CHARMM Element doc/mmff_params.doc $Revision: 1.1 $
File: MMFF_PARAMS, Node: Top, Up: (chmdoc/mmff.doc), Next: MMFFSYMB
The MMFF94 Setup Procedure And Parameter Files
* Menu:
* MMFFSYMB::
* MMFFAROM::
* MMFFHDEF::
* MMFFDEF::
* MMFFPROP::
* MMFFBOND::
* MMFFBNDK::
* MMFFANG::
* MMFFSTBN::
* MMFFDFSB::
parameters)
* MMFFOOP::
* MMFFTOR::
* MMFFVDW::
* MMFFCHG::
parameters)
* MMFFPBCI::
* MMFFSUP::
The
The
The
The
The
The
The
The
The
The
MMFFSYMB.PAR
MMFFAROM.PAR
MMFFHDEF.PAR
MMFFDEF.PAR
MMFFPROP.PAR
MMFFBOND.PAR
MMFFBNDK.PAR
MMFFANG.PAR
MMFFSTBN.PAR
MMFFDFSB.PAR
file
file
file
file
file
file
file
file
file
file
(symbolic atom types)
(aromatic atom types)
(atom types for hydrogens)
(numeric atom types)
(properties of MMFF atom types)
(bond-stretching parameters)
(empirical-rule bond parameters)
(angle-bending parameters)
(stretch-bend parameters)
(empirical-rule str-bend
The
The
The
The
MMFFOOP.PAR
MMFFTOR.PAR
MMFFVDW.PAR
MMFFCHG.PAR
file
file
file
file
(out-of-plane bending parameters)
(torsion partameters)
(van der Waals parameters)
(bond-increment "charge"
The MMFFPBCI.PAR file (empirical-rule charge paramters)
The MMFFSUP.PAR file (supplementary MMFF parameters)
File: MMFF_PARMS, Node: MMFFSYMB, Up: Top, Next: MMFFAROM, Previous: Top
1. MMFFSYMB.PAR. Starting from the input atomic species, connectivity,
and formal bond orders (for aromatic systems, for example, a Kekule
structure having alternating single and double bonds must be supplied),
the
MMFF structural perception code automatically "sets up" the calculation
by
perceiving and classifying rings, detecting aromaticitity, and creating
appropriate lists of bond, angle and torsional interactions. The atom
typing
procedures (currently overseen by subroutines XTYPE, HTYPE and RGTYPE)
then assign a 4-character symbolic atom type to each atom. Finally, the
entries in MMFFSYMB.PAR are used to translate the symbolic atom types
into
the numeric atom types actually employed in assigning force-field
parameters to the force-field interaction terms. Note that this is a
manyto-one translation, in that more than one symbolic atom type usually
corresponds to a given numeric atom type. The descriptive text strings
to
the right of the columns bearing the symbolic and numeric atom types are
given for informational purposes only.
File: MMFF_PARMS, Node: MMFFAROM, Up: Top, Next: MMFFHDEF, Previous:
MMFFSYMB
2. MMFFAROM.PAR. The assignment of symbolic atom types is actually a
two-stage process. For the carbons in benzene, for example, the first
stage,
which uses only the local connectivity, would assign a symbolic atom type
of
CE, meaning unsaturated or olefinic carbon. The second stage (currently
controlled by subroutine RGTYPE) perceives that these carbons lie in an
aromatic six-membered ring and uses the elements of MMFFAROM.PAR to
assign the correct aromatic atom type. Some lines from the version of
this
parameter file as of 2/96 are listed below:
*
*
Copyright (c) Merck and Co., Inc., 1994, 1995, 1996
*
All Rights Reserved
*
* MMFF AROMATIC SYMBOLIC TYPES VS ORIGINALLY ASSIGNED TYPES
* OLD AROM AT
RING
IM
N5
* TYPE
TYPE NUM
SIZE
L5
CAT
ANION
C* CB
6
6
0
0
0
N* NPYD 7
6
0
0
0
NCN+ NPD+
7
6
0
0
0
N+=C NPD+
7
6
0
0
0
N=+N
NPD+ 7
6
0
0
0
N2OX
NPOX 7
6
0
0
0
*
C* C5A 6
5
2
0
0
C* C5B 6
5
3
0
0
C* C5
6
5
4
0
0
N* NPYL 7
5
1
0
0
N* N5A 7
5
2
0
0
N* N5B 7
5
3
0
0
N* N5
7
5
4
0
0
CNN+
CIM+ 6
5
2
1
0
CNN+
CIM+ 6
5
3
1
0
CNN+
CIM+ 6
5
4
1
0
As in all the MMFF parameter files, lines beginning with a "*" are
comment
lines. The column labeled "L5" refers, in the case of 5-ring systems, to
the
position of the atom in question relative to the unique pi-lone-pair
containing heteroatom (which itself occupies position "1"); a "4" is an
artificial entry which is assigned when no such unique heteroatom exists,
as
for example occurs in imidazolium cations and in tetrazole anions. An
entry
of "1" in the "IM CAT" or "N5 ANION" column must also be matched for such
ionic species to convert the "OLD" (first stage) to "AROM" (second stage;
aromatic) symbolic atom type. Note: in matching the "OLD" symbolic atom
types, an "exact" match is first attempted. If this match fails, a wildcarded match, using for example "C*" is then employed.
File: MMFF_PARMS, Node: MMFFHDEF, Up: Top, Next: MMFFDEF, Previous:
MMFFAROM
3. MMFFHDEF.PAR. The symbolic atom type for a hydrogen atom is
assigned by reference to that for its parent non-hydrogen atom, using the
entries in this parameter file. Note that this approach assumes that a
given
hydrogen is bonded to a single parent and thus disallows bridging
hydrogens.
Note also that the code treats molecular hydrogen as a special case, in
as
much as there is then no "parent" atom.
