GD Mail Queue Pro plugin has support for custom SMTP services for PHPMailer. One of the services included is for the Mailgun email sending service. And, to start using this service to send emails using SMTP you need Mailgun account. After you have set up your Mailgun account, you need to get SMTP username and password to add to the GD Mail Queue Pro plugin Mailgun Service settings panel.
To get the required information, open your Mailgun account, and find the SMTP information under the Sending -> Domains panel. Mailgun supports sandbox and real and verified domains. Make sure to use the SMTP information for the domain you want to use on your website. If you want to use sandbox domains, they are very much restricted to sending emails to authorized recipients only.
Mailgun SMTP service supports additional options related to tracking of emails and tags to assign to emails.