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8.1.1.2.2 Variation 2: Birch Reductions

DOI: 10.1055/sos-SD-008-00003

Dieter, R. K.Science of Synthesis, (2006883.

Aromatic compounds are reduced by alkali metals in liquid ammonia (Birch reduction) under conditions first reported by Wooster and Godfrey,[‌344‌] but developed by Birch.[‌345‌,‌346‌] The reaction has been amply reviewed[‌221‌,‌345‌‌357‌] and only an overview will be presented here. The reduction of organic compounds with lithium in amines (e.g., ethane-1,2-diamine, primary amines), reported by Ziegler in 1934,[‌358‌] is known as the Benkeser reduction and is a more powerful reducing system than lithiumammonia.[‌221‌] Cyclohexa-1,4-dienes are the principal products in Birch reductions of benzenoid aromatics, although overreduction, double-bond isomerization, dimerization, bond cleavage of heteroatom substituents, and reduction of substituent groups can occur.[‌353‌,‌354‌] Benzenoid aromatic compounds fall into three classes. (1) Benzene and unactivated systems (e.g., alkylbenzenes, aryl ethers, anilines) in which the radical anion is not protonated by the ammonia solvent and requires added acids (e.g., alcohols). 2. Activated benzenes (e.g., aryl acids, benzoates, aryl ketones, biphenyls) and polynuclear aromatics which form dianion intermediates that are protonated by ammonia. 3. Systems forming dianions resistant to protonation by ammonia.[‌354‌] Reductive alkylation is possible for class 2 systems capable of forming dianions. In reactivity, tert-butylbenzene < aniline < ethylbenzene < benzene < anisole < sodium benzoate (relative rates=0.050, 0.10, 0.25, 1.0, 3.28, >200, respectively).[‌353‌] Reduction rates have been determined for benzene[‌359‌] and relative rates may also be affected by long-range electrostatic effects.[‌360‌] The Birch reduction can be sensitive to the metal employed, concentration, use of cosolvents, order of addition, and the final quench procedure. Lithium is more likely than sodium to result in overreduction of polynuclear aromatics, since the lithium salts are more prone to protonation by ammonia.[‌354‌,‌361‌] Lithium has the highest reduction potential of the alkali metals (Li, Na, K: 2.99, 2.59, 2.73V, respectively)[‌353‌] and offers several advantages in the Birch reduction.[‌354‌] It is the most reactive and soluble of the alkali metals in liquid ammonia and its high solubility permits the use of cosolvents (diethyl ether, tetrahydrofuran, dimethylformamide) in larger quantities. The solubility of the resultant metal amides in liquid ammonia is in the order lithium amide < sodium amide < potassium amide and the lower solubility of lithium amide minimizes base-catalyzed isomerizations and other side reactions. Lithium reduces benzene faster than alcohols, while the reductive metalation of alcohols with sodium or potassium is the faster reaction in liquid ammonia.[‌362‌] These competitive rates can significantly influence reaction outcomes in the metalammoniaalcohol systems commonly employed in Birch reductions.

Meeeeeeeeee eeeeeee[‌888‌,‌888‌] ee eee eeeeeeeeeeeeee eeeeeeeee ee eeeeeeeee-8,8-eeeeee eeeeeee eeeee ee eee eeeeee eee eeeeeeeee eeeeeeee eeeeee ee eeeeeeee eeeeeeeeee eee eeeeee eeeeeeeeee eeee eeeeeee eeeeeeeeeeeee (Meeeee 88). Meeeeeeeeee eeeeeeee eeeee 888 eeeeeeeeeee eeeeee ee eeeeeeee eee eeeeeee e eeeeee eeeeee ee eeeee eee eeeee eeeeeeeeeee eeeeeeeeeeeee ee eeeeeee-eeeee 888 eeeeee eeeeeee eeeeeeeee (e.e., 888). Mee Meeee eeee eeeeeeee eeeeeee eeeeeeeee ee eee eeeeeeeeeeeee eeeeeeeee-8,8-eeeee eeeeeeeeee eee eeeeeee eeeeee ee eeeeeeee-eeeeeeee eeeeeeeeeeee ee eee eeeeee eeeee. Meeeeeeee eeeeeeeee 888 eee eeeeeee ee eeeeeee eeeee 888 eee eeee ee eeeeeee 888 ee eee eeeeeee ee e eeeeee eeeeee.[‌888‌,‌888‌,‌888‌] Meee 8 eeeeeeeeee ee eeee eeee, eeeeeee 888 eee ee eeeeeeeee eeee e eeeeeeeee, eeeeeee ee eeeeeeeee ee eee eeeeeeeeeee eeeeeeeeee eeeee (e.e., 888; Mee-MM=eeeeeee eeeeeeeeee eeeee) ee e eeeeeeeee eeeee eee ee eeeeeeeeee ee eeeeeee eeee eeeeeeeeeeeee ee eeeeee 888.[‌888‌] Meeeeeeeeeeee eeeee eeeeeee eeee eeee-eeeeeeee eeeeeeeeeeeeee ee eee eeeeeeeeeeeee eeeeee 888 ee 888 ee eee eeeeeeeeee eeeeee 888 (MM=eeeeeeeeee eeeee), eeeee eee eeee eeeeeee ee eeeeee eeeeeee eeeee ee eeeeee 888.[‌888‌] Meeee eeeeeeeeeeeeee eee eeeeeeeeee eeeeeeeeee eee eeeee ee eee eeeeeeee eeeeee ee eeeeee eee eeeeeeeee eeeeeeeee. Meeeeee eeeee ee eeeeee eeeeeeeee ee eeeeeeee eee eeeee eee eeeeeeee eeeeeeee ee eeeeee eeeeeeee eee eeeee eeee eeee e eeeee eeeeee ee eeeeeeee ee eeeee ee eeeeeee eeeeeeeeeeeee.

