ICONST: Difference between revisions

Revision as of 10:17, 25 January 2024

In the ICONST file, geometric parameters are defined, which are then monitored or controlled in a molecular-dynamics simulation. For instance, the distance between two sites can be constrained or affected by the action of a bias potential. Finally, VASP writes the output to the REPORT file.

Overview

Two kinds of geometric parameters can be defined: primitive parameters (e.g., bond lengths or angles), and complex parameters (i.e., linear combinations of primitive coordinates). Each line defines one coordinate, and the complex coordinates must be defined after all primitive ones. The syntax reads as follows:

flag item(1) ... item(N) status
...
...
flag  c_1  ...  c_M  status

where flag specifies the type of primitive coordinate, item(1) ... item(N) is a space-separated list of integers that, e.g., specifies the ions enumerated in the order they appear in the POSCAR file (starting at 1), and status is an integer that sets the status, e.g., constrained or monitored. Here, the first line defines the syntax of a primitive coordinates $q_i$ . Assuming that $M$ primitive coordinates were specified on the first $M$ lines of the ICONST file, the last line defines a complex coordinate, where c_1 ... c_M is a space-separated list of the coefficients $c_i$ for the primitive coordinate defined in line $i$ .

For instance, the following ICONST file defines two primitive coordinates and one complex coordinate.

R 1 6 0
R 1 5 0
S 1 -1 0

The first two lines define the bonds between atom $1$ and atom $6$ , and between atom $1$ and $5$ . The complex coordinate is the difference between the two bond lengths, which is defined on the third line.

Settings for `flag`

In case of primitive coordinates

flag = R: interatomic distance between atoms item(1) and item(2).
flag = A: angle defined by atoms item(1), item(2) and item(3) (with the atom item(2) being the apex).
flag = T: torsional angle defined by atoms item(1), item(2), item(3) and item(4).
flag = M: distance between atom item(1) and the center of bond between atoms item(2) and item(3).
flag = B: distance between the center of bond between atoms item(1) and item(2) and the center of bond between atoms item(3) and item(4)
flag = P: ratio of length of the bond between atoms item(1) and item(2) and the length of the bond between atoms item(3) and item(4)
flag = W: function $\frac{1-\left(R/c\right)^M}{1-\left(R/c\right)^{N}}$ with $R$ being the bond length (in $\AA$ ) between the atoms item(1) and item(2), $c$ is the reference bond length specified as item(3), and the exponents $M$ and $N$ are defined as item(4) and item(5), respectively.
flag = X, Y, and Z: fractional (direct) coordinates linked with the lattice vectors $a$ , $b$ , and $c$ .
flag = cX, cY, and cZ: Cartesian coordinates $x$ , $y$ , and $z$ .
flag = LR: length of lattice vector item(1)
flag = LA: angle between lattice vectors item(1) and item(2)
flag = LV: cell volume (no item(i) is defined in this case)

In case of complex coordinates

flag = S: simple linear combination of primitive coordinates, i.e., $\left ( \xi=\sum_{i=1}^{M} c_i\,q_i \right)$ .
flag = C: norm of the vector of primitive coordinates, which reads $\left( \xi=\sqrt{\sum_{i=1}^{M} \,(c_i\,q_i)^2} \right)$ .
flag = D: coordination number^[1], i.e., $\left( \xi=\sum_{i=1}^{M} \frac{1-\left(q_{i}/c_{i}\right)^9}{1-\left(q_{i}/c_{i}\right)^{14}} \right)$ .
flag = IS: path-based coordinate^[2] measuring progress along discretized path represented by $N$ points $\tilde{q}(j)$ predefined in file IRCCAR, i.e., $\xi=\frac{1}{N-1}\frac{\sum_{i=1}^{N}(i-1)\exp\left(-\sum_{j=1}^{M}c_{j}(q_{j}-\tilde{q}_{j}(i))^2 \right) }{\sum_{i=1}^{N} \exp\left(-\sum_{j=1}^{M}c_{j}(q_{j}-\tilde{q}_{j}(i))^2 \right)}$
flag = IZ: path-based coordinate^[2] measuring orthogonal distance from the path $\tilde{q}$ predefined in file IRCCAR, i.e., $\xi=-\frac{1}{c_1} \log \sum_{i=1}^{N}\exp\left(-\sum_{j=1}^{M}c_{j}(q-\tilde{q}(i))^2 \right)$ with

$N$ as defined above The complex coordinates are functions defined in the space spanned by the primitive coordinates.