File: MMFF_PARMS, Node: MMFFDEF, Up: Top, Next: MMFFPROP, Previous:
MMFFHDEF
4. MMFFDEF.PAR. The procedures outlined above assign of both a symbolic
and a numeric atom type for each atom. For the purpose of matching force
field interaction terms (such as the stretching interaction between atoms
i
and j), the code first uses the so-generated primary atom type in seeking
a
match with an entry in the relevent (e.g., MMFFBOND.PAR) file. In this
process, the parameter files, which are kept in "canonical order" based
on
indices derived from the numerical atom types, are processed using a
rapid
binary search algorithm. If present, the fully qualified parameter
corresponding to the precise set of atom types (supplemented, in
ambiguous
situations, by defined bond, angle, stretch-bend, or torsion interaction
types
as described below) is used. For vdW, bond stretching, stretch-bend
interaction, and bond charge increment parameters, no equivalences are
recognized. For angle bending, out-of-plane bending, and torsion
interactions, however, whenever the fully qualified parameter is not
found,
the code executes a staged "step down" procedure in which increasingly
generic values are sought. This protocol is governed by the entries in
MMFFDEF.PAR, where the primary ("Level 1") atom types define the fully
qualified parameters. Entries from Levels 2 - 5 are employed as needed
in
subsequent searches. Those at Level 5, always "0", serve as wild cards.
Such
wild card values are used only for "wing atoms" in an angle bending or
torsional interaction or for non-central atoms in an out-of-plane
interaction.
Level 4 generally corresponds to the atomic species, Level 3 to atomic
species plus hybridization. Currently, the first two levels employ
identical
numerical atom types; additional sets of unique values for Level 1 may be
specified later if we find that certain atom types need to be defined
more
specifically. The protocol used in the step-down procedure depends on
the
interaction type (angle, torsion, out-of-plane) Thus, for bending of the
i-j-k angle, a five-stage process based in the level combinations 1-1-1,
2-2-2, 3-2-3, 4-2-4 and 5-2-5 is used. For i-j-k-l torsion interactions,
a five-stage process based on level combinations 1-1-1-1, 2-2-2-2, 3-2-25,
5-2-2-3, and 5-2-2-5 is used, where stages 3 and 4 correspond to "half
default"
or "half wild card" entries. For out-of-plane bending ijk;l, where j is
the
central atom, the five-stage protocol 1-1-1;1, 2-2-2;2, 3-2-3;3, 4-2-4;4,
5-2-5;5 is used. The final stage provides wild-card defaults for all
except
the central atom. Finally, if no parameter is found, a default rule may
be
invoked (see below). Note that the parameter lines begining with a "*"
are
comment lines and are not used, and that the symbolic atom types in the
first
column and the abbreviated text-string definitions in the right-most
portion
of the parameter line are for informational purposes only.
File: MMFF_PARMS, Node: MMFFPROP, Up: Top, Next: MMFFBOND, Previous:
MMFFDEF
5. MMFFPROP.PAR. This file defines atomic properties associated with
the MMFF
numeric atom types. As described below, these properties are used in
setting
up the MMFF energy expression and in determining values for missing
parameters
from defined empirical rules. The first two columns list the MMFF
numeric atom
type and the atomic number for that atom type. Column 3 ("crd) specifies
the
requisite number of bonded neighbors, and column 4, labeled "val", gives
the
total number of bonds made to that atom type. Where an entry shows a
two-digit
number, such as "34" for atom types 54 and 55, the valency may be either
of the
two co-joined values -- e.g., either 3 or 4. Entries of "1" in column 5
("pilp") define those atom types which have a "pi lone pair" capable of
partaking in resonance interactions with, say, an adjacent multiple bond.
Column 6, headed "mltb", specifies cases in which double ("2") or triple
("3")
bonds are expected to be made to an atom having the listed atom type.
This
information is used, for example, in the empirical rule for reference
bond
lengths discussed below in connection with the MMFFBOND.PAR file.
Entries of
"1" in this column designate cases in which intermediate hybdrization and
valence based bond shortenings are employed in that empirical rule, and
roughly
correspond to cases in which strong delocalization to a neighboring atom
can be
expected. Column 7 then specifies, through an entry of "1", the set of
"aromatic" atom types, and column 8 ("lin") in the same manner delineates
those
(necessarily dicoordinate) atom types which involve linear bond angles,
i.e.,
bond angles near 180 deg. Entries of "1" in the final column, headed,
sbmb for
"single-bond--multiple-bond", designate the set of atom types which can
be
involved in multiple bonds but alternatively can also be involved in
delocalized, formally single, bonds with a sp2 (or sp) hybridized
neighbor.
The latter instance, for example, would occur for the bond between the
two
central carbons of butadiene, each of numeric atom type 2. These entries
control the setting of the "bond type index" discussed below.
Specifically, an
nonstandard bond type index BTIJ of "1" is assigned whenever a single
bond
(formal bond order 1) is found a) between non-aromatic atoms i and j of
types I
and J for which "sbmb" entries of "1" appear in the MMFFPROP.PAR file or
b)
between aromatic atoms belonging to different aromatic rings (as in the
case of
the central C-C bond in biphenyl).
File: MMFF_PARMS, Node: MMFFBOND, Up: Top, Next: MMFFBNDK, Previous:
MMFFPROP
6.
MMFFBOND.PAR.
EBij
(1)
=
where:
bonded
The form for bond stretching used in MMFF is:
0.5*143.9325*kbIJ*Drij**2*(1 + cs*Drij + 7/12 cs**2*Drij**2),
kbIJ =
bond stretching force constant in md/angstroms for
atoms i and j of types I and J .
Drij =
rij - roIJ, the difference in angstroms between actual
and
reference bond lengths between bonded atoms i and
j of types I and J.
cs =
-2 angs**(-1), the "cubic stretch" constant.
Note: throughout this description, the indices i, j, k, ... represent
atoms;
I, J, K, ... denote the corresponding numerical MMFF atom types (or,
occasionally, the atomic species).
