CHARMM c30b1 mmff.doc

File: MMFF ]-[ Node: Top
Up: (commands.doc) -=- Next: Usage\n

             Merck Molecular Force Field (MMFF94)

* Menu:

* Usage::         How to use MMFF with CHARMM standalone
* Quanta::        How to use MMFF from QUANTA
* Status::        Current status of MMFF implementation in CHARMM
* Theory::        Basis for, parameterization and performance of MMFF94
* Funcform::      Functional form of the MMFF energy expression
* Refs::          References to papers describing MMFF94
* Parameters:(mmff_params.doc).  MMFF Parameters

File: MMFF ]-[ Node: Usage
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In order to use MMFF in CHARMM, the user has to issue the following

1. use mmff force field
2. <read mmff parameter files>
3. (a) read rtf name <MMFF-capable rtf file>, or
   (b) read merck name <file_name>
   (c) read mol2 name <file_name>
   (d) read db mol_name name <file_name>
4. read sequence  ! if input is via the rtf route (step 3 (a))
5. generate  ! note that there may be multiple segments in one .mrk file
6. patch     ! if input is via rtf/sequence route, apply appropriate patches
             ! to force a new mmff_setup; either include the keyword "mmff" 
             ! on the final patch or follow the final patch by the command:
             ! "use mmff atom types"
7. read coord, or ic build  ! if input is via the read rtf/sequence route.  

Steps 1 & 2 can be done by streaming the file "mmff_setup.STR."  An example
of this file is shown below.  Documantation on the contents and usage of the
MMFF parameter files may be found in mmff_params.doc.

Step 3a requires a MMFF-capable rtf file.  This means a file in which 
BOND records have been replaced by analogous DOUBLE or TRIPLE records for
cases in which the chemical structure (or any valid Kekule representation)
has a double or triple bond.  Mass records in a MMFF-capable rtf file 
must also be augmented to add the atomic symbol for each CHARMM atom type
after the atomic mass entry.  Note that MMFF-capable rtf files are *back 
compatible*.  That is, such rtf files can equally well be used for 
calculations that utilize the CHARMM force field.  Thus, it is *not* necessary 
to maintain two versions of the rtf files.

Format of .mrk file optionally read in step 3b

Merck-format files consist of one or more consecutive molecular-data entries.
Note: when embedded in a CHARMM input script, a mrk file must be followed by
a card reading "END" in columns 1:3.


	All entries in a Merck-format (.mrk) file have the format:
             Line #     # of Lines      Use
               1            1            Header_1
               2            1            Header_2
               3            1            Number of atoms and bonds
               4            n            Data on n atoms
              4+n           k            Bonding data on the 5*k bonds 
                                         in the structure  (Each line 
                                         contains data on five bonds)

	The format for the first header line is:


	Each field contains the following information:

                column  Description of use
                 1-70    User defined title
                71-72    Present Year (YY)
                73-75    Present Date (DDD)
                76-79    Time of Day (HHMM), e.g., "1709" for 5:09 pm
                   80    Must be a "1" for the file to be valid

	The second header line has the following format:

	Each of the fields has the following information:

                column  Description of use
                 1- 4    The string "MOL "
                 5-12    User name
                   14    Source of file : (e.g., E for MOLEDIT, C 
			 for Cambridge, D for Distance Geometry etc.)
                16-80    Column used by other programs such as the 
			 Cambridge Programs and OPTIMOL

	The format for this record is:


	Each of the fields has the following information:

                column  Description of use
                 1-5     NATOM
                 7-11    NBND

	The format for the atom records is:


