The Implemented Types of CV

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.

• STRETCH: Bond stretch: give the indexes of the 2 atoms $i1$ $i2$ , $s = (d_{i1,i2})^{2}$
• BEND: Bond angle: give the indexes of the 3 atoms defining the angle, $i1$ $i2$ $i3$ .
• TORSION: Torsion angle: give the indexes of the 4 atoms defining the torsion angle, $i1$ $i2$ $i3$ $i4$ .
• DIST: Distance between two atoms: give the indexes of the 2 atoms $i1$ $i2$ , $s = d_{i1,i2}$ .
• DISAXIS: Distance between two atoms $i1$ and $i2$ along $x$ or $y$ or $z$ direction. $i1$ $i2$ $n$ are read next on the same line. Here $n=1$ means $x$ , $n=2$ means $y$ and $n=3$ means $z$ coordinate.
• OUTP: Angle out of plane: give the indexes of the 3 atoms defining the plane and a fourth index of the atom for which the angle out of plane is computed, $i1$ $i2$ $i3$ $i4$ .
• COORD: Coordination number (CN) of one atom with respect to all the other atoms in the system. The CN is defined by a Fermi-like function

  $$CN_i = \sum_{j \neq i}^{NATOM}\frac{1}{1+e^{k(d_{ij}-d^0)}}$$ (265)

  
  
  where $i$ is the index of the selected atom, $j$ runs over all the other atoms in the system, $k$ is the parameter which determines the steepness of the decay and $d^0$ is the reference distance. After the type-name, in the same line, give $i$ $k$ $d^0$ .
• DIFFER: Difference between two distances, give the indexes of the 3 atoms defining the 2 vectors, $i1$ $i2$ $i3$ , $s = d_{i1i2}-d_{i2i3}$ .
• COORSP: 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 $jsp$ . After the type-name, in the same line, give $i$ $jsp$ $k$ $d^0$ .
• COORGROUP: Sum of the CN of a group of atoms $A$ with respect to individual group of atoms ($B$ ). CN is estimated using the Fermi function. Different cutoff distances are allowed for each type of $A$ atoms.

  $$CN = \sum_{i}^{N_A} \sum_{j}^{N_B(i)} \frac{1}{1+e^{k\left[d_{ij}-d^0(i)\right]}}$$ (266)

  
  
  After the keyword COORGROUP, $N_A$ and $k$ should be specified. In the next lines should be:
  $i$ , $N_B(i)$ , $d^0(i)$
  $j(1) \cdots j(N_B(i))$
  This has to be done for all $i$ in list of $A$ type atoms.
• COOR_RF: CN of one selected atom $i$ with respect to one selected species, $jsp$ , or a list of atoms, $j1 \cdots jn_{list}$ . The CN value is calculated as the sum of rational functions

  $$CN_i = \sum_{j \neq i}^{n_{list}} \frac{1-\left(\frac{d_{ij}}{d^0}\right)^{p}} {1-\left(\frac{d_{ij}}{d^0}\right)^{p+q}},$$ (267)

  
  
  where j runs over the indexes of the atoms belonging to $jsp$ or over the indexes given in the list $j1 \cdots jn_{list}$ . For the option of the species, you should provide, after the type-name, the indexes $i$ and $jsp$ , the exponents $p$ and $q$ , and the reference distance $d^0$ are read. If, instead, the list option is your choice, write immediately after the type-name the keyword $INDAT$ , and next the values of $i$ , $n_{list}$ , $p$ , $q$ , and $d^0$ . The indexes of the atoms belonging to the list are read from the next line.
  If the keyword $2SHELL$ is found, in the same line as $COOR\_RF$ , the first real number after this keyword is a second reference distance $d_{2sh}$ . In this case, the functional form of CN is modified, in order to take into account only the neighbors belonging to one farther shell, and $d_{2sh}$ is the average distance of these atoms from $i$ :

  $$CN_i^{2sh} = \sum_{j \neq i}^{n_{list}} \frac{1-\left(\frac{(d_{ij}-d_{2s})}{d^0}\right)^{p}} {1-\left(\frac{(d_{ij}-d_{2s})}{d^0}\right)^{p+q}}.$$ (268)

  
  
  For the modified CN the exponents must be even.

