September 7th 2016

1

Fernanda Duarte

Using Valence Bond Theory to Model

(Bio)Chemical Reactivity

Master Course for Theoretical Chemistry and Computational

Modelling (TCCM)

Department of Chemistry, Oxford

• Motivation & History of VB

• Basic Concepts

• ab initio VB theory

• Multiscale VB simulations

• Empirical VB theory

• Example EVB

General Outline of Lecture

3

Tutorial Q software

SN2 Reaction in Gas/Solvent Phase

PSRS

4

Tutorial Q software

Prepare

SimulateAnalyse3D Molecule (pdb)

Ffs param (lib/prm)

Solvent (opt)

Qprep

Input (.inp)

force field changes (.fep)

Topology

Qdyn

Final coord (.re)

Output MD (.log)

Energy (.en)

Trajectory (.tr)

Qfep

Free energy calc. input

Qcal

Free energy data

structure, averages,etc

5

Tutorial Q software

Prepare

3D Molecule (pdb)

Ffs param (lib/prm)

Solvent (opt)

Qprep

Topology

readlib./0-ff/qoplsaa.libreadlib./0-ff/prb.libreadlib./0-ff/cl-.libreadprm./0-ff/qoplsaa_prb_cl-.prmreadpdbprobr_cl.pdbboundarysphere1:C120#solvate1:C1201HOHmaketopprobr_cl.topwritetopprobr_cl.topwritepdbprobr_cl_start.pdbyquit

6

Tutorial Q software

[atoms]#charge1C1prc_C1-0.19842H2prc_H20.1206.........8H8prc_H80.06409H9prc_H90.064010H10prc_H100.064011Cl11prc_Cl11-0.2370[bonds]C1H2C1H3C1C4C1Cl11C4H5C4H6C4C7C7H8C7H9C7H10[impropers]

[charge_groups]C1H2H3C4H5H6Cl11C7H8H9H10

Cl

Br

Prepare

7

Tutorial Q software[md]steps100000temperature300stepsize1bath_coupling100

[cut-offs]q_atom99

[files]topologyprobr_cl.toprestartrelax_002.refinalrelax_003.retrajectoryrelax_003.dcdfepprobr_cl.fep

[lambdas]1.000.00

[sequence_restraints]160.10011120.100

[distance_restraints]1110.03.53.021120.03.53.01

Simulate

Cl

Br

8

Tutorial Q software

Relaxation

9

Tutorial Q software

[FEP]states2

[atoms]#QindexPDBindex#PDBIDSTATE1TYPE11#1.C1PRB.C122#1.H2PRB.H233#1.H3PRB.H344#1.C4PRB.C455#1.H5PRB.H566#1.H6PRB.H6711#1.Br11PRB.Br11812#2.Cl1CL-.Cl1

Simulate

1

47

Cl

Br

10

Tutorial Q software

[change_charges]1-0.3022-0.1984#PRB.C1dq=0.103820.14410.1206#PRB.H2dq=-0.023530.14410.1206#PRB.H3dq=-0.023540.21290.2158#PRB.C4dq=0.00295-0.0082-0.0108#PRB.H5dq=-0.00266-0.0082-0.0108#PRB.H6dq=-0.00267-0.1825-1.0000#PRB.Br11dq=-0.81758-1.0000-0.2370#CL-.Cl1dq=0.7630

[soft_pairs]17#prb_C1-prb_Br1118#prc_C1-prc_Cl11

[bond_types]166.01.581.94#prb_C1-prb_Br11278.01.511.80#prc_C1-prc_Cl11

[change_bonds]11110#1.C1-1.Br11prb_C1-prb_Br11None11202#1.C1-2.Cl1Noneprc_C1-prc_Cl11

F.7 File and format descriptions F REFERENCE GUIDE

Table 13: FEP file format

[monitor groups]: Define atom groups whose non-bonded interactions are to be moni-tored (printed in the log file).1... Topology atom number of first and following atoms in group.

[monitor group pairs]: Define pairs of monitor groups whose total non-bonded interac-tions should be calculated.1 First monitor group number.2 Second monitor group number.

[bond types]: Define Q-bond types using Morse or harmonic potentials,

EMorse = De

�1� e�↵(r�r0)

�2EHarmonic =

12kb (r � r0)

2.Morse and harmonic potentials can be mixed (but each bond type is either kind). Entrieswith four values are Morse potentials and entries with three values are harmonic.

Morse potential Harmonic potential1 Q-bond type number (starting with 1).2 Morse potential dissociation energy, De

(kcal·mol�1).Harmonic force constant kb(kcal·mol�1·A�2).

3 Exponential co-e�cient ↵ in Morse poten-tial (A�2).

Equilibrium bond length r0 in har-monic potential (A).

4 Equilibrium bond length r0 in Morse po-tential (A).

[change bonds]: Assign Q-bond types. Note: shake constraints for the redefined bondsare removed. The order in which atoms are given is not important.1 Topology atom number of first atom in bond.2 Topology atom number of second atom in bond.3... Q-bond type number (referring to numbering in bond types section) or 0 to

disable bond in state 1, state 2, ...

[angle types]: Define Q-angle types.1 Q-angle type number (starting with 1).2 Harmonic force constant (kcal·mol�1·rad�2).3 Equilibrium angle (�).

[change angles]: Assign Q-angle types.1 Topology atom number of first atom in angle.2 Topology atom number of middle atom in angle.3 Topology atom number of third atom in angle.4... Q-angle type number (referring to numbering in angle types section) or 0 to

disable angle in state 1, state 2, ...

