The Effective Fragment Potential Method The basic idea behind the effective fragment potential (EFP) method is to replace the chemically inert part of a system by EFPs, while performing a regular ab initio calculation on the chemically active part. Here "inert" means that no covalent bond breaking process occurs. This "spectator region" consists of one or more "fragments", which interact with the ab initio "active region" through non-bonded interactions, and so of course these EFP interactions affect the ab initio wavefunction. The EFP particles can be closed shell or open shell (high spin ROHF) based potentials. The "active region" can use nearly every kind of wavefunction available in GAMESS. A simple example of an active region might be a solute molecule, with a surrounding spectator region of solvent molecules represented by fragments. Each discrete solvent molecule is represented by a single fragment potential, in marked contrast to continuum models for solvation. The quantum mechanical part of the system is entered in the $DATA group, along with an appropriate basis. The EFPs defining the fragments are input by means of a $EFRAG group, and one or more $FRAGNAME groups describing each fragment's EFP. These groups define non-bonded interactions between the ab initio system and the fragments, and also between the fragments. The former interactions enter via one-electron operators in the ab initio Hamiltonian, while the latter interactions are treated by analytic functions. The only electrons explicitly treated (with basis functions used to expand occupied orbitals) are those in the active region, so there are no new two electron terms. Thus the use of EFPs leads to significant time savings, compared to full ab initio calculations on the same system. There are two types of EFP available in GAMESS, EFP1 and EFP2. EFP1, the original method, employs a fitted repulsive potential. EFP1 is primarily used to model water molecules to study aqueous solvation effects, at the RHF/DZP or DFT/DZP (specifically, B3LYP) levels, see references 1-3 and 26, respectively. EFP2 is a more general method that is applicable to any species, including water, and its repulsive potential is obtained from first principles. EFP2 has been extended to include other effects as well, such as charge transfer and dispersion. EFP2 forms the basis of the covalent EFP method described below for modeling enzymes, see reference 14. Parallelization of the EFP1 and EFP2 models is described in reference 32. MD simulations with EFP are described in reference 31. The ab initio/EFP1, or pure EFP system can be wrapped in a Polarizable Continuum Model, see references 23, 43, and 50. terms in an EFP The non-bonded interactions currently implemented are: 1) Coulomb interaction. The charge distribution of the fragments is represented by an arbitrary number of charges, dipoles, quadrupoles, and octopoles, which interact with the ab initio hamiltonian as well as with multipoles on other fragments (see reference 2 and 18). It is possible to use a screening term that accounts for the charge penetration (reference 17 and 42). This screening term is automatically included for EFP1. Typically the multipole expansion points are located on atomic nuclei and at bond midpoints. 2) Dipole polarizability. An arbitrary number of dipole polarizability tensors can be used to calculate the induced dipole on a fragment due to the electric field of the ab initio system as well as all the other fragments. These induced dipoles interact with the ab initio system as well as the other EFPs, in turn changing their electric fields. All induced dipoles are therefore iterated to self- consistency. Typically the polarizability tensors are located at the centroid of charge of each localized orbital of a fragment. See reference 41. 3) Repulsive potential. Two different forms are used in EFP1: one for ab initio-EFP repulsion and one for EFP-EFP repulsion. The form of the potentials is empirical, and consists of distributed Gaussian or exponential functions, respectively. The primary contribution to the repulsion is the quantum mechanical exchange repulsion, but the fitting technique used to develop this term also includes the effects of charge transfer. Typically these fitted potentials are located on each atomic nucleus within the fragment (see reference 3). In EFP2, polarization energies can also be augmented by screening terms, analogous to the electrostatic screening, to prevent "polarization collapse" (MS in preparation) For EFP2, the third term is divided into separate analytic formulae for different physical interactions: a) exchange repulsion b) dispersion