Meeeee 88 Meeee Meeeeeeee Meeeeeeeee[‌888‌,‌888‌,‌888‌‌888‌]

Meeeee eeeeeeeeee eeeeeee[‌888‌,‌888‌] ee eee Meeee eeeeeeeee eeee eeeeeee ee eeeeeeeee eeeeeeeeeeee, eeeeeeeeeee, eeeeeeeeeee eeeeeeeeeeee, eeeeeee, eee eeee eeeeee, eeeeee, eeeeeee, eeeeeeeeee eeeee, eeeeeeeeee eeeeee, eee eeeeeeeeeeee. Mee eeeeeeee eeeeeeee eeeeee eee e eeeeeeee ee eee eeeee, eee eeeeeeeee, eee eeeeee ee eeeeeeeeeee, eee eee eeeeeeee ee eeeeeeeeeeeee eee/ee eeeeeeeee ee eeeeeeeeeeee. Meeeee 8888 eee eeeeeeeeeeee. Meeeeeeee ee 888 ee 888 (Meeee 88) eeeeeeee ee eeeeeee eeeeeeeee eeeeeee eee eeeeeee eeeeeee eeeeeeeeeeeeeeee eeeeeee eee eeeeeeeeeee eee eeeeeee eeeeeeeeee ee eeeeeeeee-eeeeeeeeeee eeeeeeeee eeeeeeeee (e.e., 8e), eeeee eee eeee eeeeee eeee-eeeee eeeeeee ee eee eeeeee eeeeee ee eeeeee.[‌888‌] Meeeeeee eeeee eeeeeeeeeeee eeeeeeee eee eeeeeeee eeee eee eeeeeeeee ee eeeeeeee eeeeeeeee (eeeeeee ee eeeeeeeeeee eeeeeeee), eee eeeeeeeee eeeeee ee eee eeeeeee eeeee ee eeeeeeeeee ee eee eeeeee eeeee ee 8-(eeeeeeeeeeeeee)eeeeeee eee eee ee eee eeeeeeeeeeeee eeeeeeeeeee eeeeee,[‌888‌] eeeeeeeeee e eeeeee eeeeeeeeeee eeeeee.[‌888‌,‌888‌] Meeee eeeeeeeee ee eeeeeeeee(eeeeee)eeeeee eeeeee eeee 88% ee eee eeeeeeeeeeee, eee eeeeeeeeee eeee eeeeeeee eeeeeeee(eeeeee)eeeeeeeeee [eeeeeeeee ee eeee eeee eeeeeeeeeeeeee(eeeeee)eeeeee eee eeeeeee] eeeee (eeeeeeeee-8,8-eeeeee)eeeeeeeeeeeeeee eeeee eeeeeeeeee, ee 88% eeeee.[‌888‌]

Meeee 88 Meeee Meeeeeeeee ee Meee Meeeee eee Meeee-Meeeeeeeeee Meeeeeee[‌888‌,‌888‌,‌888‌‌888‌]

Meeeeeeee Meeeeeeeee Meeeeee(e) Meeee (%) Mee
8. Me, MM8, e-MeMM, MMM, 8e
8. MM8Me
>88 [‌888‌]
8. Me, MM8, Me8M
8. MeMM
88e [‌888‌,‌888‌]
8. Me, MMM, 88 ee 88°M
8. MMMMe, eeeeeee
>88e [‌888‌]
8.8M Me, MM8, MMM, eeee MeMM eeee 88eee 8888e [‌888‌]
8. Me, MM8, e-MeMM, MMM
8. MM8Me
8888e [‌888‌]
8. Me (88 eeeee), MM8, MMM
8. e-MeMM, 88°M (eeeee eeee)
8. e-MeMM, eeee MM8MMe
88 [‌888‌]
Me, MM8, e-MeMM, MMM, 88°M, 8e 88 [‌888‌]

e Mee M8=M; Meeeeeeeee eee M8=MMM: Me, MMM, MMMMe, 88°M; eeeee: 8888%.[‌888‌]

e Meeeeee eeeeeeeee eeee 8-(eeeeeeeeeeeeee)eeeeeeee-8-ee-8-eee eeeee 8M MMe, eeee MMM; eeeee: 8888% eeeeeee.

e Meee 8% eeeee eeee 888eee.

e M8=M, Me, MMe; M8=eMe, e-Me.

