ChemShell

Paul Sherwood

CLRC Daresbury Laboratory

p.sherwood@dl.ac.uk

Overview

• ChemShell overview• Introduction to Tcl• Script basics• Modules overview

¤ creating Input data objects¤ dl_poly¤ gamess

• QM/MM Methods¤ hybrid

• QM/MM models available

• Input examples

• ChemShell GUI

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

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 functionsmm_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 { 1 2 3 }¤ set a “1 2 3”¤ set a [ list 1 2 3 ]¤ $ 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 variabletclsh %

¤ { } will incorporate newlines into the list

tclsh % set a {this is a single variable}this is a single variabletclsh %

Very Simple Tcl (iv)

• Procedures¤ 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”

}

• Filesset fp [ open my.dat w ]

puts $fp “set x $x”

close $fp

…..

source my.dat

ChemShell Object types

• 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 cblock = fragment records = 0block = title records = 1phosphineblock = coordinates records = 34p 4.45165900000000e+00 0.00000000000000e+00 -8.17756491786826e-16 c 6.18573550000000e+00 -2.30082107458395e+00 1.93061811508830e+00 c 8.21288557680633e+00 -3.57856465464377e+00 9.30188790875432e-01 c 9.49481331797844e+00 -5.31433733714784e+00 2.37468849115612e+00 c 8.74959098234423e+00 -5.77236643959209e+00 4.81961751564967e+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 cc_create coords=c {h 0 0 0h 0 0 1}list_molecule coords=cdelete_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 }

Command

newopt arguments

gamess arguments

zopt arguments

Loading Objects - Z-matrices

z_create zmatrix=z {zmatrix angstromcx 1 1.0n 1 cn 2 angf 1 cf 2 ang 3 phivariables cn 1.135319cf 1.287016phi 180.constantsang 90.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 {zmatrixo%1o%2 o%1 3.h%1 o%1 1.8 o%2 121.0h%2 o%2 1.85 o%1 122.0 h%1 29.0end}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 {titlewater dimercoordinates auo 0.0000000000 0.0000000000 0.0000000000h 0.0000000000 -1.4207748912 1.0737442022h 0.0000000000 1.4207748912 1.0737442022o -4.7459987607 0.0000000000 -2.7401036621h -3.1217528345 0.0000000000 -2.0097934033h -4.4867611522 0.0000000000 -4.5020127872}

• No symbols allowed• Can also use read_xyz, read_pdb, read_xtl

Periodic Systems (i)

#c_create coords=mgo.c {space_group1cell_constants angstrom4.211200 4.211200 4.211200 90.00 90.00 90.00coordinatesMg 0.10000000 0.00000000 0.00000000O 0.50000000 0.50000000 -0.50000000Mg 0.00000000 0.50000000 -0.50000000O 0.50000000 1.00000000 -1.00000000Mg 0.50000000 0.00000000 -0.50000000O 1.00000000 0.50000000 -1.00000000Mg 0.50000000 0.50000000 0.00000000O 1.00000000 1.00000000 -0.50000000}list_molecule coords=cset p [ c_prepare_input coords=c ]

• Crystallographic cell constants can be provided, along with fractional coordinates

Periodic Systems (ii)

#c_create coords=d {titleprimitive unit cell of diamondcoordinates auc 0.8425347285 0.8425347285 0.8425347285c -0.8425347285 -0.8425347285 -0.8425347285cell au 0.00000 3.37014 3.37014 3.37014 0.00000 3.37014 3.37014 3.37014 0.00000}extend_fragment coords=d cell_indices= { -2 2 -2 2 -2 2 } result=d2

set_cell coords=d cell= { 0.00000 3.37014 3.37014 3.37014 0.00000 3.37014 3.37014 3.37014 0.00000 }

• Alternatively, input the cell explicitly, in c_create or attach to the structure later

