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Nudged Elastic Band (NEB) method

The NEB module is an implementation of the nudged elastic band (NEB) method of Jonsson et al., and it is one of two drivers in NWChem that can be used to perform minimum energy path optimizations. NEB can be used at all levels of theory, including SCF, HF, DFT, PSPW, BAND, MP2, RIMP2, CCSD, TCE.

Input to the NEB modules is contained with the NEB block

 NEB  
  ...  
 END

To run a NEB calculation the following the following task directives is used

TASK <theory> NEB  
TASK <theory> NEB ignore

where <theory> is SCF, HF, DFT, PSPW, BAND, MP2, CCSD, TCE, etc.. The Task directive with the ignore option is recommended, otherwise NWChem will crash if the path is not optimized in the allowed maximum number of iterations.

Optional input for this module is specified within the compound directive,

 NEB 
    NBEADS <integer nbeads default 5>  
    KBEADS <float kbeads default 0.1> 
    MAXITER <integer maxiter default 5>  

    STEPSIZE <integer stepsize default 1.0>  
    NHIST <integer nhist default 5> 
    ALGORITHM <integer algorithm default 0>  

    [loose | default | tight]  
    GMAX <float gmax default 0.00045>  
    GRMS <float grms default 0.00030>  
    XMAX <float xmax default 0.00018>  
    XMRS <float xmrs default 0.00012>  

    [IMPOSE]  
    [HASMIDDLE]  
    [XYZ_PATH <string xyzfilename>]  
    [RESET]  
    [PRINT_SHIFT <integer print_shift default 0>]  
 END

The following list describes the input for the NEB block

  • nbeads - number of beads (or images) used to represent the path
  • kbeads - value for the NEB spring constant
  • maxiter - maximum number of NEB path optimizations to be performed
  • stepsize - value for the stepsize used in the optimization. Typically less than 1.
  • nhist - number of histories to use for quasi-Newton optimization (algorithm =0)
  • LOOSE|DEFAULT|TIGHT - options specifying thresholds for convergence
  • gmax - value for the maximum gradient used to determine convergence
  • grms - value for the root mean square gradient used to determine convergence
  • xmax - value for the maximum cartesian step used to determine convergence
  • xrmx - value for the root mean square cartesian step used to determine convergence
  • algorithm - 0: quasi-Newton Fixed Point optimization, 1: dampled Verlet optimization, 2: refining conjugate gradient optimization
  • IMPOSE - if specified causes the initial geometries used to specify the path to be aligned with one another
  • HASMIDDLE - if specified causes the initial path to use the the “midgeom” geometry to be used as the midpoint, i.e. the initial path is defined as a linear morphing from “geometry” –> “midgeom” –> “endgeom”
  • XYZ_PATH - if specified the initial path is defined from the sequence of geometries contained in xyzfilename
  • RESET - if specified causes the NEB optimization and path to be started from scratch
  • print_shift - setting the PRINT_SHIFT directive causes the path energies and geometries to be outputed every <print_shift> steps. The current path energies are appended to the file jobname.neb_epath and the current geometries are appended to the file jobname.nebpath_"current iteration".xyz.

Setting up initial path

There are three different ways to define the initial path for NEB optimization.

  • Linear interpolation between two geometries

The geometries in the path are defined by

\[\vec{R}^i_{xyz} = \vec{R}^1_{xyz} + \frac{i-1}{nbeads-1} (\vec{R}^{nbeads}_{xyz}-\vec{R}^{1}_{xyz}), \ for \ i=1,nbeads\]

where the starting geometry \(\vec{R}^1_{xyz}\) is entered in the geometry block labeled geometry, e.g.

geometry nocenter noautosym noautoz  
O  0.00000000    -0.02293938     0.00000000  
H  0.00000000     0.55046969     0.75406534  
H  0.00000000     0.55046969    -0.75406534  
end

and the last geometry in the path \(\vec{R}^{nbeads}_{xyz}\) is entered in the geometry block label endgeom, e.g.

geometry endgeom nocenter noautosym noautoz  
O  0.00000000     0.02293938     0.00000000  
H  0.00000000    -0.55046969     0.75406534  
H  0.00000000    -0.55046969    -0.75406534  
end
  • Linear interpolation between three geometries

