In which the 
  
    
      
        λ
      
    
    {\displaystyle \lambda }
   is the reorganisation energy. Filling this result in the classically derived Arrhenius equation

leads to

With A being the pre-exponential factor which is usually experimentally determined, although a semi classical derivation provides more information as will be explained below. This classically derived result qualitatively reproduced observations of a maximum electron transfer rate under the conditions 
  
    
      
        Δ
        
          G
          
            †
          
        
        =
        λ
      
    
    {\displaystyle \Delta G^{\dagger }=\lambda }
  . For a more extensive mathematical treatment one could read the paper by Newton.
μ
        =
        
          μ
          
            o
          
        
        +
        k
        ⋅
        T
        ⋅
        log
        ⁡
        (
        γ
        ⋅
        x
        )
        +
        Ω
        ⋅
        σ
      
    
    {\displaystyle \mu =\mu ^{o}+k\cdot T\cdot \log(\gamma \cdot x)+\Omega \cdot \sigma }
  
In this equation μ represents the chemical potential, with μ° being its reference value. T stands for the temperature and k the Boltzmann constant.