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.. index:: fix charge/regulation
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fix charge/regulation command
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=============================
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Syntax
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""""""
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.. parsed-literal::
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fix ID group-ID charge/regulation cation_type anion_type keyword value(s)
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* ID, group-ID are documented in fix command
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* charge/regulation = style name of this fix command
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* cation_type = atom type of free cations
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* anion_type = atom type of free anions
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* zero or more keyword/value pairs may be appended
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.. parsed-literal::
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keyword = *pH*, *pKa*, *pKb*, *pIp*, *pIm*, *pKs*, *acid_type*, *base_type*, *lunit_nm*, *temp*, *tempfixid*, *nevery*, *nmc*, *xrd*, *seed*, *tag*, *group*, *onlysalt*, *pmcmoves*
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*pH* value = pH of the solution
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*pKa* value = acid dissociation constant
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*pKb* value = base dissociation constant
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*pIp* value = chemical potential of free cations
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*pIm* value = chemical potential of free anions
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*pKs* value = solution self-dissociation constant
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*acid_type* = atom type of acid groups
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*base_type* = atom type of base groups
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*lunit_nm* value = unit length used by LAMMPS (# in the units of nanometers)
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*temp* value = temperature
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*tempfixid* value = fix ID of temperature thermostat
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*nevery* value = invoke this fix every nevery steps
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*nmc* value = number of charge regulation MC moves to attempt every nevery steps
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*xrd* value = cutoff distance for acid/base reaction
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*seed* value = random # seed (positive integer)
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*tag* value = yes or no (yes: The code assign unique tags to inserted ions; no: The tag of all inserted ions is "0")
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*group* value = group-ID, inserted ions are assigned to group group-ID. Can be used multiple times to assign inserted ions to multiple groups.
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*onlysalt* values = flag charge_cation charge_anion.
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flag = yes or no (yes: the fix performs only ion insertion/deletion, no: perform acid/base dissociation and ion insertion/deletion)
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charge_cation, charge_anion = value of cation/anion charge, must be an integer (only specify if flag = yes)
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*pmcmoves* values = pmcA pmcB pmcI - MC move fractions for acid ionization (pmcA), base ionization (pmcB) and free ion exchange (pmcI)
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Examples
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""""""""
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.. code-block:: LAMMPS
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fix chareg all charge/regulation 1 2 acid_type 3 base_type 4 pKa 5 pKb 7 lb 1.0 nevery 200 nexchange 200 seed 123 tempfixid fT
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fix chareg all charge/regulation 1 2 pIp 3 pIm 3 onlysalt yes 2 -1 seed 123 tag yes temp 1.0
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Description
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"""""""""""
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This fix performs Monte Carlo (MC) sampling of charge regulation and
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exchange of ions with a reservoir as discussed in :ref:`(Curk1) <Curk1>`
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and :ref:`(Curk2) <Curk2>`. The implemented method is largely analogous
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to the grand-reaction ensemble method in :ref:`(Landsgesell)
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<Landsgesell>`. The implementation is parallelized, compatible with
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existing LAMMPS functionalities, and applicable to any system utilizing
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discrete, ionizable groups or surface sites.
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Specifically, the fix implements the following three types of MC moves,
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which discretely change the charge state of individual particles and
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insert ions into the systems: :math:`\mathrm{A} \rightleftharpoons
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\mathrm{A}^-+\mathrm{X}^+`, :math:`\mathrm{B} \rightleftharpoons
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\mathrm{B}^++\mathrm{X}^-`, and :math:`\emptyset \rightleftharpoons
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Z^-\mathrm{X}^{Z^+}+Z^+\mathrm{X}^{-Z^-}`. In the former two types of
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reactions, Monte Carlo moves alter the charge value of specific atoms
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(:math:`\mathrm{A}`, :math:`\mathrm{B}`) and simultaneously insert a
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counterion to preserve the charge neutrality of the system, modeling the
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dissociation/association process. The last type of reaction performs
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grand canonical MC exchange of ion pairs with a (fictitious) reservoir.
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In our implementation "acid" refers to particles that can attain charge
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:math:`q=\{0,-1\}` and "base" to particles with :math:`q=\{0,1\}`,
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whereas the MC exchange of free ions allows any integer charge values of
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:math:`{Z^+}` and :math:`{Z^-}`.