The geometries for this path are defined by

\[\vec{R}^i_{xyz} = \vec{R}^1_{xyz} + \frac{i-1}{nbeads/2-1} (\vec{R}^{nbeads/2}_{xyz}-\vec{R}^{1}_{xyz}), \ for \ i=1,nbeads/2\]

and

\[\vec{R}^i_{xyz} = \vec{R}^{nbeads/2}_{xyz} + \frac{i-nbeads/2}{nbeads/2-1} (\vec{R}^{nbeads}_{xyz}-\vec{R}^{nbeads/2}_{xyz}), \ for \ i=nbeads/2+1,nbeads\]

where the starting \(\vec{R}^1_{xyz}\) , middle \(\vec{R}_{xyz}^{nbeads/2}\) and last \(\vec{R}^{nbeads}_{xyz}\) geometries are entered in the geometry blocks geometry, midgeom and endgeom respectively, e.g.

geometry nocenter noautosym noautoz  
O  0.00000000    -0.02293938     0.00000000  
H  0.00000000     0.55046969     0.75406534  
H  0.00000000     0.55046969    -0.75406534  
end

geometry midgeom nocenter noautosym noautoz  
O  0.00000000     0.00000000     0.00000000  
H  0.00000000     0.00000000     1.00000000  
H  0.00000000     0.00000000    -1.00000000  
end

geometry endgeom nocenter noautosym noautoz  
O  0.00000000     0.02293938     0.00000000  
H  0.00000000    -0.55046969     0.75406534  
H  0.00000000    -0.55046969    -0.75406534  
end
  • Using xyz_path to explicitly input a path of geometries

The xyz_path option can also be used to define the initial path.

...  
NEB  
   ...  
  XYZ_PATH path.xyz
END  
...

where path.xyz contains a list of geometries in xyz format, e.g.

--------------- path.xyz ------------------  
                   3  
energy=  -17.107207699285738       
O           0.000000   -0.022939    0.000000  
H           0.000000    0.550469    0.754065  
H           0.000000    0.550469   -0.754065  
                   3  
energy=  -17.094903833074170       
O          -0.000003   -0.110080   -0.000000  
H          -0.000000    0.273180    0.847029  
H          -0.000000    0.273180   -0.847029  
                   3  
energy=  -17.063823686395292       
O          -0.000000   -0.000080   -0.000000  
H           0.000000   -0.000002    0.941236  
H           0.000000   -0.000002   -0.941236  
                   3  
energy=  -17.094944036147005       
O          -0.000000    0.110472   -0.000000  
H          -0.000000   -0.273172    0.846957  
H          -0.000000   -0.273172   -0.846957  
                   3  
energy=  -17.107208157343706       
O           0.000000    0.022939    0.000000  
H           0.000000   -0.550469    0.754065  
H           0.000000   -0.550469   -0.754065  
--------------- path.xyz ------------------

Convergence criteria

The defaults may be used, or the directives LOOSE, DEFAULT, or TIGHT specified to use standard sets of values, or the individual criteria adjusted. All criteria are in atomic units. GMAX and GRMS control the maximum and root mean square gradient in the coordinates. XMAX and XRMS control the maximum and root mean square of the Cartesian step.

LOOSE DEFAULT TIGHT
GMAX 0.0045d0 0.00045 0.000015
GRMS 0.0030d0 0.00030 0.00001
XMAX 0.0054d0 0.00180 0.00006
XRMS 0.0036d0 0.00120 0.00004

NEB Tutorial 1: H2O Inversion

(input:h2o-neb.nw, output:h2o-neb.nwout, datafiles: h2o-neb.neb_epath.dat h2o-neb.neb_final_epath.dat )

(xyzfiles: h2o-neb.nebpath_000001.xyz h2o-neb.nebpath_000005.xyz h2o-neb.nebpath_000010.xyz h2o-neb.nebpath_000020.xyz h2o-neb.nebpath_final.xyz )

