fix neb bugfix from Emile Maras

NEB was not working fine when using multiple proc
per replica and the keywords last/efirst or last/efirst/middle

I have corrected this in the enclosed fix_neb.cpp

I also slightly modified the nudging for this free end so that
it would be applied only when the target energy is larger than
the energy. Anyway if the target energy is lower than the energy,
the replica should relax toward the target energy without adding
any nudging.

I also modified the documentation according to this change.

doc/src/fix_neb.txt

@@ -138,17 +138,17 @@ By default, no additional forces act on the first and last replicas
 during the NEB relaxation, so these replicas simply relax toward their
 respective local minima.  By using the key word {end}, additional
 forces can be applied to the first and/or last replicas, to enable
-them to relax toward a MEP while constraining their energy.
+them to relax toward a MEP while constraining their energy E to the
+target energy ETarget.
 
-The interatomic force Fi for the specified replica becomes:
+If ETarget>E, the interatomic force Fi for the specified replica becomes:
 
 Fi = -Grad(V) + (Grad(V) dot T' + (E-ETarget)*Kspring3) T',  {when} Grad(V) dot T' < 0
 Fi = -Grad(V) + (Grad(V) dot T' + (ETarget- E)*Kspring3) T', {when} Grad(V) dot T' > 0
 :pre
 
-where E is the current energy of the replica and ETarget is the target
+The "spring" constant on the difference in energies is the specified
-energy.  The "spring" constant on the difference in energies is the
+{Kspring3} value.
-specified {Kspring3} value.
 
 When {estyle} is specified as {first}, the force is applied to the
 first replica.  When {estyle} is specified as {last}, the force is
@@ -183,10 +183,9 @@ After converging a NEB calculation using an {estyle} of
 have a larger energy than the first replica. If this is not the case,
 the path is probably not a MEP.
 
-Finally, note that if the last replica converges toward a local
+Finally, note that the last replica may never reach the target energy
-minimum which has a larger energy than the energy of the first
+if it is stuck in a local minima which has a larger energy than the
-replica, a NEB calculation using an {estyle} of {last/efirst} or
+target energy.
-{last/efirst/middle} cannot reach final convergence.
 
 [Restart, fix_modify, output, run start/stop, minimize info:]
 

src/REPLICA/fix_neb.cpp

@@ -298,12 +298,14 @@ void FixNEB::min_post_force(int vflag)
   if (ireplica == 0) vIni=veng;
 
   if (FreeEndFinalWithRespToEIni) {
-    if (me == 0) {
+    if (cmode == SINGLE_PROC_DIRECT || cmode == SINGLE_PROC_MAP) {
       int procFirst;
       procFirst=universe->root_proc[0];
       MPI_Bcast(&vIni,1,MPI_DOUBLE,procFirst,uworld);
-    }
+    }else {
-    if (cmode == MULTI_PROC) {
+      if (me == 0)
+        MPI_Bcast(&vIni,1,MPI_DOUBLE,0,rootworld);
+
       MPI_Bcast(&vIni,1,MPI_DOUBLE,0,world);
     }
   }
@@ -514,9 +516,10 @@ void FixNEB::min_post_force(int vflag)
       MPI_Allreduce(&dot,&dotall,1,MPI_DOUBLE,MPI_SUM,world);
       dot=dotall/tlen;
 
+      if (veng<EFinalIni) {
         if (dot<0) prefactor = -dot - kspringFinal*(veng-EFinalIni);
         else prefactor = -dot + kspringFinal*(veng-EFinalIni);
-
+      }
       for (int i = 0; i < nlocal; i++)
         if (mask[i] & groupbit) {
           f[i][0] += prefactor *tangent[i][0];
@@ -531,10 +534,10 @@ void FixNEB::min_post_force(int vflag)
       double dotall;
       MPI_Allreduce(&dot,&dotall,1,MPI_DOUBLE,MPI_SUM,world);
       dot=dotall/tlen;
-
+      if (veng<vIni) {
         if (dot<0) prefactor = -dot - kspringFinal*(veng-vIni);
         else prefactor = -dot + kspringFinal*(veng-vIni);
-
+      }
       for (int i = 0; i < nlocal; i++)
         if (mask[i] & groupbit) {
           f[i][0] += prefactor *tangent[i][0];