The Fragment Molecular Orbital method
coded by D.G. Fedorov, M.Chiba, T. Nagata and K. Kitaura at
Research Institute for Computational Sciences (RICS)
National Institute of Advanced Industrial Science
and Technology (AIST)
AIST Tsukuba Central 2, Umezono 1-1-1,
Tsukuba, 305-8568, Japan.
with code contributions by:
N. Asada (Kyoto U.), C. H. Choi (Kyungpook U.),
C. Steinmann (U. Copenhagen).
The method was proposed by Professor Kitaura and coworkers
in 1999, based on the Energy Decomposition Analysis (EDA,
sometimes called the Morokuma-Kitaura energy
decomposition). The FMO method is completely independent of
and bears no relation to:
1. Frontier molecular orbitals (FMO),
2. Fragment molecular orbitals (FMO).
The latter name is often used for the process of
construction of full molecular orbitals by combining MO
diagrams for parts of a molecule, ala Roald Hoffmann.
The effective fragment molecular orbital method (EFMO) is
closely related to but also bears significant difference to
FMO, and discussed below.
The FMO program was interfaced with GAMESS and follows
general GAMESS guidelines for code distribution and usage.
The users of the FMO program are requested to cite the
FMO3-RHF paper as the basic FMO reference,
D.G. Fedorov, K. Kitaura,
J. Chem. Phys. 120, 6832-6840(2004)
and other papers as appropriate (see below).
The basic idea of the method is to acknowledge the fact the
exchange and self-consistency are local in most molecules
(and clusters and molecular crystals), which permits
treating remote parts with Coulomb operators only, ignoring
the exchange. This idea further evolves into doing
molecular calculations, piecewise, with Coulomb fields due
to the remaining parts. In practice one divides the
molecule into fragments and performs n-mer calculations of
these in the Coulomb field of other fragments (n=1,2,3).
There are no empirical parameters, and the only departure
from ab initio rigor is the subjective fragmentation. It
has been observed that if performed physically reasonably,
the fragmentation scheme alters the results very little.
What changes the accuracy the most is the fragment size,
which also determines the computational efficiency of the
method.
The first question is how to get started. The easiest way
to prepare an FMO input file for GAMESS is to use the free
GUI software Facio, developed by M. Suenaga at Kyushu
University. It can do molecular modeling, automatic
fragmentation of peptides, nucleotides and saccharides and
create GAMESS/FMO input files:
http://www1.bbiq.jp/zzzfelis/Facio.html
A web bsed interface to FMO is maintained by Y. Alexeev
(Argonne National Lab):
http://www.fmo-portal.info (shut down at present)
Alternatively, if you prefer a command line interface, and
your molecule is a protein found in the PDB
http://www.rcsb.org/pdb
you can simply use the fragmentation program "fmoutil" that
is provided with GAMESS in tools/fmo, or the FMO home page
http://staff.aist.go.jp/d.g.fedorov/fmo/main.html
If you have a cluster of identical molecules, you can
perform fragmentation with just one keyword ($FMO NACUT=).
Computationally, it is always better to partition in a
geometrical way (close parts together), so that the
distance-based approximations are more efficient. The
accuracy depends mainly upon the locality of the density
distribution, and the appropriateness of partitioning it
into fragments. There is no simple connexion between the
geometrical proximity of fragmentation and accuracy.
Supposing you know how to fragment, you should choose a
basis set and fragment size. We recommend 2 amino acid
residues or 2-4 water molecules per fragment for final
energetics (or, even better, three-body with 1 molecule or
residue per fragment). For geometry optimizations one may
be able to use 1 res/mol per fragment, especially if
gradient convergence to about 0.001 is desired. Note that
although it was claimed that FMO gradient is analytic
(Chem. Phys. Lett., 336 (2001), 163.) it is not so. Neither
theory nor program for fully analytic gradient has been
developed, to the best of our knowledge up to this day
(December 21, 2006). The gradient implementation is nearly
analytic, meaning three small terms are missing, one which
can now be included using MODGRD=8+2. The magnitude of
these small terms depends upon the fragment size (larger
fragments have smaller errors). It has been our experience
that in proteins with 1 residue per fragment one gets 1e-
3...1e-4 error in the gradient, and with 2 residues per
fragment it is about 1e-4...1e-5. If you experience energy
rising during geometry optimizations, you can consider two
countermeasures:
1. increase approximation thresholds, e.g. RESPPC from
2.0->2.5, RESDIM from 2.0 -> 2.5.
2. increase fragment size (e.g. by merging very small
fragments with their neighbors).
Finally a word of caution: optimizing systems with charged
fragments in the absence of solvent is frequently not a
good idea: oppositely charged fragments will most likely
seek each other, unless there is some conformational
barrier.
For basis sets you should use general guidelines and your
experience developed for ab initio methods. There is a file
provided (HMOs.txt) that contains hybrid molecular orbitals
(HMO) used to divide the MO space along fragmentation
points at covalent bonds. If your basis set is not there
you need to construct your own set of HMOs. See the example
file makeLMO.inp for this purpose.
Next you choose a wave function type. At present one can
use RHF, DFT, MP2, CC, and MCSCF (all except MCSCF support
the 3-body expansion). Geometry optimization can be
performed with all of these methods, except CC.
Note that presence of $FMO turns FMO on.
