Constraints in Minimax


Minimax provides six types of constraints: distance, angle, projections, volume, torsion and fixed atom constraint. The definitions of the constraints are read in from file molecule.con (-C option) or the file named by the -Cf option. The constraints file is free format. The first character of each line of the file determines the type of constraint (D:distance, A:angle, P:projection, T:torsion, F:fixed atom, V:volume). Blank lines are ignored, lines with a C in column 1 are treated as comment, and an E in column 1 is accepted as end-of-file (optional).
 

Distance constraints:

dmin < d i,j < dmax    , where d i,j is the distance (Å) between atoms i and j.

Implemented by adding a harmonic penalty function to the total energy:

E penalty = 0.5 * k i,j * (max{0,dmin - d i,j} + max{0,d i,j - dmax}) 2

Definition in constraints file: (i and j are atom sequence numbers)

D  i  j  dmin  dmax  ki,j

 Angle constraints:
amin < a i,j,k < amax    , where a i,j,k is the angle (deg.) between atoms i,j,k

Implemented by adding a harmonic penalty function to the total energy:

E penalty = 0.5 * k i,j,k * (max{0,amin - a i,j,k} + max{0,a i,j,k - amax}) 2

Definition in constraints file: (i, i, k are atom sequence numbers)

A  i  j  k  amin  amax  ki,j,k,l

Torsion constraints:
tmin < t i,j,k,l < tmax    , where t i,j,k,l is the dihedral angle (deg.) between atoms i,j,k,l

Implemented by adding a harmonic penalty function to the total energy:

E penalty = 0.5 * k i,j,k,l * (max{0,tmin - t i,j,k,l} + max{0,t i,j,k,l - tmax}) 2

Definition in constraints file: (i, j, k, l are atom sequence numbers)

T  i  j  k  l  tmin  tmax  ki,j,k,l

Note:  tmin must not exceed tmax, and tmin must lie in the interval [-180,+180].


Volume constraints:

V i,j,k,l > Vmin   , where V i,k,k,l is the (signed) parallelepipedial product <(xj-xi)*(xk-xi),xl-xi> , and xi, xi, xk, xl are the coordinate vectors of atoms i,k,k and l.

Implemented by adding a harmonic penalty function to the total energy:

E penalty =  k i,j,k,l * max{0,Vmin - V i,j,k,l}2

Definition in constraints file: (i, j, k ,l are atom sequence numbers)

V  i  j  k  l  Vmin  ki,j,k,l

Note: used judiciously, this may be used as a chirality constraint.  Indeed, this type of constraint is used by the -Cs option ("preserver chirality").

Fixed atom constraints:
Atoms listed in fixed atom constraints will be kept fixed during energy minimization. Only energy terms involving at least one variable (non-fixed) atom will be computed.

Definition in constraints file: (i, j, k, l, m ... are atom sequence numbers)

F i j k l m n ....

Where i,j,k,l,m,n,... are the sequence numbers of the atoms to be fixed (up to 256 numbers per line).
 

Projection constraints:
dx,yi,j = c*p i,j  , where dx,yi,j  is the distance between atoms i and j in the orthogonal projection onto the (x,y) plane.

Implemented by adding a harmonic penalty function to the total energy:

E penalty =  0.5*k i,j* (dx,yi,j  - c*p i,j )2

Definition in constraints file: (i and j are atom sequence numbers)

P  i  j  pi,j  ki,j

Note: The parameter c is a 'scale' which will be adjusted by the program to minimize the constraint violations. Projection constraints can be used to build 3D models that fulfill 2D constraints, e.g. projected distances measured in figures from publications.


Positional constraints:

A soft sqare-well penalty function may be used to constrain atomic positions to reference positions.

Epenalty = 0.5 * ki * DH2 + ki * DH * DL   ,  where

DH = max { min { di - T , L } , 0 } , and  DL = max { di - DH - T , 0 } ,

and di is the distance from the reference point (xr , yr , zr ).

Definition in constraints file: ( i is the sequence number of the atom that is constrained):

X  i  [ xr yr zr ]  ki [ T [ L ] ]

If no reference point is specified, the atom will be constrained to the initial position. The tolerance T defaults to 0, the default for L (switch-over to linear) is at infinity.
 



A.Widmer, NIBR/CPC/CSG-SB