c) charge transfer A summary of EFP2, and its contrast to EFP1 can be found in reference 18 and 44. The repulsive potential for EFP2 is based on an overlap expansion using localized molecular orbitals, as described in references 5, 6, and 9. Dispersion energy is described in reference 34, and charge transfer in reference 39 (which supercedes reference 22's formulae). EFP2 potentials have no fitted parameters, and can be automatically generated during a RUNTYP=MAKEFP job, as described below. constructing an EFP1 RUNTYP=MOROKUMA assists in the decomposition of inter- molecular interaction energies into electrostatic, polarization, charge transfer, and exchange repulsion contributions. This is very useful in developing EFPs since potential problems can be attributed to a particular term by comparison to these energy components for a particular system. A molecular multipole expansion can be obtained using $ELMOM. A distributed multipole expansion can be obtained by either a Mulliken-like partitioning of the density (using $STONE) or by using localized molecular orbitals ($LOCAL: DIPDCM and QADDCM). The dipole polarizability tensor can be obtained during a Hessian run ($CPHF), and a distributed LMO polarizability expression is also available ($LOCAL: POLDCM). In EFP1, the repulsive potential is derived by fitting the difference between ab initio computed intermolecular interaction energies, and the form used for Coulomb and polarizability interactions. This difference is obtained at a large number of different interaction geometries, and is then fitted. Thus, the repulsive term is implicitly a function of the choices made in representing the Coulomb and polarizability terms. Note that GAMESS currently does not provide a way to obtain these EFP1 repulsive potential. Since a user cannot generate all of the EFP1 terms necessary to define a new $FRAGNAME group using GAMESS, in practice the usage of EFP1 is limited to the internally stored H2ORHF or H2ODFT potentials mentioned below. constructing an EFP2 As noted above, the repulsive potential for EFP2 is derived from a localized orbital overlap expansion. It is generally recommended that one use at least a double zeta plus diffuse plus polarization basis set, e.g. 6-31++G(d,p) to generate the EFP2 repulsive potential. However, it has been observed that 6-31G(d) works reasonably well due to a fortuitous cancellation of errors. The EFP2 potential for any molecule can be generated as follows: (a) Choose a basis set and geometry for the molecule of interest. The geometry is ordinarily optimized at your choice of Hartree-Fock/MP2/CCSD(T), with your chosen basis set, but this is not a requirement. It is good to recall, however, that EFP internal geometries are fixed, so it is important to give some thought to the chosen geometry. (b) Perform a RUNTYP=MAKEFP run for the chosen molecule using the chosen geometry in $DATA and the chosen basis set in $BASIS. This will generate the entire EFP2 potential in the run's .efp file. The only user-defined variable that must be filled in is changing the FRAGNAME's group name, to $C2H5OH or $DMSO, etc. This step can use RHF or ROHF to describe the electronic structure of the system. (c) Transfer the entire fragment potential for the molecule to any input file in which this fragment is to be used. Since the internal geometry of an EFP is fixed, one need only specify the first three atoms of any fragment in order to position them in $EFRAG. Coordinates of any other atoms in the rigid fragment will be automatically determined by the program. If the EFP contains less than three atoms, you can still generate a fragment potential. After a normal MAKEFP run, add dummy atoms (e.g. in the X and/or Y directions) with zero nuclear charges, and add corresponding dummy bond midpoints too. Carefully insert zero entries in the multipole sections, and in the electrostatic screening sections, for each such dummy point, but don't add data to any other kind of EFP term such as polarizability. This trick gives the necessary 3 points for use in $EFRAG groups to specify "rotational" positions of fragments. current limitations 1. For EFP1, the energy and energy gradient are programmed, which permits RUNTYP=ENERGY, GRADIENT, and numerical HESSIAN. The necessary programing to use the EFP gradients to move on the potential surface are programmed for RUNTYP=OPTIMIZE, SADPOINT, IRC, and VSCF, but the other gradient based potential surface explorations such as DRC are not yet available. Finally, RUNTYP=PROP is also permissible. For EFP2, the gradient terms for ab initio-EFP interactions have not yet been coded, so geometry optimizations are only sensible for a COORD=FRAGONLY run; that is, a run in which only EFP2 fragments are present. 