Blue-moon ensemble
In general, constrained molecular dynamics generates biased statistical averages. It can be shown that the correct average for a quantity can be obtained using the formula:
where stands for the statistical average of the quantity enclosed in angular parentheses computed for a constrained ensemble and is a mass metric tensor defined as:
It can be shown that the free energy gradient can be computed using the equation:[1][2][3][4]
where is the Lagrange multiplier associated with the parameter used in the SHAKE algorithm.[5]
The free-energy difference between states (1) and (2) can be computed by integrating the free-energy gradients over a connecting path:
Note that as the free-energy is a state quantity, the choice of path connecting (1) with (2) is irrelevant.
How to
The output needed to determine the blue moon ensemble averages within a Constrained molecular dynamics can be obtained by setting LBLUEOUT=.TRUE.
References
- ↑ E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989).
- ↑ W. K. Den Otter and W. J. Briels, Mol. Phys. 98, 773 (2000).
- ↑ E. Darve, M. A. Wilson, and A. Pohorille, Mol. Simul. 28, 113 (2002).
- ↑ P. Fleurat-Lessard and T. Ziegler, J. Chem. Phys. 123, 084101 (2005).
- ↑ J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).