Re: about Hydrogen Bond correlation function

From: Axel Kohlmeyer (akohlmey_at_gmail.com)
Date: Thu Nov 04 2010 - 08:59:45 CDT

On Thu, Nov 4, 2010 at 9:11 AM, Hannes Loeffler
<Hannes.Loeffler_at_stfc.ac.uk> wrote:
> On Thu, 4 Nov 2010 13:55:28 +0800
> Jun Zhang <coolrainbow_at_yahoo.cn> wrote:
>
>> Hello everyone:
>>
>> I would like to calculate the HB correlation function according to:
>>
>> c(t)=<h(0)h(t)>/<h>
>>
>> in "Nature,379:55-57". However, I have been convoluted by the meaning
>> of <>: Is it an average over all atom pair at a particular time or
>> over the entire trajectory for a particular pair? I prefer the second
>> definition, but I am not sure. Please help me. Thank you in advance.
>
> I guess what you are asking is whether the angle brackets denote an
> ensemble average or a time average.  But in the context of the paper

both.

> cited above wouldn't you want to average over all water molecules at
> some stage anyway (obviously assuming that all water molecules are
> equivalent)?  In other words, time average or ensemble average first or
> the other way round?  I would think, mathematically speaking, that
> should not make any difference (or am I wrong?).  Eventually, think
> about the situation where you have only a single HB pair.
>
> Cheers,
> Hannes.
>
>

-- 
Dr. Axel Kohlmeyer
akohlmey_at_gmail.com  http://goo.gl/1wk0
Institute for Computational Molecular Science
Temple University, Philadelphia PA, USA.

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