# PMF Calculation

From: Crystal Liu (sixian_at_ualberta.ca)
Date: Fri Aug 12 2016 - 19:15:46 CDT

Hello!
I am using the same method from the deca-alanine tutorial (
http://www.ks.uiuc.edu/Training/Tutorials/science/
10Ala-tutorial/10Ala-tutorial.pdf) to calculate PMF using Jarzynski's
method using ten repeats of work data in kcal/mol; however, only the first
cumulant (F1) plot worked, while the second cumulant (F2) plot gave me very
irregular results, when both F1 and F2 are supposed to be similar. Can
anyone point out where the problem might be? Thank you so much!

*Equation:*
[image: Inline image 3]

B= 1/kT (k=Boltzmann's constant, T=temperature - at 310K)

*Cumulant Calculation Script:*

set F1 {}

set F2 {}

for {set i 0} {\$i < 75001} {incr i 1} {

set texp 0

set t1 0

set t2 0

foreach l [array names w] {

set e [lindex \$w(\$l) \$i]

set t1 [expr \$t1 + \$e]

set t2 [expr \$t2 + \$e * \$e]

}

set B [expr 1 / 1.2]

lappend F1 [expr \$t1 / 10]

lappend F2 [expr \$t1 / 10 - (\$B * \$t2 / 10) + (\$B * \$t1 * \$t1 / 100) ]

}

*First cumulant in green, and second cumulant in blue: *

[image: Inline image 5]

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