	Each of the fields has the following information:
        Columns     Field               Description
          1-10       X                  X coordinate of the atom
         12-21       Y                  Y coordinate of the atom
         23-32       Z                  Z coordinate of the atom
         34-38       Atomic Number      (I5) field containing the type
                                         of atom. (i.e. -- 6 for Carbon;
                                         8 for Oxygen; etc...) A value 
                                         of 0 indicates a lone pair.
         40-41        Atom Subtype       (I2) field: on output, contains the
                                         MMFF atom type; is not read on input
            43        Charge Code        Formal charge code of the atom.
         45-49       Sequence Number     (I5) field containing the unique
                                         number by which every atom in 
                                         the structure can be identified.
                                         Note: in the CHARMM implementation,
                                         these quantities are not actually 
                                         read.  However, the atoms are
                                         expected to be numbered consecutively
                                         from 1 to NATOM and to correspond to 
                                         the numbers used in the bond_data 
                                         records defined below.
         51-54        Atom Name          Left justified (A4) field. 
                                         Should be unique inside a
                                         given residue. (Examples -- "C24 ",
                                         "NH  ", etc...).
         55-58        Residue Name       Right justified (A4) field.
                                         (Examples -- " 123", "123A",
         59-62        Residue Type       Left justified (A4) field.
                                         (Examples -- "TRP ", "LYS ",
         63-70        Partial Charge     (F8.4) field containing the partial
                                         charge of an atom in proton units.
                                         Note: this entry is written on output,
                                         but is not read on input.

         77-80        Segment ID         Left justified (A4) field containing 
                                         a one to four character segment ID
Note: if any of the A4 fields specified above are blank, the file reader will
construct a default name.
        The valid charge codes are:
                Code            Charge Code
                  0              Neutral
                  1               +1
                  2               -1
                  3              Radical
                  4               +2
                  5               -2
                  6               +3
                  7               -3
                  8               +4
                  9               -4


	The block of data at the end of the .mrk file contains the bonding 
	information.  Each line of bond data can contain a maximum of five 
	bond definitions.  The format for the bond data is:
        For each bond definition,
		Field       Description
                IFROM       (I5) Sequence number of the starting 
                            atom of the bond 
		ITO	    (I5) Sequence number of the terminating
                            atom of the bond 
		ITYPE       (I2) Order of the bond. (i.e. 1 for a single 
			    bond, 2 for a double bond, etc.)
                            Bond orders are always integral
end of mrk format specification

As noted, the .mrk file reader in CHARMM can read concatenated .mrk files. 
It should also be possible to 'read merck ... append'.
These two input routes should be equivalent as far as final the data 
structure is concerned.

NOTE: 1. no binary parameter files are supported for MMFF.
      2. MMFF is an all hydrogen force field -- i.e., extended atoms
         are not supported

Format of .mol2 file optionally read in step 3c

SYBYL MOL2-format files provides a complete representation of a molecule for
use with software from Tripos Inc. (including SYBYL). Details of the format
can be found in documentation from Tripos Inc.
Note: when embedded in a CHARMM input script, a mol2 file must be followed by
a card reading "END" in columns 1:3.


The exact content of MOL2 files generated by SYBYL may vary based on
different processing of the molecules. However, it should at least contain
the following records:


These four sections provide different information about the molecule
and are necessary to reconstruct the molecule.



    num_atoms num_bonds num_subst num_feat num_sets

    This entry indicates the name of the molecule and has a string format.

    This indicates the number of atoms in the molecule. Integer format.

    This indicates the number of bonds in the molecule. Integer format.

    This indicates the number of substructures in the molecule. Integer format.

    This indicates the number of features in the molecule. Integer format.

    This indicates the number of sets in the molecule. Integer format.

    This indicates the molecule type.

    This indicates the type of charges associated with the molecule.

@<TRIPOS>ATOM section

    The format of this section contains the following information

    (atom_id atom_name x y z atom_type subst_id subst_name charge)

    and has the following format:


    Each of the fields has the following information:

         column  Field       Description of use

          1- 8   atom_id     the ID number of the atom at the time the mol2
                             file was created
          9-12   atom_name   the name of the atom
         17-26   x           the x coordinate of the atom
         27-36   y           the y coordinate of the atom
         37-46   z           the z coordinate of the atom
         48-51   atom_type   the SYBYL atom type for the atom
         55-58   subst_id    the ID number of the substructure containing
                             the atom
         60-63   subst_name  the name of the substructure containing the atom
         70-77   charge      the charge associated with the atom

@<TRIPOS>BOND section

    The format of this section contains the following information

    (bond_id origin_atom_id target_atom_id bond_type)

    and has the following format:


    Each of the fields has the following information:

         column  Field         Description of use

          2- 6  bond_id        the ID number of the bond at the time the mol2
                               file was created
          7-11  origin_atom_id the ID number of the atom at one end of the bond
         12-16  target_atom_id the ID number of the atom at the other end
                               of the bond
         18-19  bond_type      the SYBYL bond type


    The data line contains the substructure ID, name, root atom of the
    substructure, substructure type, dictionary type, chain type, subtype,
    number of inter substructure bonds, SYBYL status bits, and user defined
    comment. Information contained in this section is not read nor used by
    the MMFF module. The format is open for this section.

