“It’s very rare that…” or “It’s very rarely that…”

I’ve read and heard “It’s very rarely that opportunity knocks twice” and I wonder whether it shouldn’t be “rare” instead. Since “it” (in this particular case) is a nominative pronoun introducing the noun clause, I would expect an adjective instead of an adverb. e.g. it’s very interesting that/it’s very unusual that/it’s most unlikely that/etc.

For example, I wouldn’t say “It’s very rarely for a person to live to be a hundred.” To be honest, If I had to say something like that, I would probably say “It’s unusual for a person to live to be a hundred”. Assuming, however, that I had to use either “rare” or “rarely”, I think I would spontaneously choose “It’s very rare…”

In a sentence like “It’s very ______ that opportunity knocks twice”, should we say “It’s very rare” or “It’s very rarely”? The same question goes for similar sentences like the other example.

EDIT - I expect an answer explaining why one form is correct and the other isn't (or that maybe both are correct) and also expect comments on the two sentences I've posted.

Short answer:

The Original Poster's sentence using the adverb rarely is an it-cleft construction. The clause following the adverb is a relative clause which has gaps in it. In contrast, the Original Poster's sentence using the adjective rare is an extraposition. The clause following this adjective is not a relative clause. It is a normal subordinate finite clause with no gaps in—often called a content clause. Although they look very similar, the two types of sentence are very different.

Full answer:

It’s very rare that opportunity knocks twice.

It’s very rare for a person to live to be a hundred.

It's very rarely that opportunity knocks twice.

OK, so there are two particular types of sentence in English with it at the beginning that look very similar, and can occasionally even look identical. As it happens, sentences (1) and (3) here are mutually exclusive in the sense that they cannot be alternative versions of the same type of sentence. Rather, they exemplify two very different and interesting constructions which happen to look very similar.

It-clefts

Bob gave you the elephant.
It was Bob who gave you the elephant.
It was Bob that gave you the elephant.
?It was Bob gave you the elephant.

Sentence (4) is a canonical sentence. It follows our everyday, mundane expectations of a normal English sentence. Sentences (5) and (6) convey the same information, but this information is arranged differently and the sentences carry a different sort of emphasis or focus. They seem to place a lot of emphasis on the word Bob. We can say that the noun phrase Bob has been foregrounded. The rest of the information in the sentence is usually said to have been backgrounded and appears in a relative clause at the end of the sentence.

Sentences like these are called clefts because the information in the canonical version of the sentence has been split or 'clefted' into two different constituents. One bit of it gets foregrounded and the other bit backgrounded and put in a relative clause. They are it-clefts, of course because the Subject position in these sentences has been filled by a meaningless dummy subject, the word it.

The foregrounded part of an it-cleft is the semantic antecedent for the relative clause. So in (5) and (6) the word Bob is the antecedent for the relative clause who/that gave you the elephant. But unlike normal restrictive (also called integrated) relative clauses, the antecedent and relative clause in an it-cleft do not form a single constituent. So, for example, in (5), there is no single noun phrase "[Bob who gave you the elephant]". Rather we have the noun phrase Bob appearing as the Complement of the verb BE and another separate constituent who gave you the elephant occurring outside of the nucleus of the clause.

These relative clauses are nonetheless more like restrictive relative clauses than non-restrictive ones. For example, these relative clauses can, of course, be introduced by the word that, as in example (6) above, whereas non-restrictive relative clauses cannot. Notice as well that when the verb in the relative clause has its own subject, it can occur bare without the words that, who or which. In the example above the verb gave does not have its own subject and so example (7) with a bare relative clause is degraded and may be ungrammatical for some speakers. Compare that with examples (8-11) below.

You gave the mongoose to Sheila.
It was Sheila [who you gave the mongoose to].
It was Sheila [that you gave the mongoose to].
It was Sheila [you gave the mongoose to].

Here we see that example (11) with a bare relative clause is perfectly acceptable because the verb gave has its own subject, the word you.

Lastly, notice that because the bracketed strings are relative clauses, they have gaps in which are semantically co-indexed with the antecedent. So we can model (9) above like this:

It was Sheila_i [that you gave the mongoose to _____i ].
It was Sheila [that you gave the mongoose to ~~Sheila~~ ].

One thing that does separate out these types of relative clauses from integrated relative clauses, however, is that they can take a wider range of antecedents than normal relative clauses. So we can have adverbs or adverb phrases, for example, as the foregrounded antecedents in it-clefts:

It was only recently_i [that I noticed ______i how much money had gone missing].
It was only recently [that I noticed ~~only recently~~ how much money had gone missing].

In the sentences above, we see the adverb phrase only recently appearing as the antecedent for the relative clause.

Extrapositions

In English we don't really like to have clauses functioning as the Subjects of sentences. The main reason for this seems to be that they are very difficult to process:

That you went and asked my ex-girlfriend out without asking me first made me mad.
For her to accept your offer so enthusiastically seemed poor taste .
To do that kind of thing to your best friend can be very bad for your health.
For people who engage in such activities to be subject to freak kicking-accidents as they leave the building is not unknown.

The sentences above are all grammatical, but we don't like to use sentences like these ones very much because the clauses functioning as Subjects make them clunky and hard going. It is much more normal for us to shunt those clauses down to the end of the sentence where they appear as separate Complements of the verb and then to stick a dummy pronoun, the word it in Subject position:

It made me mad [that you went and asked my ex-girlfriend out without asking me first].
It seemed poor taste [for her to accept your offer so enthusiastically].
It can be very bad for your health [to do that kind of thing to your best friend].
It is not unknown [for people who engage in such activities to be subject to freak kicking-accidents as they leave the building].

We often see sentences like this with an adjective functioning as a Predicative Complement of the verb BE:

To feed the lions is dangerous.
It is dangerous [to feed the lions].

