Learn English – golden rule to judge what the word “which” stands for in a sentence

SHORT VERSION:

1. I have nothing of which to complain.
2. I have to make a decision of which to choose.

Two different sorts of relative clause are involved in these sentences.

• In 1, of which to complain is a bound relative clause modifying nothing: of which stands for the complement of complain.

• In 2, which to choose is a free relative clause acting as a nominal, the object of the preposition of. The preposition phrase of which to choose is the complement of the noun decision; this construction is a standard way of expressing the object of a 'nominalized' transitive verb.

  my decision of X is equivalent to I decide X.

  In practice, however, this is pretty stiff and unnatural, because decide usually takes a clausal complement rather than a nominal direct object. With decision most speakers will omit the of:

  I have to make a decision which to choose.

LONGER VERSION:
At one level this is a fairly simple question, involving a contrast between a bound relative clause and a free relative clause. At another level, however, the question is significantly complicated by the fact that neither sentence is straightforwardly idiomatic: both involve transformations of the underlying expressions.

Let’s start by simplifying: rewriting your two sentences with the infinitivals in the relative clauses recast as ordinary finite verbs. This will make the underlying structures easier to identify (but there will still be lots of complications). Infinitivals like those in your sentences are understood to take the subject of the matrix clause as their own subjects.

1. I have nothing of which to complain. → I have nothing of which I complain, or more idiomatically → I have nothing of which I can complain.
2. I have to make a decision of which to choose. → I have to make a decision of which I choose, or more idiomatically → I have to make a decision of which I will choose

(That last sentence in fact is still not particularly natural—I'll come back to that later.)

Let’s now look first at the ‘cores’ of those two relative clauses, the pieces I’ve put in boldface, and see how they work. A relativizer—a wh- word or that—points rightward to a missing element, a ‘trace’ or ‘gap’ which must be supplied from context, like the blank in a fill-in-the-blank question. In effect, the relativizer is a ‘variable’, so let’s represent it as X

• In sentence 1, the verb complain takes a preposition phrase with of (or about) as its complement. Both X and the preposition of are needed to make a meaningful English clause:

  ☒ I can complain X
  ☑ I can complain of X.

  Note that in this case the preposition of might have been left ‘stranded’ at the end of the relative clause:

  I have nothing which I can complain of.

  In sentence 1, then, of is part of the relative clause.

• In sentence 2, however, of is not part of the relative clause. The verb choose takes a noun phrase as its object but does not take a preposition phrase headed by of as its complement^†, so we can’t put the of inside it:

  ☑ I will choose X.
  ☒ I will choose of X.

  ^{† Just to make things more complicated, choose can take a preposition phrase headed by between or among as its complement; but that’s not relevant here.}

  In sentence 2, then, of is not part of the relative clause.

  ... Then where does it come from? Of with a nominalized transitive verb—in your example, decision < decide—in many cases introduces the object of the underlying verb:

  I define X as Y → my definition of X as Y

  And that's really the only way you can parse a decision of which to choose: which to choose is the object of decide and thus the 'oblique' object of decision. But as explained in the 'Short Version' this is not a very natural way of expressing that thought

All this at last brings us around to the 'simple' part of the question. Relative clauses have two very different uses, 'bound' and 'free':

• In sentence 1, of which to complain is a 'bound relative clause'. It is 'bound' to the word nothing^‡—that is, which points backward to nothing in the matrix clause and 'modifies' it. As a modifier the relative clause would be described in tradtional terms as adjectival.

  ^{‡ If you want to get really technical, it's actually bound to thing—syntactically the 'words' nothing, something, anything, everything are determinate noun phrases, D+NP, and following modifiers are taken to lie in the NP piece modifying the head thing: [_Dno _NP[thing of which to complain]].}

• In sentence 2, which to choose is a 'free relative clause*. It isn't 'bound' to a particular entity in the matrix clause but acts independently as the object of the preposition of. As object of a preposition the relative clause would be described in traditional terms as nominal.