Two types of constant pressure/temperature dynamics are available in CHARMM. The weak coupling method for temperature and pressure control described in the paper by Berendsen et al. (JCP 81(8) p3684 1984) was the first constant pressure and temperature algortihm implemented in CHARMM. Extended system constant pressure and temperature algorithms have now been implemented based on the work of Andersen (JCP 72(4) p2384 1980), Nose & Klein (Mol Physics 50(5) p1055 1983), Hoover (Phys. Review A 31(3) p1695 1985). Additionally, a variant on the extended system method which treats the control variables by means of a Langevin equation is available (Feller, Zhang, Pastor & Brooks, JCP, 103, 4613 (1995)).

Shape matrix propagation and coordinates scaling for triclinic unit cell is done according to D. Brown and J.H.R. Clarke in Computer Physics Comm. 62 (1991) 360-369.

A constant surface tension algorithm is included which is useful for studying interfacial systems where one wishes to allow the area to change dynamically during the simulation. The dynamical equations and statistical ensemble are discussed in (Zhang, Feller, Brooks & Pastor, JCP, 103, 10252 (1995)).

```
[Syntax DYNAmics CPT]
DYNAmics CPT ... cpt-spec
cpt-spec::= [ pressure-spec ] [ temperature-spec ] [ surface-tension-spec ]
pressure-spec::= PCONST {[PINTernal]} {BEREndsen berensen-spec} ref-pressure-spec
{ PEXTernal } { langevin-piston-spec } [ IUPTEN int ]
temperature-spec::= { TCONst [TCOUpling real] [TREFerence real] } ! Berendsen
{ }
{ HOOVer [TMASs real] [ REFT real] } ! Hoover
berensen-spec::= [COMPressibility real] [PCOUpling real]
langevin-piston-spec::= piston-mass-spec [PGAMMA real] [TBATH real]
surface-tension-spec::= [SURFace] [TENSion real]
piston-mass-spec::= [PMASs real]
[PMXX real] [PMYY real] [PMZZ real] [PMXY real] [PMXZ real] [PMYZ real]
ref-pressure-spec::= [PREFerence real] [PREFInitial real] [PREFFinal real]
[PRXX real] [PRYY real] [PRZZ real] [PRXY real] [PRXZ real] [PRYZ real]
[PIXX real] [PIYY real] [PIZZ real] [PIXY real] [PIXZ real] [PIYZ real]
[PFXX real] [PFYY real] [PFZZ real] [PFXY real] [PFXZ real] [PFYZ real]
[VOLUME real]
```

Only a few changes are needed to a standard CHARMM dynamics input file to run a CPT MD simulation. There are a few things to note :

- The CPT algorithm is invoked by the CPT keyword.
- It’s not possible to use LANGEVIN dynamics with the constant pressure or temperature algorithm.
- All the non-Langevin dynamics keywords have the same meaning as the in a standard dynamics input file. This includes the keywords STRT and REST.

The CPT specific keywords (apart from CPT itself) are :

- PCONstant - do a constant pressure calculation. Extended system
algorithm is the default, weak-coupling is available with BEREndsen keyword.

- TCONstant - do a constant temperature calculation with the weak-
coupling algorithm. HOOVer constant temperature is only available with PCONstant simulations.

The CPT module is only available for use with the leap-frog integrator

To be used with Berendsen algorithm:

COMPressibility <real> - the isothermal compressibility (atmospheres**-1). PCOUple <real> - the pressure coupling constant (picoseconds).

To be used with extended system algorithm:

PMASs <real> - the mass of the pressure piston (amu) PGAMma <real> - Langevin piston collision frequency (1/ps) TBATh <real> - Langevin piston bath temperature TENSion <real> - reference surface tension (dyne/cm) IUPTEN <int> - unit number, P tensor at every step To be used with either constant pressure algorithm: PREFerence <real> - the reference pressure (atmospheres). (for isotropic pressure) PREFInitial <real> - initial reference pressure tensor (atmospheres). (for isotropic pressure) PREFFnitial <real> - final reference pressure tensor (atmospheres). (for isotropic pressure) PRXX,PRYY,PRZZ <real> - the reference pressure tensor (atmospheres). PRXY,PRXZ,PRYZ (for anisotropic pressure) PIXX,PIYY,PIZZ <real> - initial reference pressure tensor (atmospheres). PIXY,PIXZ,PIYZ (for anisotropic pressure) PFXX,PFYY,PFZZ <real> - final reference pressure tensor (atmospheres). PFXY,PFXZ,PFYZ (for anisotropic pressure) PREFI,PREFF,PIXX...,PFXX... - are used for linear pressure ramping

To be used with Berendsen algorithm

TCOUple <real> - the temperature coupling constant (picoseconds). TREFerence <real> - the berendsen reference temperature (K).

To be used with extended system (HOOVer) algorithm

TMASs <real> - the mass of the thermal piston (kcal*mol^-1*ps^2). REFT <real> - the hoover reference temperature (K).

Note

for full descriptions of these parameters and the suggested values to use see the reference given above.

Suggested values for solvated systems:

```
COMPressibility (beta) = 4.63e-5 /atm (for proteins)
PCOUple = 5.0 ps (or more)
PREF = 1.0 atm (default)
PMASs = 500 amus (default is infinity)
TCOUPle = 5.0 ps (or more)
TREF = 298.0 K (default)
REFT = 298.0 K (default)
TBATh = 298.0 K (default)
TMASs = 1000.0 kcal ps^2 (default is infinity)
TENSion = 0.0 (default, results in regular constant pressure)
```

Although the heating and equilibration commands are the same as for standard dynamics it is possible to use the CPT algorithm to perform both without velocity modification (c.f. Langevin dynamics).

The algorithm requires the use of the CHARMM CRYSTAL facility for constant pressure dynamics. If only Berendsen constant temperature is requested, then the crystal code need not be used.

For the Berendsen algorithm, when a reference pressure term ( PRXX,PRYY,PRZZ,PRXY,PRXZ,PRYZ is set to a very large negative number (less than -9999.0), then this component of the pressure will not be considered. For orthorhombic simulations, the particular box length will not change (for example, if the command says: PRXX 1.0 PRYY -10000. PRZZ -10000. then only the box length in the x direction will change during dynamics). If a cubic simulation is performed, then the pressure terms corresponding to the large negative values are not considered in the calculation of the instentaneous pressure.

For the extended system pressure algorithm, setting any component of the piston mass array to zero will cause the corresponding simulation cell length to remain constant. For example when using the orthormobic cell, setting pmxx=pmyy=0 results in only the zdirection changing during the dynamics (and it changes according to the z component of the pressure tensor). This is the standard method for interfacial NPAT systems.

A discussion of Hoover temperature control can be found in the documentation file nose.doc. The temperature control implemented in the velocity verlet integrator is very similar to the one used in the leapfrog integrator. NOTE: Hoover temp control only works in conjunction with constant pressure

The Berendsen pressure/temperature control scheme may not be appropriate for inhomegenous systems (protein in water, aqueous membrane, interfacial systems). This is especially true if SHAKE constraints are used on one component. A full discussion is given in the paper by Feller, Zhang, Pastor and Brooks (JCP, 9/15/95).

The extended system pressure algorithm can be run with temperature control (resulting in isothermal-isobaric ensemble) or without (resulting in isoenthalpic ensemble). The Berendsen pressure method must be run with the constant temperature control (the ensemble for these methods is unknown).

If PINTernal is used (default), then the pressure is determined by the internal virial and the atoms in the box are instantaneously scaled in a homogeneous response to the altered box dimensions. If PEXTernal is used, then the external virial (related to the force required to maintain the symmetry constraint) is used and the atom positions are not instantaneously scaled by box size changes. The PEXTernal option is normally used for minimization, but may be used with molecular dynamics. It is not recommended for large systems.

The pressure tensor (extended system) on every integration step is saved to the formatted file indicated by unit number specified by IUPTEN; this allows calculation of viscosity using the Green-Kubo relationship. The viscosity is computed from the integral of the autocorrelation function of the off-diagonal elements of the P tensor, scaled by V/kT; see J. Phys. Chem. 100:17011-17020 (1996). The column order of the data is:

Time PIXX PIXY PIXZ PIYX PIYY PIYZ PIZX PIZY PIZZ

Basic constant pressure, appropriate for a cubic simulation cell, box length is coupled to the trace of the pressure tensor, using langevin on pressure piston degree of freedom. This also works for a non cubic cell, but in that case each length moves independently to maintain a constant pressure tensor. Constant volume is the limit pmass -> infinity (implementation in CHARMM: Set pmass = 0 for constant V).

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pconstant pmass 400.0 pref 1.0 pgamma 20.0 - tbath 300.0

Constant normal pressure, constant area. Appropriate for orthorombic cell where only the z direction is allowed to change. The box length in z direction is coupled to the z component of the pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pconstant pmzz 225.0 pmxx 0.0 pmyy 0.0 pref 1.0

Constant pressure (stress) tensor. Each box length moves independently to maintain the desired pressure tensor.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pconstant pmass 225.0 przz 1.0 prxx 2.0 pryy 3.0

Constant pressure, constant surface tension. Z direction moves independently of x and y and is coupled to the bulk pressure (z component of pressure tensor). X and y box lengths move to maintain constant surface tension. Note: this is only appropriate for interfacial systems where the interface is perpendicular to the z axis.

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pconstant pmass 225.0 pref 1.0 surface tension 50.0

Constant pressure and temperature (NPT)

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pconstant pmass 400.0 pref 1.0 pgamma 20.0 - tbath 300.0 tcons hoover reft 300. tmass 1000.

Basic constant temperature using the Hoover method

dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - HOOVer TMASs 1000.0 REFT 298.0

Constant T with calculation of pressure data; this will also print the surface tension in the output log, useful for studying interfacial systems. The optional IUPTEN keyword will store the pressure tensor data for every timestep.

open unit 29 card write name dyn.ptn dynamics cpt leap restart time 0.001 nstep 10000 iseed 314159 - pcons pmass 0.0 pint pref 1. iupten 29 - hoover tmass 1000.0 reft 293.0

Process the pressure commands for the system. There are three modes :

Mode 1 : Initialise all pressure arrays.

Syntax: PRESsure INITialise

Mode 2 : Calculate and print the instantaneous pressures for a system.

Syntax: PRESsure INSTantaneous TEMPerature <Real> VOLUme <Real> - NDEGf <Integer> NOPRint

The external isotropic pressure and tensor are calculated if a volume is present. The isotropic internal pressure is calculated if a volume is present and a temperature has been given. If no degrees of freedom are specified then a value of 3*NATOM is taken be default. The virials are always printed. NOPRint will suppress all printing.

Mode 3 : Print the averages and fluctuations.

PRESsure STATistics