theory of hybrid quantum mechanics/molecular mechanics...
TRANSCRIPT
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Theory of Hybrid Quantum Mechanics/Molecular Mechanics
Methods (QM/MM)
CHEM 4021/8021 Video VII.i
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Motivation
Gain an understanding of solvent structure …or protein environment, etc.
While maintaining the ability to make and break bonds
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What about solvent structure?
• Can we treat the solvent with MM and the solute with QM?
QM MM
Energy Expression:
Ecomplete = EQM + EMM + EQM/MM
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Partion the Energy Expression
• EQM
• EMM usual Force Field Terms
QM MM
Energy Expression:
Ecomplete = EQM + EMM + EQM/MM
HQM = !12
µ "i2 !
i# ! µ
Zk
rk!
k# +Gµ!
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Partion the Energy Expression
• EQM
• EMM usual Force Field Terms
• EQM/MM Core challenge in QM/MM methods
QM MM
Energy Expression:
Ecomplete = EQM + EMM + EQM/MM
HQM = !12
µ "i2 !
i# ! µ
Zk
rk!
k# +Gµ!
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Partion the Energy Expression
• EQM/MM
• One electron interaction terms and electrostatics for interaction between QM and MM regions
• Point Charges! Must add non-bonded terms
QM
MM
Energy Expression:
Ecomplete = EQM + EMM + EQM/MM
HQM /MM = ! µZk
rk!
k" +
ZKZk
rKrkK ,k
MM ,QM
"
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Partion the Energy Expression
• Boundaries Through Space
• Boundaries Through Bonds
QM
MM
Energy Expression:
Ecomplete = EQM + EMM + EQM/MM
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Unpolarized Interactions
• Compute the QM/MM interaction energy in a similar way to non-bonded FF interactions
• Use standard Lennard-Jones combining rules and assume the QM ! and " values are the same for the atom type in the FF.
• # is a parameter to deal with charged versus neutral molecules to treat solvent polarization
HQM /MM =!qi
CM1qjrijj
Solvent
!i
Solute
! + 4"ij# ij12
rij12 "
# ij6
rij6
#
$%%
&
'((
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Unpolarized Interactions
• Example: Kaminski and Jorgensen’s AM1/OPLS/CM1 (AOC) – AM1 for the solute (Perform MC simulation) – OPLS for the solvent – Charges (qi) for the solute are from the CM1 charge model – Treats polar solvation effects well (e.g. rotameric
equilibria) but not as good for non-polar solvents – Treats solvation free energy effects along a reaction
coordinate
HQM /MM =!qi
CM1qjrijj
Solvent
!i
Solute
! + 4"ij# ij12
rij12 "
# ij6
rij6
#
$%%
&
'((
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Polarized/Unpolarized Interactions
• Allow the environment (MM part) to polarize the QM part
• Separate the interaction of the MM part with the solute electrons and the solute nuclei
HQM /MM =qmrimm
MMAtoms
!i
SoluteElectrons
! +Zkqmrkm
+ 4!km" km12
rkm12 "
" km6
rkm6
#
$%
&
'(
)
*+
,
-.
k
MMAtoms
!k
Solutenuclei
!
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Polarized/Unpolarized Interactions
• HMM (Traditional FF) • HQM/MM (Separated electrostatic + nonbonded part)
• How does HQM change?
HQM = !
12
µ "i2 !
i# ! µ
Zk
rk!
k# +Gµ!
Hcomplete = HQM + HMM + HQM/MM
HQM = !12
"i2
i
N
# !Zk
rik!
k
SoluteNuclei
#i
N
# qmrim+
1riji< j
#m
MMAtoms
#i
N
# +ZkZlrklk<l
#
Recall from earlier
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Fully Polarized Interactions
• Use a polarizable FF where each MM atom type/molecule is assigned a polarizability tensor, #
• Allow for induced dipoles, µind=#E, where E is the electric field
• Allow the induced dipoles to interact with QM system
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Theory of Hybrid Quantum Mechanics/Molecular Mechanics
Methods (QM/MM)
CHEM 4021/8021 Video VII.ii
![Page 14: Theory of Hybrid Quantum Mechanics/Molecular Mechanics ...pollux.chem.umn.edu/8021/Lectures/QM_MM_12.pdf · Integrated Molecular Orbital Molecular Mechanics Method (IMOMM) • Align](https://reader035.vdocuments.net/reader035/viewer/2022062402/5ede1cd9ad6a402d66696672/html5/thumbnails/14.jpg)
Partitions that cross covalent bonds
• What if we don’t want to treat this: • But THIS! Solute/QM
Solvent/MM
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Partitions that cross covalent bonds Can we consider the bulky portions of the
ligand as MM?
