Constraints and Restraints

CONSTRAINTS ... END CONSTRAINTS

Within this input block you can specify several constraints and restraints on the atoms.
Please note, that for calculations using the Gromos QM/MM-interface (see section 9.16) the atom indices refer to the ordering of the atoms as it appears in the respective Gromos coordinate http. In all cases the indices of dummy atoms start sequentially from total-number-of-atoms plus one.

The following suboptions are possible:

FIX ALL

All coordinates of all atoms are kept fixed.
For wavefunction optimization via simulated annealing.

FIX QM

All coordinates of all QM atoms are kept fixed.
This is the same as above unless you are running a QM/MM calculation with the Gromos interface code.

FIX MM

All coordinates of all MM atoms are kept fixed.
This is ignored unless you are running a QM/MM calculation with the Gromos interface code.

FIX SOLUTE

All coordinates of all solute atoms are kept fixed.
This is ignored unless you are running a QM/MM calculation with the Gromos interface code. The definition of what is a solute is taken from the respective GROMOS topology http.

FIX SEQUENCE

All coordinates of a series of atoms are kept fixed.
This keyword is followed by the index numbers of the first and the last atoms to be fixed in the next line. Example:
FIX SEQUENCE
5 25      all coordinates of atoms no. 5 to 25 are kept fixed

FIX ELEMENT [SEQUENCE]

All coordinates of all atoms belonging to the same element are kept fixed. This works across pseudopotential types or QM and MM atoms in case of a QM/MM calculation. The keyword is followed by the core charge of the respective element. With the optional SEQUENCE modifier two more numbers are read in, specifying the first and the last index of a sequence of atoms to which this keyword will be applied. Example:
FIX ELEMENT
8         all coordinates of oxygen atoms are kept fixed

FIX PPTYPE [SEQUENCE]

All coordinates of all atoms belonging to the same potential type are kept fixed. The keyword is followed by the atom type index number on the next line, corresponds to the sequence of how the atom types are specified in the &ATOMS section of the CPMD input. In case of a QM/MM calculation this is expanded to respective classical atom types. In this case the QM atom types come first followed by the GROMOS atom types. With the optional SEQUENCE modifier two more numbers are read in, specifying the first and the last index of a sequence of atoms to which this keyword will be applied. Example:
FIX PPTYPE SEQUENCE
  2   5 25      atoms corresponding to the second atom type with an index between 5 and 25 are kept fixed

FIX ATOMS

All coordinates of certain atoms can be fixed.
This keyword is followed by the number of atoms to be fixed and a list of these atoms specifying them by the number of their position in the input http (NOTE: in the file GEOMETRY.xyz the atoms have the same ordering). Example:
FIX ATOMS
5    2  5 20 21 23     all coordinates of atoms 2, 5, 20, 21, and 23 are kept fixed

FIX COORDINATES

Certain coordinates of atoms are fixed.
This keyword is followed by the number of atoms with fixed coordinates and a list of these atoms together with flags indicating which coordinates are fixed. A zero indicates a fixed coordinate. Example:

2				Two atoms have fixed coordinates
1	1	1	0	for atom #1 $z$ is fixed
4	0	1	0	for atom #4 $x$ and $z$ are fixed

FIX COM

Fix the center of mass.
NOTE: This currently works only for OPTIMIZE GEOMETRY and not for the LBFGS optimizer.

FIX STRUCTURE [SHOVE]

This keyword starts a group of individual constraints where whole structural units can be fixed. The keyword is followed by the number of individual constraints on the next line.

DIST

$n1$ $n2$ $R$
Fixes the distance $R$ between the atoms $n1$ and $n2$ .

STRETCH

$n1$ $n2$ $R$
Fixes $R^2$ defined by the atoms $n1$ and $n2$ .

DIFFER

$n1$ $n2$ $n3$ $R$
Fixes $R_{12}-R_{23}$ defined by the atoms $n1$ , $n2$ , and $n3$ , where $R_{ab}$ is the distance between atoms a and b.

BEND

$n1$ $n2$ $n3$ $\theta$
Fixes the bending angle defined by the atoms $n1$ , $n2$ and $n3$ .

TORSION

$n1$ $n2$ $n3$ $n4$ $\Theta$
Fixes the torsion angle defined by the atoms $n1$ , $n2$ , $n3$ and $n4$ .

OUTP

$n1$ $n2$ $n3$ $n4$ $\Theta$
``Out of Plane''; Angle between plane ($n1$ , $n2$ , $n3$ ) and atom $n4$ is fixed.

RIGID

$nr$ $n1$ $n2$ ... $nx$
Keeps the structure formed by the $nr$ atoms $n1$ , $n2$ , ...
You can put your atom index in several lines. The number of constraints nfix is equal to $3nr-6$ for $nr>2$ ($nfix=1$ for $nr=2$ ).

COORD

$n1$ $\kappa$ $Rc$ $d^0$
``Coordination constraint'' for atom $n1$ . The parameters $\kappa$ and $Rc$ for the Fermi function are given in Bohr ($Rc$ ) and 1/Bohr ($\kappa$ ), (or in Angstrom ($Rc$ ) and 1/Angstrom ($\kappa$ ) if the keyword ANGSTROM was set), see Ref. [202].

COORSP

$n1$ $jsp$ $\kappa$ $Rc$ $d^0$
Fixes the coordination number (CN) of one selected atom $i$ with respect to only one selected species $jsp$ . The CN is defined by a Fermi like function as for $COORD$ , but in this case $j$ runs only over the atoms belonging to the selected species $jsp$ .