Mind: All complex coordinates must be defined after the last primitive coordinate. Whenever complex coordinates are defined, the primitive coordinates are only the basis for their definition, and their status is ignored.

Settings for `item(i)`

It depends on the setting of flag. In most cases, item(i) is an integer specifying either the position of the atom or the lattice vector in the POSCAR file. Mind that two atoms are needed to define a bond length, three atoms are required for a bonding angle, etc. In the special case of the flag W, also some additional parameters, i.e., the reference bond length (generally a floating-point number) and exponents used in the definition (integers) are defined via item(i). See the description of the corresponding flag.

Settings for `status`

status = 0: the coordinate is constrained.
status = 4: the coordinate is affected by a Fermi-type step function
status = 5: the coordinate defines the collective variable in metadynamics
status = 7: the coordinate is monitored
status = 8: the coordinate is affected by a harmonic potential

Use cases and examples

Define two constraints

The following constrains the bond lengths between atoms 1 and 5, and between atoms 1 and 6.

 R 1 5 0
 R 1 6 0

Use complex coordinates

Consider, for instance, the ICONST file with the following lines:

R 1 6 0
R 1 5 0
S 1 -1 0

The first two lines define two primitive coordinates - bonds between the atoms $1$ and $6$ , and between the atoms $1$ and $5$ . The complex coordinate is the difference between the two bond lengths which is defined on the third line. Mind that whenever complex coordinates are defined, the primitives are used only as a basis for their definition. Consequently, the two primitive coordinates are not constrained in the simulation (despite status=0). Thus, the only controlled parameter is the complex coordinate. Therefore, to fix the first bond length and the complex coordinate at the same time, the ICONST file should be modified as follows:

Consider the same system as discussed above and assume that the reference distance for the bond between atoms 1 and 6 is 1.1 $\AA$ , while that for the bond between 1 and 5 is 1.5 $\AA$ . The coordination number can be fixed in two equivalent ways. The first definition makes use of the complex type D, in which case the corresponding ICONST would be written like this:

R 1 6 0
R 1 5 0
D 1.1 1.5 0

In this case, the exponents appearing in numerator and denominator of the defining formula for D (see above) are fixed at the values 9 and 14, respectively. Alternatively, one can fix the same coordination number using the W primitive and S complex coordinates. This can be accomplished as follows:

W 1 6 1.1 9 14 0
W 1 5 1.5 9 14 0
S 1 1 0

The advantage of this format is that the coefficients M and N (see above the definition of W) can be set for each distance separately. Moreover, this format allows for an easy and intuitive definition of scaled sums of (and/or differences between) multiple coordination numbers - simply via a suitable choice of coefficients linked with S, which can be positive, negative, or zero.

Restrictions on the volume and/or shape of the simulation cell

In the context of a molecular dynamics simulation in NpT ensemble, the ICONST file can be used to impose restrictions on the volume and/or shape of the simulation cell. The following examples cover some of the most important scenarios:

1.) Simulation with a constant cell volume and variable shape.

LV 0

2.) Variable lengths of lattice vectors but fixed lattice angles.

LA 1 2 0
LA 1 3 0
LA 2 3 0

3.) A cubic cell with variable volume but fixed shape. Note that the S type constraints involving the lengths of the lattice vectors ( $a_i - a_j = 0$ ) are chosen so as to preserve ratios $a_1:a_2:a_3=1:1:1$ , as required by the cubic shape.

