From: Ivan Vyalov (vyalov_at_mis.mpg.de)
Date: Sat Apr 21 2012 - 14:13:37 CDT

On 04/21/2012 12:50 AM, Axel Kohlmeyer wrote:
> On Fri, Apr 20, 2012 at 3:49 PM, Ivan Vyalov<vyalov_at_mis.mpg.de> wrote:
>> On 04/20/2012 09:11 PM, Axel Kohlmeyer wrote:
>>>
>>> On Apr 20, 2012, at 6:43 AM, Ivan Vyalov<vyalov_at_mis.mpg.de> wrote:
>>>
>>>> Hi all!
>>>>
>>>>
>>>> I have a question related to the normalization of rdf in VMD. I've seen
>>>> the previous thread about it
>>>> www.ks.uiuc.edu/Research/vmd/mailing_list/vmd-l/18223.html
>>>> but it seems that problem of opener has disappeared but mine is still
>>>> here. I get the same problem with limiting behaviour of g(r).
>>> Which version of VMD are you using?
>>>
>>> How do you compute the integral?
>>> The value of g(r) is binned and the r is taken as the center of the bin.
>>>
>>> Axel
>>>
>>>> The system is 4169 SPC/E water molecules at 306 K in the box with cell
>>>> length 50 \AA{}.
>>>> What I need is to calculate Kirkwood-Buff integral. h(r) looks well in
>>>> general:
>>>> img846.imageshack.us/img846/6460/56853809.png
>>>> but its integral multiplied by r^2 diverges(here it's just a sum h(r)r^2
>>>> not multiplied by dr and is a little bigger than the proper integral, but it
>>>> doesn't change the problem):
>>>> img812.imageshack.us/img812/2722/handintegral.png
>>>>
>>>> At first, I equilibrated system for 1ns, but when I've obtained this
>>>> behaviour I continued to equilibrate for 2 ns more with the same result.
>>>> Here is the tail of h(r) which is noisy but definitely lies above zero in
>>>> average.
>>>> img210.imageshack.us/img210/9803/htail.png
>>>> If I average more taking wider bins I get the following picture:
>>>> img252.imageshack.us/img252/8083/htailbroadbin.png
>>>>
>>>>
>>>> This looks quite strange even though I know about difficulties with such
>>>> calculations.
>>>> The question is obvious, is everything alright with the normalization of
>>>> g(r) in VMD?
>>>>
>>>> However, it can be something else rather than normalization because
>>>> functions of different pairs behave differently:
>>>> img191.imageshack.us/img191/8205/handintegralall.png
>>>> This means that OO and HH have positive component in h(r) and OH --
>>>> negative.
>>>>
>>>> Any help and ideas are much appreciated!
>>>>
>>>> thanks in advance,
>>>> Ivan
>>
>> Hello Axel,
>>
>> I used VMD 1.9 and 1.9.1 and they both give the same result.
>>
>> Here's the better plot of integral calculated as (scipy)
>> cumsum(h*r**2*(r[1]-r[0]))
>> http://img62.imageshack.us/img62/9466/handrightintegral.png
>>
>> The problem comes from positive tail in h, can it be from PME(I took grid
>> spacing equal to 1\AA{})? From the other hand if I take the average of h(r)
>> from 15 to 25 \AA{} and subtract it from h(r), integral converges and it
>> seems to me that the error is constant.
>> http://img401.imageshack.us/img401/871/hshiftedandrightintegra.png
> can you please try running your g(r) calculation with a smaller
> bin size, say 0.01 instead of the default of 0.1?
> and let us know if that makes matters better or
> worse or has no impact at all.
>
> thanks,
> axel.
>
>
>
>

Hi Axel, thanks for your help!

Yes, I've given them in the opening post, sorry they are not proper
hyperlinks. So here is the tail of h(r) with bin equal to 0.01 \AA{}:
http://img210.imageshack.us/img210/9803/htail.png
and this one with 0.5 \AA{}
http://img252.imageshack.us/img252/8083/htailbroadbin.png

About the electrostatics, I've switched off the charges by
"reloadCharges". And here are the results:
http://img151.imageshack.us/img151/3600/handintegralooandoonoch.png
h(r) with no charges is green and corresponding integral is cyan. And
again, integral should oscillate near the limiting value but it goes up.

thank you,
Ivan