Sentence structures to start an informal email

Question

Are these correct sentence structures to start an email to friend? If no, How to correct the sentence structures?

1. The purpose of I am sending this email is to..
2. The purpose I am sending this email is to..
3. The reason for sending this email is to..

Answer 1

#1 and #2 are not grammatically correct. The third one is, but it is a bit clumsy.

You could say, as MorganFR stated:

The reason for which I am sending this email is ...

Or even:

The reason I am sending this email is ...

In fact, "to" at the end of each proposition already conveys an idea of reason/purpose/goal, so you could simply say:

I am sending this email to ...

Answer 2

I'll add to the previous answer that numbers 1 and 2 are not grammatically correct, and the third one is still pretty formal.

You say that this is an informal email to a friend, but your formality is more on par with sending a business email.

To a friend, I'd just start the message without the formal introduction. If you are writing to invite them to an activity, you might start with:

Hey Parthiban, I'm going to the Comic Con and wanted to invite you to come too.

If you are wanting to ask them to do you a favor, you could start with:

Hi Parthiban, I need your help. Can you do ....

If you are wanting to thank them for something, you could start with:

Hello Parthiban. I wanted to send you a quick note to let you know how grateful I am for ...

The point is that the structure you're seeking advice on is a formal structure that isn't used in informal writing between friends. However, that more formal tone might be more appropriate on a business email, especially with somebody who you don't know well.

When we learn foreign languages (I have some experience with both Spanish and Portuguese, in addition to my native English) we often think in terms of the one right way to speak. However, there are distinct differences in formality depending on whom you are addressing (and in some cultures this is even more pronounced than in most English-speaking countries). These differences in tones are referred to as registers. In our native languages, we change our register depending on the audience, and usually without conscious thought. (Consider, for example the way you talk to a child, versus the way you talk to your neighbor, versus the way you talk to an older relative.) When we learn a new language, we also need to learn when to use which registers, and that is why I've made a distinction between a professional email and an email to a friend.