Surfaces and solids
Until 2008, for treating covalently connected fragments,
FMO had fully relaxed electron density of the detached
bonds. This method is now known as FMO/HOP (HOP=hybrid
orbital projection operator). It allows for a full
polarization of the system and is thus well suited to very
polar systems, such as proteins with charged residues. In
2008, an alternative fragmentation was suggested, based on
adaptive frozen orbitals (AFO), FMO/AFO. In it, the
electron density for each detached bond is first computed
in the automatically generated small model system (with the
bond intact), and in the FMO fragment calculations this
electron density is frozen. It was found that FMO/AFO works
quite well for surfaces and solids, where there is a dense
network of bonds to be detached in order to define
fragments (and the detached bonds interact quite strongly).
In addition, by restricting the polarization, FMO/AFO was
found to give a more balanced properties for large basis
sets (triple-zeta with polarization or larger), or in
comparing different isomers. However, for proteins with
charged residues the original FMO/HOP scheme has a better
accuracy (except large basis sets). At this point, FMO/AFO
was applied to zeolites only, and some more experience is
needed to give more practical advice to applications.
FMO/AFO is turned on by a nonzero rafo(1) parameter (rafo
array provides the thresholds to build model systems).
FMO variants
In 2007, Dahlke et al. introduced the Electrostatically
Embedded Many-Body Expansion method (see E. E. Dahlke and
D. G. Truhlar, J. Chem. Theory Comput. 4, 1-6 (2008) for
more recent work). This method is essentially FMO with the
RESPPC approximation (point charges for the electrostatic
field) applied to all fragments, with the further provision
that these charges may be defined at will (whereas RESPPC
uses Mulliken charges), and they are kept frozen (not
optimized, as in FMO). Next, Kamiya et al. suggested a fast
electron correlation method (M. Kamiya, S. Hirata, M.
Valiev, J. Chem. Phys. 128, 074103 (2008)), where again FMO
with the RESPPC approximation to all fragments is applied
with the further provision that the charges are derived
from the electrostatic potential (so called ESP charges),
and BSSE correction is added. The Dahlke's method was
generalized in GAMESS with the introduction of an arbitrary
hybrid approach, in which some fragments may have fixed and
some variationally optimized charges. This implementation
was employed in FMO-TDDFT calculations of solid state
quinacridone (see Ref. 16 below) by using DFT/PBC frozen
charges. The present energy only implementation is mostly
intended for such cases as that (i.e., TDDFT), and some
more work is needed to finish it for general calculations.
To turn this on, set RESPPC=-1 and define NOPFRG for frozen
charge fragments to 64, set frozen charges in ATCHRG.
Another FMO-like method is EFMO, see its own subsection
below. EFMO itself is related to several methods (PMISP: P.
Soederhjelm, U. Ryde, J. Phys. Chem. A 2009, 113, 617?627;
another is G. J. O. Beran, J. Chem. Phys. 2009, 130,
164115).
Effective fragment molecular orbital method (EFMO)
EFMO has been formulated by combining the physical models
in EFP and FMO, namely, in EFMO, fragments are computed
without the ESP (of FMO), and the polarization is estimated
using EFP models of fragment polarizabilities, which are
computed on the fly, so this can be thought of as
automatically generated potentials in EFP. Consequently,
close dimers are computed quantum-mechanically (without
ESP) and far dimers are computed using the electrostatic
multipole models of EFP. At present, only vacuum closed-
shell RHF and DFT are supported, for energy and gradient;
and only molecular clusters can be computed (no systems
with detached bonds). From the user point of view, EFMO
functionality is very intensively borrowed from FMO, and
the calculation setup is almost identical. Most additional
physical models such as PCM are not supported in EFMO. EFMO
should not be confused with FMO/EFP. The latter uses FMO
for some fragments and EFP for others. EFMO uses the same
model (EFMO), which is neither FMO nor EFP. For
approximations, EFMO at present has only RESDIM.
EFMO references are:
1. Effective Fragment Molecular Orbital Method: A Merger of
the Effective Fragment Potential and Fragment Molecular
Orbital Methods.
C. Steinmann, D. G. Fedorov, J. H. Jensen
J. Phys. Chem. A 114, 8705-8712 (2010).
2. The Effective Fragment Molecular Orbital Method for
Fragments Connected by Covalent Bonds.
C. Steinmann, D. G. Fedorov, J. H. Jensen
PLoS One, 7, e41117(2012).
3. Mapping enzymatic catalysis using the effective fragment
molecular orbital method: towards all ab initio
biochemistry.
C. Steinmann, D. G. Fedorov, J. H. Jensen
PLoS One 8, e60602 (2013).
Guidelines for approximations with FMO3
Three sets are suggested, for various accuracies:
low: resppc=2.5 resdim=2.5 ritrim(1)=0.001,-1,1.25
medium: resppc=2.5 resdim=3.25 ritrim(1)=1.25,-1,2.0
high: resppc=2.5 resdim=4.0 ritrim(1)=2,2,2
For correlated runs, add one more value to ritrim, equal to
the third element (i.e., 1.25 or 2.0). Note that gradient
runs do not support nonzero RESDIM and thus use RESDIM=0 if
gradient is to be computed. The "low" level of accuracy
for FMO3 has an error versus full ab initio similar to
FMO2, except for extended basis sets (6-311G** etc) where
it is substantially better than FMO2. Thus the low level is
only recommended for those large basis sets, and if a
better level cannot be afforded. The medium level is
recommended for production FMO3 runs; the high level is
mostly for accuracy evaluation in FMO development. The
cost is roughly: 3(low), 6(medium), 12(high). This means
that FMO3 with the medium level takes roughly six times
longer than FMO2.