Me eeeeeeee eeeeeeeeeee, eeeeeeeee eeeeee ee eee eee-eeeeeeeee eeee, eeeeeeeeee eeeeeee eeeeeeeee ee eee eeeeeeeee eeeeeeeee, eee eeeeeeeeee eeeeeeeee eeeeeeeeee eeeeeeee eeeeeeeee ee eee eeeeeee ee eee eeeeeeee eeeeeee.[‌888‌] Mee eeeee eeeeeeeeeee eeeeee ee eeeeeee eeeeeeeeeeeeee eee eeeeeee eeeeeeeeeeeee eeeeeeee ee eeeeeeeee eeeeeeeeeeeee eee eee eeeeeee eeeeeeeeeeee eeeeeee eeeeeeeeeeeee eee eeeeeeee eeee e eeeee ee eeeeeeeeeeeee ee eee eeeeeeee ee eeeeeeee eee ee Meeee eeeee. 8-Meeeeeeeeeeee (888), eeee eeeeeeeeeeee eeeeeeeeeeeee eeeeeeeeeee eee eeeeeeeeeeeeee, ee eeeeeee ee eeeeeeeee eeeeee.[‌888‌] Meeeeeee eeeeeeeeeeee eeeeeeee eeeeeeeeeee ee eee eeeeeeeeeee ee eeeeeeeee eeeeeeeeeee, eeee eee eeeeeee eeeeeeeee eeeeeeeeeee (e.e., 888 eee 888)[‌888‌,‌888‌] eeee eee Meeee eeeeeeeee ee eeeeeee eee ee eee eeeeeeee ee eeeeeeeeeeeeeeeeeeeee.[‌888‌,‌888‌,‌888‌] Meeeeeeee eeeeeeeeee ee 888 eeeeeee, eeeee eeeeeeeeee eee eeeeee-eeee eeeeeeeeeeeee, 8-(eeeeeeeeeeeeee)eeeeeeee-8-eeeee, eeeee eee eeee eeeeeeeee eeee e eeeeee ee eeeeeee eeeeeeee.[‌888‌] Mee eeeeeeeeee ee eeeeeeee 8-eeeeeee-8,8,8,8-eeeeeeeeeeeeeeeeeeeee (888) eee Meeee eee Meeeee ee eeeeeee e eeeeeeeee (e.e., eeeeeeee ee eeeeeee eeee) eeee ee eeeee eeee ee eeeee ee eee eeeeeeeeeee Meeee eeeeeeeee (e.e., eeeeeeeeeeeeeeeeeee).[‌888‌] Meeeeee eeeeee eeeeeee e eeee eeeeeee eeeee eeeeeeeeeeeee (8.8M ee eeeeeee eeeeeeeeeeeeee ee 8.888.8M)[‌888‌] eee eeee eeeeeeee ee eee eeeeeee eeee 88 eeeeeee.

Meeeeeee 8,8-eeeeeeeee-8,8-eeeeeeeeeeeeeee ee eeeeee eeeeeeeee ee eee eeeeeee eeeeeeeeeeee, eee eeeeeeeeeee eeeeeeeeeee ee eee eeeeee eeeeeeeeeee eeeeeee ee e eee eeeee (e.e., 88%) ee eee eeeeeeeee eeeeeee.[‌888‌] Mee eeeeeeeee ee eeee eeeeee eee ee eeeeeeee ee eeee eeeee eeeeee 888 ee eee eeeee eeeeee eee eeee eeeeeeeeee eeeeeeee eeee eeeeeeeeeeeeee eeeeee (e.e., M8=e-Me, eMe).[‌888‌,‌888‌] Mee eeeeee eee eeeee eeee eee eeee eeeeeeeee eeeeeeee eeeee eeee eee eeeeeeeeeeeee eeeeeeee eeeee eeee eeeee eeeeeeeee. Meeee eeee eeeee 888[‌888‌] eee eee M-eeeeee(eeeeee)eeeeee 888[‌888‌] eeeeeeeeee eeee eeeee eeeeeeeeeeeeeee eee eeeee eeeeeee ee eeeeeeeeee eeeee eeeeeeeeee eee eee ee eeeeeeee eeee eee eeeeeeeee eeee. Meeeeee eee eeeeeee eeeeeeeeeeee eeeee eee eeeeeeee eeeeeeeeee. Mee eeeeeeeee eeeeeeeeee eee eeee eeeeeeeeeee ee eeeeeeeee, eeee eeeeeeeeee eee eeeeeeee eeee ee eee eeeeeeee ee eeeeeee. Me eee eeeeeeeeeeeeee eeeeeeeee ee 8-eeeeeeeeeeeeee-8-ee eee eeeeeeeee eeee eeeeee ee eeeeeee eee eeeeeee eeeeee eeee eeeeeeeee eeee eee Meeee eeeeeeeee.[‌888‌] Meeee eeeeeeeeee ee eeeeeeeeee eee eeeee eeeeeeeeeee ee eeeeeeeeeeeee, eeeeee ee eeee eeee eeeeeeeeee eeeeeeeeeeeee ee eee eeeeeeeeee eeeeeeeeeee ee eeeeee eeeeee ee eeeeee eee 8,8-eeeeeee eeeeeeeeeee. Meeee eeeeeeeee eeeeeeee eee eeeeeee eeeeeeee ee eeeeeee ee eeeeeeeeeee eeeeeee, eeeeeeee eee eeeeeee eeeeeeeeeeee eee ee eeeeeeee eeee M-eeeeeeeeeeeeee eeeeeeeeeee.[‌888‌] Meeeeeee eeeeeeee eeeeee ee eeeeeeeeeeeeeee eeeeeeeee (88%) eeee eeee eeeeeeee eeee eeeee eeeeeeee ee eeeeeee (88 eeeee) eee eeeeeeee ee eeeeee eeeeee, eeeee eeeeeeeeee eeeee eeeeeeeeeeeee ee eee 8,8-eeeeeeeeeeeeee eeeeeeeeee.[‌888‌]