2. The ab initio part of the system must be treated with RHF, ROHF, UHF, the open shell SCF wavefunctions permitted by the GVB code, or MCSCF. DFT analogs of RHF, ROHF, and UHF may also be used. Correlated methods such as MP2 and CI should not be used. 3. EFPs can move relative to the ab initio system and relative to each other, but the internal structure of an EFP is frozen. 4. The boundary between the ab initio system and EFP1's must not be placed across a chemical bond. However, see the discussion below regarding covalent bonds. 5. Calculations must be done in C1 symmetry at present. 6. Reorientation of the fragments and ab initio system is not well coordinated. If you are giving Cartesian coordinates for the fragments (COORD=CART in $EFRAG), be sure to use $CONTRL's COORD=UNIQUE option so that the ab initio molecule is not reoriented. 7. If you need IR intensities, you have to use NVIB=2. The potential surface is usually very soft for EFP motions, and double differenced Hessians should usually be obtained. practical hints for using EFPs At the present time, we have only two internally stored EFP potentials suitable for general use. These model water, using the fragment name H2ORHF or H2ODFT. The H2ORHF numerical parameters are improved values over the values which were presented and used in reference 2, and they also include the improved EFP-EFP repulsive term defined in reference 3. The H2ORHF water EFP was derived from RHF/DH(d,p) computations on the water dimer system. When you use it, therefore, the ab initio part of your system should be treated at the SCF level, using a basis set of the same quality (ideally DH(d,p), but probably other DZP sets such as 6-31G(d,p) will give good results as well). Use of better basis sets than DZP with this water EFP has not been tested. Similarly, H2ODFT was developed using B3LYP/DZP water wavefunctions, so this should be used (rather than H2ORHF) if you are using DFT to treat the solute. Since H2ODFT water parameters are obtained from a correlated calculation, they can also be used when the solute is treated by MP2. As noted, effective fragments have frozen internal geometries, and therefore only translate and rotate with respect to the ab initio region. An EFP's frozen coordinates are positioned to the desired location(s) in $EFRAG as follows: a) the corresponding points are found in $FRAGNAME. b) Point -1- in $EFRAG and its FRAGNAME equivalent are made to coincide. c) The vector connecting -1- and -2- is aligned with the corresponding vector connecting FRAGNAME points. d) The plane defined by -1-, -2-, and -3- is made to coincide with the corresponding FRAGNAME plane. Therefore the 3 points in $EFRAG define only the relative position of the EFP, and not its internal structure. So, if the "internal structure" given by points in $EFRAG differs from the true values in $FRAGNAME, then the order in which the points are given in $EFRAG can affect the positioning of the fragment. It may be easier to input water EFPs if you use the Z-matrix style to define them, because then you can ensure you use the actual frozen geometry in your $EFRAG. Note that the H2ORHF EFP uses the frozen geometry r(OH)=0.9438636, a(HOH)=106.70327, and the names of its 3 fragment points are ZO1, ZH2, ZH3. * * * Building a large cluster of EFP particles by hand can be tedious. The RUNTYP=GLOBOP program described below has an option for constructing dense clusters. The method tries to place particles near the origin, but not colliding with other EFP particles already placed there, so that the clusters grow outwards from the center. Here are some ideas: a) place 100 water molecules, all with the same coords in $EFRAG. This will build up a droplet of water with particles close together, but not on top of each other, with various orientations. b) place 16 waters (same coords, all first) followed by 16 methanols (also sharing their same coords, after all waters). A 50-50 mixture of 32 molecules will be created, if you choose the default of picking the particles randomly from the initial list of 32. c) to solvate a solute, add the solute in the $DATA group at or near the origin. Add the solvent molecules near by (same coords is ok), and run the globop run with RNDINI as demonstrated below. (optional, add MCTYP=3 to $GLOBOP input) Example, allowing the random cluster to have 20 geometry optimization steps: $contrl runtyp=globop coord=fragonly $end $globop rndini=.true. riord=rand mcmin=.true. mctyp=4 nblock=0 $end $statpt nstep=20 $end $efrag coord=cart FRAGNAME=WATER O1 -2.8091763203009 -2.1942725073400 -0.2722207394107 H2 -2.3676165499399 -1.6856118830379 -0.9334073942601 H3 -2.1441965467625 -2.5006167998896 0.3234583094693 ...repeat this 15 more times... FRAGNAME=MeOH O1 4.9515153249 .4286994611 1.3368662306 H2 5.3392575544 .1717424606 3.0555957053 C3 6.2191743799 2.5592349960 .4064662379 H4 5.7024200977 2.7548960076 -1.5604873643 H5 5.6658856694 4.2696553371 1.4008542042 H6 8.2588049857 2.3458272252 .5282762681 ...repeat 15 more times... $end $water ...give a full EFP2 potential for water... $end $meoh ...give a full EFP2 potential for methanol... $end Note that the random cluster generation now proceeds into a full Monte Carlo simulation. * * * The translations and rotations of EFPs with respect to the ab initio system and one another are automatically quite soft degrees of freedom. After all, the EFP model is meant to handle weak interactions! Therefore the satisfactory location of structures on these flat surfaces will require use of a tight convergence on the gradient: OPTTOL=0.00001 in the $STATPT group. The effect of a bulk continuum surrounding the solute plus EFP waters can be obtained by using the PCM model, see reference 23 and 43. To do this, simply add a $PCM group to your input, in addition to the $EFRAG. The simultaneous use of EFP and PCM allows for gradients, so geometry optimization can be performed. global optimization If there are a large number of particles to move (EFP and/or FMO and/or atom groups), it is difficult to locate the lowest energy structures by hand. Typically these are numerous, and one would like to have a number of them, not just the very lowest energy. The RUNTYP of GLOBOP contains a Monte Carlo procedure to generate a random set of starting structures to look for those with the lowest energy at a single temperature. If desired, a simulated annealing protocol to cool the temperature may be used. These two procedures may be combined with a local minimum search, at some or all of the randomly generated structures. The local minimum search is controlled by the usual geometry optimizer, namely $STATPT input, and thus permits the optimization of any ab initio atoms. The Monte Carlo procedure by default uses a Metropolis algorithm to move just one of the fragments. The method of Parks to move all fragments simultaneously is also allowed. The present program was used to optimize the structure of water clusters. Let us consider the case of the twelve water cluster, for which the following ten structures were published by Day, Pachter, Gordon, and Merrill: 1. (D2d)2 -0.170209 6. (D2d)(C2) -0.167796 2. (D2d)(S4) -0.169933 7. S6 -0.167761 3. (S4)2 -0.169724 8. cage b -0.167307 4. D3 -0.168289 9. cage a -0.167284 5. (C1c)(Cs) -0.167930 10. (C1c)(C1c) -0.167261 A test input using Metropolis style Monte Carlo to examine 300 geometries at each temperature value, using simulated annealing cooling from 200 to 50 degrees, and with local minimization every 10 structures was run ten times. Each run sampled about 7000 geometries. One simulation found structure 2, while two of the runs found structure 3. The other seven runs located structures with energy values in the range -0.163 to -0.164. In all cases the runs began with the same initial geometry, but produced different results due to the random number generation used in the Monte Carlo. Clearly one must try a lot of simulations to be confident about having found most of the low energy structures. In particular, it is good to try more than one initial structure, unlike what was done in this test. Ab initio atoms can be addressed using FMO, either in multiple fragments, or perhaps a single large fragment. Alternatively, ab initio atoms can be put into groups and used directly in globop, which for small systems has a lower overhead than FMO. In the case of large molecules separated into multiple fragments, the keywords NPRBND, PRSEP, IBNDS, and INDEP are applicable. These specify the atoms in each set of fragments or groups whose bond is cut in the fragmentation process. The paired atoms are constrained during the Monte Carlo procedure to ensure that the bond is not spacially broken. In the case where a fragment that is being translated or rotated is paired with two or more fragments, the movement is repeated on all attached fragments, after randomly choosing which pair is the starting point. For example, given a molecule split into five fragments such that: A-B-C-D-E where A,B,C,D,E are the fragments. If C is chosen for a translation, either B or D will be randomly chosen to be the starting pair. When B is chosen as the starting pair, C, D, and E will all be translated by the same amount: A-B--C-D-E