Some of the default tolerances were changed as of January
2009, when FMO 3.2 was included in GAMESS. In general,
stricter parameters are now enforced when using FMO3, which
of course is intended to produce more accurate results. If
you wish to reproduce earlier results with the new code,
use the input to revert to the earlier values:
former -> FMO2 or FMO3 (as of 1/2009)
RESPPC: 2.0 2.0 2.50
RESDIM: 2.0 2.0 3.25
RCORSD: 2.0 2.0 3.25
RITRIM: 2.0,2.0,2.0,2.0 -> 1.25,-1.0,2.0,2.0 (FMO3 only)
MODESP: 1 0 1
MODGRD: 0 10 0
and two other settings which are not strictly speaking FMO
keywords may change FMO results:
MTHALL: 2 -> 4 (FMO/PCM only, see $TESCAV)
DFT grid: spherical -> Lebedev (FMO-DFT only, see $DFT)
Note that FMO2 energies printed during a FMO3 run will
differ from those in a FMO2 run, due to the different
tolerances used.
How to perform FMO-MCSCF calculations
Assuming that you are reasonably acquainted with ab initio
MCSCF, only FMO-specific points are highlighted. The active
space (the number of orbitals/electrons) is specified for
the MCSCF fragment. The number of core/virtual orbitals for
MCSCF dimers will be automatically computed. The most
important issue is the initial orbitals for the MCSCF
monomer. Just as for ab initio MCSCF, you should exercise
chemical knowledge and provide appropriate orbitals. There
are two basic ways to input MCSCF initial orbitals:
A) through the FMO monomer density binary file
B) by providing a text $VEC group.
The former way is briefly described in INPUT.DOC (see
orbital conversion). The latter way is really identical to
ab initio MCSCF, except the orbitals should be prepared for
the fragment (so in many cases you would have to get them
from an FMO calculation). Once you have the orbitals, put
them into $VEC1, and use the IJVEC option in $FMOPRP (e.g.,
if your MCSCF fragment is number 5, you would use $VEC1 and
ijvec(1)=5,0). For two-layer MCSCF the following
conditions apply. Usually one cannot simply use F40
restart, because its contents will be overwritten with RHF
orbitals and this will mess up your carefully chosen MCSCF
orbitals. Therefore, two ways exist. One is to modify A)
above by reordering the orbitals with something like
$guess guess=skip norder=1 iorder(28)=29,30,31,32,28 $end
Then the lower RHF layer will converge RHF orbitals that
you reorder with iorder in the same run (add 512 to nguess
in $FMO). This requires you know how to reorder before
running the job so it is not always convenient. Probably
the best way to run two-layer MCSCF is verbatim B) above,
so just provide MCSCF monomer orbitals in $VEC1. Finally,
it may happen that some MCSCF dimer will not converge.
Beside the usual MCSCF tricks to gain convergence as the
last resort you may be able to prepare good initial dimer
orbitals, put them into $VEC2 ($VEC3 etc) and read them
with ijvec. SOSCF is the preferred converger in FMO, and
the other one (FULLNR) has not been modified to eradicate
the artefacts of convergence (due to detached bonds). In
the bad cases you can try running one or two monomer SCF
iterations with FULLNR, stop the job and use its orbitals
in F40 to do a restart with SOSCF. We also found useful to
set CASDII=0.005 and nofo=10 in some cases running FOCAS
longer to get better orbitals for SOSCF.
How to perform multilayer runs
For some fragments you may like to specify a different
level of electron correlation and/or basis set. In a
typical case, you would use high level for the reaction
center and a lower level for the remaining part of the
system. The set up for multilayer runs is very similar to
the unilayer case. You only have to specify to what layer
each fragment belongs and for each layer define DFTTYP,
MPLEVL, SCFTYP as well as a basis set. If detached bonds
are present, appropriate HMOs should be defined. See the
paragraph above for multilayer MCSCF. Currently geometry
optimizations of multilayer runs require adding 128 to
NGUESS, if basis sets in layers differ from each other.
How to mix basis sets in FMO
You can mix basis sets in both uni and multilayer cases.
The difference between a 2-layer run with one basis set per
layer and a 1-layer run with 2-basis sets is significant:
in the former case the lower level densities are converged
with all fragments computed at the lower level. In the
latter case, the fragments are converged simultaneously,
each with its own basis set. In addition, dimer corrections
between layers will be computed differently: with the lower
basis set in the former case and with mixed basis set in
the latter. The latter approach may result in unphysical
polarization, so mixing basis sets is mainly intended to
add diffuse functions to anionic (e.g., carboxyl) groups,
not as a substitute for two-layer runs.
How to perform FMO/PCM calculations
Solvent effects can be taken into account with PCM. PCM in
FMO is very similar to regular PCM. There is one basic
difference: in FMO/PCM the total electron density that
determines the electrostatic interaction is computed using
the FMO density expansion up to n-body terms. The cavity
is constructed surrounding the whole molecule, and the
whole cavity is used in each individual m-mer calculation.
There are several levels of accuracy (determined by the "n"
above), and the recommended level is FMO/PCM[1(2)],
specified by:
$pcm ief=-10 icomp=2 icav=1 idisp=1 ifmo=2 $end
$fmoprp npcmit=2 $end
$tescav ntsall=240 $end
$pcmcav radii=suahf $end
Many PCM options can be used as in the regular PCM. The
following restrictions apply:
IEF may be only -3 or -10, IDP must be 0.
Multilayer FMO runs are supported. Restarts are limited to
IREST=2, and in this case PCM charges (the ASCs) are not
recycled. However, the initial guess for the charges is
fairly reasonable, so IREST=2 may be useful although
reading the ASCs may be implemented in future.
Note for advanced users. IFMO < NBODY runs are permitted.
