Electron correlation energy Ecorr

Following Lowdin [7], we define the electron correlation energy, Ecorr, to be... 

Since the problem of correlated motion of the N electrons cannot be dealt with adequately by the Hartree-Fock method, even in the limit of an infinite basis set (i.e., B —> oo), it is expected that the ground-state electronic energy and estimation of the first few excited-state energy levels of even small molecules can be several electron volts away from thermodynamic or spectroscopic reality the difference Eexp—EHF is often called the correlation energy Ecorr ... 

After the computation of 4>hf became routinely feasible in the 1960s [4], much of the work in quantum computational chemistry has been devoted to the computation from first principles of the total energy, E, via the calculation of the correlation energy, Ecorr/ moving from systems with a few electrons to larger ones, with lighter or heavier atoms. In the latter case, relativistic effects make an increasingly important contribution. 

Electronic excitation is usually connected with an unpairing of electrons, which, as a rule of thumb, contributes 1 eV correlation energy change per pair. Furthermore, even the usual definition of the correlation energy (Ecorr = Eexact — Ehf) IS not unambiguous for excited states because a HE self-consistent field (SCF) description (which is used as uncorrelated reference) is rarely possible. Because the degree of sophistication of the theoretical treatment that can be performed is usually limited, it is important to know which main factors influence the magnitude of the electron-correlation contributions. 

The next step in a generalization of the independent electron-pair correlation is to include the interpair correlation contributions as well. The recipe of the general independent electron-pair approximation (lEPA) is hence to calculate independently the correlation-energy contributions Ecorr for any pair of spin orbitals, i. e. the correlation energy accounted for by the wave function... 

The lack of correlation is the actual source of aU errors. In particular, a Slater determinant incorporates exchange correlation, i.e., the motion of two electrons with parallel spins is correlated (the so-called Fermi correlation). Unfortunately, the motion of electrons with opposite spins remains uncorrelated. It is common to define correlation energy, corr> as the difference between the exact nonrelativistic energy of the system, eo, and the Hartree-Fock energy, Eo, obtained in the limit that the basis set approaches completeness Ecorr = fo - o- The simplest manner to understand the inclusion of the correlation effects is through the method of configuration interaction (Cl). The basic idea is to diagonalize the N-electron Hamiltonian in a basis of N-electron functions we represent the exact wave function as a linear combination of N-electron trial functions and use the linear variational method. 

To avoid confusion, it should be stressed that telectron correlation energy as used in this paper stands for improvement of e-e interaction term contribution beyond the Hartree-Fock (HF) level, Ecorr = Eexact EHF Eexact < Ehf)< s it can be calculated e.g. by (l/r)-perturbation theory in 2" and higher orders, or by configurations interaction method. In condensed matter physics, electron correlation usually stands for an account for Coulomb e-e interaction at least on Hartree or HF level. On the HF level not only repulsive e-e term is present (like on Hartree level where spin... 

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