word choice - Usage of "expect to" and "expectation to/of"

I've written:

I expect to see you on Monday. I'm
counting the days.

To improve it, I've changed it in:

With the expectation to see you on
Monday, I'm counting the days.

A friend told me: No! You should write the following.

With the expectation of seeing you
on Monday, I'm counting the
days.

Who's the smart one? My friend or me? Is there a general rule to apply here? Like with expect/expectation, but also for willing/wish, etc.

Answer

One of the properties of individual words in a language - and often one of the hardest for foreigners to learn - is what linguists call their "subcategorization frame" : the particular kinds of word and phrase that they require, or allow, to follow them in a sentence.

Rhodri's answer is generally correct: "expect" requires a direct object, which may be of various types including a "that" clause ("I expect that he will come", and an infinitive clause ("I expect to win").
But "expectation" has different requirements: it may take a direct object only if that is a "that" clause ("His expectation that I would come"; any other object must be expressed in a PP (prepositional phrase) introduced by "of": "my expectation of winning").

The bit I disagree with in Rhodri's answer is the implication that because it is a noun, "expectation" cannot take a direct infinitive. This is not so: "expectation" does not take an infinitive, but "ability" can: ("His ability to climb came in useful").