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doc/tutorial_drude.txt
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<script type="text/javascript"
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src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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</script>
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({ TeX: { equationNumbers: {autoNumber: "AMS"} } });
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</script>
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Tutorial for Thermalized Drude oscillators in LAMMPS :h3
|
||||
|
||||
This tutorial explains how to use "Drude
|
||||
oscillators"_drude_oscillators.html in LAMMPS to simulate polarizable
|
||||
systems. As an illustration, the input files for a simulation of 250
|
||||
phenol molecules are documented. First of all, LAMMPS has to be
|
||||
compiled with the USER-DRUDE package activated. Then, the data file
|
||||
and input scripts have to be modified to include the Drude dipoles and
|
||||
how to handle them.
|
||||
|
||||
:line
|
||||
|
||||
[Overview of Drude induced dipoles]
|
||||
|
||||
Polarizable atoms acquire an induced electric dipole moment under the
|
||||
action of an external electric field, for example the electric field
|
||||
created by the surrounding particles. Drude oscillators represent
|
||||
these dipoles by two fixed charges: the core (DC) and the Drude
|
||||
particle (DP) bound by a harmonic potential. The Drude particle can be
|
||||
thought of as the electron cloud whose center can be displaced from
|
||||
the position of the the corresponding nucleus.
|
||||
|
||||
The sum of the masses of a core-Drude pair should be the mass of the
|
||||
initial (unsplit) atom, \(m_C + m_D = m\). The sum of their charges
|
||||
should be the charge of the initial (unsplit) atom, \(q_C + q_D = q\).
|
||||
A harmonic potential between the core and Drude partners should be
|
||||
present, with force constant \(k_D\) and an equilibrium distance of
|
||||
zero. The (half-)stiffness of the "harmonic bond"_bond_harmonic.html
|
||||
\(K_D = k_D/2\) and the Drude charge \(q_D\) are related to the atom
|
||||
polarizability \(\alpha\) by
|
||||
|
||||
\begin\{equation\} K_D = \frac 1 2\, \frac \{q_D^2\} \alpha
|
||||
\end\{equation\}
|
||||
|
||||
Ideally, the mass of the Drude particle should be small, and the
|
||||
stiffness of the harmonic bond should be large, so that the Drude
|
||||
particle remains close ot the core. The values of Drude mass, Drude
|
||||
charge, and force constant can be chosen following different
|
||||
strategies, as in the following examples of polarizable force
|
||||
fields.
|
||||
|
||||
"Lamoureux and Roux"_#Lamoureux suggest adopting a global
|
||||
half-stiffness, \(K_D\) = 500 kcal/(mol Å<sup>2</sup>) —
|
||||
which corresponds to a force constant \(k_D\) = 4184 kJ/(mol
|
||||
Å<sup>2</sup>) — for all types of core-Drude bond, a
|
||||
global mass \(m_D\) = 0.4 g/mol (or u) for all types of Drude
|
||||
particle, and to calculate the Drude charges for individual atom types
|
||||
from the atom polarizabilities using equation (1). This choice is
|
||||
followed in the polarizable CHARMM force field. :ulb,l
|
||||
|
||||
"Schroeder and Steinhauser"_#Schroeder suggest adopting a global
|
||||
charge \(q_D\) = -1.0e and a global mass \(m_D\) = 0.1 g/mol (or u)
|
||||
for all Drude particles, and to calculate the force constant for each
|
||||
type of core-Drude bond from equation (1). The timesteps used by these
|
||||
authors are between 0.5 and 2 fs, with the degrees of freedom of the
|
||||
Drude oscillators kept cold at 1 K. In both these force fields
|
||||
hydrogen atoms are treated as non-polarizable. :ule,l
|
||||
|
||||
The motion of of the Drude particles can be calculated by minimizing
|
||||
the energy of the induced dipoles at each timestep, by an interative,
|
||||
self-consistent procedure. The Drude particles can be massless and
|
||||
therefore do not contribute to the kinetic energy. However, the
|
||||
relaxed method is computationall slow. An extended-lagrangian method
|
||||
can be used to calculate the positions of the Drude particles, but
|
||||
this requires them to have mass. It is important in this case to
|
||||
decouple the degrees of freedom associated with the Drude oscillators
|
||||
from those of the normal atoms. Thermalizing the Drude dipoles at
|
||||
temperatures comparable to the rest of the simulation leads to several
|
||||
problems (kinetic energy transfer, very short timestep, etc.), which
|
||||
can be remediated by the "cold Drude" technique ("Lamoureux and
|
||||
Roux"_#Lamoureux).