Notice that we cannot use adverbs in this way. Adverbs cannot normally function as Predicative Complements of the verb BE and almost never when the verb BE is used in its ascriptive sense like this:

*To feed the lions is dangerously.
*It is dangerously to feed the lions.

The Original Poster's examples:

It’s very rare that opportunity knocks twice.

It’s very rare for a person to live to be a hundred.

It's very rarely that opportunity knocks twice.

Sentences (1) and (2) are extrapositions. We can give clunky but canonical versions of these sentences as follows:

[That opportunity knocks twice] is very rare.
[For a person to live to a hundred] is very rare.

Notice that we cannot replace the adjective rare with the adverb rarely here, because rarely cannot freely function as a Predicative Complement:

1.# *That opportunity knocks twice is very rarely. (ungrammatical)

2.# *For a person to live to a hundred is very rarely. (ungrammatical)

Sentence (3), however, is not an extraposition. It would be ungrammatical if it was, as is shown in (1#) above. Rather it is an it-cleft. The canonical version of this sentence is:

3.# Opportunity knocks twice very rarely.

In example (3) the adverb rarely has been foregrounded, and the rest of the information occurs in a relative clause at the end. The relative clause has a gap in it which is co-indexed with the adverb phrase very rarely:

It is very rarely_i [that opportunity knocks twice _____i].
It is very rarely [that opportunity knocks twice ~~very rarely~~].

Notice that we cannot use the adjective rare in sentence 3#:

*Opportunity knocks twice very rare. (ungrammatical)

So although the Original Poster's sentences with rare and rarely seem very similar, they are, in fact, completely different!

The example you give has multiple possible syntactic interpretations, as FumbleFingers alludes to in his comment.

The crux here isn’t so much adjective rare vs. adverb rarely, but more what kind of it the subject is and, consequently, what the basic structure of the sentence is. It as the subject of a sentence can be either a regular pronoun (in the literal sense, meaning pro-noun, i.e., standing in for an actual noun phrase and thus having a particular reference), and functioning as the real, semantic subject of the sentence; or it can be a dummy pronoun that doesn’t have any real referentiality and is only needed for purely syntactic reasons—in this case, there is a semantic subject somewhere else.

If we take “it” to be a dummy-it, then that logical, semantic subject must be “that opportunity knocks twice”. The sentence is then equivalent to “That opportunity knocks twice is very [rare/rarely]” (this type of replacing a subject with a dummy-it and then having the real subject at the end is called extraposition). In this case the subject is represented twice, as it were: once in purely syntactic terms by the preliminary dummy subject “it”; and again at the end of the clause by the logical and semantic subject “that opportunity knocks twice”. If we collate those two representations into one and just say that the subject is X, then the structure of the sentence is underlyingly simply “X is very rare(ly)”, and it’s clear that very rare(ly) can only be a subject complement. Since adverbs like rarely cannot function as subject complements, but adjectives like rare can, very rare is the only possibility here.
If, on the other hand, we take “it” to be a true pronoun, with an implied antecedent not present in the sentence, then we have a wholly different structure: “it” is the actual subject, so “that opportunity knocks twice” cannot be—it must be something else. In a copular clause like this, the only options realistically available are adverbial phrase and subject complement. As stated above, adjectives like rare can function as subject complements; so can noun clauses like “that opportunity knocks twice”. But you can’t have two subject complements like that. Luckily, rarely, being an adverb, can function as the other option, an adverbial phrase, which solves things: “It” is the subject, “is” is the verb, “very rarely” is an adverbial phrase modifying the verb, and “that opportunity knocks twice” is the subject complement.

With the second way of parsing the sentence, the antecedent to it is usually something like “the reason” or “the case” or “the problem”. Alternatively, you can interpret it as being a shortening of “It is rarely [the case/reason/problem/…] that…”, which would be another case of a construction with an extraposed subject, this time equivalent to “The case/reason/problem is very rarely that opportunity knocks twice”.

In the sentence given, you’d need a slightly contrived context for the that interpretation to make much sense semantically—after all, if opportunity knocks twice, that is rarely a problem. With a bit of licence, though, something like the following might work: “I’ve never known much luck. Missed chances pass me by like so many fireflies in the headlights. If ever I end up doing something a second time over, it’s rarely that opportunity knocks twice, more often it’s a case of it never raining but pouring.”

But the difficulty of wrangling that interpretation is due to the particular semantics of your sentence. Other examples would work differently. For example, “She’s missed so many classes this term. It’s rarely that she cuts school, it’s just that she can’t get out of bed in the morning and ends up being late.”

(This is all, of course, assuming the traditional role of rare as an adjective and rarely as an adverb.

I’m sure there are speakers who confuse the two and end up using rarely as an adjective—after all, adjectives in -ly are not rare (excuse the pun), as your own example “It’s not unlikely that…” exemplifies.

While I have no statistics to back me up here, I would expect that using rarely as an intended adjective in construction #1 would be considered ungrammatical by the vast majority of native speakers. Using rare as an intended adverb in construction #2 would likely fare slightly better, but would probably still be ungrammatical to most.

In other words, I’d say the assumption that we’re using rare(ly) in their traditionally accepted roles is a fair one to make.)

It can only be "rare". There is no doubt that:

(1) It is very rare that opportunity knocks twice

is a case of extraposition of a sentential subject and that

(2) That opportunity knocks twice is very rare

is the corresponding sentence without extraposition. In both cases, "very rare" is subjective predicative complement. From an intuitive semantic point of view, this is quite obvious: what is claimed to be very rare is the possibility that opportunity should knock twice.

Adverbial "rarely" would be impossible as subjective PC in either version; that is particularly clear in the non-extraposed version.