"determined to not" is correct and usable in written English and can be used when you are expressing a strong intention to not do something.
For example: "He was determined to not give up the fight."
"I was determined to not move".
The Eckhouses are determined to not make an Italian facsimile.
"I'm determined to not let it change me.
"But we were determined to not worry about that," she says.
Knowing she doesn't suffer fools, I was determined to not waste her time.
From the beginning I was determined to not just be a flash in the pan.
Executives at PepsiCo and Coca-Cola are determined to not fade away before the Accelerade onslaught.
"I was just determined to not let him fall by the wayside," he said.
However, Mignolet is determined to not let any speculation affect him and shrugged off suggestions he is struggling to cope.
Determined to not worry about the future, I tucked into British Midland's free onboard champagne with gusto.
Golubev dictated nearly every point, determined to not let Nadal run him from side to side with his forehand.
