From Gerunds and Infinitives: Their Noun Roles
"The infinitive is often a complement used to help define an abstract noun. Here is a very partial list of abstract nouns, enough to suggest their nature. Try following these adjectives with an infinitive phrase (their desire to play in the championship game, a motivation to pass all their courses, her permission to stay up late, a gentle reminder to do your work) to see how the phrase modifies and focuses the noun."
"determination" is one of those abstract nouns requiring an infinitive complement. Of course, most native English speakers would just rely on their ears and be correct.