# Physical Properties

A core philosophy of this framework is that users should be able to seamlessly curate data sets of physical properties and then estimate that data set using computational methods without significant user intervention and using sensible, well validated workflows.

This page aims to provide an overview of which physical properties are supported by the framework and how they are computed using the different calculation layers.

In this document \(\left<X\right>\) will be used to denote the ensemble average of an observable \(X\).

## Density

The density (\(\rho\)) is computed according to

where \(M\) and \(V\) are the total molar mass and volume the system respectively.

### Direct Simulation

The density is estimated using the default simulation workflow without modification. The estimation of liquid densities is assumed.

### MBAR Reweighting

The density is estimated using the default reweighting workflow without modification. The estimation of liquid densities is assumed.

## Dielectric Constant

The dielectric constant (\(\varepsilon\)) is computed from the fluctuations in a systems dipole moment (see Equation 7 of [1]) according to:

where \(\vec{\mu}\), \(V\) are the systems dipole moment and volume respectively, \(k_b\) the Boltzmann constant, \(T\) the temperature, and \(\varepsilon_0\) the permittivity of free space.

Note

In *v0.2.2* and earlier of the framework the variance was computed as
\(\left<{\left(\vec{\mu} - \left<\vec{\mu}\right>\right)}^2\right>\) in order to match the
mdtraj implementation which has been used in previous studies by the OpenFF
Consortium (see for example [2]). The two approaches should be numerically
indistinguishable however.

### Direct Simulation

The dielectric is estimated using the default simulation workflow
which has been modified to use the specialized `AverageDielectricConstant`

protocol in place of the default
`AverageObservable`

protocol. The estimation of liquid dielectric constants is assumed.

### MBAR Reweighting

The dielectric is estimated using the default reweighting workflow
which has been modified to use the specialized `ReweightDielectricConstant`

protocol in place of the default
`ReweightObservable`

protocol. It should be noted that the `ReweightDielectricConstant`

protocol employs
bootstrapping to compute the uncertainty in the average dielectric constant, rather than attempting to propagate
uncertainties in the average dipole moments and volumes. The estimation of liquid dielectric constants is assumed.

## Enthalpy of Vaporization

The enthalpy of vaporization \(\Delta H_{vap}\) (see [3]) can be computed according to

where \(H\), \(E\), and \(V\) are the enthalpy, total energy and volume respectively.

Under the assumption that \(V_{gas} >> V_{liquid}\) and that the gas is ideal the above expression can be simplified to

where \(U\) is the potential energy, \(T\) the temperature and \(R\) the universal gas constant. This simplified expression is computed by default by this framework.

### Direct Simulation

**Liquid phase**: The potential energy of the liquid phase is estimated using the default simulation workflow, and divided by the number of molecules in the simulation box using the`divisor`

input of the`AverageObservable`

protocol.**Gas phase**: The potential energy of the gas phase is estimated using the default simulation workflow, which has been modified so thatthe simulation box only contains a single molecule.

all periodic boundary conditions have been disabled.

all simulations are performed in the NVT ensemble.

the production simulation is run for 15000000 steps at a time (rather than 1000000 steps).

all simulations are run using the OpenMM reference platform (CPU only) regardless of whether a GPU is available. This is fastest platform to use when simulating a single molecule in vacuum with OpenMM.

The final enthalpy is then computed by subtracting the gas potential energy from the liquid potential energy
(`SubtractValues`

) and adding the \(RT\) term (`AddValues`

). Uncertainties are propagated through the subtraction
by the normal means using the uncertainties package.

### MBAR Reweighting

**Liquid phase**: The potential energy of the liquid phase is estimated using the default reweighting workflow, and divided by the number of molecules in the simulation box using an extra`DivideValue`

protocol.**Gas phase**: The potential energy of the gas phase is estimated using the default reweighting workflow, which has been modified so that all periodic boundary conditions have been disabled.

The final enthalpy is then computed by subtracting the gas potential energy from the liquid potential energy
(`SubtractValues`

) and adding the \(RT\) term (`AddValues`

). Uncertainties are propagated through the subtraction
by the normal means using the uncertainties package.

## Enthalpy of Mixing

The enthalpy of mixing \(\Delta H_{mix}\left(x_0, \cdots, x_{M-1}\right)\) for a system of \(M\) components is computed according to

where \(H_{mix}\) is the enthalpy of the full mixture, and \(H_i\), \(x_i\) are the enthalpy and the mole fraction of component \(i\) respectively. \(N_{mix}\) and \(N_i\) are the total number of molecules used in the full mixture simulations and the simulations of each individual component respectively.

When re-weighting cached data to compute \(H_{mix}\) we make the approximation that the kinetic energy contributions cancel out between the mixture and each of the components, and hence can be computed by only re-weighting the NPT reduced potential:

where \(u \equiv \beta \left(U + pV\right)\) is the NPT reduced potential, \(U\) the potential energy, \(p\) the pressure and \(V\) the volume.

