# How to determine compressibility?

**URL:** <https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787>\
**Category:** User discussions\
**Created:** [September 9, 2020, 2:23am UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787 "2020-09-09T02:23:29Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![lqhenwunai](https://avatars.discourse-cdn.com/v4/letter/l/4da419/32.png) [@lqhenwunai](https://gromacs.bioexcel.eu/u/lqhenwunai)\
**Post date:** [September 9, 2020, 2:23am UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787/1 "2020-09-09T02:23:29Z")

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GROMACS version:2020.2  
GROMACS modification: Yes/No

Dear all,

I am trying to run an npt calculation for a pure organic solvent system. How to determine the compressibility then?

Many thanks in advance.

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**Author:** ![alevilla](https://dub1.discourse-cdn.com/flex017/user_avatar/gromacs.bioexcel.eu/alevilla/32/439_2.png) [@alevilla](https://gromacs.bioexcel.eu/u/alevilla)\
**Post date:** [September 14, 2020, 8:33am UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787/2 "2020-09-14T08:33:51Z")

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Hi,

you can calculate isothermal compressibility

1. by calculating volume fluctuation. \< volume fluctuation \> \_NPT= V \* k\_B \* T \* isothermal compressibility (see p 53 chapter Fluctuations Allen Tildesley Book "computer simulation of liquids)
2. by running NVT simulation at slightly different volume and applying  
isothermal compressibility = - 1/V \* (dV/dP)\_T

Kind regards  
Alessandra

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**Author:** ![Tijanar](https://dub1.discourse-cdn.com/flex017/user_avatar/gromacs.bioexcel.eu/tijanar/32/1498_2.png) [@Tijanar](https://gromacs.bioexcel.eu/u/Tijanar)\
**Post date:** [July 20, 2022, 1:02pm UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787/3 "2022-07-20T13:02:09Z")

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Hello @alevilla ,

Thank you for the suggestions regarding the isothermal compressibility.  
In the comment 2, by “different volume”, how much the volume need to be increased, e.g. dV = ~(0.1)^3 nm^3 will be okay? What is (dV/dP)\_T? Is dV = V2-V1? What will be the pressure as is it fluctuating through the NVT similation?

I wonder, if there is any data base for liquids and their isothermal compressibility?

Please suggest.  
Regards  
Ranajit

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**Author:** ![alevilla](https://dub1.discourse-cdn.com/flex017/user_avatar/gromacs.bioexcel.eu/alevilla/32/439_2.png) [@alevilla](https://gromacs.bioexcel.eu/u/alevilla)\
**Post date:** [August 11, 2022, 9:30am UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787/4 "2022-08-11T09:30:47Z")

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Hi,

The difference in volume should be tiny ( 1 % ?), but it may also depend on the dimension of the system. Good to have a look in literature there are a lot of systematic study on liquid properties (using MD). In my previous post, dV is the difference between the volume of the two simulations.

If useful, gmx energy can provide isothermal compressibility from volume fluctuation

Concerning a database, you can have a look to CRC Handbook of Chemistry and Physics [http://www.hbcponline.com](http://www.hbcponline.com)

I hope it helps.  
Alessandra

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**Author:** ![Tijanar](https://dub1.discourse-cdn.com/flex017/user_avatar/gromacs.bioexcel.eu/tijanar/32/1498_2.png) [@Tijanar](https://gromacs.bioexcel.eu/u/Tijanar)\
**Post date:** [August 16, 2022, 2:54am UTC](https://gromacs.bioexcel.eu/t/how-to-determine-compressibility/787/5 "2022-08-16T02:54:55Z")

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> [@alevilla](#):
>
> gmx energy can provide isothermal compressibility from volume fluctuation

Thank you @alevilla for your comment.