Subject: summary: equilibriation of liquids

From: [email-masked] (Ross Underhill)
Date: Mon, 19 Dec 1994 08:47:28 -0500

Attached is a list of replies I got to my query about accelerating
convergence to equilibrium for a liquid and making sure you are at a global
minimum.  

        Part of my original problem was that my liquid was made up of large
branched molecules which tend to get hooked on each other.  Also I suspect
my periodic box was just not big enough.

        While there were some unique ideas, most of the replies suggested
using either monte carlo codes or "annealing" at higher temperatures.  I
confess I'm not to keen on the latter as I've found it to be a two edged
sword.  Yes, it helps you get over barriers that geometry minimization can't
but at the same time the other side of the barrier can be a high energy
configuration which you then get frozen in.  Anyway, Thanks a lot to all who
replied.

Here are the replies except for one which asked not to be passed on.

  when we simulate the supercritical dilute mixture system close to the
critical point, we will find the strange noise (fluctuation) in the monitor
values such as temperature, if we prepare the critical state directly.
That is, the initial state is the critical state itself.

However if I prepare the critical state close to the critical point gradually
using the liquid equilibrium state near triple point, the fluctuations of
monitor value are very reasonable.

  It seems to concern the density fluctuations.
If there exists artificial density fluctuations in the system, the
fluctuations of monitor values are not real and the state must be a local
minimum.

  furthermore, this phenomena depends on the ensemble.
For example, If we use Nose emsemble, we can not avoid the un-natural
fluctuations of monitor values.
This influences on the time-dependent correlation functions.
I think you should use microcanonical ensemble after preparing state using
velocity scaling MD.

  Your idea is very resonable to get the equilibrium state far from triple
point.
The frequecy of collisions is much greater in the liquid state near triple
point than in the state far from the triple point.
So the simulation time is shorter and the state we get seems to be a
global minimum.

  I'm not sure what state you need to prepare, because of there seems to
be the same problem. You can avoid getting the local minimum state if
you use the near-triple-pointstate as an initial state and then gradually
prepare the state that you need.

For the dilute mixture, this is much more important, because the solvent
molecules gather around the solute molecule because of density fluctuations in
solvent. If there exists un-natural density fluctuations in solvent, these
influences the radial distribution between solute and solvent, and hence has
influence on the solubility.
If you need the solubility, grand canonical montecarlo is best.
Will you estimate the solubility by integrating the radial distribution
function ?

Good luck !

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There are some musings on equilibration in the Questions
and Net parts of the amber web material,

	 http://www.amber.ucsf.edu/amber/amber.html

which may be of interest.

Bill Ross

I am interested in similar problems of solvation with glucose derivatives.
I'm just getting started, but what I have done to avoid the local minimum
problem is perform simulated annealing.  I start the box of liquid at
1000K, cooling geometrically to 300K.  High temperature dynamics should
allow the system to sample a good portion of phase space, and hopefullly
the minimum conforomation will be a true global minimum.  This comes from my
days as an NMR spectroscopist, where this is a the technique used.  During
this annealing with NMR, however, the NOE force constants were scaled high
and the other forces were scaled up to their full values as the system
cooled.  I haven't scaled specific interactions with the current modeling
I am doing.  As I am just starting out, I'm not sure if this is going to
work or not, but it does have some intuitive justification.

Good luck, and keep in touch.

James Brown
Center for Advanced Research in Biotechnology
Rockville, MD

Heating up the sample to a high temperature (say 700K), running a (short)
trajectory and then cooling down (slowly) to the desired temperature should
aid equilibration in any NVT ensemble.

Cheers,
Ferenc

Ferenc Molnar

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ÿÿwà	ÿÿâ-
on CCL, take a look at the following paper:

"Methods for Accelerating Chain Folding and Mixing",
Liu and Berne, J. Chem. Phy. 99(8), 15 oct. 93.

The method discussed there is called "The Fluctuating Sigma Method".
They use a time dependent Lennard-Jhones sigma to enhance the mixing
of a binary mixture. You can apply this method to your system to get
faster equilibration.

Best Wishes,
Silviu.

****************************************************
*  Silviu Zilberman                                *
*  Tel - Aviv University                           *
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*  Israel                                          *
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	Which package are you using? I use insightII running discover 2.95
and have just about overcome most of my teething problems in getting a box
of water to behave correctly before using it to model the interactions to
various drugs.

	Discover allows the use of double cutoffs and switching functions
to smooth the transitions between the non-bond cutoffs. Kit Lau has a recent
paper detailing water simulations in J Phys Chem, 98, No. 35 1994 p8785,
although I have not fully read through the paper it does point out some
important points about switching functions. If you need further help don't
hesitate to ask, though i'll be going home for Christmas and won't be back
until early Jan now, i'll give you any help I can.

Andy

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If you are doing MD on a liquid, it should not get stuck in local minima.
A liquid should be diffusing enough that it shouldn't stay long in any
one conformation.  Have you checked a diffusion constant, or translational
order coefficient, or something else to make sure that you are not frozen?

I'm not sure why compressing your box would help you converge faster,
unless you're pushing molecules into unfavorable contacts, and they
squirt out like watermelon seeds.

-Steve Stuart
[email-masked]

This calculation should lead to the interaction of the solute, i, and the
solvent, j. This should lead to Gij. But to calculate solubility you also need
to know Gii the energy to release the solute from itself. Are you going to put
i in i solvent to measure this?

Butch
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rreira                             [email-masked]
Department of Chemistry                    (706) 542-2050 or 2051
The University of Georgia                  (706) 542-9454 FAX
Athens, GA  30602

Looking for a global minimum energy conformation of bulk water
is probably not what you want to do.  Generally one looks for
establishing a conformational equilibrium at some given temperature
and pressure - so that you can obtain the correct distribution
of neighbours and orientations of hydrogen bonds, etc.

Most of my experience with simulating water has been using MC
techniques - many people feel that force-bias MC helps in
establishing equilibrium in bulk water simulations.  The reference
is "On the force bias Monte Carlo simulation of water: methodology,
optimization and comparison with molecular dynamics", M. Rao,
C. Pangali and B.J. Berne, Mol. Phys. 37, 1773 (1979).

My own preference would be to equilibrate your water sample with
a MC program, which involves fewer numerical approximations than
does MD, and then use the MD when you insert your solute.

Heather Gordon
Chemistry, Queens' U.

What exactly do you mean by "local minima"? How do you detect them?

   volume to the final value for the full MD run.   Is anyone aware of any
   other tricks one can do to increase the speed of convergence to equilibrium,
   or more important avoid falling into a local minimum.  I would appreciate
   any pointers or references I could get.

My preferred technique for setting up equilibrium configurations is
not to start from a lattice (as most people seem to do) but start
with a simulation box much bigger than what I finally want (let's
say five times bigger) into which I place the molecules at random
positions and with random orientations. Then I start the dynamics
and continously make the box smaller, until the correct size is
reached. I have never had any problems with that approach, even
when generating extremely dense hard-sphere configurations (close
to the glass transition).

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Dr. Ross Underhill
Royal Military College of Canada
Kingston, Ontario
(613) 541-6000 X6175