CEPA Methods Research Articles

Comparison of CEPA and CP-MET methods

Comparison of CEPA and CP-MET methods

Comparison of CEPA and CP-MET methods

The known CEPA variants CEPA (v) withv = 0,1,2,3 and two new ones withv = 4, 5 are compared both formally and for various numerical examples with CP-MET. The main conclusions are: 1. In those situations where both CP-MET and the CEPA variants are justified (i.e. for “good” closed shell states) the correlation energies obtained with the 7 different schemes differ very little (by something like ±2%), with CEPA (1) closest to CP-MET (difference usually a fraction of 1%) and CEPA (4) nearly as close; this is rather insensitive to whether one uses canonical or localized orbitals. Even CEPA (3) is not too far from CP-MET, which confirms an earlier suggestion of Kelly. 2. In those cases where one of the 7 schemes fails (e.g. due to near degeneracy as in covalent molecules at large internuclear distances) the other 6 usually fail as well, though CEPA (0) is then somewhat poorer than the other schemes. Then no longer CEPA (1) but rather CEPA (3) is closest to CP-MET and then all schemes converge much better in a localized representation. 3. CEPA (2) usually leads to best agreement with experiment since it simulates to some extent triple substitutions. In none of the studied examples does CP-MET show a significant superiority as compared to the other schemes. Possible improvements to extend the domain of applicability of these methods are discussed.

ChemInform Abstract: AB INITIO CALCULATIONS OF THE POTENTIAL ENERGY SURFACE OF THE REACTION OF SINGLET METHYLENE WITH THE HYDROGEN MOLECULE

The potential energy surface for the insertion of singlet methylene into H2 has been computed on theab initio SCF level as well as with inclusion of electron correlation by means of the CEPA method. The results are compared with those of previous semiempirical,ab initio SCF and CI calculations. The system is a prototype of a reaction where an allowed and a symmetry-forbidden path can compete. The electron correlation energy was found to be very different for different regions of the surface, but did not have much influence on the optimum reaction path. From the computed heat of the reaction, the heat of formation of singlet methylene was estimated to be 101.5 kcal/mol. According to the calculations the reaction does not need any activation energy.

Generalized k-particle brillouin conditions and their use for the construction of correlated electronic wavefunctions

The variational form of the Schrödinger equation is shown to be equivalent to a set of generalized Brillouin conditions in terms of arbitrary antihermitean operators R. For a special choice of these R in second-quantization language, k-particle Brillouin conditions are derived that are a generalization of the “generalized one-particle Brillouin conditions” of Levy and Berthier. The application of these conditions to one-particle and two-particle hamiltonians is discussed. A two-particle generalization of the Fock operator is derived and an iterative variational pair-cluster scheme is derived. It is shown that CEPA and SCEP methods satisfy an approximate rather than an exact set of Brilouin conditions.

Ab initio Calculations of the potential energy surface of the reaction of singlet methylene with the hydrogen molecule

The potential energy surface for the insertion of singlet methylene into H2 has been computed on theab initio SCF level as well as with inclusion of electron correlation by means of the CEPA method. The results are compared with those of previous semiempirical,ab initio SCF and CI calculations. The system is a prototype of a reaction where an allowed and a symmetry-forbidden path can compete. The electron correlation energy was found to be very different for different regions of the surface, but did not have much influence on the optimum reaction path. From the computed heat of the reaction, the heat of formation of singlet methylene was estimated to be 101.5 kcal/mol. According to the calculations the reaction does not need any activation energy.

A PNO-CI and CEPA investigation of unstable boron-nitrogen and boron-oxygen compounds

The PNO-CI and CEPA methods have been applied to the calculation of spectroscopic properties (equilibrium geometries, force constants, vibrational freq