Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables (CVs). The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work, we discuss how auxiliary variables can be mapped in CV space. We show that maps of auxiliary variables allow one to analyze both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyze the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.
REFERENCES
1.
D.
Wales
, Energy Landscapes with Applications to Clusters, Biomolecules and Glasses
(Cambridge University Press
, 2003
).2.
P.
Das
, M.
Moll
, H.
Stamati
, L. E.
Kavraki
, and C.
Clementi
, Proc. Natl. Acad. Sci. U. S. A.
103
, 9885
(2006
).3.
M. A.
Rohrdanz
, W.
Zheng
, M.
Maggioni
, and C.
Clementi
, J. Chem. Phys.
134
, 124116
(2011
).4.
M.
Ceriotti
, G. A.
Tribello
, and M.
Parrinello
, Proc. Natl. Acad. Sci. U. S. A.
108
, 13023
(2011
).5.
P. I.
Zhuravlev
, C. K.
Materese
, and G. A.
Papoian
, J. Phys. Chem. B
113
, 8800
(2009
).6.
H.
Stamati
, C.
Clementi
, and L. E.
Kavraki
, Proteins: Struct., Funct., Bioinf.
78
, 223
(2010
).7.
P. J.
Steinhardt
, D. R.
Nelson
, and M.
Ronchetti
, Phys. Rev. B
28
, 784
(1983
).8.
G. A.
Tribello
, F.
Giberti
, G. C.
Sosso
, M.
Salvalaglio
, and M.
Parrinello
, J. Chem. Theory Comput.
13
, 1317
(2017
).9.
G.
Gobbo
, M. A.
Bellucci
, G. A.
Tribello
, G.
Ciccotti
, and B. L.
Trout
, J. Chem. Theory Comput.
14
, 959
(2018
).10.
F.
Giberti
, M.
Salvalaglio
, and M.
Parrinello
, IUCrJ
2
, 256
–266
(2015
).11.
E. E.
Santiso
and B. L.
Trout
, J. Chem. Phys.
134
, 064109
(2011
).12.
S.
Pipolo
, M.
Salanne
, G.
Ferlat
, S.
Klotz
, A. M.
Saitta
, and F.
Pietrucci
, Phys. Rev. Lett.
119
, 245701
(2017
).13.
F.
Pietrucci
and W.
Andreoni
, Phys. Rev. Lett.
107
, 085504
(2011
).14.
G. M.
Torrie
and J. P.
Valleau
, J. Comput. Phys.
23
, 187
(1977
).15.
S.
Marsili
, A.
Barducci
, R.
Chelli
, P.
Procacci
, and V.
Schettino
, J. Phys. Chem. B
110
, 14011
(2006
).16.
A.
Laio
and M.
Parrinello
, Proc. Natl. Acad. Sci. U. S. A.
99
, 12562
(2002
).17.
A.
Barducci
, G.
Bussi
, and M.
Parrinello
, Phys. Rev. Lett.
100
, 020603
(2008
).18.
E.
Darve
, D.
Rodríguez-Gómez
, and A.
Pohorille
, J. Chem. Phys.
128
, 144120
(2008
).19.
S.
Piana
and A.
Laio
, J. Phys. Chem. B
111
, 4553
(2007
).20.
O.
Valsson
and M.
Parrinello
, Phys. Rev. Lett.
113
, 090601
(2014
).21.
J.
Pfaendtner
and M.
Bonomi
, J. Chem. Theory Comput.
11
, 5062
(2015
).22.
J.
Kirkwood
, J. Chem. Phys.
3
, 300
(1935
).23.
J.
Wang
, R. M.
Wolf
, J. W.
Caldwell
, P. A.
Kollman
, and D. A.
Case
, J. Comput. Chem.
25
, 1157
(2004
).24.
G.
Bussi
, D.
Donadio
, and M.
Parrinello
, J. Chem. Phys.
126
, 014101
(2007
).25.
E.
Lindahl
, B.
Hess
, and D.
van der Spoel
, J. Mol. Model.
7
, 306
(2001
).26.
G. A.
Tribello
, M.
Bonomi
, D.
Branduardi
, C.
Camilloni
, and G.
Bussi
, Comput. Phys. Commun.
185
, 604
(2014
).27.
28.
B.
Kuchta
and R. D.
Etters
, Phys. Rev. B
38
, 6265
(1988
).29.
R. D.
Etters
and B.
Kuchta
, J. Chem. Phys.
90
, 4537
(1989
).30.
J. J.
Potoff
, J. R.
Errington
, and A. Z.
Panagiotopoulos
, Mol. Phys.
97
, 1073
(1999
).31.
T.
Sanghi
and N. R.
Aluru
, J. Chem. Phys.
136
, 024102
(2012
).32.
H. J. C.
Berendsen
, J. P. M.
Postma
, W. F.
van Gunsteren
, A.
DiNola
, and J. R.
Haak
, J. Chem. Phys.
81
, 3684
(1984
).33.
M.
Salvalaglio
, T.
Vetter
, F.
Giberti
, M.
Mazzotti
, and M.
Parrinello
, J. Am. Chem. Soc.
134
, 17221
(2012
).34.
F.
Giberti
, M.
Salvalaglio
, M.
Mazzotti
, and M.
Parrinello
, Chem. Eng. Sci.
121
, 51
(2015
).35.
I.
Gimondi
and M.
Salvalaglio
, J. Chem. Phys.
147
, 114502
(2017
).36.
I.
Gimondi
and M.
Salvalaglio
, Mol. Syst. Des. Eng.
3
, 243
(2018
).37.
M.
Souaille
and B.
Roux
, Comput. Phys. Commun.
135
, 40
(2001
).38.
M. R.
Shirts
and J. D.
Chodera
, J. Chem. Phys.
129
, 124105
(2008
).39.
Z.
Tan
, E.
Gallicchio
, M.
Lapelosa
, and R. M.
Levy
, J. Chem. Phys.
136
, 144102
(2012
).40.
P.
Tiwary
and M.
Parrinello
, J. Phys. Chem. B
119
, 736
(2015
).41.
M.
Bonomi
, A.
Barducci
, and M.
Parrinello
, J. Comput. Chem.
30
, 1615
(2009
).42.
M.
Bonomi
et al., Comput. Phys. Commun.
180
, 1961
(2009
).43.
D.
Frenkel
and B.
Smit
, Understanding Molecular Simulation
, 2nd ed. (Academic Press
, London
, 2002
).44.
C.
Michel
, A.
Laio
, and A.
Milet
, J. Chem. Theory Comput.
5
, 2193
(2009
).45.
P. G.
Bolhuis
, C.
Dellago
, and D.
Chandler
, Proc. Natl. Acad. Sci. U. S. A.
97
, 5877
(2000
).46.
P.
Tiwary
and M.
Parrinello
, Phys. Rev. Lett.
111
, 230602
(2013
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
