Paul Sherwood CLRC Daresbury Lab.

Paul Sherwood CLRC Daresbury Lab. P.sherwood@dl.ac.uk
QM/MM Modelling Paul Sherwood CLRC Daresbury Lab.

Plan for the course Tuesday p.m Wednesday a.m. Wednesday p.m.
Lecture 1 Lecture 2 Wednesday a.m. Lecture 3 Wednesday p.m. Practical Session

QM/MM Modelling Lecture 1 Concepts and Theory

Overview Rationale Notation Historical overview Energy expression
inner, outer boundary, link etc Historical overview Energy expression Additive vs Subtractive QM/MM Coupling Mechanical, electrostatic, polarised Link Atom treatments Choice of QM and MM models Conformational complexity Geometry optimisation algorithms

The QM/MM Modelling Approach
Couple quantum mechanics and molecular mechanics approaches QM treatment of the active site reacting centre excited state processes (e.g. spectroscopy) problem structures (e.g. complex transition metal centre) Classical MM treatment of environment enzyme structure zeolite framework explicit solvent molecules bulky organometallic ligands

Terminology Usually we can view QM/MM calculations as a combination of
a QM calculation on a small region of the system A surrounding environment modelled by a MM calculation Optionally, some treatment, e.g. dielectric response of the region outside the outer region is included.

Termination of the QM region
Boundary region approaches Boundary atoms are present in both QM and MM calculations Range of representations within QM code Modified ab-initio atom with model potential Semi-empirical parameterisation Frozen orbitals Re-parameterised MM potentials Link atom schemes Terminating (link) atoms are invisible to MM calculations Hydrogen, pseudo-halogen, etc.

QM/MM - One idea, Many schemes!
QM/MM Couplings Unpolarised QM polarisation choice of charges? MM polarisation shell model dipole polarisabilities O2 I2 O1 L I1 O2 I2 Termination Atoms Chemical type hydrogen atoms,… MM Charge perturbations charge deletion, charge shift, double link atoms… Constraints Total Energy Expression “Additive” E(O,MM) + E(IL,QM) Link atom corrected E(O,MM) + E(IL,QM) - E(L,MM) “Subtractive” E(OI,MM) + E(IL,QM) - E(IL,MM)

Historical Overview 1976 Warshel, Levitt MM+Semi-empirical
study of Lysozyme 1986 Kollmann, Singh QUEST ab-initio (Gaussian-80/UCSF) + AMBER 1990 Field, Bash, Karplus CHARMM/AM1 full semi-empirical dynamics implementation 1992 Bernardi, Olivucci, Robb MMVB simulation on MC-SCF results using VB 1995 van Duijnen, de Vries HONDO/DRF direct reaction field model of polarisation 1995 Morokuma IMOMM mechanical embedding with “hidden variable” optimisation 1996 Bakowies and Thiel MNDO/MM mechanical, electrostatic and polarised semi-empirical models Eichler, Kölmel, and Sauer QM/Pot subtractive coupling of GULP/TURBOMOLE

Additive Energy Expressions
Without link atom correction E(O,MM) + E(I,QM) + E(IO,QM/MM) Link atom correction E(O,MM) + E(IL,QM) + E(IO,QM/MM) - E(L,MM) Boundary methods E(OB,MM) + E(IB,QM) + E(IBO,QM/MM) Highly variable in implementation QM/MM couplings, QM termination etc Advantages No requirement for forcefield for reacting centre Can naturally build in electrostatic polarisation of QM region - effects of environment of excitations etc Disadvantages Electrostatic coupling of the two regions, E(IO,QM/MM) is problematic with link atoms Need for boundary atom parameterisation Applications Solvation Enzymes Zeolites

Subtractive QM/MM Coupling
Energy Expression E(OI,MM) + E(IL,QM) - E(IL,MM) includes link atom correction can treat polarisation of both the MM and QM regions at the force-field level Termination Any (provided a force field model for IL is available) Advantages Potentially highly accurate and free from artefacts Can also be used for QM/QM schemes (e.g. IMOMO, Morokuma et al) Disadvantages Need for accurate forcefields (mismatch of QM and MM models can generate catastrophes on potential energy surface) No electrostatic influence on QM wavefunction included Applications Zeolites (Sauer et al) Organometallics (Morokuma et al)

Choice of QM Model Applicability Attributes
Most QM methods are suitable semi-empirical Empirical valence bond (Warshel, MOLARIS) MM-VB (Robb, fitted to CASSCF) ab-initio DFT Gaussian basis Plane wave (CP) - Zeigler, Parrinello, Rothlisburger Attributes For electrostatic embedding need to insert extra nuclei in Hamiltonian Cost implications, eg derivatives, Hessians

Choice of MM model Choice of parameterisation based on chemical applications Current implementations based on Macromolecular force fields CHARMM, Quest (AMBER) MM2/MM3 MNDO/MM, IMOMM Commercial generation eg CFF (Discover) Electronegativity equalisation Shell Model

Valence Force Fields (i)
Used for covalently bound molecules and networks Terms associated with bonded groups bonds e.g. harmonic, quartic angles dihedral (torsion) angles sin,cos (rotational barriers) harmonic (e..g planarity constraints) sometimes other cross-terms bond-bond coupling bond-angle coupling

Valence forcefields (ii)
Non-bonded terms Summed over all non-covalently-bound pairs always exclude bonded pairs exclude 1,3 interactions for angles sometimes scale 1,4 interactions for dihedrals van der Waals Buckingham, Lennard-Jones electrostatics simple coulomb (qiqj/r) Need to decide the atomic charges … distance-dependent dielectric Approximate correction for solvation Examples MM2, AMBER, CHARMM, UFF, CFF, CVFF

