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definition of chemical potential
- Ojaghlou
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8 years 8 months ago #38
by Ojaghlou
Dear Cassandra-Developer, dear users,
I have several questions, regarding to GCMC ensemble. I would appreciate if you could help me.
Firstly the unit of chemical potential is KJ/mol but when I check the .log file it gives me the chemical potential in atomic unit and when I compare KJ/mol to atomic unit I've got another answer.
In here the chemical potential was :8.78 KJ/mol
*********** Fugactiy Info ***************
Chemical Potential of sp 1 is 0.878000000E+03in atomic units
de Broglie wavelength of species 1 in box 1 is
0.2375761156 Angstrom
secondly, user guide says that "the chemical potential differs from the actual chemical by a constant". could you please explain me that what is the constant potential??? and what kind of definition have you used for computing the chemical potential, excess chemical potential and de Broglie wavelength ?
Kind Regards,
Neda
I have several questions, regarding to GCMC ensemble. I would appreciate if you could help me.
Firstly the unit of chemical potential is KJ/mol but when I check the .log file it gives me the chemical potential in atomic unit and when I compare KJ/mol to atomic unit I've got another answer.
In here the chemical potential was :8.78 KJ/mol
*********** Fugactiy Info ***************
Chemical Potential of sp 1 is 0.878000000E+03in atomic units
de Broglie wavelength of species 1 in box 1 is
0.2375761156 Angstrom
secondly, user guide says that "the chemical potential differs from the actual chemical by a constant". could you please explain me that what is the constant potential??? and what kind of definition have you used for computing the chemical potential, excess chemical potential and de Broglie wavelength ?
Kind Regards,
Neda
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- ryangmullen
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8 years 8 months ago #43
by ryangmullen
The input file requires the chemical potential in kJ/mol. Internally, Cassandra converts this number into atomic units. The conversion factor is 100. So a chemical potential of 8.78 kJ/mol = 878 atomic units.
The shifted chemical potential, mu_shift, differs from the true chemical potential, mu, by a constant which is different for each species. The constant is generally difficult to compute, which is why we absorb it into mu_shift. Each mu_shift will correspond to a specific pressure, but it generally takes a few trial and error simulations to find the mu_shift for the pressure you want. In Cassandra 1.0, each mu_shift corresponds to a specific particle number, regardless of box size. This error will be corrected in Cassandra 1.1; each mu_shift will correspond to a specific number density. Specifically,
mu_shift = mu + kT * ln(Q_rot+int * Z_frag * Omega_dih / Z_int)
where Q_rot+int = Q(1,V,T) * Lambda^3 / V. Q(1,V,T) is the canonical partition function of a single molecule and Lambda is the de Broglie wavelength. Omega_dih = (2pi)^(number of dihedrals). Z_int = Z(1,V,T) / (V * Z_rot). Z(1,V,T) is the configurational partition function of a single molecule, and Z_rot is 4pi if the molecule is linear, or 8pi^2 if the molecule is nonlinear. Z_frag is the product of configurational integrals for each disconnected fragment. If your species has only 1 fragment per molecule, then Z_frag = Z_int.
In GCMC, mu_shift is an input parameter. Cassandra does not compute it.
The de Broglie wavelength is:
Lambda = h * (beta / 2pi * mass)^(1/2)
The shifted chemical potential, mu_shift, differs from the true chemical potential, mu, by a constant which is different for each species. The constant is generally difficult to compute, which is why we absorb it into mu_shift. Each mu_shift will correspond to a specific pressure, but it generally takes a few trial and error simulations to find the mu_shift for the pressure you want. In Cassandra 1.0, each mu_shift corresponds to a specific particle number, regardless of box size. This error will be corrected in Cassandra 1.1; each mu_shift will correspond to a specific number density. Specifically,
mu_shift = mu + kT * ln(Q_rot+int * Z_frag * Omega_dih / Z_int)
where Q_rot+int = Q(1,V,T) * Lambda^3 / V. Q(1,V,T) is the canonical partition function of a single molecule and Lambda is the de Broglie wavelength. Omega_dih = (2pi)^(number of dihedrals). Z_int = Z(1,V,T) / (V * Z_rot). Z(1,V,T) is the configurational partition function of a single molecule, and Z_rot is 4pi if the molecule is linear, or 8pi^2 if the molecule is nonlinear. Z_frag is the product of configurational integrals for each disconnected fragment. If your species has only 1 fragment per molecule, then Z_frag = Z_int.
In GCMC, mu_shift is an input parameter. Cassandra does not compute it.
The de Broglie wavelength is:
Lambda = h * (beta / 2pi * mass)^(1/2)
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