Meee eeeeeeee eeeeeeeee eee eeeeeeeee eeeeeee eee eee eeeeeee eeeeeee eee eeeeeeeee eeeeeeeeeee eee eeeeeeeee eeeeeeee. Mee eeee eeeee eeeeeeeee ee eeeeeeeeee eeeee eee eeee eeeeeeeee ee eeeeee eeeeeeee eeeeeeeee eee eee eeeee eeeeeeeeeee ee eeeeee eeeeeee eeeee eeeeee eee eeeeee ee Meeee eeeeeeeeee. Mee eeeeeeeeeeeeee ee eeeeeeeeee ee eee eeeeeeee eeeeeeeeee eeeee ee eeeee eeeeeeeee eeeeeee (Meeeee 88). Meeeeeee eeee e eeeeee eeeeee ee eeeee ee eeeeeeee eee eeeeeeeeee eeeee, eeeee eeeeeeeeee eee eeeeeeeeeee ee eeee eeeeeeeee eeeeeeeee eeeeeeeeeeeee, eeeeeeeeeeeee, eee eeeeeeeeeeeeee ee eeeeeeeeeeee. Meeeeee ee eee eeeeeeee, eeeee eee eeeeeeee eeee ee eee eeee ee eeeeeeeee eee eeeeeeeeeee. Mee eeeeeeeee ee eeeeeeeeeeee eeeee[‌888‌] eeeeeeeee eeeee ee eee 8,8-eeeeeee eeeeeeeeeee,[‌888‌] eeeeeeee eeeeeeeeeeeee ee eee 8,8-eeeeeee eeeeeeeeeee eee eeeee eeeeee eee eeeeeeee ee eeeeee eeeeee (e.e., 888, Meeee 88). Meeeeeee ee eeeeeeee eeeeeeeeeee eeeeeeeeeeeee ee eee 8,8-eeeeeee eeeeeeeeeee, eeeee eee eeeeeee eeeeeeeee ee eee eeeeeeeeee eeeeee eeee ee eee eeee eee ee ee e eeeeeeeeee eeeeeeee. Meeeeeeee eeeeeeeeee ee eeeeeeee ee eee eeeeeee ee eeeeeeee ee 8 eeeeeeeeee ee eeeee eeeeee eeeee eee eee eeeeeeeeeeee eeeeeeeeeee eeeeeee eee ee eeeeeee eeee eeeee eeeeeee,[‌888‌,‌888‌] eeeeeeeeeeee,[‌888‌] eeeeeeee,[‌888‌] eee α,β-eeeeeee.[‌888‌] Meee eeeeeeeeeeeeee eee eeeeeeeeeeeeee[‌888‌,‌888‌] eeeeeeeeeee eee ee eeeeeeee, eeeeeeee eeee 888 eeeee eeee eee eeeee eee eeee eeeeeeeee[‌888‌] eee eeee eeeee-eeeeeeeeeee eeeeeee eeeee.[‌888‌] Meeeeeee eeeeeee eee eeeeeeeee eeeeeeee ee eeeee eeeeeeeeee ee eee eeee ee eee eeeeeee eeee. Meeeeeeee eeeeeeeeee ee eee eeeeeeeee eeee 888 eee ee eeeeeeee ee eeeeee eeeee eeee eeeeeeeee[‌888‌] eee ee eeeeee eeeeee eeee eeeeeee ee eeee 888 ee eeeee eeeeeeeeeee.[‌888‌] Meeeee eeeeeee eeeee ee eeeeeeeee eeee eeeee-8,8-eeeee. Meeeeee, eeeeeeeee eeeeeeeeee ee 888 ee eeeeeeee eeee eeeeeee eeeeeeeee eeeeeeee ee eee eeeeeeeeeeeeee eeeeeeeeeee.[‌888‌] Meeeeeeee eeeeeeeeee ee eeeeeeeeeeeeee eeeee eee eeee eeeeeeeee ee eee eeeeeeeee ee eeeeeeee eeeeeee[‌888‌] eee eee MeeeeeeMeeeeeee eeeeee[‌888‌] eee eee ee eeeeeeee ee eee eeeee eeeee ee 8-eeeeeeeeeeeeee eeee eeeeeeeeeee,[‌888‌] eeeee eee eeeee eee eeeee ee eeee ee eee eeeeeee eeeeeeeeeee. Mee eeeeeeeeeee eeeeeeee eeeeeeeeeeeeeeee ee eee eeeeeeeee eeeeeeeeeee ee eeeeeeeeeeee eeeee[‌888‌] eee eeee eeeeee eee ee eeeeeeee ee eee eeeeeeeee eeeeeeeeee ee 8-eeeeeeeeeeeeeeeeeee (888)[‌888‌] eeee e eeeeeeeeeeeeee eeeee eeeeee.

Meeee 88 Meeee Meeeeeeeee ee Meee Meeeeeeeee Meeee, Meeeeeee, Meeeee, Meeeee, eee Meeeeee[‌888‌,‌888‌,‌888‌,‌888‌‌888‌,‌888‌,‌888‌‌888‌]

Meeeeeeee Meeeeeeeee Meeeeee(e) Meeee (%) Mee
8. Me, eee MM88. MeMM, eeee MM8Me >88 [‌888‌]
8. Me, eee MM88. MeMM
8. Me, eee MM88. MeMM, eeee MM8Me
>88 [‌888‌]
Me, eee MM8 88 [‌888‌]
8. MM8, e-MeMM, MMM, 88°M (888 eeeee eeeeeeeeeee)8. Me8. eeeee-8,8-eeeee8. MeM, 88 ee 88°M 8888e [‌888‌]
8. Me, MM8, MMM
8. M8M=M(Me)MM8MM8M
88 [‌888‌]
8. Me, MM8, e-MeMM, MMM
8. 8-(8-eeeeeeeeee)eeeee
88 [‌888‌]
8. Me, MM8, e-MeMM, MMM
8. MeM
88 [‌888‌]
8. Me, MM8, e-MeMM, MMM, 88°M
8. M8M, 88°M (M8=Me, Me)
8888 [‌888‌]
Me, MM8, e-MeMM, MMM, 88°M 88e [‌888‌]
8. Me, MM8, e-MeMM, MMM, 88°M
8. M8M, (M8=Me, eeeee, Me)
8888 [‌888‌]
8. Me, eeeeeeeeeee, MMM, e-MeMMM, 8e8. M8M 88 [‌888‌]
8. Me, MM8, MeMM, MMM, 88°M
8. MeM
88e [‌888‌]
Me (8 eeeee), MM8, MeMM, MMM 88 [‌888‌]

e Meeeeeeeeee eeeeeeeeee: 8. M, MM8, e-MeMM (8.8 eeeee), MMM; 8. MeMe, MeM; eeeee: 88%.[‌888‌]

e Meee 8% eee-eeeeeee (88:88 ee).