A few entries taken from the MMFFBOND.PAR file are shown below:
At. Types
BTIJ I
J
kbIJ
roIJ
Origin/Comment
------------------------------------------------------0
1
1
4.258 1.508 C94
0
1
2
4.539 1.482 C94
0
1
3
4.190 1.492 C94
0
1
5
4.766 1.093 C94
0
1
6
5.047 1.418 C94
0
1
10 4.664 1.436 C94
0
2
2
9.505 1.333 C94
1
2
2
4.814 1.430 #C94
1
2
3
4.565 1.468 C94
C94
X94
E94
#C94
#X94
#E94
= CORE MMFF94 parameter - obtained from ab initio data
= EXTD MMFF94 parameter - fit to additional ab initio data
= r0 from fit to X-ray data, kb from empirical rule
= r0 lies between C94 and E94 values, kb from empirical rule
= r0 lies between X94 and E94 values, kb from empirical rule
= r0 and k both from empirical rules
The first entry, labeled BTIJ, is the "bond type" index discussed above
in
connection with the MMFFPROP.PAR file. As described there, this index
normally takes the value 0 but ocassionally takes the value 1. Thus, the
parameter whose three numerical indices are "0 2 2" describes a normal
double bond between olefinic carbons (reference bond length, 1.333 angs),
whereas the next-listed parameter with numerical indices "1 2 2"
describes a delocalized but formally single bond between two such
carbons, e.g., as for the central carbon-carbon bond in butadiene
(reference
bond length, 1.430 angs). The last column, labeled "Origin/Comment",
currently (as of 2/96) distinguishes core MMFF parameters derived in the
extended MMFF parameterization from ab initio data (labeled "C94")
from parameters derived from crystallographic data (labeled "E94").
The latter parameters take their reference bond lengths from fits to
experimentally determined structures, and then use the empirical rule
discussed below in connection with the MMFFBNDK.PAR file to assign the
force constant. The "#C94" designation for the "1 2 2" parameter
indicates
that the reference bond length for this parameter reflects an intentional
compromise between the ab-initio derived value (e.g., for butadiene,
which
gives 1.447 angs) and (shorter) values more typically found in
crystallographic
structures (which tend to involve "push-pull" delocalization that
increases
the pi-bond order across the central, formally single C-C bond).
The canonical ordering reflected in the table is defined through an
integer index, CXB, which is computed as
CXB = MC*(I*MA +J) + BTIJ,
where BTIJ is the bond-type index, MC is an integer equal to at least the
maximum permissible bond-type index +1, MA is an integer equal to the
maximum numerical atom-type index + 1, and atom type I is less than or
equal to J. Thus, the first atom type, I, changes least rapidly and the
bondindex BTIJ changes most rapidly, such that parameters which reference the
same atom types but different bond types appear consecutively in the
file.
As in the case of other force-field interaction terms discussed below,
this
canonical index is used in the binary-search algorithm used to detect the
presence or absence of a specific parameter (i.e., a specific BTIJ, I, J
combination).
File: MMFF_PARMS, Node: MMFFBNDK, Up: Top, Next: MMFFANG, Previous:
MMFFBOND
7. MMFFBNDK.PAR. The entries in this file govern the empirical rule
used for bond-stretching force constants when a parameterized value
derived
from fits to ab initio second derivatives is unavailable. MMFF uses an
inverse sixth-power dependence1 to relate the desired force constant to
the
force constant values tabulated in MMFFBNDK.PAR for a specific bond
length,
usually that expected for a single bond between atoms i and j of the
associated atomic numbers.2 Specifically, MMFF takes
kbIJ = kbref (roref /roIJ)**6
(2)
where kbref and roref are the force constants and associated reference
bond
lengths given in MMFFBNDK.PAR and roIJ is the reference bond length
retrieved from the MMFFBOND.PAR parameter file or calculated from an
empirical-rule procedure contained in the code (see below). This rule
was used
to generate the force constants tabulated in MMFFBOND.PAR for the
extendedparameterization entries labeled "E94".
The format of MMFFBNDK.PAR is as shown below:
i
atomic number
j
roref
kbref
Source
---------------------------------------------1
6
1.084
5.15
C94
1
7
1.001
7.35
C94
1
8
0.947
9.10
C94
1
9
0.92
10.6
E94
1
14
1.48
2.3
E94
1
15 1.415
2.95
C94
1
16 1.326
4.30
C94
C94 =
E94 =
Fitted to ab-initio derived core MMFF94 force constants
Based on Herschberg/Laurie parameterization of Badger's rule
Note that kbref and roref depend only on the atomic species for i and j
rather
than on their associated MMFF numeric atom types. The reference force
constants kbref labeled C94 were determined by requiring that the force
constants kbIJ given by eq 2 closely reproduce the core, computationally
derived force constants tabulated in MMFFBOND.PAR when the associated
computationally derived reference bond lengths roIJ are used in the
empirical
rule -- i.e., with a rms deviation of 0.75 md/angs, as against a rms
value of
5.81 md/angs. (Badger's rule also performed reasonably well, but gave a
somewhat higher rms deviation of 1.06 md/angs). The force constants
kbref for
the entries labeled E94 could not be calibrated against known reference
values
in a comparable manner. Instead, these force constants were calculated
from
the tabulated roref values using Herschbach and Laurie's parameterization
of
Badger's rule [3]. Indeed, the empirical rule employed in MMFF would
employ
this implementation of Badger's rule directly, with roIJ given as shown
below,
should a case arise for which the atomic parameters required for eq 2
were
unavailable.
Reference values not supplied in the parameter tables are assigned
using
a modified form of the Schomaker-Stevenson rule [4] similar to that
described
by Blom and Haaland [5]. Specifically, MMFF takes
roIJ = roI + roJ - c |xI - xJ|**n - d
(3)
where roI and roJ represent bond-order adjusted covalent radii for atom
types I
and J, xI and xJ are Pauling-scale electronegativities defined by Allred
and
Rochow and depend only on the atomic species [6], c is a proportionality
constant, n is the power dependence of the electronegtive term, and d is
a
"shrinkage" factor which recognizes that the reference bond lengths in a
force
field calculation tend to be somewhat shorter than the optimized bond
lengths
for which the comparison with observed bond lengths is to be made. The
quantities in eq (3) are provided explicitly in the program code.
File: MMFF_PARMS, Node: MMFFANG, Up: Top, Next: MMFFSTBN, Previous:
MMFFBNDK
8. MMFFANG.PAR.
cubic expansion:
EAijk
(4)
=
where:
the
Most angle-bending interactions are described using a
0.5 * 0.043844 * kaIJK * DTijk**2 * (1 + cb*DTijk),
kaIJK =
angle bending force constant in md-angs/rad**2 for
angle between atoms i, j and k of atom types I, J and K.