Shell Model Force fields
Typically used for ionic solids Leading terms are non-bonded Electrostatics often based on formal charges polarisability of ions included by splitting total ion charge in Core (often +ve) and Shell (-ve), modelling the valence electrons Shell can shift in response to electrostatic forces, restoring forces from harmonic “spring” van der Waals sometimes compute using shell position Can also incorporate 3-body terms some bond angles are preferred over others, introducing some covalent character Core position Shell position

Choice of MM Model Practical considerations Future prospects
for link atoms schemes must be able to remove selected forcefield terms from topology need vdW parameters for interaction with QM (always) QM charges and/or forcefield terms (sometimes) numerical noise (e.g. cutoffs) important for transition states etc. Future prospects DMA, polarisabilities

QM/MM Non-bonded Interactions
Short-range forces (van der Waals) Typically will follow MM conventions (pair potentials etc), sometimes reparameterisation is performed to reflect replacement of point charges interactions with QM/MM electrostatic terms. Electrostatic interactions: Mechanical Embedding in vacuo QM calculation coupled classically to MM via point charges at QM nuclear sites Electrostatic Embedding MM atoms appear as centres generating electrostatic contribution to QM Hamiltonian Polarised Embedding MM polarisability is coupled to QM charge density

Mechanical Embedding Advantages Drawbacks Examples
MM and QM energies are separable separate MM relaxation, annealing etc possible QM/MM terms can be integrated directly into the forcefield No interactions between link atoms and MM centres QM energies, gradient, Hessian are the same cost as gas phase Drawbacks No model for polarisation of QM region QM/MM electrostatic coupling requires atomic charges for QM atoms generally these will be dependent on reaction coordinate Examples IMOMM (Morokuma) MNDO/MM (Bakowies and Thiel)

Electrostatic Embedding
(i) Assign MM Charges for pure MM system Derived from empirical schemes (e.g. as part of forcefield) Fitted to electrostatic potentials Formal charges (e.g. shell model potentials) Electronegativity equalisation (e.g. QEq) (ii) Delete MM charges on atoms in inner region Attempt to ensure that MM “defect” + terminated QM region has correct total charge approximately correct dipole moment (iii) Insert charges on MM centres into QM Hamiltonian Explicit point charges Smeared point charges Semi-empirical core interaction terms Make adjustments to closest charges (deletion, shift etc)

Creation of neutral embedding site (i) Neutral charge groups
Deletion according to force-field neutral charge-group definitions

Creation of neutral embedding site (i) Neutral charge groups
Total charge conserved, poor dipole moments

Creation of neutral embedding site (ii) Polar forcefields
O-x O-x Si+2x O-x O-x bond dipole models, e.g. for zeolites (Si +0.5x, O -0.5x)

Creation of neutral embedding site (ii) Polar forcefields
O-0.5x H O-0.5x H Si H O-0.5x H O-0.5x

Creation of neutral embedding site (iii) Double link atoms
H C C N N C C H R O Suggestion from Brooks (NIH) for general deletion (not on a force-field neutral charge-group boundary)

Creation of neutral embedding site (iii) Double link atoms
H C H C H C N H H N C R H O All fragments are common chemical entities, automatic charge assignment is possible.

Boundary adjustments Q2 M2 M1 L Q1 M2 Q2 M3 Q3
Some of the classical centres will lie close to link atom (L) Artefacts can result if charge at the M1 centre is included in Hamiltonian, many adjustment schemes have been suggested Adjustments to polarising field can be made independently from specification of MM…MM interactions Similar adjustments may are needed if M1 is classified as a boundary atom, depending on M1 treatment. Q2 M2 M1 L Q1 M2 Q2 M3 Q3

Boundary Adjustments (i) Selective deletion of 1e integrals
L1: Delete integrals for which basis functions i or j are sited on the link atom L found to be effective for semi-empirical wavefunctions difference in potential acting on nearby basis functions causes unphysical polarisation for ab-initio QM models L3: Delete integrals for which basis functions i and j are cited on the link atom and qA is the neighbouring MM atom (M1) less consistent results observed in practice † † Classification from Antes and Thiel, in Combined Quantum Mechanical and Molecular Mechanical Methods, J. Gao and M. Thompson, eds. ACS Symp. Ser., Washington DC, 1998.

Boundary Adjustments (ii) Deletion of first neutral charge group
L2 - Exclude charges on all atoms in the neutral group containing M1 Maintains correct MM charge leading error is the missing dipole moment of the first charge group Generally reliable free from artefacts arising from close contacts Limitations only applicable in neutral group case (e.g. AMBER, CHARMM) neutral groups are highly forcefield dependent problematic if a charge group needs to be split Application biomolecular systems

Creation of neutral embedding site Double Link Atoms
Conventional QM/MM schemes Break into H3C and CH3 Neutral fragments (in this simple case) Non-zero individual dipoles Replace QM CH3 with some form of terminated group (L-CH3) Finite total dipole moment Often further adjustment to MM charges is required (may create additional charge and dipole errors). Double link atom Dipole generally well approximated by superposition of bonds C H H H H C H C H H H H H H C H H C H H H MM QM

Boundary adjustments (iv) Gaussian Blur
Delocalise point charge using Gaussian shape function Large Gaussian width : electrostatic coupling disappears Narrow Gaussian width : recover point charge behaviour Intermediate values short range interactions are attenuated long range electrostatics are preserved Importance of balance - apply to entire MM system or to first neutral group Particularly valuable for double-link atom scheme where MM link atom charge lies within QM molecular envelope

Gaussian Blur: QM/MM Ethane
C H H C H H H MM QM Aggregate dipole moment, with MM atoms broadened Large Gaussian width dipole converges to that of the QM methane ( 0 ) Small Gaussian width point charges polarise the QM region, away from the C-H bond Compare with dipole of MM methyl group (0.18)

