diff -Naur lammps-25Aug09/doc/fix_nvt.html lammps-27Aug09/doc/fix_nvt.html --- lammps-25Aug09/doc/fix_nvt.html 2009-05-12 07:33:47.000000000 -0600 +++ lammps-27Aug09/doc/fix_nvt.html 2009-08-27 12:51:09.000000000 -0600 @@ -25,16 +25,17 @@
  • zero or more keyword/value pairs may be appended -
  • keyword = drag +
  • keyword = drag or chain -
      drag value = drag factor added to thermostat (0.0 = no drag) 
+
      drag value = drag factor added to thermostat (0.0 = no drag)
+  chain value = yes or no 
 
    
 
 
 
    Examples:
 
    
 
    fix 1 all nvt 300.0 300.0 100.0
-fix 1 all nvt 300.0 300.0 100.0 drag 0.2 
+fix 1 all nvt 300.0 300.0 100.0 drag 0.2 chain no 
 
    
 
    Description:
 
    
@@ -55,15 +56,29 @@
 of (roughly) 100 time units (tau or fmsec or psec - see the
 units command).
 
    
+
    The chain keyword determines whether Nose/Hoover chains are used or
+not.  If chain is specified as no, then the original Nose/Hoover
+formulation is used.  If chain is specified as yes, which is the
+default, then chains as described in (Martyna) are used
+which include extra non-physical variables which couple to the
+thermostat.  Nose/Hoover chains provide a more robust NVT integrator,
+overcoming non-ergodic sampling issues and energy oscillations found
+with ordinary Nose/Hoover dynamics.  Our implementation uses one chain
+and integrates the equations of motion via a Trotter expansion good to
+2nd order accuracy in the timestep size.
+
    
 
    In some cases (e.g. for solids) the temperature of the system can
-oscillate undesirably when a Nose/Hoover thermostat is applied.  The
-optional drag keyword will damp these oscillations, although it
-alters the Nose/Hoover equations.  A value of 0.0 (no drag) leaves the
-Nose/Hoover formalism unchanged.  A non-zero value adds a drag term;
-the larger the value specified, the greater the damping effect.
-Performing a short run and monitoring the temperature is the best way
-to determine if the drag term is working.  Typically a value between
-0.2 to 2.0 is sufficient to damp oscillations after a few periods.
+oscillate undesirably when a Nose/Hoover thermostat is applied, though
+this should be less of a problem if Nose/Hoover chains are used.  The
+optional drag keyword will damp these oscillations in an ad-hoc
+fashion, by altering the Nose/Hoover equations so that they no longer
+exactly sample the canonical ensemble.  A value of 0.0 (no drag)
+leaves the Nose/Hoover formalism unchanged.  A non-zero value adds a
+drag term; the larger the value specified, the greater the damping
+effect.  Performing a short run and monitoring the temperature is the
+best way to determine if the drag term is working.  Typically a value
+between 0.2 to 2.0 is sufficient to damp oscillations after a few
+periods.
 
    
 
    IMPORTANT NOTE: Unlike the fix temp/berendsen
 command which performs thermostatting but NO time integration, this
@@ -159,7 +174,7 @@
 
    
 
    Default:
 
    
-
    The keyword defaults are drag = 0.0.
+
    The keyword defaults are drag = 0.0 and chain = yes.
 
    
 
    
 
@@ -167,4 +182,9 @@
 
 
    (Hoover) Hoover, Phys Rev A, 31, 1695 (1985).
 
    
+
+
+
    (Martyna) Martyna, Klein, Tuckerman, J Chem Phys, 97, 2635 (1992);
+Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117.
+
    
 
diff -Naur lammps-25Aug09/doc/fix_nvt.txt lammps-27Aug09/doc/fix_nvt.txt
--- lammps-25Aug09/doc/fix_nvt.txt	2009-05-12 07:33:47.000000000 -0600
+++ lammps-27Aug09/doc/fix_nvt.txt	2009-08-27 12:51:09.000000000 -0600
@@ -18,14 +18,15 @@
 Tdamp = temperature damping parameter (time units) :l
 
 zero or more keyword/value pairs may be appended :l
-keyword = {drag} :l
-  {drag} value = drag factor added to thermostat (0.0 = no drag) :pre
+keyword = {drag} or {chain} :l
+  {drag} value = drag factor added to thermostat (0.0 = no drag)
+  {chain} value = {yes} or {no} :pre
 :ule
 
 [Examples:]
 
 fix 1 all nvt 300.0 300.0 100.0
-fix 1 all nvt 300.0 300.0 100.0 drag 0.2 :pre
+fix 1 all nvt 300.0 300.0 100.0 drag 0.2 chain no :pre
 
 [Description:]
 
@@ -46,15 +47,29 @@
 of (roughly) 100 time units (tau or fmsec or psec - see the
 "units"_units.html command).
 
