Disclaimer: This code doesn’t search for a single exact match, so for domain\j_doe it may return domain\j_doe_from_external_department‘s email address if such similarly named account also exists. If such behaviour is undesirable, then either use a samAccountName filter intead of an anr one used below or filter the results additionally.
I have used this code successfully (where “account” is the user logon name without the domain (domain\account):
// get a DirectorySearcher object
DirectorySearcher search = new DirectorySearcher(entry);
// specify the search filter
search.Filter = "(&(objectClass=user)(anr=" + account + "))";
// specify which property values to return in the search
search.PropertiesToLoad.Add("givenName"); // first name
search.PropertiesToLoad.Add("sn"); // last name
search.PropertiesToLoad.Add("mail"); // smtp mail address
// perform the search
SearchResult result = search.FindOne();