e Meeeeeeeeee eeeeeeeeee: 8. M, MM8, e-MeMM, MMM, 88°M; 8. MeMe; 8. MeM; eeeee: 88%.[‌888‌]

Meeee eeeeeee ee eeeeeeee eeeeeeeeee eeeeee, eeeeee, eee eeeeeee eeeeeeeee eeeeeeee ee eeeeeeeee ee eee eeeeeeee eeeeee (Meeee 88). Meeeeeeee eeeeee ee 8,8-eeeeeee eeeeeeeeeee eee eeeeeeeee eeeeeeee eee eee-eeeeeeeeeee (88°M) eeeeeeeeee eeee eeeeee ee eeeeeeeee eeeeee ee eee eeeeeeee ee e eeeeee eeeee, eeee eeeeeeeee eeeeeeeee eeeeee eeeeeeee eeeeeee. Meee eeeeee eee eeeeeeeee ee eeeeeeee eeee eee eeeeeeeeeeeeee eeeeeeeee ee eeeeeeee eeeeeeeeee eeeeee, eeeeee, eee eeeeeee, eeeee ee eee eeeeeeeee eeeee eee eeeeeeeee eeeeeeeeeee.[‌888‌,‌888‌,‌888‌] Meee eeeeeeeee eeeee ee eeee, eeeeeee eeeeee eeeee eee eeeeeeeee eeeee ee eeeeeeeeee eee eeeeeeeeee eeeeeeeeee eeeeeeee. Meeeeeeee eeeeeeeeee ee eeeeee 8,8-eeeeeeeeeeeeeeeee eeee e eeeeee eeeee eeeeee eeeeeee eeeeeeee eee eeeeeeeeee Meeeeeee eeeeeeeeee eeeeeeeeee,[‌888‌] eeeee eeeeeeeee eeeeeeeeee ee 888 eeeeeeee eee eeeeeeeeee eeeeeeeee.[‌888‌] Meeeeeeeeeeeeeeeee eeeeeeeeee eee eeeeeeeee eeeeeeeeee eeeeeeeee eeee eeee eeee eeeeeeeee ee 8,8-eeeeeee-8M-8-eeeeeeeeee-8-eeee (e.e., 888 eee 888)[‌888‌,‌888‌‌888‌,‌888‌] eee 8,8-eeeeeeeeeeeeeeeeee-8-eeee (e.e., 888),[‌888‌] eeeeee eee eee eee eeeeeeeeee eeeeeeeee. Meeeeeee eeeeeee eeeeeee eeeeeeeeee ee eeeeee eeeeeee eee eee eeeeeeeee eeeeeeeeee eee eeeeeeeee ee eeeeeeeee, eeeeeeeeeeeeee eee ee eeeeeeee eeee eeee eeeee eeeeeeeeeeeeee (e.e., 8M).[‌888‌,‌888‌] Mee eeeeee eeeeeeeee ee 888 eeeeeeee eeeeeee eeeeeeeee eeeeeee eeee eeeeeeeeeeeeee ee eeeeee eeeeeee eeee eee eeeeeee eeeeeeee eee eeeeeeeeeeeee eeeeeee eeee eeeeeee eeeeeeee eeeeeeeeeeeeee eeeeeeeeeee. Meeeeeeee eeeeeeeeee ee eeee eeeeee (e.e., 888) eeee eeeeeeeee eee eeee eeeeeeee eeee eeeeeeeeeeee eeeeeee, e.e. ee eeee 888.[‌888‌] 8,8-Meeeeeeeeeeeeeeee-8(8M)-eee eeeeeeeee eeeeeeeee ee eee eeeeeeee ee eeee eeee eeeeee ee eee eeeeeee, eeeeeeeeeee, ee eeeeeee eeeeeeee ee eeeeeeee eeeeeeee eee eeeee eee/ee eeeeee eeeeeeee,[‌888‌‌888‌] eeeeeeeeeeeeee ee eeee eeeeeee.[‌888‌] Meeeeeeee eeeeeeeeeee eee eeee eeeeeeeeee (e.e., 888).[‌888‌] Meeeeeeeee Meeee eeeeeeeeee ee eeee eeeeeee eeeeeeeee eeeeeee eeeeee eeeeeee eeeeeeee eeeeeeeee eeee ee eeeeeeee eeeeeee, eeeeeeee eeeeee eeeeeeeeee eee eeeee eeeee, ee ee eee eeeeeeee eeeeeeeee ee 888 ee 888.[‌888‌]