|
||||
|
||||
Two closely related models are used to represent polarization through
|
||||
"charges on a spring": the core-shell model and the Drude
|
||||
model. Although the basic idea is the same, the core-shell model is
|
||||
normally used for ionic/crystalline materials, whereas the Drude model
|
||||
is normally used for molecular systems and fluid states. In ionic
|
||||
crystals the symmetry around each ion and the distance between them
|
||||
are such that the core-shell model is sufficiently stable. But to be
|
||||
applicable to molecular/covalent systems the Drude model includes two
|
||||
important features:
|
||||
|
||||
The possibility to thermostat the additional degrees of freedom
|
||||
associated with the induced dipoles at very low temperature, in terms
|
||||
of the reduced coordinates of the Drude particles with respect to
|
||||
their cores. This makes the trajectory close to that of relaxed
|
||||
induced dipoles. :olb,l
|
||||
|
||||
The Drude dipoles on covalently bonded atoms interact too strongly
|
||||
due to the short distances, so an atom may capture the Drude particle
|
||||
(shell) of a neighbor, or the induced dipoles within the same molecule
|
||||
may align too much. To avoid this, damping at short of the
|
||||
interactions between the point charges composing the induced dipole
|
||||
can be done by "Thole"_#Thole functions. :ole,l
|
||||
|
||||
:line
|
||||
|
||||
[Preparation of the data file]
|
||||
|
||||
The data file is similar to a standard LAMMPS data file for
|
||||
{atom_style full}. The DPs and the {harmonic bonds} connecting them
|
||||
to their DC should appear in the data file as normal atoms and bonds.
|
||||
|
||||
You can use the {polarizer} tool (Python script distributed with the
|
||||
USER-DRUDE package) to convert a non-polarizable data file (here
|
||||
{data.102494.lmp}) to a polarizable data file ({data-p.lmp})
|
||||
|
||||
polarizer -q -f phenol.dff data.102494.lmp data-p.lmp :pre
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||||
|
||||
This will automatically insert the new atoms and bonds.
|
||||
The masses and charges of DCs and DPs are computed
|
||||
from {phenol.dff}, as well as the DC-DP bond constants. The file
|
||||
{phenol.dff} contains the polarizabilities of the atom types
|
||||
and the mass of the Drude particles, for instance:
|
||||
|
||||
# units: kJ/mol, A, deg
|
||||
# kforce is in the form k/2 r_D^2
|
||||
# type m_D/u q_D/e k_D alpha/A3 thole
|
||||
OH 0.4 -1.0 4184.0 0.63 0.67
|
||||
CA 0.4 -1.0 4184.0 1.36 2.51
|
||||
CAI 0.4 -1.0 4184.0 1.09 2.51 :pre
|
||||
|
||||
The hydrogen atoms are absent from this file, so they will be treated
|
||||
as non-polarizable atoms. In the non-polarizable data file
|
||||
{data.102494.lmp}, atom names corresponding to the atom type numbers
|
||||
have to be specified as comments at the end of lines of the {Masses}
|
||||
section. You probably need to edit it to add these names. It should
|
||||
look like
|
||||
|
||||
Masses :pre
|
||||
|
||||
1 12.011 # CAI
|
||||
2 12.011 # CA
|
||||
3 15.999 # OH
|
||||
4 1.008 # HA
|
||||
5 1.008 # HO :pre
|
||||
|
||||
:line
|
||||
|
||||
[Basic input file]
|
||||
|
||||
The atom style should be set to (or derive from) {full}, so that you
|
||||
can define atomic charges and molecular bonds, angles, dihedrals...
