# Electric force in DNA molecule

Given that distance between O-H and N-H bonds are 0.11 nm and

How do I compute the net force exerted from Thymine and Adenine? A hint given is:

Hint: To keep calculations fairly simple, yet reasonable, consider only the forces due to the O–H–N and the N–H–N combinations, assuming that these two combinations are parallel to each other.

Do I compute the force on O due to H and N like:

$$F_{OH} = k \frac{e^2}{(0.17 \times 10^{-9})^2}$$

$$F_{ON} = k \frac{e^2}{(0.28 \times 10^{-9})^2}$$

$$F_{O} = k \frac{e^2}{(0.17 \times 10^{-9})^2} - k \frac{e^2}{(0.28 \times 10^{-9})^2}$$

Then about the HN part? Do I consider that 1 molecule or something?

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that looks pretty good. assuming you only have to consider the forces due to the two hydrogen bonds (O~H and N~H), then you've done the O~H part. –  Ethan Jan 27 '13 at 8:34
@user1544418, I did do the ON part too? Or do you mean I can now proceed to compute the force on the N (on Adenine) in a similar way and sum up those forces? –  Jiew Meng Jan 27 '13 at 9:16
yes exactly. be sure you realize that the forces are symmetric - the force on adenine is the same as that on thymine (this is newtons third law). –  Ethan Jan 27 '13 at 9:29

It's not going to be so easy, if you want anything better than a very crude estimate. The + and - charges indicated on illustrations of molecules depict a relative absence or gathering of electron probability clouds in the region, respectively failing to balance with the positive nuclear charge or overwhelming it. You'd have to know the wavefunctions of the electrons, their molecular orbitals, and compute integrals over those all pairs of volume elements in the clouds for both regions.

As a practical approximation, there might some sense in using some average central point, a sort of center of mass, for each charged region of each molecule, and apply Coulomb's law. But this isn't likely to be accurate. It could be if the charged regions were spherical, then just as with gravity the integrals work out to be the same as the simple Coulomb's law. Unfortunately molecules aren't shaped like that.

If you are wanting to know the force between two molecules, or parts of a molecule, you should know that the charged regions will change shape - as the molecules move closer, the electrons, and whole atoms, "feel" the presence of other charges and are tugged. The molecules will electrically polarize each other.

So, instead of using Coulomb to estimate the force, it's better to calculate the electrostatic potential energy as a function of position, accounting for the way the molecules will distort each other at any given distance.

Of course, even better is to do a full-blown quantum mechanical calculation including spins and fully anti-symmetric wavefunctions and all that, but for DNA or even just a single base pair, that's a lot of number crunching.

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I think the purpose of the hint is to say we just ignore the forces from other molecules and just focus on the O, H & N? –  Jiew Meng Jan 27 '13 at 9:12