Format of .mol2 file optionally read in step 3d

SYBYL MOL2 database files have a format identical to that described in
step 3c. If the database is read in as an external file, there is no need
to put "END" at the end of every mol2 molecule.

end of mol2 format specification

NOTE: (1) Each atom in the MOL2 file should have a unique atom name in order
          for the MMFF bond types to be assigned properly.
      (2) For external database reading capability, the maximum length of
          a molecule name in the MOL2 database file is currently set to be
          a string of 20 UPPERCASE characters. A molecule name is read in
          the line of mol_name in @<TRIPOS>MOLECULE section.
      (3) Due to the fact that bonds are not explicitly typed in the MOL2
          format, a conversion of MOL2 non-integer bond type (e.g. ar and am)
          into MMFF recognizable type was made.  The type of an amide bond
          is always set to be 2. For aromatic bonds within an aromatic ring,
          they are assigned to be alternating single and double bonds.
          The algorithm first separates aromatic bonds (and the associated
          atoms) from any integer-type bond. It arbitrarily sets the first
          aromatic bond to be a single bond and then starts a loop of
          aromatic bond assignment. During the course of assignment,
          the surrounding connectivity information of an atom with aromatic
          bond type is taken into account.  However, problems may still occur
          during this step. The authors welcome reports of any problematic

Examples of MMFF usage in CHARMM are given in mmff*.inp files in the test 

File: MMFF ]-[ Node: Quanta
Up: Top -=- Next: Status -=- Previous: Usage\n

Here is the current "prescription" for to use MMFF in CHARMm from

(1) In the CHARMm menu, select "MMFF" within the "CHARMm MODE" menu item.

(2) Proceed as you normally would; until an alternative MODE is selected,  
    all requests for CHARMm energy services will use the MMFF force field.

Note: QUANTA communicates with CHARMm by writing a .mrk (Merck-format) file
named .charmm_mmff.  Because MMFF does not recognize special "aromatic" or
"resonant" bond orders (e.g., 7), a translation to a 'Kekule' structure is
made as the .mrk file is being written.  On some ocassions, the routines in
QUANTA that make this translation (as of February 1996) do so incorrectly.  
It is therefore safest - and sometimes *necessary* - for the QUANTA user to
first employ the Molecular Editor to change the structure to Kekule format,
to examine it visually, and to repair incorrect bonding if needed.

Quanta also sends the requisite "stream mmff_setup.STR" and "read Merck"
commands to CHARMm.  A typical mmff_setup.STR file is shown below:

* setup of MMFF in CHARMM
use mmff force field

open read form unit 1 name "$CHM_DATA/MMFFSUP.PAR"
read parameter card mmff SUPP unit 1
read parameter card mmff PROP name "$CHM_DATA/MMFFPROP.PAR"
read parameter card mmff SYMB name "$CHM_DATA/MMFFSYMB.PAR"
read parameter card mmff DEFI name "$CHM_DATA/MMFFDEF.PAR"
read parameter card mmff BNDK name "$CHM_DATA/MMFFBNDK.PAR"
read parameter card mmff HDEF name "$CHM_DATA/MMFFHDEF.PAR"
read parameter card mmff AROM name "$CHM_DATA/MMFFAROM.PAR"
read parameter card mmff VDW  name "$CHM_DATA/MMFFVDW.PAR"
read parameter card mmff BOND name "$CHM_DATA/MMFFBOND.PAR"
read parameter card mmff CHRG name "$CHM_DATA/MMFFCHG.PAR"
read parameter card mmff PBCI name "$CHM_DATA/MMFFPBCI.PAR"
read parameter card mmff ANGL name "$CHM_DATA/MMFFANG.PAR"
read parameter card mmff STBN name "$CHM_DATA/MMFFSTBN.PAR"
read parameter card mmff DFSB name "$CHM_DATA/MMFFDFSB.PAR"
read parameter card mmff OOPL name "$CHM_DATA/MMFFOOP.PAR"
read parameter card mmff TORS name "$CHM_DATA/MMFFTOR.PAR"
close unit 1


