QM/MM Theory and Examples with ORCA

Transcription

1 QM/MM Theory and Examples with ORCA Marius Retegan Max Planck Institute for Chemical Energy Conversion Stiftstr Mülheim an der Ruhr

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3 QM/MM: an historical overview 1976: Warshell and Levitt Theoretical Studies of Enzymic Reactions : Dielectric, Electrostatic and Steric Stabilization of the Carbonium Ion in the Reaction of Lysozyme A. WAECZIEL AND M. LEVITT Medical Research Council Laboratory of Molecular Biology Hills Road, Cambridge CB.2 2&H, EnglundJ and Department of Chemical Physics The Weizmunn Institute of Science Rehovot, Israel (Received 12 September 1975, and in revised form 10 February 1976) F. 1990: Field, Bash, Karplus A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations Martin J. Field, Paul A. Bash, and Martin Karplus Department of Chemistry, 12 Oxford Street, Harvard University, Cambridge, Massachusetts Received 30 June 1989; accepted 14 November 1989 (b) b IQ

4 Partitioning of the system S (QM/MM) O (MM) I (QM) S entire system; O outer region; I inner region The boundary region (yellow) can be seen as the region were the QM and MM procedures are modified or augmented in any way. The QM-MM partitioning is considered fixed, i.e. QM and MM remain the same during the calculation. The MM and QM region interact, the total energy is not equal to the sum of the energies of the subsystem.

5 Evaluating the energy of the system Additive QM/MM coupling Subtractive QM/MM coupling the last term describes the QM-MM coupling the MM calculation is performed only on the outer layer implementation is somewhat involved MM calculation in which a certain region has been cut out and replaced by a QM treatment it is easy to implement parameters are required for the inner region the QM-MM coupling is treated at the MM level

6 Molecular mechanics (MM) energy A force field refers to the form and parameters of the mathematical functions used to evaluate the energy. AMBER (Assisted Model Building and Energy Refinement) CHARMM (Chemistry at HARvard Molecular Mechanics) OPLS (Optimized Potential for Liquid Simulations) GROMOS (GROningen MOlecular Simulation) UFF (Universal Force Field)

7 Bonded interactions I Bonds Angles i j i θ0 k r0 j fourth order Morse cosine based Urey-Bradley

8 Bonded interactions II Proper dihedrals ɸ is defined as the angle between the ijk and jkl, planes with zero corresponding to the cis conformation ɸ0 l Improper dihedrals (out-of-plane) used to keep aromatic groups planar l j k i i j k Ryckaert-Bellemans

9 Non-bonded interactions van der Waals interaction Electrostatic interaction AMBER (Lorentz-Berthelot) OPLS (geometric) The Coulomb energy falls slower than the Lennard-Jones energy

10 QM-MM interaction The crucial part of the QM/MM method lies in how the QM-MM interaction is described. The bonding and van der Waals interactions are handled at the classical level. Bonding terms appear only when the boundary cuts through bonds van der Waals terms Lennard-Jones parameters have to be assigned to the QM atoms the force field might not cover them; even if they exist for a given configuration, should you change them if you consider a reaction? Electrostatic terms can be treated using different embeddings: mechanical electrostatic polarized

11 Mechanical embedding In the mechanical embedding the QM-MM interaction is treated on the same footing as the MM-MM interactions Advantages there is no interaction between the link atoms and point charges; QM-MM interaction can be integrated directly into the force field; QM energies, gradient and Hessian are at the same cost as in gas phase. Disadvantages QM/MM electrostatic coupling requires atomic charges for the QM atoms; QM region is not polarized.

