Correlation energy atomic

MP2 correlation energy calculations may increase the computational lime because a tw o-electron integral Iran sfonnalion from atomic orbitals (.40 s) to molecular orbitals (MO s) is ret]uired. HyperClicrn rnayalso need additional main memory arul/orcxtra disk space to store the two-eleetron integrals of the MO s. 

Size-extensivity is of importance when one wishes to compare several similar systems with different numbers of atoms (i.e., methanol, ethanol, etc.). In all cases, the amount of correlation energy will increase as the number of atoms increases. However, methods that are not size-extensive will give less correlation energy for the larger system when considered in proportion to the number of electrons. Size-extensive methods should be used in order to compare the results of calculations on different-size systems. Methods can be approximately size-extensive. The size-extensivity and size-consistency of various methods are summarized in Table 26.1. 

Electron correlation. Electrons in an atom or molecule do not move entirely independently of each other but their movements are correlated. The associated correlation energy is often neglected in SCF calculations. 

Petersson and coworkers have extended this two-electron formulation of asymptotic convergence to many-electron atoms. They note that the second-order MoUer-Plesset correlation energy for a many-electron system may be written as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons ... 

The most difficult part in calculating absolute stabilities (heat of formation) is the correlation energy. For calculating energies relative to isolated atoms, the goal of tire... 

We have used the basis set of the Linear-Muffin-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed the Vosko-Wilk-Nusair parametrization for the exchange-correlation energy density and potential. In conjunction with this we have treated the alloying effects for random and partially ordered phases with a multisublattice generalization of the coherent potential approximation (CPA). 

In molecular applications the calculation of the HF energy is a still more difficult problem. It should be observed that, in the SCF-MO-LCAO now commonly in use, one does not determine the exact HF functions but only the best approximation to these functions obtainable within the framework given by the ordinarily occupied AO s. Since the set of these atomic orbitals is usually very far from being complete, the approximation may come out rather poor, and the correlation energy estimated from such a calculation may then turn out to be much too large in absolute order of magnitude. The best calculation so far is perhaps Coulson s treatment of... 

It should be observed that the subscript exact here refers to the lowest eigenvalue of the unrelativistic Hamiltonian the energy is here expressed in the unit Aci 00(l+m/Mz) 1 and Z is the atomic number. If the HE energies are taken from Green et al.,8 we get the correlation energies listed in the first column of Table I expressed in electron volts. The slow variation of this quantity is noticeable and may only partly be understood by means of perturbation theory. 

Arai, T., and Onishi, T., J. Chem. Phys. 26, 70, Correlation energies in atoms and electron affinities. Survey of two- three-and four-electron systems of atoms and ions. 

Table 13-8. Self-interaction error components for Coulomb and exchange energies (Ej + Ex) as well as for the correlation energy (Ec), and the resulting sum for the H atom, the H2 molecule, and the H3 transition structure [kcal/mol]. Data taken from Csonka and Johnson, 1998.

Levy, M., S. C. Clement, and Y. Tal. 1981. Correlation Energies from Hartree-Fock Electrostatic Potentials at Nuclei and Generation of Electrostatic Potentials from Asymptotic and Zero-Order Information. In Chemical Applications of Atomic and Molecular Electrostatic Potentials, P. Politzer, and D. G. Truhlar, Eds. Plenum Press, New York. 

Weighted-Density Exchange and Local-Density Coulomb Correlation Energy Functionals for Finite Systems—Applications to Atoms. Phys. Rev. A 48, 4197. 

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