The 3d-vector construct allows one to specify a three-dimensional real vector. The construct is also used to specify a 3x3 matrix by entering one row at a time. A 3d-vector takes the form:

  ( real real real )

or

( [TAIL=atom-selection] [HEAD=atom-selection] )

This defines the tail or the head of the vector as the center of mass of the specified atom selections using the mass atom property and the main coordinate set x,y,z. If HEAD is not specified, it defaults to (0,0,0); similarly for TAIL.

The matrix construct allows one to specify a 3x3 real matrix. There are several modes available to specify rotation matrices. An arbitrary 3x3 matrix can be specified by using the MATRix construct. Note: all rotations are counterclockwise.

• AXIS vector real specifies input through the axis vector (see above) and the rotation angle kappa (in degrees).
• EULEr vector specifies input through the Eulerian angles q1,q2,q3. q1 is the rotation around the z axis, q2 around the new x axis, and q3 around the new z axis.
• LATTman vector specifies input through Lattman's angles (q+=q1+q3, q2, q-=q1-q3).
• MATRix vector vector vector specifies direct input of the matrix by three 3d-vectors.
• QUATernions real real real real specifies quaternions q0, q1, q2, q3, which are defined as:
  • q0 = cos(q2/2)cos(q1+q3/2)
  • q1 = sin(q2/2)cos(q1-q3/2)
  • q2 = sin(q2/2)sin(q1-q3/2)
  • q3 = cos(q2/2)sin(q1+q3/2)
  with the constraint that
  • q20+q21+q22+q23=1
• SPHErical vector specifies input through spherical polar angles psi, phi, and kappa. Psi and phi specify the rotation axis. Psi is the inclination versus the y-axis; Phi is the azimuthal angle, i.e., the angle between the x-axis and the projection of the axis into the x,z plane; and kappa is the rotation around the rotation axis.

A rotation matrix is specified by a rotation axis (2,3,4) and a rotation angle (40 degrees) around the axis (counterclockwise rotation):

  AXIS=( 2, 3, 4 )  40.

Here a matrix is specified by direct input:

  MATRix=( 1. 3. 5. ) 
         ( 4. 2. 1. ) 
         ( 2. 1. 8. ) 

The last example shows how to specify a rotation matrix by using the Eulerian angles q1,q2,q3:

  EULEr=( 30. 40. 120. )