Hartree-Fock Potential Energy Surface Calculations

Hartree-Fock Potential Energy Surface Calculations Asymptotic Behaviour of Single Determinantal Wavefunctions.—In general, a single determinantal wavefunction, whether or not it is at the Hartree-Fock limit, does not provide an adequate description of a molecular system over the complete range of intemuclear separations, because of the failure of such a function to describe... 

Several basis sets were examined in order to select the most convenient and best fitted set for high-quality calculations. The Hartree-Fock (HF) 3-21 -I- G(d) calculation reasonably represents a potential-energy surface calculated at the MP2/6-311-I--I- G(2df,2pd) level. A full-dimensional ab initio potential-energy surface including all degrees of freedom was used in a ab initio dynamics calculation at the HF/3-21 - -G(d) level. Such dynamics calculations were further pursued in a later paper. A functional representation of the potential-energy surface for the reaction has been discussed and the study extended to the reaction... 

A theoretical study based on PM3 frontier molecular orbital (FMO) and potential energy surface (PES) analysis at the restricted Hartree-Fock (RHF)/6-31+G level was performed to examine the reaction of l-amino-2-ethoxycarbonyl-pyridinium mesitylenesulfonate and acrylonitrile in the presence of Hilnig s base leading to the formation of l,2-dihydropyrido[l,2-A]pyridazinium inner salt 17 <1999JOC9001>. The calculations indicated that both the [3+2] cycloaddition reaction and the ring expansion occurred in a concerted manner rather than through a stepwise mechanism via a zwitterionic intermediate 16 (Scheme 1). 

The presence or absence of a homoaromatic interaction is often based solely on the distance between the non-bonded atoms. Distances greatly over 2.0 A are thought to lead to a p-p overlap that is too small to make any significant contribution. This simplistic approach is not necessarily reliable as shown by Cremer et al. (1991). Their calculations on the homotropylium cation [12] indicate a double-minimum potential energy surface with respect to variations of the C(l)-C(7) distance at the Hartree-Fock level of theory. At the MP4(SDQ) level of theory, only a single-minimum curve was found with the minimum at 2.03 A. The calculated potential energy curves are quite flat in this region. 

The great speed and known properties of RHF calculations are not sufficient justification for a limitation to RHF methods when they are inherently inappropriate. It is worth remarking that most potential-energy surfaces describing reactions, and many describing dissociations are inappropriate for RHF methods. Restricted Hartree-Fock methods are also of limited validity in many situations where two or more surfaces are at nearly the same energy. 

A somewhat modified MO LCAO scheme, without restriction on the identity of spin orbitals (p and

unrestricted Hartree-Fock (UHF) method and is usually used to treat open-shell systems (free radicals, triplet states, etc.). Electron correlation is partially taken into account in this method, and therfore it can be expected to be more efficient than the RHF method when applied to calculate potential energy surfaces of chemical rearrangements whose intermediate or final stages may involve the formation of free- or bi-radical structures. The potentialities of the UHF method are now under active study in organic reaction calculations. Also, it is successfully coming into use in chemisorption computations (6). 

The equilibrium geometries of Cp2M (M = Yb, Eu, Sm) were studied by ab initio pseudopotential calculations at the Hartree-Fock (HF), MP2 and CSID levels. In the Hartree-Fock calculations [118] all the metallocenes favoured regular sandwich-type equilibrium structures with increasingly shallow potential energy surfaces for the bending motions along the series, M = Ca, Yb, Sr, Eu, Sm, and Ba. 

However, it should be emphasized that use of these less rigorous methods for the calculation of potential-energy surfaces should be viewed with great caution. Even for a system which dissociates properly in the Hartree-Fock approximation, recent research by Kaufman and co-workers [142] has shown that even the INDO method is not capable of giving an accurate or even realistic surface for Li+ + H2 when compared point by point to Lester s accurate Hartree-Fock surface [117]. 

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