CCSD

Figure B3.1.9 [83] displays the errors (in pieometres eompared to experimental findings) in the equilibrium bond lengths for a series of 28 moleeules obtained at the FIF, MP2-4, CCSD, CCSD(T), and CISD levels of theory using three polarized eorrelation-eonsistent basis sets (valenee DZ tlu-ough to QZ).

Clearly, the HF method, independent of basis, systematically underestimates the bond lengdis over a broad percentage range. The CISD method is neither systematic nor narrowly distributed in its errors, but the MP2 and MP4 (but not MP3) methods are reasonably accurate and have narrow error distributions if valence TZ or QZ bases are used. The CCSD(T), but not the CCSD, method can be quite reliable if valence TZ or QZ bases are used. 

Coupled cluster calculations are similar to conhguration interaction calculations in that the wave function is a linear combination of many determinants. However, the means for choosing the determinants in a coupled cluster calculation is more complex than the choice of determinants in a Cl. Like Cl, there are various orders of the CC expansion, called CCSD, CCSDT, and so on. A calculation denoted CCSD(T) is one in which the triple excitations are included perturbatively rather than exactly. 

Coupled cluster calculations give variational energies as long as the excitations are included successively. Thus, CCSD is variational, but CCD is not. CCD still tends to be a bit more accurate than CID. 

Another technique, called Brueckner doubles, uses orbitals optimized to make single excitation contributions zero and then includes double excitations. This is essentially equivalent to CCSD in terms of both accuracy and CPU time. 

CCSD/aug—cc—pVQZ Atomization energy 7 kcal/mol mean abs. dev. 

Coupled Cluster methods, including doubles (energies and optimizations) or singles and doubles (energies only), and optional triples terms (CCD, CCSD, CCSD(T)). 

Including triply excited configurations is often needed in order to obtain very accurate results with MP4, QCISD or CCSD (see Appendix A for some of the computational details). The following example illustrates this effect. 

The very large basis set we used does not enable either the HF or MP2 method to predict an accurate structure for FOOF. CCSD does pretty well using only the 6-31G(d) basis set and produces a structure in excellent agreement with experiment with the larger basis set. 

The QCISD method is also very closely related to coupled cluster theory, with singles and doubles (CCSD). In contrast to QCISD. 

CBS extrapolation 155, 278 CBS methods 10, 96, 155 cost vs. G2 methods 159 CBS-4 method 155 CBS-Q method 155 CCSD keywords 114 CH bond dissociation 186 charge xxxv, xlii, 15, 286 predicted atomic li charge distribution 20 Cheeseman 53 chlorine (atomic) 137, 159 chlorobenzene 165 chromium hexacarbonyl 52 Cioslowski 198 CIS keyword... 

The concept has been generalized in the ONIOM method to include several layers, for example using high level ab initio (e.g. CCSD(T)) in the central part, lower-level electronic structure theory (e.g. MP2) in an intermediate layer and a force field to treat the outer layer. 

The CCSD energy is given by the general CC equation (4.53), and amplitude equations are derived by multiplying (4.50) with a singly excited determinant and integrating (analogously to eq. (4.54)). 

Since the singly excited determinants effectively relax the orbitals in a CCSD calculation, non-canonical HF orbitals can also be used in coupled cluster methods. This allows for example the use of open-shell singlet states (which require two Slater determinants) as reference for a coupled cluster calculation. 

It has later been shown that the resulting equations are identical to CCSD where some of the terms have been omitted. The omitted terms are computationally inexpensive, and there appears to be no reason for using the less complete QCISD over CCSD (or QCISD(T) in place of CCSD(T)), although in practice they normally give very similar results. There are a few other methods which may be considered either as CISD with addition of extra terms to make them approximately size extensive, or as approximate versions of CCSD. Some of the methods falling into this category are Averaged... 

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