COOR_RF

$n1$ $jsp$ $p$ $q$ $Rc$ $d^0$
CN of one selected atom $i$ with respect to one selected species, $jsp$ . The CN value is calculated as the sum of rational functions

$$CN_i = \sum_{j \neq i}^{n_{list}} \frac{1-\left(\frac{d_{ij}}{d^0}\right)^{p}} {1-\left(\frac{d_{ij}}{d^0}\right)^{p+q}},$$ (277)

where j runs over the indexes of the atoms belonging to $jsp$ or over the indexes given in the list $j1 \cdots jn_{list}$ .

BNSWT

$n1$ $n2$ $p$ $q$ $Rc$ $d^0$
Reciprocal CN between 2 selected atoms, defined with the same functional form as the one described for $COOR\_RF$ . This coordinate states the presence of the bond between the two atoms $i$ and $j$ .

TOT_COOR

$isp$ $jsp$ $p$ $q$ $Rc$ $d^0$
Average CN of the atoms belonging to a selected species $isp$ with respect to a second selected species, $jsp$ , or with respect to a given list of atoms, $j1 \cdots jn_{list}$ . The same functional forms and input options are used, as those described for $COOR\_RF$ , but the index of one selected species $isp$ is read in place of the index of one atom.

$n1$ , ... are the atom numbers, $R$ distances and $\Theta$ angles. A function value of -999. for $R$ or $\Theta$ refers to the current value to be fixed. The constraint is linearly added to the CP Lagrangian according to the Blue Moon ensemble prescription[203]. The values of the Lagrange multipliers and of the actual constraint are printed in the http CONSTRAINT.
The options DIST, STRETCH, BEND, TORSION, OUTP, DIFFER, COORD, COORSP, COOR_RF, TOT_COOR can have an optional additional keyword at the end of the line of the form
DIST 1 2 -999. GROWTH 0.001
The keyword GROWTH indicates that the constraint value should be changed at each time step. The rate of change is given after the keyword in units per atomic time unit, i.e. independent from the current length of a time step.
Note: In MD runs only the actual initial value (-999.) can be fixed.
The SHOVE option requires an additional entry at the end of each constraint line. This entry has to be either $-1$ , 0 , or $1$ . The constraint is then either fixed (0 ) or allowed to shrink ($-1$ ) or grow ($1$ ).

RESTRAINTS [HYPERPLANE [K=scal]

]
Defines restraints.

nres

Number of restraints.

DIST

$n1$ $n2$ $R$ $kval$
Restrains the distance $R$ between the atoms $n1$ and $n2$ by a harmonic potential.

STRETCH

$n1$ $n2$ $R$ $kval$ Restrains $R^2$ defined by the atoms $n1$ and $n2$ by a harmonic potential.

DIFFER

$n1$ $n2$ $n3$ $R$ $kval$ Restrains $R_{12}-R_{23}$ defined by the atoms $n1$ , $n2$ , and $n3$ , where $R_{ab}$ is the distance between atoms a and b by a harmonic potential.

BEND

$n1$ $n2$ $n3$ $\theta$ $kval$
Restrains the bending angle defined by the atoms $n1$ , $n2$ and $n3$ by a harmonic potential.

TORSION

$n1$ $n2$ $n3$ $n4$ $\Theta$ $kval$
Restrains the torsion angle defined by the atoms $n1$ , $n2$ , $n3$ and $n4$ by a harmonic potential.

OUTP

$n1$ $n2$ $n3$ $n4$ $\Theta$ $kval$ ``Out of Plane''; Angle between plane ($n1$ , $n2$ , $n3$ ) and atom $n4$ is restrained by a harmonic potential.

RESPOS

$n1$ , $x_0$ , $y_0$ , $z_0$ $d_0$ $kval$ Restrains the position $\mathbf{R}=(x,y,z)$ of atom $n1$ to oscillate around $\mathbf{R}_0=(x_0,y_0,z_0)$ with a constraint harmonic potential $V_c=(kval/2)(\vert\mathbf{R}-\mathbf{R}_0\vert-d_0)^2$ . The limits $kval=0$ and $kval \to \infty$ correspond to free and fixed atomic positions, respectively. The keyword GROWTH is not supposed to be used for this restraint. For the sake of clarity and consistency with the atomic units used through the code, coordinates and distances are expected to be in atomic units (not $\mathrm{\AA}$ ).

$n1$ , ... are the atom numbers, $R$ distances and $\Theta$ angles. A function value of -999. for $R$ or $\Theta$ refers to the current value. The restraining potential is harmonic with the force constant $kval$ . The options can have an optional additional keyword at the end of the line of the form
DIST 1 2 -999. 0.1 GROWTH 0.001
The keyword GROWTH indicates that the constraint value should be changed at each time step. The rate of change is given after the keyword in units per atomic time unit.
If the keyword HYPERPLANE is set, the system is not restrained around a point in the collective variable space but in an hyperplane. This hyperplane is defined as going through a point in the collective variable space, defined from the $R$ and $\Theta$ above, and by a vector defined from the $kval$ values. K=scal applies a scaling to the vector defining the hyperplane so as to modulate the strength of the restraint.
The energy formula for an hyperplane restraint is then:
$E_r=\frac{1}{2}\left((\vec{c}-\vec{c}_0)\cdot \vec{n}\right)^2$ ,
where the vectors are vectors in the collective variable space.
If a http RESVAL is found after parsing the input, the current restraint target values will be replaced by the values found in this http.

PENALTY

The weight factors for the penalty function for stretches, bends and torsions are read from the next line.