### Direct Simulation

**Mixture**: The enthalpy of the full mixture is estimated using the default simulation workflow and divided by the number of molecules in the simulation box using the`divisor`

input of the`AverageObservable`

protocol.**Components**: The enthalpy of each of the components is estimated using the default simulation workflow, divided by the number of molecules in the simulation box using the`divisor`

input of the`AverageObservable`

protocol, and weighted by their mole fraction*in the mixture simulation box*using the`WeightByMoleFraction`

protocol.

The final enthalpy is then computed by summing the component enthalpies (`AddValues`

) and subtracting these from
the mixture enthalpy (`SubtractValues`

). Uncertainties are propagated through the summation and subtraction by the
normal means using the uncertainties package.

### MBAR Reweighting

**Mixture**: The reduced potential of the full mixture is estimated using the default reweighting workflow and divided by the number of molecules in the reweighting box using an extra`DivideValue`

protocol.**Components**: The reduced potential of each of the components is estimated using the default reweighting workflow, divided by the number of molecules in the reweighting box using an extra`DivideValue`

protocol, and weighted by their mole fraction using the`WeightByMoleFraction`

protocol.

The final enthalpy is then computed by summing the component enthalpies (`AddValues`

), subtracting these from
the mixture enthalpy (`SubtractValues`

), and multiplying by \(1 / \beta\) (`MultiplyValue`

). Uncertainties are propagated
by the normal means using the uncertainties package.

## Excess Molar Volume

The excess molar volume \(\Delta V_{excess}\left(x_0, \cdots, x_{M-1}\right)\) for a system of \(M\) components is computed according to

where \(V_{mix}\) is the volume of the full mixture, and \(V_i\), \(x_i\) are the volume and the mole fraction of component \(i\) respectively. \(N_{mix}\) and \(N_i\) are the total number of molecules used in the full mixture simulations and the simulations of each individual component respectively, and \(N_A\) is the Avogadro constant.

### Direct Simulation

**Mixture**: The molar volume of the full mixture is estimated using the default simulation workflow and divided by the molar number of molecules in the simulation box using the`divisor`

input of the`AverageObservable`

protocol.**Components**: The molar volume of each of the components is estimated using the default simulation workflow, divided by the molar number of molecules in the simulation box using the`divisor`

input of the`AverageObservable`

protocol, and weighted by their mole fraction*in the mixture simulation box*using the`WeightByMoleFraction`

protocol.

The final excess molar volume is then computed by summing the component molar volumes (`AddValues`

) and subtracting these from
the mixture molar volume (`SubtractValues`

). Uncertainties are propagated through the summation and subtraction by the
normal means using the uncertainties package.

### MBAR Reweighting

**Mixture**: The enthalpy of the full mixture is estimated using the default reweighting workflow and divided by the molar number of molecules in the reweighting box using an extra`DivideValue`

protocol.**Components**: The enthalpy of each of the components is estimated using the default reweighting workflow, divided by the molar number of molecules in the reweighting box using an extra`DivideValue`

protocol, and weighted by their mole fraction using the`WeightByMoleFraction`

protocol.

The final enthalpy is then computed by summing the component enthalpies (`AddValues`

) and subtracting these from
the mixture enthalpy (`SubtractValues`

). Uncertainties are propagated through the summation and subtraction by the
normal means using the uncertainties package.

## Solvation Free Energies

Solvation free energies are currently computed using the Yank free energy package using direct molecular simulations. By default the calculations attempt to use 2000 solvent molecules, and the alchemical lambda spacings are selected using the built-in ‘trailblazing’ algorithm.

See the Yank documentation for more details.

## Host-Guest Binding Free Energy

Warning

The computation of this property is still in beta. Users are heavily recommended to validate any calculations involving this property.

Host-guest binding free energies are currently computed using the attach-pull-release (APR) method [4] through integration with the pAPRika framework.

## References

- 1
Alice Glättli, Xavier Daura, and Wilfred F van Gunsteren. Derivation of an improved simple point charge model for liquid water: spc/a and spc/l.

*The Journal of chemical physics*, 116(22):9811–9828, 2002.- 2
Kyle A Beauchamp, Julie M Behr, Ariën S Rustenburg, Christopher I Bayly, Kenneth Kroenlein, and John D Chodera. Toward automated benchmarking of atomistic force fields: neat liquid densities and static dielectric constants from the thermoml data archive.

*The Journal of Physical Chemistry B*, 119(40):12912–12920, 2015.- 3
Junmei Wang and Tingjun Hou. Application of molecular dynamics simulations in molecular property prediction. 1. density and heat of vaporization.

*Journal of chemical theory and computation*, 7(7):2151–2165, 2011.- 4
David R Slochower, Niel M Henriksen, Lee-Ping Wang, John D Chodera, David L Mobley, and Michael K Gilson. Binding thermodynamics of host–guest systems with smirnoff99frosst 1.0. 5 from the open force field initiative.

*Journal of Chemical Theory and Computation*, 15(11):6225–6242, 2019.