+The {chain} keyword determines whether Nose/Hoover chains are used or
+not.  If {chain} is specified as {no}, then the original Nose/Hoover
+formulation is used.  If {chain} is specified as {yes}, which is the
+default, then chains as described in "(Martyna)"_#Martyna are used
+which include extra non-physical variables which couple to the
+thermostat.  Nose/Hoover chains provide a more robust NVT integrator,
+overcoming non-ergodic sampling issues and energy oscillations found
+with ordinary Nose/Hoover dynamics.  Our implementation uses one chain
+and integrates the equations of motion via a Trotter expansion good to
+2nd order accuracy in the timestep size.
+
 In some cases (e.g. for solids) the temperature of the system can
-oscillate undesirably when a Nose/Hoover thermostat is applied.  The
-optional {drag} keyword will damp these oscillations, although it
-alters the Nose/Hoover equations.  A value of 0.0 (no drag) leaves the
-Nose/Hoover formalism unchanged.  A non-zero value adds a drag term;
-the larger the value specified, the greater the damping effect.
-Performing a short run and monitoring the temperature is the best way
-to determine if the drag term is working.  Typically a value between
-0.2 to 2.0 is sufficient to damp oscillations after a few periods.
+oscillate undesirably when a Nose/Hoover thermostat is applied, though
+this should be less of a problem if Nose/Hoover chains are used.  The
+optional {drag} keyword will damp these oscillations in an ad-hoc
+fashion, by altering the Nose/Hoover equations so that they no longer
+exactly sample the canonical ensemble.  A value of 0.0 (no drag)
+leaves the Nose/Hoover formalism unchanged.  A non-zero value adds a
+drag term; the larger the value specified, the greater the damping
+effect.  Performing a short run and monitoring the temperature is the
+best way to determine if the drag term is working.  Typically a value
+between 0.2 to 2.0 is sufficient to damp oscillations after a few
+periods.
 
 IMPORTANT NOTE: Unlike the "fix temp/berendsen"_fix_berendsen.html
 command which performs thermostatting but NO time integration, this
@@ -150,9 +165,13 @@
 
 [Default:]
 
-The keyword defaults are drag = 0.0.
+The keyword defaults are drag = 0.0 and chain = yes.
 
 :line
 
 :link(Hoover)
 [(Hoover)] Hoover, Phys Rev A, 31, 1695 (1985).
+
+:link(Martyna)
+[(Martyna)] Martyna, Klein, Tuckerman, J Chem Phys, 97, 2635 (1992);
+Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117.
diff -Naur lammps-25Aug09/doc/minimize.html lammps-27Aug09/doc/minimize.html
--- lammps-25Aug09/doc/minimize.html	2008-06-27 11:40:03.000000000 -0600
+++ lammps-27Aug09/doc/minimize.html	2009-08-27 12:51:09.000000000 -0600
@@ -18,7 +18,7 @@
 
 
    Examples:
 
    
diff -Naur lammps-25Aug09/doc/minimize.txt lammps-27Aug09/doc/minimize.txt
--- lammps-25Aug09/doc/minimize.txt	2008-06-27 11:40:03.000000000 -0600
+++ lammps-27Aug09/doc/minimize.txt	2009-08-27 12:51:09.000000000 -0600
@@ -15,7 +15,7 @@
 etol = stopping tolerance for energy (unitless)
 ftol = stopping tolerance for force (force units)
 maxiter = max iterations of minimizer
-maxeval = max number of total force/energy evaluations :ul
+maxeval = max number of force/energy evaluations :ul
 
 [Examples:]
 
diff -Naur lammps-25Aug09/doc/reset_timestep.html lammps-27Aug09/doc/reset_timestep.html
--- lammps-25Aug09/doc/reset_timestep.html	2009-08-18 12:16:59.000000000 -0600
+++ lammps-27Aug09/doc/reset_timestep.html	2009-08-27 12:51:09.000000000 -0600
@@ -45,8 +45,8 @@
 if necessary.  New specifications for dump and restart files can be
 given after the reset_timestep command is used.
 
