sentence: In order to directly compare MS-RMD and QM / MM free energy profiles , umbrella sampling was performed with a CV defined as ζ , which is a function of the excess proton CEC ( r ) and the center of mass of the carboxyl groups of the E203 ( r ) and the E148 ( r ) residues :10 The excess proton CEC coordinate , however , was defined as 11where the r is the position of the jth heavy atom in the QM region , which is either the water oxygen atoms or the carboxyl oxygen atoms in the E203 or the E148 , and the r is the position of the ith hydrogen atom bound to those heavy atoms .