|
||||
|
||||
The {polarizer} tool also outputs certain lines related to the input
|
||||
script (the use of these lines will be explained below). In order for
|
||||
LAMMPS to recognize that you are using Drude oscillators, you should
|
||||
use the fix {drude}. The command is
|
||||
|
||||
fix DRUDE all drude 1 1 1 0 0 2 2 2 :pre
|
||||
|
||||
or, equivalently
|
||||
|
||||
fix DRUDE all drude C C C N N D D D :pre
|
||||
|
||||
The 0, 1, 2 (or N, C, D) following the {drude} keyword have the
|
||||
following meaning: There is one tag for each atom type. This tag is 1
|
||||
(or C) for DCs, 2 (or D) for DPs and 0 (or N) for non-polarizable
|
||||
atoms. Here the atom types 1 to 3 (C and O atoms) are DC, atom types
|
||||
4 and 5 (H atoms) are non-polarizable and the atom types 6 to 8 are
|
||||
the newly created DPs.
|
||||
|
||||
By recognizing the fix {drude}, LAMMPS will find and store matching
|
||||
DC-DP pairs and will treat DP as equivalent to their DC in the
|
||||
{special bonds} relations. It may be necessary to extend the space
|
||||
for storing such special relations. In this case extra space should
|
||||
be reserved by using the {extra} keyword of the {special_bonds}
|
||||
command. With our phenol, there is 1 more special neighbor for which
|
||||
space is required. Otherwise LAMMPS crashes and gives the required
|
||||
value.
|
||||
|
||||
special_bonds lj/coul 0.0 0.0 0.5 extra 1 :pre
|
||||
|
||||
Let us assume we want to run a simple NVT simulation at 300 K. Note
|
||||
that Drude oscillators need to be thermalized at a low temperature in
|
||||
order to approximate a self-consistent field (SCF), therefore it is not
|
||||
possible to simulate an NVE ensemble with this package. Since dipoles
|
||||
are approximated by a charged DC-DP pair, the {pair_style} must
|
||||
include Coulomb interactions, for instance {lj/cut/coul/long} with
|
||||
{kspace_style pppm}. For example, with a cutoff of 10. and a precision
|
||||
1.e-4:
|
||||
|
||||
pair_style lj/cut/coul/long 10.0
|
||||
kspace_style pppm 1.0e-4 :pre
|
||||
|
||||
As compared to the non-polarizable input file, {pair_coeff} lines need
|
||||
to be added for the DPs. Since the DPs have no Lennard-Jones
|
||||
interactions, their {epsilon} is 0. so the only {pair_coeff} line
|
||||
that needs to be added is
|
||||
|
||||
pair_coeff * 6* 0.0 0.0 # All-DPs :pre
|
||||
|
||||
Now for the thermalization, the simplest choice is to use the "fix
|
||||
langevin/drude"_fix_langevin_drude.html.
|
||||
|
||||
fix LANG all langevin/drude 300. 100 12435 1. 20 13977 :pre
|
||||
|
||||
This applies a Langevin thermostat at temperature 300. to the centers
|
||||
of mass of the DC-DP pairs, with relaxation time 100 and with random
|
||||
seed 12345. This fix applies also a Langevin thermostat at temperature
|
||||
1. to the relative motion of the DPs around their DCs, with relaxation
|
||||
time 20 and random seed 13977. Only the DCs and non-polarizable
|
||||
atoms need to be in this fix's group. LAMMPS will thermostate the DPs
|
||||
together with their DC. For this, ghost atoms need to know their
|
||||
velocities. Thus you need to add the following command:
|
||||
|
||||
comm_modify vel yes :pre
|
||||
|
||||
In order to avoid that the center of mass of the whole system
|
||||
drifts due to the random forces of the Langevin thermostat on DCs, you
|
||||
can add the {zero yes} option at the end of the fix line.
|
||||
|
||||
If the fix {shake} is used to constrain the C-H bonds, it should be
|
||||
invoked after the fix {langevin/drude} for more accuracy.
|
||||
|
||||
fix SHAKE ATOMS shake 0.0001 20 0 t 4 5 :pre
|
||||
|
||||
IMPORTANT NOTE: The group of the fix {shake} must not include the DPs.
|
||||
If the group {ATOMS} is defined by non-DPs atom types, you could use
|
||||
|
||||
Since the fix {langevin/drude} does not perform time integration (just
|
||||
modification of forces but no position/velocity updates), the fix
|
||||
{nve} should be used in conjunction.