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Here we provide several practical examples for modeling charge
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regulation effects in solvated systems. An acid ionization reaction
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(:math:`\mathrm{A} \rightleftharpoons \mathrm{A}^-+\mathrm{H}^+`) can be
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defined via a single line in the input file
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.. code-block:: LAMMPS
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fix acid_reaction all charge/regulation 2 3 acid_type 1 pH 7.0 pKa 5.0 pIp 7.0 pIm 7.0
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where the fix attempts to charge :math:`\mathrm{A}` (discharge
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:math:`\mathrm{A}^-`) to :math:`\mathrm{A}^-` (:math:`\mathrm{A}`) and
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insert (delete) a proton (atom type 2). Besides, the fix implements
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self-ionization reaction of water :math:`\emptyset \rightleftharpoons
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\mathrm{H}^++\mathrm{OH}^-`. However, this approach is highly
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inefficient at :math:`\mathrm{pH} \approx 7` when the concentration of
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both protons and hydroxyl ions is low, resulting in a relatively low
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acceptance rate of MC moves.
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A more efficient way is to allow salt ions to participate in ionization
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reactions, which can be easily achieved via
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.. code-block:: LAMMPS
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fix acid_reaction all charge/regulation 4 5 acid_type 1 pH 7.0 pKa 5.0 pIp 2.0 pIm 2.0
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where particles of atom type 4 and 5 are the salt cations and anions,
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both at chemical potential pI=2.0, see :ref:`(Curk1) <Curk1>` and
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:ref:`(Landsgesell) <Landsgesell>` for more details.
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Similarly, we could have simultaneously added a base ionization reaction
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(:math:`\mathrm{B} \rightleftharpoons \mathrm{B}^++\mathrm{OH}^-`)
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.. code-block:: LAMMPS
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fix base_reaction all charge/regulation 2 3 base_type 6 pH 7.0 pKb 6.0 pIp 7.0 pIm 7.0
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where the fix will attempt to charge :math:`\mathrm{B}` (discharge
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:math:`\mathrm{B}^+`) to :math:`\mathrm{B}^+` (:math:`\mathrm{B}`) and
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insert (delete) a hydroxyl ion :math:`\mathrm{OH}^-` of atom type 3. If
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neither the acid or the base type is specified, for example,
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.. code-block:: LAMMPS
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fix salt_reaction all charge/regulation 4 5 pIp 2.0 pIm 2.0
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the fix simply inserts or deletes an ion pair of a free cation (atom
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type 4) and a free anion (atom type 5) as done in a conventional
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grand-canonical MC simulation.
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The fix is compatible with LAMMPS sub-packages such as *molecule* or
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*rigid*. That said, the acid and base particles can be part of larger
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molecules or rigid bodies. Free ions that are inserted to or deleted
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from the system must be defined as single particles (no bonded
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interactions allowed) and cannot be part of larger molecules or rigid
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bodies. If *molecule* package is used, all inserted ions have a molecule
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ID equal to zero.
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Note that LAMMPS implicitly assumes a constant number of particles
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(degrees of freedom). Since using this fix alters the total number of
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particles during the simulation, any thermostat used by LAMMPS, such as
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NVT or Langevin, must use a dynamic calculation of system
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temperature. This can be achieved by specifying a dynamic temperature
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compute (e.g. dtemp) and using it with the desired thermostat, e.g. a
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Langevin thermostat:
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.. code-block:: LAMMPS
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compute dtemp all temp
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compute_modify dtemp dynamic yes
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fix fT all langevin 1.0 1.0 1.0 123
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fix_modify fT temp dtemp
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The chemical potential units (e.g. pH) are in the standard log10
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representation assuming reference concentration :math:`\rho_0 =
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\mathrm{mol}/\mathrm{l}`. Therefore, to perform the internal unit
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conversion, the length (in nanometers) of the LAMMPS unit length must be
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specified via *lunit_nm* (default is set to the Bjerrum length in water
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at room temperature *lunit_nm* = 0.71nm). For example, in the dilute
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ideal solution limit, the concentration of free ions will be
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:math:`c_\mathrm{I} = 10^{-\mathrm{pIp}}\mathrm{mol}/\mathrm{l}`.
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The temperature used in MC acceptance probability is set by *temp*. This
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temperature should be the same as the temperature set by the molecular
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dynamics thermostat. For most purposes, it is probably best to use
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*tempfixid* keyword which dynamically sets the temperature equal to the
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chosen MD thermostat temperature, in the example above we assumed the
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thermostat fix-ID is *fT*. The inserted particles attain a random
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velocity corresponding to the specified temperature. Using *tempfixid*
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overrides any fixed temperature set by *temp*.
