CBS-4 method

We will consider several of these multi-job models in Chapter 7, including Gaussian-1 and Gaussian-2 theory and their variants and several Complete Basis Set (CBS) methods. 

A variety of compound methods have been developed in an attempt to accurately model the thermochemical quantities we have been considering. These method-s attempt to achieve high accuracy by combining the results of several different calculations as an approximation to a single, very high level computation which is much too expensive to be practical. We will consider two families of methods the Gaussian-n methods and the Complete Basis Set (CBS) methods. 

The Complete Basis Set (CBS) methods were developed by George Petersson and several collaborators. The family name reflects the fundamental observation underlying these methods the largest errors in ab initio thermochemical calculations result from basis set truncation. 

There are other defined CBS methods, including the very accurate and very expensive CBS-APNO, but we will be focusing on CBS-4 and CBS-Q. 

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 main difference between the G1/G2 and CBS methods is the way in which they try to extrapolate the correlation energy, as described below. Both tire G1/G2 and CBS methods come in different flavours, depending on the exact combinations of metliods used for obtaining the above four contributions. 

There are several different CBS methods, each having its own set of prescriptions and resulting computational cost and accuracy, they are known under the acronyms CBS-4, CBS-q, CBS-Q and CBS-APNO. As an explicit example, we will take the CBS-Q model, " which is computationally similar to the G2(MP2) method. 

Petersson et al. had earlier proposed [23] an alternative expression E(n) = Eoo + ]CiSn+i A/(l + 1/2)6 in the context of the CBS methods developed in his group. The summation is carried out numerically in that paper, but in fact an elegant analytical approximation exists for... 

The barriers for this reaction calculated for a range of higher-level procedures (Table 6.22) [49] show that the CBS methods agree well with experiment while their G2 counterparts generally overestimate the... 

The CBS methods of Petersson and coworkers (22,25,25-30) extrapolate the basis set and add empirical terms to extrapolate to experiment. Two especially powerful versions of the CBS approach are CBS-4 (30) and CBS-Q (30). For CBS-Q, the empirical terms are based on the overlap matrix and the spin contamination (which arises in some partial treatments of the electron correlation). CBS-4 also includes these terms plus a term based on the number of electrons in the system. 

A chloroform-water mixture is the extraction solvent for the contaminants branch (CB) method, proposed by Eppley (36). The CB method has been adopted by the Association of Official Analytical Chemists as the official method for determination of aflatoxins in groundnuts and their byproducts (17). 

M Carvajal, F Mulholland, RC Garner. Comparison of the EASI-EXTRACT immunoaffinity concentration procedure with the AOAC CB method for the extraction and quantitation of aflatoxin B, in raw ground unshelled. J Chrom 511 379-383, 1990. 

Scheme 11.1 also summarizes other impressive examples of the performance of the CBS method [1-8]. Several excellent reviews on the CBS method have appeared recently [1, 2], and no detailed discussion of the development of the process or substrate scope shall be presented in this review. Please note, however, that the oxazaborolidine-catalyzed borane reduction of ketones is a prime example of bi-functional catalysis [2, 9] - as shown in Scheme 11.2, the current mechanistic picture involves simultaneous binding of both the ketone and the borane to the Lewis-acidic (boron) and Lewis-basic (nitrogen) sites of the catalyst A. In the resulting ternary complex B, the reaction partners are synergistically activated toward hydride transfer. 

Complete Basis Set Methods Petersson et al.61-63 developed a series of methods, referred to as complete basis set (CBS) methods, for the evaluation of accurate energies of molecular systems. The central idea in the CBS methods is an extrapolation procedure to determine the projected second-order (MP2) energy in the limit of a complete basis set. This extrapolation is performed pair by pair for all the valence electrons and is based on the asymptotic convergence properties of pair correlation energies for two-electron systems in a natural orbital expansion. As in G2 theory, the higher order correlation contributions are evaluated by a sequence of calculations with a variety of basis sets. 

Several empirical corrections are added to the resulting energies in the CBS methods to remove the systematic errors in the calculations (see Table 10). The CBS-Q method contains a two-electron correction term similar in spirit to the higher level correction used in G2 theory, a spin correction term to account for errors resulting from spin contamination in UHF wavefunctions for open-shell systems, and a correction to the sodium atom to account for core-valence correlation effects. The CBS-4 and CBS-q methods also contain a one-electron... 

The CBS methods are available as keywords in the Gaussian program. The CBS-Q, CBS-q, and CBS-4 methods are incorporated in Gaussian 9475 and later versions. The CBS-QB3 method is available in Gaussian 98."... 

A geometry optimization (at the HF/3-21G1 1 or MP2/6-31G level, depending on the particular CBS method)... 

For some CBS methods, a QCISD(T) single-point calculation... 

Note, as with Gaussian methods, the semiempirical aspect of CBS methods. 

We will concentrate on Gaussian-type and CBS methods, because these have been the most widely-used and have thus accumulated an archive of results, are the most accessible, and because several versions of them are available. However, there are other high-accuracy multistep methods, such as the Weizmann procedures of Martin and de Oliveira, W1 and W2 [188], and of Boese et al., W3 and W4 [189], which like the CBS methods are based on basis set extrapolation. W1 and W2 have a mean absolute deviation of about 1 kJ mol 1 (not 1 kcal mol-1), and incorporate relativistic effects, and W2 has no empirical parameters, unlike the Gaussian and CBS methods. W3 and W4 methods have similar errors to W1 and W2, and the authors speculate on the reasons for the obstinate 0.1 kcal/mol barrier . These very accurate methods are still limited molecules of about or less than the reach of CBS-APNO. 

Of the Gaussian-type and CBS methods, for high accuracy on very small molecules CBS-APNO is the appropriate choice, and for large molecules the choice falls on CBS-4M with the acceptance of the possibility of moderately large errors. For intermediate size molecules the best choice is probably between G3 (MP2) and CBS-QB3. Recall that G3(MP2) is much faster than G3, with little loss of accuracy in most cases note too that G4(MP2) will compete with and when widely... 

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