.. _units:

The following are preferred APBS units.

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Numbers
=======

Many quantities are scaled by Avogadro's number, the number of atoms in a mole (mol), :math:`N_A = 6.02214076 \times 10^{23} \, \text{mol}^{-1}`.

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Length
======

The preferred unit of length is the ångström (Å), equal to 10\ :sup:`-10` meters.

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Volume
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The preferred unit of volume is Å\ :sup:`3`, equal to 10\ :sup:`-27` liters.

=========================
Density and concentration
=========================

The preferred unit of density is number per Å\ :sup:`3`, corresponding to a
concentration of approximately 1660.5391 mol L\ :sup:`-1` or molar (M).

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Temperature
===========

The preferred unit of temperature is Kelvin (K).

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Charge
======

The preferred unit of charge is :math:`e_c = 1.602176634 \times 10^{−19} \, \text{C}`.
The following number is often useful:  :math:`N_A e_c = 9.64853321233 \times 10^4 \, \text{C} \, \text{mol}^{-1}`.

======
Energy
======

The preferred unit of energy is :math:`k_B \, T` or :math:`R \,T` where

* Boltzmann's constant: :math:`k_B = 1.38064852 \times 10^{-23} \, \text{J} \, \text{K}^{-1}`
* Gas constant: :math:`R = N_A k_B = 8.31446261815324 \text{J} \, \text{K}^{-1} \, \text{mol}^{-1}`
* Temperature: :math:`T`

If :math:`T \approx 298 \, \text{K}`, then :math:`R\, T \approx 2.49 \, \text{kJ}`.

===============
Surface tension
===============

The preferred unit for surface tension is kJ mol\ :sup:`-1` Å\ :sup:`-2`.
Values for the surface tension of water in these models often range from 0.105 to 0.301 kJ mol\ :sup:`-1` Å\ :sup:`-2`. [#Sharp]_
However, these values can vary significantly depending on the model used. [#Thomas]_ [#Wagoner]_

========
Pressure
========

The preferred unit for pressure is kJ mol\ :sup:`-1` Å\ :sup:`-3`.
Values for the surface tension of water in these models vary significantly depending on the model used (e.g., between 0.0004 and 0.146 kJ mol\ :sup:`-1` Å\ :sup:`-3`). [#Thomas]_ [#Wagoner]_

=======================
Electrostatic potential
=======================

The preferred unit of electrostatic potential is :math:`k_B \, T \, e_c^{-1}` or :math:`R \, T \, e_c^{-1}`.
If :math:`T \approx 298 \, \text{K}`, then :math:`k_B \, T \, e_c^{-1} = R \, T \, e_c^{-1} \approx 0.0256 \, \text{J} \, \text{C}^{-1} = 25.6 \, \text{mV}`.

.. [#Sharp] Sharp KA, Nicholls A, Fine RF, Honig B. Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects. Science, 252, 106-109, 1991. DOI:`10.1126/science.2011744 <http://doi.org/10.1126/science.2011744>`_.

.. [#Thomas] Thomas DG, Chun J, Zhen C, Wei GW, Baker NA. Parameterization of a geometric flow implicit solvation model. J Comput Chem, 34, 687-695, 2013. DOI:`10.1002/jcc.23181 <https://doi.org/10.1002/jcc.23181>`_.

.. [#Wagoner] Wagoner JA and Baker NA.  Assessing implicit models for nonpolar mean solvation forces: The importance of dispersion and volume terms. Proc Natl Acad Sci USA, 103, 8331-9336, 2006. DOI:`10.1073/pnas.0600118103 <https://doi.org/10.1073/pnas.0600118103>`_.