This 2nd Lt., either infantry or artillery is wearing a frock coat with state buttons, and armed with sword.
His shoulder straps look to be the Smith’s Patent type, and the background color could be either infantry or artillery. The buttons on this 2nd lieutenant’s frock coat are state buttons (most likely New York, as the letters on the belt plate look to be “NY”), not federal pattern. A nice pose, standing with his Model 1850 foot officer sword in hand.
No back mark.