|
||||
|
||||
fix NVE all nve :pre
|
||||
|
||||
Finally, do not forget to update the atom type elements if you use
|
||||
them in a {dump_modify ... element ...} command, by adding the element
|
||||
type of the DPs. Here for instance
|
||||
|
||||
dump DUMP all custom 10 dump.lammpstrj id mol type element x y z ix iy iz
|
||||
dump_modify DUMP element C C O H H D D D :pre
|
||||
|
||||
The input file should now be ready for use!
|
||||
|
||||
You will notice that the global temperature {thermo_temp} computed by
|
||||
LAMMPS is not 300. K as wanted. This is because LAMMPS treats DPs as
|
||||
standard atoms in his default compute. If you want to output the
|
||||
temperatures of the DC-DP pair centers of mass and of the DPs relative
|
||||
to their DCs, you should use {thermo_style custom} with respectively
|
||||
{f_LANG\[1\]} and {f_LANG\[2\]}. These should be close to 300. and
|
||||
1. on average.
|
||||
|
||||
thermo_style custom step temp f_LANG\[1\] f_LANG\[2\] :pre
|
||||
|
||||
:line
|
||||
|
||||
[Thole screening]
|
||||
|
||||
Dipolar interactions represented by point charges on springs may not
|
||||
be stable, for example if the atomic polarizability is too high for
|
||||
instance, a DP can escape from its DC and be captured by another DC,
|
||||
which makes the force and energy diverge and the simulation
|
||||
crash. Even without reaching this extreme case, the correlation
|
||||
between nearby dipoles on the same molecule may be exagerated. Often,
|
||||
special bond relations prevent bonded neighboring atoms to see the
|
||||
charge of each other's DP, so that the problem does not always appear.
|
||||
It is possible to use screened dipole dipole interactions by using the
|
||||
"{pair_style thole}"_pair_thole.html. This is implemented as a
|
||||
correction to the Coulomb pair_styles, which dampens at short distance
|
||||
the interactions between the charges representing the induced dipoles.
|
||||
It is to be used as {hybrid/overlay} with any standard {coul} pair
|
||||
style. In our example, we would use
|
||||
|
||||
pair_style hybrid/overlay lj/cut/coul/long 10.0 thole 2.6 10.0 :pre
|
||||
|
||||
This tells LAMMPS that we are using two pair_styles. The first one is
|
||||
as above ({lj/cut/coul/long 10.0}). The second one is a {thole}
|
||||
pair_style with default screening factor 2.6 ("Noskov"_#Noskov) and
|
||||
cutoff 10.0.
|
||||
|
||||
Since {hybrid/overlay} does not support mixing rules, the interaction
|
||||
coefficients of all the pairs of atom types with i < j should be
|
||||
explicitly defined. The output of the {polarizer} script can be used
|
||||
to complete the {pair_coeff} section of the input file. In our
|
||||
example, this will look like:
|
||||
|
||||
pair_coeff 1 1 lj/cut/coul/long 0.0700 3.550
|
||||
pair_coeff 1 2 lj/cut/coul/long 0.0700 3.550
|
||||
pair_coeff 1 3 lj/cut/coul/long 0.1091 3.310
|
||||
pair_coeff 1 4 lj/cut/coul/long 0.0458 2.985
|
||||
pair_coeff 2 2 lj/cut/coul/long 0.0700 3.550
|
||||
pair_coeff 2 3 lj/cut/coul/long 0.1091 3.310
|
||||
pair_coeff 2 4 lj/cut/coul/long 0.0458 2.985
|
||||
pair_coeff 3 3 lj/cut/coul/long 0.1700 3.070
|
||||
pair_coeff 3 4 lj/cut/coul/long 0.0714 2.745
|
||||
pair_coeff 4 4 lj/cut/coul/long 0.0300 2.420
|
||||
pair_coeff * 5 lj/cut/coul/long 0.0000 0.000
|
||||
pair_coeff * 6* lj/cut/coul/long 0.0000 0.000
|
||||
pair_coeff 1 1 thole 1.090 2.510
|
||||
pair_coeff 1 2 thole 1.218 2.510
|
||||
pair_coeff 1 3 thole 0.829 1.590
|
||||
pair_coeff 1 6 thole 1.090 2.510
|
||||
pair_coeff 1 7 thole 1.218 2.510
|
||||
pair_coeff 1 8 thole 0.829 1.590
|
||||
pair_coeff 2 2 thole 1.360 2.510
|
||||
pair_coeff 2 3 thole 0.926 1.590
|
||||
pair_coeff 2 6 thole 1.218 2.510
|
||||
pair_coeff 2 7 thole 1.360 2.510
|
||||
