CHARMM c30b1 nose.doc

The documentation of Nose-Hoover method - Masa Watanabe
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             **********************************************
             *   Nose-Hoover Molecular Dynamics command   *
             **********************************************


This module offers access to the Constant-Temperature molecular
dynamics defined by Nose-Hoover equations of motion (described in
S.Nose JCP, 81 P511 (1984) and W.G. Hoover, Phy. Rev. A31, p1695 (1985))
This method has the advantage that it is a continuous dynamics with
well defined conserved quantities. [Other temperature scaling methods,
available in CHARMM (included Berendsen method in Leap-frog
integrator) have discontinuous dynamics.]

*Menu:

* Syntax::     Syntax of the Nose-Hoover command
* Main::       Nose-Hoover method main commands and descriptions
* Exam::       Example of Nose-Hoover Method



File: Nose ]-[ Node: Syntax
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                 **************************************
                 * Syntax for the Nose-Hoover Command *
                 **************************************


   The original Hamiltonian for Nose dynamics is defined as follow:

               H = H0 + HB
                 = H0(p/s,q) + P^2/2Q + (f+1)kTlns     (1)

where f is a degree of freedom of the physical system. This Hamiltonian 
was originally propoesed by Nose in his JCP paper. The equations of motions 
defined by Eq. (1) are solved numerically in order to achieve the canonical
ensemble MD simulation. Hoovers extended the Nose's analysis. He derives a 
slightly different set of equations of motions which dispense with the 
time-scaling parameter s by transforming p' = p/s, S = lns and dt' = dt/s. 
Then he define the conserved quantity:

               H = H0(p',q) + P^2/2Q + (f+1)kTS             (2)

This is not Hamiltonian any more, but this energy is conserved thourghout
simulation.
    In Nose-Hoover method, two different types of constant temperature
methods can be called: (1) simple method: system coupled to one heat
bath (2) multi-bath method: different parts of system can be coupled to
different heat baths.
    In addtion, Nose-Hoover method in this release can be invoked under
parallel platforms. To run Nose-Hoover dynamics in parallel machines, this
dynamics has to be called under a velocity verlet integrator. In order to
call the velocity verlet, please refer to "dynamics.doc".


Keywords in [...] are optional. Defaults values are given in (...).

(1) Simple (one heat-bath) method:
----------------------------------

To call Nose-Hoover MD method, "nose" must be specified in usual dynamics
command, such as

    DYNamics NOSE [RSTN] TREF (300.0) QREF (1.0D+50) NCYC (10) - 
             IUNO (-1)  NSNOS (10) etc

Subcommands:
------------
     NOSE :== specification of Nose-Hoover method with one heat bath
    [RSTN]:== reset command for S in Eq (2)
     TREF :== Desired Temperature of the system (Defult = 300K)
     QREF :== magnitured of Coupling, Q,  (Defult=1.0D+50 -> large QREF
              leads the typical microcanonical ensembel MD simulation)
     IUNO :== unit of file that output from Nose-Hoover can be
              written. (describ more detail later section)
    NSNOS :== Frequency of writing output from Nose-Hoover method
    NCYC  :== number of recursive loop of kinetic energy in order to
              achieve the convergence values.


(2) Multi Heat-Bath Method
--------------------------

In order to call multi-heat bath method, you have to specify the
following command before you call dynamics command.

   NOSE  I
   CALL J  atom-selection-option
   COEF J  QREF (1.0D+50) TREF (300)  
   TOL (1.0D-10) 
   NCYC (10)
   [CLEAR]
   END

   DYNamics  [RSTN] IUNO (-1)  NSNOS (10) etc -

Subcommands:
-----------
      I     :== number of heat bath in the system (Maxmum 10)
      CALL  :== assigns the specified atom into Jth heat bath
      COEF  :== assignments of Jth heat bath's coupling and 
                desired temperature (you can use the different
                temperature in each heat bath.)
      TOL   :== tolerance of kinetic energy convergence 
      CLEAR :== clear all assignments in Nose-Hoover method



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                 *****************************
                 * Nose-Hoover Main Commands *
                 *****************************


NOSE
----
When entering the Nose-Hoover module for CHARMM, it is nessesary to
specify the number of heat baths in the system. If you are going to
use one heat bath, you can call Nose-Hoover module from DYNAmic
module. But if you have a plan to use more than one, you have to
specifiy it before calling DYNAmic module. Also Nose-Hoover methods 
are working with Verlet and Velocity Verlet algorithms in this points.
If you want to used a velocity Verlet, specifiy it in DYNAmic module.
(DYNAmic VVER .....). Otherwise, Verlet algorithm is used in the MD 
simulation. For parallel platforms, a velocity Verlet must be used in
order to run Nose-Hoover dynamics.