Boundary adjustments (iii) Charge shift
Delete charge on M1 Add an equal fraction of q(M1) to all atoms M2 Add correcting dipole to M2 sites (implemented as a pair of charges) charge and dipole of classical system preserved Leading sources of residual error is that Q---L dipole moment is not equivalent to Q------M Q2 M2 M1 L Q1 M2 Q2 M3 Q3

QM/MM coupling - Proton Affinity Tests
Simplified alcohol test set based on [1] AMBER charge model QM region is small (HOCH3 in all cases) Include systems with 1, 2 and 3 link atoms, Ethanol, i-Propanol, t-Butanol Fixed geometries (from 3-21G QM optimisations) Compare Pure QM L2 (delete first charge group) Shift (move charge from first atom to neighbours, add dipole. Double link atom + Gaussian Blur H CH3 O C H H H CH3 O C CH3 H H CH3 O C CH3 CH3 [1] I. Antes and W. Thiel, in “Hybrid Quantum Mechanical and Molecular Mechanical Methods” J. Gao (ed.) ACS Symp.Ser. 712, ACS, Washington, DC, 1998.

Computed Proton Affinities

Electrostatic Embedding Summary
Advantages Capable of treating changes in charge density of QM important for solvation energies etc No need for a charge model of QM region can readily model reactions that involve charge separation Drawbacks Charges must provide a reliable model of electrostatics reparameterisation may be needed for some forcefields Danger of spurious interactions between link atoms and charges QM evaluation needed to obtain accurate MM forces QM energy, gradient, Hessian are more costly than gas phase QM

Polarised embedding schemes
Incorporate polarisation of classical region most appropriate used when the forcefield itself is based on explicit polarisability back-coupling of polarised charge density to QM calculation can sometimes be omitted Approaches Iterative solution of dipole polarisabilities Direct Reaction Field Hamiltonian (van Duijnen, de Vries) solution of coupled polarisabilities using relay matrix possibility of including 2-electron dispersion terms implemented in HONDO and GAMESS-UK Shell model-based schemes atomic charge is split into core and valence electron shell, connected by a harmonic spring QUASI solid-state embedding scheme

Solid-state Embedding Scheme
Classical cluster termination Base model on finite MM cluster QM region sees fitted correction charges at outer boundary QM region termination Ionic pseudopotentials (e.g. Zn2+, O2-) associated with atoms in the boundary region Forcefield Shell model polarisation Classical estimate of long-range dielectric effects (Mott/Littleton) Energy Expression Uncorrected MM QM Advantages suitable for ionic materials Disadvantages require specialised pseudopotentials Applications metal oxide surfaces

Implementation of solid-state embedding
Under development by Royal Institution and Daresbury Based on shell model code GULP, from Julian Gale (Imperial College) Both shell and core positions appear as point charges in QM code (GAMESS-UK) Self-consistent coupling of shell relaxation Import electrostatic forces on shells from GAMESS-UK relax shell positions GAMESS-UK SCF & shell forces GULP shell relaxation GAMESS-UK atomic forces GULP forces

Polarised Embedding Schemes Summary
Advantages more accurate treatment of solvation effects allows coupling to systems where the best forcefields are based on polarisation (e.g. shell model potentials for metal oxide systems) Drawbacks Additional cost solution of coupled polarisabilities some schemes will require additional SCF iterations requirement for polarised force-field danger of electrostatic instabilities close to boundaries difficult to apply reliably when using link atoms

QM Termination Schemes
Link atom schemes Hydrogen atoms Adjusted electronegativity Hamiltonian shift operator pseudohalogen (Hyperchem) Methyl groups (Cummins, Gready) Boundary schemes Frozen Orbitals Local SCF scheme (Rivail) Generalised hybrid orbital (Gao) ab-initio implementation (Friesner) Pseudopotentials Gaussian basis (Yang), Plane-wave (Rothlisberger) Adjusted connection atoms (Thiel) semi-empirical mimic for attached methyl group

Adjusted Connection Atoms
Semi-empirical parameterisation of boundary atom Implemented in the MNDO package (Thiel el a) No link atoms needed, boundary atom sited at MM centre Typically boundary atom is C, parameterised to mimic CH3

Localised Orbital Approaches (i)
LSCF (Rivail et al) Semi-empirical Single orbital on QM boundary atom (pointing outwards) is frozen, based on calculation on a fragment (case-by-case set up) GHO (Generalised Hybrid Orbital, Gao et al. Semi-empirical (being extended to ab-initio) Single orbital (sp3 hybrid) on MM boundary centre (pointing inwards) Remaining 3 hybrid (“auxiliary orbitals”) are populated with fixed density matrix elements to produce correct MM charge Semi-empirical parameters of the MM centre are adjusted based on model compounds (expected to be transferable)

Localised orbital Approaches (ii)
QSite implementation (Friesner et al) Ab-initio implementation, in Jaguar package Based on calculations on model fragments, using a particular basis set Local orbitals include contribution from connected atoms (not just the QM and MM centres Adjustment of MM parameters performed on a case-by-case basis, currently being used for protein system

Positioning of link atoms
Initial placement Usually on terminated bond Unconstrained Additional degrees of freedom present in geometry optimisation and MD e.g. CHARMM, QUEST Constrained Need to take into account forces on link atoms, shared internal coordinate definitions (IMOMM) chain-rule differentiation (QM/Pot, ChemShell)

Deletion of MM terms Q2 M2 M1 L Q1 M2 Q2 M3 Q3
General rule: Keep all MM terms involving one or more M atoms When using link atoms constrained to bond direction, delete (or adjust) to avoid double counting angle Q2-Q1-M1 (duplicates Q2-Q1-L) torsion Q3-Q2-Q1-M1 When L is free to optimise sometimes additional restraint terms (e.g. Q2-Q1-L) are added to ensure stability. Q2 M2 M1 L Q1 M2 Q2 M3 Q3