How will we compute the energy if the partition
crosses covalent bonds?
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Partitions that cross covalent bonds How will we compute the
energy if the partition crosses covalent bonds?
Mechanical Embedding
Ecomplete = EQMsmall + EMM
big !EMMsmall( )
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How will we compute the energy if the partition
crosses covalent bonds?
Mechanical Embedding
Linking Regions:
Partitions that cross covalent bonds
Ecomplete = EQMsmall + EMM
big !EMMsmall( )
CH H
H
H
QM Region
Model System with capping H atom
CH H
H
CHH
HMM
Region
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Partitions that cross covalent bonds How will we compute the
energy if the partition crosses covalent bonds?
Mechanical Embedding
Ecomplete = EQMsmall + EMM
big !EMMsmall( )
Problems:
How do you take the gradient? Do you follow the MM or QM PES?
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Integrated Molecular Orbital Molecular Mechanics Method (IMOMM)
• Align the atoms that the small and large region have in common (e.g. force cut bonds to be along the same vector)
• Within these constraints, write expressions for the gradient as sums of the MM and QM gradients
• Has also been generalized for QM/QM’
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Our own N-layered Integrated molecular Orbital and molecular Mechanics (ONIOM)
This idea can be extended beyond two
layers
Ehigh(Real) $ EONIOM = Elow(Real) + Emedium(Intermediate) + Ehigh(Small) – Elow(Intermediate) – Emedium(Small)
Highest level QM
QMlow
MM
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Theory of Hybrid Quantum Mechanics/Molecular Mechanics
Methods (QM/MM)
CHEM 4021/8021 Video VII.iii
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Beyond Sterics: Electrostatic Embedding
• Example: A large protein where charged residues in the MM region will polarize the QM region
• Extend our idea of a polarized/unpolarized partition for non-bonded terms
• Include terms for the bonds cut by the QM/MM boundary!
QM Region
CH H
H
CHH
HMM
Region
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Beyond Sterics: Electrostatic Embedding
• Cap QM region with H’s. Compute HQM like before.
• Don’t compute for capping H atoms
HQM = !12
"i2
i
N
# !Zk
rik!
k
SoluteNuclei
#i
N
# qmrim+
1riji< j
#m
MMAtoms
#i
N
# +ZkZlrklk<l
#
QM Region
CH H
H
CHH
HMM
Region
CH H
H
H
Model System with capping H atom
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Beyond Sterics: Electrostatic Embedding
• Bond stretching for bonds cut by the QM/MM boundary are treated with MM potential
• Angle bending (atomMM-atomMM-atomQM) are treated with MM potential
• Fictitious bond angles involving capping atom (e.g. atomQM-atomMM-Hcapping) have very large force constants
• Torsions also use MM potential when 2 MM and 2 QM or 3 MM and 1 QM atoms are involved.
• Sometimes charges must be modified as well
QM Region
CH H
H
CHH
HMM
Region
CH H
H
H
Model System with capping H atom
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Case Study: Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis
Lundberg, Kawatsu, Vreven, Frisch, and Morokuma. J. Chem. Comput. Chem. 2008, 5, 220-234.
Two layer ONIOM calculations: B3LYP is the high level of AMBER is the low level
Scheme 1. General Reaction for Isopenicillin N Synthase Including the Proposed [Fe(IV)dO] Intermediatea
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Case Study: Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis
Lundberg, Kawatsu, Vreven, Frisch, and Morokuma. J. Chem. Comput. Chem. 2008, 5, 220-234.
Choosing the Size of the QM Space
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Case Study: Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis
Lundberg, Kawatsu, Vreven, Frisch, and Morokuma. J. Chem. Comput. Chem. 2008, 5, 220-234.
Figure 2. Geometries and spin populations for the intermediate with end-on bound dioxygen in the quintet state (52 INT) optimized using the active-site model (silver) and the ONIOM QM:MM model (blue).
Example of how the size of the QM
region can impact your results
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Case Study: Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis
Lundberg, Kawatsu, Vreven, Frisch, and Morokuma. J. Chem. Comput. Chem. 2008, 5, 220-234.