Here are some instructions on how to configure an IIS Application Pool to run as a domain account.
The gist is to ensure that the account is a member of the IIS_WPG group on the local machine. Then start the application pool.
To be sure, run this command:
aspnet_regiis -ga MachineName\AccountName
as this document states:
Also, don't forget to create an SPN for the account:
setspn -A MSSQLSvc/ databaseservername.fullyqualifieddomainname