Core modules: DL_POLY

• 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 ctarget catom pconnect 1 2endquery

charge c -0.15charge h 0.15

DL_POLY Example

# dummy forcefieldread_input dl_poly.ff {bond c c 100 1.5bond c h 100 1.0angle c c c 100 120angle c c h 100 120vdw h h 2500 1000000vdw c c 2500 1000000vdw h c 2500 1000000htor c c c c 100 0.0 i-j-k-lcharge c -0.15charge 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 providedcharmm.preinit charmm_script=all.charmm coords=charmm.c# Store type names from the topology fileload_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

theory=dl_poly : [ list \ list_option=full \ cutoff = [ expr 15 / 0.529177 ] \ scale14 = { 1.0 1.0 } \ 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 ]

• Then provide dl_poly interface with

¤ .psf (topology) charmm_psf =¤ .rtf (for atom types) charmm_mass_file=¤ .inp parameter files charmm_parameter_file=

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 residuesset residues [ pdb_to_res "4tapap_wat83.pdb" ]# load coordinatesread_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

CCP1 QM/MM Optimiser

• Developed by Richard Hall (Manchester) as a QM/MM optimisation routine¤ DLC central residue

¤ CG outer relaxation (e.g. Amber)

• Interface exists, but for QM-only optimisation at present.

• Not available in the workshop build

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, 831-837 (1994)speciesLi core 1.000Na core 1.000...buckinghamLi core O shel 426.480 0.3000 0.00 0.0 10.0Na core O shel 1271.504 0.3000 0.00 0.0 10.0...springMg 349.95Ca 34.05...}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 structurecharmm.preinit script=charmm.in coords=charmm.c

# ChemShell commands with theory=charmmhdlcopt theory=charmm coords=charmm.c

# destroy charmm processcharmm.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=0.005dyn1 initvelset nstep 0while {$nstep < 10000 } { dyn1 force dyn1 step ..... # additional Tcl commands here incr nstep}dyn1 configure temperature=300# etcdyn1 destroy

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...

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 Interface

• Can be built in two ways¤ 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

GAMESS-UK example - basis library

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

energy coords=c \ theory=gamess : { basisspec = { { sto-3g *} {dzp o} } } \ energy=e

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

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

¤ 1997 Eichler, Kölmel, and Sauer QM/Pot• subtractive coupling of GULP/TURBOMOLE

Hybrid Module

• All control data held in Tcl lists created¤ 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

E

x

E

x

x

xM L

L

M1 1

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

Hybrid Computational Schemes

Termination AtomsChemical typehydrogen atoms, pseudopotentials adjusted connection atoms, localised orbitals

Charge perturbationsnone, charge deletion, charge shift, selection of 1e integrals, double link atoms

QM/MM CouplingsUnpolarised

QM polarisation

choice of charges?

MM polarisation¤ shell model¤ dipole polarisabilities

Total Energy ExpressionUncorrected

E(M,MM) + E(QL,QM)

Boundary corrected

E(M,MM) + E(QL,QM) - E(L,MM)

Subtractive

E(MQ,MM) + E(QL,QM) - E(QL,MM)

M1

M2

Q1

Q2

L

M2 Q2

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.

Inner Region

Boundary Region

Outer Region

Conventional QM/MM Scheme

• Termination¤ hydrogen, adjusted connection

atom, pseudo-halogen

• Coupling¤ Unpolarised ¤ QM polarisation¤ MM Polarisation (Direct Reaction

Field)

• Energy Expression¤ No correction (Q2-Q1-L force

constant mimics Q2-Q1-M1)

• MM Charge Adjustments¤ Deletion (first charge group)

¤ Shift (M1->M2)

¤ Integral selection (semi-empirical)

• Advantages¤ Robust

• Disadvantages¤ charge perturbation at boundary

• Applications ¤ zeolites ¤ enzymes

Subtractive QM/MM Coupling

• Energy ExpressionE(MQ,MM) + E(QL,QM) - E(QL,MM) ¤ includes boundary correction¤ can treat polarisation of both the

