In chemistry, a lactam is a cyclic amide. The name is derived from two chemical terms, lactone, referring to a cyclic ketone, and amide, a compound containing a nitrogen atom next to a carbonyl group. Lactams are named according to the size of the cyclic ring in the lactam: \alpha-lactams, \beta-lactams, \gamma-lactams and \delta-lactams contain rings made of three, four, five or six atoms, respectively. \alpha-lactams are also called aziridinones. Many widely used antibiotic drugs, including the penicillins and cephalosporins, owe their activity to the presence of a \beta-lactam structure. The lactams may have substitutions added to the nitrogen atom or any of the non-carbonyl carbon atoms in the base structure.
General synthetic methods exist for the organic synthesis of lactams.

 L actams form by copper catalyzed 1,3-dipolar cycloaddition of alkynes and nitrones in the Kinugasa reaction
  Diels-Alder reaction between cyclopentadiene and chlorosulfonyl isocyanate (CSI) can be utilized to obtain both β- as well as γ-lactam. At lower temp (−78 °C) β-lactam is the preferred product. At optimum temperatures, a highly useful γ-lactam known as Vince Lactam is obtained

Beckmann Rearrangement

An acid-induced rearrangement of oximes to give amides.
This reaction is related to the Hofmann and Schmidt Reactions and the Curtius Rearrangement, in that an electropositive nitrogen is formed that initiates an alkyl migration.

Mechanism of the Beckmann Rearrangement

Oximes generally have a high barrier to inversion, and accordingly this reaction is envisioned to proceed by protonation of the oxime hydroxyl, followed by migration of the alkyl substituent "trans" to nitrogen. The N-O bond is simultaneously cleaved with the expulsion of water, so that formation of a free nitrene is avoided.

Schmidt Reaction

Mechanism of the Schmidt Reaction

Reaction of carboxylic acids gives acyl azides, which rearrange to isocyanates, and these may be hydrolyzed to carbamic acid or solvolysed to carbamates. Decarboxylation leads to amines.

The reaction with a ketone gives an azidohydrin intermediate, which rearranges to form an amide:

Alkenes are able to undergo addition of HN3 as with any HX reagent, and the resulting alkyl azide can rearrange to form an imine:

Tertiary alcohols give substitution by azide via a carbenium ion, and the resulting alkyl azide can rearrange to form an imine.
Kinugasa reaction

General structure of a nitrone
A nitrone is the N-oxide of an imine and a functional group in organic chemistry. The general structure is R1R2C=NR3+O- where R3 is different from H.
A nitrone is 1,3-dipole in 1,3-dipolar cycloadditions. It reacts with alkenes to form an isoxazolidine:

One example of this reaction type is the reaction of various Baylis-Hillman adducts with C-Phenyl-N-methylnitrone forming an isoxazolidine in which R1 is phenyl, R2 is hydrogen and R3 is a methyl group .
Nitrones react with terminal alkynes and a copper salt to beta-lactam. This reaction is also called The Kinugasa reaction  for example in this reaction:

The first step in this reaction is a dipolar cycloaddition of the nitrone with the in situ generated copper(I) acetylide to a 5-membered ring structure which rearranges in the second step.
 My Problem
Why is the β-lactams are more reactive to hydrolysis conditions than are linear amides or larger lactams?
This strain is further increased by fusion to a second ring, as found in most β-lactam antibiotics. This trend is due to the amide character of the β-lactam being reduced by the aplanarity of the system. The nitrogen atom of an ideal amide is sp2-hybridized due to resonance, and sp2-hybridized atoms have trigonal planar bond geometry. As a pyramidal bond geometry is forced upon the nitrogen atom by the ring strain, the resonance of the amid bond is reduced, and the carbonyl becomes more ketone-like. Nobel laureate Woodward described a parameter h as a measure of the height of the trigonal pyramid defined by the nitrogen (as the apex) and its three adjacent atoms. h corresponds to the strength of the β-lactam bond with lower numbers (more planar; more like ideal amides) being stronger and less reactive.[5] Monobactams have h values between 0.05 and 0.10 angstroms (Å). Cephems have h values in of 0.20–0.25 Å. Penams have values in the range 0.40–0.50 Å, while carbapenems and clavams have values of 0.50–0.60 Å, being the most reactive of the β-lactams toward hydrolysis.

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