The document describes the Effective Fragment Molecular Orbital (EFMO) method, which blurs the boundary between quantum mechanical and molecular mechanical approaches. EFMO extracts multipoles and polarizabilities from monomer quantum calculations to model polarization effects classically. It also performs dimer quantum calculations to model covalent and non-Coulomb interactions directly. EFMO has been implemented in GAMESS and shows improved accuracy over the Fragment Molecular Orbital method for modeling the 20-residue Trp cage peptide.

1. Blurring
the
boundary
between
linear
scaling
QM,
QM/MM
and
polarizable
force
fields
The
Effec(ve
Fragment
Molecular
Orbital
Method
Jan
H.
Jensen,
Casper
Steinmann,
Mikael
Wisto1
Ibsen,
Kasper
Tho1e
University
of
Copenhagen
Dmitri
Fedorov
AIST,
Japan
1

2. The
Fragment
Molecular
Orbital
(FMO2)
method
(and
most
other
fragmentaEon
methods)
2

3. The
Fragment
Molecular
Orbital
(FMO2)
method
(and
most
other
fragmentaEon
methods)
Many-­‐body
PolarizaEon:
Monomer
SCF
in
the
Coulomb
field
of
all
other
monomers
Iterated
to
self-­‐consistency
3

4. The
Fragment
Molecular
Orbital
(FMO2)
method
(and
most
other
fragmentaEon
methods)
Non-­‐Coulomb
effects:
Dimer
SCF
in
the
Coulomb
field
of
all
other
monomers
Iterated
to
self-­‐consistency
4

5. The
Fragment
Molecular
Orbital
(FMO2)
method
(and
most
other
fragmentaEon
methods)
Coulomb
effects:
Coulomb
energy
in
the
Coulomb
field
of
all
other
monomers
5

6. The
EffecEve
Fragment
Molecular
Orbital
(EFMO)
method
(Using
ideas
from
the
EffecPve
Fragment
PotenPal
(EFP)
method)
Monomer
SCF
in
the
gas
phase
Extract
mulPpoles
and
dipole
polarizability
6

7. The
EffecEve
Fragment
Molecular
Orbital
(EFMO)
method
(Using
ideas
from
the
EffecPve
Fragment
PotenPal
(EFP)
method)
Many-­‐body
polarizaEon
Computed
classically
using
induced
dipoles
for
enPre
system
7

8. The
EffecEve
Fragment
Molecular
Orbital
(EFMO)
method
(Using
ideas
from
the
EffecPve
Fragment
PotenPal
(EFP)
method)
Coulomb
and
Non-­‐Coulomb
effects
dimer
SCF
in
the
gas
phase
8

9. The
EffecEve
Fragment
Molecular
Orbital
(EFMO)
method
(Using
ideas
from
the
EffecPve
Fragment
PotenPal
(EFP)
method)
Coulomb
effects
Computed
using
staPc
mulPpoles
9

10. MP2
(DFT
doesn’t
scale
well)
+
0
10

11. Covalent
FragmentaEon
(ElectrostaPc
screening
crucial)
11

12. Implemented
in
GAMESS
With
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
Pme
spent
in
MP2
dimers)
12

13. To
Do
QM/”MM”
PCM
Large
parts
of
MM
region
o1en
frozen
=
Requires
only
monomer
gas
phase
calculaPons
for
that
region
=
Very
fast
13

14. To
Do
Flexible
EFP/Polarizable
“Force
Field”
covalent
dimers
∑ (E )
N
E EFMO = ∑ EI0 + 0
IJ − EI0 − EJ − EIJ
0 POL
I IJ
( )
N
+ ∑ EIJ + EIJ /CT + EIJ + Etot
ES XR Disp POL
IJ
Important
miscellanea
EFMO
GUI:
FRAGIT
(Mikael
Ibsen)
TS
search
algorithms
(Kasper
Tho1e)
14

15. Funding:
EU
(IRENE
collab
program)
Thank
You!
QuesEons
Now?
QuesEons
Later?
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a
comment
on
hgp://proteinsandwavefuncEons.blogspot.com/2011/07/my-­‐presentaPon-­‐for-­‐watoc-­‐2011.html
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