Conformational Complexity
The Problem! QM/MM schemes combine the cost of QM the computational complexity of large MM systems Special treatments are needed for flexible molecules For mechanical embedding, hidden variables can reduce number of coordinates by exploring QM PES in presence of adiabatically relaxed MM environment (eg IMOMM) For electrostatic embedding, a charge fit to the QM charge density can be used to accelerate MM relaxation around a frozen QM core A.J. Turner et al, PCCP 1, p1323, 1999 Zhang et al, J. Chem. Phys., 112, p3483, 2000 Molecular dynamics and free energy techniques will be increasingly important computationally demanding for ab-initio QM, requirement for HPC implementations

QM/MM Geometry Optimisation
Small Molecules Internal coordinates (delocalised, redundant etc) Full Hessian O(N3) cost per step BFGS, P-RFO Macromolecules Cartesian coordinates Partial Hessian (e.g. diagonal) O(N) cost per step Conjugate gradient L-BFGS Coupled QM/MM schemes Combine cartesian and internal coordinates Reduce cost of manipulating B, G matrices Define subspace (core region) and relax environment at each step reduce size of Hessian exploit greater stability of minimisation vs. TS algorithms Use approximate scheme for environmental relaxation

HDLCopt optimiser (I) hdlcopt Key elements:
Hybrid Delocalised Internal Coordinate scheme (Alex Turner, Walter Thiel, Salomon Billeter) Developed within QUASI project O(N) overall scaling per step Key elements: Order N algorithm: use delocalised internal coordinates, defined separately for each reside, O(N3 ) with residue, O(N) overall. mix in cartesian coordinates to the internal coordinate generation (increases redundance but introduces dependent on translations and rotations Iterate optimisation of each reside

HDLC Optimiser (ii) Residue specification, often taken from a pdb file (pdb_to_res) allows separate delocalised coordinates to be generated for each residue Can perform P-RFO TS search in the first residue with relaxation of the others increased stability for TS searching Much smaller Hessians Further information on algorithm S.R. Billeter, A.J. Turner and W. Thiel, PCCP 2000, 2, p 2177

QM/MM Modelling Lecture 2 QM/MM Implementations

Outline Implementation Issues Three QM/MM software approaches
what factors affect the design Three QM/MM software approaches QM added as an extension to forcefield MM environment added to a small-molecule treatment Modular scheme with a range of QM and MM methods ChemShell Concepts and sample modules Approaches to periodic systems High Performance Computing Approach within QUASI Parallel computing techniques within GAMESS-UK, DL_POLY etc Tutorial Session Simple Tcl & ChemShell scripts, using the PyMOL GUI

Implementation Issues
Most implementations are based on existing QM and MM packages Implementers face a basic conflict between modularity keeping programs separate minimal modifications to allow easy upgrades Performance and Functionality supporting more complex interactions minimising overhead, recalculation, file access etc

Software Approaches QM/MM Implementations can
QM added as an extension to forcefield CHARMM/GAMESS-UK MM environment added to a small-molecule treatment ONIOM (G98) GAMESS-UK/AMBER Gaussian/AMBER (Manchester) Modular scheme with a range of QM and MM methods specialised optimisation algorithms e.g. ChemShell

QM/MM Software Approach (i)
Specialised for a classical modelling approach, by integrating QM code into MM package CHARMM + GAMESS(US), MNDO (Harvard & NIH) AMBER + Gaussian (UCSF, Manchester) QM/Pot, GULP + TURBOMOLE (Berlin) CHARMM + GAMESS (UK) Daresbury & Bernie Brooks, Eric Billings (NIH) Similar to existing ab-initio interfaces; CHARMM side follows coupling to GAMESS(US) (Milan Hodoscek) Support for Gaussian delocalised point charges Advantages Good MD capabilities, model building etc Disadvantages Restricted to certain classes of systems by forcefield choice

QM/MM Software Approach (ii)
Extend QM code by adding MM environment as a perturbation QM code is “in control” MM environment will typically be relaxed for each QM structure (hidden coordinates) e.g. ONIOM (Gaussian), IMOMM, Gaussian/AMBER (Manchester) Advantages Familiarity for quantum chemists Tools for small molecule manipulation (internal coordinates, transition state search etc) are available Disadvantages Relatively poor tools for management of conformational search of QM/MM surface, QM/MM dynamics etc

ONIOM Widely available, part of Gaussian98
Subtractive energy expression E(OI,MM) + E(IL,QM) - E(IL,MM) Includes implementation of Forcefields AMBER and UFF Both high and low levels can be QM (IMOMO)

QM/MM Software Approach (iii)
Modular approach covering a range of MM and QM codes e.g. ChemShell Advantages Flexibility of applications areas Ability to choose the best QM code for the specific task Ease of update of component codes Disadvantages Software Complexity range of forcefield types wide variation in QM and MM program design Close integration needed for performance (e.g. HPC), but weak coupling simplifies maintenance

Script design goals Keep all control input together in one place
Avoid proliferation of small scripts and control files Permit flexible user scripting Support heirarchical command structure (modules can invoke each other) Relationship between modules should be clear from the script The same module should be able to appear more than once (with different control arguments) Re-entrant invocation should be possible for some modules (e.g. optimisers) Support both loosely-coupled and efficient execution Provide option to keep data objects accessed by different modules in memory

