1 S Density Embedded VB/MM – A Hybrid ab-initio VB/MM with Electrostatic Embedding Avital Sharir-Ivry a , Hadar A. Crown a , Wei Wu b , Avital Shurki a† * a Department of Medicinal Chemistry and Natural Products, The Lise Meitner-Minerva Center for Computational Quantum Chemistry, School of Pharmacy, The Hebrew University of Jerusalem, Jerusalem 91120, Israel b Department of Chemistry, Center for Theoretical Chemistry and State Key Laboratory of Physical Chemistry of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen, Fujian 361005, China Supporting Material Equations 7 - derivation For a simple two diabatic states system the solution of the Schrödinger equation at the point where the two states cross (i.e. the energy of the two states is equal, 22 11 H H = ) is: 12 12 11 1 S H H E + + = (1S) where 11 H is the energy of state 1, 12 S is the overlap between the two states and 12 H is the corresponding resonance integral. The resonance energy which is the energy difference between the adiabatic energy (as obtained in Eq. 1S) and the energy of the diabatic state is: 12 12 11 12 11 12 12 11 11 1 1 S S H H H S H H H E +  =  + + =  (2S) At the crossing point, 22 11 H H = , hence 11 H can also be written as ) ( 2 1 22 11 11 H H H + = , leading to the following formula: