In CHARMM, multiple time scales method (MTS) algorithm is similar to code of the algorithm described in the paper by Tuckerman, Berne, and Martyna [J.C.P., 97, 1990 (1992)]. Please refer to this paper for details of derivations of this MTS-RESPA method. In addtion, more details can be seen in J. Chem. Phys. 99, 8063 (1993) and J. Phys. Chem., 99, 5680 (1995) by M. Watanabe and M. Karplus. In this new release, MTS method can be called under parallel platforms. All modules under MTS should work in parallel. To run CHARMM in parallel, please refer to parallel.doc.

The MTS method can be combined with Langevin dynamics via the LN algorithm, described by Barth and Schlick [J.Chem.Phys., 1998, in press]. This version includes the slow forces via extrapolation and is expected to allow larger timesteps than reversible MTS-RESPA. See general notes at the end of this documentation file. LN algorithm was implemented in CHARMM by Eric Barth (8/97) and Adrian Sandu (7/98).

In this documentation we refer to the rRESPA code as MTS-RESPA (performing Newtonian dynamics) and to the LN code as MTS-LN (performing Langevin dynamics).

In this Multiple Time scaled method in CHARMM, a reversible RESPA (Reference System Propagator Algorithm) is modified. (See Tuckerman’s paper about a reversible RESPA.) Two types of reversible RESPA methods can be used in CHARMM.

Single reversible RESPA (Two-time-scale propagator)

MTSmethod 1 I mts-spec END I :: multiple time scales (Integer) - See Description mts-spec:: selection of hard forces or fast time scaled force [BOND] ! Forces from all Bond-stretching motions [ANGL] ! Forces from all angle-bending motions [DIHE] ! Forces from all diheral motions and all improper ! torsional motion [ALL ] ! Forces from all internal motions which are ! defined in CHAMM force fields [MASS] 1 M ! Nonbonded forces involving atoms whose masses are ! less than M. M is a mass weight. [SLFG] ! Nonbonded forces separation by long- and short- ! range forces (see more detail in the text) [CLEA] ! Clear MTS module and assignments

Double reversible RESPA (Three-time-scale propagator)

MTSmethod I J mts-spec END I and J :: multiple time scales (Integers) - See Description mts-spec:: selections of fast and medium time scaled forces [BOND] K ! Forces from all Bond-stretching motions [ANGL] K ! Forces from all angle-bending motions [DIHE] K ! Forces from all diheral motions and all improper ! torsional motion [ALL ] K ! Forces from all internal motions which are ! defined in CHAMM force fields [MASS] K M ! Nonbonded forces involving atoms whose masses are ! less than M. M is a mass weight. [SLFG] ! Nonbonded forces separation by long- and short- ! range forces (see more detail in the text) [CLEA] ! Clear MTS module and assignments K is 1 or 2 - 1 - force considered as a short time scaled 2 - force considered as a medium time scaled

In both single and double RESPA methods, all interaciton forces, which are not selected by MTS command, are considered as a long time scaled degree of freedom

You can see the more details in J. Chem. Phys. 99, 8063 (1993) and J. Phys. Chem., 99, 5680 (1995) by M. Watanabe and M. Karplus.

MASS (Atomic Mass force separation)

If MASS is selected, separating mass should be given.

MTS . . MASS K M END

K is the force considered as a short or medium time scaled. This should be 1 or 2 ( 1 for short and 2 for medium ) M is the atomic mass. Separate the force contributions by the atomic mass. Contributions from the atom less than M mass is considered as the faster time scaled motions than those from the atom more than M mass.

See the more details about this in J. Phys. Chem. 99, 5680 (1995), by M. Watanabe and M. Karplus.

SLFG (Short-Long Range force separation)

If SLFG is selected, Short range force cutoff distance (RSCUT), switching function healing length (RHEA), and Buffer healing length (BUFF) should be given by the following way:

MTS . SLFG RSCUT [number (6.0)] RHEA [number (1.0)] BUFF [number (1.0)] END [number] is the distance in the unit of Angstrom. (..) is the default values.

See the more details about these lengths in J. Phys. Chem. 98, 6885, (1994) by D.D.Humphreys, R.A.Friesner, and B.J. Berne.

MTS method approach is effective for special system where a separation between the fast and slow time components is natural. The nature of CHARMM force field allow us to separate some time scales. But in gener there will be coupling between those motions, so this leads the limitation of time scales.

In Multiple time scale, I and J are the number of cycle that you want to calculate short time scaled and medium time scaled motions, respectively, before calculating long time scaled motion.

