Strict NCS
Coordinate is related by NCS to input coordinate according to

(18.3) 
where is a 3x3 rotation matrix and is a translation vector.
The matrices and the vectors are entered using the
XNCSrelation and NCSRelation statements. The first 3
input vectors correspond to the ROWS of , and
the 4th vector
is . It
is not necessary to input the identity transformation, since the
program sets it by default, but the user may do so for completeness.
The NCSrelated interprotomer nonbonded contacts can be turned
on by turning on the packing energies PVDW and PELE. Under
this option, these energies are for NCSrelated molecules only; the
lattice energies are automatically shut off.
Many users will have the NCS relations defined in a skew frame
(an auxiliary
frame) in which the NCS relations have simple forms (e.g., pure rotations).
The SKEW option allows a user to specify the relation between this frame
and the orthogonal Å frame using a rotation
matrix and translation vector. Coordinates in the skew
frame are also given in Å. In this case, XNCSrelation and NCSRelation
statements take the NCS relations
in the skew frame. To use this option, SKEW must be given before
XNCSrelation and NCSRelation.
For defining the skew frame, the algebraic
conventions of Bricogne's (1976) skewing and averaging
method
have been adopted, except
that the reference frame is the orthogonal frame
used by XPLOR. This corresponds to Bricogne's ijk frame. The matrix
is Bricogne's “transition matrix."
The vector gives the coordinates of the origin of the skew frame
in the reference frame, and therefore corresponds to Bricogne's
.
Using the following conventions:
 = input coordinate in reference
orthogonal Å frame
 = NCSrelated coordinate
in orthogonal Å frame
 = input coordinate in skew frame
 = NCSrelated coordinate
in skew frame
 = skew (transition) matrix
 =
= origin of skew
frame in the reference
frame (in Bricogne's package, is in
fractional crystallographic coordinates; is the cell
orthogonalization matrix)
 = rotation matrix relating
and (in
skew frame)
 = translation vector
relating and
one obtains the following relationships:

(18.4) 

(18.5) 

(18.6) 

(18.7) 

(18.8) 

(18.9) 

(18.10) 
Users wishing to convert their Bricogne GENERATE mode 1 input to the XPLOR
input should note the following:
 is input as ROWS, not columns as in GENERATE.
 The skew vector is input after the skew matrix, and is
given in orthogonal Å.
 It is not necessary to input the Identity NCS operation.
 The NCS rotation matrices are input as rows, not columns.
Subsections
XplorNIH 20231110