MM and QM regions at the force-field level

• Termination¤ Any (provided a force field model

for QL is available)

• Advantages¤ Potentially highly accurate (free

from artefacts)¤ Can also be used for QM/QM

schemes (e.g. IMOMO, Morokuma et al)

• Disadvantages¤ Need for accurate forcefields¤ Possible catastrophies on potential

energy surface¤ No electrostatic influence on QM

wavefunction

• Applications¤ Zeolites (Sauer et al)

¤ under development, theory=subtractive

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• 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

C

NC

C

O

H R

N

H

C

O

R

Creation of neutral embedding site (i) Neutral charge groups

• Total charge conserved, poor dipole moments

C

NC

C

O

H R

N

H

C

O

R

H H

Creation of neutral embedding site (ii) Polar forcefields

bond dipole models, e.g. for zeolites (Si +0.5x, O -0.5x)

O-x O-x

O-x

O-x

Si+2x

Creation of neutral embedding site (ii) Polar forcefields

O-0.5x O-0.5x

O-0.5x

O-0.5x

Si

H

H

HH

• Select with dipole_adjust=yes

Creation of neutral embedding site (iii) Double link atoms

• Suggestion from Brooks (NIH) for general deletion (not on a force-field neutral charge-group boundary)

C

NC

C

O

H R

N

H

C

O

R

Creation of neutral embedding site (iii) Double link atoms

• All fragments are common chemical entities, automatic charge assignment is possible.

C

N

CC

O

HR

N

H

C

O

R

H H

H H

Boundary adjustments

¤ 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.

M2

M1 Q1

Q2

Q2M2

M3 Q3

L

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

use coupling=L1 with qm_theory=mndo

¤ 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.

lr

qlV j

lA

Ai

Aij

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

¤ use coupling=L2 with groups = { … }

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

¤ Requested using coupling=shift

M2

M1 Q1

Q2

Q2M2

M3 Q3

L

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

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

MM QM

C C

H

H

H H

H

H

HH

Compare with dipole of MM methyl group (0.18)

Ethane Dipole Moment (au)

0

0.1

0.2

0.3

0.4

0.5

0.1 1 10

MM Gaussian Blur (Angstroms)

Electrostatic EmbeddingSummary

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

QM

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

• Advantages¤ suitable for ionic materials

• Disadvantages¤ require specialised pseudopotentials

• Applications¤ metal oxide surfaces

MM

GULP - GAMESS-UK coupling

• Features¤ From Julian Gale (Imperial

College), classical energies including shell model

¤ Self-consistent coupling of shell relaxation to GAMESS-UK

• Import electrostatic forces on shells from GAMESS-UK

• relax shell positions

¤ Defect energies (Mott Littleton scheme) a posteriori

¤ MPI parallel version available.

¤ Use coupling=shift (without any bonds, and with some shells in MM region, include_qm_force=yes for GULP

ChemShell - hybrid module

GULP shell relaxation

GAMESS-UK SCF & shell forces

GAMESS-UK atomic forces

GULP forces

The Cerius-2 GUI

• Provides control of QM, MM, and QM/MM calculations using HDLCOpt, Newopt, and Dynamics modules

• Writes a ChemShell script comprising¤ control parameters¤ job-specific segments

• To set up a new system, execute% make_run_dir

first to create cerius-2 files and link some ChemShell template scripts

• See /workshop/examples/chemsh/SDK & manual

Example files

SDK/ SUMMARY charmm/ chemgui/ dl_poly/ dynamics/ field/ force/ fragment/ gamess/ gaussian/ gulp/ hdlcopt/

hybrid/ irc/ matrix/ mndo/ mopac/ newopt/ newopt_alex/ parallel/ quasi/ surface/ turbomole/ xtal/ zmatrix/

• http://www.dl.ac.uk/TCSC/QuantumChem/ChemShell/quasi_www/manual/manual.html