File: MMFF ]-[ Node: Status
Up: Top -=- Next: Theory -=- Previous: Quanta\n

Status of MMFF implementation into CHARMM (February 1996)

This implementation of MMFF in CHARMM is principally due to Ryszard
Czerminski (MSI) and Jay Banks (first of MSI, later a consultant
to Merck and to NIH), working in conjunction with Tom Halgren (Merck).

Features currently supported in CHARMM/MMFF

  (1) energy, first & second derivatives
  (2) minimization
  (3) dynamics
  (4) most ATOM based cutoff options (force switch is not implemented for
      vdW interactions; for vdW force shift, a generalized version is used 
      with beta=4 -- see Steinbach and Brooks, J. Comput. Chem., 15, 667-683 
  (5) fast routines, implelented using the "PARVEC" paradigm
  (6) the multiple time step algorithm (should work, if it does not use custom 
      calls for energy services)
  (7) PERT, BLOCK, and TSM free energy methods, but only for a limited range 
      of problems.  The current MMFF setup code requires that the input 
      structure be a valid chemical species (e.g., no more than four bonds 
      to carbon), and therefore does not allow for dummy atoms.  However, 
      it should be possible to use TSM for internal-coordinate perturbations 
      and BLOCK for perturbations in which the blocks are not interbonded 
      (examples are given in the mmff*pert*.inp scripts that may be found in 
      the test directory).  For PERT, it is also possible to use rtf/sequence 
      input and to add dummy atom(s) after the "generate" command has done a 
      MMFF  setup on the original data structure.  This would be accomplished 
      by applying one or more patches and then, without repeating the MMFF 
      setup (e.g., without again giving the generate command), using scalar 
      commands to set the MMFF atom types and partial charges.  See the 
      mmff_pert.inp script that may be found in the test directory (if it is 
      up to date). In this case, parameters for the dummy atom(s) are read 
      from the MMFFSUP.PAR supplementary-parameters file. An example of such 
      a file is shown below:

   -------------------------- MMFFSUP.PAR ------------------------------------
       1    1    0    0    1    0    0    2
   !  NV,  NS, MUA,  NQ,  NB,  NO, NSB,  NT
   ! NV    - supplementary VDW parameters
   ! NS    - supplementary BOND strech parameters
   ! MUA   - not used
   ! NQ    - supplementary CHARge parameters
   ! NB    - supplementary ANGL bending parameters
   ! NO    - supplementary OOPL parameters
   ! NSB   - not used
   ! NT    - supplementary TORSional parameters
      0.25      0.2       12.       0.8        0.5
      99     0.100     0.100     0.100     0.000 - DUMMY
   0   5   99     1.000     0.500   parameters for dummy atoms
   0   1    5   99     0.100   120.000   parameters for dummy atoms
   0  99    5    1    5   0.000   0.000   0.100   parameters for dummy atoms
   0  99    5    1    6   0.000   0.000   0.100   parameters for dummy atoms

Major features NOT currently implemented in CHARMM/MMFF:

  (1) bonds between primary atoms and image atoms.
  (2) Some cutoff options.  In particular,
        group-based cutoffs are not supported.
  (3) Fast multipoles.

Other known limitations:

  (1) correlation analysis tools have not been implemented for MMFF specific 
      energy terms -- e.g. it is not possible to calculate the correlation
      function for an out-of-plane bending angle, etc ...     
  (2) .mrk files do not have group information -- i.e. residues = groups
  (3) only all-atom models (no extended atoms)

There are probably other problems/limitations/bugs. Your comments about 
limitations of the current MMFF implementation in CHARMM (and bugs) will be 
very valuable.

Similarly, comments about deficiencies (as well as of particular strengths!) 
of the current MMFF parametrization would be very valuable for Tom Halgren, 
the author of MMFF.

