I try to solve the following equations for some system solvated in the water. The goal is to obtain value in kcal/mol. Unfortunately, I cannot reach the desired output. May someone help me?
The variables are:
n = 1 (single electron exchanged)
rA = 3.68Å
rD = 2.90Å
R = 6.58Å
ε∞ = 5.2 F/m
ε0 = 78.408 F/m
My try:
\begin{gather} \lambda \ =\ ( ne)^{2}\left(\frac{1}{2r_{A}} +\frac{1}{2r_{B}} -\frac{1}{R}\right)\left(\frac{1}{\epsilon _{\infty }} -\frac{1}{\epsilon _{0}}\right) \notag\\ \notag\\ \lambda \ -\ reorganization\ energy\ [ ?\ kcal/mol] \notag\\ \notag\\ n\ -\ number\ of\ exchanged\ electrons\ [ =1] \notag\\ e\ -\ electron\ charge\ \left[ =\ 1.602\times 10^{-19} C\right] \notag\\ r_{A} -\ radius\ of\ the\ acceptor\ cavity\ [ =3.68Å ] \notag\\ r_{D} -\ radius\ of\ the\ donor\ cavity\ [ =2.50Å ]\\ R\ -\ intermolecular\ distance\ [ =6.18Å ] \notag\\ \epsilon _{\infty } \ -\ optical\ dielectric\ constant\ [ =5.2] \notag\\ \epsilon _{0} \ -\ static\ dielectric\ constant\ [ =78.408] \notag\\ \notag\\ \mathbf{Conversion:} \notag\\ \notag\\ r_{A} \ =\ 3.68Å \ =0.368nm \notag\\ r_{D} \ =\ 2.50ÅA =0.250nm \notag\\ R=6.18Å =0.618nm \notag\\ \epsilon _{\infty } \ =\ 5.2\times 8.854\times 10^{-12}\frac{F}{m} =4.604\times 10^{-11}\frac{F}{m} \notag\\ \epsilon _{0} \ =\ 78.408\times 8.854\times 10^{-12}\frac{F}{m} =6.942\times 10^{-10}\frac{F}{m} \notag\\ \notag\\ \notag\\ \mathbf{Calculation} : \notag\\ \notag\\ \lambda \ =\ 2.566\times 10^{-38} \ [ C] \ \left(\frac{1}{0.736\ [ nm]} +\frac{1}{0.500\ [ nm]} -\frac{1}{0.618\ [ nm]}\right)\left(\frac{1}{4.604\times 10^{-11}\frac{F}{m}} -\frac{1}{6.942\times 10^{-10}\frac{F}{m}}\right) \notag\\ \lambda \ =\ 2.566\times 10^{-38} \ [ C] \ \left( 1.359\left[\frac{1}{nm}\right] +2\left[\frac{1}{[ nm]}\right] -1.618\left[\frac{1}{nm}\right]\right)\left(\frac{1}{4.604\times 10^{-11}\frac{F}{m}} -\frac{1}{6.942\times 10^{-10}\frac{F}{m}}\right) \notag\\ \notag\\ \lambda \ =\ \left( 2.566\times 10^{-38}\right) \ [ C] \ \times 1.741\left[\frac{1}{nm}\right] \times \left( 2.028\times 10^{10}\right)\left[\frac{m}{F}\right] \notag\\ \lambda \ =\ 9.06\ \times 10^{-28}\left[\frac{C\times m}{nm\times F}\right] \ \notag\\ \lambda \ =\ 9.06\ \times 10^{-28}\left[ 10^{9}\frac{C\times nm}{nm\times F}\right] \ \notag\\ \lambda \ =\ 9.06\ \times 10^{-19}\left[\frac{C}{F}\right] \ \notag\\ \notag \end{gather}