A new algorithm is presented for obtaining points on a steepest descent path from the transition state of the reactants and products. In mass‐weighted coordinates, this path corresponds to the intrinsic reaction coordinate. Points on the reaction path are found by constrained optimizations involving all internal degrees of freedom of the molecule. The points are optimized so that the segment of the reaction path between any two adjacent points is given by an arc of a circle, and so that the gradient at each point is tangent to the path. Only the transition vector and the energy gradients are needed to construct the path. The resulting path is continuous, differentiable and piecewise quadratic. In the limit of small step size, the present algorithm is shown to take a step with the correct tangent vector and curvature vector; hence, it is a second order algorithm. The method has been tested on the following reactions: HCN→CNH, SiH2+H2→SiH4, CH4+H→CH3+H2, F−+CH3F→FCH3+F−, and C2H5F→C2H4+HF. Reaction paths calculated with a step size of 0.4 a.u. are almost identical to those computed with a step size of 0.1 a.u. or smaller.

An improved algorithm for reaction path following

A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initioSCF–MO calculations.

Optimization of equilibrium geometries and transition structures

The method of natural localized molecular orbitals (NLMOs) is presented as a novel and efficient technique for obtaining LMOs for SCF and CI wave functions. It is an extension of the previously developed natural atomic orbital (NAO) and natural bond orbital (NBO) methods, and uses only the information contained in the one‐particle density matrix. Results are presented for methane and cytosine to indicate that NLMOs closely resemble LMOs obtained by the Boys and Edmiston–Ruedenberg methods, with the exception that the NLMO procedure automatically preserves the MO σ–π separation in planar molecules. The computation time is modest, generally only a small fraction of the SCF computation time. In addition, the derivation of NLMOs from NBOs gives direct insight into the nature of the LMO ‘‘delocalization tails,’’ thus enhancing the role of LMOs as a bridge between chemical intuition and molecular wave functions.

Natural localized molecular orbitals

We have carried out ab initio UHF/6-31G* calculations on the hydroxymethyl radical, CH 2 OH, and have found the equilibrium structure to be nearly planar with barriers to internal rotation occurring at staggered and eclipsed geometries, in good agreement with experiment. The electronic structure of the radical was analyzed via the “different hybrids for different spins” natural bond orbital (DHDS NBO) procedure, which finds separate Lewis structures for each of the spin systems. The α spin Lewis structure resembles that of the anion; the β spin Lewis structure resembles the corresponding cation. This simple picture, in conjunction with Bent's rule, allows one to understand the principal electronic factors which dictate the structure of the radical CH 2 group and its torsional and inversion potentials. Charge transfer between oxygen non-bonding orbitals and the empty radical orbital in the β spin system is the dominant interaction determining the torsional potential. Smaller hyperconjugative interactions in the α spin system resemble interactions in closed-shell molecules and directly oppose the effect of radical hyperconjugation, thus illustrating the central idea that open-shell potential energy features result from competition between the two different spin systems.

Analysis of the geometry of the hydroxymethyl radical by the “different hybrids for different spins” natural bond orbital procedure

Ammonia-borane and related compounds as dihydrogen sources.

Information theory can be used to evaluate the quality of a wave function by considering its ability to give values for some observables as close as possible to the experimental ones. A new method for improving the quality of a wave function is proposed. This paper deals exclusively with the HF (/b X//sup 1/ Sigma /sup +/) molecule.

Molecular properties and basis set quality: An approach based on information theory

Theoretical study of the azido-tetrazole isomerization

Hydrogen abstraction reactions with R, X≡H, CH3, NH2,OH, and F have been studied at the abinitio 6-31G – UHF level. However, energetic properties were computed at the CI level. Rate constants and A...

Étude théorique des réactions d'abstraction d'hydrogène, avec R, X≡H, CH3, NH2,OH et F

Recent Advances in the Quantum Theory of Polymers

In this work, the heats of formation of some small molecules containing one or more of the following groups. CH3, CF3, NH2, NHF, NF2, NO2, OH, F are studied. The calculations have been carried out theoretically, using the isodesmic procedure of Pople et al. In most cases, the thermal corrections were introduced using experimental (when available) or theoretical (at the SCF 6–31G level) vibrational frequencies. It was found that this correction is relatively negligible (compared to the accuracy of the heats of formation determined); nevertheless, the vibrational frequencies remain useful for determining the heat capacity and the entropy. We observe that the heats of formation, in families such as XCH3-nFn, XNH2-nFn, and CH4-nXn, are related by quasilinear relations (ΔHf ≈ a + bn). Finally, the NF2 and NO2 substituents have large and comparable destabilization effects on the heat of formation. All the other substituents are stabilizing; the importance of the stabilization effect depends on the number of fluorine atoms.

Georges Leroy

Papers

Molecular properties and basis set quality: An approach based on information theory

Theoretical study of the azido-tetrazole isomerization

Étude théorique des réactions d'abstraction d'hydrogène, avec R, X≡H, CH3, NH2,OH et F

Recent Advances in the Quantum Theory of Polymers

The theoretical study of the heats of formation of organic compounds containing the substituents CH3, CF3, NH2, NF2, NO2, OH and F