LDA variants

In Chapter 17 you saw epoxides acting as electrophiles in Sn2 reactions. They can be used to alkylate enolates providing epoxide opening is assisted by coordination to a Lewis acidic metal ion in this case the lanthanide yttrium(III). The new C-C bond in the product is coloured black. Note that the ketone starting material is unsymmetrical, but has protons only to one side of the carbonyl group, so there is no question over which enolate will form. The base is one of the LDA variants we showed you on p. 668—LHMDS. 

At the same time, the LDA gave an a posteriori justification of the old Xa method by Slater, because the latter is a special LDA variant without correlation. The corresponding spin-dependent version of the LDA is called a local spin-density approximation (LSDA or LSD or just spin-polarized LDA), and even now when people talk of LDA functionals, they always refer to its generalized form for systems with (potentially) unpaired spins. Among the most influential LDA parametrizations, the one of von Barth and Hedin (BH) [154] and the one of Vosko, Wilk and Nusair (VWN) [155] are certainly worth mentioning. The latter is based on the very accurate Monte Carlo-type calculations of Ceperley and Alder [156] for the uniform electron gas, as indicated above. 

Stork first demonstrated the utility of protected cyanohydrins as acyl anion equivalents in 1971 [2]. The acetal-protected cyanohydrin 8 was transformed into the corresponding anion with LDA in THF/HMPA, which was then alkylated with a range of alkyl halides, including secondary bromides (Scheme 2). A mild acidic hydrolysis yielded a cyanohydrin, which provided the ketone after treatment with base. The Stork cyanohydrin alkylation and its variants have become important methods in natural product synthesis [3,4]. 

A major advantage of the sequence presented here is that the aldehyde group is protected at the siloxycyclopropane stage, which allows convenient storage of this stable intermediate. Of equal importance is the valuable carbanion chemistry that can be carried out a to the ester function. Efficient substitution can be achieved by deprotonation with LDA and subsequent reaction with electrophiles.12-13-6 This process makes several a-substituted [1-formyl esters available. Other ring opening variants of siloxycyclopropanes - mostly as one-pot-procedures - are contained in Scheme I. They underscore the high versatility of these intermediates for the synthesis of valuable compounds.6 Chiral formyl esters (see Table, entries 2-5) are of special... 

Michael addition of a dithiane anion 20, generated from the dithiane 19 with butyllithium, to the butenolide 21 creates the enolate 22 which has been efficiently alkylated in situ by 3,4,5-trimethoxybenzyl chloride to give 24 (mp 146-146.5 °C) in 65% overall yield. Protona-tion of 22 furnished the Michael adduct 23, which again can be deprotonated16 with LDA at — 78 °C to give 22 and alkylated (trimethoxybenzyl chloride, THF, HMPA, 3 h at — 78 °C, 18 h at 20 °C) to yield 24. Both variants are equally completely diastereoselective giving rise to the trans- product. 

Based on our previous results on the nucleophilic alkenoylation of aldehydes via metallated a, 3-unsaturated aminonitriles [50], we now envisaged an enanti-oselective variant. Thus, the enantiopure a-aminonitriles 60 were metallated with LDA and by reaction with aldehydes the adducts 61 could be obtained. Subsequent cleavage of the aminonitrile function with silver nitrate led to the desired a -hydroxyenones 62 in overall yields of 29-80% and enantiomeric excesses ee of 50-69%. Alternatively, the conjugate addition of the lithiated aminonitrile 63 to t-butyl crotonate led to the y-keto ester 63 in 35% yield and an enantiomeric excess ee of >90% (Scheme 1.1.18). 

LDA came into general use in the 1970s, and you may meet more modern variants derived from butyllithium and isopropylcyeiohexylamine (lithium isopropylcyclo-hexylamide, LICA) or 2,2.6,6-tetramethyl piperidine... 

The quantity ffffr.r. a ) is the frequency-dependent XC kernel for which common approximations are applied frequency-independent (adiabatic) local density approximations (LDA), adiabatic generalized gradient approximations (GGA), hybrid-DFT variants such as the popular functionals B3LYP and PBEO in which Kxc contains an admixture of Hartree-Fock ( exact ) exchange X,... 

Further, there are asymptotically corrected XC kernels available, and other variants (for instance kernels based on current-density functionals, or for range-separated hybrid functionals) with varying degrees of improvements over adiabatic LDA, GGA, or commonly used hybrid DFT XC kernels [45]. The approximations in the XC response kernel, in the XC potential used to determine the unperturbed MOs, and the size of the one-particle basis set, are the main factors that determine the quality of the solutions obtained from (13), and thus the accuracy of the calculated molecular response properties. Beyond these factors, the quality of the... 

Even more interesting, however, is the observation (12) that molecular dissociat ion energies determined by Equation 10, in combination with a variant of the LDA for correlation ( O), are in excellent agreement with experiment for homonuclear diatomic... 

Variants of TosMIC and imines have also been utilized for imidazole synthesis. For example, benzotriazol-1-ylmethyl isocyanide (BetMIC), 1320, reacts with aldimines 1321, like TosMIC, to form imidazoles 1322. In this case, the benzotriazolyl group stabilizes the anion formed in the first step and is spontaneously eliminated from the intermediate imidazoline. BetMIC derivatives are found to be unstable in the presence of strong bases such as LDA, -BuLi, and NaH. The most effective conditions for all of these reactions are found to be potassium /i t/-butoxide in DMSO or THF (Scheme 337) <1997H(44)67>. 

Figure 2 shows the HF, two DFT variants (LDA and gradient corrected BLYP), and MBPT(2) band structures of polyethylene calculated with the 6-31G basis set [66]. The MBPT(2) bands are above the HF and below the DFT ones. The correlation shift is different at different points in the bands, being around 2 eV for the first two bands. For the third band, the shift is about 5 eV at 0 and 3 eV at n/a. Table 3 list the calculated and measured peaks, the positions of which are not sensitive to the distribution of the incident radiation in the spectra [66]. The HF values are much larger than the measured data while DFT results are too small. As expected, MBPT(2) greatly reduces the... 

This statement is verified in Table 8. Note that in Table 8 both variants of treating the spin are consistently restricted to the first order corrections in 1/c as the magnetization-dependent functional of [44] is analytically known only in this limit. On the other hand, both versions of the spin-dependent functionals lead to more realistic results than the unpolarized formalism (83) together with the unpolarized RLDA. This is demonstrated in Fig.6 where the percentage deviation of the predicted IPs from the experimental data is plotted (For the spin-dependent results the complete nonrelativistic LDA Exc[n,, n has been combined with the generalized spin-densities (100) in Eq.(99)). Improvements are observed in particular for the light elements and the lanthanides. 

The mercury atom is frequently chosen as a test system for relativistic methods because it has a simple closed-shell electronic structure (5d 6s ) and exhibits strong relativistic effects. In Table 3.1, we compare results obtained with two variants of the two-component second-order DKH approach [18,19] to results of a four-component DKS method [53]. All calculations presented were obtained with the LDA-VWN functional [130]. 

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