pair_coeff 2 8 thole 0.926 1.590
|
||||
pair_coeff 3 3 thole 0.630 0.670
|
||||
pair_coeff 3 6 thole 0.829 1.590
|
||||
pair_coeff 3 7 thole 0.926 1.590
|
||||
pair_coeff 3 8 thole 0.630 0.670
|
||||
pair_coeff 6 6 thole 1.090 2.510
|
||||
pair_coeff 6 7 thole 1.218 2.510
|
||||
pair_coeff 6 8 thole 0.829 1.590
|
||||
pair_coeff 7 7 thole 1.360 2.510
|
||||
pair_coeff 7 8 thole 0.926 1.590
|
||||
pair_coeff 8 8 thole 0.630 0.670 :pre
|
||||
|
||||
For the {thole} pair style the coefficients are
|
||||
|
||||
the atom polarizability in units of cubic length
|
||||
the screening factor of the Thole function (optional, default value specified by the pair_style command)
|
||||
the cutoff (optional, default value defined by the pair_style command) :ol
|
||||
|
||||
The special neighbors have charge-charge and charge-dipole
|
||||
interactions screened by the {coul} factors of the {special_bonds}
|
||||
command (0., 0., and 0.5 in the example above). Without using the
|
||||
pair_style {thole}, dipole-dipole interactions are screened by the
|
||||
same factor. By using the pair_style {thole}, dipole-dipole
|
||||
interactions are screened by Thole's function, whatever their special
|
||||
relationship (except within each DC-DP pair of course). Consider for
|
||||
example 1-2 neighbors: using the pair_style {thole}, their dipoles
|
||||
will see each other (despite the {coul} factor being 0.) and the
|
||||
interactions between these dipoles will be damped by Thole's
|
||||
function.
|
||||
|
||||
:line
|
||||
|
||||
[Thermostats and barostats]
|
||||
|
||||
Using a Nose-Hoover barostat with the {langevin/drude} thermostat is
|
||||
straightforward using fix {nph} instead of {nve}. For example:
|
||||
|
||||
fix NPH all nph iso 1. 1. 500 :pre
|
||||
|
||||
It is also possible to use a Nose-Hoover instead of a Langevin
|
||||
thermostat. This requires to use "{fix
|
||||
drude/transform}"_fix_drude_transform.html just before and after the
|
||||
time intergation fixes. The {fix drude/transform/direct} converts the
|
||||
atomic masses, positions, velocities and forces into a reduced
|
||||
representation, where the DCs transform into the centers of mass of
|
||||
the DC-DP pairs and the DPs transform into their relative position
|
||||
with respect to their DC. The {fix drude/transform/inverse} performs
|
||||
the reverse transformation. For a NVT simulation, with the DCs and
|
||||
atoms at 300 K and the DPs at 1 K relative to their DC one would use
|
||||
|
||||
fix DIRECT all drude/transform/direct
|
||||
fix NVT1 ATOMS nvt temp 300. 300. 100
|
||||
fix NVT2 DRUDES nvt temp 1. 1. 20
|
||||
fix INVERSE all drude/transform/inverse :pre
|
||||
|
||||
For our phenol example, the groups would be defined as
|
||||
|
||||
group ATOMS type 1 2 3 4 5 # DCs and non-polarizable atoms
|
||||
group CORES type 1 2 3 # DCs
|
||||
group DRUDES type 6 7 8 # DPs :pre
|
||||
|
||||
Note that with the fixes {drude/transform}, it is not required to
|
||||
specify {comm_modify vel yes} because the fixes do it anyway (several
|
||||
times and for the forces also). To avoid the flying ice cube artifact
|
||||
"(Lamoureux)"_#Lamoureux, where the atoms progressively freeze and the
|
||||
center of mass of the whole system drifts faster and faster, the {fix
|
||||
momentum} can be used. For instance:
|
||||
|
||||
fix MOMENTUM all momentum 100 linear 1 1 1 :pre
|
||||
|
||||
It is a bit more tricky to run a NPT simulation with Nose-Hoover
|
||||
barostat and thermostat. First, the volume should be integrated only
|
||||
once. So the fix for DCs and atoms should be {npt} while the fix for
|
||||
DPs should be {nvt} (or vice versa). Second, the {fix npt} computes a
|
||||
global pressure and thus a global temperature whatever the fix group.