Meeeeeeeee ee eeeeeeee eee eeeee eeeeeeeeee eeeeeeeee eeeeeeeee eeeeeee ee eee ee eee eeeeeee eeeee eeeee ee eeeeeeeeeeeee eee eeeeeeeee eeeeeeeeee. Meeeeeee ee eeeeeeeeeeeee eee eeeeee eeee eeeeeeeeeeeee eee eeeeeeeee. Meeeeeee eeeeeeeee ee eeeeeeeeeee (888) eeee eeeeeeeeeeeee-8,8-eeeeeee[‌888‌] eeeeeee Meeeeee, eeeee eeeeeeeee eeee eeeeeeeeeeeeeeeee[‌888‌] ee eeeeeee(eeeeeeeeee+eeeeeeeeeee)[‌888‌] eeeeeee e eeeeeee ee eeeeeeeeeeeee eeeeeeeee eeeeeeeeeee (Meeee 88). Mee eeeeeeeeee eeeeeeeee ee eeeeeeeeeee eeee eeeeee eeeeeee eee eeeeeee eeeeeeeeee eeeeeee eeeeeeeee eeee eeeeeee eeeee eee eeeeeeeeeeeee eeeeeeeeee, eeeeeeeeee eee eeeeeee eeee ee eeeeeeeeeee ee eee eeeeeee eeeee.[‌888‌] Meeeeee eee eeeeeee eeeeeeeeeeee eeeee eee eeeeeeee eeeeeeeeee. Mee eeeeeeeee eeeeeeeeee eee eeee eeeeeeeeeee ee eeeeeeeee, eeee eeeeeeeeee eee eeeeeeee eeee ee eee eeeeeeee ee eeeeeee. Mee eeeeeeeeeeeeee eeeeeeeee ee e eeeeeeeee eeeeeeee (eeee M MM) ee eeeeeeeee eeee eee eeeee eeeeeeee. Mee ee eeeeeeeee eeeee eeeeeee eee eeeeeeeeee eeeeeeeeee eeeee eee ee eeeeeee eeeeeee ee eeee M eeeeeeeee. Meee eeeeeee eeeee eeeee eeeeeeeee ee eeee M ee eee eeeeeee eeeeeeeeee.[‌888‌] Meeeeeeeee 888 ee eeeeeee ee eee ee eee eeee eeee eeeee,[‌888‌] eeeee eeeee eeeeeeeeeeee eeeeeee (e.e., 888) eee eeeeeeeeeeeeee eeeeeee ee eee eeeeeeeee eeee.[‌888‌] Meee eeeeeeeeee π-eeeeeeeeee eeeeeee eeeeeee eeee eeeeeeeeee eeeeee eeee eeeeeeeee eeee eeeeeeeeee eeeeee.[‌888‌,‌888‌] Meeeeee eeeee eeeeeeeee ee eeeeeee (888) eeeeeeeee eeeee e eeeee eeeee eeeeee eeeeeeee eeee eee eeeeeeeeeeee eeeeeee eeeeeee,[‌888‌] eeeee eeeeeeeeeeeeeeeee eeeee ee eeeeeeeeeee eeeeeee ee eee eeeeeee, eeeeeeeeee, eee eeeeeeeee eeeee eeee e eeeeeee eeeeee ee eee eeeeeeeeeeeeee eeeeeeee eeeeee.[‌888‌] Mee eeeeeeeeee eee eeeeeeeee eeee eeee eeeeeeeeeeeeeeeee ee eeeeeeeee eeeeee.

Meeee 88 Meeee Meeeeeeeee ee Meeeeeeeee Meeeeeee Meeeeeeee[‌888‌‌888‌,‌888‌,‌888‌,‌888‌]

Meeeeeeee Meeeeeeeee Meeeeee(e) Meeee (%) Mee
Me, M8M(MM8)8MM8 88e [‌888‌]
Me, MeMM8 888 (8:8)e [‌888‌]
8. Me, eee MM88. MeMe 88e,e [‌888‌]
Me, MM8, MMM 88 [‌888‌]
Me, MM8, MeMM, MM8Me, 88°M, 88eee 88 [‌888‌]
Me e [‌888‌]

e 88% ee eeeeeee.

e Meeeeeeeeee eeeeeeeeee: Me, MeMM8, MeMM8; eeeee: 88% (8:8).[‌888‌]

e Mee M8=M.

e Meeeeeeeee eee M8=Me: 8. Me, eee MM8; 8. MeMe; eeeee: 88%.

e Mee eeeeeeee.

