Process proc = new Process();

proc.StartInfo.Domain = "YourDomain";
proc.StartInfo.UserName = "Username";
proc.StartInfo.Password = "YourPassword";

Process proc = new System.Diagnostics.Process();
System.Security.SecureString ssPwd = new System.Security.SecureString();
proc.StartInfo.UseShellExecute = false;
proc.StartInfo.FileName = "C:/YourPath/YourProcess.exe";
proc.StartInfo.Arguments = "Args"; //Arguments if any, otherwise delete this line
proc.StartInfo.Domain = "domainname";
proc.StartInfo.UserName = "username";
proc.StartInfo.Password = "password";
proc.Start();