Two questions about Nose-Hoover chains

[Andrew DeYoung]

Hi,

I am a graduate student and am relatively new, in the last year, to MD
simulations. If you have time, may I ask you for advice about concepts
related to Nose-Hoover chains?

(1) Do you happen to know of any good review-type articles or tutorials on
the concept of Nose-Hoover chains. Unfortunately, I am not so strong in
either statistical mechanics or Lagrangian mechanics, so when I read (for
example) the original Nose-Hoover chain papers by Martyna, I get lost very
quickly.

I understand that the basic Nose-Hoover method relies on the introduction of
a heat bath and an associated friction parameter; this friction parameter
modifies the equation of motion (i.e., Newton's equation) by adding an
additional term which contains the momentum of the friction parameter xi and
a mass parameter Q.

I also understand that the basic Nose-Hoover method can be non-ergodic and
to remedy this, Nose-Hoover chains are introduced. Are Nose-Hoover chains
simply additional friction parameters xi? Or are they additional
thermostats "chained" to the original Nose-Hoover thermostat? Can you
recommend any overview reading to help me get the basic conceptual idea?

(2) Why are (multiple) Nose-Hoover chains not implemented in the leap frog
(md) integrator? This is NOT a criticism; I am just curious if there is any
conceptual idea behind the inability to use chains with the leap frog
algorithm.

Thank you so very much for your time!

Andrew DeYoung
Carnegie Mellon University

[Shirts, Michael (mrs5pt)]

Hi, all-

Guess this is my baliwick-

Post by Andrew DeYoung
(1) Do you happen to know of any good review-type articles or tutorials on
the concept of Nose-Hoover chains. Unfortunately, I am not so strong in
either statistical mechanics or Lagrangian mechanics, so when I read (for
example) the original Nose-Hoover chain papers by Martyna, I get lost very
quickly.

Not right off. I got my understanding reading the original paper. Frenkel
and Smit has some additional explanations.

Post by Andrew DeYoung
I understand that the basic Nose-Hoover method relies on the introduction of
a heat bath and an associated friction parameter; this friction parameter
modifies the equation of motion (i.e., Newton's equation) by adding an
additional term which contains the momentum of the friction parameter xi and
a mass parameter Q.

It's not really a friction parameter per se. Think of it as a coupling term
that allows kinetic energy to pass between a bath and the system of
interest. There's another equivalent way to think of it as changing the
length of each timestep, but that's a little confusing.

Post by Andrew DeYoung
I also understand that the basic Nose-Hoover method can be non-ergodic and
to remedy this, Nose-Hoover chains are introduced. Are Nose-Hoover chains
simply additional friction parameters xi? Or are they additional
thermostats "chained" to the original Nose-Hoover thermostat? Can you
recommend any overview reading to help me get the basic conceptual idea?

Each new link in the chain is a new bath -- so each bath is itself sharing
getting energy from another bath. As you add chains, the system becomes
chaotic, moving the system closer to ergodicity. The original paper +
Frenkel and Smit are the sources I used.

Post by Andrew DeYoung
(2) Why are (multiple) Nose-Hoover chains not implemented in the leap frog
(md) integrator? This is NOT a criticism; I am just curious if there is any
conceptual idea behind the inability to use chains with the leap frog
algorithm.

It's possible in either integrator. The simple answer is too complicated
bookkeeping. You have to write out the equations in a somewhat different
way that just got too hard to code together. I'm working on ways of
simplifying the bookkeeping in 5.0 so that all integration methods are
available (where possible) in both leapfrog and verlet, and are put together
in a more intuitive, extensible way.

Note that the ergodicity in NH chains occurs only in the limit of inifinite
chains. Likely in 5.0, NH chains will be replaced with NH-Langevin, where
the NH bath is thermostatted using Langevin dynamics. This is provably
ergodic and is simpler.

Best,
~~~~~~~~~~~~
Michael Shirts
Assistant Professor
Department of Chemical Engineering
University of Virginia
***@virginia.edu
(434)-243-1821