ChemShell A Tcl interpreter for Computational Chemistry Interfaces
ab-initio (GAMESS-UK, Gaussian, CADPAC, TURBOMOLE, MOLPRO, NWChem etc) semi-emprical (MOPAC, MNDO) MM codes (DL_POLY, CHARMM, GULP) optimisation, dynamics (based on DL_POLY routines) utilities (clusters, charge fitting etc) coupled QM/MM methods Choice of QM and MM codes A variety of QM/MM coupling schemes electrostatic, polarised, connection atom, Gaussian blur .. QUASI project developments and applications e.g. Organometallics, Enzymes, Oxides, Zeolites

ChemShell Extended Tcl Interpreter Scripting capability
Interfaces to a range of QM and MM codes including GAMESS-UK DL_POLY MNDO97 TURBOMOLE CHARMM GULP Gaussian94 Implementation of QM/MM coupling schemes link atom placement, forces etc boundary charge corrections

ChemShell Architecture - Languages
An extended Tcl interpeter, written in.. Tcl Control scripts Interfaces to 3rd party executables GUI construction (Tk and itcl) Extensions C Tcl command implementations Object management (fragment, matrix, field, graph) Tcl and C APIs I/O Open GL graphics Fortran77 QM and MM codes: GAMESS-UK, GULP, MNDO97, DL_POLY

ChemShell Architecture
Core ChemShell Tcl interpreter, with code to support chemistry data: Optimiser and dynamics drivers QM/MM Coupling schemes Utilities Graphics GAMESS-UK (ab-initio, DFT) MNDO (semi-empirical) DL_POLY (MM) GULP (Shell model, defects) Features Single executable possible Parallel implementations External Modules CHARMM TURBOMOLE Gaussian94 MOPAC AMBER CADPAC Features Interfaces written in Tcl No changes to 3rd party codes

Object Caching During a run objects can be cached in memory, the command to request this is the name of the object (similar to a declaration in a compiled language) # fragment c c_create coords=c { h 0 0 0 h 0 0 1 } list_molecule coords=c delete_object c # No file is created here Confusion of objects with files can lead to confusion!!

Energy Gradient Evaluators
Many modules are designed to work with a variety of methods to compute the energy and gradient. The procedure relies on the interfaces to the codes being consistent, each comprises a set of callable functions e.g. initialisation energy, gradient kill update the particular set of functions being requested by a command option, usually theory= Example evaluators (depends on locally available codes) gamess, turbomole dl_poly, charmm mopac, mndo hybrid You can write your own in Tcl

Hybrid Module All control data held in Tcl lists created Implements
by setup program (Z-matrix style input) by scripts or GUI etc from user-supplied list of QM atoms provided as an argument Implements Book-keeping Division of atom lists addition of link atoms summation of energy/forces Charge shift, and addition of a compensating dipole at M2 Force resolution when link atoms are constrained to bond directions, e.g. the force on first layer MM atom (M1) arising from the force on the link atom is evaluated: Uses neutral group cutoff for QM/MM interactions

Hybrid Module Typical input options qm_theory= mm_theory=
qm_region = { } list of atoms in the QM region coupling = type of coupling groups = { } neutral charge groups cutoff = QM/MM cutoff atom_charges = MM charges

HPC Exploitation Adapt Tcl interpreter to run in parallel, master-slave architecture one node reads input, all nodes execute commands in-core storage of data objects replicated: default distributed: specific matrix objects Use of parallel third party codes (e.g. TURBOMOLE) Direct coupling to parallel codes: GA-based GAMESS-UK MPI-based MNDO, GULP, DL_POLY

GAMESS-UK Parallel Implementation
Replicated data scheme store P, F, S etc on every node minimal communications (load balancing, global sum) up to ca basis functions Message-passing version (MPI, TCGMSG) SCF and DFT Suitable for < 32 processors Global Array version: Parallel functionality SCF, DFT, MP2, SCF Hessian Parallel algorithms GAs for in-core storage of transformed integrals (to vvoo) and MP2 amplitudes parallel linear algebra (PEIGS, DIIS, MXM etc) GA-mapped ATMOL file system

QM/MM Thrombin Benchmark
QM/MM calculation on thrombin pocket: QM region (69 Atoms) is modelled by SCF 6-31G calculation (401 GTOs), total system size for the classical calculation is 16,659 atoms. QM/MM interaction was cut off at 15 angstroms using a neutral group scheme (leading to the inclusion in the QM calculation of 1507 classical centres). Scaling for Thrombin + Inhibitor (NAPAP) + Water Number of Nodes

QM/MM Modelling Tutorial Practical QM/MM Calculations with the ChemShell Software

ChemShell basics ChemShell control files are Tcl Scripts
Usually we use a .chm suffix ChemShell commands have some additional structure, usually they take the following form command arg1=value1 arg2=value2 Arguments can serve many functions mm_defs=dl_poly.ff Identify a data file to use coords=c Use object c as the source of the structure use_pairlist=yes Provide a Boolean flag (yes/no, 1/0,, on/off) list_option=full Provide a keyword setting theory=gamess Indicate which compute module to use Sometimes command arg1=value1 arg2=value2 data

Very Simple Tcl (i) Variable Assignment (all variables are strings)
set a 1 Variable use [ set a ] $a Command result substitution [ <Tcl command> ] Numerical expressions set a [ expr 2 * $b ] Ouput to stdout puts stdout “this is an output string”

Very Simple Tcl (ii) Lists - often passed to ChemShell commands as arguments set a { } set a “1 2 3” set a [ list ] $ is evaluated within [ list .. ] and “ “ but not { } [ list … ] construct is best for building nested lists using variables Arrays - not used in ChemShell arguments, useful for user scripts Associative - can be indexed using any string set a(1) 1 set a(fred) x parray a

Very Simple Tcl (iii) Continuation lines: can escape the newline
tclsh % set a “this \ is \ a single variable” this is a single variable tclsh % { } will incorporate newlines into the list tclsh % set a {this is a single variable} this a single variable tclsh %

