The document presents the Effective Fragment Molecular Orbital (EFMO) method for calculating interaction energies in large chemical systems. EFMO divides the system into molecular fragments and calculates energies in a fragment-based approach. It computes monomer energies using gas phase self-consistent field calculations to extract properties. It then calculates interaction energies between nearby fragments (within a cutoff distance) using dimer self-consistent field calculations, and long-range electrostatic interactions between all fragment pairs. EFMO provides a parameter-free method for efficiently studying interaction energies in large biochemical systems.

1. Department of Chemistry
The Effective Fragment Molecular Orbital Method:
The development and application of a parameter free force field
Casper Steinmann
Department of Chemistry
University of Copenhagen
Supervisor: Professor Jan H. Jensen
University of Copenhagen, Feb. 12th, 2013
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2. Department of Chemistry
Outline
• Motivation
• Current approaches to treat large systems
• My work
• Applications
• Conclusions and Outlook
University of Copenhagen, Feb. 12th, 2013
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3. Department of Chemistry
Motivation
• Understand and improve enzyme catalysis
• Large systems are problematic in a computer
• Not one go-to program
KE Ranaghan, AJ Mulholland (2010), Int. Rev. Phys. Chem.
University of Copenhagen, Feb. 12th, 2013
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4. Department of Chemistry
Current approaches to treat large systems
QM/MM
Fragment Based
QM Method
MM
And the other ones …
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5. Department of Chemistry
I want to study interaction energies …
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6. Department of Chemistry
Effective Fragment Potential Method (EFP2)
• EFP2 is a model potential derived from first principles
• Multipole moments
• Dipole polarizability tensors
• Among others …
doi: 10.1063/1.472045
doi: 10.1021/jp002747h
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Effective Fragment Potential Method (EFP2)
N N
E EFP 2
=E HF
− ∑ E = ∑ ( EIJ + EIJ + EIJ ) + Etot
0
I
ES XR CT POL
I IJ
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8. Department of Chemistry
The Effective Fragment Potential Method (EFP2)
N N
E EFP 2
=E HF
− ∑ EI = ∑ ( EIJ + EIJ + EIJ ) + Etot
ES XR CT POL
I IJ
Many-body polarization
Computed classically
using induced dipoles
for entire system
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9. Department of Chemistry
I want interaction energies and internal energies …
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10. Department of Chemistry
Fragment Based Methods
Fragment Molecular Orbital (FMO2)
And most other fragmentation methods
N N
E FMO2 = ∑ EI + ∑ (EIJ − EI − EJ )
I IJ
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11. Department of Chemistry
Fragment Based Methods
Fragment Molecular Orbital (FMO2)
And most other fragmentation methods
N N
E FMO2 = ∑ EI + ∑ (EIJ − EI − EJ )
I IJ
Many-body Polarization:
Monomer SCF in the
Coulomb field of all
other monomers
Iterated to
self-consistency
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12. Department of Chemistry
Fragment Based Methods
N N
E FMO2 = ∑ EI + ∑ (EIJ − EI − EJ )
I IJ
Non-Coulomb effects:
Dimer SCF in the
Coulomb field of all
other monomers
Iterated to
self-consistency
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13. Department of Chemistry
Fragment Based Methods
N N
E FMO2 = ∑ EI + ∑ (EIJ − EI − EJ )
I IJ
Coulomb effects:
Coulomb energy in the
Coulomb field of all
other monomers
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14. Department of Chemistry
Fragment Based Methods
• The FMO2 method
• All monomers converge in the Coulomb field of all other
monomers iteratively.