Delta t = J * Dtau2 = I * J * Dtau1

where Dtau1 and Dtau1 are the integral time step for short and medium time scaled motions respectively and Delta t is the integration time step of long time scaled motions. Dtau1 is defined in DYNAmic module as TIME.

MTS-RESPA method uses the velocity Verlet algorithm. MTS-LN algorithm solves the simple Langevin equation and relies on position Verlet and on constant extrapolation. For MTS-RESPA (Newtonian dynamics) use “DYNA VVER ...” For MTS-LN (Langevin dynamics) define FBETA and use “DYNA LNX ...”

Energy and forces from Urey-Bradely term is incoporated with bond command.

MTS-RESPA method is interacted with Nose-Hoover method. In order to call Nose- Hoover method, you have to use Nose-Hoover module (see nose.doc and testcase for MTS method.)

If you are using with SHAKE, i.e. treat water molecules by SHAKE and other molecules without SHAKE, you MUST specify SHAKE BEFORE calling MTS command.

If you are going to use IMAGE module, you also have to specify the module before calling MTS module.

MASS selection only works with ATOM nonbonded selection. (See

`nonbond`)all NONBOND and UPDATE options listed before calling MTS module are highly recommended.

If SLFG selection is used, update frequency of nonbond list may be specifically assigned in order to achieve the better energy conservation of the system instead of using the automatic update frequency (INBFRQ -1).

ENERGY module has to be called before calling MTS or after calling dynamics. Otherwise, ENERGY cannot be calculated.

Selections of MTS method depend on energy routines and nonbond options. Followings are lists of possible selections. (In the lists, SHAKE means whether SHAKE method can be applied to the only environment, such as water molecules.)

GROUP selection

S - Single reversible RESPA method D - Double reverisble RESPA method Scalar include fast and slow routine. (SLFG only works with fast scalar routine.) X - acceptable selection ---------------------------------------------- Selection | Vector | Scalar | SHAKE | S | D | S | D | S | D ---------------------------------------------- BOND | X | | X | X | X | X ANGL | X | | X | X | X | X DIHE | X | | X | X | X | X ALL | X | | X | X | X | X MASS | | | | | | SLFG | | | X | X | X | X ---------------------------------------------- MASS selection dosen't work with GROUP option.

ATOM selection

S - Single reversible RESPA method D - Double reverisble RESPA method X - acceptable selection ---------------------------------------------- Selection | Vector | Scalar | SHAKE | S | D | S | D | S | D ---------------------------------------------- BOND | X | X | X | X | X | X ANGL | X | X | X | X | X | X DIHE | X | X | X | X | X | X ALL | X | X | X | X | X | X MASS | X | X | X | X | | SLFG | | | X | X | X | X ----------------------------------------------