QREF
----
QREF is the thermal inertia parameter which controls the rate of
temperature fluctuations. Too high value of QREF results in slow enegy
flow between the system and heat bath, and the limit of QREF -->
infinity we regain conventional MD. On the other hand, if QREF is too
small, long-lived, weakly damped oscillations of the energy occur,
resulting in poor equilibration. It is necessary to choose right QREF
to achieve satisfactory damping of these correlations. QREF should be
between 10 and 1000.

NCYC and TOL
------------
Nose-Hoover equation of motion for scaling factor S shows that it
depends on the kinetic energy of the system. In the same time,
molecular velocity depends on scaling factor S. So in order to solve
these equations of motion, it requires an iterative process to get
convergence of kinetic energies. NCYC is a number of iteration of this
process and TOL is a tolerance to reach convergence of kinetic
energies. If SHAKE is used for molecules, NCYC is about 3 to 5 in order
to reach convergence. 

atom-selection-option
---------------------
If more than one heat bath are used in the MD simulation, you have to
specify which atoms belong to which heat bath. In order to assign them
in particular heat bath, you have to use atom-selection module in
CHARMM. See select.doc to use atom selection syntax.

RSTN
----
Reset command to set S in Eq. (2) equl to zero. Reseting of scaling
parameter S doesn't change the dynamics of physical system at all.
Sometimes S may become very large numbers during equilibration MD
simulations, so setting S to zero may be necesrry

OUTPUT FILE
-----------
If you set IUNO a positive integer, the output of some quantities from
Nose-Hoover method will be written in UNIT IUNO.  This output contains
following:

 1st line: Number of step, Number of degree of freedom, NSNOS (defined
           above) 
 
 Then at every NSNOS times, following output will be written:
         
           Step, Time (ps), Total Energy
           S value, Temperatue  for each heat bath

By using this output file, you can calculate the average temperature
of system in each heat bath. In addition to that, S value can be used 
in order to get free energy of the system [Check Branka and
Parrinello, Mol Phys, 58, 989 (1986)]



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              *****************************************
              * Examples for using Nose-Hoover Method *
              *****************************************

=== Example of Nose-Hoover input-file ==

1) One-heat-bath Selection
              .
              .
              .
SHAKE BOND ANGLE TOL 1.0D-9

UPDATE INBFRQ 5 IHBFRQ 0  -
       CUTIM 8.0  IMGFRQ 5 -
       ATOM SHIFT VATOM VSWITCH -
       CUTNB 8.0  CTOFNB 7.5   CTONNB 6.5  EPS 1.0 CDIE

OPEN WRITE UNIT 31 CARD NAME @9FOR015.RST

DYNA NOSE QREF 50.0 TREF 300.0 NCYC 5 FIRSTT 200 -
     STRT NSTEP 100  TIME 0.001 NPRINT 10 IPRFRQ 100 -
     IUNREA -30 IUNWRI 31  IUNCRD -1  IUNVEL  -1 -
     KUNIT -41  NSAVC 50  NSAVV 50 ISVFRQ 1000

2) Two-heat-bath selection
In this example, ethane (ETHA) in water system is used.

NOSE 2                       ! two heat baths are used. First all
                             ! molecules are assigned into heat bath #1
CALL 2 SELE RESNAME ETHA END ! put ethane in heat bath #2
COEF 1 QREF 50.0 TREF 300.0
COEF 2 QREF 50.0 TREF 300.0
NCYC 5
END

OPEN WRITE UNIT 31 CARD NAME @9FOR015.RST

DYNA STRT NSTEP 100  TIME 0.001 NPRINT 10 IPRFRQ 100 -
     IUNREA -30 IUNWRI 31  IUNCRD -1  IUNVEL -1 FIRSTT 100.0 -
     KUNIT -41  NSAVC 50  NSAVV 50 ISVFRQ 1000

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