DTijk =
Tijk - ToIJK, the difference between actual and
reference i-j-k bond angles in degrees.
cb =
-0.007 deg**(-1), the "cubic-bend" constant.
For linear or near-linear bond angles such as those which occur in
alkynes,
nitriles, isonitriles, azides, and diazo compounds, we employ the form
used
in DREIDING[7] and UFF[8]:
EAijk
(5)
=
143.9325 * kaIJK * (1 + cos(Tijk))
where kaIJK and Tijk are as defined above. Angle terms i-j-k are
included
in all cases in which atoms i and k are bonded to a common central atom
j.
The format of MMFFANG.PAR is depicted below:
---- Atom Types ---ATIJK I
J
K
kaIJK
ToIJK
Origin/comment
------------------------------------------------------------------0
0
1
0
0.000 108.100
0:*-1-* MMFF94 DEF
0
1
1
1
0.851 109.608
C94
0
1
1
2
0.736 109.445
C94
0
2
1
5
0.632 110.292
C94
0
2
1
6
1.074 108.699
C94
0
2
1
10 1.160 107.963
E94
0
3
1
3
0.974 111.746
E94
0
1
2
3
2
2
C94
X94
E94
#E94
1
2
2
=
=
=
=
5
2
2
0.650 108.385
0.747 121.550
0.796 126.284
C94
C94
E94
CORE MMFF94 parameter - obtained from ab initio data
EXTD MMFF94 parameter - fit to additional ab initio data
theta0 from fit to X-ray data, ka from empirical rule
theta0 and ka both from empirical rules
The seven columns define the angle-type index ATIJK, the atom types for
the
wing, central, and wing atoms in the angle, the force constant in
md-angs/rad**2, the reference bond angle in degrees, and the origin of
the
parameter, where "C94" and "E94" have meanings analogous to those
discussed
above. In particular, the latter combine reference angles obtained by
fitting
to crystallographic geometries with empirical-rule force constants
calculated as noted below.
The angle-bending parameters employ angle-type indices ATIJK ranging
between 0 and 8. Their meanings are as defined below:
ATIJK
Structural significance
-------------------------------------------------------------------------0
The angle i-j-k is a "normal" bond angle
1
Either bond i-j or bond j-k has a bond type of 1
2
Both i-j and j-k have bond types of 1; the sum is 2.
3
The angle occurs in a three-membered ring
4
The angle occurs in a four-membered ring
5
Is in a three-membered ring and the sum of the bond types is
1
6
Is in a three-membered ring and the sum of the bond types is
2
7
Is in a four-membered ring and the sum of the bond types is 1
8
Is in a four-membered ring and the sum of the bond types is 2
The canonical ordering of the angle parameters is such that the
atom-type
index J changes least rapidly and the angle-type index ATIJK changes most
rapidly. Atom type I is always less than or equal to K and changes less
rapidly than K. All angle interactions having a common central atom type
thus appear together in the file. The canonical-order index, CXA, is
computed
as:
CXA = MC*(J*MA**2 + I*MA + K) + ATIJK
where MA is again the maximum permissible atom type +1, and MC is at
least
one greater than the maximum permissible angle-type index.
The procedure used to assign force constants kaIJK and the reference
angles ToIJK for a particular i-j-k interaction is analogous to that
described
above for bond stretching. Note that the MMFF angle bending parameters
also
include default parameters which have zero values for atom types I and K
(and a zero value for the listed force constant); the first parameter
listed
above, for example, is of this type. These parameter entries are used to
assign reference bond angles for interactions I-J-K of angle-type M =
ATIJK
when the parameter file contains neither the fully-qualified M:I-J-K
parameter nor any related parameter obtained by successively
equivalencing
atom types I, J and K to simpler atom types in the manner described above
in
connection with the MMFFDEF.PAR file. In such a case, the "M:0-J-0"
entries
are used to assign the reference angle, and procedure based on a
previously
published an empirical rule (but employing slightly different parameters)
is
then employed to calculate the force constant [9]. (If no match on M and
J is
found either, information relating to hydridization and ring size is used
to
assign the reference value.) These default reference values were
generated
by averaging over I and K for all M:I-J-K reference bond angles
determined
either from the MP2/6-31G* structures used in core MMFF or from the
crystallographic structures used in the extended CSD parameterization.
File: MMFF_PARMS, Node: MMFFSTBN, Up: Top, Next: MMFFDFSB, Previous:
MMFFANG
9.
MMFFSTBN.PAR
EBAijk
where:
to
The form used for stretch-bend interactions is:
= 2.51210 (kbaIJK*Drij + kbaKJI*Drkj)*DTijk,
kbaIJK =
(6)
force constant in md/rad for i-j stretch coupled
i-j-k bend.
kbaKJI =
force constant for k-j stretch coupled to i-j-k bend.
and Dr and DT are defined as above. Currently, stretch-bend interactions
are
omitted when the i-j-k interaction corresponds to a linear bond angle.
The format of the MMFFSTBN.PAR file is illustrated below:
--- Atom Types --SBTIJK
I
J
K
kbaIJK
kbaKJI Origin/Comment
-----------------------------------------------------------------0
1
1
1
0.206 0.206 C94
0
1
1
2
0.136 0.197 C94
0
1
2
1
0.250 0.250 C94
0
1
2
2
0.203 0.207 C94
2
1
2
2
0.222 0.269 C94
2
1
2
3
0.244 0.292 C94
0
1
2
5
0.215 0.128 C94
1
2
2
2
0.250 0.219 C94
2
2
2
3
0.155 0.112 C94
0
2
2
5
0.207 0.157 C94
C94 - CORE MMFF94 parameter, from fits to HF/6-31G* 2nd D's
X94 - EXTD MMFF94 parameter, also from fits to HF/6-31G* 2nd D's
All the parameters listed in the file represent values derived by fitting
to
HF/6-31G* energy derivatives. Note that the format is similar to that
employed for angle bending. Two force constants are listed, however. The
first, kbIJK, couples i-j-k bending with the stretching of the i-j bond,
whereas the second, kbaKJI, couples i-j-k bending to k-j stretching. The
requisite reference bond lengths and bond angle are taken from the
respective
bond and angle parameter sets, with the stretch-bend type SBTIJK listed
in
the first column serving with the atom types to establish the proper
connection.