which maintains the relative position of C, D, and E. Setting INDEP=1 will not propagate the translation: A-B--CD-E So that only C is moved. The same approach is used for rotations. Since a small translation or rotation can result in a significant change in the total system, it is advised that case be taken when using solvent molecules and to the size of boundary conditions. If a propagated movement moves a fragment outside the boundary, a warning will be printed and the step will be discarded as a proximity alert. Also, the pair binding is not implemented for RNDINI=.TRUE. To initialize a set of solvent molecules around pair bonded fragments, include the pair bonded fragments in IFXFMO. The Metrpolis Monte Carlo procedure involves the movement of groups that are internally rigid. To introduce some internal flexibility for FMO and ab initio groups, a secondary Monte Carlo search where the entire system is held rigid while the atoms in one group are moved is implemented. The secondary Monte Carlo occurs when a FMO or ab initio group is translated and occurs for that group. The lowest energy internal configuration for the secondary Monte Carlo is used when evaluating the step of the primary Monte Carlo search. The temperature at which the secondary Monte Carlo is used in the case of simulated annealing is set by SMTEMP and the number of steps in each secondary search is given by NSMTP. To turn on this feature, set the values of SMTEMP and NSMTP to non-zero values. Monte Carlo references: N.Metropolis, A.Rosenbluth, A.Teller J.Chem.Phys. 21, 1087(1953). G.T.Parks Nucl.Technol. 89, 233(1990). Monte Carlo with local minimization: Z.Li, H.A.Scheraga Proc.Nat.Acad.Sci. USA 84, 6611(1987). Simulated annealing reference: S.Kirkpatrick, C.D.Gelatt, M.P.Vecci Science 220, 671(1983). The present program is described in reference 15. It is patterned on the work of D.J.Wales, M.P.Hodges Chem.Phys.Lett. 286, 65-72 (1998). QM/MM across covalent bonds Recent work by Visvaldas Kairys and Jan Jensen has made it possible to extend the EFP methodology beyond the simple solute/solvent case described above. When there is a covalent bond between the portion of the system to be modeled by quantum mechanics, and the portion which is to be treated by EFP multipole and polarizability terms, an additional layer is needed in the model. The covalent linkage is not so simple as the interactions between closed shell solute and solvent molecules. The "buffer zone" between the quantum mechanics and the EFP consists of frozen nuclei, and frozen localized orbitals, so that the quantum mechanical region sees a orbital representation of the closest particles, and multipoles etc. beyond that. Since the orbitals in the buffer zone are frozen, it need extend only over a few atoms in order to keep the orbitals in the fully optimized quantum region within that region. The general outline of this kind of computation is as follows: a) a full quantum mechanics computation on a system containing the quantum region, the buffer region, and a few atoms into the EFP region, to obtain the frozen localized orbitals in the buffer zone. This is called the "truncation run". b) a full quantum mechanics computation on a system with all quantum region atoms removed, and with the frozen localized orbitals in the buffer zone. The necessary multipole and polarizability data to construct the EFP that will describes the EFP region will be extracted from the wavefunction. This is called the "MAKEFP run". It is possible to use several such runs if the total EFP region is quite large. c) The intended QM/MM run(s), after combining the information from these first two types of runs. As an example, consider a protonated lysine residue which one might want to consider quantum mechanically in a protein whose larger parts are to be treated with an EFP. The protonated lysine is NH2 + / H3N(CH2)(CH2)(CH2)--(CH2)(CH) \ COOH The bonds which you see drawn show how the molecule is partitioned between the quantum mechanical side chain, a CH2CH group in the buffer zone, and eventually two different EFPs may be substituted in the area of the NH2 and COOH groups to form the protein backbone. The "truncation run" will be on the entire system as you see it, with the 13 atoms in the side chain first in $DATA, the 5 atoms in the buffer zone next in $DATA, and the simplified EFP region at the end. This run will compute the full quantum wavefunction by RUNTYP=ENERGY, followed by the calculation of localized orbitals, and then truncation of the localized orbitals that are found in the buffer zone so that they contain no contribution from AOs outside the buffer zone. The key