Very Simple Tcl (iv) Procedures Files
Sometimes needed to pass to ChemShell commands to provide an action proc my_procedure { my_arg1 my_arg2 args } { puts stdout “my_procedure” return “the result” } Files set fp [ open my.dat w ] puts $fp “set x $x” close $fp ….. source my.dat

ChemShell Object types
fragment - molecular structure creation: c_create, load_pdb …. Universal!! zmatrix z_create, newopt, z_surface matrix creation: create_matrix, energy and gradient evaluators, dynamics field creation: cluster_potential etc, graphical display, charge fits GUI only 3dgraph

ChemShell Object Representations
Between calculations, and sometimes between commands in a script, objects are stored as files. Usually there is no suffix, objects are distinguished internally by the block structure. % cat c block = fragment records = 0 block = title records = 1 phosphine block = coordinates records = 34 p e e e-16 c e e e+00 c e e e-01 c e e e+00 c e e e+00 …….... Multi block objects are initiated by an empty block (e.g. fragment) Unrecognised blocks are silently ignored

Object Caching During a run objects can be cached in memory, the command to request this is the name of the object (similar to a declaration in a compiled language) # fragment c c_create coords=c { h 0 0 0 h 0 0 1 } list_molecule coords=c delete_object c # No file is created here Confusion of objects with files can lead to confusion!!

Object Input and Output
If you access an object from a disk, ChemShell will always update the disk copy when it has finished (there is no easy way of telling if a command or procedure has changed it). Usually this is harmless (e.g. output formats are precise enough), but unrecognised data in the input will not be present in the output, take a copy if you need to keep it. E.g. if a GAMESS-UK punchfile contains a fragment object and a single data field (e.g. the potential) you can use it as both a fragment object and a field object % rungamess test % cp test.pun my_structure % cp test.pun my_field % chemsh …….

Energy Gradient Evaluators
Many modules are designed to work with a variety of methods to compute the energy and gradient. The procedure relies on the interfaces to the codes being consistent, each comprises a set of callable functions e.g. initialisation energy, gradient kill update the particular set of functions being requested by a command option, usually theory= Example evaluators (depends on locally available codes) gamess, turbomole dl_poly, charmm mopac, mndo hybrid You can write your own in Tcl

Module options, using the :
The : syntax is used to pass control options to sub-module. e.g. when running the optimiser, to set the options for the module computing the energy and gradient. {} can be used if there is more than one argument to pass on. Nested structures are possible using Tcl lists newopt function=zopt : { theory=gamess : { basis=sto3g } zmatrix=z } gamess arguments Command zopt arguments newopt arguments

Loading Objects - Z-matrices
z_create zmatrix=z { zmatrix angstrom c x 1 1.0 n 1 cn 2 ang f 1 cf 2 ang 3 phi variables cn cf phi constants ang end } z_list zmatrix=z set p [ z_prepare_input zmatrix=z ] puts stdout $p z_create provides input processor for the z-matrix object z_list can be used to display the object in a readable form z_prepare_input provides the reverse transformation if you need something to edit z_to_c provides the cartesian representation

Additional Z-matrix features (i)
Can include some atoms specified using cartesian coordinates Can use symbols for atom-path values (i1,i2,i3) Can append % to symbols to make them unique (e.g. o%1) Can create/destroy and set variables using Tcl commands z_create zmatrix=z1 { zmatrix o%1 o%2 o%1 3. h%1 o% o% h%2 o% o% h%1 29.0 end } z_var zmatrix=z1 result=z2 control= "release all" z_substitute zmatrix=z2 values= {r2=3.0 r3=2.0} z_list zmatrix=z2

Additional Z-matrix features (ii)
Combine cartesian and internal definitions z_create zmatrix=z1 { coordinates ... zmatrix .... end } c_to_z will create a fully cartesian z-matrix

Loading Data Object - Coordinates
c_create coords=h2o.c { title water dimer coordinates au o h h o h h } No symbols allowed Can also use read_xyz, read_pdb, read_xtl

Periodic Systems (i) Crystallographic cell constants can be provided, along with fractional coordinates # c_create coords=mgo.c { space_group 1 cell_constants angstrom coordinates Mg O Mg O Mg O Mg O } list_molecule coords=c set p [ c_prepare_input coords=c ]

Periodic Systems (ii) Alternatively, input the cell explicitly, in c_create or attach to the structure later # c_create coords=d { title primitive unit cell of diamond coordinates au c c cell au } extend_fragment coords=d cell_indices= { } result=d2 set_cell coords=d cell= { }

QM Code Interfaces Provides access to third party codes
GAMESS-UK MOPAC MNDO TURBOMOLE Gaussian98 Standardised interfaces argument structure hamiltonian (includes functional) charge, mult, scftype basis (internal library or keywords) accuracy direct symmetry maxcyc...

GAMESS-UK Interface Can be built in two ways Notes
Interface calls GAMESS-UK and the job is executed using rungamess (so you may need to have some environment varables set) parallel execution can be requested even if ChemShell is running serially GAMESS-UK is built as part of ChemShell mainly intended for parallel machines energy coords=c \ theory=gamess : { basis=dzp hamiltonian=b3lyp } \ energy=e Notes The jobname is gamess1 unless specified Some code-specific options dumpfile= specify dumpfile routing getq = load vectors from foreign dumpfile

GAMESS-UK example - basis library
energy coords=c \ theory=gamess : { basisspec = { { sto-3g *} {dzp o} } } \ energy=e basisspec has the structure { { basis1 atoms-spec1} {basis2 atomspec2} ….. } Assignment proceeds left to right using pattern matching for atom labels * is a wild card This example gives sto-3g for all atoms except o Library can be extended in the Tcl script (see examples/gamess/explicitbas.chm) ECPs are used where appropriate for the basis