The stretch-bend types are defined in terms of the constituent bond types
BTIJ
and BTJK and the angle type ATIJK as shown below:
Stretch-Bend
Angle
---- Bond Type ---Type
Type
I-J
J-K
----------------------------------------------------------0
0
0
0
1
1
1
0
2
2
0
1
3
2
1
1
4
4
0
0
5
3
0
0
6
5
1
0
7
5
0
1
8
6
1
1
9
7
1
0
10
7
0
1
11
7
1
1
Canonical order is established through an index, CXBA, which is
computed
from the stretch-bend type and the atom types in much the same maner as
was
described above for the index CXA. The ordering of the tabulated
parameters
therefore follows the same prescription.
The matching of stretch-bend interactions with tabulated parameters
proceeds much as described above, i.e. by comparing the CXBA index for
the
M:I-J-K combination of interest (where M = SBTIJK) to the indices stored
with
the entries in the parameter file. In this case, however, default
parameters
are used whenever the fully qualified M:I-J-K parameter is not found in
the
initial search. (Thus, no atom-type equivalences are employed.) The
default
parameters are taken from the MMFFSBDF.PAR file, as described below.
File: MMFF_PARMS, Node: MMFFDFSB, Up: Top, Next: MMFFOOP, Previous:
MMFFSTBN
10.
MMFFDFSB.PAR.
The format of this file is illustrated below:
Row in
-- Periodic Table -Force constant
IR
JR
KR
kbaIJK
kbaKJI
-----------------------------------------------0
1
0
0.15
0.15
0
1
1
0.10
0.30
0
1
2
0.05
0.35
0
1
3
0.05
0.35
0
1
4
0.05
0.35
0
2
0
0.00
0.00
0
2
1
0.00
0.15
0
2
2
0.00
0.15
0
2
3
0.00
0.15
0
2
4
0.00
0.15
1
1
1
0.30
0.30
1
1
2
0.30
0.50
Note that the tabulated force constants depend only on the rows in the
periodic table to which the constituent atoms i, j and k belong.
Wherever
possible, they represent averages of the core-MMFF stretch bend
parameters
for each given row combination; for new row combinations, they reflect
trends in the core-MMFF stretch-bend force constants.
File: MMFF_PARMS, Node: MMFFOOP, Up: Top, Next: MMFFTOR, Previous:
MMFFDFSB
11.
MMFFOOP.PAR.
For out-of-plane bending, MMFF uses the quadratic form
EOOPijk;l
(5)
=
where:
angs/rad.
koopIJK;L =
Xijk;l
0.5 * 0.043844 * koopIJK;L * Xijk;l**2,
out-of-plane bending force constant in md-
= angle in degrees between the bond j-l and the
plane i-j-k, where j is the central atom.
The angle Xijk;l is computed for all tricoordinate centers using the
Wilson
definition [10]. Note that three such out-of-plane angles arise at each
trigonal center j, as any one of the attached atoms i, k and l can serve
as
the "out of plane" atom. In MMFF, all three such angles are assigned the
same koop force constant.
The format of the MMFFOOP.PAR file is depicted below:
------ Atom Types -----I
J
K
L
koopIJK;L
Origin/Comment
------------------------------------------------------------------0
2
0
0
0.020
*-2-*-* C94 DEF
1
2
1
2
0.030
C94
1
2
2
2
0.027
C94
1
2
2
3
0.026
C94
1
2
2
5
0.013
C94
2
2
2
5
0.013
C94
2
2
3
5
0.012
C94
2
2
5
5
0.006
C94
2
2
5
6
0.027
C94
C94 - CORE MMFF94 parameter, from fits to HF/6-31G* 2nd D's
#C94 - Value adjusted from CORE MMFF94 value
E94 - Value assigmed by analogy
The canonical index, CXO, is computed as:
CXO = J*MA**3 + I*MA**2 + K*MA + L,
where MA is as defined previously, L is greater than or equal to K, and K
is
greater than or equal to I. This ordering groups together in the file
all outof-plane entries which share a common central atom type J. The entries
for which atom types I, K and L are zero serve as default values; they
match out-of-plane interactions for which the fully qualified I-J-K-L
parameter is not found. Wherever possible, the default force constants
approximate the average of the force constants for the central atom type
J
derived in the fit to the HF/6-31G* second derivatives in the core- MMFF
parameterization. The entries labeled "C94" were derived from the ab
initio
data , whereas entries labeled "E94" were assigned by analogy to values
found for similar atom types for which computationally derived values
were
available.
File: MMFF_PARMS, Node: MMFFTOR, Up: Top, Next: MMFFVDW, Previous:
MMFFOOP
12. MMFFTOR.PAR. MMFF employs the three-fold representation also used
in
MM2 [11] and MM3 [12]:
ETijkl = 0.5 * (V1*(1 + cosW) + V2*(1 - cos2W) + V3*(1 + cos3W))
(8)
where W is the i-j-k-l dihedral angle in degrees. The constants V1, V2
and
V3 depend on the atom types I, J, K and L for atoms i, j, k and l, where
i-j,
j-k and k-l are bonded pairs and i is not equal to l.
The format of the parameter file is illustrated below:
--- Atom Types --TTIJKL I
J
K
L
V1
V2
V3
Origin/Comment
-------------------------------------------------------------------------0
0
1
1
0
0.000
0.000
0.300
C94 0:*-11-* Def
5
0
1
1
0
0.200
-0.800
1.500
C94 5:*-1-1-*
Def
0
1
1
1
1
0.103
0.681
0.332
C94
5
1
1
1
1
0.144
-0.547
1.126
C94
0
1
1
1
2
-0.295
0.438
0.584
C94
0
1
1
1
3
0.066
-0.156
0.143
C94
0
1
1
1
5
0.639
-0.630
0.264
C94
0
1
1
1
6
-0.688
1.757
0.477
C94
5
1
1
1
6
0.000
0.000
0.054
C94
C94
X94
E94
#E94
-
CORE MMFF94 parameter EXTD MMFF94 parameter EXTD MMFF94 parameter Adjusted from empirical
from
also
from
rule
fits to conformational energies
from fits to conformational E's
empirical rule
value
The first column gives the value of the torsion type index, TTIJKL. This
index normally takes the value "0", but is "1" when the j-k bond has a
bond
type index BTJK of 1, is "2" when BTJK is "0" but BTIJ and/or BTKL is
"1", is
"4" when i, j, k, and l are all members of the same 4-membered ring, and
is "5" when the four atoms are members of a 5-membered ring which is
not aromatic and contains no unsaturation.