input groups for this run are $contrl $truncn doproj=.true. plain=.true. natab=13 natbf=5 $end This will generate a total of 6 localized molecular orbitals in the buffer zone (one CC, three CH, two 1s inner shells), expanded in terms of atomic orbitals located only on those atoms. The truncation run prepares template input files for the next run, including adjustments of nuclear charges at boundaries, etc. The "MAKEFP" run drops all 13 atoms in the quantum region, and uses the frozen orbitals just prepared to obtain a wavefunction for the EFP region. The carbon atom in the buffer zone that is connected to the now absent QM region will have its nuclear charge changed from 6 to 5 to account for a missing electron. The key input for this RUNTYP=MAKEFP job is the six orbitals in $VEC, plus the groups $guess guess=huckel insorb=6 $end $mofrz frz=.true. ifrz(1)=1,2,3,4,5,6 $end $stone QMMMbuf $end which will cause the wavefunction optimization for the remaining atoms to optimize orbitals only in the NH2 and COOH pieces. After this wavefunction is found, the run extracts the EFP information needed for the QM/MM third run(s). This means running the Stone analysis for distributed multipoles, and obtaining a polarizability tensor for each localized orbital in the EFP region. The QM/MM run might be RUNTYP=OPTIMIZE, etc. depending on what you want to do with the quantum atoms, and its $DATA group will contain both the 13 fully optimized atoms, and the 5 buffer atoms, and a basis set will exist on both sets of atoms. The carbon atom in the buffer zone that borders the EFP region will have its nuclear charge set to 4 since now two bonding electrons to the EFP region are lost. $VEC input will provide the six frozen orbitals in the buffer zone. The EFP atoms are defined in a fragment potential group. The QM/MM run could use RHF or ROHF wavefunctions, to geometry optimize the locations of the quantum atoms (but not of course the frozen buffer zone or the EFP piece). It could remove the proton to compute the proton affinity at that terminal nitrogen, hunt for transition states, and so on. Presently the gradient for GVB and MCSCF is not quite right, so their use is discouraged. Input to control the QM/MM preparation is $TRUNCN and $MOFRZ groups. There are a number of other parameters in various groups, namely QMMMBUF in $STONE, MOIDON and POLNUM in $LOCAL, NBUFFMO in $EFRAG, and INSORB in $GUESS that are relevant to this kind of computation. For RUNTYP=MAKEFP, the biggest choices are LOCAL=RUEDENBRG vs. BOYS, and POLNUM in $LOCAL, otherwise this is pretty much a standard RUNTYP=ENERGY input file. Source code distributions of GAMESS contain a directory named ~/gamess/tools/efp, which has various tools for EFP manipulation in it, described in file readme.1st. A full input file for the protonated lysine molecule is included, with instructions about how to proceed to the next steps. Tips on more specialized input possibilities are appended to the file readme.1st. Simpler potentials Since the EFP model's electrostatics is a set of distributed multipoles (monopole to octopole) and distributed polarizabilities (dipole), it is possible to generate some water potentials found in the literature by setting many EFP terms to zero. It is also necessary to provide a Lennard-Jones 6-12 repulsive potential, and then make a choice to follow the EFP1 type formula for QM/EFP repulsion. Accordingly, EFP1 type calculations can be made with the following water potentials, FRAGNAME=SPC, SPCE, TIP5P, TIP5PE, or POL5P The Wikipedia page http://en.wikipedia.org/wiki/Water_model defines the first four of these, which are not polarizable potentials. The same web site references the primary literature, so that is not repeated here. POL5P is a polarizable potential, with parameters given by D.Si and H.Li J.Chem.Phys. 133, 144112/1-8(2010) references The first paper is more descriptive, while the second presents a very detailed derivation of the EFP1 method. Reference 18 is an overview article on EFP2. Reference 44 is the most recent review. The model development papers are: 1, 2, 3, 5, 6, 9, 14, 17, 18, 22, 23, 26, 31, 32, 34, 39, 41, 42, 43, 44, 46, 50, 51, 55, 57, 58. 1. "Effective fragment method for modeling intermolecular hydrogen bonding effects on quantum mechanical calculations" J.H.Jensen, P.N.Day, M.S.Gordon, H.Basch, D.Cohen, D.R.Garmer, M.Krauss, W.J.Stevens in "Modeling the Hydrogen Bond" (D.A. Smith, ed.) ACS Symposium Series 569, 1994, pp 139-151. 2. "An effective fragment method for modeling solvent effects in quantum mechanical calculations". P.N.Day, J.H.Jensen, M.S.Gordon, S.P.Webb, W.J.Stevens, M.Krauss, D.Garmer, H.Basch, D.Cohen J.Chem.Phys. 105, 1968-1986(1996). 