# Re: amber-developers: evb based mixing

From: Ilyas Yildirim <yildirim.pas.rochester.edu>
Date: Tue, 18 Oct 2005 13:48:40 -0700

Hi Dave,

Sorry for the late reply. I was busy with moving to a new apartment, so
could not check out my emails regularly. The purpose of this modification
was to use the dummy atoms in the initial state, too. According to AMBER
8, we can have dummy atoms at the final state. We (me and Dr. Harry Stern
from U of R, Dept. of Chemistry) tried to mimic the smooth transition of
the original mixing function, (1-lambda)^klambda, around lambda=0, too. In
order to do that, we have put some extra constraints on the mix. function
when lambda=0 and lambda=1. Normally, the function needs to satisfy the
following conditions (I will use the notation 'x' rather 'lambda'):

f(x=0)=1
f(x=1)=0

where f(x) is the mix. function. We put the following constraints:

f^(n)(x=1)=f^(n)(x=0)=0

where f^(n)(x) is the 'n'th derivative of the new mix. function. As
n->infinity, the new mix. function becomes a step function. Using a large
'n' value is, therefore, not a good choice. We used n=6 and n=7 cases,
for the test cases. So, when someone solves this new mix. function with
the added new constraints, the mix. function becomes as

f(x,k) = (1-x)^k * sum_(i=0 to k-1) { combination(k-1+i,i) * x^i }

Here, combination(x,y) is the combination function. Namely,

combination(x,y) = x!/[(x-y)!*y!]

where
x! = x*(x-1)*(x-2)*...*2*1

As I wrote above, the reason why we did this modification is to make use
of dummy atoms at the initial state too. Hopefully I will prepare an
example case, such as for c->ic and ic->c transformations. I have done
these transformations, and the delta(G) for each transformation was as
follows:

delta(G) of c->ic ~= +49.49 kcal/mol
delta(G) of ic->c ~= -48.64 kcal/mol

These simulations were 700 ps simulations in explicit water, and only the
last 200 ps is used in the calculations. If you have any other questions,
just send me an email.

Best,

PS: icfe=1 will use the old mix. function while icfe=2 will use the new
mix. function.

On Tue, 11 Oct 2005, David A. Case wrote:

> On Mon, Oct 10, 2005, Ilyas Yildirim wrote:
> >
> > I have modified some files in \$AMBERHOME/src/sander to include a new
> > mixing function for the TI approach. The old mixing function is
> >
> > f(x,k) = (1-x)^k
> >
> > while the new mix. function is
> >
> > f(x,k) = (1-x)^k * sum_(i=0 to k-1) { combination(k-1+i,i) * x^i }
> >
> > The old mixing function is still available. In order to use the old
one,
> > set icfe=1. If u want to use the new mix. function, use icfe=2 option.
I
> > put a test case in \$AMBERHOME/test/ti_eth2meth_gas directory. A
> > file is available in this test case directory.
>
> Thanks, Ilyas. Can you expand on the above description some? What is
the
> definition of "combination"? And can you add a few setences about what
the
> purpose of this is, and what values of "k" you find to be good ones,
etc?
> Readers will need some guidance about how/when/why to use icfe=2 rather
than
> icfe=1.
>
> ...thanks...dave
>
>

```--
Ilyas Yildirim
---------------------------------------------------------------
- Department of Chemisty       -				-
- University of Rochester      -				-
- Hutchison Hall, # B10        -				-
- Rochester, NY 14627-0216     - Ph.:(585) 275 67 66 (Office)	-
- http://www.pas.rochester.edu/~yildirim/			-
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```
Received on Wed Apr 05 2006 - 23:49:52 PDT
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