Is a mono-molecular spring possible? I have seen and read a lot of springs being used in the macroscopic world, and I also know that things can behave differently on a much smaller scale. My question is could a single piece of molecules act as a spring, if so how does it stores energy when in a compressed state? (Compare tension spring)
 A: Polymers are large molecules (macromolecules), and they behave like springs if stretched. The interesting thing is that their elasticity doesn't come from energy, but from entropy.
Also much smaller molecules, like CO, can be used as springs. In cases such as this, the energy is stored in the interatomic bond.
A: Any smooth energy minimum of a system (such as an atomic bond) acts as an enthalpic spring following Hooke's Law for small perturbations. The reason is that any smooth minimum looks like a parabola up close (as demonstrated by a Taylor series expansion, $E(x_0+\delta x)\approx E(x_0)+E^\prime(x_0)\delta x+E^{\prime\prime}(x_0)\delta x^2/2$, which is just $E^{\prime\prime}(x_0)\delta x^2/2$ relative to the energy at the minimum, where the first derivative is zero). Such a parabola corresponds to a spring constant of $E^{\prime\prime}(x_0)$ and a restoring force of $F=-E^{\prime\prime}(x_0)\delta x$ either in tension or in compression.
The energy stored via compressive or tensile strain is electrostatic. The spring constant is on the order of 100 N/m for ionic bonds and greater than approximately 1000 N/m for stronger double or triple covalent bonds. From this stiffness, you can calculate the energy for a given displacement using the relations given above. For condensed matter whose stiffness is primarily enthalpic (which is most condensed matter other than, notably, elastomers, whose stiffness is primarily entropic), you can use the atomic spring constant and the atomic spacing $x_0$ to estimate the bulk modulus of the material $K\sim E^{\prime\prime}(x_0)/x_0$.
Thus, the stiffness of essentially all condensed matter around you arises from "springiness" at the atomic scale—that is, an electrostatic restoring force for disturbances to the equilibrium bond spacing. In this context, you can think of compressive stress as moving up very slightly to the left of the minimum of the energy potential between atoms.
A: The obvious example of this is DNA, which is doubly helical.
The bending and stretching properties of DNA have been extensively studied. There is a review article on the Nature web site, or Google for DNA elasticity for many, many more articles.
However the mechanism of the spring like action is (generally) different in helical molecules. In a macroscopic spring the elasticity comes from twisting of the wire of the spring. In helical molecules like DNA the elasticity comes from interactions (typically hydrogen bonds) between adjacent strands of the molecule.
