I think our readers need a good explanation for this question based on user55119's comment "The question arises, why isn't the alkynyl group in the TS axial having a smaller A-value than the methyl. Switch the methyl and alkynyl group in the red structure. Both reagents (green and red) are S-(P)-BINOLs having a two fold axis of symmetry. After all, these TSs are rationalizations."
OP's original question was:
I found an alternative transition state (red) that yields the opposite enantiomer. What am I doing wrong?
First, I need to clarify that the reducing reagent we are talking about is $\ce{BINAL-OEt}$ $(\ce{LiAlH(Binol)OEt})$, which gives pretty high enantioselectivity (than when used $\ce{LiAlH2(Binol)}$) for reduction of ketones that have a $\pi$-system directly attached on one side of the carbonyl group.
The chiral $\ce{BINAL-OEt}$ can be prepared by using enanthiomerically pure BINOL $(\ce{Binap(OH)2^{*}})$. The stereoisomer considering here is 2,2'-dihydroxy 1,1'-binaphthyl (BINOL), which shows atropisomerism (Ref.1) defined by $M$ and $P$ notations (alternatively, $R$ and $S$ notations, respectively). Atropisomers are stereoisomers arising because of hindered rotation about a single bond:
![Atropisomerism](https://cdn.statically.io/img/i.sstatic.net/SPSwn.jpg)
For BINOL, $\ce{A = A' = OH}$ (the highest priority group) and $\ce{B = B' = benzo}$ function (the lowest priority group). Thus, stereochemistry of BINOL group of both Red and Green transition states are $P$ (or $S$).
It is known fact that these atropisomers can transforem chirality to substrates it attached to. For example, the aluminum atom in $\ce{BINAL-OEt}$ is a chiral center based on the use of $M$- or $P$-BINOL. Thus, when enanthiomerically pure $P$-BINOL is reacted with equimolar amounts of $\ce{LiAlH4}$ and ethanol would result a diastereomeric mixture:
$$\ce{LiAlH4 + Binap(OH)2^{*} + EtOH -> LiAl^sHBinap(O2)^{*}OEt + LiAl^rHBinap(O2)^{*}OEt}$$
As I'd explain later in the text (vide infra), each of these two diastereomers would give opposite enanthiomer (when used in pure isomer form) in the reduction reaction in hand. Based in these information, as I pointed out in my comment (and as OP agrees on), the two Green and Red Zimmerman-Traxler Chair-Like Transition States (Ref.2) are not the same:
![Zimmerman-Traxler Chair-Like Transition States](https://cdn.statically.io/img/i.sstatic.net/kKV11.jpg)
If you look closely, you would realize that the $\ce{Al}$ stereocenter in each of two Green and Red Transition States are not not identical (c.f., the orentation of napthyhyl ring the bottom box, which is identical in both Green and Red TSs). I assigned the on in Green TS as $s$ while that in Red TS as $r$. To my knowledge, these two TSs are arisen from the reaction of same starting material with each of diastereomers (the optical active reducing reagents) I mensioned earlier:
$$\ce{LiAl^sHBinap(O2)^{*}OEt + LiAl^rHBinap(O2)^{*}OEt}$$
But, it is not possible becase only one of these two diastereomers should be using in the reaction. Therefore, one of these two transition states should be negated.
About user55119's comment: Zimmerman and Traxler have suggested these Chair-Like Transition States to explain the resulting stereochemistry of a reaction, which are as suggested by user55119, in deed rationalizations. Besides, having the alkynyl group in the axial position in the TS is not just because steric reason (even if having a smaller A-value than the methyl). There are other factors such as $n,\pi$-repulsion forces (Ref.1, and Ref.3-4):
![Electronic effect](https://cdn.statically.io/img/i.sstatic.net/q73BN.jpg)
As shown in the above diagram, favorism to the accepted TS is govenrned by a repulsive interaction between the $\pi$ system of the ketone (here it is alkynyl group) and the lone pair of an oxygen atom of the $\ce{BINAL-OEt}$.
References:
- Jean Michel Brunel, "BINOL: A Versatile Chiral Reagent," Chem. Rev. 2005, 105(3), 857–898 (DOI: https://doi.org/10.1021/cr040079g).
- Howard E. Zimmerman and Marjorie D. Traxler, "The Stereochemistry of the Ivanov and Reformatsky Reactions. I," J. Am. Chem. Soc. 1957, 79(8), 1920–1923 (DOI: https://doi.org/10.1021/ja01565a041).
- R. Noyori, I. Tomino, Y. Tanimoto, and M. Nishizawa, "Asymmetric synthesis via axially dissymmetric molecules. 6. Rational designing of efficient chiral reducing agents. Highly enantioselective reduction of aromatic ketones by binaphthol-modified lithium aluminum hydride reagents," J. Am. Chem. Soc. 1984, 106(22), 6709–6716 (DOI: https://doi.org/10.1021/ja00334a041).
- R. Noyori, "Centenary Lecture. Chemical multiplication of chirality: science and applications," Chem. Soc. Rev. 1989, 18, 187-208 (DOI: https://doi.org/10.1039/CS9891800187).