The torsion parameters are ordered using the canonical index
CXT = MC*(J*MA**3 + K*MA**2 + I*MA + L) + TTIJKL
In this case, as of 2/96, MC (the maximum permissible torsion-type index
plus
1) and MA (the maximum permitted atom type plus 1) are set to 6 and 136,
respectively, to insure that CXT will fit within a 32-bit integer word.
Thus,
J changes least rapidly and K next least rapidly. For I, L and TTIJKL,
the
effect on the ordering can be seen in the portion of the MMFFTOR.PAR file
displayed above.
Requests for one-, two- and three-fold torsion parameters which can
not
be resolved using the primary numeric MMFF atom types and the associated
torsion-type index TTIJKL are first handled via the step-down procedure
outlined above in connection with the MMFFDEF.PAR file, and then, if
necessary,
by invoking an empirical rule distinct from but patterened after those
used by
Mayo, Olafson and Goddard in DREIDING [7] and by Rappe and co-workers in
their
successor force field, UFF [8]. The request may terminate with fully
wildcarded
M:0-J-K-0 parameters (where for simpilicity M denotes the torsion-type
index
TTIJKL) or, in a few cases, may access "half-wildcard" M:0-J-K-L or M:IJ-K-0
parameters. For those J-K bond types covered in the core MMFF
parameterization,
the wildcarded parameters M:0-J-K-0, M:0-J-K-L, or M:I-J-K-0 were
generated by
averaging all explicitly determined M:I-J-K-L parameters over I and L,
respectively. For M:I-J-K-L parameters not covered in core MMFF but
required
for the extended CSD parameterization, wildcarded parameters of the type
M:0-J-K-0 were generated from the empirical rule just cited. Thus, the
additional torsion interactions covered in the extended MMFF
parameterization
utilize default parameters which depend only on the torsion type and the
atom
types of the central two atoms.
File: MMFF_PARMS, Node: MMFFVDW, Up: Top, Next: MMFFCHG, Previous:
MMFFTOR
13. MMFFVDW.PAR. For van der Waals interactions, MMFF employs the
recently developed "Buffered 14-7" form (eq 9) together with an
expression which relates the minimum-energy separation R*II to the
atomic polarizability aI (eq 10), a specially formulated combination rule
(eqs 11, 12), and a Slater-Kirkwood expression for the well depth eIJ (eq
13) [13]:
Evdwij
=
eIJ*{1.12R*IJ/(Rij+0.12R*IJ)}**7 *
{1.07 R*IJ**7/(Rij**7 + 0.07R*IJ**7) - 2}
(9)
R*II = AI * aI**(PEXP)
(10)
R*IJ =
(11)
0.5 * (R*II + R*JJ) * (1 + AFACT(1 - exp(-BFACT*gIJ**2)))
gIJ = (R*II - R*JJ)/(R*II + R*JJ)
(12)
eIJ =
(13)
181.16*GI*GJ*aIaJ/[(aI/NI)**0.5 + (aJ/NJ)**0.5]*R*IJ**(-6)
The first non-comment line in the parameter file contains five
floating
point numbers which define the variables PEXP, AFACT, BFACT, DARAD, and
DAEPS, respectively. PEXP (currently 0.25), AFACT (currently 0.2) and
BFACT
(currently 12.0) are used in the equations shown above; DARAD and DAEPS
are used as explained below. The format of the remainder of the
parameter
file is illustrated below:
At. Type I
aI
NI
AI
GI
D_AI
Symb.
Origin/Comment
--------------------------------------------------------------------------1
1.050 2.490 3.890 1.282
CR
E94
2
1.350 2.490 3.890 1.282
C=C
E94
3
1.100 2.490 3.890 1.282
C=O
E94
5
0.250 0.800 4.200 1.209
HC
C94
6
0.700 3.150 3.890 1.282
A
OR
C94
7
0.650 3.150 3.890 1.282
A
O=C
C94
10 1.000 2.820 3.890 1.282
A
NC=O
C94
21 0.150 0.800 4.200 1.209
D
HOR
C94
24 0.150 0.800 4.200 1.209
D
HOCO
C94
E94
C94
X94
- From empirical rule (JACS 1992, 114, 7827)
- Adjusted in fit to HF/6-31G* dimer energies and geometries
- Chosen in the extension of the paratererization for MMFF94
Column 1 contains the numerical atom type, and column 2 contains the
associated atomic polarizability aI in units of angs**3.
Note that the
effective-electron numbers N and the scale factors A and G depend only on
the
atomic species for the interacting atoms i and j, not on the full MMFF
numeric
atom type. Column 6, labeled "D_AI" specifies whether the atom type in
question
is considered to be a hydrogen bond donor ("D"), acceptor ("A"), or
neither
("-"). When either i or j is a hydrogen-bond donor, MMFF uses the simple
arithmetic mean (0.5 (R*II + R*JJ)) instead of eq 11 to obtain R*IJ. If
the
i-j interaction is a donor-acceptor interaction, MMFF also scales R*IJ as
given
by eq 11 by DARAD (currently 0.8) and eIJ as given by eq 13 by DAEPS
(currently
0.5). For informational purposes only, column 7 lists a representative
MFFF
symbolic atom type.
File: MMFF_PARMS, Node: MMFFCHG, Up: Top, Next: MMFFPBCI, Previous:
MMFFVDW
14. MMFFCHG.PAR.
Coulombic form
EQij
(14)
=
MMFF uses the buffered
332.0716*qi*qj/(D*(Rij + d)),
where qi and qj are partial atomic charges, Rij is the internuclear
separation
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 distancedependent dielectric constant is also supported). In MMFF, 1,4interactions
are scaled by a factor of 0.75. The distance buffering (d > 0) prevents
infinite attractive electrostatic energies from overwhelming the bounded
repulsive vdW interaction given by eq 9 as oppositely charged atomic
centers
approach.
