HSE energy function
The similarity of two HSE vectors A and B of length N can be measured using the following RMS deviation:
RMSD ( A , B ) = ∑ i = 1  N  ( ( A u i    − B u i    )  2  + ( A d i    − B d i    )  2  )    2 N     ,   MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@5B92@
where {A,B}ui MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGG7bWEcqWGbbqqcqGGSaalcqWGcbGqcqGG9bqFdaWgaaWcbaGaemyDau3aaSbaaWqaaiabdMgaPbqabaaaleqaaaaa@35D6@ and {A,B}di MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqGG7bWEcqWGbbqqcqGGSaalcqWGcbGqcqGG9bqFdaWgaaWcbaGaemizaq2aaSbaaWqaaiabdMgaPbqabaaaleqaaaaa@35B4@ are the up and down values of the i'th index. RMSD (A, B) can be used to describe the energy of structure SA where A is the HSE vector of SA and B is the HSE vector of the native structure. These definitions are easily extended to the CN measure. The energy functions are the only optimization criteria used by the MCS and TS algorithms.