correspondence vs correspond

correspondence is a noun but correspond is not a noun.

Word	Noun	Adjective	Verb	Adverb
correspondence	Yes	No	No	No
correspond	No	No	Yes	No

correspondence (noun)	correspond (noun)
similarity by virtue of corresponding
compatibility of observations
(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
communication by the exchange of letters
the relation of corresponding in degree or size or amount

correspondence (verb)	correspond (verb)
	exchange messages
	be compatible, similar or consistent; coincide in their characteristics
	take the place of or be parallel or equivalent to
	be equivalent or parallel, in mathematics