The main function I am interested to use is tanh; therefore did not
write the exact form of the function. Sorry for that. Here is the function
I am interested to use:
f(x,k) = {1+tanh[k*(2x-1)]}/2
where x = lambda.
=> V(lambda) = f(lambda,k) * V0 + [1 - f(lambda,k)] * V1
I am particularly interested on the k values 3,4,5,6. I am not sure what
you mean by "gradual". When I plot this function for the above k values,
they are both zero and one at lambda=0 and lambda=1, respectively. And
compared to (1-lambda)^k, I do not see a big difference, except that it is
zero at lambda=0. It seems like a gradual function, but as I said, I dont
know how gradual this function should be in order it to be used in TI
calculations.
Best regards,
On Tue, 8 Mar 2005, David A. Case wrote:
> On Thu, Mar 03, 2005, Ilyas Yildirim wrote:
>
> > In my prev. emails, I was asking why AMBER does not let us use dummy
> > atoms in the initial state when k is not equal to 1 (pp.134, note #2). And
> > as far as I understand, the reason lies at the parameter function chosen
> > in Eq. # 5 (pp.133). When I plot the function, (1-lambda)^k, it seems
> > that when we have dummy atoms at the initial state, the transformation
> > will be sharp. It is not as gradual as it is when we have dummy atoms at
> > the final state.
> >
> > So, we were thinking that if we use a parameter function,
> > tanh[k(2lambda-1)], such that the Eq. 5 becomes,
> >
> > V(lambda)= tanh[k(2lambda-1)]*V0 + {1 - tanh[k(2lambda-1)]}*V1
> >
> > the problem might be solved. When we plot the function tanh[k(2lambda-1)],
> > we see that the initial and the final transformations look gradual.
>
> Just a quick note: the function you use not only has to "look gradual", you
> have to be able to show (presumably analytically) that it decays very stongly
> as a function of lambda, so that the net effect of vdW interactions remains
> finite. Offhand, it doesn't look like your function does this; the
> coefficient of V0 doesn't even go to zero as lambda -> 0. Apologies if I am
> missing something here....
>
> ....dac
>
> -----------------------------------------------------------------------
> The AMBER Mail Reflector
> To post, send mail to amber.scripps.edu
> To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu
>
>
--
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/ -
---------------------------------------------------------------
-----------------------------------------------------------------------
The AMBER Mail Reflector
To post, send mail to amber.scripps.edu
To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu
Received on Tue Mar 08 2005 - 21:53:00 PST
