CCSD theory computational considerations

The parent azine systems discussed in this chapter, compounds 1-4, have not been prepared experimentally, but there has been continuing interest in their theoretical analysis. The past 10 years have seen the incorporation of computational chemistry into the mainstream of chemical research, facilitated by the advancement of computer hardware, and computational software and methods. Hence, not surprisingly, recent studies have been performed using advanced methods, such as MP2, CCSD, and a considerable number of density functional theory (DFT) calculations. Azines have been investigated in terms of structural features, aromaticity, kinetic and thermodynamic stability, and decomposition reactions. 

One of the simplest chemical reactions involving a barrier, H2 + H —> [H—H—H] —> II + H2, has been investigated in some detail in a number of publications. The theoretical description of this hydrogen abstraction sequence turns out to be quite involved for post-Hartree-Fock methods and is anything but a trivial task for density functional theory approaches. Table 13-7 shows results reported by Johnson et al., 1994, and Csonka and Johnson, 1998, for computed classical barrier heights (without consideration of zero-point vibrational corrections or tunneling effects) obtained with various methods. The CCSD(T) result of 9.9 kcal/mol is probably very accurate and serves as a reference (the experimental barrier, which of course includes zero-point energy contributions, amounts to 9.7 kcal/mol). 

All of the levels of theory listed in Table 1.1 predict the C-H bond length with accuracy within 1 %. One piece of cheering information from Table 1.1 is that the DFT method predicts this bond length as accurately as the much more computationally expensive CCSD approach. The error in the ionization energy predicted by HF is substantial, but all three of the other methods give better predictions. The higher levels of theory (MP2 and CCSD) give considerably more accurate results for this quantity than DFT. 

The selection rules for the QM harmonic oscillator pennit transitions only for An = 1 (see Section 14.5). As Eq. (9.47) indicates diat the energy separation between any two adjacent levels is always hm, the predicted frequency for die = 0 to n = 1 absorption (or indeed any allowed absorption) is simply v = o). So, in order to predict die stretching frequency within the harmonic oscillator equation, all diat is needed is the second derivative of the energy with respect to bond stretching computed at die equilibrium geometry, i.e., k. The importance of k has led to considerable effort to derive analytical expressions for second derivatives, and they are now available for HF, MP2, DFT, QCISD, CCSD, MCSCF and select other levels of theory, although they can be quite expensive at some of the more highly correlated levels of theoiy. 

Instead, practical methods involve a subset of possible Slater determinants, especially those in which two electrons are moved from the orbitals they occupy in the HF wavefunction into empty orbitals. These doubly excited determinants provide a description of the physical effect missing in HF theory, correlation between the motions of different electrons. Single and triple excitations are also included in some correlated ab initio methods. Different methods use different techniques to decide which determinants to include, and all these methods are computationally more expensive than HF theory, in some cases considerably more. Single-reference correlated methods start from the HF wavefunction and include various excited determinants. Important methods in inorganic chemistry include Mpller-Plesset perturbation theory (MP2), coupled cluster theory with single and double excitations (CCSD), and a modified form of CCSD that also accounts approximately for triple excitations, CCSD(T). 

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