# Force constant scaling

From: guardiani_at_fi.infn.it
Date: Tue Aug 31 2010 - 09:45:14 CDT

Dear all,

I am trying to run umbrella sampling simulations applying an harmonic
restraint
to a collective variable corresponding to the distance between two
groups of atoms. I decided to use a force constant of 15
Kcal/(mol*Ang^2), but reading the manual I later realized that the
force constant is rescaled by the square of the width of the bins of
the collective variable. As I am using bins of 0.2 Ang, as I
understand, the real value of the force constant is 15/(0.2)^2 = 375
Kcal/(mol*Ang^2). Now, I am a little confused. Which force constant
should I enter in the program that performs the WHAM analysis, 15 or
375 Kcal/(mol*Ang^2) ?

Also, I would like to ask if there is an optimal criterion to choose the force
constant for an umbrella sampling simulation. My goal is to compare the PMF
generated through umbrella sampling with the PMF computed applying the
Jarzynski equality to a set of constant velocity SMD simulations ran with a
force constant of 10 Kcal/(mol*Ang^2). As I understand the force constant for
umbrella sampling should be higher than the one used in standard SMD, but how
much higher ?

Thank you very much for your help ank kind regards,

Carlo Guardiani

PS: I paste here my ColvarsConfig file so you can have a more precise idea of
what I am doing.

********************************************************************************

colvarsTrajFrequency 1
colvarsRestartFrequency 1

colvar {

name COMdistXY

width 0.2

lowerboundary 6.0
upperboundary 17.0

lowerwallconstant 10.0
upperwallconstant 10.0

distanceXY {

main {

atomnumbers { 6633 6640 6654 6661 6675 6694 6716 6735 }

}

ref {

atomnumbers { 1681 1703 1719 1730 1742 1763 1778 1795 }

}

axis { (-0.60, 0.26, 0.26) }

}
########END OF DISTANCE BLOCK#########################

}

########END OF COLVAR BLOCK###########################

harmonic {

name umbrella

colvars COMdistXY

centers 6.0

forceConstant 15.0

#################################
# Only in NAMD 7.2.3
# targetCenters 15.0
# targetNumStages 90
##################################

targets 17.0

targetsNumsteps 11000000

}

##########END OF HARMONIC BLOCK#########################

histogram {

colvars COMdistXY

outputFreq 1

}

##########END OF HISTOGRAM BLOCK#########################

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