**From:** Vermaas, Joshua (*Joshua.Vermaas_at_nrel.gov*)

**Date:** Fri Jul 20 2018 - 11:35:19 CDT

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Hi Jun,

These kinds of questions are pretty deep in general, but mostly get covered in a statistical physics/statistical mechanics class. In addition to the resources Giacomo sent, here are my super-basic explanations to distill the answer into about a paragraph:

#1, if your force field is a perfect description of your system, an unbiased MD system will populate states based on the underlying partition function for the system, which means that most of your time will be spent populating boring, low-energy states.

#2 The partition function gives you an answer here too. Lets say there is a 5kT barrier to leave a low energy state. The probability of sampling at the top of the barrier is only 0.007 the probability of sampling the bottom of the well. Since there are so few samples being taken at the top of the barrier, you can't discriminate easily between a true population ratio of 0.007 or something that is an order of magnitude higher or lower, meaning that you don't know how high your barrier is based on limited sampling. Given long enough simulation times, these probabilities will become more accurate, but typically our simulations are much too short, so the uncertainty in barrier heights would be very extreme without biases applied to ensure adequate sampling everywhere.

#3 Imagine a perfectly flat free energy surface, so that the unbiased simulation will equally sample everything along the reaction coordinate. Now lets apply a harmonic bias. What will the population distribution look like? Well, I paid attention in quantum, and basically this becomes a harmonic oscillator, whose solution is a gaussian probability distribution. Real systems won't have a flat free energy surface, so the deviations from gaussian behavior tell you something about the underlying free energy surface. Is the distribution shifted to the right? Then we know that the free energy surface has a negative slope at our bias point, and the degree of the distribution shift tells us how negative the slope is. That is the intuitive guide to how WHAM works, there is just more math involved.

-josh

On 2018-07-20 06:48:29-06:00 owner-namd-l_at_ks.uiuc.edu wrote:

These fundamental questions are best covered by textbooks:

"Introduction to modern statistical mechanics" (David Chandler)

"Understanding Molecular Simulation: From Algorithms to Applications" (Daan Frenkel and Berend Smit)

"Free Energy Calculations: Theory and Applications in Chemistry and Biology" (Cristophe Chipot and Andrew Pohorille)

"Statistical Mechanics: Theory and Molecular Simulation" (Mark Tuckerman)

This is not a complete list, but should get you started. You should also search the mailing list archives for this or other MD codes, because this question is recurring.

On Thu, Jul 19, 2018 at 4:54 PM Junwoong Yoon <junwoony_at_andrew.cmu.edu<mailto:junwoony_at_andrew.cmu.edu>> wrote:

Dear NAMD users,

I am a beginner in NAMD. I have several questions about the fundamentals of MD and WHAM. These might be trivial to you but I really want to understand how MD and WHAM work beforehand. I already did some research to answer these questions but it was a bit difficult to fully understand as a beginner..--_000_BYAPR09MB2584EFA5D81F73344B0BD359E4510BYAPR09MB2584namp_--

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