Please direct comments to:

Ryszard Czerminski, MSI
phone:  (617)229-8875 x 217

Tom Halgren, Merck Research Laboratories.
phone: (908) 594-7735


File: MMFF ]-[ Node: Theory
Up: Top -=- Next: Refs -=- Previous: Status\n The Merck Molecular Force Field (MMFF94)

       A Broadly Parameterized, Computationally Derived Force Field 
                  for Organic and Bio-organic Systems 

                           Thomas A. Halgren
              Merck Research Laboratories, Rahway, New Jersey 07065

                             February, 1996

1. Introducing The Merck Molecular Force Field.

The Merck Molecular Force Field (MMFF) represents a systematic attempt
to combine the best features of such well-regarded force fields as MM3,
OPLS, AMBER, and CHARMM into a *single* force field that is equally
adept in small-molecule and macromolecular applications.  In particular,
MMFF strives for MM3-like accuracy for small molecules in a force field
that can be used with confidence in condensed-phase simulations.  

References to five papers introducing MMFF94 are given elsewhere within
this documentation.

2. The Basis and Motivation for the Formulation of MMFF.

Ideally, a single molecular mechanics/dynamics force field would reproduce 
all of the following, and other, molecular properties accurately both in 
gas-phase and in condensed-phase simulations: 

	* molecular geometries
	* conformational and stereoisomeric energies
	* torsional barriers and torsion-profile energies
	* intermolecular-interaction energies
	* intermolecular-interaction geometries
	* vibrational frequencies
	* heats of formation

Because of their relatively simple construction, however, current force 
fields necessarily make a variety of compromises.  MMFF94 focusses on 
accurately reproducing conformational and intermolecular-interaction energies.
It also regards molecular geometries, torsional barriers, and intermolecular-
interaction geometries as being relatively important.  Vibrational 
frequencies have been parameterized against a combination of theoretical
and experimental data, but are regarded as being less important.  Heats of 
formation are not normally needed to understand such qunatities as differences 
in ligand-enzyme binding energies, and are not addressed in MMFF. 

To be widely applicable, MMFF could not be parameterized against experimental 
data because far too little data of high quality are available, especially for 
conformational and intermolecular-interaction energies.  Instead, MMFF has 
been derived almost solely from computational data, though experimental data
have been used liberally in its validation.

Many of the processes we wish to model at Merck occur in condensed phases.  
Like many other well-known force fields, MMFF therefore employs effective pair 
potentials that reflect in an averaged sense the enhancement of the charge 
distribution in a high-dielectric medium due to molecular polarizability; a 
better, but still future, approach would of course be to include polarizability 

3. Discussion

The principal distinguishing feature of MMFF is that it is primarily
computationally derived.  This approach is made possible because of recent
increases in computing power; it is made necessary because pertinent
experimental data are lacking for many of the chemical structures a force field
suitable for general use in chemical and pharmaceutical applications must be
prepared to handle.  MMFF's parameterization utilizes a large amount of
high-quality computational data -- ca. 500 molecular structures optimized at
the HF/6-31G* level, 475 structures optimized at the MP2/6-31G* level, 380
structures evaluated at the composite "MP4SDQ/TZP" level using MP2/6-31G*-
optimized geometries, and 1450 structures evaluated in single-point 
calculations at the MP2/TZP level. This core has been significantly expanded 
by using data from approximately 2800  Cambridge Structural Database 
structures in conjunction with additional computational data and with a 
series of carefully calibrated empirical rules and default-parameter 
assignment procedures.  This expanded parametrization embraces nearly all 
stable organic compounds in a systematic, objective, and consistent way, 
making "missing parameters" virtually a thing of the past.

The computationally derived "core" MMFF parameters cover a broad range
of functional groups.  Among "monofunctional" chemical families, MMFF has been
parameterized for alkanes, alkenes, alcohols, phenols, ethers, aldehydes,
ketones, ketals, acetals, hemiketals, hemiacetals, amines, amides, peptides,
ureas, imides, carboxylic acids, esters, carboxylate anions, ammonium cations,
thiols, mercaptans, disulfides, halides (chlorides and fluorides), imines,
iminium cations, amine N-oxides, hydroxylamines, hydroxamic acids, amidines,
guanidines, amidinium cations, guanidinium cations, imadazolium cations,
aromatic hydrocarbons, and heteroaromatic compounds.  The structural coverage
is quite broad for many of these chemical families, but still is somewhat 
limited for others. 

