the molecular axis. A nonlinear molecule, where the atoms do not lie along a single axis, like water (H2O), has three rotational degrees of freedom, In physics and chemistry, a degree of freedom is an independent physical parameter in the chosen parameterization of a physical system. More formally, given a parameterization of a physical system, the number of degrees of freedom is the smallest number n {\textstyle n} of parameters whose values need to be known in order to always be possible to determi For a structure consisting of two or more atoms, the whole structure also has rotational kinetic energy, where the whole structure turns about an axis. A linear molecule, where all atoms lie along a single axis, such as any diatomic molecule and some other molecules like carbon dioxide (CO2), has two rotational degrees of freedom, because it can rotate about either of two axes perpendicular to the molecular axis. A nonlinear molecule, where the atoms do not lie along a single axis, like water (H2O), has three rotational degrees of freedom, because it can rotate around any of three perpendicular axes. In special cases, such as adsorbed large molecules, the rotational degrees of freedom can be limited to only one. A structure consisting of two or more atoms also has vibrational energy, where the individual atoms move with respect to one another. A diatomic molecule has one molecular vibration mode: the two atoms oscillate back and forth with the chemical bond between them acting as a spring. A molecule with N atoms has more complicated modes of molecular vibration, with 3N − 5 vibrational modes for a linear molecule and 3N − 6 modes for a nonlinear molecule. As specific examples, the linear CO2 molecule has 4 modes of oscillation, and the nonlinear water molecule has 3 modes of oscillation Each vibrational mode has two energy terms: the kinetic energy of the moving atoms and the potential energy of the spring-like chemical bond(s). Therefore, the number of vibrational energy terms is 2(3N − 5) modes for a linear molecule and is 2(3N − 6) modes for a nonlinear molecule. Both the rotational and vibrational modes are quantized, requiring a minimum temperature to be activated. The "rotational temperature" to activate the rotational degrees of freedom is less than 100 K for many gases. For N2 and O2, it is less than 3 K. The "vibrational temperature" necessary for substantial vibration is between 103 K and 104 K, 3521 K for N2 and 2156 K for O2. Typical atmospheric temperatures are not high enough to activate vibration in N2 and O2, which comprise most of the atmosphere. (See the next figure.) However, the much less abundant greenhouse gases keep the troposphere warm…