H2O Inversion Pathway

Title "H2O inversion calculation"
echo
start h2o-neb

geometry nocenter noautosym noautoz  
O  0.00000000    -0.02293938     0.00000000  
H  0.00000000     0.55046969     0.75406534  
H  0.00000000     0.55046969    -0.75406534  
end  

geometry endgeom nocenter noautosym noautoz  
O  0.00000000     0.02293938     0.00000000  
H  0.00000000    -0.55046969     0.75406534  
H  0.00000000    -0.55046969    -0.75406534  
end  
#### Gaussian DFT ####  
basis  
* library 3-21G  
end  

dft  
  xc b3lyp  
  maxiter 5001  
  cgmin  
end  

neb  
  nbeads 10  
  kbeads 1.0  
  maxiter 10  
  stepsize 0.10  
  print_shift 1  
end  
task dft neb ignore
neb  
  # increase the number of images  
  nbeads 20  
  kbeads 1.0  
  stepsize 1.0  
  maxiter 30  
  loose  
end 
task dft neb ignore

After each optimization step the path energies are outputed as follows

neb: Path Energy #                    9  
neb:                     1  -75.970000166349976       
neb:                     2  -75.973958450556779       
neb:                     3  -75.973964391052448       
neb:                     4  -75.973965560274110       
neb:                     5  -75.973961077512683       
neb:                     6  -75.973087554095144       
neb:                     7  -75.965847261117744       
neb:                     8  -75.950292780255126       
neb:                     9  -75.932932759963109       
neb:                    10  -75.921912278179292       
neb:                    11  -75.921834552460439       
neb:                    12  -75.932680002200939       
neb:                    13  -75.949868818688529       
neb:                    14  -75.965372754426866       
neb:                    15  -75.972788885848303       
neb:                    16  -75.973958649400714       
neb:                    17  -75.973965255113598       
neb:                    18  -75.973964962774133       
neb:                    19  -75.973959526041568       
neb:                    20  -75.970000163960066     

Another way to keep track of the optimization process is to run the following grep command on the output file.

