Analytical formulae are derived for the zero-point vibrational energy and anharmonicity corrections of cohesive mode Gr\"{u}neisen parameter within Einstein model cubic lattices (sc, bcc fcc) hexagonal close-packed structure. This extends work done by Lennard Jones Ingham in 1924, Corner 1939 Wallace 1965. The based on description two-body contributions an inverse power expansion (extended Lenn...