12 Electrostatic embedding The major shortcomings of the mechanical embedding scheme can be eliminated by performing the QM calculation in the presence of the MM charge model. Assign charges for the MM system derived from empirical schemes; fitted to electrostatic potential; electronegativity equalisation (e.g. QEq). Ensure that QM and MM regions have an integer total charge Insert charges into QM Hamiltonian explicit point charges; smeared point charges; semi-empirical core interaction terms;

13 Electrostatic embedding Advantages capable of treating changes in the QM density; important for solvation energies etc there is no need for a charge model of QM region. can readily model reactions that involve charge separation Disadvantages spurious interactions at the boundary; QM evaluation is needed to obtain accurate MM forces; QM energy, gradient, Hessian are more costly than gas phase QM.

14 Polarizable embedding Polarize once the point charges in the MM region are polarized by the QM electric field but the polarized charges don't act back on the QM region Self-consistent formulation allow for mutual polarization and iterate until convergence Requirements a force field that allows for polarization charge-on-spring, AMOEBA, SIBFA significantly more computing time The very first application of QM/MM method used polarized embedding

15 Boundaries across covalent bonds Proteins are linear polymers, therefore bonds will be cut link atom or cap atom hydrogen atom parametrized atom connection atom pseudo-halogen localized orbitals local self consistent field generalized hybrid orbital Q2 Q1 M1 M2 Q2 Q1 M1 M2 Q2 Q1 M1 M2 L link atom LSCF GHO simple and intuitive easy to implement close point charges provide a more fundamental way of describing the boundary more complicated to implement

16 Link atoms Overpolarization of the QM density by the close point charges deletion of one-electron integrals associated with link atoms deletion of point charges close to the QM region smearing the charges redistribute the charges in the link region Q2 Q1 M1 M2 Q2 Q1 M1 M2 L GHO redistributed charge

17 Link atoms: more details The position is defined as a function of the position of Q1 and M1. Forces acting on the link atom are relayed onto the atoms that define the link atom. M1 M3 M2 The link atom does not have MM parameters. Some bonded terms have to be deleted to avoid double counting, e.g. Q1-M1, Q2-Q1-M1, Q3-Q2-Q1-M1 Q1 Q2 Q3 L

18 Reviews related to QM/MM methods Reviews H. M. Senn and W. Thiel DOI: /anie Theoretical Chemistry QM/MM Methods for Biomolecular Systems Hans Martin Senn* and Walter Thiel* Advances in Quantum and Molecular Mechanical (QM/MM) Simulations for Organic and Enzymatic Reactions Keywords: enzyme catalysis molecular simulations QM/MM calculations theoretical chemistry ORLANDO ACEVEDO*, AND WILLIAM L. JORGENSEN*, Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut RECEIVED ON JUNE 12, 2009 CON SPECTUS Acevedo, Jorgensen Acc. Chem. Res., 2009, 1, 142. pplication of combined quantum and molecular mechanical (QM/ A Angewandte Chemie Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Angew. Chem. Int. Ed. 2009, 48, Senn, Thiel Angew. Chem. Int. Ed., 2009, 48, MM) methods focuses on predicting activation barriers and the structures of stationary points for organic and enzymatic reactions. Characterization of the factors that stabilize transition structures in solution and in enzyme active sites provides a basis for design and optimization of catalysts. Continued technological advances allowed for expansion from prototypical cases to mechanistic studies featuring detailed enzyme and condensed-phase environments with full integration of the QM calcucurrent Topic lations and configurational sampling. This required improved algorithms featuring fast QM methods, advances in computing changes in free enerpubs.acs.org/biochemistry gies including free-energy perturbation (FEP) calculations, and enhanced configurational sampling. In particular, the present Account highlights development of the PDDG/PM3 semi-empirical QM method, computation Combined Quantum Mechanics/Molecular Mechanics (QM/MM) of multi-dimensional potentials of mean force (PMF), incorporation of onmethods Computational Enzymology the-fly QM in Montein Carlo (MC) simulations, and a polynomial quadrature method for efficient modeling of proton-transfer Marc reactions. W. van der Kamp* and Adrian J. Mulholland* The utility of this QM/MM/MC/FEP methodology is illustrated for a variety of organic reactions including substitution, Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K. decarboxylation, elimination, and pericyclic reactions. A comparison to experimental kinetic results on medium effects has verified the accuracy of the QM/MM approach in the full range of solvents from hydrocarbons to water to ionic liquids. CorABSTRACT: Computational enzymology is a rapidlytheory maturing that iswith continuum-based treatments of solvaresponding results from ab initio and density functional (DFT)field methods increasingly integral to understanding mechanisms of enzyme-catalyzed reactions tion reveal deficiencies, particularly for protic solvents. Also summarized in this Account are three specific QM/MM applications and their practical applications. Combined quantum mechanics/molecular to biomolecular (1) methods a recent study that clarified thefield. mechanism for the mechanics systems: (QM/MM) are important in this By treating thereaction of 2-pyrone derivatives catalyzed reacting speciessynthase with a quantum mechanical method (i.e., a methodrather that calculates by macrophomate as a tandem Michael-aldol sequence than a Diels-Alder reaction, (2) elucidation of the van der Kamp, Mulholland Biochemistry, 2013, 52, the electronic structure of the active site) and including the enzyme environment