LA 1 2 0
LA 1 3 0
LA 2 3 0
LR 1 0
LR 2 0
LR 3 0
S  1  0  0  0  0  0 0
S  0  1  0  0  0  0 0
S  0  0  1  0  0  0 0
S  0  0  0  1 -1  0 0
S  0  0  0  1  0 -1 0
S  0  0  0  0  1 -1 0

4.) An orthorhombic cell with variable volume but fixed shape. Here, in order to fix ratios between the lengths of the lattice vectors ( $a_1:a_2:a_3$ ), we define the constraints of the form $c_i*a_i + c_j*a_j = 0$ . For instance, if the cell vectors are such that the relative proportions of their lengths are $a_1:a_2:a_3=1:1.5:2$ , the following ICONST can be used:

LA 1 2 0
LA 1 3 0
LA 2 3 0
LR 1 0
LR 2 0
LR 3 0
S  1  0  0  0      0    0 0
S  0  1  0  0      0    0 0
S  0  0  1  0      0    0 0
S  0  0  0  1.5 -1.0  0.0 0
S  0  0  0  2.0  0.0 -1.0 0
S  0  0  0  0.0  4.0 -3.0 0

@@ Line 1: / Line 1: @@
-Geometric parameters that are controlled in molecular dynamics (e.g. constrained or affected by the action of a bias potential) are defined in the file {{TAG|ICONST}}. Two kinds of geometric parameters can be defined: primitive
+In the {{TAG|ICONST}} file, geometric parameters are defined, which are then monitored or controlled in a molecular-dynamics simulation. For instance, the distance between two sites can be constrained or affected by the action of a bias potential. Finally, VASP writes the output to the {{TAG|REPORT}} file.
-(such as bond lengths or angles), and complex (e.g. linear combinations of primitive coordinates). Each coordinate is defined in a separate line, the complex coordinates must be defined after primitive ones. In order to define a primitive coordinate, the following syntax is used:
-<math>FLAG</math> atom(1) ... atom(N) <math>STATUS</math>
+== Overview ==
+Two kinds of geometric parameters can be defined:
+primitive parameters (e.g., bond lengths or angles), and complex parameters (i.e., linear combinations of primitive coordinates). Each line defines one coordinate, and the complex coordinates must be defined after all primitive ones.
+The syntax reads as follows:
-where <math>FLAG</math> is a character used to define a type of primitive coordinate:
+ flag item(1) ... item(N) status
+ ...
+ ...
+ flag  c_1  ...  c_M  status
-<math>R</math> - interatomic distance between atom(1) and atom(2)
+where <code>flag</code> specifies the type of primitive coordinate, <code>item(1) ... item(N)</code> is a space-separated list of integers that, e.g., specifies the ions enumerated in the order they appear in the {{TAG|POSCAR}} file (starting at 1), and <code>status</code> is an integer that sets the status, e.g., constrained or monitored. Here, the first line defines the syntax of a primitive coordinates <math>q_i</math>. Assuming that <math>M</math> primitive coordinates were specified on the first <math>M</math> lines of the {{TAG|ICONST}} file, the last line defines a complex coordinate, where <code>c_1  ...  c_M</code> is a space-separated list of the coefficients <math>c_i</math> for the primitive coordinate defined in line <math>i</math>.
-<math>A</math> - angle (with atom(2) being the apex)
-<math>T</math> - torsion
-<math>M</math> - distance between atom(1) and the centre of bond between atom(2) and atom(3)
-<math>X, Y, Z</math> - fractional (direct) coordinates for the lattice vectors <math>a</math>, <math>b</math>, and <math>c</math>
-atom(i) is an integer specifying the position of the atom in the {{TAG|POSCAR}} file (obviously, two atoms are needed to define a bond length, three atoms are required for a bonding angle, etc...), {{TAG|STATUS}} is an integer distinguishing between the constraint ({{TAG|STATUS}}=0), the coordinate affected by bias potential ({{TAG|STATUS}}=5), and the monitored (otherwise uneffected) coordinate ({{TAG|STATUS}}=7). The following example shows the {{TAG|ICONST}} file specifying two constraints - bond lengths between the atoms 1 and 5, and between the atoms 1 and 6:
+For instance, the following {{TAG|ICONST}} file defines two primitive coordinates and one complex coordinate.
+ R 1 6 0
   R 1 5 0
-  R 1 6 0
+  S 1 -1 0
-The complex coordinates are functions defined in the space of primitive coordinates. All complex coordinates must be defined after the last primitive coordinate. Assuming that <math>M</math> primitive coordinates (<math>q_i</math>) were specified on the first <math>M</math> lines of the {{TAG|ICONST}} file, the following syntax is used to define a complex coordinate: \\
+The first two lines define the bonds between atom <math>1</math> and atom <math>6</math>, and between atom <math>1</math> and <math>5</math>. The complex coordinate is the difference between the two bond lengths, which is defined on the third line.
+== Settings for <code>flag</code> ==
+===In case of primitive coordinates===
+*<code>flag</code> = R: interatomic distance between atoms <code>item(1)</code> and <code>item(2)</code>.
+*<code>flag</code> = A: angle defined by atoms <code>item(1)</code>, <code>item(2)</code> and <code>item(3)</code> (with the atom <code>item(2)</code> being the apex).
+*<code>flag</code> = T: torsional angle defined by atoms <code>item(1)</code>, <code>item(2)</code>, <code>item(3)</code> and <code>item(4)</code>.
+*<code>flag</code> = M: distance between atom <code>item(1)</code> and the center of bond between atoms <code>item(2)</code> and <code>item(3)</code>.
+*<code>flag</code> = B: distance between the center of bond between atoms <code>item(1)</code> and <code>item(2)</code> and the center of bond between atoms <code>item(3)</code> and <code>item(4)</code>
+*<code>flag</code> = P: ratio of length of the bond between atoms <code>item(1)</code> and <code>item(2)</code> and the length of the bond between atoms <code>item(3)</code> and <code>item(4)</code>
+*<code>flag</code> = W: function <math>\frac{1-\left(R/c\right)^M}{1-\left(R/c\right)^{N}}</math> with <math>R</math> being the bond length (in <math>\AA</math>) between the atoms <code>item(1)</code> and <code>item(2)</code>, <math>c</math> is the reference bond length specified as <code>item(3)</code>, and the exponents <math>M</math> and <math>N</math> are defined as <code>item(4)</code> and <code>item(5)</code>, respectively.
+*<code>flag</code> = X, Y, and Z: fractional (direct) coordinates linked with the lattice vectors <math>a</math>, <math>b</math>, and <math>c</math>.
+*<code>flag</code> = cX, cY, and cZ: Cartesian coordinates  <math>x</math>, <math>y</math>, and <math>z</math>.
+*<code>flag</code> = LR: length of lattice vector <code>item(1)</code>
+*<code>flag</code> = LA: angle between lattice vectors <code>item(1)</code> and <code>item(2)</code>
+*<code>flag</code> = LV: cell volume (no <code>item(i)</code> is defined in this case)
+===In case of complex coordinates===
+*<code>flag</code> = S: simple linear combination of primitive coordinates, i.e., <math>\left ( \xi=\sum_{i=1}^{M} c_i\,q_i \right)</math>.
+*<code>flag</code> = C: norm of the vector of primitive coordinates, which reads <math>\left( \xi=\sqrt{\sum_{i=1}^{M} \,(c_i\,q_i)^2} \right)</math>.
+*<code>flag</code> = D: coordination number<ref>[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.90.238302 M. Iannuzzi, A. Laio, M. Parrinello, Phys. Rev. Lett. 90, 238302 (2003)]</ref>, i.e.,  <math>\left( \xi=\sum_{i=1}^{M} \frac{1-\left(q_{i}/c_{i}\right)^9}{1-\left(q_{i}/c_{i}\right)^{14}} \right)</math>.
+*<code>flag</code> = IS: path-based coordinate<ref name="branduardi:jcp:07">[https://aip.scitation.org/doi/abs/10.1063/1.2432340 D. Branduardi, F. L. Gervasio, M. Parinello, J. Chem. Phys. 126, 54103 (2007)]</ref> measuring progress along discretized path represented by <math> N </math> points <math> \tilde{q}(j) </math> predefined in file {{TAG|IRCCAR}}, i.e., <math>\xi=\frac{1}{N-1}\frac{\sum_{i=1}^{N}(i-1)\exp\left(-\sum_{j=1}^{M}c_{j}(q_{j}-\tilde{q}_{j}(i))^2 \right) }{\sum_{i=1}^{N} \exp\left(-\sum_{j=1}^{M}c_{j}(q_{j}-\tilde{q}_{j}(i))^2 \right)} </math>