|
||||
We do want the pressure to correspond to the whole system, but we want
|
||||
the temperature to correspond to the fix group only. We must then use
|
||||
the {fix_modify} command for this. In the end, the block of
|
||||
instructions for thermostating and barostating will look like
|
||||
|
||||
compute TATOMS ATOMS temp
|
||||
fix DIRECT all drude/transform/direct
|
||||
fix NPT ATOMS npt temp 300. 300. 100 iso 1. 1. 500
|
||||
fix_modify NPT temp TATOMS press thermo_press
|
||||
fix NVT DRUDES nvt temp 1. 1. 20
|
||||
fix INVERSE all drude/transform/inverse :pre
|
||||
|
||||
:line
|
||||
|
||||
[Rigid bodies]
|
||||
|
||||
You may want to simulate molecules as rigid bodies (but polarizable).
|
||||
Common cases are water models such as "SWM4-NDP"_#SWM4-NDP, which is a
|
||||
kind of polarizable TIP4P water. The rigid bodies and the DPs should
|
||||
be integrated separately, even with the Langevin thermostat. Let us
|
||||
review the different thermostats and ensemble combinations.
|
||||
|
||||
NVT ensemble using Langevin thermostat:
|
||||
|
||||
comm_modify vel yes
|
||||
fix LANG all langevin/drude 300. 100 12435 1. 20 13977
|
||||
fix RIGID ATOMS rigid/nve/small molecule
|
||||
fix NVE DRUDES nve :pre
|
||||
|
||||
NVT ensemble using Nose-Hoover thermostat:
|
||||
|
||||
fix DIRECT all drude/transform/direct
|
||||
fix RIGID ATOMS rigid/nvt/small molecule temp 300. 300. 100
|
||||
fix NVT DRUDES nvt temp 1. 1. 20
|
||||
fix INVERSE all drude/transform/inverse :pre
|
||||
|
||||
NPT ensemble with Langevin thermostat:
|
||||
|
||||
comm_modify vel yes
|
||||
fix LANG all langevin/drude 300. 100 12435 1. 20 13977
|
||||
fix RIGID ATOMS rigid/nph/small molecule iso 1. 1. 500
|
||||
fix NVE DRUDES nve :pre
|
||||
|
||||
NPT ensemble using Nose-Hoover thermostat:
|
||||
|
||||
compute TATOM ATOMS temp
|
||||
fix DIRECT all drude/transform/direct
|
||||
fix RIGID ATOMS rigid/npt/small molecule temp 300. 300. 100 iso 1. 1. 500
|
||||
fix_modify RIGID temp TATOM press thermo_press
|
||||
fix NVT DRUDES nvt temp 1. 1. 20
|
||||
fix INVERSE all drude/transform/inverse :pre
|
||||
|
||||
:line
|
||||
|
||||
:link(Lamoureux)
|
||||
[(Lamoureux)] Lamoureux and Roux, J Chem Phys, 119, 3025-3039 (2003)
|
||||
|
||||
:link(Schroeder)
|
||||
[(Schroeder)] Schröder and Steinhauser, J Chem Phys, 133,
|
||||
154511 (2010).
|
||||
|
||||
:link(Jiang)
|
||||
[(Jiang)] Jiang, Hardy, Phillips, MacKerell, Schulten, and Roux,
|
||||
J Phys Chem Lett, 2, 87-92 (2011).
|
||||
|
||||
:link(Thole)
|
||||
[(Thole)] Chem Phys, 59, 341 (1981).
|
||||
|
||||
:link(Noskov)
|
||||
[(Noskov)] Noskov, Lamoureux and Roux, J Phys Chem B, 109, 6705 (2005).
|
||||
|
||||
:link(SWM4-NDP)
|
||||
[(SWM4-NDP)] Lamoureux, Harder, Vorobyov, Roux, MacKerell, Chem Phys
|
||||
Let, 418, 245-249 (2006)
|
||||
|
||||
Reference in New Issue
Block a user