canonical MP4 theory if no further approximations are made. In the local treatment, large savings can be achieved by two techniques: (1) neglecting or treating at a lower (second order) level pair correlation between distant pairs, and (2) restricting the correlation basis to the atomic orbitals in the spatial vicinity of the correlated pair. These techniques have been used in our previous local correlation treatment for variational CI, coupled electron pair (CEPA), and approximate coupled cluster (ACCD) wave functions. The MP4 method is more economical than these techniques because of the absence of iterative cycles. Implementation with single, double, and quadruple substitutions is discussed.

Local configuration interaction: An efficient approach for larger molecules

Abstract The first full implementation of the localized configuration interaction technique at the variational CI, CEPA-2 and variational CEPA levels is described. Timings are presented for a double-zeta plus polarization calculation on butadiene. The restriction of the correlation space to local basis functions results in a spectacular enhancement of the efficiency of the CI loop. The loss in the correlation energy is only a few percent; we argue that most of the loss is due to the exclusion of intramolecular basis set superposition artifacts.

Geometry optimization in redundant internal coordinates

The gradient geometry‐optimization procedure is reformulated in terms of redundant internal coordinates. By replacing the matrix inverse with the generalized inverse, the usual Newton–Raphson–type algorithms can be formulated in exactly the same way for redundant and nonredundant coordinates. Optimization in redundant coordinates is particularly useful for bridged polycyclic compounds and cage structures where it is difficult to define physically reasonable redundancy‐free internal coordinates. This procedure, already used for the geometry optimization of porphine, C20N4H14, is illustrated here at the ab initio self‐consistent‐field level for the four‐membered ring azetidine, for bicyclo[2.2.2]octane, and for the four‐ring system C16O2H22, the skeleton of taxol.

Comparison of the boys and Pipek-Mezey localizations in the local correlation approach and automatic virtual basis selection

Our implementation of Pipek–Mezey population localization is described. It is compared with other localization schemes and its use in the framework of the local correlation method is discussed. For such use, this localization is shown to be clearly superior to Boys in the case of physically well‐localized systems. Our current algorithm for selection of local virtual spaces is also described.