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The
energy of the torsion angle formed by the atoms
i, j, k and l,
Et-i,j,k,l is:
Et-ijkl
= Kt-ijkl[
1 + cos(
nt-ijklTijkl
- dt-ijkl )
]
where
T is the varying torsion angle formed by the
ordered atoms i, j, k and l,
Kt is the force constant,
nt the periodicity and
dt is the phase shift. In
addition a group of four atoms may have a
multiplicity (M) of such functions, each
with a different force constant, periodicity and
phase shift.
The
Torsion record must appear only after the
Atom Inclusion Types have been defined. This
record must also appear after the Atom Inclusion
Group record if Groups are used in this
record. The Torsion record has the following
format:
|
:TORSION
|
|
|
:Typei:Typej:Typek:Typel:
|
M
|
|
|
|
Kt-ijkl
|
nt-ijkl
|
dt-ijkl
|
|
|
|
...
|
...
|
...
|
|
|
:Typei:Typej:Typek:Typel:
|
M
|
|
|
|
Kt-ijkl
|
nt-ijkl
|
dt-ijkl
|
|
|
|
...
|
...
|
...
|
|
|
...
|
|
:END
|
The
opening and closing keywords, like all keywords,
begin with a colon and start on column one of their
respective lines. The body of the data section may
contain any number of grouped lines. The groups may
be separated from one another by blank
lines.
Each
group starts with a list of four Atom Inclusion
Type or Group names followed by one
number, the multiplicity of the term M. This
must be followed by exactly M lines, each
line containing three numbers. The first number is
the maximum torsion energy in units of kcal/mol;
this must not be zero and a negative value is
acceptable but will precipitate a warning. The
second number is the periodicity, which must be a
positive integer of at least one. The last number
is the phase shift in degrees, this must be a
number between -180 and +180. These lines must not
contain anything beyond the numbers.
A
torsion type defined for Inclusion Atom
Types :A:B:C:D: will serve equally well for a
torsion of Types :D:C:B:A:. Only the first
instance of a definition of a torsion type will be
saved. Subsequent definitions for the same torsion
type will be silently ignored. Therefore,
definitions using Groups should be placed at
the end of the list so that the generic definitions
do not override the specific
definitions.
The
program Yup.fpf
will expand Groups into their component
Types, hash each quartet of Types
into a numerical code, and sort the codes. This
forms the index table. The force parameters are
converted to internal units used by
YUP
and these numbers form the data table. The index
and data tables are written to the unformatted
file: "Torsion
Constants".
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