They are denoted by FMOm/PCM[n], where m=NBODY and n=IFMO.
In FMOm/PCM[n], the ASCs are computed with n-body level.
The difference between FMO2/PCM[1] and FMO2/PCM[1(2)] is
that in the former the ASCs are computed at the 1-body
level, whereas for the former at the 2-body level, but
without self-consistency (which would be FMO2/PCM[2]).
Probably, FMO3/PCM[2] should be regarded as the most
accurate and still affordable (with a few thousand nodes)
method. However, FMO3/PCM[1(2)] (specified with NBODY=3,
IFMO=2 and NPCMIT=2) is much cheaper and slightly less
accurate than FMO3/PCM[2]. FMO3/PCM[3] is the most
accurate and expensive level of all.
How to perform FMO/EFP calculations
Solvent effects can also be taken into account with the
Effective Fragment Potential model. The presence of both
$FMO and $EFRAG groups selects FMO/EFP calculations. See
the $EFRAG group and the $FMO group for details.
In the FMO/EFP method, the Quantum Mechanical part of the
calculation in the usual EFP method is replaced by the FMO
method, which may save time for large molecules such as
proteins.
In the present version, only FMOn/EFP1 (water solvent only)
is available for RHF, DFT and MP2. One can use the MC
global optimization technique for FMO/EFP by RUNTYP=GLOBOP.
Of course, the group DDI (GDDI) parallelization technique
for the FMO method can be used.
Geometry optimization or saddle point search for FMO
The standard optimizers in GAMESS are now well
parallelized, and thus recommended to be used with FMO up
to the limit hardwired in GAMESS (2000 atoms). In practice,
if more than about 1000 atoms are present, numeric Hessian
updates often result in the improper curvature and
optimization stops. One can either do a restart, or use
RUNTYP=OPTFMO (which does not diagonalize the Hessian).
RUNTYP=OPTIMIZE applies to Cartesian coordinates or DLC.
RUNTYP=OPTFMO works only with Cartesian coordinates. If
your system has more than 2000 atoms you can consider
RUNTYP=OPTFMO, which can now use Hessian updates and
provides reasonable way to optimize although it is not as
good as the standard means in RUNTYP=OPTIMIZE.
A transition state search for FMO can be performed with
RUNTYP=SADPOINT using either Cartesian coordinates or DLC.
IRC calculations can be performed.
FMO hessian calculations
Analytic FMO Hessian with RUNTYP=HESSIAN may be computed
for RHF, ROHF, UHF, RDFT, and UDFT in the gas phase (no
PCM, EFP etc), provided that RESPCC is set to 0.
Molecular dynamics with FMO
MD can be run for any FMO method, which has the gradient
implemented. However, in many cases the approximations in
the gradient for a particular method may lead to large
discrepancies in MD. The following methods have a fully
analytic gradient (which has to be turned on with $FMO
keyword MODGRD=42): FMO-RHF, FMO-MP2, FMO-RHF/EFP; the
following condition should be satisfied: no ESP
approximations, RESPPC=0.
Pair interaction energy decomposition analysis (PIEDA)
PIEDA can be performed for the PL0 and PL states. The PL0
state is the electronic state in which fragments are
polarised by the environment in its free (noninteracting)
state. The simplest example is that in a water cluster,
each molecule is computed in the electrostatic field
exerted by the electron densities of free water molecules.
The PL state is the FMO converged monomer state, that is,
the state in which fragments are polarised by the self-
consistently converged environment. Namely, following the
FMO prescription, fragments are recomputed in the external
field, until the latter converges. Using the PL0 state
requires a series of separate runs; and it also relies on a
"free state" which can be defined in many ways for
molecules with detached covalent bonds.
What should be done to do the PL0 state analysis?
1. run FMO0.
This computes the free state for each fragment, and those
electron densities are stored on file 30 (to be renamed
file 40 and reused in step 3).
2. compute BDA energies (if detached bonds are present),
using sample files in tools/fmo/pieda. This corrects for
artifacts of bond detaching, and involves running a model
system like H3C-CH3, to amend for C-C bond detaching.
3. Using results of (1) and (2), one can do the PL0
analysis. In addition to pasting the data from the two
punch files in steps 1,2 and the density file in step 1
should be provided.
What should be done to do the PL state analysis? The PL
state itself does not need either the free state or PL0
results. However, if the PL0 results are available,
coupling terms can be computed, and in this case IPIEDA is
set to 2; otherwise to 1.
So the easiest and frequently sufficient way to run PIEDA
is to set IPIEDA=1 and do not provide any data from
preceding calculations. The result of a PIEDA calculation
is a set of pair interaction energies (interfragment
interaction energies), decomposed into electrostatic,
exchange-repulsion, charge transfer and dispersion
contributions.
Finally, PIEDA (especially for the PL state) can be thought
of as FMO-EDA, EDA being the Kitaura-Morokuma decomposition
(RUNTYP=MOROKUMA). In fact, PIEDA (for the PL state) in
the case of just two fragments of standalone molecules is
entirely equivalent to EDA, which can be easily verified,
by running the full PIEDA analysis (ipieda=2). Note that
PIEDA can be run as direct SCF, whereas EDA cannot be, and
for large fragments PIEDA code can be used to perform EDA.
Also, EDA in GAMESS has no explicit dispersion.
In 2012, PIEDA/PCM was developed describing the solvent
screening. RO-PIEDA based on RO-(HF, MP2 or CC) may be
used for radicals. Grimme's dispersion models may be used
in PIEDA.
