SMTP Module not sending email
You probably have to be auth to be able to send mail from gmail's SMTP (smtp user/ smtp password).
Moreover, you have to "allow" the sender's email in your google account.

theMailYouSendFrom@whatever.com have to be allowed to send mail with account yourAccount@gmail.com; somewhere in gmail's parameters, you can validate this mail.

I remember there is a limit, 450 mails/day for each google account (this could have change now, that was 3 or 4 years ago), and more with payed gapps.