of a polyatomic gas molecule is a linear space of dimension 3n, because each atom can be independently displaced in each of three orthogonal axis directions. However, some three of these dimensions are just translation of the molecule by an infinitesimal displacement vector, and others are just rigid rotations of it by an infinitesimal angle about some axis. Still others may correspond to relative rotation of two parts of the molecule about a single bond that connects them. The independent deformation modes—linearly independent ways to actually deform the molecule, that strain its bonds—are only the remaining dimensions of this space. As in the case diatomic molecules, each of these deformation modes counts as two vibrational degrees of freedom for energy storage purposes: one for the potential energy stored in the strained bonds, and one for the extra kinetic energy of the atoms as they vibrate about the rest configuration of the molecule. In particular, if the molecule is linear (with all atoms on a straight line), it has only two non-trivial rotation modes, since rotation about its own axis does not displace any atom. Therefore, it has 3n − 5 actual deformation modes. The number of energy-storing degrees of freedom is then f = 3 + 2 + 2(3n − 5) = 6n − 5. For example, the linear nitrous oxide molecule (with n = 3) has 3n − 5 = 4 independent infinitesimal deformation modes. Two of them can be described as stretching one of the bonds while the other retains its normal length. The other two can be identified which the molecule bends at the central atom, in the two directions that are orthogonal to its axis. In each mode, one should assume that the atoms get displaced so that the center of mass remains stationary and there is no rotation. The molecule then has f = 6n − 5 = 13 total energy-storing degrees of freedom (3 translational, 2 rotational, 8 vibrational). At high enough temperature, its molar heat capacity then should be cP,m = 7.5 R = 62.63 J⋅K−1⋅mol−1. For cyanogen and acetylene (n = 4) the same analysis yields f = 19 and predicts cP,m = 10.5 R = 87.3 J⋅K−1⋅mol−1. A molecule with n atoms that is rigid and not linear has 3 translation modes and 3 non-trivial rotation modes, hence only 3n − 6 deformation modes. It therefore has f = 3 +