Luboš Vrbka Homepage : Constants, conversions, potentials, …

Some useful data…

constants

elementary charge $e = 1.60217646\times 10^{-19}\,\mathrm{C}$
speed of light $c = 2.9979245\times 10^{8}\,\mathrm{m\cdot s^{-1}}$
vacuum permittivity $\varepsilon_0 = 8.8541878176\times 10^{-12}\,\mathrm{Fm^{-1} (C^2\,N^{-1}\,m^{-2})}$
Boltzmann constant $k_B = 1.3806503\times 10^{-23}\,\mathrm{JK^{-1} (kg\,m^2\,s^{-2}\, K^{-1})}$
Avogadro number $N_A = 6.0221415\times 10^{23}\,\mathrm{mol^{-1}}$
Molar gas constant $R = N_A\cdot k_B = 8.314472\,\mathrm{J\,K^{-1}\,mol^{-1} (kg\,m^2\,s^{-2}\,K^{-1}\,mol^{-1})}$

$1\,\mathrm{mol\cdot L^{-1}} = N_A\cdot 10^{-27}\,\mathrm{molecules\cdot \AA^{-3}}} = 6.02214179\times 10^{-4}\,\mathrm{molecules\cdot \AA^{-3}}$
$1\,k_BT = T \times 1.3806503\times 10^{-23}\,\mathrm{J\cdot molecule^{-1}}$
$\displaystyle 1\,k_BT = T \times 1.3806503\times 10^{-23}\,\frac{\mathrm{J}}{4184\,\mathrm{J\cdot kcal^{-1}}} \frac{N_A \cdot \mathrm{molecule}}{\mathrm{molecule}} = \frac{T}{503.2189736}\,\mathrm{kcal\cdot mol^{-1}} = \frac{T}{120.2722212}\,\mathrm{kJ\cdot mol^{-1}}$
therefore, $1\,\mathrm{kcal\cdot mol^{-1}} \doteq 1.6774\,k_BT (\mathrm{at}\ 300\,\mathrm{K})$
and $1\,\mathrm{kJ\cdot mol^{-1}} \doteq 0.4009\,k_BT (\mathrm{at}\ 300\,\mathrm{K})$

$\mathrm{e}^{-\frac{\textrm{PMF}}{k_BT}} = 4\pi r^2 g(r)$
$\displaystyle V_{\mathrm{c}} = \frac{1}{4\pi\varepsilon_0\varepsilon_r}\frac{q_1q_2}{r}$
$\displaystyle \left|\vec{F_{\mathrm{c}}}\right| = \left|-\left(\frac{dV_{\mathrm{c}}}{dr}\right)\right| = \frac{1}{4\pi\varepsilon_0\varepsilon_r}\frac{q_1q_2}{r^2}$
for POL3 potential and two unit charges ( $\varepsilon_r = 106)$
$\displaystyle V_{\textrm{c}} = \frac{1}{4\pi\cdot\varepsilon_0\cdot 106}\frac{e^2}{r} \mathrm{J\cdot molecule^{-1}} \cdot \frac{10^{10}\cdot N_A\cdot\mathrm{molecule}}{4184\,\mathrm{J\cdot kcal^{-1}}} \doteq \frac{3.1319}{r}\,\mathrm{kcal\cdot mol^{-1}}$ with distance given in $\mathrm{\AA}$