CBS extrapolation

CBS models typically include a Hartree-Fock calculation with a very large basis set, an MP2 calculation with a medium-sized basis set (and this is also the level where the CBS extrapolation is performed), and one or more higher-level calculations with a medium-to-modest basis set. The following table outlines the components of the CBS-4 and CBS-Q model chemistries ... 

CBS-4 is the less expensive of these two methods. It begins with a FlF/3-21G(d) geometry optimization the zero-point energy is computed at the same level. It then uses a large basis set SCF calculation as a base energy, and an MP2/6-31+Gt calculation with a CBS extrapolation to correct the energy through second order. A... 

Remember that the CBS models begin with a large enough SCF calculation to obtain the desired level of accuracy (see Chapter 7) therefore, no explicit extrapolation of the SCF energy is included. CBS extrapolation involves computing the second-order and infinite-order corrections to the energy. 

The parameter 8,y serves to retain size consistency in the CBS extrapolation for finite values of N. Full Cl pair energies, (N), may be obtained from the... 

Because the interelectronic cusp is difficult to describe well with one-electron basis functions, pair correlation energies converge much more slowly (as N" ) than SCF energies (which converge as f ). This fact makes the use of CBS extrapolations of the correlation energy very beneficial in terms of both accuracy and computational cost. 

CBS extrapolation is illustrated in the following figure which depicts the extrapolation for the helium atom ... 

Consult the works listed in the references for a full discussion of CBS extrapolation. 

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... 

We have recently employed the Dunning correlation-consistent basis sets for our pair natural orbital CBS extrapolation algorithm, Eqs. (2.1) and (2.2) [50]. The results produced a substantial improvement over the raw second-order energies, but were inferior to the (lmax + ) 3 extrapolations listed in Table 4.4. The residual underestimation of... 

Application of CBS extrapolations to the A5-ketosteroid isomerase-catalyzed conversion of A5-androstene-3,17-dione to the A4 isomer (Fig. 4.10) provides a test case for extensions to enzyme kinetics. This task requires integration of CBS extrapolations into multilayer ONIOM calculations [56, 57] of the steroid and the active site combined with a polarizable continuum model (PCM) treatment of bulk dielectric effects [58-60], The goal is to reliably predict absolute rates of enzyme-catalyzed reactions within an order of magnitude, in order to verify or disprove a proposed mechanism. 

Results of [14] have shown that for the test set of G2 [10] the mean absolute deviation of the CBS extrapolated atomization energies from the experimental ones is ca. 0.5 kcal/mole, whereas in the G2 theory itself the mean absolute deviation is 1.4 kcal/mole. However, in addition to the average deviation, the G2 theory contains also a systematic error, which does not appear in the CBS limit. Thus one may assume... 

Next the effect of basis set size is considered, i.e., potential uncertainty in the CBS extrapolation. For reaction (7) there is little difference (0.3 kJmol ) between TZ and QZ reaction energies, while this difference is 3.6 kJmol for reaction (8). Because AE is already close to the convergence limit and is extrapolated by only 0.3 and 2.6 kJ mol , respectively, the CBS extrapolation introduces little uncertainty, less than 0.2 kJ mol . For reaction (10) the AE results are already converged before extrapolation (see Table 9.2). 

Currently, the recommended formula of ccCA utilizes separate HE and MP2 CBS extrapolations, though the necessity of separate extrapolations is still debated [2,65, 66]. The CBS limit of the HE energy is calculated using the formula. 

The value of C is 1.63 and comes from a study by Halkier and coauthors, where an optimal value for two-point HE CBS extrapolations using triple-zeta and quadruple-zeta basis sets was based on comparison to numerical HE energies [67]. Using this value, HE energies for a test set of nine diatomics were within 1 mEh of the numerical HE limits. The (l//max) CBS fit of Schwartz is expressed as... 

The basis sets most commonly used for CBS extrapolations are the correlation consistent (cc) basis sets such as cc-pVnZ and aug-cc-pVnZ (Section 15.4). Eor a review of basis sets, see F. Jensen, WIREs Comput. Mol. Sci. 2012, doi 10.1002/wcms.ll23. 

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