    
-
    This command cannot be used when any fixes are defined that keeps
-track of elapsed time to perform time-dependent operations.  Examples
+
    This command cannot be used when any fixes are defined that keep track
+of elapsed time to perform time-dependent operations.  Examples
 include the "ave" fixes such as fix
 ave/spatial.  Also fix
 dt/reset and fix deposit.
diff -Naur lammps-25Aug09/doc/reset_timestep.txt lammps-27Aug09/doc/reset_timestep.txt
--- lammps-25Aug09/doc/reset_timestep.txt	2009-08-18 12:16:59.000000000 -0600
+++ lammps-27Aug09/doc/reset_timestep.txt	2009-08-27 12:51:09.000000000 -0600
@@ -42,8 +42,8 @@
 if necessary.  New specifications for dump and restart files can be
 given after the reset_timestep command is used.
 
-This command cannot be used when any fixes are defined that keeps
-track of elapsed time to perform time-dependent operations.  Examples
+This command cannot be used when any fixes are defined that keep track
+of elapsed time to perform time-dependent operations.  Examples
 include the "ave" fixes such as "fix
 ave/spatial"_fix_ave_spatial.html.  Also "fix
 dt/reset"_fix_dt_reset.html and "fix deposit"_fix_deposity.html.
diff -Naur lammps-25Aug09/src/fix_nvt.cpp lammps-27Aug09/src/fix_nvt.cpp
--- lammps-25Aug09/src/fix_nvt.cpp	2009-07-02 12:01:55.000000000 -0600
+++ lammps-27Aug09/src/fix_nvt.cpp	2009-08-27 12:56:19.000000000 -0600
@@ -12,7 +12,8 @@
 ------------------------------------------------------------------------- */
 
 /* ----------------------------------------------------------------------
-   Contributing author: Mark Stevens (SNL)
+   Contributing authors: Mark Stevens (SNL)
+                         Andy Ballard (U Maryland) for Nose/Hoover chains
 ------------------------------------------------------------------------- */
 
 #include "string.h"
@@ -50,9 +51,24 @@
   t_stop = atof(arg[4]);
   double t_period = atof(arg[5]);
 
-  if (narg == 6) drag = 0.0;
-  else if (narg == 8 && strcmp(arg[6],"drag") == 0) drag = atof(arg[7]);
-  else error->all("Illegal fix nvt command");
+  drag = 0.0;
+  chain = 1;
+
+  int iarg = 6;
+  while (iarg < narg) {
+    if (strcmp(arg[iarg],"drag") == 0) {
+      if (iarg+2 > narg) error->all("Illegal fix nvt command");
+      drag = atof(arg[iarg+1]);
+      if (drag < 0.0) error->all("Illegal fix nvt command");
+      iarg += 2;
+    } else if (strcmp(arg[iarg],"chain") == 0) {
+      if (iarg+2 > narg) error->all("Illegal fix nvt command");
+      if (strcmp(arg[iarg+1],"yes") == 0) chain = 1;
+      else if (strcmp(arg[iarg+1],"no") == 0) chain = 0;
+      else error->all("Illegal fix nvt command");
+      iarg += 2;
+    } else error->all("Illegal fix nvt command");
+  }
   
   // error checks
   // convert input period to frequency
@@ -88,6 +104,7 @@
   // Nose/Hoover temp init
 
   eta = eta_dot = 0.0;
+  eta2 = eta2_dot = 0.0;
 }
 
 /* ---------------------------------------------------------------------- */
@@ -129,6 +146,9 @@
   dtv = update->dt;
   dtf = 0.5 * update->dt * force->ftm2v;
   dthalf = 0.5 * update->dt;
+  dt4 = 0.25 * update->dt;
+  dt8 = 0.125 * update->dt;
+
   drag_factor = 1.0 - (update->dt * t_freq * drag);
 
   if (strcmp(update->integrate_style,"respa") == 0) {
@@ -155,12 +175,29 @@
   delta /= update->endstep - update->beginstep;
   t_target = t_start + delta * (t_stop-t_start);
 
-  // update eta_dot
+  // update eta, eta_dot, eta2, eta2_dot
+
+  int nlocal = atom->nlocal;
+  if (igroup == atom->firstgroup) nlocal = atom->nfirst;
+
+  if (chain) {
+    eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+    factor2 = exp(-dt8*eta2_dot);
+    eta_dot *= factor2;
+    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+    eta_dot += f_eta*dt4;
+    eta_dot *= drag_factor;
+    eta_dot *= factor2;
+    eta += dthalf*eta_dot;
+    eta2 += dthalf*eta2_dot;
+
+  } else {
+    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+    eta_dot += f_eta*dthalf;
+    eta_dot *= drag_factor;
+    eta += dtv*eta_dot;
+  }
 