The partial atomic charges qi used in eq 14 are constructed from
initial full or fractional formal atomic charges q0I (usually zero, but,
e.g.,
+1/3 for guanidinium nitrogens) by adding contributions from bond charge
increments wKI which describe the polarity of the bonds to atom i from
attached atoms k. Thus, wKI is the contribution to the total charge on
atom i of atom type I accumulated from, and at the expense of, its bonded
neighbor k of atom type K. Specifically, MMFF computes qi as
qi = (1 - nI*uI)*q0I + uI*Sum(K)q0K + Sum(K)wKI
(15)
where wKI = - wIK and where the sums on the right hand side run over the
nI =
crd(I) atoms k of MMFF atom type K directly attached to atom i. (Crd(I)
comes
from MMFFPROP.PAR.) In this equation, q0I and q0K are the formal charges
assigned in the atom typing procedure (usually, by subroutine XTYPE), and
the
sum of the first two terms gives the "effective" fractional formal atomic
charge residing on atom i. This approach allows a formal atomic charge
initially affixed by the atom-typing procedure (e.g., q0I) to be shared
in a
prescribed manner with the neighbors bonded to the atom in question. For
example, for the series PO4(-3), HPO4(-2), H2PO4-, H3P04, it allows
allows the
partial charges on the terminal oxygens (each represented by the same
numerical
atom type, "32") to vary in a way which properly reflects the partial
charges
obtained from fits to the 6-31G* electrostatic potential. In particular,
the
difference between the resultant charges qi calculated for the single
terminal
oxygen in H3PO4 and for the four equivalent terminal oxygens in PO4(-3)
comes
to -0.375, half (because u32 = -0.5) the difference of -0.75 in the q0K
charges
(i.e., 0.00 and -0.75, respectively) and reasonably in accord with the
difference of -0.42 found by fitting the electrostatic potential.
The bond charge wKI increments are taken from MMFFCHG.PAR, and the
disbursement-fraction factors uI come from MMFFPBCI.PAR. The format of
the MMFFCHG.PAR file is as shown below:
BTIK
I
K
wIK
Origin/Comment
-------------------------------------------0
1
1
0.0000
#C94
0
1
2
-0.1382
C94
0
1
3
-0.0610
#C94
0
1
5
0.0000
#C94
0
1
6
-0.2800
#C94
0
1
10
-0.3001
C94
0
2
2
0.0000
#C94
1
2
2
0.0000
#C94
1
2
3
-0.0144
C94
C94 - CORE MMFF94 parameter, obtained from fit to dipole moments
#C94 - CORE MMFF94 parameter, either fixed or adjusted to fit
HF/6-31G* interaction energies
X94 - EXTD MMFF94 parameter, obtained from fit to dipole moments
#X94 - EXTD MMFF94 parameter, fixed in the fit to dipole moments
E94 - derived from partial bond charge increments (empirical rule)
The BTIK are the previously discussed bond types. Note that the "0 1 2"
line, for example, indicates that a (carbon) atom of type "2" in a "1 2" CC bond gains a charge of -0.1382 from the polarity of the bond, while the
atom of type "1" gains an equal and opposite charge of +0.1382. The
parameter lines identified by the label "#C94" list bond charge
increments which were held fixed in the fit to molecular dipole moments
used
in the derivation of the "C94" values.
File: MMFF_PARMS, Node: MMFFPBCI, Up: Top, Next: MMFFSUP, Previous:
MMFFCHG
15. MMFFPBCI.PAR.
below:
The format of the MMFFPBCI.PAR file as illustrated
Atom
type I
pI
uI
Origin/Comment
--------------------------------------------1
0.000
0.00
E94
2
-0.135
0.00
E94
3
-0.095
0.00
E94
30 -0.166
0.00
E94
31
0.161
0.00
E94
32 -0.732
0.50
E94
The uI parameters, which usually are zero, are used in the equation given
above for qi. The pI are used to estimate missing bond-charge increments
as
wKI = pI - pK
(16)
Because of the additive decomposition they give of the bond charge
increments
wKI, the pI are called "partial bond charge increments". They have been
shown
to reproduce the ab-initio parameterized wKI with an rms error of about
20% and
were used to generate the bond charge increments labeled "E94" in the
MMFFCHG.PAR file.
File: MMFF_PARMS, Node: MMFFSUP, Up: Top, Next: (chmdoc/mmff.doc),
Previous: MMFFPBCI
16. MMFFSUP.PAR. This file allows additional MMFF parameters of various
types to be added, and also allows existing parameters to be redefined
(i.e.,
overwritten, replaced). The supplementary parameters are read from a
file
assigned to unit "INP". The supplementary-parameters file consists of a
header
card, followed by sets of cards specifying supplementary parameters of
various
types.
Note: the current (February 1996) CHARMM implementation is incomplete.
In
this implementtion, the subtype sections *in some cases* can appear in
any
order. In particular, the VDW, BOND, ANGLE, and TORSION sections are
initiated by a header record of that name.
These headers, which *must*
be
present in these four cases, allow CHARMM to position the supplementaryparameters file at the first "real" data record for that block. CHARMM
then
reads just the requested number of data records (e.g., NB records of
"BOND"
type). For readability, it is therefore permissible to close the block
with a record like "END_VDW."
Alternatively, or in addition, any number
of
comment records of arbitrary format can be added after the "real" data.
Unfortunately, the current implementation treats blocks of bond-chargeincrement and out-of-plane bending parameters differently. Here, *no*
header
record is allowed. Rather, as in other implementations of the MMFF
parameter
reading facility, the code assumes that the supplementary-parameters file
will
be read sequentially and will be positioned properly when supplementary
parameters of any given subtype, including these two, are to be read.
Fortunately, there is a work-around. First, order the reading of the
main
MMFF parameter files as is shown in the mmff_setup.STR example in the
mmff.doc
file. Second, specify the supplementary parameters in the order shown
below.
