• ## Outreach

From: Ivan Vyalov (vyalov_at_mis.mpg.de)
Date: Fri Apr 20 2012 - 14:49:21 CDT

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:
>>
>>
>> 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!
>>
>> 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