Relax,Don't worry too much. I'm no legal expert but employment contracts only bind obligations up to and including notice period, they are not licenses for indentured labour. Its hardly in their interest to pursue you for anything, with the exception of any sign on bonus or any benefits yet received.It won't really bother them much, as a big company, there will be plenty more where you came from (unlike a smaller company who would be aggrieved at the wasted cost of recruitment)Though bailing at the last minute will of course make them angry and burn your bridges some what with that department at least. You may consider being diplomatic and omitting that you are bailling for a better offer, but just say that your personal circumstances have changed in a way that makes it impossible for you to accept their offer. (don't lie, as this is dishonest just present it as a confidential matter, which is your right)