Low-temperature isomers of the water hexamer

Transcription

1 Low-temperature isomers of the water hexamer Volodymyr Babin and Francesco Paesani Department of Chemistry & Biochemistry, University of California, San Diego, La Jolla, CA

2 Hundreds of years Thousands of pages XSEDE13 San Diego CA July 25, / 25

3 Unanswered Questions Does supercooled water has two phases and a second critical point? Does normal liquid water consists of smaller clusters of two different states of water? XSEDE13 San Diego CA July 25, / 25

4 Liquid Water XSEDE13 San Diego CA July 25, / 25

5 Hydrogen Bond Network XSEDE13 San Diego CA July 25, / 25

6 J.A. MORRONE, V. SRINIVASAN, D. SEBASTIANI, AND R. CAR, Proton momentum distribution in water: an open path integral molecular dynamics study, J. Chem. Phys. 126, (2007), pp XSEDE13 San Diego CA July 25, / 25

7 T.E. MARKLAND, AND B.J. BERNE, Unraveling quantum mechanical effects in water using isotopic fractionation, PNAS 109, (2012), pp α l v = (x D,l/x H,l ) x D,v /x H,v ) XSEDE13 San Diego CA July 25, / 25

8 Trimer/Tetramer/Pentamer Nearly planar XSEDE13 San Diego CA July 25, / 25

9 Hexamers XSEDE13 San Diego CA July 25, / 25

10 XSEDE13 San Diego CA July 25, / 25

11 Born-Oppenheimer approximation: 1) Electronic ground state for clamped nuclei. [CCSD(T) is very demanding: memory O(N 4 atom), time O(N 8 atom)] 2) QM treatment of the nuclei. [not necessarily cheap either] XSEDE13 San Diego CA July 25, / 25

12 5 E E prism (kcal/mol) HBB2-pol WHBB-6 WHBB TTM3-F q-tip4p/f MP2/aug-cc-pVTZ CCSD(T)-F12(b)/VDZ-F Ecage E prism = 0.25 kcal/mol [CCSD(T)/CBS by Tschumper et al] Isomer index XSEDE13 San Diego CA July 25, / 25

13 q-tip4p/f Model Potentials S. HABERSHON, T.E. MARKLAND, AND D.E. MANOLOPOU- LOS, Competing quantum effects in the dynamics of a flexible water model, J. Chem. Phys. 131, (2009), pp TTM3-F G.S. FANOURGAKIS AND S.S. XANTHEAS, Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water, J. Chem. Phys. 128, (2008), pp WHBB Y. WANG, X. HUANG, B.C. SHEPLER, B.J. BRAAMS, AND J.M. BOWMAN, Flexible, ab initio potential, and dipole moment surfaces for water. I. Tests and applications for clusters up to the 22-mer, J. Chem. Phys. 134, (2011), pp HBB2-pol G. R. MEDDERS, V. BABIN, AND F. PAESANI, A Critical Assessment of Two-Body and Three-Body Interactions in Water, JCTC 9(2), (2013), pp XSEDE13 San Diego CA July 25, / 25

14 q-tip4p/f Very crude intra-molecular terms. Geometry-independent point charges. No polarization. E N = E a + E ab a a<b XSEDE13 San Diego CA July 25, / 25

15 TTM3-F Ab initio intra-molecular sector. Ab initio geometry-dependent charges. Polarizable site. E N E a + E ab a a<b XSEDE13 San Diego CA July 25, / 25

16 WHBB & HBB2-pol E N = V 1 (x a ) a + a<b V 2 (x a,x b ) + a<b<c +V ind (x 1,...,x N ) V 3 (x a,x b,x c ) Ab initio intra-molecular sector. Ab initio 2-/3-body terms. Polarizable site(s). XSEDE13 San Diego CA July 25, / 25

17 Partition Function Z = trexp( βh ) = = lim dq 1...dq P exp( βe P ) P tre βh = tre β(k +V ) = lim tr [e βk /P e βv /P] P } P {{} Trotter q 1 e βk /P e βv /P q 2 exp [ βmωp(q 2 1 q 2 ) 2 /2 βv (q 2 )/P ], ωp 2 = P E P = 1 P P V (q a ) + mω2 P a=1 2 P a=1 (q a+1 q a ) 2 h 2 β 2 XSEDE13 San Diego CA July 25, / 25

18 Path Integral Molecular Dynamics Linear transformation to normal modes. J. CAO AND B.J. BERNE, A Born Oppenheimer approximation for path integrals with an application to electron solvation in polarizable fluids, J. Chem. Phys. 99, (1993), pp Fictitious momenta conjugate to these new variables. Nose-Hoover chains at every degree of freedom. M.E. TUCKERMAN, B.J. BERNE, G.J. MARTYNA, AND M.L. KLEIN, Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals, J. Chem. Phys. 99, (1993), pp XSEDE13 San Diego CA July 25, / 25

19 Replica Exchange Two chains sampling different (but related) densities π 1 (x) and π 2 (x) can be joined into a chain that samples q = (x,y) π(q) = π 1 (x)π 2 (y). The q = (x,y) q = (y,x) move with Metropolis acceptance probability { } { min 1, π(q ) = min 1, π } 1(y)π 2 (x) π(q ) π 1 (x)π 2 (y) preserves π(q) = π 1 (x)π 2 (y). XSEDE13 San Diego CA July 25, / 25

20 Performance on Gordon 1e+05 Wall Time [s] RE-PIMD (32 beads/32 replicas) PIMD (256 beads, 30K) # processors XSEDE13 San Diego CA July 25, / 25

21 Results (TTM3-F) TTM3-F (classical) 0.8 TTM3-F (PIMD, 32 beads) fraction prism cage fraction prism cage T (K) T (K) Nuclear quantum effects favor cage over prism. XSEDE13 San Diego CA July 25, / 25

22 Prism XSEDE13? San Diego CA? July 25, 2013 Cage 21 / 25

23 q-tip4p/f TTM3-F WHBB HBB2-pol 1 Fraction Fraction Fraction Classical Quantum (D2O) Quantum (H2O) Temperature (K) Temperature (K) Temperature (K) Temperature (K) Prism (1) Cage (2) Book (3,4,5) Prism-Book (6) Other (7 13) XSEDE13 San Diego CA July 25, / 25

24 Free Energies F Cage F Prism = k B T ln #Cage #Prism F Cage F Prism E + k B T n Cage /k B T ln 1 e hω n 1 e hωprism n /k B T XSEDE13 San Diego CA July 25, / 25

25 Free Energies 0.2 TTM3-F WHBB HBB2-pol F Cage F Prism (kcal/mol) D2O H2O Temperature (K) Temperature (K) Temperature (K) XSEDE13 San Diego CA July 25, / 25

26 Summary There is several nearly iso-energetic non-planar isomers of water hexamer. Their thermal equilibrium is due a subtle balance between energetic, entropic, and nuclear quantum effects. The relative stability of the prism isomer increases upon substitution of H 2 O with D 2 O. CAICE XSEDE13 San Diego CA July 25, / 25