-  f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
-  eta_dot += f_eta*dthalf;
-  eta_dot *= drag_factor;
-  eta += dtv*eta_dot;
   factor = exp(-dthalf*eta_dot);
 
   // update v and x of only atoms in group
@@ -172,8 +209,6 @@
   double *mass = atom->mass;
   int *type = atom->type;
   int *mask = atom->mask;
-  int nlocal = atom->nlocal;
-  if (igroup == atom->firstgroup) nlocal = atom->nfirst;
 
   if (rmass) {
     if (which == NOBIAS) {
@@ -188,7 +223,6 @@
 	  x[i][2] += dtv * v[i][2];
 	}
       }
-
     } else if (which == BIAS) {
       for (int i = 0; i < nlocal; i++) {
 	if (mask[i] & groupbit) {
@@ -218,7 +252,6 @@
 	  x[i][2] += dtv * v[i][2];
 	}
       }
-
     } else if (which == BIAS) {
       for (int i = 0; i < nlocal; i++) {
 	if (mask[i] & groupbit) {
@@ -235,6 +268,14 @@
       }
     }
   }
+
+  if (chain) {
+    eta_dot *= factor2;
+    f_eta = t_freq*t_freq * (factor * factor * t_current/t_target - 1.0);
+    eta_dot += f_eta * dt4;
+    eta_dot *= factor2;
+    eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+  }
 }
 
 /* ---------------------------------------------------------------------- */
@@ -254,6 +295,8 @@
   int nlocal = atom->nlocal;
   if (igroup == atom->firstgroup) nlocal = atom->nfirst;
 
+  if (chain) factor = 1.0;
+
   if (rmass) {
     if (which == NOBIAS) {
       for (int i = 0; i < nlocal; i++) {
@@ -264,7 +307,6 @@
 	  v[i][2] = v[i][2]*factor + dtfm*f[i][2];
 	}
       }
-      
     } else if (which == BIAS) {
       for (int i = 0; i < nlocal; i++) {
 	if (mask[i] & groupbit) {
@@ -288,7 +330,6 @@
 	  v[i][2] = v[i][2]*factor + dtfm*f[i][2];
 	}
       }
-      
     } else if (which == BIAS) {
       for (int i = 0; i < nlocal; i++) {
 	if (mask[i] & groupbit) {
@@ -307,11 +348,82 @@
 
   t_current = temperature->compute_scalar();
 
-  // update eta_dot
+  // update eta, eta_dot, eta2, eta2_dot
+  // chains require additional velocity update and recompute of current T
 
-  f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
-  eta_dot += f_eta*dthalf;
-  eta_dot *= drag_factor;
+  if (chain) {
+    eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+    factor2 = exp(-dt8*eta2_dot);
+    eta_dot *= factor2;
+    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+    eta_dot += f_eta*dt4;
+    eta_dot *= drag_factor;
+    eta_dot *= factor2;
+    eta += dthalf*eta_dot;
+    eta2 += dthalf*eta2_dot;
+ 
+    factor = exp(-dthalf*eta_dot);
+
+    if (rmass) {
+      if (which == NOBIAS) {
+	for (int i = 0; i < nlocal; i++) {
+	  if (mask[i] & groupbit) {
+	    dtfm = dtf / mass[type[i]];
+	    v[i][0] = v[i][0] * factor;
+	    v[i][1] = v[i][1] * factor;
+	    v[i][2] = v[i][2] * factor;
+	  }
+	}
+      } else if (which == BIAS) {
+	for (int i = 0; i < nlocal; i++) {
+	  if (mask[i] & groupbit) {
+	    temperature->remove_bias(i,v[i]);
+	    dtfm = dtf / mass[type[i]];
+	    v[i][0] = v[i][0] * factor;
+	    v[i][1] = v[i][1] * factor;
+	    v[i][2] = v[i][2] * factor;
+	    temperature->restore_bias(i,v[i]);
+	  }
+	}
+      }
+
+    } else {
+      if (which == NOBIAS) {
+	for (int i = 0; i < nlocal; i++) {
+	  if (mask[i] & groupbit) {
+	    dtfm = dtf / mass[type[i]];
+	    v[i][0] = v[i][0] * factor;
+	    v[i][1] = v[i][1] * factor;
+	    v[i][2] = v[i][2] * factor;
+	  }
+	}
+      } else if (which == BIAS) {
+	for (int i = 0; i < nlocal; i++) {
+	  if (mask[i] & groupbit) {
+	    temperature->remove_bias(i,v[i]);
+	    dtfm = dtf / mass[type[i]];
+	    v[i][0] = v[i][0] * factor;
+	    v[i][1] = v[i][1] * factor;
+	    v[i][2] = v[i][2] * factor;
+	    temperature->restore_bias(i,v[i]);
+	  }
+	}
+      }
+    }
+
+    t_current = temperature->compute_scalar();
+
+    eta_dot *= factor2;
+    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+    eta_dot += f_eta * dt4;
+    eta_dot *= factor2;
+    eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+
+  } else {
+    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+    eta_dot += f_eta*dthalf;
+    eta_dot *= drag_factor;
+  }
 }
 
