give/put/apply one’s mind to (doing) sth.
专心（认真）做某事。
这里的to是介词。
He gave his mind to the arrangements for the next day.
他认真考虑第二天的安排。
He always gives his mind to reading books or doing his homework in his study.
他总是专心地在他的书房里看书或做作业。
You could do fine in the world if you put your mind to it.
如果认真去做，任何事都可以做好。
She could have been a brilliant pianist if she'd put her mind to it.
如果她专心致志，坚持到底，她本可以成为一名杰出的钢琴家。
In spare moments he applied his mind to how rockets could be used to make money.
在业余时间他潜心研究如何能用火箭来赚钱。
close one’s mind to (doing) sth.不去想(做)某事
open one’s mind to (doing) sth愿意(做)某事
She has closed her mind to last year's traumas.
她不再去想去年遭受的创伤。
She also stimulated his curiosity and opened his mind to other cultures.
她还激发了他的好奇心，使他愿意了解其他文化。
have a mind to do sth想做某事
The captain of the guard looked as if he had a mind to challenge them
警卫队长看上去似乎想向他们挑战。
He raged on about how he had a good mind to resign.
他还在大发脾气，叫嚷着真想辞职不干了。
I have half a mind to move elsewhere.
我有点想搬到别处去。
to 是介词.的常用结构：
1.动词+介词to+动名词
(1) admit to doing sth. 承认做了某事
(2) apply to doing sth. 适用于做某事
(3) object to doing sth. 反对做某事
(4) see to doing sth. 负责做某事
(5) stick to doing sth. 坚持做某事
(6) take to doing sth. 喜欢上做某事，逐渐习惯做某事
2.动词+宾语+介词to+动名词
(1) apply oneself to doing sth. 专心致力于做某事
(2) devote sth. to doing sth. 把……献给做某事
(3) devote oneself to doing sth. 献身于做某事
(4) limit sth. to doing sth. 把……限制在做某事的范围内
(5) reduce sb. to doing sth. 使某人沦为做某事
3.动词+名词+介词to+动名词
(1) give one's life to doing sth. 献身于做某事
(2) give one's mind to doing sth. 专心做某事
(3) have a dislike to doing sth. 厌恶做某事
(4) have an eye to doing sth. 注意做某事
(5) have an objection to doing sth. 反对(反感)做某事
(6) pay attention to doing sth. 注意做某事
(7) set one's mind to doing sth. 决心做某事
4.be+形容词+介词to+动名词
(1) be equal to doing sth. 等于做某事，能胜任做某事
(2) be used to doing sth. 习惯于做某事
(3) be opposed to doing sth. 反对做某事
(4) be reduced to doing sth. 使某人沦为做某事
(5) be devoted to doing sth. 把时间(钱，精力等)献给做某事
(6) be limited to doing sth. 把……限制在做某事的范围内
5.其他结构+介词to+动名词
(1) get down to doing sth. 开始做某事，认真处理某事
(2) look forward to doing sth. 盼望做某事
(3) What do you say to doing sth? 你认为做某事如何?