At liberty to do sth：If someone is at liberty to do something, they’re having the right or freedom to do something, or have been given permission to do it. （表示一个人可以自由地、随意地、不受约束地做某事。）
例句1：I know you’re curious about the case, but I’m not at liberty to talk about it.
例句2：I am not at liberty to discuss my client’s case, especially reveal their names.
Take liberty of doing something：to do something that will have an effect on someone else, without asking their permission. （冒昧做某事而不顾忌别人的感受，或者是擅自做某事而不考虑规则和约束。这个短语通常用过去式且大多用于正式场合，如常见于书信中。）参考例句如下：
- I took the liberty of telling Mary that her husband had borrowed five thousand dollars from me. （我冒昧地告诉玛丽她先生向我借五千块的事）
- I took the liberty of asking an old friend of mine to join us for dinner. （我擅自邀请了一位老朋友和我们共进晚餐）