The expression for the Grüneisen constant of a 1D chain with Mie potential exactly coincides with the results of MacDonald and Roy. Using the relation between the Grüneisen parameter and interatomic potential one can derive the simple necessary and sufficient condition for Negative Thermal Expansion in perfect crystals with pair interactions Π Π ‴ ( a ) a > − − ( d − − 1 ) Π Π ″ ( a ) . A proper description of the Grüneisen parameter represents a stringent test for any type of interatomic potential.