Many of the bifunctional compounds included in the parameterization are
unsaturated analogs of families listed above, i.e.: conjugated alkenes and
aromatic hydrocarbons (e.g., styrenes); alpha,beta-unsaturated variants of
amides, imines, aldehydes, ketones, carboxylic acids, esters, and carboxylate
anions; vinylic ethers, alcohols, amines and esters; and allylic aldehydes,
ketones, amines and alcohols.  Other bifunctional compounds include:
beta-ketoacids; beta-hydroxyesters; dicarboxylic acids; 1,2-diols, 1,2-diamines
and 1,2-dithiols; and nonconjugated dienes.  A limited selection of alkanes,
amines, ketones, halides and ethers containing 4- or 5-membered rings has also
been included. Compounds containing SO2 and phosphate groups have been 
parameterized as a part of the extension of MMFF's parameterization mentioned 

Another important advantage of MMFF is that nearly all of its parameters
have been determined in a mutually consistent fashion from the full set
of computational data.  In most other force fields, parameters are
determined for one functional group at a time, and then frozen before
moving on to the next functional group.  This approach fails to allow
for correlations that can make one subset of the parameters
inappropriate for fitting data on subsequent functional groups.  MMFF's
derivation, in contrast, simultaneously employed all data (e.g., on
conformational energies) in determining the associated parameters (e.g.,
torsion).  Furthermore, the parameter derivation procedures were
iterated between three and four times, in order to allow each class of
parameters (e.g., bond and angle reference values, quadratic force 
constants, charges, torsion parameters) to be determined in a mutually 
consistent fashion in the context of successively refined values for 
parameters belonging to other classes.

The reliance almost solely on computational data, the quality and
quantity of the supporting ab initio calculations, and the methodology
used in deriving mutually consistent values for most classes of
parameters, together with novel elements of its functional form, combine
to make MMFF's derivation unusual and possibly unique.  They also
combine to produce a force field that by contemporary standards
performs very well.  MMFF reproduces the computational data used in its
parameterization with rms deviations of 0.006 angs for bond lengths,
1.16 deg for bond angles, 5 deg for most torsion angles, 0.31 kcal/mol
for conformational energies, and 0.50 kcal/mol for comparisons of
relative energies along torsion profiles.  Crucially important
intermolecular-interaction energies and geometries closely adhere to
benchmarks established using ab initio calculations on small-molecule dimers. 
Molecular charge distributions are also described reasonably well: rms 
deviations are 0.39 D for HF/6-31G* molecular dipole moments and 5.5 deg 
for dipole directions.  

In addition, MMFF predicts experimental bond lengths, bond angles, and 
vibrational frequencies essentially as accurately as does MM3, and 
reproduces conformational energies and rotational barriers to 
0.4 kcal/mol rms, about as well as can be expected given the disparate
nature and uncertain accuracy of the experimental results. These results 
are encouraging, because they demonstrate that fitting MMFF to high-quality 
theoretical data has simultaneously conferred the ability to fit experiment.  
In contrast to experimentally derived force fields, MMFF's great strength is 
that it can be expected to perform equally well for the wide range of systems 
for which it has been parameterized but for which no experimental data are 

I expect a computational approach like the one employed for MMFF to be
indispensable in future efforts to derive still more accurate force
fields which, for example, may explicitly incorporate polarizability and
represent the electrostatic potential more accurately than is possible
using only atom-centered charges.  Fortunately, further improvements in
computer technology can be expected to make it increasingly feasible
both to utilize the more complex force fields which result and to employ
even more rigorous computational models to generate the data needed to
parameterize them.  I doubt that any other approach will be capable of
producing a physically superior force field which not only performs
accurately in condensed-phase simulations but is parameterized sufficiently 
broadly to support the full range of significant pharmaceutical, organic and 
biochemical applications.

