Subject: Re: CCL:Chem Topic: Excited States

From: michael nolan <[email-masked]>
Date: Wed, 12 Mar 1997 18:59:30 +0000 (GMT)

>
> IMPOSING ORTHOGONALITY - DFT TECHNIQUES
>
>       Traditionally, excited states have not been one of the strong
> points of density functional theory.  This is due to the difficulty
> in ensuring orthogonality to the ground state wave function when
> no wave functions are being used in the calculation.
>
>       The easiest excited states to find using density functional
> theory techniques are those which are the lowest state of a given
> symmetry thus using a ground state calculation.
>
>       A promising techniques is one which uses a variational bound
> for the average of the first M states of a molecule.
>
>       A few other options have been examined.  However, there is not
>     yet a large enough volume of work applying DFT to excited states to
> predict the reliability of any of these techniques.
>
	The imp himself has spoken

***************************************************************************************
Michael Nolan (nearly BSc.)			Dublin City University (quantum chem.)
41 Woodview					Chemistry + german Year 4
Lucan
Co. Dublin
Ireland / Republic of Ireland / ROI / Eire

Email: [email-masked]

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

You might like to check out Goerling's method in phys rev A nov/dec 1996.

>From [email-masked] Tue Mar 11 05:52 EST 1997
From: <[email-masked]>
Subject: Re: CCL:Thermodynamic integration
To: [email-masked] (Jonathan Arthur)
Date: Tue, 11 Mar 1997 11:53:05 +0100 (NFT)

Hi, there:

> I am trying to perform a molecular dynamics calculation of the free 
> energy for the mutation of a water molecule into a methane molecule 
> in solution. I am using the thermodynamic integration technique. 
> Although I have been trying for quite a while, gradually finding 
> the bugs in my code, I have still not been able to reproduce the 
> literature values for this reaction.
> 
> I am starting to suspect that I may not have a correct understanding
> of how this technique is used. While the many references I have 
> consulted talk of 'accumulating the partial derivative dU/dlambda'
> they do not describe exactly what this partial derviative is in 
> terms of the positions, velocites etc that can be accumulated each 
> time step.

First thing: what you want to calculate is:

                        1
      delta G = integral  < dU(x,lambda) / dlambda >       dlambda
                        0                           lambda

In the simulation, the integrand comes from a discrete number of points
and your integral is approximated via a standard rule, such as Simpson,
or trapezoidal:
                   N
      delta G ~ sum  { < dU(x,lambda) / dlambda >            +
                   0                             lambda(k)  
                       < dU(x,lambda) / dlambda >            }  x
                                                 lambda(k+1)
                     { lambda(k+1) - lambda(k) } / 2

The choice of N, the number of windows, can be critical for `mutation'-
type free energy calculation...  My experience is that it is often more 
efficient to use few windows (say less than 30) with extensive sampling
than the contrary. Be sure, though, that the integrand varies smoothly.

Now, for that kind of simulation,  I assume that you `grow' bonds, con-
comittently with increasing van der Waals radii. This deserves particu-
lar attention, especially if bonds are shaken. What you should evaluate
here is the contribution to the free energy of the constraints changing
the bond lengths from lambda = 0 to 1. Simply, the latter can be calcu-
lated from:

      dUconstraint / dlambda = {(Fij . rij) / |rij|} x (drij / dlambda)

where Fij is the force dur to the constraint and rij is the constrained
bond length.

One last,  trivial thing.  For the above mutation, I guess you decouple
the process into subprocesses, dedicated to electrostatic and internal+
van der Waals parameters... It is always safer to do so, especially for 
`absolute' free energies, than mutating everything simultaneously - un-
less species at lambda = 0 and 1 are topologically identical (say K+ ->
Na+).

Hope this helps...

Chris
_______________________________________________________________________

Chris Chipot                         
Laboratoire de Chimie Theorique          Phone:      (33) 3-83-91-25-96
U.R.A. C.N.R.S. No 510                   Fax:        (33) 3-83-91-25-30
Universite Henri Poincare - Nancy I       
B.P. 239
54506 Vandoeuvre-les-Nancy Cedex         E-mail: [email-masked]
_______________________________________________________________________