• BNSWT: 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 $j$ . After the type-name, give $i$ , $j$ , $p$ , $q$ , and $d^0$ .
• TOT_COOR: 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.
• DISPL1: Average displacement of one group of species with respect to a second group of species, computed along one specified direction in space (lattice axis in crystals). This CV is useful to study diffusion processes in condensed matter. If the keyword $MIL$ is found, the 3 Miller indexes, which define the direction in space, are read immediately after (default: $\mathbf{v}=(hkl)=(100)$ ).
• COORDIS:
• PLNANG: Angle between two planes. Each plane is defined by the coordinates of 3 atoms; after the type-name, give the indexes of the 3 atoms defining the first plane, $i1$ $i2$ $i3$ , and the indexes of the atoms defining the second plane, $j1$ $j2$ $j3$ .
• HBONDCH:
• DIFCOOR: Difference between the CN of two different atoms, $i1$ and $i2$ , with respect to the same species $jsp$ , or the same 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 two selected atoms are read, $i1$ and $i2$ , rather than one.
• RMSD_AB: Given two atomic configurations $A$ and $B$ , the root mean square displacements (RMSD) of the actual configuration from $A$ , $rmsdA$ , and from $B$ , $rmsdB$ , are calculated (global translation and rotation are subtracted by the method of quaternions). The RMSD can be calculated on selected group of species: after the type name give the number of species ($NUMSPEC$ ) and the indexes of the selected species ( $IS_{1} \cdots IS_{NUMSPEC}$ ). If $NUMSPEC = 0$ all the species are included. If in the same line the keyword $\mathbf{FILEAB}$ is found, next the http name is read, where the atomic positions of the configurations $A$ and $B$ are given. Otherwise the http name is by default $\mathbf{STRUCTURE\_AB}$ . File format: 2 consecutive blocks of $1+NATOM$ lines. In each block, the first line is a title (Character) and it is followed by the list of atomic coordinates in a.u. ( $element\_name x y z$ ).
• COOR_CHAIN: Conditioned CN. Given three species $isp1$ , $isp2$ , and $isp3$ , the following average CN is calculated

  $$CN = \frac{1}{N_{sp1}}\sum_{i1=1}^{N_{sp1}}\left[ \sum_{i2=1}^{N_... ...}\right)^{p}}{1-\left( \frac{d_{i2i3}}{d_{23}^{0}}\right)^{p+q}}\right)\right].$$ (269)

  
  
  After the type-name, the parameters $isp1$ , $isp2$ , $isp3$ , $p$ , $q$ , $d_{12}^0$ , and $d_{23}^0$ are read.
• HYDRONIUM:
• DIS_HYD:
• SPIN: Distance between a selected atom and the center of the spin polarization $(\rho_{\uparrow} - \rho_{\downarrow})$ , where $\rho_{}$ indicate the polarized density. The center is located where the difference is maximum, and this kind of variable is useful only when some spin polarization is present. The position of the center in systems with PBC can be calculated by the definition proposed by Resta [79,123]. Obviously, this CV can be used only together with $LSD$ . After the type-name, give the index of the selected atom.
• VOLVAR: Volume of the cell. It can be used only with NPE/NPT MD.
• CELLSIDE: Length of one cell's side: give the cell-side's index $i$ ($i_a=1$ ,$i_b=2$ ,$i_c=3$ ).It can be used only with NPE/NPT MD.
• CELLANGLE: Cell-angle: give the cell-angle's index $i$ ( $i_{\alpha}=1$ , $i_{\beta}=2$ , $i_{\gamma}=3$ )). It can be used only with NPE/NPT MD.
• VCOORS This CV represents the coordination of one point (V) with respect to a selected species of atoms $jspec$ in the system:
  

  $$CN^{jspec}_{V}=\sum^{N_{jspec}}_{i\in jspec}{1\over 1 + e^{k(d_{iV}-d_0)}}$$ (270)

  
  After the keyword the parameters $jspec,k,d_0$ are read. In the next line the coordinates of the point $V$ are read in a.u.
• DIPOLE The dipole of the atoms $i_1,...,i_N$ with respect to the atom $j$ is defined as:
  

  $$\vec D_j={1\over Q}\sum_{i=i_1,..,i_N}q_i(\vec r_i -\vec r_j);\;\;\; Q=\sum_{i=i_1,..,i_N} q_i$$ (271)

  
  The three spherical coordinates of $\vec D_j$ , that is $(\rho_j,\theta_j,\phi_j)$ , can be used independently as CV. The keywords are DIPOLERHO, DIPOLETHA, DIPOLEPHI. In the same line after the keywords are read the index of the atom $j$ and the number $N$ of atoms which constitute the dipole. In the next two lines are read the indexes of the $N$ atoms and the corresponding charge $q_i$ .

If $CELL$ $FULL$ is defined in the first line of the MTD input, none of the CV defined above is used. The CV are the 6 cell parameters. In the section $DEFINE$ $VARIABLE$ , the number of CV is 6 and in the following 6 lines the scaling factors are given: for each line write the index $i$ of the corresponding CV ($i_a=1$ ,$i_b=2$ ,$i_c=3$ , $i_{\alpha}=4$ , $i_{\beta}=5$ , $i_{\gamma}=6$ ) followed by $SCF$ or $SCA$ and the desired values (see the description at the beginning of this subsection).