 /* ---------------------------------------------------------------------- */
@@ -348,13 +460,26 @@
     delta /= update->endstep - update->beginstep;
     t_target = t_start + delta * (t_stop-t_start);
 
-    // update eta_dot
+    if (chain) {
+      eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+      factor2 = exp(-dt8*eta2_dot);
+      eta_dot *= factor2;
+      f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+      eta_dot += f_eta*dt4;
+      eta_dot *= drag_factor;
+      eta_dot *= factor2;
+      eta += dthalf*eta_dot;
+      eta2 += dthalf*eta2_dot;
+      
+    } else {
+      f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
+      eta_dot += f_eta*dthalf;
+      eta_dot *= drag_factor;
+      eta += dtv*eta_dot;
+    }
     
-    f_eta = t_freq*t_freq * (t_current/t_target - 1.0);
-    eta_dot += f_eta*dthalf;
-    eta_dot *= drag_factor;
-    eta += dtv*eta_dot;
     factor = exp(-dthalf*eta_dot);
+
   } else factor = 1.0;
 
   if (rmass) {
@@ -367,7 +492,6 @@
 	  v[i][2] = v[i][2]*factor + dtfm*f[i][2];
 	}
       }
-
     } else if (which == BIAS) {
       for (int i = 0; i < nlocal; i++) {
 	if (mask[i] & groupbit) {
@@ -415,6 +539,14 @@
       }
     }
   }
+
+  if (ilevel == nlevels_respa-1 && chain) {
+    eta_dot *= factor2;
+    f_eta = t_freq*t_freq * (factor * factor * t_current/t_target - 1.0);
+    eta_dot += f_eta * dt4;
+    eta_dot *= factor2;
+    eta2_dot += (temperature->dof * eta_dot*eta_dot - t_freq*t_freq) * dt4;
+  }
 }
 
 /* ---------------------------------------------------------------------- */
@@ -471,9 +603,11 @@
 void FixNVT::write_restart(FILE *fp)
 {
   int n = 0;
-  double list[2];
+  double list[4];
   list[n++] = eta;
   list[n++] = eta_dot;
+  list[n++] = eta2;
+  list[n++] = eta2_dot;
 
   if (comm->me == 0) {
     int size = n * sizeof(double);
@@ -492,6 +626,8 @@
   double *list = (double *) buf;
   eta = list[n++];
   eta_dot = list[n++];
+  eta2 = list[n++];
+  eta2_dot = list[n++];
 }
 
 /* ---------------------------------------------------------------------- */
@@ -519,6 +655,7 @@
       error->warning("Group for fix_modify temp != fix group");
     return 2;
   }
+
   return 0;
 }
 
@@ -536,6 +673,9 @@
   dtv = update->dt;
   dtf = 0.5 * update->dt * force->ftm2v;
   dthalf = 0.5 * update->dt;
+  dt4 = 0.25 * update->dt;
+  dt8 = 0.125 * update->dt;
+
   drag_factor = 1.0 - (update->dt * t_freq * drag);
 }
 
diff -Naur lammps-25Aug09/src/fix_nvt.h lammps-27Aug09/src/fix_nvt.h
--- lammps-25Aug09/src/fix_nvt.h	2008-04-08 16:55:40.000000000 -0600
+++ lammps-27Aug09/src/fix_nvt.h	2009-08-27 12:51:03.000000000 -0600
@@ -37,12 +37,12 @@
   void reset_dt();
 
  protected:
-  int which;
+  int which,chain;
   double t_start,t_stop;
   double t_current,t_target;
   double t_freq,drag,drag_factor;
-  double f_eta,eta_dot,eta,factor;
-  double dtv,dtf,dthalf;
+  double f_eta,eta_dot,eta,eta2_dot,eta2,factor,factor2;
+  double dtv,dtf,dthalf,dt4,dt8;
 
   int nlevels_respa;
   double *step_respa;