SMTP settings can be a bit tricky to get right, but they do work if correctly configured. My notes about it are here:
I would make sure the site "Default Email From Address" in Site Settings is the same address used for the smtp account.
Some users have also reported that when using google they need to change this to true:
<add key="DisableDotNetOpenMail" value="false" />
which will disable DotNetOpenMail and make it use the normal .NET smtp classes. It has always worked for me but some users get TLS errors and disabling DotNetOpenMail seems to solve it.
Hope it helps,