[torsion types]: Define Q-torsion types.1 Q-torsion type number (starting with 1).2 Force constant = 1

2 ·barrier height (kcal·mol�1).3 Periodicity (number of maxima per turn).4 Phase shift (�).

[change torsions]: Assign Q-torsion types. Note: The order of atoms (1, 2, 3, 4 or 4, 3,2, 1) is not important.1 Topology atom number of first atom in torsion.

65

F.7 File and format descriptions F REFERENCE GUIDE

Table 13: FEP file format

[monitor groups]: Define atom groups whose non-bonded interactions are to be moni-tored (printed in the log file).1... Topology atom number of first and following atoms in group.

[monitor group pairs]: Define pairs of monitor groups whose total non-bonded interac-tions should be calculated.1 First monitor group number.2 Second monitor group number.

[bond types]: Define Q-bond types using Morse or harmonic potentials,

EMorse = De

�1� e�↵(r�r0)

�2EHarmonic =

12kb (r � r0)

2.Morse and harmonic potentials can be mixed (but each bond type is either kind). Entrieswith four values are Morse potentials and entries with three values are harmonic.

Morse potential Harmonic potential1 Q-bond type number (starting with 1).2 Morse potential dissociation energy, De

(kcal·mol�1).Harmonic force constant kb(kcal·mol�1·A�2).

3 Exponential co-e�cient ↵ in Morse poten-tial (A�2).

Equilibrium bond length r0 in har-monic potential (A).

4 Equilibrium bond length r0 in Morse po-tential (A).

[change bonds]: Assign Q-bond types. Note: shake constraints for the redefined bondsare removed. The order in which atoms are given is not important.1 Topology atom number of first atom in bond.2 Topology atom number of second atom in bond.3... Q-bond type number (referring to numbering in bond types section) or 0 to

disable bond in state 1, state 2, ...

[angle types]: Define Q-angle types.1 Q-angle type number (starting with 1).2 Harmonic force constant (kcal·mol�1·rad�2).3 Equilibrium angle (�).

[change angles]: Assign Q-angle types.1 Topology atom number of first atom in angle.2 Topology atom number of middle atom in angle.3 Topology atom number of third atom in angle.4... Q-angle type number (referring to numbering in angle types section) or 0 to

disable angle in state 1, state 2, ...

[torsion types]: Define Q-torsion types.1 Q-torsion type number (starting with 1).2 Force constant = 1

2 ·barrier height (kcal·mol�1).3 Periodicity (number of maxima per turn).4 Phase shift (�).

[change torsions]: Assign Q-torsion types. Note: The order of atoms (1, 2, 3, 4 or 4, 3,2, 1) is not important.1 Topology atom number of first atom in torsion.

65

1

47

Cl

Br

11

Tutorial Q software

TS

PSRS

From G2 Method∆G‡=13.04 ; ∆G0=-5.35

12

Tutorial Q software

Analyse

Qfep

Free energy calc. input

Qcal

Free energy data

structure, averages,etc

51#numberoffiles/frames20#numberofstatesandoff-diagonals0.5961612350#kTandnumberofpointstoskip51#numberofbins10#minimumpointsforbin2.345#gasphaseshift1#numberofdiagonalelements

1276.543000#st1and2,A=Hij,mu=eta=r0=01-1#linearcomb.ofstates(E=e1-e2)

fep_000_1.000.enfep_001_0.980.en.........fep_050_0.000.enstop

V12 = Aexp{−a(r1 − r10 )2}

13

Tutorial Q software

PSRS

Bonds being Broken/Formed

14

Tutorial Q software

Bonds being Broken/Formed

Trajectory VMD

15

Tutorial Q software

Analyse

Qfep

Free energy calc. input

Qcal

Free energy data

structure, averages,etc

----------QAnalyseMapsSUMMARY---------------------Analysedwithversion:0.1.10

DIRNAMESdG#dG0RS_lTS_lPS_l1-RS_000/13.35-5.580.84000.50000.12002-TS_000/12.94-4.760.86000.50000.12003-PS_000/12.18-6.490.82000.50000.1200

Assumingnormaldistribution...

N=3MeanSt.devMediandG#12.820.5912.94dG0-5.610.87-5.58

From G2 Method

∆G‡=13.04 ; ∆G0=-5.35

16

Tutorial Q software

17

Tutorial Q software

18

Tutorial Q software

19

Tutorial Q software

exp{��Gi(Xn)�} = exp{��G(�m)�}hexp{�(✏i(X

n)� "m(Xn))�}im

20

Different Flavours of VB

Program Capabilities Website Comments Reference

MOLARIS-XG

EVB, FEP, AC http://laetro.usc.edu/software.html

Available for purchase from the USC

Warshel and coworkers

Q EVB, FEP, LIE http://xray.bmc.uu.se/~aqwww/q/

Free for academic use. Available upon request

Åqvist and coworkers

VM/MM VB/MMDE-VB/MM

Available upon request avitalsh@ekmd.huji.ac.il.

Interface program that communicates between XMVB and MOLARIS

Shurki and coworkers

MS-EVB MS-EVB In house implementation in LAMMPS MD package

Voth and coworkers

Tinker/Charmm

MS-EVB

AMBER Distributed Gaussian EVB http://ambermd.org/

AMBER license is required for GPU version

Case and coworkers