3. "The effective fragment model for solvation: internal rotation in formamide" W.Chen, M.S.Gordon, J.Chem.Phys., 105, 11081-90(1996) 4. "Transphosphorylation catalyzed by ribonuclease A: Computational study using ab initio EFPs" B.D.Wladkowski, M. Krauss, W.J.Stevens J.Am.Chem.Soc. 117, 10537-10545(1995) 5. "Modeling intermolecular exchange integrals between nonorthogonal orbitals" J.H.Jensen J.Chem.Phys. 104, 7795-7796(1996) 6. "An approximate formula for the intermolecular Pauli repulsion between closed shell molecules" J.H.Jensen, M.S.Gordon Mol.Phys. 89, 1313-1325(1996) 7. "A study of aqueous glutamic acid using the effective fragment potential model" P.N.Day, R.Pachter J.Chem.Phys. 107, 2990-9(1997) 8. "Solvation and the excited states of formamide" M.Krauss, S.P.Webb J.Chem.Phys. 107, 5771-5(1997) 9. "An approximate formula for the intermolecular Pauli repulsion between closed shell molecules. Application to the effective fragment potential method" J.H.Jensen, M.S.Gordon J.Chem.Phys. 108, 4772-4782(1998) 10. "Study of small water clusters using the effective fragment potential method" G.N.Merrill, M.S.Gordon J.Phys.Chem.A 102, 2650-7(1998) 11. "Solvation of the Menshutkin Reaction: A Rigourous test of the Effective Fragement Model" S.P.Webb, M.S.Gordon J.Phys.Chem.A 103, 1265-73(1999) 12. "Evaluation of the charge penetration energy between nonorthogonal molecular orbitals using the Spherical Gaussian Overlap approximation" V.Kairys, J.H.Jensen Chem.Phys.Lett. 315, 140-144(1999) 13. "Solvation of Sodium Chloride: EFP study of NaCl(H2O)n" C.P.Petersen, M.S.Gordon J.Phys.Chem.A 103, 4162-6(1999) 14. "QM/MM boundaries across covalent bonds: frozen LMO based approach for the Effective Fragment Potential method" V.Kairys, J.H.Jensen J.Phys.Chem.A 104, 6656-65(2000) 15. "A study of water clusters using the effective fragment potential and Monte Carlo simulated annealing" P.N.Day, R.Pachter, M.S.Gordon, G.N.Merrill J.Chem.Phys. 112, 2063-73(2000) 16. "A combined discrete/continuum solvation model: Application to glycine" P.Bandyopadhyay, M.S.Gordon J.Chem.Phys. 113, 1104-9(2000) 17. "Evaluation of charge penetration between distributed multipolar expansions" M.A.Freitag, M.S.Gordon, J.H.Jensen, W.J.Stevens J.Chem.Phys. 112, 7300-7306(2000) 18. "The Effective Fragment Potential Method: a QM-based MM approach to modeling environmental effects in chemistry" M.S.Gordon, M.A.Freitag, P.Bandyopadhyay, J.H.Jensen, V.Kairys, W.J.Stevens J.Phys.Chem.A 105, 293-307(2001) 19. "Accurate Intraprotein Electrostatics derived from first principles: EFP study of proton affinities of lysine 55 and tyrosine 20 in Turkey Ovomucoid" R.M.Minikis, V.Kairys, J.H.Jensen J.Phys.Chem.A 105, 3829-3837(2001) 20. "Active site structure & mechanism of Human Glyoxalase" U.Richter, M.Krauss J.Am.Chem.Soc. 123, 6973-6982(2001) 21. "Solvent effect on the global and atomic DFT-based reactivity descriptors using the EFP model. Solvation of ammonia." R.Balawender, B.Safi, P.Geerlings J.Phys.Chem.A 105, 6703-6710(2001) 22. "Intermolecular exchange-induction and charge transfer: Derivation of approximate formulas using nonorthogonal localized molecular orbitals." J.H.Jensen J.Chem.Phys. 114, 8775-8783(2001) 23. "An integrated effective fragment-polarizable continuum approach to solvation: Theory & application to glycine" P.Bandyopadhyay, M.S.Gordon, B.Mennucci, J.Tomasi J.Chem.Phys. 116, 5023-5032(2002) 24. "The prediction of protein pKa's using QM/MM: the pKa of Lysine 55 in turkey ovomucoid third domain" H.Li, A.W.Hains, J.E.Everts, A.D.Robertson, J.H.Jensen J.Phys.Chem.B 106, 3486-3494(2002) 25. "Computational studies of aliphatic amine basicity" D.C.Caskey, R.Damrauer, D.McGoff J.Org.Chem. 67, 5098-5105(2002) 26. "Density Functional Theory based Effective Fragment Potential" I.Adamovic, M.A.Freitag, M.S.Gordon J.Chem.Phys. 118, 6725-6732(2003) 27. "Intraprotein electrostatics derived from first principles: Divid-and-conquer approaches for QM/MM calculations" P.A.Molina, H.Li, J.H.Jensen J.Comput.Chem. 24, 1971-1979(2003) 28. "Formation of alkali metal/alkaline earth cation water clusters, M(H2O)1-6, M=Li+, K+, Mg+2, Ca+2: an effective fragment potential caase study" G.N.Merrill, S.P.Webb, D.B.Bivin J.Phys.Chem.A 107, 386-396(2003) 29. "Anion-water clusters A-(H2O)1-6, A=OH, F, SH, Cl, and Br. An effective fragment potential test case" G.N.Merrill, S.P.Webb J.Phys.Chem.A 107,7852-7860(2003) 30. "The application of the Effective Fragment Potential to molecular anion solvation: a study of ten oxyanion- water clusters, A-(H2O)1-4" G.N.Merrill, S.P.Webb J.Phys.Chem.A 108, 