Meee eeeeee ee eeeeeeeeeeeee ee eeeeeeee ee Meeee eeeeeeeeee eeeeeee ee 8,8-eeeeeeeeeee eeeeeeeee-8,8-eeeeee eee ee eeeeeee eeeeee ee eeeeee, eeeeeee eeeeee eeeeeeeeeee ee eeeeeeeeee ee e eeeeeeeee (e.e., 888 eeee 8, 888 eeee 8, Meeeee 88). Me 8-(eeeeeeeeeeeeee)eeeeeee eee 8,8-eee(eeeeeeeeeeeeee)eeeeeee, eee eee-eeeeeeeeeeee eeeeeeeeeeee (e.e., eee/eeeee=8:8 eee 8:8, eeeeeeeeeeee) eeeee eeeeeeeeeee ee eee eeeeee eeeeeeeee eeeeee eeee eee eeee eeeeeeee eee eeeeeeeeeee ee eee 8-eeeeeeee.[‌888‌,‌888‌] Meeeeeeeeeee eeeeeee ee eeeeeeeee eeeeeeeeeeeee ee eee eeeeeeeee (e.e., eeeeeeeeeeee, eeeeeeeeeeeeee) eeeeee eee eeee ee eeeeeee M8,8-eeeeee eeeeeee eee eeeee eeeeeeeee eee eee eeeeeeeee eeeeeeeeeee eeeee. Meee eee eeeee-eeeeeeeee eee eeeeee eeee eeee eee 8-eeeeeeeeeee, eeeeeeee eee eeee eeeeeeee eee 8-eeeeeeeeeee. Meeeeeeeeee eee eeeee eeeeeeeeeeeee ee eee eeeee-eeeeee (e.e., eeeee/eee=8:8 eee 8-eeeeeeeeeeeeeeee eeee eee 888% eeeee eee 8-eeee-eeeeeeeeeeee).[‌888‌] Mee eeeeeeeeeeeeee eeeeeee ee eeee eeeeeeeeeee ee eeeeeeeee eeeeeee eeeeeee eee eee eeee ee e eeeee eee eeeeeeeeeeeeeeeeeeee (eeeeee eeeeeeeeee), eeeee eeeeeeeeeeeeeeeeeeee (eeeeeeee eeeeeeee eeeeeeeeee), ee eee eeeeeeeeeeeeeeeeeeee (eeeeee eeeeeeee eeeeeeeee), eeeeeeee eeeeeeeeee ee eee eeeeeee ee eeeeeeeee. Meeeeee eeeeeeeeeeee eeeeeeeeeeee eeeeeee eee eee eeeeeeee eeeeeeeeeeeeeeeee ee eeeeeeeee eeeeeeeeeee (e.e., Meeee 88, 888, 888, 888; Meeee 88, 888).[‌888‌] Mee eeeeeeee ee eeeeeeeee eeeeeeeee eeeeeee eeeeee ee eeeeeeeee eeeeeee eeeeeee eee eeeeeeeee eeee eee eeeeeeeeeeeeeeee (e.e., eeeee eeeeeeeeee eeeee ee eeeeeeee eeee ee eeeeeee) eee/ee eeeeeeeeeeeeeeeee ee eee eeeeeeeee eeeeeee eee eeeeeeeeeeeeee eeeeeeeeeee ee eee eeeeeee eeeee ee eeeeeeeee eeeeeeeeeeeee.[‌888‌,‌888‌]

Mee Meeee eeeeeeeeee ee eeeeeeee eeeeeeeee eeee eeeeeeeee ee eeeeeeeeeeeeee eeeeeeeee eeeeeeeee ee e eeeeeeee eeeeeeeee eeeeeeeeeee eeeeeeeee eee eee eeeeeeeeeeeee eeeeeeeeeeee ee eeeeeeeeeeee eee eeeeeeeeeeeee (Meeeee 88). Meee eeeeee 888 eee eeeeeee eeeeeeeee eeee eeee eeeeee 888, eeeee eee ee eeeeeeeeeee eeee e eeeeeee ee eeeeeeeeeee eeeeeeeeeeeeee eee eeeeeeeeeeeee eeeeee[‌888‌,‌888‌] ee eee eeee eeeee (e.e., ee eeee 888 eee 888) ee eee eeeeeee eeeeeeeeee[‌888‌,‌888‌] ee eeeee 888 ee eeeeee 888 eee 888 eeeee eeeeeeeeee. Meeeeeeeeeeee ee 888 ee eee eeeeeeeeee eeeeeeeee-8,8-eeeee 888 eeeeeeee eeeeeeeeeeeee eee MeeeeMeeee eeeeeeeee, eeeeeeeee eeeeeeee eeeeeee 888.[‌888‌] Meee- eee eeeeeeeeeeeee (e.e., 888) eeee ee eeeeeeeeeeee (e.e., 888)[‌888‌] eeeee eeee eeeeeeeee eee ee eeeeeeeeeee eeeeeeeee ee eeeeeee eeeeeeeeeeee eeeeeeeee (e.e., ee eeee 888) ee eeeeeeeee eeee eeeeeee eeeeeeee ee eeeeeeeeeeeee eeeeeeeeeeeeee ee eeeeeee.[‌888‌] Meeeeeeeee eeeee eeeeeeeeee ee eeee eeeeeee, eeee eeeeeeeeee eeeee, ee eeeee eeeeeeeeeee 888 eeeeee eeeeeeee eeee eee eeeeeee eeeeeeeeeeeeee eeeeeeeeeee ee eeeeeeee eeeee eeeeeeeee 888 (e.e., Meeee 88, eeeeeeee 888).[‌888‌] Meeeeeeeeeeee, eeeeeeeeee eeeeeeeeeee ee eeee eeeeeee 888 eeeeeeee ee eeeeeeeeeeeeee eeeeeeeeee eeeee ee eeeeeeeeee eeeeeeeeeee 888 (e.e., Meeee 88, 888888, 888, eee 888), eeeee eee ee eeeeeeee ee eeeeeeeeeeeeeeeee 888[‌888‌,‌888‌] ee eeeeeeeeeee eeeeeeeeeeeeee ee eeeeeeee eeeeeeeee 888 eeee e eeeee eeeeeeeeee eeeeeeeeeee.[‌888‌‌888‌] Meeeeeeeeee ee eee eeeeeee eeeeee eee eeeeeeee eeeee ee eeeeeeeeee eeeeeeeeeee 888 eee 888 (e.e., Meeee 88, eeeeeeee 888) eee eeeeeeeeeeeee eeeeeeee. Mee eeeeeeeeeeee ee eeeeeeeeeeeeee eeeeeeeeeeeeeee eeeeeeeee eee eee Meeee eeeeeeeee ee eeeee eeeeeeeee ee eeeeeee eeeeeeeeeee ee Meeeee 88. Meee eeeeeeeee eeeeeeee eeeee Meeee eeeeeeeeee (e.e., eeeeeeee ee eeeeeeeeee eeeeeeeeeeee) eee eeeeeeeee eeeeeeeeeeeee eeeeee.[‌888‌]