Excited states
At present, one can use CI, MCSCF, or TDDFT to compute
excited states in FMO. MCSCF is discussed separately
above, so here only TDDFT and CI are explained. They are
enabled by setting the IEXCIT option (EXCIT(1) defines the
excited state's fragment ID).
Two levels are implemented for TDDFT (FMO1-TDDFT and FMO2-
TDDFT). In the former, only monomer TDDFT calculations are
performed, whereas the latter adds pair corrections from
TDDFT dimers. PCM may be used for solvent effects with
TDDFT (PCM[1] is usually sufficient).
CI can only be done for CIS at the monomer level (nbody=1),
FMO1-CIS. The set-up for CI is similar to that for TDDFT.
Selective and sussystem FMO
Sometimes, one is interested only in some pair
interactions, for example, between ligand and protein, or
the opposite, only pair interactions within ligand. This
saves a lot of CPU time by omitting all other pair
calculations, but does not give the total properties. To
use this feature, define MOLFRG and MODMOL. RUNTYP=ENERGY
only is implemented.
In the subsystem analysis, one can divide fragments into
subsystems and obtain various properties of subsystems.
Frozen domain
To accelerate geometry optimisations, one can specify that
the electronic state of the first layer in a 2-layer FMO
can be computed at the initial geometry and consequently be
frozen. One can define the polarizable buffer (equal to
layer 2) and frozen domain (layer 1). Fragments in the
polarizable buffer which contain the atoms active in
geometry optimisation form the active domain. The
fragments in the active domain should have a nonzero
separation from the frozen domain. In FMO/FD all dimers in
the polarizable buffer are computed; in FMO/FDD only those
dimers which have at least one monomer in the active domain
are computed. FMO/FD and FNI/FDD are only implemented for
RUNTYP=OPTIMIZE. MODFD and IACTAT in $FMO specify
FMO/FD(D) atop of the usual multilayer FMO setup with some
atoms frozen in geometry optimization by the standard means
(i.e., IACTAT in $STATPT). Note that in FMO/FD(D) the
Hessian as used in RUNTYP=OPTIMIZE is formed only for the
atoms in the second layer, so this upper layer should not
have more than the GAMESS limit (currently, 2000 atoms).
IMOMM with FMO
IMOMM (namely, SIMOMM) calculations can be performed with
the "MO" in IMOMM treated using FMO, i.e., this is like
QM/MM but without electronic embedding of QM by MM.
This calculation uses Tinker, a plug-in source code,
available from the GAMESS web site. You should compile and
link in the Tinker plug-in by changing a single line in
comp/compall/lked,
set TINKER=false
into
set TINKER=true
In addition, you should change MAXATM=10 (the maximum
number of atoms in the whole system, as used by Tinker) in
several GAMESS source files into MAXATM=12000 (this number
is used inside Tinker). If you need a larger number,
change it within Tinker as well. After changing this,
recompile and link GAMESS.
The input file style is in general like that of SIMOMM
(q.v.). Different from regular FMO, the atomic coordinates
are given in $TINXYZ, not in $FMOXYZ. The fragmentation in
FMO applies to QM atoms only, selected by IQMATM, and
numbered consequently in FMO, so that INDAT in $FMO applies
to the atoms renumbered from 1 (defined in IQMATM). Other
than $FMOXYZ being superceded by $TINXYZ, the rest of FMO
options is like in normal FMO. IMOMM based on FMO is
usually referred to as FMO/MM for short, although "FMO-
based SIMOMM" is probably easier to understand. The
somewhat tautological FMO-IMOMM has also been used by some.
Covalent boundaries between FMO and MM are supported (via
link atoms). FMO/MM can be used to run geometry
optimizations, whichis really what it is designed for.
Analyzing and visualizing the results
Annotated outputs provided in tools/fmo have matching
mathematical formulae added onto the outputs, for easier
reading.
Facio (http://www1.bbiq.jp/zzzfelis/Facio.html) can plot
various FMO properties such as interaction energies, using
interactive GUI viewers.
To plot orbitals for an n-mer, set NPUNCH=2 in $SCF and
PLTORB=.T. There are several ways to produce cube files
with electron densities. They are described in detail in
tools/fmo/fmocube/README. To plot pair interaction maps,
use tools/fmo/fmograbres to generate CSV files from GAMESS
output, which can be easily read into Gnuplot or Excel.
FMO portal offers tools for visialising FMO results:
http://www.fmo-portal.info/ (shut down at present).
Parallelization of FMO runs with GDDI
The FMO method has been developed within a 2-level
hierarchical parallelization scheme, group DDI (GDDI),
allowing massively parallel calculations. Different groups
of processors handle the various monomer, dimer, and maybe
trimer computations. The processor groups should be sized
so that GAMESS' innate scaling is fairly good, and the
fragments should be mapped onto the processor groups in an
intelligent fashion.
This is a very important and seemingly difficult issue. It
is very common to be able to speed up parallel runs at
least several times just by using GDDI better. First of
all, do not use plain DDI and always employ GDDI when
running FMO calculations. Next, learn that you can and
should divide nodes into groups to achieve better
performance. The very basic rule of thumb is to try to have
several times fewer groups than jobs. Since the number of
monomers and dimers is different, group division should
reflect that fact. Ergo, find a small parallel computer
with 8-32 nodes and experiment changing just two numbers:
ngrfmo(1)=N1,N2 and see how performance changes for your
particular system.
Limitations of the FMO method in GAMESS
1. Dimensions: in general none, except that the standard
GAMESS engines RUNTYP=OPTIMIZE and IRC are limited to 2000
atoms (for FD(D), domain B may not exceed this limit). The
limit can be increased by changing the source and
recompiling GAMESS (see elsewhere).
