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. 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, one or more $FRAGNAME groups describing each fragment's EFP, and a $FRGRPL group. These groups define non-bonded interactions between the ab initio system and the fragments, and 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 (e.g. 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.
At ISU, the EFPs are currently used to model RHF/DZP water molecules in order to study aqueous solvation effects, for example references 1,2,3. Our co-workers at NIST have also used EFPs to model parts of enzymes, see reference 4.
The non-bonded interactions currently implemented are:
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 molecular dipole polarizability tensor can be obtained during a Hessian run ($CPHF), and a distributed LMO polarizability expression is also available ($LOCAL: POLDMC).
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 repulsive potential, or the charge interpenetration screening parameters.
Since you cannot develop all terms necessary to define a new EFP's $FRAGNAME group using GAMESS, in practice you will be limited to using the internally stored H2OEF2 potential mentioned below.
At the present time, we have only one EFP suitable for general use. This EFP models water, and its numerical parameters are internally stored, using the fragment name H2OEF2. These numerical parameters are improved values over the H2OEF1 set which were presented and used in reference 2, and they also include the improved EFP-EFP repulsive term defined in reference 3. The H2OEF2 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.
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:
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 first of these is more descriptive, and the second has a very detailed derivation of the method. The latest EFP developments are discussed in the 3rd paper.