Information was originally formed the way you describe and was used in this sense beginning in the 15th century (source). However, in the mid 16th century, it started to refer just to the knowledge delivered rather than the act of delivering it. Today, information is still used in the original sense only in certain legal contexts.
Explanation went through the same process, but both senses are still in use.
However, V-ation does not mean to V. The suffix -ation is actually two suffixes:
- -ate, which is used in many Latin loanwords and in this case describes doing or making something into a certain state (e.g., duplicate, separate, aggravate, instantiate, automate), and
- -ion, which makes a noun describing the either the act or the result of doing a verb.
This construction is not the same as the infinitive form of the bare verb. You can sometimes use an infinitive as a noun the same way you could use -ation, but in all the examples I can think of, you could also use the gerund (-ing).
These are all very similar, but I think (1) is the most idiomatic in casual use but the others are more acceptable for highly formal use:
- Automating the factory would cost jobs.
- To automate the factory would cost jobs.
- Automation of the factory would cost jobs.