# [gmx-users] Box size and potential energy calculation

Tim Harder mail at tim-harder.de
Sun Jan 23 13:25:39 CET 2011

```
On 1/23/11 12:58 PM, Christian Mötzing wrote:
> Am Sonntag, den 23.01.2011, 09:40 +1100 schrieb Mark Abraham:
>> On 23/01/2011 2:36 AM, Christian Mötzing wrote:
>>> Am Samstag, den 22.01.2011, 11:39 +1100 schrieb Mark Abraham:
>>>> On 21/01/2011 6:47 AM, Christian Mötzing wrote:
>>>>> Hi,
>>>>>
>>>>> I currently read through the GMX manual 4.5.3. I have two questions:
>>>>>
>>>>> 1) Density is calculated by the density of the material and the box
>>>>> volume. But I can't find a reference on how the box size is calculated.
>>>>> Can you point me to some literature?
>>>> The volume of the box is the determinant of the matrix formed by the box
>>>> vectors. If that matrix is upper- or lower-triangular, then the volume
>>>> is the product of the entries in the leading diagonal.
>>> Ok and where do the box vectors come from? I read the a atom/molecule
>>> has a vector for the position and a vector for the velocity/direction
>>> its heading. Are the box vectors determined by the vectors which have
>>> the maximal component for one axis in the system?
>> The size of the box, if any, is imposed by the user before the
>> simulation begins (e.g with editconf). It may have periodic boundary
>> conditions. Its size may vary if the simulation is not in a
>> constant-volume ensemble.
> For the waterbox simulation I got the box size does vary over time. PBC
> is also used. It is important for me to know whether the box size
> depends on the position of the molecules or whether the box size is
> calculated by the force the molecules create when bumping on the virtual
> wall of the box. If you can point me to some literature where this is
> explained I would be really happy. :)

Hey Christian,

the box is merely a theoretical construction and usually has no walls but
everything "goes out" to the left "re-enters" on the right. The keyword here
is periodic boundary condition (pbc). If you put a molecule in the box it
will happily drift around, even leave the box and re-enter at will. If
your box
is big enough, that should not be a problem, only when it gets to small
is when mirror images start "seeing" each other.
To visualize this effect try VMD, Representations, periodic tab and select
the different checkboxes.

The box size varies with the changing pressure of the entire system (if you
run NPT simulations, which I guess you are). Here Gromacs tries to keep
the pressure constant by allowing the system more room when the pressure
rises and restricts it a bit when the pressure falls to much. Keyword
here would
be barostat.

Best
Tim

>> It sounds like doing some tutorial material would give you some good
>> context in which to continue learning.
>>
>> Mark
>>
>>>>> 2) I wanted to look up the calculation of the potential energy. Do I
>>>>> understand the calculation correctly:
>>>>> - pairwise sum over all molecules
>>>>> - for each pair Coulomb, Lennard-Jones and bonded terms are summed
>>>>> aswell
>>>>> - the calculation involves the position of the molecules (for example
>>>>> Lennard-Jones)
>>>> Well that's vaguely accurate. Bonded terms can involve more than pairs
>>>> of atoms.
>>>>
>>>> Mark
>>> Christian
>>>
>

```

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