A new extension of QM/MM methods: the adaptive buffered-force QM/MM method

Transcription

1 A new extension of QM/MM methods: the adaptive buffered-force QM/MM method Letif Mones Engineering Department, University of Cambridge

2 Overview Basic concept of the QM/MM methods MM vs. QM parts Challenging issues in QM/MM methods adaptivity of QM region problems at the QM/MM interface force convergence General overview of QM/MM methods energy vs. force based methods Adaptive buffered force QM/MM method theory and purpose of abfqm/mm Application of abfqm/mm method structural results energetic results Implementation of abfqm/mm into program packages 2

3 Basic concept of QM/MM The Fathers of QM/MM For the development of multiscale models for complex chemical systems Published items of topic QM/MM source: webofknowledge.com Citations of topic QM/MM Martin Karplus Michael Levitt source: nobelprize.org Arieh Warshel source: webofknowledge.com 3

4 Basic concept of QM/MM Evolution of QM/MM 1976 mid 90s today A. Warshel and M. Levitt, J. Mol. Biol., 103, 227 (1976) Theory of the model conventional QM/MM adaptive methods Concept of validation comparison to experimental results comparison to full QM or QM/MM with large QM region 4

5 Basic concept of QM/MM Levels of description of all atom systems MM level QM level + computationally fast (no treatment of electrons) + relatively large systems (1000 to millions of atoms) + relatively long simulation times (microseconds) + good approx. when valence state is unchanged + folding, solvation, binding free energy + chemical accuracy (formation and cleavage of bonds) + electronic degrees of freedom are partly or completely taken into account + investigation of chemical reactions + good when no MM parameters are available or simple form of MM cannot be used chemical reactions cannot be investigated problems when parameters are not available simple form of potential cannot describe complex systems (e.g. transition metals) computationally very demanding relatively small systems relatively short simulation times 5

6 Basic concept of QM/MM QM/MM methods Aim: complicated systems (e.g. chemical reactions) larger systems (e.g. biochemical systems) longer timescales than what QM can perform Solution: let s combine MM (computational fastness) with QM (accuracy) In practice: chemically interesting part is treated quantum mechanically the rest of the system is described by lower level (MM) computation of interaction between QM and MM regions 6

7 Challenging issues in QM/MM Choosing the QM region parts where electronic degrees of freedom cannot be neglected should be QM computational cost type of QM region: fixed (QM region is permanent during dynamics) adaptive (QM region can be changed during dynamics) mobile environment - solvent exchange mobile active region - penetration, adhesion, crack propagation 7

8 Challenging issues in QM/MM Problems at the boundary Nonbonded interactions: interaction between the QM region and MM atoms level of description - mechanical embedding (MM level) - electrostatic embedding (QM/MM level) - polarized embedding (QM/MMpol level) criterion of quantum mechanical force convergence - strong locality - MM charges are far from the QM centre (large QM region) G. Csányi et. al, J. Phys. Condens. Matter, 17, R691 (2005) electron spill out effect - ignoring some matrix elements - ignoring potential terms from adjacent neutral MM groups - shifting adjacent MM charges away - rescaling MM charges close to QM - Gaussian distribution representation of point charges 8

9 Challenging issues in QM/MM Problems at the boundary Bonded interactions: cutting the bond between QM and MM atoms minimizing the number of broken bonds chemically sensible bond cutting treatment of bond cutting - link atoms - boundary atoms (pseudopotentials) - frozen localized orbitals (e.g. LSCF, GHO) how to take them into account? QM region selection at the active centre of Lysozyme - complete neglect - reference calculations QM MM 9

