The verb allow can be used in three different syntactic constructions indicating what is allowed. Here are the three constructions with examples from the Corpus of Contemporary American English:
(a) with a gerund complement indicating what is allowed: allow [gerund phrase]
the president last month unveiled plans to allow [drilling in Atlantic waters from Virginia to mid-Florida]
Sets up Web portals that standardize policies and allow [purchasing across state lines]
Note that in this construct, the verb does not include an object indicating the entity which is being allowed, nor is the gerund complement introduced with of, as in the first example from the question. This would be grammatical, though:
Allows modeling and resolving
(b) with just a noun phrase object indicating what is allowed: allow [noun phrase]
and are working with the school administrators to allow [use of personal devices in our schools].
The learning commons has extended its hours of operation to allow [more access to its physical space].
(c) with a noun phrase object (indicating the patient of the allowing) and an infinitive complement (indicating what is allowed): allow [noun phrase] [infinitive phrase]
Note that the only construct showing both what is allowed and the recipient of the allowance is (c).
we're not going to allow [them] [to disrupt this debate and take the focus off the real issue here].
Certainly parents who allow [their children] [to consume violent entertainment products] do share some of the responsibility.
These tools and resources allow [you] [to connect, communicate, collaborate, and create].
Note that the recipient of the allowance isn't always a person or person-like entity:
Only nine states allow [life-sustaining treatment] [to be withheld from patients in a persistent vegetative state].
Note also that this constructions requires both a direct object and an infinitive complement. The verb allow cannot be used with just an infinitive complement; that is, constructions like "allow to [verb]" are ungrammatical. The following examples which I found via Google are clearly written by non-native speakers and are not grammatical:
* What smartphone allows to connect my computer to it for surfing ?
* Image drag and drop allows to create executable files
* Will java allow to use functional interfaces as methods?