• Dimers converge in the static Coulomb field
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15. Department of Chemistry
I want interaction energies and internal energies …
FAST
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16. Department of Chemistry
Fragment Based Methods
N RI ,J ≤Rcut RI ,J >Rcut
E EFMO = ∑ EI0 + ∑ (EIJ − EI0 − EJ0 − EIJ ) +
0 POL
∑ ES POL
EIJ +Etot
I IJ IJ
Monomer SCF in the
gas phase
Extract multipoles,
and dipole polarizabilities
PLoS ONE 2012, 7:e41117
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17. Department of Chemistry
Fragment Based Methods
N RI ,J ≤Rcut RI ,J >Rcut
E EFMO = ∑ EI0 + ∑ (EIJ − EI0 − EJ0 − EIJ ) +
0 POL
∑ ES POL
EIJ +Etot
I IJ IJ
Many-body polarization
Computed classically
using induced dipoles
for entire system
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18. Department of Chemistry
Fragment Based Methods - EFMO
N RI ,J ≤Rcut RI ,J >Rcut
E EFMO = ∑ EI0 + ∑ (EIJ − EI0 − EJ0 − EIJ ) +
0 POL
∑ ES POL
EIJ +Etot
I IJ IJ
Coulomb and
Non-Coulomb effects
dimer SCF in the
gas phase
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19. Department of Chemistry
Fragment Based Methods - EFMO
N RI ,J ≤Rcut RI ,J >Rcut
E EFMO = ∑ EI0 + ∑ (EIJ − EI0 − EJ0 − EIJ ) +
0 POL
∑ ES POL
EIJ +Etot
I IJ IJ
Coulomb effects
Computed using
static multipoles
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20. Department of Chemistry
Fragment Based Methods - EFMO
N RI ,J ≤Rcut
E COR = ∑ EICOR + ∑ (EIJ − EICOR − EJ ) +0
COR COR
I IJ
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21. Department of Chemistry
Covalent Fragmentation - EFMO
University of Copenhagen, Feb. 12th, 2013 PLoS ONE 2012, 7:e41117
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Software to help setup calculations: FragIt
• Use SMARTS to find places to break bonds
PLoS ONE 2012, 7:e44480
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23. Department of Chemistry
Software to help setup calculations: FragIt
• Use SMARTS to find places to break bonds
Chignolin (10 residues)
PLoS ONE 2012, 7:e44480
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24. Department of Chemistry
Fragment Based Methods - EFMO Gradients
Trp cage (20 residues)
2 residues/fragment
EFMO FMO2
Error in energy -4.3 6.4 kcal/mol
MP2/6-31G(d) gradient 314 409 minutes
20 cores
(most time spent in MP2 dimers)
PLoS ONE 2012, 7:e41117
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25. Department of Chemistry
Fragment Based Methods - EFMO QM/”MM”
E EFMO = EA + EA / F + EF
RA,J ≤Rcut RA,J >Rcut
E EFMO
=E + 0
A ∑ (E 0
AJ
0 0
−E −E −E
A J
POL
AJ )+ ∑ ES POL
E AJ + Etot
J∈F J∈F
Active
Frozen
University of Copenhagen, Feb. 12th, 2013 arxiv.org/abs/1212.6172
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Proof of concept – chorismate mutase
ONIOM: MP2/cc-pVDZ:EFMO-RHF/6-31G(d)
16 Å
ΔH ≠ = 18 vs 13 (exp) kcal/mol
University of Copenhagen, Feb. 12th, 2013 arxiv.org/abs/1212.6172
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Conclusion and Outlook
• Fast polarizable force field
• Applicable to any system
EFMO/PCM
Fully flexible EFPs
N RI ,J ≤Rcut RI ,J >Rcut
E FIEFMO
= ∑E + 0
I ∑ 0 0 0
(E − E − E − E
IJ I J
POL
IJ )+ ∑ ES CT XR Disp POL
(EIJ + EIJ + EIJ + EIJ ) +Etot
I IJ IJ
Combine MP2:RHF-D optimization
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28. Department of Chemistry
Acknowledgements
• Jan Jensen
• Dmitri Fedorov, AIST, Japan
• Colleagues at the Department of Chemistry
• Friends and Family
• In silico Rational Engineering of Novel Enzymes (IRENE)
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29. Department of Chemistry
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30. Department of Chemistry
Thank you for listening
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