Tutorial_6_5C2H6_pmf

Tutorial_6_5C2H6_pmf - Oscar Tutorial 6 page 1 Tutorial 6...

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Oscar Tutorial 6 page 1 Tutorial 6: Ethane Potentials of Mean Force The Boltzmann equation provides the relationship between energy and probability. If we know how the free energy depends on some coordinate r , then the probability distribution for that coordinate is P(r) = e -G(r)/RT Equation 1 There are many cases where we do not know how the energy depends on a coordinate of interest, and we would like to determine it. In such cases, we can run a simulation and measure the probability distribution P(r) . We can then calculate an effective free energy, V(r) , by inverting equation 1: V(r) = -RT ln(P(r)) Equation 2 This effective free energy is called a potential of mean force (PMF) . Let us consider a specific case, where the coordinate of interest is the ethane torsion angle φ . The difference in PMF between two points, V( φ 2 ) – V( φ 1 ) , is equal to the reversible work done when ethane rotates from φ 1 to φ 2 , averaged over all degrees of freedom, i.e. , all values of bond lengths and bond angles. PMFs for bond stretching and bond angle bending Open the Excel workbook(s) you used for your bond and angle data from the longer MD simulation on ethane (Sim2). You will create two histograms of the data, one for a bond length (either H-C or C-C) and another for a bond angle (either H-C-H or H-C-C). You will then calculate the PMFs from the observed probability distributions.
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