2. CHARMM may not be combined with FMO, and some other
extensions may not work. Not every illegal combination is
trapped, caveat emptor!
3. RUNTYP is limited to ENERGY, GRADIENT, OPTIMIZE, OPTFMO,
IRC, FMO0, MD, GLOBOP, SADPOINT, FMOHESS and RAMAN only:
Do not even try other ones!
4. Three-body FMO-MCSCF and FMO-TDDFT are not implemented.
5. No MOPAC semiempirical methods may be used, but DFTB was
interfaced with FMO..
What will work the same way as ab initio:
The various SCF convergers, all DFT functionals, in-core
integrals, direct SCF.
Restarts with the FMO method
RUNTYP=ENERGY can be restarted from anywhere before
trimers. To restart monomer SCF, copy file F40 with monomer
densities to the grandmaster node. To restart dimers,
provide file F40 and monomer energies ($FMOENM).
Optionally, some dimer energies can be supplied ($FMOEND)
to skip computation of corresponding dimers.
RUNTYP=GRADIENT can be easily restarted from monomer SCF
(which really means it is a restart of RUNTYP=ENERGY, since
gradient is computed at the end of this step). Provide
file F40. There is another restart option (1024 in $FMOPRP
irest=), supporting full gradient restart, requiring,
however, that you set this option in the original run
(whose results you use to restart). To use this option, you
would also need to keep (or save and restore) F38 files on
each node (they are different).
RUNTYP=OPTIMIZE can be restarted from anywhere within the
first RUNTYP=GRADIENT run (q.v.). In addition, by
replacing FMOXYZ group, one can restart at a different
geometry.
RUNTYP=OPTFMO can be restarted by providing a new set of
coordinates in $FMOXYZ and, optionally, by transferring
$OPTRST from the punch into the input file.
Note on accuracy
The FMO method is aimed at computation of large molecules.
This means that the total energy is large, for example, a
6646 atom molecule has a total energy of -165,676 Hartrees.
If one uses the standard accuracy of roughly 1e-9 (that
should be taken relatively), one gets an error as much as
0.001 hartree, in a single calculation. FMO involves many
ab initio single point calculations of fragments and their
n-mers, thus it can be expected that numeric accuracy is 1-
2 orders lower than that given by 1e-9. Therefore, it is
compulsory that accuracy should be raised, which is done by
default.
The following default parameters are reset by FMO:
ICUT/$CONTRL (9->12), ITOL/$CONTRL(20->24),
CONV/$SCF(1e-5 -> 1e-7),
CUTOFF/$MP2 (1e-9->1e-12), CUTTRF/$TRANS(1e-9->1e-10).
CVGTOL/$DET,$GUGDIA (1e-5 -> 1e-6)
This to some extent slows down the calculation (perhaps on
the order of 10-15%). It is suggested that you maintain
this accuracy for all final energetics. However, you may
be able to drop the accuracy a bit for the initial part of
geometry optimization if you are willing to do manual work
of adjusting accuracy in the input. It is recommended to
keep high accuracy at the flat surfaces (the final part of
optimizations) though. For DFT the numeric grid's accuracy
may be increased in accordance with the molecule size, e.g.
extending the default grid of 96*12*24 to 96*20*40.
However, some tests indicate that energy differences are
quite insensitive to this increase.
FMO References
I. Basic FMO papers
A book chapter contains an introduction to FMO basics:
Theoretical development of the fragment molecular
orbital (FMO) method, D. G. Fedorov, K. Kitaura,
in "Modern methods for theoretical physical chemistry of
biopolymers", E. B. Starikov, J. P. Lewis, S. Tanaka,
Eds., pp 3-38, Elsevier, Amsterdam, 2006.
There is now a full FMO book (11 chapters), which contains
an introduction to FMO aimed at general application
chemists, and a wealth of practical advice on doing FMO
calculations:
The Fragment Molecular Orbital Method: Practical
Applications to Large Molecular System,
D. G. Fedorov, K. Kitaura, Eds.,
CRC Press, Boca Raton, FL, 2009.
FMO reviews:
D. G. Fedorov, K. Kitaura (Feature Article)
J. Phys. Chem. A 111, 6904-6914 (2007).
D. G. Fedorov, T. Nagata, K. Kitaura (Perspective)
Phys. Chem. Chem. Phys., 14, 7562-7577 (2012)
A review of FMO in the context of other fragment-based
methods is
M. S. Gordon, D. G. Fedorov, S. R. Pruitt,
L. V. Slipchenko Chem. Rev. 112, 632-672 (2012).
A very concise and detailed mathematical formulation of FMO
including various extensions and property calculations is
published as
Mathematical formulation of the fragment molecular
orbital method.
T. Nagata, D. G. Fedorov, K. Kitaura.
In "Linear-Scaling Techniques in Computational Chemistry
and Physics". R. Zalesny, M. G. Papadopoulos,
P. G. Mezey, J. Leszczynski, Eds., pp. 17-64,
Springer, New York, 2011.
1. Fragment molecular orbital method: an approximate
computational method for large molecules"
K. Kitaura, E. Ikeo, T. Asada, T. Nakano, M. Uebayasi
Chem. Phys. Lett., 313, 701(1999).
