To calculate ΔG0 of transition from the state A to state B,
it is necessary to sum time spent in the state A and time spent in the state B.
Next, ΔG can be calculated as:
\[\Delta G_{0,AB} = -kT \log {{\sum_{i=1}^{n_B} t_{Bi}} \over {\sum_{j=1}^{n_A} t_{Ai}}},\]
where k = 8.314 J mol-1 K-1, T is temperature in K and log is
the natural logarithm (base e).
Confidence intervals and standard errors of ΔG0 can be calculated from temperature and the number of transitions from A to B (nA) and the number of transitions from B to A (nB).
In a system with multiple forms, the number of transitions from A to B (nA) and the number of transitions from B to A (nB) must be numbers of accomplished transitions. For example, in a system with states A, B and C and with transitions A → B → A → B → A → B → C → B → C → B → A → B → A → B → C → B → A, the number of transitions from A to C nA = 2 (two transitions in red) and the number of transitions from C to A nC = 2 (two transitions in blue).
Alternatively, it is possible to run a series of nA simulations starting
from A until they reach B and a series of nB simulations starting from B
until they reach A. Then, ΔG can be calculated as:
\[\Delta G_{0,AB} = -kT \log {n_A {\sum_{i=1}^{n_B} t_{Bi}} \over { n_B \sum_{j=1}^{n_A} t_{Ai}}}.\]
It is important to run all simulation until they reach the desired state or to modify the
formula to:
\[\Delta G_{0,AB} = -kT \log {n_A ({\sum_{i=1}^{n_B} t_{Bi}} + m_B t_{max}) \over { n_B (\sum_{j=1}^{n_A} t_{Ai}} + m_A t_{max})},\]
where nA and nB are numbers of finished runs (the transition observed)
starting from A and B, respectively, mA and mB are numbers of unfinished
runs (the transition not observed, terminated at tmax), respectively.
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