Blue moon ensemble calculations - Revision history

Csheldon at 10:00, 18 October 2024

2024-10-18T10:00:40Z

← Older revision		Revision as of 10:00, 18 October 2024
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	The information needed to determine the blue moon ensemble averages within a [[:Category:Constrained molecular dynamics\|Constrained molecular dynamics]] can be obtained by setting {{TAG\|LBLUEOUT}}=.TRUE. The following output is written for each MD step in the file {{FILE\|REPORT}}:		The information needed to determine the blue moon ensemble averages within a [[:Category:Constrained molecular dynamics\|Constrained molecular dynamics]] can be obtained by setting {{TAG\|LBLUEOUT}}=.TRUE., cf. [[Blue_moon_ensemble\|blue moon ensemble]] for details of the theory. The following output is written for each MD step in the file {{FILE\|REPORT}}:

	>Blue_moon		>Blue_moon

Karsai at 13:12, 16 October 2024

2024-10-16T13:12:02Z

← Older revision		Revision as of 13:12, 16 October 2024
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	[[Category:Howto]]		[[Category:Advanced molecular-dynamics sampling]][[Category:Howto]]

Karsai: /* References */

2024-10-16T13:10:56Z

References

← Older revision		Revision as of 13:10, 16 October 2024
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	paste energy.dat zet.dat \|awk 'BEGIN {a=0.;b=0.} {a+=$1*$2;b+=$2} END {print a/b}'		paste energy.dat zet.dat \|awk 'BEGIN {a=0.;b=0.} {a+=$1*$2;b+=$2} END {print a/b}'

	~~==References==~~
	~~<references>~~
	~~<ref name="Ryckaert77">[http://dx.doi.org/10.1016/0021-9991(77)90098-5 J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).]</ref>~~
	~~<ref name="Carter89">[http://dx.doi.org/10.1016/S0009-2614(89)87314-2 E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989).]</ref>~~
	~~<ref name="Otter00">[http://dx.doi.org/10.1080/00268970009483348 W. K. Den Otter and W. J. Briels, Mol. Phys. 98, 773 (2000).]</ref>~~
	~~<ref name="Darve02">[http://dx.doi.org/10.1080/08927020211975 E. Darve, M. A. Wilson, and A. Pohorille, Mol. Simul. 28, 113 (2002).]</ref>~~
	~~<ref name="Fleurat05">[http://dx.doi.org/10.1063/1.1948367 P. Fleurat-Lessard and T. Ziegler, J. Chem. Phys. 123, 084101 (2005).]</ref>~~
	~~<ref name="Ryckaert77">[http://dx.doi.org/10.1016/0021-9991(77)90098-5 J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).]</ref>~~
	~~</references>~~
	----		----

	[[Category:Howto]]		[[Category:Howto]]

Karsai: Created page with "The information needed to determine the blue moon ensemble averages within a Constrained molecular dynamics can be obtained by setting {{TAG|LBLUEOUT}}=.TRUE. The following output is written for each MD step in the file {{FILE|REPORT}}: >Blue_moon lambda |z|^(-1/2) GkT |z|^(-1/2)*(lambda+GkT) b_m> 0.585916E+01 0.215200E+02 -0.117679E+00 0.123556E+03 with the four numerical terms indicatin..."

2024-10-16T13:10:35Z

Created page with "The information needed to determine the blue moon ensemble averages within a Constrained molecular dynamics can be obtained by setting {{TAG|LBLUEOUT}}=.TRUE. The following output is written for each MD step in the file {{FILE|REPORT}}: >Blue_moon lambda |z|^(-1/2) GkT |z|^(-1/2)*(lambda+GkT) b_m> 0.585916E+01 0.215200E+02 -0.117679E+00 0.123556E+03 with the four numerical terms indicatin..."

New page

The information needed to determine the blue moon ensemble averages within a [[:Category:Constrained molecular dynamics|Constrained molecular dynamics]] can be obtained by setting {{TAG|LBLUEOUT}}=.TRUE. The following output is written for each MD step in the file {{FILE|REPORT}}:

>Blue_moon
lambda |z|^(-1/2) GkT |z|^(-1/2)*(lambda+GkT)
b_m> 0.585916E+01 0.215200E+02 -0.117679E+00 0.123556E+03

with the four numerical terms indicating <math>\lambda_{\xi_k}</math>, <math>|Z|^{-1/2}</math>, <math>\left ( \frac{k_B T}{2 |Z|} \sum_{j=1}^{r}(Z^{-1})_{kj} \sum_{i=1}^{3N} m_i^{-1}\nabla_i \xi_j \cdot \nabla_i |Z| \right ) </math>, and <math>\left ( |Z|^{-1/2} [\lambda_k +\frac{k_B T}{2 |Z|} \sum_{j=1}^{r}(Z^{-1})_{kj} \sum_{i=1}^{3N} m_i^{-1}\nabla_i \xi_j \cdot \nabla_i |Z|] \right ) </math>, respectively.

{{NB|mind| <math> \left ( \frac{1}{2 |Z|} \sum_{j=1}^{r}(Z^{-1})_{kj} \sum_{i=1}^{3N} m_i^{-1}\nabla_i \xi_j \cdot \nabla_i |Z| \right ) </math> is defined as <math> G </math> in the {{FILE|REPORT}} file. This is an arbitrary character and has no relation to Green's functions, reciprocal lattice vectors, etc.}}

Note that one line introduced by the string 'b_m>' is written for each constrained coordinate. With this output, the free energy gradient with respect to the fixed coordinate <math>{\xi_k}</math> can conveniently be determined (by the equation given above) as a ratio between averages of the last and the second numerical terms. In the simplest case when only one constraint is used, the free energy gradient can be obtained as follows:

grep b_m REPORT |awk 'BEGIN {a=0.;b=0.} {a+=$5;b+=$3} END {print a/b}'

As an example of a blue moon ensemble average, let us consider the calculation of an unbiased potential energy average from constrained MD. For simplicity, only a single constraint is assumed. Here we extract <math>|Z|^{-1/2}</math> for each step and store the data in an auxiliary file zet.dat:
grep b_m REPORT |awk '{print $3}' > zet.dat
Here we extract potential energy for each step and store the data in an auxiliary file energy.dat:
grep e_b REPORT |awk '{print $3}' > energy.dat
Finally, the weighted average is determined according to the first formula shown above:
paste energy.dat zet.dat |awk 'BEGIN {a=0.;b=0.} {a+=$1*$2;b+=$2} END {print a/b}'

==References==
<references>
<ref name="Ryckaert77">[http://dx.doi.org/10.1016/0021-9991(77)90098-5 J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).]</ref>
<ref name="Carter89">[http://dx.doi.org/10.1016/S0009-2614(89)87314-2 E. A. Carter, G. Ciccotti, J. T. Hynes, and R. Kapral, Chem. Phys. Lett. 156, 472 (1989).]</ref>
<ref name="Otter00">[http://dx.doi.org/10.1080/00268970009483348 W. K. Den Otter and W. J. Briels, Mol. Phys. 98, 773 (2000).]</ref>
<ref name="Darve02">[http://dx.doi.org/10.1080/08927020211975 E. Darve, M. A. Wilson, and A. Pohorille, Mol. Simul. 28, 113 (2002).]</ref>
<ref name="Fleurat05">[http://dx.doi.org/10.1063/1.1948367 P. Fleurat-Lessard and T. Ziegler, J. Chem. Phys. 123, 084101 (2005).]</ref>
<ref name="Ryckaert77">[http://dx.doi.org/10.1016/0021-9991(77)90098-5 J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977).]</ref>
</references>
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[[Category:Howto]]