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The *xrd* keyword can be used to restrict the inserted/deleted
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counterions to a specific radial distance from an acid or base particle
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that is currently participating in a reaction. This can be used to
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simulate more realist reaction dynamics. If *xrd* = 0 or *xrd* > *L* /
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2, where *L* is the smallest box dimension, the radial restriction is
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automatically turned off and free ion can be inserted or deleted
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anywhere in the simulation box.
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If the *tag yes* is used, every inserted atom gets a unique tag ID,
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otherwise, the tag of every inserted atom is set to 0. *tag yes* might
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cause an integer overflow in very long simulations since the tags are
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unique to every particle and thus increase with every successful
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particle insertion.
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The *pmcmoves* keyword sets the relative probability of attempting the
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three types of MC moves (reactions): acid charging, base charging, and
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ion pair exchange. The fix only attempts to perform particle charging
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MC moves if *acid_type* or *base_type* is defined. Otherwise fix only
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performs free ion insertion/deletion. For example, if *acid_type* is not
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defined, *pmcA* is automatically set to 0. The vector *pmcmoves* is
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automatically normalized, for example, if set to *pmcmoves* 0 0.33 0.33,
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the vector would be normalized to [0,0.5,0.5].
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The *only_salt* option can be used to perform multivalent
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grand-canonical ion-exchange moves. If *only_salt yes* is used, no
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charge exchange is performed, only ion insertion/deletion (*pmcmoves* is
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set to [0,0,1]), but ions can be multivalent. In the example above, an
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MC move would consist of three ion insertion/deletion to preserve the
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charge neutrality of the system.
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The *group* keyword can be used to add inserted particles to a specific
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group-ID. All inserted particles are automatically added to group *all*.
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Output
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""""""
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This fix computes a global vector of length 8, which can be accessed by
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various output commands. The vector values are the following global
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quantities:
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* 1 = cumulative MC attempts
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* 2 = cumulative MC successes
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* 3 = current # of neutral acid atoms
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* 4 = current # of -1 charged acid atoms
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* 5 = current # of neutral base atoms
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* 6 = current # of +1 charged base atoms
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* 7 = current # of free cations
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* 8 = current # of free anions
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Restrictions
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""""""""""""
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This fix is part of the MC package. It is only enabled if LAMMPS
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was built with that package. See the :doc:`Build package
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<Build_package>` doc page for more info.
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The :doc:`atom_style <atom_style>`, used must contain the charge
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property, for example, the style could be *charge* or *full*. Only
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usable for 3D simulations. Atoms specified as free ions cannot be part
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of rigid bodies or molecules and cannot have bonding interactions. The
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scheme is limited to integer charges, any atoms with non-integer charges
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will not be considered by the fix.
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All interaction potentials used must be continuous, otherwise the MD
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integration and the particle exchange MC moves do not correspond to the
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same equilibrium ensemble. For example, if an lj/cut pair style is used,
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the LJ potential must be shifted so that it vanishes at the cutoff. This
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can be easily achieved using the :doc:`pair_modify <pair_modify>`
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command, i.e., by using: *pair_modify shift yes*.
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.. note::
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Region restrictions are not yet implemented.
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Related commands
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""""""""""""""""
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:doc:`fix gcmc <fix_gcmc>`,
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:doc:`fix atom/swap <fix_atom_swap>`
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Default
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"""""""
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pH = 7.0; pKa = 100.0; pKb = 100.0; pIp = 5.0; pIm = 5.0; pKs = 14.0;
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acid_type = -1; base_type = -1; lunit_nm = 0.71; temp = 1.0; nevery =
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100; nmc = 100; xrd = 0; seed = 0; tag = no; onlysalt = no, pmcmoves =
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[1/3, 1/3, 1/3], group-ID = all
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----------
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.. _Curk1:
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**(Curk1)** T. Curk, J. Yuan, and E. Luijten, "Coarse-grained simulation of charge regulation using LAMMPS", preprint (2021).
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.. _Curk2:
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**(Curk2)** T. Curk and E. Luijten, "Charge-regulation effects in nanoparticle self-assembly", PRL (2021)
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.. _Landsgesell:
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**(Landsgesell)** J. Landsgesell, P. Hebbeker, O. Rud, R. Lunkad, P. Kosovan, and C. Holm, "Grand-reaction method for simulations of ionization equilibria coupled to ion partitioning", Macromolecules 53, 3007-3020 (2020).
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Axel Kohlmeyer