Dynamic electron correlation energy

For example, the quality of a large-scale Cl calculation also depends on the choice of expansion CSFs, but this choice, which is dictated by the need to calculate quantitatively the dynamical electron correlation energy, is much different from that of a typical modern MCSCF calculation, which is more concerned with near-degeneracy, avoided-crossing and spin-recoupling effects. 

The CCS, CC2, CCSD, CC3 hierarchy has been designed specially for the calculation of frequency-dependent properties. In this hierarchy, a systematic improvement in the description of the dynamic electron correlation is obtained at each level. For example, comparing CCS, CC2, CCSD, CC3 with FCI singlet and triplet excitation energies showed that the errors decreased by about a factor 3 at each level in the coupled cluster hierarchy [18]. The CC3 error was as small as 0.016 eV and the accuracy of the CC3 excitation energies was comparable to the one of the CCSDT model [18]. 

This chapter begins with a discussion of how to include non-dynamical and dynamical electron correlation into the wave function using a variety of methods. Because the mathematics associated with correlation techniques can be extraordinarily opaque, the discussion is deliberately restricted for the most part to a qualitative level an exception is Section 7.4.1, where many details of perturbation theory are laid out - those wishing to dispense with those details can skip this subsection without missing too much. Practical issues associated with the employ of particular techniques are discussed subsequently. At the end of the chapter, some of the most modem recipes for accurately and efficiently estimating the exact correlation energy are described, and a particular case study is provided. 

Insofar as the latter process docs not involve any orbital reoptimization for any particular state, it provides a wave function that is roughly equivalent in quality only to an HF wave function for the ground state. Of course, this may still be useful for a number of purposes. CIS results for six excited states of benzene are included in Table 14.2, as are results from other levels of theory that will be discussed later. The CIS results are qualitatively useful, insofar as the states are correctly ordered, and the error is fairly systematic - all states are predicted to be too high in energy by an average of 0.7 eV. The worst prediction is for the lowest excited state, which is known to have significant dynamical electron correlation, and is therefore challenging for the CIS method. 

To improve the relative energies, a single-point perturbational calculation was done on both species to correct for dynamical electron correlation. CASPT2N was not available, and the CAS-MP2 method used here, with the 6-31G basis, can lead to suspect results [67]. Nevertheless, the values obtained for these two species seem reasonable ... 

The term "electron correlation energy" is usually defined as the difference between the exact nonrelativistic energy and the energy provided by the simplest MO wave function, the mono-determinantal Hartree-Fock wave function. This latter model is based on the "independent particle" approximation, according to which each electron moves in an average potential provided by the other electrons [14]. Within this definition, it is customary to distinguish between non dynamical and dynamical electron correlation. 

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