
Overview
This section provides some information about the quantities computed and displayed to the standard output. Much of the output to the standard
output is selfexplanatory, so here we focus on the quantities computed and output as averages or as block averages.
This section is valid for the most current version of the code and was last updated for version 5.0.1.
Please see the essay on Chemical Potential for information about the various types of chemical
potential computed and output into standard output.
Please see the essay on Pressure for information about the various types of pressure computed and output
into standard output.
Average Accumulation
The following quantities are added into the averages after every attemped Monte Carlo move.
 Total energy
 Individual energy components
 Total energy squared
 Specific density
 Volume
 Number density of each component and also the total number density
 Mol fraction
 Number of each type of molecule in each box
 Heat of vaporization (pV/n=RT): This is the method described in Equation (2) of
Martin and Biddy 2005
H_{vap}(pV/n=RT) = <
(U_{vap}/N_{vap})  (U_{liq}/N_{liq}) + RT
>
The following quantities are added into the averages after every full Monte Carlo cycle.
The following quantities are added into the averages every time the virial pressure is computed.
 Virial Pressure. The pressure in Towhee is computed using the molecular virial.
 Stress tensor
 Enthalpy. Computed in Towhee using the thermodynamic relation H = U + pV.
 Enthalpy squared
 pV (pressure times volume)
 Heat of vaporization (Direct): This uses a direct computation of H = U + pV in each phase.
H_{vap}(Direct) = <
(U_{vap} + p_{vap} * V_{vap})/N_{vap}
 (U_{liq} + p_{liq} * V_{liq})/N_{liq}
>
 Heat of vaporization (vapor p): This is the method described in Equation (1) of
Martin and Biddy 2005
H_{vap}(vapor p) = <
(U_{vap}/N_{vap})  (U_{liq}/N_{liq})
+ p_{vap} * (V_{vap}/N_{vap}  V_{liq}/N_{liq})
>
The following quantities are added into the averages every time a volume move is attempted and it does
not result in an infinite energy change (hard overlap)
 dU/dV: the change in potential energy for a trial change in volume. This is used to compute the thermodynamic pressure.
The following quantities are computed every time the appropriate chemical potential is measured
 Isolation chemical potential.
 NVT insertion chemical potential.
 NpT insertion chemical potential.
 Gibbs total chemical potential
The following quantities are computed using the values of other quantities
 Ideal density chemical potential (u (Density)). Computed using the average volume and the average number of molecules.
 Henry's law coefficients. This is computed from the residual chemical potential and the number density.
Henry(i) = k_{B} T < Sum_{j=1}^{n}{ number density(j) } > * Exp[ < μ_{residual}(i) > / k_{B} T ]
 Ideal Pressure. Computed from the average total number density.
 Thermodynamic Pressure. Computed using the Ideal Pressure and dU/dV following the work of
Hummer et al. 1998.
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