2. Fragment molecular orbital method: application to
polypeptides
T. Nakano, T. Kaminuma, T. Sato, Y. Akiyama,
M. Uebayasi, K. Kitaura Chem.Phys.Lett. 318, 614(2000).
3. Fragment molecular orbital method: analytical energy
gradients
K. Kitaura, S.-I. Sugiki, T. Nakano, Y. Komeiji,
M. Uebayasi, Chem. Phys. Lett., 336, 163(2001).
4. Fragment molecular orbital method: use of approximate
electrostatic potential
T. Nakano, T. Kaminuma, T. Sato, K. Fukuzawa,
Y. Akiyama, M. Uebayasi, K. Kitaura
Chem. Phys. Lett., 351, 475(2002).
5. The extension of the fragment molecular orbital method
with the many-particle Green's function,
K. Yasuda, D. Yamaki, J. Chem. Phys. 125, 154101(2006).
6. The role of the exchange in the embedding electrostatic
potential for the fragment molecular orbital method.
D. G. Fedorov, K. Kitaura
J. Chem. Phys. 131, 171106(2009).
7. Analytic second derivatives of the energy in the
fragment molecular orbital method.
H. Nakata, T. Nagata, D. G. Fedorov, S. Yokojima, K.
Kitaura, S. Nakamura, J. Chem. Phys. 138 (2013) 164103.
II. FMO in GAMESS
1. A new hierarchical parallelization scheme: generalized
distributed data interface (GDDI), and an application to
the fragment molecular orbital method (FMO).
D. G. Fedorov, R. M. Olson, K. Kitaura, M. S. Gordon,
S. Koseki J. Comput. Chem. 25, 872-880(2004).
2. The importance of three-body terms in the fragment
molecular orbital method.
D. G. Fedorov and K. Kitaura
J. Chem. Phys. 120, 6832-6840(2004).
3. On the accuracy of the 3-body fragment molecular orbital
method (FMO) applied to density functional theory
D. G. Fedorov and K. Kitaura
Chem. Phys. Lett. 389, 129-134(2004).
4. Second order Moeller-Plesset perturbation theory based
upon the fragment molecular orbital method.
D. G. Fedorov and K. Kitaura
J. Chem. Phys. 121, 2483-2490(2004).
5. Multiconfiguration self-consistent-field theory based
upon the fragment molecular orbital method.
D. G. Fedorov and K. Kitaura
J. Chem. Phys. 122, 054108/1-10(2005).
6. Multilayer Formulation of the Fragment Molecular Orbital
Method (FMO).
D. G. Fedorov, T. Ishida, K. Kitaura
J. Phys. Chem. A. 109, 2638-2646(2005).
7. Coupled-cluster theory based upon the Fragment Molecular
Orbital method.
D. G. Fedorov, K. Kitaura
J. Chem. Phys. 123, 134103/1-11 (2005)
8. The polarizable continuum model (PCM) interfaced with
the fragment molecular orbital method (FMO).
D. G. Fedorov, K. Kitaura, H. Li, J. H. Jensen,
M. S. Gordon, J. Comput. Chem., 27, 976-985(2006)
9. The three-body fragment molecular orbital method for
accurate calculations of large systems,
D. G. Fedorov, K. Kitaura
Chem. Phys. Lett. 433, 182-187(2006).
10. Pair interaction energy decomposition analysis,
D. G. Fedorov, K. Kitaura
J. Comp. Chem. 28, 222-237(2007).
11. On the accuracy of the three-body fragment molecular
orbital method (FMO) applied to Moeller-Plesset
perturbation theory,
D. G. Fedorov, K. Ishimura, T. Ishida, K. Kitaura,
P. Pulay, S. Nagase
J. Comput. Chem., 28, 1476-1484 (2007).
12. The Fragment Molecular Orbital method for geometry
optimizations of polypeptides and proteins,
D.G.Fedorov, T. Ishida, M. Uebayasi, K. Kitaura
J.Phys.Chem.A, 111, 2722-2732(2007).
13. Time-dependent density functional theory with the
multilayer fragment molecular orbital method
M. Chiba, D. G. Fedorov, K. Kitaura
Chem. Phys. Lett. 444, 346-350 (2007).
14. Time-dependent density functional theory based upon the
fragment molecular orbital method
M. Chiba, D. G. Fedorov, K. Kitaura
J. Chem. Phys. 127, 104108(2007).
15. Polarizable continuum model with the fragment molecular
orbital-based time-dependent density functional theory.
M. Chiba, D. G. Fedorov, K. Kitaura
J. Comput. Chem. 29, 2667-2676 (2008).
16. Theoretical Analysis of the Intermolecular Interaction
Effects on the Excitation Energy of Organic Pigments: Solid
State Quinacridone.
H. Fukunaga, D.G.Fedorov, M. Chiba, K. Nii, K. Kitaura
J. Phys. Chem. A 112, 10887-10894 (2008).
17. Covalent Bond Fragmentation Suitable To Describe Solids
in the Fragment Molecular Orbital Method.
D. G. Fedorov, J. H. Jensen, R. C. Deka, K. Kitaura
J. Phys. Chem. A 112, 11808-11816 (2008).
18. Excited state geometry optimizations by time-dependent
density functional theory based on the fragment molecular
orbital method.
M. Chiba, D. G. Fedorov, T. Nagata, K. Kitaura
Chem. Phys. Lett. 474, 227-232 (2009).
19. Derivatives of the approximated electrostatic
potentials in the fragment molecular orbital method.
T. Nagata, D. G. Fedorov, K. Kitaura,
Chem. Phys. Lett. 475, 124-131 (2009).
20. A combined effective fragment potential - fragment
molecular orbital method. I. The energy expression and
initial applications.
T. Nagata, D. G. Fedorov, K. Kitaura, M. S. Gordon,
J. Chem. Phys. 131, 024101 (2009).
21. Analytic gradient for the adaptive frozen orbital bond
detachment in the fragment molecular orbital method.
