I finally got SQL Server configured so that I could send emails to users on my domain from within a stored procedure using msdb.dbo.sp_send_dbmail
but I'm currently unable to use this method to send messages to external email addresses (those outside my domain). When I attempt to send outside my domain, I get the following error message:
The mail could not be sent to the recipients because of the mail server failure. (Sending Mail using Account 1 (2015-10-30T10:00:25). Exception Message: Cannot send mails to mail server. (Mailbox unavailable. The server response was: 5.7.1 Unable to relay).