Meeeee 88 Meeeeeeee Meeeeeeeee Meeeeeeee eeee Meeee Meeeeeeeee[‌888‌,‌888‌,‌888‌,‌888‌,‌888‌,‌888‌‌888‌]

Meeeee 88 Meeeeee Meeee Meeeeeeeee ee Meeeeeeee Meeeeeeeeeee[‌888‌,‌888‌,‌888‌]

Meeeeeeeeeee Meeeeeeee

[(8M,8M)-8,8-Meeeeeee-8-(8-eeeeeeeeeeeeeee-8,8-eeee-8-ee)eeeeeeeeeee]eeeeeeee (888):[‌888‌]

Me e eeee ee Me (88ee, 8.8eeee) ee eeeeeee eeeeeeeee MM8 (88eM) eee eeeee, eeeeeeee, e eeee ee eeeeeee 888 (88ee, 8.888eeee) eee e-MeMM (8.8eM) ee eee MMM (8eM) eeee e eeeeee ee 8eee. Mee eeeeeee eee eeeeeee eee 8e eee eeee eeeeeeee eeee MM8Me. MM8 eee eeeeeeeeee, eee eeeeeee eee eeeeeee eeee M8M, eee eee eeeee eee eeeeeeeee eeee Me8M (8×8eM). Mee Me8M eeeeeee eee eeeeee eeee eeeee eee eeeee (Me8MM8). Meeeeee ee eee eeeeeee eeeeeeeee eee eeeeeee; eeeee: 88ee (88%).

8,8,8,8,8,8-Meeeeeeeeeeeeeeeeee-8(8M)-eee (888):[‌888‌]

M eeee ee eeeee 888 (88e, 8.888eee), ee MMM (888eM) (eeeee eeee MMM eee eeeeeeeee eeee Me) eee MM8 (888eM) ee e eeeee-eeeeee eeeee eeeeeeee eeee e eeeeeee, eeeeeeee eeeeee, eee e eeee eeee eeeeee eeee, eee eeeeeee eeee Me eeee (8.8e, 8.88eee) eeee 888eee, eeeeeeeee eeee eee eeeeeeee ee eeeee, eee eee eeeeeee eee eeeeeee eee 88eee; eeee eee MeMM (88e) ee eMeMM (88e) eee eeeee eeee e 8888-eee eeeeee. Me eeee eeeee eeeee eee e eeeeeeee eee eeeeeee ee eeeee eeee eee eee ee eeee eeeeeeee. Meee eee eeeeee eeeeeeeeee ee eeeeeeee eee eeeeeee eeeeeeeeeee. Meee eee eeee eeeee eee eeeeeeeeeee, eee MM8 eee eeeeeeeeee, Me8M eee M8M eeee eeeee, eee eeeeee eeeeeeeee, eee eee eeeeeee eeeee eee eeeeeeeeeee. Mee eeeeeeee Me8M eeeeeeee eeee eeeeee eeee eeeee, eeeee (M8MM8), eeeeeeeeeeee, eee eeeeeeeee (ee 88888°M/88Meee) ee eeee e eeeeeee eeeeeeeeee 888% ee eeeeeeeee 888; eeeee: 88.888.8e (8888%). Mee eeeeeee eee eeeeeeeee eeee eee eeeeeeeeeeeeeeeeeeeeee eeeeeeeeee.

8-(8-{[(Meeeeeeeeeeeeeee)eee]eeeeeeee}eeeeeeeee-8,8-eeeeee)-8,8-eeeeeeeeeeeeee-8-ee (888):[‌888‌]

Me e eeeee eeeeeeeeee ee Me eeeeee (888ee, 88eeee) eee eeeeeeeeeee (88ee, 8.88eeee) ee MMM (8eM) eee eeeeee eeeee (ee. 88eee) e eeee ee 888 (888ee, 8eeee) eee eeeeeeeeeeeee (888ee, 8.8eeee) ee MMM (8eM) ee 88°M eeeee ee eeeee eeeeeeeeee. Meeeeeee eee eeeeeeeee eee 8e ee eee eeee eeeeeeeeeee. Mee eeeeeee eee eeee eeeeeeeeee eeee M8M (8eM) eee eeeeeeeee eeee Me8M (8×88eM). Mee eeeeeee eeeee eee eeeee (Me8MM8) eee eee eeeeeeee eeee eeeeeee (88Meee) ee eeee e eeeeeee, eeeee eee eeeeeeee ee eeeeee eeeeeeeeeeeeee (eeeeeee eeeeeee, eeeeee/MeMMe) ee eeeeee eee eeee eeeeeee; eeeee: 888ee (88%).

8-[(8-Meeeeeeee-8-eeeeeeeeeeeeeeee-8,8-eeeeee)eeeeee]eeeee (888):[‌888‌]

Me (888ee, 88eeee) eee eeeee ee eeeeee ee e eeeeeee eeee ee 888 (888ee, 8eeee) ee eee MM8 (88eM) eee MMM (8eM) ee eee eeeeeeee ee MeMM (8.88e) ee 88°M. Mee eeeeeee eee eeee eeeeeee eee 88eee eee eee MM8 eee eeeeeee ee eeeeeeeeeee ee ee. Mee eeeeeee eee eeeeeeeee eeee Me8M eee eeeeeeeeeeeeeee ee eeee eeeeeee; eeeee: 888ee (88%); eeeee eeee eeeeeeeeeeeeeeee eeeeeeeeeee (88%).

References