D. G. Fedorov, P. V. Avramov, J.H. Jensen, K. Kitaura,
Chem. Phys. Lett. 477, 169-175 (2009).
22. Fragment molecular orbital study of the electronic
excitations in the photosynthetic reaction center of
Blastochloris viridis.
T. Ikegami, T. Ishida, D. G. Fedorov, K. Kitaura,
Y. Inadomi, H. Umeda, M. Yokokawa, S. Sekiguchi,
J. Comp. Chem. 31, 447-454 (2010).
23. Open-Shell Formulation of the Fragment Molecular
Orbital Method.
S. R. Pruitt, D. G. Fedorov, K. Kitaura, M. S. Gordon
J. Chem. Theor. Comp. 6, 1-5 (2010)
24. Energy gradients in combined fragment molecular orbital
and polarizable continuum model (FMO/PCM) calculation.
H. Li, D. G. Fedorov, T. Nagata, K. Kitaura,
J. H. Jensen, M. S. Gordon
J. Comput. Chem. 31, 778-790 (2010).
25. Nuclear-Electronic Orbital Method within the Fragment
Molecular Orbital Approach.
B. Auer, M. V. Pak, S. Hammes-Schiffer,
J. Phys. Chem. C 114, 5582-5588 (2010).
26. Importance of the hybrid orbital operator derivative
term for the energy gradient in the fragment molecular
orbital method.
T. Nagata, D. G. Fedorov, K. Kitaura,
Chem. Phys. Lett. 492, 302-308 (2010).
27. Systematic Study of the Embedding Potential Description
in the Fragment Molecular Orbital Method.
D. G. Fedorov, L. V. Slipchenko, K. Kitaura,
J. Phys. Chem. A 114, 8742-8753 (2010).
28. A combined effective fragment potential - fragment
molecular orbital method. II. Analytic gradient and
application to the geometry optimization of solvated
tetraglycine and chignolin.
T. Nagata, D. G. Fedorov, T. Sawada, K. Kitaura,
M. S. Gordon, J. Chem. Phys. 134, 034110 (2011).
29. Geometry optimization of the active site of a large
system with the fragment molecular orbital method.
D. G. Fedorov, Y. Alexeev, K. Kitaura,
J. Phys. Chem. Lett. 2, 282-288 (2011).
30. Fully analytic energy gradient in the fragment
molecular orbital method.
T. Nagata, K. Brorsen, D. G. Fedorov, K. Kitaura,
M. S. Gordon, J. Chem. Phys. 134, 124115(2011).
31. Analytic energy gradient for second-order Moeller-
Plesset perturbation theory based on the fragment molecular
orbital method.
T. Nagata, D. G. Fedorov, K. Ishimura, K. Kitaura,
J. Chem. Phys. 135, 044110 (2011).
32. Large-Scale MP2 Calculations on the Blue Gene
Architecture Using the Fragment Molecular Orbital Method.
G. D. Fletcher, D. G. Fedorov, S.R.Pruitt, T.L.Windus,
M. S. Gordon, J. Chem. Theory Comput. 8, 75-79(2012).
33. Energy decomposition analysis in solution based on the
fragment molecular orbital method.
D.G.Fedorov, K.Kitaura
J.Phys.Chem. A 116, 704-719(2012).
34. Analytic gradient and molecular dynamics simulations
using the fragment molecular orbital method combined with
effective potentials.
T. Nagata, D. G. Fedorov, K. Kitaura
Theor. Chem. Acc. 131, 1136 (2012).
35. Geometry Optimizations of Open-Shell Systems with the
Fragment Molecular Orbital Method.
S. R. Pruitt, D. G. Fedorov, M. S. Gordon,
J. Phys. Chem. A, 116, 4965-4974 (2012).
36. Analytic gradient for second order Moeller-Plesset
perturbation theory with the polarizable continuum model
based on the fragment molecular orbital method.
T. Nagata, D. G. Fedorov, H. Li, K. Kitaura,
J. Chem. Phys., 136, 204112 (2012).
37. Reducing scaling of the fragment molecular orbital
method using the multipole method.
C. H. Choi, D. G. Fedorov
Chem. Phys. Lett. 543, 159-165(2012).
38. Unrestricted Hartree-Fock based on the fragment
molecular orbital method: energy and its analytic gradient.
H. Nakata, D. G. Fedorov, T. Nagata, S. Yokojima, K.
Ogata, K. Kitaura, S. Nakamura
J. Chem. Phys. 137, 044110 (2012).
39. Analytic gradient for the embedding potential with
approximations in the fragment molecular orbital method.
T. Nagata, D. G. Fedorov, K. Kitaura
Chem. Phys. Lett. 544, 87-93 (2012).
40. Analysis of solute-solvent interactions in the fragment
molecular orbital method interfaced with the effective
fragment potentials: theory and application to solvated
griffithsin-carbohydrate complex.
T. Nagata, D. G. Fedorov, T. Sowada, K. Kitaura
J. Phys. Chem. A, 116, 9088-9099 (2012).
41. Open-shell pair interaction energy decomposition
analysis (PIEDA): Formulation and application to the
hydrogen abstraction in tripeptides.
M.C.Green, D.G.Fedorov, K.Kitaura, J.S.Francisco,
L.V.Slipchenko, J.Chem.Phys. 138 (2013) 074111.
Other FMO references including applications can be found
at:
http://staff.aist.go.jp/d.g.fedorov/fmo/main.html
EFMO references are given in its own subsection.
created on 7/7/2017