be to do: (1)表示事先商定、安排或准备要做的事情。如：
The students are to meet at the school gate tomorrow. 明天学生们将在学校大门口集会。
2）表示可能性，必要、责任、义务、禁止等。如：
Her necklace was not to(couldn't)be found. 她的项链找不到了。
be going to do:
1) 表示将要发生的事情或打算最近要进行的动作。如： It is going to rain soon. 快要下雨了。
2) 在含有条件状语从句的主从复合句中，主句一般不用be going to，而常用will（第一人称用shall）。如：
The football match will be put off if it rains tomorrow. 如果明天下雨，足球赛将被推迟举行。
be about to do:
1) 表示即将发生的动作，在时间上指最近的将来。如： We are about to start. 我们就要出发了。
The new school year is about to begin. 新学年开学在即。
2) 在含有be about to do的句子中，不能再加时间状语。如： Wrong: The medical team is about to start immediately.
Right: The medical team is about to start. 医疗队就要出发了。
附：be to do 用法的详细讲解：
be to +动词不定式中的be to用作情态习语, 这时的be to do表示: “计划”、“安排”、“义务”、“应该”、“可能”、“命运”等。(have to, ought to)。如: He is to have a holiday. (表示将来)
The committee is to meet today. (表示计划、安排)
You are to go to the hotel where rooms have already been booked for you.
1. 表示 “将”、“计划”、“安排”。(意思接近于be going to)
如： Their daughter is to get married soon.
It was the last film at the cinema，which was to close next day.
was/ were to do 表示过去曾经计划要做的事，或者过去应当做的事，而且从现在的角度来看已经实现了。
如：
I felt nervous because I was soon to leave home for the first time.
The expedition was to start in a week's time.
was/ were to have done, 表示 “本打算”、“本计划”或“本应当” 做的事而没有做成或没有发生。
如:
I was to have seen him last Wednesday, but he didn't come.
We were to have been married last year.
2. 表示 “义务”、“应该” 。(意思接近于should， must， ought to， have to)
如： No one is to leave the building. 谁也不得离开这楼房。
You are not to smoke in this room.=You are not supposed to smoke in this room.
You are to be back by 10 o'clock. 你必须十点以前回来。
3. 表示可能性, 相当于can, may 如:
Such books are to be found in the library. 这样的书在图书馆里就能找到。
Not a single sound was to be heard. 一点儿声音也听不到。
Not a soul was to be seen. 看不到一个人影。
She was nowhere to be found. 哪儿也找不到她。
She was never to see his wife and family again.
4. 表示 “命运”, 将来必然要发生的事, 译作 “注定……”。如：
He came to power, but he was to play dearly for it: soon he was assassinated. They said goodbye, little knowing they were never to meet again。
5. 用于“if…were to do”，表示虚拟语气。如：
If it were to rain tomorrow, the sports meeting would be put off. 如果明天下雨, 运动会就会延期。