10 Overview of QM/MM methods Basic type of QM/MM methods 8 >< Energy based methods >: Force based methods E QM/MM (QM + MM) = f 8 >< >: 8 E QM (QM), E MM >< (MM), E QM$MM (QM + MM), E MM (QM),... >: 9 >= >; F QM/MM i (QM + MM) = f 8 >< >: F QM F MM i (QM 0 +MM 0 ), i (QM 00 +MM 00 ), r in,r out,r... 9 >= >; F QM/MM i (QM + MM) i total energy is a function of several terms forces are the derivatives of the total energy energy and momentum conservation boundary problem can be eliminated force convergence can be achieved adaptive QM region QM region is fixed boundary problems can appear force convergence problem at the boundary or even in the centre of QM region total energy function does not necessarily exist no energy/momentum conservation 10

11 Overview of QM/MM methods Energy based QM/MM methods >: 8 >< 9 >= 8 >< 9 >= >: >; Additive energy >: mixing >; Subtractive energy mixing E QM/MM (QM + MM) = EQM (QM) + E MM (MM) +E QM$MM (QM + MM) E QM/MM (QM + MM) = EMM (QM + MM) +E QM (QM) E MM (QM) + electrostatic coupling between QM and MM regions (QM/MM level) short-range boundary problems (spill out effect) long-range boundary problems + no convergence and boundary problem QM/MM interaction is treated on the MM level special (i.e. reactive) force fields may be required when QM region is significantly perturbed during the simulations Conventional QM/MM A. Warshel and M. Levitt, J. Mol. Biol., 103, 227 (1976) IMOMM F. Maseras and K. Morokuma, J. Comp. Chem., 16, 1170 (1995) IMOMO S. Humbel et al., J. Chem. Phys., 105, 1959 (1996) ONIOM M. Svensson et al., J. Phys. Chem., 100, (1996) 11

12 Overview of QM/MM methods Force based QM/MM methods >< >: >= >; Smooth force mixing 2 Abrupt force mixing F QM/MM i (QM + MM) = FQM i (QM 0 +MM 0 ) (1 )F MM i (QM 00 +MM 00 ) F QM/MM i (QM + MM) = F QM i (QM 0 +MM 0 ) if i 2 QM F MM i (QM 00 +MM 00 ) if i 2 MM 2 [0, 1] + + λ is a smooth function smooth transition + + QM - MM change is abrupt zero transition limit Hot spot T. Kerdcharoen et al., Chem. Phys., 211, 313 (1996) Adaptive QM/MM for solvents R. E. Bulo et al., J. Chem. Theory Comput., 5, 2212 (2009) LOTF G. Csányi et al., Phys. Rev. Lett., 93, (2004) Adaptive buffered force QM/MM N. Bernstein et al., Phys. Chem. Chem. Phys., 14, 646 (2012) 12

13 Overview of QM/MM methods >: The conventional QM/MM method 8 >< 8 Additive energy mixing QM/MM: >: >< 9 >= >; E QM/MM (QM + MM) = EQM (QM) + E MM (MM) +E >: QM$MM (QM + MM) F QM/MM i (QM + MM) i QM MM Problems: fixed QM region force convergence is not guaranteed ad hoc solutions to get reasonable results unreliable validation of the method cancellation of errors 13

14 abfqm/mm: Theory How to obtain accurate QM/MM forces? simple electrostatic embedding of a small QM region in the field of external MM charges does not yield correct QM forces (especially at the boundary) extend the active QM region by a buffer region to get converged and accurate QM forces in the active region Buffer QM rbuffer MM Force error of carboxyl atoms of key residue Glu in Lysozyme 14

15 abfqm/mm: Theory How to obtain accurate QM/MM forces? Keep forces of active QM region Extend QM region to get converged QM forces Buffered QM FQM active MM active QM conventional QM/MM calculations FMM FQM Reduce QM region to get converged MM forces Core QM FMM Keep forces of active MM region N. Bernstein et al., Phys. Chem. Chem. Phys., 14, 646 (2012) 15