DL_POLY Interface Features
Energy and gradient routines from DL_POLY (Bill Smith UK, CCP5) General purpose MM energy expression, including approximations to CFF91 (e.g. zeolites) CHARMM AMBER MM2 Topology generator automatic atom typing parameter assignment based on connectivity topology from CHARMM PSF input FIELD, CONFIG, CONTROL are generated automatically FIELD is built up using terms defined in the file specified by mm_defs= argument Periodic boundary conditions are limited to parallelopiped shaped cells Can have multiple topologies active at one time

DL_POLY forcefield terms
Terms are input using atom symbols (or * wild card) Individual keyword terms: bond mm2bond quarbond angle mm2angle quarangle ptor mm2tor htor cfftor aa-couple aat-couple vdw powers m_n_vdw 6_vdw mm2_vdw Input units are kcal/mol, angstrom etc in line with most forcefield publications For full description see the manual

Automatic atom type assigment
Forcefield definition can incorporate connectivity-based atom type definitions which will be used to assign types Atom types are hierarchical, most specific applicable type will be used (algorithm is iterative) e.g. to use different parameters for ipso-C of PPh3 define a new type by a connection to phosphorous query ci "ipso c" supergroup c target c atom p connect 1 2 endquery charge c -0.15 charge h 0.15

DL_POLY Example # dummy forcefield read_input dl_poly.ff {
bond c c bond c h angle c c c angle c c h vdw h h vdw c c vdw h c htor c c c c i-j-k-l charge c -0.15 charge h 0.15 } energy theory=dl_poly : mm_defs = dl_poly.ff coords=c energy=e

Using DL_POLY with CHARMM Parameters
Replicates CHARMM energy expression (without UREY) Uses standard CHARMM datafiles Requires CHARMM program + script to run as far as energy evaluation for initial setup Atom charges and atom types are obtained by communication with a running CHARMM process (usually only run once) # run charmm using script provided charmm.preinit charmm_script=all.charmm coords=charmm.c # Store type names from the topology file load_charmm_types2 top_all22_prot.inp charmm_types # These requires CTCL (i.e. charmm running) set types [ get_charmm_types ] set charges [ get_charmm_charges ] set groups [ get_charmm_groups ] # charmm.shutdown

Using DL_POLY with CHARMM Parameters
Then provide dl_poly interface with .psf (topology) charmm_psf = .rtf (for atom types) charmm_mass_file= .inp parameter files charmm_parameter_file= theory=dl_poly : [ list \ list_option=full \ cutoff = [ expr 15 / ] \ scale14 = { } \ atom_types= $types \ atom_charges= $charges \ use_charmm_psf=yes \ charmm_psf_file=4tapap_wat961.psf \ charmm_parameter_file=par_all22_prot_mod.inp \ charmm_mass_file= $top ]

Core modules: Geometry Optimisers
Small Molecules Internal coordinates (delocalised, redundant etc) Full Hessian O(N3) cost per step BFGS, P-RFO Macromolecules Cartesian coordinates Partial Hessian (e.g. diagonal) O(N) cost per step Conjugate gradient L-BFGS Coupled QM/MM schemes Combine cartesian and internal coordinates Reduce cost of manipulating B, G matrices Define subspace (core region) and relax environment at each step reduce size of Hessian exploit greater stability of minimisation vs. TS algorithms Use approximate scheme for environmental relaxation

QUASI - Geometry Optimisation Modules
newopt A general purpose optimiser Target functions, specified by function = copt : cartesian (obsolete) zopt: z-matrix (now also handles cartesians) new functions can be written in Tcl (see example rosenbrock) For QM/MM applications e.g. P-RFO adapted for presence of soft modes Hessian update includes partial finite difference in eigenmode basis New algorithms can be coded in Tcl using primitive steps (forces, updates, steps, etc). hessian Generates hessian matrices (e.g. for TS searching)

Newopt example - minimisation
# # function zopt allows the newopt optimiser to work with # the energy as a function of the internal coordinates of # the molecule newopt function=zopt : { theory=gamess : { basis=dzp } } \ zmatrix=z

Newopt example - transition state determination
# functions zopt.* allow the newopt optimiser to work with # the energy as a function of the internal coordinates of # the molecule set args "{theory=gamess : { basis=3-21g } zmatrix=z}" hessian function=zopt : [ list $args ] \ hessian=h_fcn_ts method=analytic newopt function=zopt : [ list $args ] \ method=baker \ input_hessian=h_fcn_ts \ follow_mode=1

HDLCopt optimiser hdlcopt
Hybrid Delocalised Internal Coordinate scheme (Alex Turner, Walter Thiel, Salomon Billeter) Developed within QUASI project O(N) overall scaling per step Key elements: Residue specification, often taken from a pdb file (pdb_to_res) allows separate delocalised coordinates to be generated for each residue Can perform P-RFO TS search in the first residue with relaxation of the others increased stability for TS searching Much smaller Hessians Further information on algorithm S.R. Billeter, A.J. Turner and W. Thiel, PCCP 2000, 2, p 2177

HDLCopt example # procedure to update the last step
proc hdlcopt_update { args } { parsearg update { coords } $args write_xyz coords= $coords file=update.xyz end_module } # select residues set residues [ pdb_to_res "4tapap_wat83.pdb" ] # load coordinates read_pdb file=4tapap_wat83.pdb coords=4tapap_wat83.c hdlcopt coords=4tapap_wat83.c result=4tapap_wat83.opt \ theory=mndo : { hamiltonian=am1 charge=1 optstr={ nprint=2 kitscf=200 } } \ memory=200 residues= $residues \ update_procedure=hdlcopt_update

