Physical constant table  

electron charge e  1.602 176 53 x 10^{19} C = 1/6.24150948E+18 C  
electric constant \epsilon_o  8.854 187 817... x 10^{12} F m^{1} =8.854187817 x 10^{12} C^{2}/(N . m^{2}) [or C^{2}/(J.m)]  
electric dipole  1 a.u. 8.47836 x 10^{30} Cm, 1 D (the debye unit D ) = 3.336 x 10^{30} Cm = 0.20822678 eA)  
Avogadro constant N_A  6.022 1415 x 10^{23} mol^{1 }  
Boltzmann constant k  1.380 6505 x 10^{23} J K^{1 }  
atomic mass constant m_u  1.660 538 86 x 10^{27} kg  
molar gas constant R  8.314 472 J mol^{1} K^{1 }  
Planck constant h  6.626 0693 x 10^{34} J s  
Planck constant over 2 pi \bar h  1.054 571 68 x 10^{34} J s  
Faraday constant F  96 485.3383 C mol^{1} = N_{a} * e = 1.602E19 * 6.022E+23 (capacitance, formula: A s V^{1}) faraday (Fd): A unit of electric charge. The British electrochemist and physicist Michael Faraday (17911867) determined that the same amount of charge is needed to deposit one mole of any element. This amount of charge, equal to about 96 485 coulombs, became known as Faraday's constant. Later, it was adopted as a convenient unit for measuring the charges used in electrolysis. One faraday is equal to the product of Avogadro's number (see mole) and the charge (1 e) on a single electron. 

concentration in molarity of standard state of water  55.5 M  
(energy unit) cal  4.184 J  
(concentration unit) M  1mol/liter = 1mol/cubic decimeter ~ (equivalent to) 1660.5 A^{3}/molecule ~ 11.84 A/pair molecule distance, unit transform: 1M = 6.022 x 10^{4} A^{3 }  
Units in equation  

Poisson Equation 
∇ · ε(r)
∇ φ(r,t) = ρ (r) with possible boundary condition (as applied in biomolecular ele): φ(r) = Q/(4*pi*ε*r) or: ∇ · ε(r) ∇ φ(r,t) = 4*pi*ρ (r) with possible boundary condition (as applied in biomolecular ele): φ(r) = Q/ ε*r if using the finite difference or the finite element solving above partial differential equation, and take units \AA (length), e(charge), and relative dielectric constant\epsilon (unitless), then after obtaining the solution, the transformation of the potential \phi to unit kcal/mol/e is ( *4172.83 for the first eq, 332 for the second eq): ( the correct solution can not be obtained only through scaling the boundary values, but fixing the equation form) 