The followings are examples of MTS method. Also you can check two testcases for MTS method.

```
! Multiple Time Scaled Method Start
! Part I - Single Reversible RESPA method
MTS 6 ! Integration time steps of 0.5fs for short time scale motions
! and 3.0fs for long time scales are used.
BOND ! Forces from all bond-stretching and bond bending motions
ANGL ! are treated as hard forces or short time scale degree of
! freedom
END
DYNA VVER STRT NSTEP 1000 TIME 0.0005 -
NPRINT 100 IPRFRQ 1000 -
INBFRQ 20 IHBFRQ 0 FIRSTT 200.0 -
IUNREA -30 IUNWRI 31 IUNCRD -32 IUNVEL -33 -
KUNIT -34 IUNO -41 NSAVC 5 NSAVV 5 NSNOS 10 ISVFRQ 1000
! Part II
! Double Reversible RESPA method
! Mass-scaling selection
MTS 5 2 ! Integration time steps -
! 0.5fs for short time scale motions
! 2.5fs for medium time scale motions and
! 5.0fs for long time scale motions
MASS 2 3.0 ! Nonbonded forces acting on atoms whose mass is less
! than 3.0g are treated as medium time scale.
BOND 1 ! Forces from all bond-stretching and angle-bending
ANGL 1 ! motions are considered as short time scale motions
DIHE 2 ! Forces from all dihedral and imporper torsion motions
! are considered as medium time scale.
END ! Rest of force contributions are considered as long time
! scaled motions
DYNA VVER REST NSTEP 1000 TIME 0.0005 -
NPRINT 100 IPRFRQ 1000 -
INBFRQ 20 IHBFRQ 0 -
IUNREA 30 IUNWRI 31 IUNCRD -32 IUNVEL -33 -
KUNIT -34 IUNO -41 NSAVC 5 NSAVV 5 NSNOS 10 ISVFRQ 1000
!
! PartIII
! Short-long range selection of MTS
!
MTS 2 3 ! Integrated time step
! 0.5fs for the fast time scale
! 1.0fs for the medium time scale
! 3.0fs for the slow time scale
BOND 1 ! Forces from all bond-streching and angle-bending
ANGLE 1 ! motions are consideered as fast time scale motions
DIHE 2 ! Forces from all dihedral and improper torsion motions
! are considered as medium time scale
SLFG RSCUT 6.0 RHEA 2.0 BUFF 1.0
! Short-long range forces selection
! Short range forces are cut-off at 6.0A
END
DYNA VVER STRT NSTEP 200 TIME 0.0005 -
NPRINT 10 IPRFRQ 1000 -
FIRSTT 300.0 IUNREA -30 IUNWRI -31 IUNCRD -1 IUNVEL -1 -
KUNIT -1 IUNO -1 NSAVC 5 NSAVV 5 NSNOS 10 ISVFRQ 1000 -
TSTRUC 300
STOP
```

```
! PartIV
! LN algorithm - MTS with Langevin dynamics
!
! Langevin coupling parameter needs to be defined
SCALAR FBETA SET 20 SELE ALL END
! Shake, if needed
SHAKE BONH PARAM TOL 1.0D-9 SELE RESNAME TIP3 END
MTS 4 24 ! Integrated time step
! 0.5 fs for the fast timestep
! 2.0 fs for the medium timestep
! 48.0 fs for the slow timestep
BOND 1 ! Forces from all bond-streching and angle-bending
ANGLE 1 ! motions are consideered as fast time scale motions
DIHE 1 ! Forces from all dihedral and improper torsion motions
! are considered as medium time scale
SLFG RSCUT 6.0 RHEA 2.0 BUFF 1.0
! Distance class definition
! Short range forces are cut-off at 6.0A
END
DYNA LNX STRT NSTEP 200 TIME 0.0005 -
NPRINT 10 IPRFRQ 1000 -
FIRSTT 300.0 IUNREA -30 IUNWRI -31 IUNCRD -1 IUNVEL -1 -
KUNIT -1 IUNO -1 NSAVC 5 NSAVV 5 NSNOS 10 ISVFRQ 1000 -
TSTRUC 300
STOP
```

The algorithm relies on existing CHARMM force splitting routines under the MTS command. The LN slow forces are incorporated via extrapolation as opposed to “impulses” as in the MTS-RESPA method. This alleviates severe resonance problems and permits larger outer timesteps to be used for additional speedup.

The LN algorithm is compatible with SHAKE and with the use of boundary conditions. Any other combinations of options have not been tested.

There are several parameters that are set for a LN simulation:

Langevin parameter gamma (FBETA in CHARMM notation), the damping constant:

- Recommended value = 5 to 20 ps^(-1)

Too small a value will render the simulation unstable. On the other hand, the larger gamma is, the greater the overdamping of the low-frequency modes. The above recommendation reflects a balance found by experimentation. Gamma can also be simulation-goal dependent.

Timestep Protocol for force splitting:

Dt(fast) = inner TIMESTEP for updating the "fast" forces * Recommended value = 0.5 -- 1 fs (no shake) 1 -- 2 fs (with shake) Dt(medium) = K1*Dt(fast), update frequency for "medium" forces * Recommended value = 1 -- 3 fs Dt(long) = K2*Dt(medium), update frequency for "slow" forces * Recommended value = 6 -- 200 fs

Larger computational savings can be realized with a larger Dt(long). However, the speedup is limited and reaches an asymptotic value since the evaluation of medium forces becomes increasingly costly.

The asymptotic maximum speedup can be reached for outer timesteps of 24 or 48 fs, for example, but the precise value depends on the timestep protocol employed and the application system. This should be tested carefully by the user for the problem at hand.

Definition of the force splitting classes:

Recommended Protocol –:

* Fast forces = BOND 1, ANGL 1, DIHE 1 * Medium forces = Nonbond cutoff cutoff distance = 6 A - 8 A healing region = 1 A - 3 A buffer region = 1 A - 3 A SLFG RSCUT [cutoff distance] RHEA [healing region] BUFF [buffer region] * Longrange forces = remaining terms

Nonboned pairlists are currently updated in the LN code every outer timestep; it is possible (but more costly) to attempt the updating every medium timestep.

The nonbonded pairlist is updated in the current implementation every Dt(long).

The GROUP electrostatics option works much better than ATOM electrostatics. Use of the latter is discouraged based on our test problems.

Note

All the LN parameters above can be sensitive to the specific protocol used for the dynamics simulations and are problem dependent (see discussion of results in the LN papers).

For further guidance, feel free to contact Tamar Schlick at the email: schlick@nyu.edu