Contraction Schemes

Many basis sets are just identihed by the author s surname and the number of primitive functions. Some examples of this are the Huzinaga, Dunning, and Duijneveldt basis sets. For example, D95 and D95V are basis sets created by Dunning with nine s primitives and hve p primitives. The V implies one particular contraction scheme for the valence orbitals. Another example would be a basis set listed as Duijneveldt 13s8p . 

SBKJC VDZ Available for Li(4.v4/>) through Hg(7.v7/ 5d), this is a relativistic basis set created by Stevens and coworkers to replace all but the outermost electrons. The double-zeta valence contraction is designed to have an accuracy comparable to that of the 3—21G all-electron basis set. Hay-Wadt MB Available for K(5.v5/>) through Au(5.v6/ 5r/), this basis set contains the valence region with the outermost electrons and the previous shell of electrons. Elements beyond Kr are relativistic core potentials. This basis set uses a minimal valence contraction scheme. These sets are also given names starting with LA for Los Alamos, where they were developed. 

This section gives a listing of some basis sets and some notes on when each is used. The number of primitives is listed as a simplistic measure of basis set accuracy (bigger is always slower and usually more accurate). The contraction scheme is also important since it determines the basis set flexibility. Even two basis sets with the same number of primitives and the same contraction scheme are not completely equivalent since the numerical values of the exponents and contraction coefficients determine how well the basis describes the wave function. 

McLean Chandler VTZ Available for Na through Ar(12.v8/i) and 2s9p) with several contraction schemes. 

Basch Available for Sc through Cu(15.v8/ 5d) with several contraction schemes. The transition metal set yields slightly higher energy than Wachters set. 

Table 9.7 Dunning s [5s3p] contraction scheme for Huzinaga s (10s6p)...

All of the above basis sets are of the segmented contraction type. Modem contracted basis sets aimed at producing very accurate wave functions often employ a general contraction scheme. The ANO and cc basis sets below are of die general contraction type. 

In the oxidative Eschenmoser sulfide contraction (Scheme 11), thioamide 59 is oxidized by benzoyl peroxide to give either a symmetrical disulfide or the O-benzoate of the thiolactam-S-oxide. In any event, the once-nucleophilic thioamide sulfur atom is now forced to adopt the role of electrophile a reactivity umpolung has, in effect, been achieved.13 The nucleophilic enamide 65 attacks the sulfur atom leading to the formation of sulfur-bridged intermediate 66. The action of a phosphine or a phosphite thiophile on the putative episulfide then gives vinylogous amidine 67. 

Thermolysis of the pyrazoline 1037 in chlorobenzene gave (76TL2513) triazinotetrazole 1038, which on further heating decomposed to 1040 and 1039. The reaction occurred by sequential ring expansion and contraction (Scheme 195). 

While the acronym STO-3G is designed to be informative about the contraction scheme, it is appropriate to mention an older and more general notation that appears in much of the earlier literature, although it has mostly fallen out of use today. In that notation, the STO-3G H basis set would be denoted (3s)/[Is]. The material in parentheses indicates the number and type of primitive functions employed, and the material in brackets indicates the number and type of contracted functions. If first-row atoms are specified too, the notation for STO-3G would be (6s3p/3s)/[2slp/ls]. Thus, for instance, lithium would require 3 each (since it is STO-3G) of Is primitives, 2s primitives, and 2p primitives, so the total primitives are 6s3p, and the contraction schemes creates a single Is, 2s, and 2p set, so the contracted functions are... 

One feature of the Pople basis sets is that they use a so-called segmented contraction. This implies that the primitives used for one basis function are not used for another of the same angular momentum (e.g., no common primitives between the 2s and 3s basis functions for phosphorus). Such a contraction scheme is typical of older basis sets. Other segmented split-valence basis sets include the MIDI and MAXI basis sets of Huzinaga and co-workers, which are named MIDI-1, MIDI-2, etc., MAXI-1, MAXI-2, etc. and vary in the number of primitives used for different kinds of functions. 

Both of the above approaches employed a metal ion as a template about which the corrin cyclization was performed, but the nickel or cobalt ions could not subsequently be removed. In order to obtain metal-free corrins, a new route was therefore devised (67AG865) which employed the novel principle of sulfide contraction (Scheme 22). Thus the sodium salt of the precorrin (284) (Scheme 23) was transformed into the thiolactam (285), and loose complexation with zinc(II) ions caused cyclization to give (286), which was treated with benzoyl peroxide and acid to give the ring-expanded compound (287). Contraction with TFA/DMF gave the corrins (288) and (289), and the major of these (289) was desulfurized with triphenylphosphine and acid to give (288). Finally, demetallation with TFA gave the required metal-free corrin (290), a source for a whole variety of metal derivatives. 

In recent years a compromise has been found which presently dominates polyatomic calculations. Each function fj is expanded as a linear combination of gaussian orbitals (f is then called a contracted gaussian function). Since this is basically a numerical fitting procedure, various choices have been suggested for the contraction scheme. The most popular choices are presently Pople s approximations (15) to Slater orbitals and Dunning s approximations (16) to free atom Hartree-Fock orbitals. 

Dunning-type contractions are characterized by considerable flexibility in the valence part of the primitive space. Typically, the outermost primitive functions are not contracted at all, contraction being reserved for the inner parts of the valence orbitals and the core orbitals. The commonest contracted set of this type is probably the [4s 2p] contraction of the (9s 5p) set. Unfortunately, there are at least two such double zeta contraction schemes in use, as well as an erroneous one. Some care may be required to reproduce results asserted to be obtained with a Huzinaga-Dunning [4s 2p] basis . Because of the relatively flexible contraction scheme these basis sets usually perform well, especially when large primitive sets such as van Duijneveldt s (13s 8p) sets are used. However, it should be noted that such primitive sets are difficult to contract this way without significant loss of accuracy at the atomic SCF level, unless very large contracted sets are used. 

Valence basis set for Cs and Ba including the outermost 5s, 5p and 5d electrons. fcThe s and p valence basis sets were optimized for the contraction scheme 311. 

By choosing the contracting scheme, it is possible to determine the contracted gaussian functions which best approximate Slater functions,88 Hartree-Fock atomic orbitals,89-90 etc. It should be noted that the size and balance (revealed, for example, by the optimum ratio of the number of s-type and p-type functions) of the basis are definite factors which control the quality of the final result (e.g., ref. 90). 

Dithiins (151) are made by reaction of aldehydes with 1,3-dithiols. Treatment of these with suitable electrophilic oxidizing agents, e.g. Br2, forms 1,2-dithiolylium ions (4) by ring contraction (Scheme 27) (66AHC(7)39). The synthesis may be applied to ben-zodithiolylium ions as well. A synthesis of the dithiole antibiotic holomycin (Section 4.31.4) from a 1,3-dithiin is related in concept (77JOC2891). 

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