Dear All,
It is not so clear in the manual on how the potential energy is calculated
- explicitely - for some terms (esp. van der Waals). There are parameters
derived for some molecules in other force fields, and transferring
those parameters for AMBER simulations needs a good understanding of the
AMBER potential energy function. Whether those parameters can be
transferred or not is out of the scope of this email. Amber 7 manual has
Appendix C written by Allison Howard and Bill Ross, which talks about
AMBER parameter development. I would like to go step by step on each term
in the potential energy function. If you see any mistakes, I will
appreciate to hear your response on them.
1. Bond and Angle: The equation used to calculate the bond and angular
energies in AMBER are the same: K*(x-x_eq)^2, where x is the bond/angle
measured, x_eq is the equilibrium bond distance or angle, and K is the
force constant. In some force fields, they use (0.5*K_r) as force constant
to describe the bond and angular energies, but this is not true in AMBER
potential energy. For instance, in parm99.dat the following entries define
the CT-CT and CT-CT-CT parameters:
CT-CT 310.0 1.526 JCC,7,(1986),230; AA, SUGARS
CT-CT-CT 40.0 109.50
What this says is that the bond and angular energies for CT-CT bond and
CT-CT-CT angle are calculated as follows:
E_bond = (310.0)*(r-1.526)^2
E_angle = (40.0)*(x-109.50)^2
The units of the parameters are such that at the end the energy is in
kcal/mol.
2. Torsions: From Amber 7 Manual (pp 290), the equation used to calculate
the torsional energy is as follows:
T_tor = (PK/IDIVF)*(1+cos(PN*phi-PHASE))
For instance in parm99, the parameters for CT-CT-CT-CT is
CT-CT-CT-CT 1 0.18 0.0 -3.
CT-CT-CT-CT 1 0.25 180.0 -2.
CT-CT-CT-CT 1 0.20 180.0 1.
What this says is, the energy for this torsion is explicitly calculated as
E_tor = (0.20/1)*(1+cos(phi-180)) + (0.25/1)*(1+cos(2*phi-180)) +
(0.18/1)*(1+cos(3*phi-0.0))
In some force fields, the torsional part of the potential energy function
is calculated as
E_tor = Sum [ (Vn/2)*(1+cos(n*phi-phase))]
In AMBER, the energy barrier Vn is not directly used. For instance, PK is
given/written explicitly in the parm99.dat file, which is equal to Vn/2.
There is also the 1-4 terms in the energy calculations, which I am not
going to talk here. The main difference between different force fields is
the scaling factor used in the 1-4 calculations. Again, the scope of this
email message is not to discuss whether parameters can be transferred from
one force field to another.
3. van der Waals: According to AMBER 7 manual, the vdw parameters given in
.dat files are R* and e. R* is half the interatomic distance at the
minimum energy point, and e is the potential well depth of the minimum
enery point between 2 atoms of the same type. Mixing different atom types
are done by taking the root of the product.
In some force fields, the vdw energy term explicitly uses the minimum
interactomic distance R. So, the vdw pot. energy term in those
force fields are
E_vdw = E0 *[ (R0/R)^12 - 2(R0/R)^6].
where E0 is the potential well depth of the minimum energy point, and R0
is the interatomic distance at the minimum energy point.
I am not so clear how AMBER explicitly calculates the vdw energy. For
instance, in parm99.dat file, the vdw parameters for CT is
CT 1.9080 0.1094 Spellmeyer
where R/2=1.9080 and e=0.1094. If it is going to calculate the vdw energy
of two CT type atom, how is it done using these parameter set? Is it
E_vdw = 0.1994 * [ ((2*1.9080)/R )^12 - 2 * ((2*1.9080)/R)^6 ] ?
PS: I am excluding the 1-4 term here.
4. electrostatic: This part uses the resp charges in AMBER, so a direct
charge transfer from a force field to AMBER is not possible. It needs to
be calculated.
I am really hesitant to transfer parameters from one force field to
another, but sometimes it needs to be done. I will appreciate any comments
on this issue. Thanks in advance.
Best regards,
Ilyas Yildirim, Ph.D.
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= Department of Chemistry - 2145 Sheridan Road =
= Northwestern University - Evanston, IL 60208 =
= Ryan Hall #4035 (Nano Building) - Ph.: (847)467-4986 =
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http://www.pas.rochester.edu/~yildirim/ =
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Received on Mon Oct 04 2010 - 13:00:05 PDT
