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 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). Probably, FMO3/PCM 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. FMO3/PCM 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 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.