16 abfqm/mm: Theory Adaptive buffered-force QM/MM active QM region is adaptive extended QM region (buffer) and reduced QM region (core) each MD step requires two calculations: 1. buffered QM/MM (with extended QM region) 2. reduced QM/MM (only core QM) or EVB or full MM abrupt force mixing scheme (no energy and momentum conservation) special thermostat is required ( massive adaptive Langevin, Nosé-Hoover chain-langevin) A. Jones and B. Leimkuhler, J. Chem. Phys., 135, (2011) hysteretic algorithm for the different regions N. Bernstein et al., Phys. Chem. Chem. Phys., 14, 646 (2012) rin buffer active QM rout 16

17 abfqm/mm: Applications Structural validation: pure water and solvated chloride ion pure water solvated chloride ion full QM full MM QM/MM Simulation details: Central water molecule QM water molecules MM water molecules QM: BLYP, GTH, DZVP MM: ftip3p 84 / 1222 water molecules 4-53 ps simulation length N. Bernstein et al., Phys. Chem. Chem. Phys., 14, 646 (2012) 17

18 abfqm/mm: Applications Energetic validation: a nucleophilic substitution reaction Cl (aq) + MeCl (aq) ClMe (aq) + Cl (aq) d2 d1 ξ = d1 - d2 Simulation details: QM: BLYP, GTH, DZVP MM: ftip3p, GAFF, EVB 46 / 1698 water molecules rqm = A, rbuffer = A Cs. Várnai, N. Bernstein, L. Mones and G. Csányi, J. Phys. Chem. B, 117, (2013) 18

19 abfqm/mm: Applications Energetic validation: calculation of pka pk a = F [H kt ln10 log 2 O] 10 c 0 pk a = log 10 K a K a = [A ][H+ ] [HA] d = ΔF abfqm/mm classical alchemy ΔF2 ΔF1 ΔF = ΔF1 + ΔF2 reaction coordinate 19

20 abfqm/mm: Applications Energetic validation: calculation of pka roh Simulation details: QM: BLYP, GTH, DZVP MM: ftip3p, Amber ff99sb 113 / 1214 water molecules rqm = A, rbuffer = A Cs. Várnai, N. Bernstein, L. Mones and G. Csányi, J. Phys. Chem. B, 117, (2013) 20

21 abfqm/mm: Applications Energetic validation: water autoprotolysis Zn 2+ OD OA DRCN = RCN(O D ) RCN(O A ) P RCN(O D/A )= P Hatoms i 1 ( r i r 0 ) 1 ( r i r 0 ) adqm/mm: rqm = A abfqm/mm: rqm = A, rbuffer = A Simulation details: QM: MNDO(d) MM: ftip3p, Amber ff99sb 87 / 3303 water molecules rqm = A, rbuffer = A 21

22 abfqm/mm: Applications Energetic validation: phosphodiester hydrolysis d1 RS TS or IS? d2 PS DD = d1 - d1 Simulation details: QM: BLYP, GTH, DZVP MM: ftip3p, Amber ff99sb 86 / 3903 water molecules rqm = A, rbuffer = A 22

23 abfqm/mm: Implementations Implementation of abfqm/mm Original version: QUIP libatoms.org Advanced implementations: Amber v. 13 / 14 ambermd.org CP2K manual.cp2k.org/trunk/ 23

24 abfqm/mm: Implementations New features in abfqm/mm hysteretic inner & outer radii for core / qm / bulk regions permanent core / qm / bulk atom list specifications temporary core / qm / bulk atom list specifications atom / group based selection open thermostats: massive adaptive Langevin, Nosé-Hoover chain-langevin breakable bond specification oxidation number specification to calculate the charge of the actual QM region abfqm/mm restart 24

25 Acknowledgement Gábor Csányi University of Cambridge, UK Noam Bernstein Naval Research Laboratory, USA Csilla Várnai University of Warwick, UK Ben Leimkuhler Andrew Jones University of Edinburgh, UK Ross Walker Andreas Götz San Diego Supercomputer Center, USA Teodoro Laino Zurich Research Laboratory, Switzerland 25