Rmd Abstract Inverse probability of treatment weighted estimators and doubly-robust estimators including augmented inverse probability of treatment weight and targeted minimum loss-based estimators are widely used in causal inference to estimate and draw inference about the average effect of a treatment. As an intermediate step, these estimators require estimation of key nuisance parameters, which are often regression functions. Typically, regressions are estimated using maximum likelihood and parametric models. Confidence intervals and p-values may be computed based on standard asymptotic results, such as the central limit theorem and the delta method. However, in high-dimensional settings maximum likelihood estimation often breaks down and standard procedures no longer yield correct inference.
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The solvated electrons add to the aromatic ring to give a radical anion. The added alcohol supplies a proton to the radical anion and also to the penultimate carbanion; for most substrates ammonia is not acidic enough. The reduction of benzoic acid is illustrated in equation 2. The location on the ring where the radical anion is initially protonated determines the structure of the product. With an electron donor such as methoxy MeO , alkyl protonation has been thought by some investigators as being ortho i.
Other investigators have thought the protonation is meta 1,3 to the substituent. Arthur Birch favored meta protonation. With electron withdrawing substituents, protonation has been thought to occur at the site of the substituent ipso or para 1,4 , but this is also unclear. For electron withdrawing groups the double bonds of the product avoid the substituents. The placement preference of groups during the reaction and in the final product is termed regioselectivity.
Overall details of the reaction mechanism[ edit ] The solution of metal in ammonia provides electrons which are taken up by the aromatic ring to form the corresponding radical anion B in the first step of the reaction.
This is followed by protonation by the alcohol to form a cyclohexadienyl radical C. Next, a second electron is transferred to the radical to form a cyclohexadienyl carbanion D. In the last step a second proton leads the cyclohexadienyl carbanion to the unconjugated cyclohexadienyl product. These steps are outlined below for the case of anisole. The reaction is known to be third order — first order in aromatic, first order in the alkali metal, and first order in the alcohol.
Reaction regioselectivity[ edit ] The Birch reduction has several intricate mechanistic features. For aromatics with electron withdrawing groups such as carboxyl, the substituent groups avoid the double bonds.
In both cases, with electron donating and with withdrawing groups, the residual double bonds are unconjugated see below. The reaction mechanisms accounting for this regioselectivity are a topic of great scientific interest. The essential features are: In liquid ammonia alkali metals dissolve to give a blue solution thought of simplistically as having "free electrons". The electrons are taken up by the aromatic ring, one at a time. Once the first electron has been absorbed, a radical anion has been formed.
Next the alcohol molecule donates its hydroxylic hydrogen to form a new C—H bond ; at this point a radical has been formed.
This is followed by the second electron being picked up to give a carbanion of the cyclohexadienyl type i. Then this cyclohexadienyl anion is protonated by the alcohol present. The protonation takes place in the center of the cyclohexadienyl system. This regio- selectivity is characteristic. Where the radical anion is initially protonated determines the structure of the product.
With an electron donor such as methoxy MeO or with an alkyl group, protonation has been thought by some investigators as being ortho i. With electron withdrawing substituents, protonation has been thought to occur at the site of the substituent ipso , or para 1,4. Again, there has been varied opinion. The placement preference of groups in the mechanism and in the final product is termed regioselectivity.
The reaction mechanism provides the details of molecular change as a reaction proceeds. In the case of donating groups, A. In a simple computation of the electron densities of the radical anion revealed that it was the ortho site which was most negative and thus most likely to protonate. Additionally, the second protonation was determined computationally to occur in the center of the cyclohexadienyl anion to give an unconjugated product.
The uncertainty in the chemical literature is now only of historical significance. Indeed, some further computational results have been reported, which vary from suggesting a preference for meta radical-anion protonation to suggesting a mixture of ortho and meta protonation. Both experiment and computations were in agreement with the early computations. With electron withdrawing groups there are examples in the literature demonstrating the nature of the carbanion just before final protonation,[ citation needed ] revealing that the initial radical-anion protonation occurs para to the withdrawing substituent.
The remaining item for discussion is the final protonation of the cyclohexadienyl anion. The more modern and computations were in agreement. The original mechanism of the Birch reduction invoked protonation of a radical anion that was meta to the ring methoxy and alkyl groups. It further proposed that the last step, protonation of a cyclohexadienyl anion, occurred ortho with respect to these substituents. The correct mechanism O is depicted below. He suggested the meta attack results from "opposition of the ortho and para initial charge".
Burnham in concluded that protonation is unlikely to occur predominantly at the ortho position and the reaction most probably occurs at the meta position but may occur at both sites at similar rates.
But he did note that publication by Burnham  favored meta attack. In publications Birch collaborated with Leo Radom in a study that concluded that electron densities at the ortho and meta positions to be close with a slight ortho preference, but with mixtures of ortho and meta protonation occurring.
The reasoning was that carbanions are much more basic than the corresponding radical anions and thus will react more exothermically and less selectively in protonation. Experimentally it was determined that less deuterium at the ortho site than meta resulted for a variety of methoxylated aromatics.
This is a consequence of the greater selectivity of the radical anion protonation. Computations e. Also, it was ascertained that frontier orbital densities did not, and these had been used in some previous reports. Subsequently, in and Birch published twice still suggesting that meta protonation was preferred. However, textbooks, publishing on the mechanism of the Birch Reduction, have noted that ortho protonation of the initial radical anion is preferred.
Thus, as depicted below, the structure of the penultimate dianion D is characterized by its being subject to trapping by alkyl halides. Mechanism of reduction of benzoic acids, including possible alkylation This dianion results independent of whether alcohol is used in the reduction or not. Thus the initial protonation by tert-butyl alcohol or ammonia is para rather than ipso as seen in the step from B to C.
Thus as shown in the figure below there are three resonance structures B, C and D for the carbanion. With bond orders modifying simple exchange integrals in a Mulliken-Wheland-Mann computation it was shown that electron density at the central atom 1 become largest.
I was inspired to ask this because of a comment that NileRed made in his video on Birch reduction of benzene - he mentioned as an aside that Birch reduction is used to make meth, but that it is the hydroxyl group next to the aromatic ring that is reduced in that reaction. This got me thinking about why that might be the case. My understanding of the theory is weak though, which is why I started this thread. Anyway, forget about ephedrine.
Oh no, there's been an error
Tujinn Lithium in ethylamine Benkeser reduction C. This reaction is quite unlike catalytic hydrogenation, which usually reduces the aromatic ring all the way to a cyclohexane. In water, it rapidly decomposes to produce a silicone polymer while giving off hydrochloric acid. Because of its reactivity and wide availability, it is frequently used in the synthesis of silicon-containing organic compounds.
BENKESER REDUCTION PDF