833-839(2004) 31. "The effective fragment potential: small clusters and radial distribution functions" H.M.Netzloff, M.S.Gordon J.Chem.Phys. 121, 2711-4(2004) 32. "Fast fragments: the development of a parallel effective fragment potential method" H.M.Netzloff, M.S.Gordon J.Comput.Chem. 25, 1926-36(2004) 33. "Theoretical investigations of acetylcholine (Ach) and acetylthiocholine (ATCh) using ab initio and effective fragment potential methods" J.Song, M.S.Gordon, C.A.Deakyne, W.Zheng J.Phys.Chem.A 108, 11419-11432(2004) 34. "Dynamic polarizability, dispersion coefficient C6, and dispersion energy in the effective fragment potential method" I.Adamovic, M.S.Gordon Mol.Phys. 103, 379-387(2005) 35. "Solvent effects on the SN2 reaction: Application of the density functional theory-based effective fragment potential method" I.Adamovic, M.S.Gordon J.Phys.Chem.A 109, 1629-36(2005) 36. "Theoretical study of the solvation of fluorine and chlorine anions by water" D.D.Kemp, M.S.Gordon J.Phys.Chem.A 109, 7688-99(2005) 37. "Modeling styrene-styrene interactions" I.Adamovic, H.Li, M.H.Lamm, M.S.Gordon J.Phys.Chem.A 110, 519-525(2006) 38. "Methanol-water mixtures: a microsolvation study using the Effective Fragment Potential method" I.Adamovic, M.S.Gordon J.Phys.Chem.A 110, 10267-10273(2006) 39. "Charge transfer interaction in the effective fragment potential method" H.Li, M.S.Gordon, J.H.Jensen J.Chem.Phys. 124, 214108/1-16(2006) 40. "Incremental solvation of nonionized and zwitterionic glycine" C.M.Aikens, M.S.Gordon J.Am.Chem.Soc. 128, 12835-12850(2006) 41. "Gradients of the polarization energy in the Effective Fragment Potential method" H.Li, H.M.Netzloff, M.S.Gordon J.Chem.Phys. 125, 194103/1-9(2006) 42. "Electrostatic energy in the Effective Fragment Potential method: Theory and application to benzene dimer" L.V.Slipchenko, M.S.Gordon J.Comput.Chem. 28, 276-291(2007) 43. "Polarization energy gradients in combined Quantum Mechanics, Effective Fragment Potential, and Polarizable Continuum Model Calculations" H.Li, M.S.Gordon J.Chem.Phys. 126, 124112/1-10(2007) 44. "The Effective Fragment Potential: a general method for predicting intermolecular interactions" M.S.Gordon, L.V.Slipchenko, H.Li, J.H.Jensen Annual Reports in Computational Chemistry, Volume 3, pp 177-193 (2007). 45. "An Interpretation of the Enhancement of the Water Dipole Moment Due to the Presence of Other Water Molecules" D.D.Kemp, M.S.Gordon J.Phys.Chem.A 112, 4885-4894(2008) 46. "Solvent effects on optical properties of molecules: a combined time-dependent density functional/effective fragment potential approach" S.Yoo, F.Zahariev, S.Sok, M.S.Gordon J.Chem.Phys. 129, 144112/1-8(2008) 47. "Modeling pi-pi interactions with the effective fragment potential method: The benzene dimer and substituents" T.Smith, L.V.Slipchenko, M.S.Gordon J.Phys.Chem.A 112, 5286-5294(2008) 48. "Water-benzene interactions: An effective fragment potential and correlated quantum chemistry study" L.V.Slipchenko, M.S.Gordon J.Phys.Chem.A 113, 2092-2102(2009) 49. "Ab initio QM/MM excited-state molecular dynamics study of Coumarin 151 in water solution" D.Kina, P.Arora, A.Nakayama, T.Noro, M.S.Gordon, T.Taketsugu Int.J.Quantum Chem. 109, 2308-2318(2009) 50. "Damping functions in the effective fragment potential method L.V.Slipchenko, M.S.Gordon Mol.Phys. 197, 999-1016 (2009) 51. "A combined effective fragment potential-fragment molecular orbital method. 1. the energy expression" T.Nagata, D.G.Fedorov, K.Kitaura, M.S.Gordon J.Chem.Phys. 131, 024101/1-12(2009) 52. "Alanine: then there was water" J.M.Mullin, M.S.Gordon J.Phys.Chem.B 113, 8657-8669(2009) 53. "Water and Alanine: from puddles(32) to ponds(49)" J.M.Mullin, M.S.Gordon J.Phys.Chem.B 113, 14413-14420(2009) 54. "Structure of large nitrate-water clusters at ambient temperatures: simulations with effective fragment potentials and force fields with implications for atmospheric chemistry" Y.Miller, J.L.Thoman, D.D.Kemp, B.J.Finlayson-Pitts, M.S.Gordon, D.J.Tobias, R.B.Gerber J.Phys.Chem.A 113, 12805-12814(2009) 55. "Quantum mechanical/molecular mechanical/continuum style solvation model: linear response theory, variational treatment, and nuclear gradients" H.Li J.Chem.Phys. 131, 184103/1-8(2009) 56. "Aqueous solvation of bihalide anions" D.D.Kemp, M.S.Gordon J.Phys.Chem.A 114, 1298-1303(2010) 57. "Exchange repulsion between effective fragment potentials and ab initio molecules" D.D.Kemp, J.M.Rintelman, M.S.Gordon, J.H.Jensen Theoret.Chem.Acc. 125, 481-491(2010). 58. Modeling Solvent Effects on Electronic Excited States A.DeFusco, N.Minezawa, L.V.Slipchenko, F.Zahariev, M.S.Gordon J.Phys.Chem.Lett. 2, 2184-2192(2011)