Third, when the associated NV, NB, NA, and NT count variables are
nonzero,
include VDW, BOND, ANGLE, and TORSION headers, but *do not* supply an END
card, or any other data, following the parameter data cards. In this
way, if
NQ, for example, is nonzero but NV or NB is not, the supplementary
parameters file will have been left positioned at the first bond-chargeincrement parameter line at the time the reading of this data is called
for.
To determine when the implementation for reading supplementary parameters
has
been made complete, go to the mmff source directory and issue the
command:
"grep -i find_loc *.src". You will see the file-positioning find_loc
commands
bearing the arguments "VDW", "BOND", "TORSION" AND "ANGLE". If you also
see
others bearing such arguments as "CHARGE" and "OUTPLANE", you will know
that
these blocks also require header records. At this point, it will also be
possible to add "trailer" records and to position the subblocks in
arbitrary
order.
a.
First read header card for the supplementary-parameters file:
READ(INP,'(8I5)') NV, NB, NQ, NP, NA, NO, NBA, NT
NV -- NT are numbers of supplementary parameters:
Quantity and definition
------------------------------------
Block header
----------------------
NV
NB
NQ
NP
VDW
BOND
---------
NA -NO -NBA NT --
van der waals parameters
bond stretch paramaters
bond charge increment parameters
partial bond charge increment
parameters (not yet implemented)
angle bending parameters
out-of-plane bending parameters
stretch-bend interaction (not yet
implemented)
torsion parameters
ANGLE
TORSION
The block identifiers need to be specified in addition to the
numerical
data defined in the fllowing sections.
b. If NV is nonzero, first read new values for various vdw control
parameters:
READ(INP,'(5F10.5)') PEXP, AFACT, BFACT, DARAD, DAEPS
NOTE: each nonzero value replaces the value supplied in the first
line of
the MMFFVDW.PAR file (zero values are ignored). See the description
of
the MMFFVDW.PAR file for the meaning of these parameters.
Then read NV supplementary vdW parameters:
DO I=1,NV
READ(INP,'(I5,4F10.3,1X,A1)') I, aI, NI, AI, GI, D_AI
ENDDO
These six quantities provide additional or replacement values for the
corresponding items on the MMFFVDW.PAR parameter lines.
I
aI
NI
AI
GI
-
MMFF numeric atom type
polarizability for an atom of type I
Slater-Kirkwood effective electron number
"A" value
"G" value
D_AI
string
c.
-
Donor ("D"), acceptor ("A"), or "neither" ("-") character
If nonzero, read "NB" supplementary stretching parameters:
DO I=1,NB
READ(INP,'(I1,I4,I5,2F8.3,A)') BTIJ, I, J, kbIJ, roIJ, COMMENT
ENDDO
BTIJ
- bond-type index for this bond between atoms of types I and
I, J
kbIJ
roIJ
COMMENT
-
J
d.
MMFF atom types for atoms i and j
stretching force constant in md/angstrom
reference bond length in angstroms
optional comment field
If nonzero, read "NQ" supplementary bond charge increments:
DO K=1,NQ
READ(INP,'(I1,I4,I5,2F8.3,A)') BTIK, I, K, wIK
ENDDO
BTIK
- bond-type index for this bond between atoms of types I and
I, K
wIK
- MMFF atom types for atoms i and k.
- bond-charge increment in electron units, added to the atom
K.
of
higher atom type and subtracted from the atom of lower atom
type
e. If nonzero, read "NP" partial bond charge increments (not yet
implemented
as of February 1996):
DO K=1,NP
READ(INP,'(I1,I4,I5,F10.5)') I, pI, uI
ENDDO
I
pI
- MMFF atom type
- partial-bond-increment change in electrons, used
to estimate "missing" bond charge increments
- formal charge distribution factor
uI
f.
If nonzero, read "NA" supplementary angle bending parameters:
DO I=1,NA
READ(INP,'(I1,I4,2I5,4F8.3,A)') ATIJK, I, J, K, kaIJK, ToIJK,
COMMENT
ENDDO
ATIJK
-
angle-type index
I, J, K
kaIJK
ToIJK
COMMENT
g.
-
MMFF atom types for atoms i, j, k
bending force constant in md-angs/rad**2
reference bond angle in degrees
optional comment field
If nonzero, read "NO" supplementary out-of-plane parameters:
DO I=1,NO
READ(INP,'(4I5,F10.3,A)') I, J, K, L, koopIJK;L, COMMENT
ENDDO
I, J, K, L
-
MMFF atom types for atoms i, j, k and l, where j is
koopIJK;L
COMMENT
-
central atom
out-of-plane bending force constant in md-angs/rad**2
optional comment field
the
h. If nonzero, read "NBA" supplementary stretch-bending parameters (not
yet
implemented as of February 1996):
DO I=1,NBA
READ(INP,'(I1,I4,2I5,4F8.3,A)') SBTIJK, I, J, K, kbaIJK, kbaKJI,
COMMENT
ENDDO
i.
SBTIJK
I, J, K
kbaIJK
-
kbaKJI
-
COMMENT
-
stretch-bend-type index
MMFF atom types for atoms i, j, k
stretch-bending force constant in md/rad
coupling i-j stretching with i-j-k bending
stretch-bending force constant in md/rad
coupling k-j stretching with i-j-k bending
optional comment field
If nonzero, read "NT" supplementary torsion angle parameters:
DO I=1,NT
READ(INP,'(I1,I4,3I5,3F8.3,A)') TTIJKL, I, J, K, L, V1, V2, V3,
COMMENT
ENDDO
TTIJKL
I, J, K, L
V1, V2, V3
COMMENT
- torsion-type index
- MMFF atom types for atoms i, j, k, l
- one-fold, two-fold, three-fold barrier constants in
kcal/mol
- optional comment field
-------------------------------------------------------------------------References:
---------[1] Roy, R. S. Proc. Phys. Soc., Ser. 2, 1968, 1, 445-448.
[2] Peterson, M. R.; Csizmadia, I. G. J. Mol. Struct. 1985, 123, 399412; cf.
Table 1.
[3] Herschbach, D. R.; Laurie, V. W. J. Chem. Phys. 1961, 35, 458-463.
[4] Schomaker, V.; Stevenson, D. P. J. Am. Chem. Soc. 1941, 63, 37-40.
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