File: MMFF ]-[ Node: Funcform
Up: Top -=- Next: Top -=- Previous: Theory\n

        The MMFF energy expression can be written as

EMMFF = Sum EBij  + Sum EAijk  + Sum EBAijk  + Sum EOOPijk;l  	          (1)
                  + Sum ETijkl  + Sum EvdWij  + Sum EQij

where the constituent terms, each expressed in kcal/mol, are defined as 
shown below.

1. Bond Stretching.  MMFF employs the quartic function:  

EBij  =  0.5*143.9325*kbIJ*Drij**2*(1 + cs*Drij + 7/12 cs**2*Drij**2),    (2)

where kbIJ is the force constant in md/angs, Drij = rij - roIJ is the
difference in Angstroms between actual and reference bond lengths, and cs = -2
angs**(-1) is the "cubic stretch" constant.  This function corresponds to an
expansion through fourth order of a Morse function with an "alpha" of 2
angs**(-1).  Results published in a recent high-level ab initio study [1] show
this value for alpha to be a representative one.  Note: throughout this
Account, the indices i, j, k, ... represent atoms and I, J, K, ... denote the
corresponding numerical MMFF atom types. 

2. Angle Bending.  MMFF normally uses the cubic expansion:

EAijk  =  0.5 * 0.043844 * kaIJK * DTijk**2 * (1 + cb*DTijk),             (3)
where kaIJK is the force constant in md-ang/rad**2, DTijk = Tijk - ToIJK is
the difference between actual and reference bond angles in degrees, and
cb = -0.007 deg**(-1) is the "cubic-bend" constant.  

For linear or near-linear bond angles, MMFF instead employs the well-behaved 
form used in DREIDING [2] and UFF [3]:

EAijk  =  143.9325 * kaIJK * (1 + cos(Tijk))                             (4)

3. Stretch-Bend Interactions.  MMFF employs the form:

EBAijk   = 2.51210 * (kbaIJK * Drij + kbaKJI * Drkj) * DTijk,             (5)

where kbaIJK and kbaKJI are force constants in md/rad which couple the i-j and 
k-j  stretches to the i-j-k bend, and Drij, Drjk and DTijk are as defined
above. Stretch-bend interactions are omitted for linear bond angles. 

4. Out-of-Plane Bending at Tricoordinate Centers.  MMFF uses the form:

EOOPijk;l  =  0.5 * 0.043844 * koopIJK;L * Xijk;l**2,                     (6) 
where koopIJK;L is the force constant in md-angs/rad**2 and Xijk;l is the
Wilson angle [4] in degrees between the bond j-l and the plane i-j-k. Because
it uses eq 3 for the "in-plane" angles, MMFF is able to properly describe the
nonplanar centers found, e.g., in enamines, sulfonamides, and even amides. 

5. Torsion Interactions.  MMFF uses the three-fold representation employed 
in MM2 and MM3, where W is the i-j-k-l dihedral angle:

ETijkl = 0.5 * (V1 (1 + cosW) + V2 (1 - cos2W) + V3 (1 + cos3W))          (7)

        6. Van der Waals Interactions.  MMFF employs the recently developed
"Buffered 14-7" form (eq 8) together with an expression which relates the
minimum-energy separation R*II to the atomic polarizability aI (eq 9), a
specially formulated combination rule (eqs 10, 11), and a Slater-Kirkwood
expression for the well depth epsIJ (eq 12) [5]: 

Evdwij  =  epsIJ*{1.07R*IJ/(Rij+0.07R*IJ)}**7 *  
                 {1.12 R*IJ**7/(Rij**7 + 0.12R*IJ**7) - 2}                (8)

R*II = AI * aI**(0.25)                                                    (9)

R*IJ =  0.5 * (R*II + R*JJ) * (1 + 0.2 (1 - exp(-12*gIJ**2)))            (10) 

gIJ = (R*II - R*JJ)/(R*II + R*JJ)                                        (11)

eIJ =  181.16*GI*GJ*aIaJ/[(aI/NI)**0.5 + (aJ/NJ)**0.5]*R*IJ**(-6)        (12)

