I have a google apps account for my domain and use the gmail like email feature of google apps. I find that if I send mail from the googles web interface may email goes through great. If I send email from WordPress on my domain I find that a lot of email does not go through.
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WP Mail SMTP is a WordPress plugin called, which can be used to send email through Google's SMTP servers. Install the plugin then use the following settings:
SMTP Host: smtp.gmail.com
SMTP Port: 465
Encryption: Use SSL encryption
Authentication: Yes
Username: Your full Gmail address or Google App email
Password: your account password
