A Lewis acid accepts an electron pair to form a coordinate covalent bond. A Lewis base supplies that pair. This definition covers reactions without proton transfer: pairs the empty acceptor orbital of boron with the nitrogen lone pair.
Metal cations commonly act as Lewis acids by coordinating ligands. Coordination to a carbonyl oxygen can increase the electrophilicity of the carbonyl carbon, explaining many catalytic effects. proton transfer concerns proton donation; Lewis acidity instead describes electron-pair acceptance, so the two classifications answer different questions.
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