Chemical potential for SPC/E water at 1 atm and 300 K

Hello everyone,

I'm performing GCMC simulations of liquid water using the SPC/E force field.
What I want is to have a simulation running at around 1 atm and about 998 g/l at 300 K.

I saw in the literature that for the SPC/E force field, these conditions for the simulation are given when the chemical potential is -38.09 ( dx.doi.org/10.1063/1.5046835 ).
I tried using this value in Cassandra without success, since the simulations converge to huge pressures (average 6248 stddev 551, from a equilibration run with about 10^8 steps, which is not much, but I believe it gives the trend).

Doing some tests, I got that a chemical potential of about -48.25 gives me something close to the thermodynamic conditions I want.
From Cassandra's paper I know that a shifted chemical potential is used, but I thought it was just internally.
Since it seems that it's not the case, and that the shifted chemical potential is the parameters given by the user, I'd like to know:

1) Is there any formula to convert between the shifted chemical potential and the chemical potential that I got from the literature? I did not find this expression in the manual.

2) In case there's not, how do I know that the chemical potential of -48.25 gives me the condition that I want. I mean, how do I know it's not -48.2, or -48.3, for instance. I ask because since it's a simulation of a liquid, the pressures changes a lot and the standard deviations are in the orders of magnitude of the pressure itself (average 231, stddev 160). Do I really need to run simulations with more than 10^10 steps just to get an idea of the values?

Regards,
Henrique

Hi Ryan,

Thank you very much for pointing me out to the right direction.
Somehow I've missed the equation in the user guide, sorry about that.

Anyways, I followed your suggestion and got the Qrot term from McQuarrie.
I did the math more than once, but after converting the chemical potential from the reference I gave in the first post, I get a shifted chemical potential of -28.682 kJ/mol.
Since this value is greater than the chemical potentials I tested and got huge pressures, it is expected that I'll get even higher pressures.

This is the expression I used for Qrot:

with \Theta_A = 40.1 K, \Theta_B = 20.9 K, \Theta_C = 13.4 K, as provided in Table 8-1 of McQuarrie for H₂O.
Using a temperature of 300 K I get Qrot = 43.4539334 which leads me to value of 9.4079 that should be added to the chemical potential to get the shifted chemical potential, hence the value of -28.682 kJ/mol.

Did I miss something?

Regards,
Henrique