19 Programs that can be interfaced with ORCA GROMACS (gromacs.org) pdynamo (pdynamo.org) ChemShell (chemshell.org) GAUSSIAN TURBOMOLE GAMESS-UK MOLPRO MNDO04 MOPAC QM codes ChemShell Tcl scripts Integrated routines: data management geometry optimization molecular dynamics generic force fields QM/MM coupling CHARMMxx academic CHARMmxx Accelrys GROMOS96 DL_POLY GULP MM codes

20 pdynamo a library of functions energy calculations; geometry optimizations; transition state searches; reaction path calculations; molecular dynamics simulations; Monte Carlo simulations. support for AMBER, CHARMM and OPLS; semi-empirical QM methods; a density functional theory QM method; coupling to ORCA. How we use QM/MM additive scheme; hydrogen link atom; redistributed charges scheme; QM-MM electrostatic interaction are treated using the electrostatic embedding.

21 ORCA/pDynamo: workflow QM level of theory MM force field parameters coordinates partitioning of the system Start Create the QM input EQM and EQM-MM elec EMM EQM-MM bonded and vdw Stop pdynamo ORCA

22 ORCA/pDynamo: in practice A designed protein consisting of only ten amino acids (chignolin) MM QM QM: BP86 def2-svp MM: OPLS, only amino acids

23 ORCA/pDynamo: in practice pdynamo generated input file (chignolin.inp) bp86 def2- svp engrad % pointcharges "chignolin.pc" * xyz H C C O O H H *

24 ORCA/pDynamo: in practice Point charges file (chignolin.pc)

25 ORCA/pDynamo: in practice ORCA generated engrad file (chignolin.engrad) # Number of atoms 7 # The current total energy in Eh # The current gradient in Eh/bohr # The atomic numbers and current coordinates in Bohr

26 Azurin as a protein scaffold for transition metals Gly45 His46 His117 Cu Cys112 Does iron bind to the copper site? Met121 His46, His117 and Cys112 are arranged in a roughly trigonal-planar geometry The oxygen atom of Gly45 and the sulfur of Met121 are more distant

27 QM/MM simulation protocol classical MM simulations (pdynamo) build hydrogens vacuum refinement of the added atoms solvate & neutralize the system molecular dynamics (200 ps of NVT with constrained QM region) hybrid QM/MM simulations (ORCA/pDynamo) geometry optimizations spectroscopic properties McLaughlin, Retegan et al. J. Am. Chem. Soc, 2012, 134,

28 Zero field splitting (ZFS) VTVH Mössbauer Experiment magnetic Mössbauer 4.2 and 80 K fitting of the spectra using the spin Hamiltonian gives D = 15.1 cm 1 Theory QM/MM mechanical D = 17.1 cm 1 QM/MM electrostatic D = 14.8 cm 1 ZFS is sensitive to electrostatic effects inside the active site cavity.

29 Demo