+*<code>flag</code> = IZ: path-based coordinate<ref name="branduardi:jcp:07"/> measuring orthogonal distance from the path <math> \tilde{q} </math> predefined in file {{TAG|IRCCAR}}, i.e., <math>\xi=-\frac{1}{c_1} \log \sum_{i=1}^{N}\exp\left(-\sum_{j=1}^{M}c_{j}(q-\tilde{q}(i))^2 \right) </math> with
+<math> N </math>  as defined above
+The complex coordinates are functions defined in the space spanned by the primitive coordinates.
+{{NB|mind|All complex coordinates must be defined after the last primitive coordinate. Whenever complex coordinates are defined, the primitive coordinates are only the basis for their definition, and their status is ignored.}}
+== Settings for <code>item(i)</code> ==
+It depends on the setting of <code>flag</code>. In most cases, <code>item(i)</code> is an integer specifying either the position of the atom or the lattice vector in the {{TAG|POSCAR}} file. Mind that two atoms are needed to define a bond length, three atoms are required for a bonding angle, etc. In the special case of the flag <code>W</code>, also some additional parameters, i.e., the reference bond length (generally a floating-point number) and exponents used in the definition (integers) are defined via <code>item(i)</code>. See the description of the corresponding <code>flag</code>.
+== Settings for <code>status</code> ==
-<math>FLAG</math>  <math>c_1</math>  <math>c_2</math>  ...  <math>c_M</math>  <math>STATUS  </math>
+* <code>status</code> = 0: the coordinate is constrained.
+* <code>status</code> = 4: the coordinate is affected by a Fermi-type step function
+* <code>status</code> = 5: the coordinate defines the collective variable in metadynamics
+* <code>status</code> = 7: the coordinate is monitored
+* <code>status</code> = 8: the coordinate is affected by a harmonic potential
-where <math>c_i</math> is a coefficient for the primitive coordinate defined at the line <math>i</math>. The number of coefficients must be the same as the number of primitive coordinates.  The following types of complex coordinates are supported:
+== Use cases and examples ==
-<math>S</math> - linear combination of primitive coordinates, i.e., <math>\left ( \xi=\sum_{i=1}^{M} c_i\,q_i \right)</math>
+=== Define two constraints ===
-<math>C</math> - norm of vector of primitive coordinates, <math>\left( \xi=\sqrt{\sum_{i=1}^{M} \,(c_i\,q_i)^2} \right)</math>
+The following constrains the bond lengths between atoms 1 and 5, and between atoms 1 and 6.
-<math>D</math> - coordination number  <math>\left( \xi=\sum_{i=1}^{M} \frac{1-\left(q_{i}/c_{i}\right)^9}{1-\left(q_{i}/c_{i}\right)^{14}} \right)</math>
+  R 1 5 0
+  R 1 6 0
-As in the case of primitive coordinates, {{TAG|STATUS}} allows to distinguish between the geometric constraint, the coordinate affected by a bias potential and the monitored coordinate. Whenever complex coordinates are defined, the primitives are used only as a basis for their definition. Consider, for instance, the {{TAG|ICONST}} file with the following lines:
+=== Use complex coordinates ===
+Consider, for instance, the {{TAG|ICONST}} file with the following lines:
   R 1 6 0
   R 1 5 0
   S 1 -1 0
-The first two lines define two primitive coordinates - bonds between the atoms <math>1</math> and <math>6</math>, and between the atoms <math>1</math> and <math>5</math>. The complex coordinate - difference between the two bond lengths - is defined on the third line. Consequently, the two primitive coordinates are not constrained in the simulation (despite {{TAG|STATUS}}=0), the only controlled parameter is the complex coordinate. Clearly, in order to fix the first bond length and the complex coordinate at the same time, the {{TAG|ICONST}} file should be modified as follows:
+The first two lines define two primitive coordinates - bonds between the atoms <math>1</math> and <math>6</math>, and between the atoms <math>1</math> and <math>5</math>. The complex coordinate is the difference between the two bond lengths which is defined on the third line. Mind that whenever complex coordinates are defined, the primitives are used only as a basis for their definition. Consequently, the two primitive coordinates are not constrained in the simulation (despite <code>status</code>=0). Thus, the only controlled parameter is the complex coordinate. Therefore, to fix the first bond length and the complex coordinate at the same time, the {{TAG|ICONST}} file should be modified as follows:
   R 1 6 0
   R 1 5 0
@@ Line 35: / Line 74: @@
   S 1 0 0
-== Related Tags and Sections ==
+Consider the same system as discussed above and assume that the reference distance for the bond between atoms 1 and 6 is 1.1 <math>\AA</math>, while that for the bond between 1 and 5 is 1.5 <math>\AA</math>.
-{{TAG|MDALGO}}
+The coordination number can be fixed in two equivalent ways.
+The first definition makes use of the complex type D, in which case the corresponding ICONST would be written like this:
+ R 1 6 0
+ R 1 5 0
+ D 1.1 1.5 0
+In this case, the exponents appearing in numerator and denominator of the defining formula for D (see above) are fixed at the values 9 and 14, respectively. Alternatively, one can fix the same coordination number using the W primitive and S complex coordinates. This can be accomplished as follows:
+ W 1 6 1.1 9 14 0
+ W 1 5 1.5 9 14 0
+ S 1 1 0
+The advantage of this format is that the coefficients M and N (see above the definition of W) can be set for each distance separately. Moreover, this format allows for an easy and intuitive definition of scaled sums of (and/or differences between) multiple coordination numbers - simply via a suitable choice of coefficients linked with S, which can be positive, negative, or zero.
+=== Restrictions on the volume and/or shape of the simulation cell ===
+In the context of a [https://www.vasp.at/wiki/index.php/MDALGO#NpT-simulation_with_Langevin_thermostat molecular dynamics simulation in NpT ensemble], the {{TAG|ICONST}} file can be used to impose restrictions on the volume and/or shape of the simulation cell. The following examples cover some of the most important scenarios:
+.) Simulation with a constant cell volume and variable shape.
+ LV 0
+.) Variable lengths of lattice vectors but fixed lattice angles.
+ LA 1 2 0
+ LA 1 3 0
+ LA 2 3 0
+.) A cubic cell with variable volume but fixed shape. Note that the S type constraints involving the lengths of the lattice vectors (<math>a_i - a_j = 0</math>) are chosen so as to preserve ratios <math>a_1:a_2:a_3=1:1:1</math>, as required by the cubic shape.
+ LA 1 2 0
+ LA 1 3 0
+ LA 2 3 0
+ LR 1 0
+ LR 2 0
+ LR 3 0
+ S  1  0  0  0  0  0 0
+ S  0  1  0  0  0  0 0
+ S  0  0  1  0  0  0 0
+ S  0  0  0  1 -1  0 0
+ S  0  0  0  1  0 -1 0
+ S  0  0  0  0  1 -1 0
+.) An orthorhombic cell with variable volume but fixed shape. Here, in order to fix ratios between the lengths of the lattice vectors (<math>a_1:a_2:a_3</math>),
+we define the constraints of the form <math>c_i*a_i + c_j*a_j = 0</math>.  For instance, if the cell vectors are such that the relative proportions of their lengths are <math>a_1:a_2:a_3=1:1.5:2</math>,  the following {{TAG|ICONST}} can be used:
+ LA 1 2 0
+ LA 1 3 0
+ LA 2 3 0
+ LR 1 0
+ LR 2 0
+ LR 3 0
+ S  1  0  0  0      0    0 0
+ S  0  1  0  0      0    0 0
+ S  0  0  1  0      0    0 0
+ S  0  0  0  1.5 -1.0  0.0 0
+ S  0  0  0  2.0  0.0 -1.0 0
+ S  0  0  0  0.0  4.0 -3.0 0
+==Related tags and articles==
+{{TAG|SHAKETOL}},
+{{TAG|SHAKEMAXITER}},
+{{TAG|MDALGO}}, {{FILE|REPORT}}
 ----
-[[The_VASP_Manual|Contents]]
+[[Category:Files]][[Category:Input files]][[Category:Symmetry]][[Category:Molecular dynamics]][[Category:Ensemble properties]][[Category:Biased molecular dynamics]]
-[[Category:Files]]