Most vdW well depths and radii conform to simple systematic trends 
adduced from high-quality experimental data on vdW interactions of rare-
gas atoms and of small molecules with one another [5]

        7. Electrostatic Interactions.  MMFF uses the buffered Coulombic 

EQij  =  332.0716*qi*qj/(D*(Rij + d)),                                   (13)

where qi and qj are partial atomic charges, Rij is the internuclear separa-
tion in angs, d = 0.05 angs is the "electrostatic buffering" constant, and D is
the "dielectric constant" (normally taken as D = 1, though use of a distance-
dependent dielectric constant is also supported).  Partial atomic charges qi
are constructed from initial full or fractional formal atomic charges (usually
zero, but, e.g., -0.5 for carboxylate oxygens) by adding contributions from
bond charge increments wKI which describe the polarity of the bonds to atom i
>from attached atoms k.  Specifically, MMFF computes qi as 

qi = q0i + Sum wKI                                                       (14)

where wIK= - wKI. 1,4-interactions are scaled by a factor of 0.75.  Distance 
buffering (d > 0) prevents infinite attractive electrostatic energies from 
overwhelming the bounded repulsive vdW interaction given by eq 8 as 
oppositely charged atomic centers approach.  

Unlike MM2 and MM3, MMFF employs a unit dielectric constant, and
thereby allows straightforward application to condensed-phase simulations
employing explicit solvent molecules.  Like AMBER [6], CHARMM [7], OPLS [8] and
other force fields used in molecular dynamics simulations, MMFF describes
hydrogen bonding interactions as being essentially electrostatic in nature,
whereas MM2 (1987 parameters and later) and MM3 in some cases attribute a
significant portion of the stabilization energy to an attractive vdW term which
would not be attenuated upon immersion in a high-dielectric medium.  This
difference, too, may serve to make MMFF more readily applicable to
condensed-phase simulations. 


[1] Orozco, M.; Luque, F. J. J. Comput. Chem. 1993, 881-894.

[2] Mayo, S. L.; Olafson, B. D.; Goddard III, W. A. J. Phys. Chem. 1990, 94,

[3] Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard III, W. A; Skiff, W.
M. J. Am. Chem. Soc. 1992, 114, 10024-10035, and references therein. 

[4] Wilson, E. B., Jr; Decius, J. C.; Cross, P. C., Molecular Vibrations;
Dover: New York, 1955, Chapter 4. 

[5] Halgren, T. A. J. Am. Chem. Soc. 1992, 114, 7827-7843.

[6] Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A. J. Comput. Chem. 
1986, 7, 230-252;  Weiner, S. J.; Kollman, P. A.; Nguyen, D. T.; Case, D. A.; 
Singh, U. C.; Ghio, C.; Alagona, G.; Profeta, S.; Weiner, P. J. Am. Chem. Soc. 
1984, 106, 765-784. 

[7] Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.;
Swaminathan, S.; Karplus, M. J. Comput. Chem. 1983, 4, 187-217. 

[8] Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. Soc. 1988, 110, 1657-
1666, and references therein.

File: MMFF ]-[ Node: Refs
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The following five papers introduce the MMFF94 force field:

[1] "Merck Molecular Force Field. I. Basis, Form, Scope, Parameterization, and
Performance of MMFF94," Thomas A. Halgren, J. Comput. Chem., 17, 490-519 

[2] "Merck Molecular Force Field. II. MMFF94 van der Waals and Electrostatic
Parameters for Intermolecular Interactions," Thomas A. Halgren, J. Comput. 
Chem., 17, 520-552 (1996)

[3] "Merck Molecular Force Field. III. Molecular Geometries and Vibrational 
Frequencies for MMFF94," Thomas A. Halgren, J. Comput. Chem., 17, 553-586 

[4] "Merck Molecular Force Field. IV. Conformational Energies and Geometries 
for MMFF94," Thomas A. Halgren and Robert B. Nachbar, J. Comput. Chem., 17, 
587-615 (1996).

[5] "Merck Molecular Force Field. V. Extension of MMFF94 Using Experimental
Data, Additonal Computational Data, and Empirical Rules," Thomas A. Halgren, 
J. Comput. Chem., 17, 616-641 (1996).

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