GULP Interface Simple interface to GULP energy and forces
GULP licensing from Julian Gale GULP must be compiled in in alpha version only for the workshop ChemShell fragment object supports shells Shells are relaxed by GULP with cores fixed, ChemShell typically controls the core positions Provide forcefield in standard GULP format

GULP interface example
read_input gulp.ff { # from T.S.Bush, J.D.Gale, C.R.A.Catlow and P.D. Battle # J. Mater Chem., 4, (1994) species Li core Na core ... buckingham Li core O shel Na core O shel spring Mg Ca } add_shells coords=mgo.c symbols= {O Mg} newopt function=copt : [ list coords=mgo.c theory=gulp : [ list mm_defs=gulp.ff ] ]

ChemShell CHARMM Interface
Full functionality from standard academic CHARMM Dual process model CHARMM runs a separate process CHARMM/Tcl interface (CTCL, Alex Turner) uses named pipe to issue CHARMM commands and return results. commands to export data for DL_POLY and hybrid modules atomic types and charges neutral groups topologies and parameters Acccess to coupling models internal to CHARMM GAMESS(US), MOPAC GAMESS-UK (under development) collaboration with NIH explore additional coupling schemes (e.g. double link atom)

CHARMM Interface - example
# start charmm process, create chemshell object # containing the initial structure charmm.preinit script=charmm.in coords=charmm.c # ChemShell commands with theory=charmm hdlcopt theory=charmm coords=charmm.c # destroy charmm process charmm.shutdown

Molecular Dynamics Module
Design Features Generic - can integrate QM, MM, QM/MM trajectories Based on DL_POLY routines Integration by Verlet leap-frog SHAKE constraints Quaternion rigid body motion NVT, NPT, NVE integration Script-based control of primitive steps Simulation Protocols equilibration simulated annealing Tcl access to ChemShell matrix and coordinate objects e.g. force modification for harmonic restraint Data output trajectory output, restart files

Molecular Dynamics - arguments
Object oriented syntax follows Tk etc dynamics dyn1 coords=c … etc Arguments theory= module used to compute energy and forces coords= initial configuration of the system timestep= integration timestep (ps) [0.0005] temperature= simulation temperature (K) [293] mcstep= Max step displacement (a.u.) for Monte Carlo [0.2] taut= Tau(t) for Berendsen Thermostat (ps) [0.5] taup= Tau(p) for Berendsen Barostat (ps) [5.0] compute_pressure= Whether to compute pressure and virial (for NVT simulation) verbose= Provide additional output energy_unit= Unit for output

Molecular dynamic - arguments
Arguments (cont.) rigid_groups= rigid group (quaternion defintions) constraints= interatomic distances for SHAKE ensemble= Choice of ensemble [NVE] frozen= List of frozen atoms trajectory_type= Additional fields for trajectory (> 0 for velocity, > 1 for forces) trajectory_file= dynamics.trj file for trajectory output Methods: Dyn1 configure temperature=300 configure - modify simulation parameters initvel - initialise random velocities forces - evaluate molecular forces step - Take MD step

Molecular Dynamics - More methods
update - Request MM or QM/MM pairlist update mctest - Test step (Monte Carlo only) output - print data (debugging use only printe - print step number, kinetic, potential, total energy, temperature, pressure volume and virial. get - Return a variable from the dynamics, temperature, input_temperature, pressure, input_pressure, total_energy, kinetic_energy, potential_energy time trajectory - Output the current configuration to the trajectory file destroy - free memory and destroy object fcap - force cap load - recover positions/velocities dump - save positions/velocities dumpdlp - write REVCON

Molecular Dynamics - Example
dynamics dyn1 coords=c theory=mndo temperature=300 timestep=0.005 dyn1 initvel set nstep 0 while {$nstep < } { dyn1 force dyn1 step # additional Tcl commands here incr nstep } dyn1 configure temperature=300 # etc dyn1 destroy

Hybrid Module All control data held in Tcl lists created Implements
by setup program (Z-matrix style input) by scripts or GUI etc from user-supplied list of QM atoms provided as an argument Implements Book-keeping Division of atom lists addition of link atoms summation of energy/forces Charge shift, and addition of a compensating dipole at M2 Force resolution when link atoms are constrained to bond directions, e.g. the force on first layer MM atom (M1) arising from the force on the link atom is evaluated: Uses neutral group cutoff for QM/MM interactions

Hybrid Module Typical input options qm_theory= mm_theory=
qm_region = { } list of atoms in the QM region coupling = type of coupling groups = { } neutral charge groups cutoff = QM/MM cutoff atom_charges = MM charges

Object Oriented Interfaces
Purpose To allow a script to manage multiple instances of the same data structure Support for recursive/reentrant algorithms Examples PE surface drivers newopt, dynamics Coordinate transformation routines copt, zopt, dlcopt QM and MM interfaces dl_poly, mopac Syntax Modelled on Tk, itcl, and other object-oriented Tcl extensions mopac mop1 coords=water.c energy=water.e hamiltonian=am1 mop1 energy # additional invocations mop1 delete

Using multiple objects - A QM/MM optimisation scheme
newopt1 Object types newopt: optimiser object zopt: Z-matrix/cartesian transformation dl_poly: MM energy and forces hopt: Custom written target function (150 lines of Tcl) Instances zopt1: reduced (active site) coordinates zopt2: environment coordinates newopt1: master optimisation, QM/MM hamiltonian, in a reduced coordinate space newopt2: relax the environment using a pure MM energy expression hopt newopt2 zopt2 dl_poly2 zopt1 hybrid dl_poly1 mopac

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P. Sherwood, in J. Grotendorst (Ed
P. Sherwood, in J. Grotendorst (Ed.), Modern Methods and Algorithms in Quantum Chemistry. NIC Series, Jülich, 2000, vol., p

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