[WE24397:NWChem/NEB/Example2] bylaska% grep @ h2o-neb.nwout  
@neb    
@neb NEB Method  
@neb algorithm      =         0  
@neb maxiter        =        10  
@neb nbeads         =        10  
@neb nhist          =         5  
@neb natoms         =         3  
@neb stepsize       = 0.100E+01  
@neb trust          = 0.100E+00  
@neb kbeads         = 0.100E+00  
@neb Gmax tolerance = 0.450E-03  
@neb Grms tolerance = 0.300E-03  
@neb Xmax tolerance = 0.180E-03  
@neb Xrms tolerance = 0.120E-03  
@neb    
@neb Step    Intrinsic E    Mid-Point E      Minimum E      Maximum E   Gmax     Grms     Xrms     Xmax   Walltime  
@neb ---- -------------- -------------- -------------- -------------- -------- -------- -------- -------- --------  
@neb    1     -75.951572     -75.921109     -75.970632     -75.921109  0.55875  0.01606  0.14221  1.54029    454.9  
@neb    2     -75.953755     -75.923180     -75.972590     -75.923177  0.38930  0.01116  0.01588  0.45644    624.4  
@neb    3     -75.956726     -75.924391     -75.972861     -75.924387  0.25587  0.00961  0.03673  0.83118    805.2  
@neb    4     -75.957861     -75.924279     -75.973059     -75.924275  0.23572  0.00894  0.01793  0.24399    971.8  
@neb    5     -75.959613     -75.925045     -75.973869     -75.925036  0.10257  0.00464  0.03197  0.20350   1152.8  
@neb    6     -75.959964     -75.925503     -75.973957     -75.925486  0.04762  0.00196  0.00905  0.10433   1316.4  
@neb    7     -75.960068     -75.925822     -75.973956     -75.925791  0.03897  0.00141  0.00308  0.04432   1519.9  
@neb    8     -75.960091     -75.925914     -75.973959     -75.925877  0.03707  0.00127  0.00070  0.01691   2055.8  
@neb    9     -75.960129     -75.926078     -75.973962     -75.926028  0.03353  0.00108  0.00127  0.03707   2297.2  
@neb   10     -75.960142     -75.926142     -75.973963     -75.926085  0.03199  0.00101  0.00054  0.00420   2756.6  
@neb   NEB calculation not converged  
@neb    
@neb NEB Method  
@neb algorithm      =         0  
@neb maxiter        =        30  
@neb nbeads         =        20  
@neb nhist          =         5  
@neb natoms         =         3  
@neb stepsize       = 0.100E+01  
@neb trust          = 0.100E+00  
@neb kbeads         = 0.100E+01  
@neb Gmax tolerance = 0.450E-02  
@neb Grms tolerance = 0.300E-02  
@neb Xmax tolerance = 0.540E-02  
@neb Xrms tolerance = 0.360E-02  
@neb    
@neb Step    Intrinsic E    Mid-Point E      Minimum E      Maximum E   Gmax     Grms     Xrms     Xmax   Walltime  
@neb ---- -------------- -------------- -------------- -------------- -------- -------- -------- -------- --------  
@neb    1     -75.960225     -75.921704     -75.973965     -75.921669  0.24799  0.00398  0.00272  0.08741   3966.5  
@neb    2     -75.960339     -75.921782     -75.973965     -75.921745  0.24794  0.00328  0.00199  0.12148   5023.2  
@neb    3     -75.960424     -75.921742     -75.973965     -75.921701  0.19390  0.00286  0.00164  0.08342   5741.4  
@neb    4     -75.960494     -75.921849     -75.973965     -75.921804  0.19681  0.00266  0.00143  0.09030   6079.7  
@neb    5     -75.960646     -75.921874     -75.973965     -75.921820  0.17459  0.00240  0.00241  0.22047   6751.5  
@neb    6     -75.960674     -75.921856     -75.973965     -75.921797  0.14246  0.00165  0.00060  0.00256   7572.3  
@neb    7     -75.960724     -75.921884     -75.973966     -75.921817  0.13004  0.00153  0.00082  0.05401   7893.3  
@neb    8     -75.960747     -75.921892     -75.973966     -75.921822  0.12809  0.00149  0.00038  0.00237   8631.2  
@neb    9     -75.960792     -75.921912     -75.973966     -75.921835  0.12267  0.00142  0.00075  0.05081   9222.0  
@neb   10     -75.960813     -75.921923     -75.973966     -75.921841  0.11902  0.00138  0.00035  0.00212  10163.2  
@neb   11     -75.960834     -75.921934     -75.973966     -75.921846  0.11569  0.00135  0.00035  0.00203  10478.3  
@neb   12     -75.961060     -75.922060     -75.973966     -75.921889  0.07709  0.00104  0.00365  0.30944  10863.8  
@neb   13     -75.961255     -75.922186     -75.973966     -75.921919  0.04600  0.00087  0.00309  0.19999  11357.0  
@neb   14     -75.961405     -75.922286     -75.973966     -75.921927  0.03549  0.00079  0.00244  0.03857  11860.0  
@neb  NEB calculation converged

Zero Temperature String Method

The STRING module is an implementation of the zero temperature string method of vanden Eijden et al., and it is one of two drivers in NWChem that can be used to perform minimum energy path optimizations. STRING can be used at all levels of theory, including SCF, HF, DFT, PSPW, BAND, MP2, RIMP2, CCSD, TCE.

Input to the STRING module is contained with the STRING block

 STRING
  ...
 END

To run a STRING calculation the following the following task directives is used

TASK <theory> STRING
TASK <theory> STRING ignore

where <theory> is SCF, HF, DFT, PSPW, BAND, MP2, CCSD, TCE, etc.. The Task directive with the ignore option is recommended, otherwise NWChem will crash if the path is not optimized in the allowed maximum number of iterations.

Optional input for this module is specified within the compound directive,

 STRING 
    NBEADS <integer nbeads default 5> 
    MAXITER <integer maxiter default 5> 

    STEPSIZE <integer stepsize default 1.0> 
    NHIST <integer nhist default 5>  
    INTERPOL <integer algorithm default 1>  

    FREEZE1 <logical freeze1 default .false.>  
    FREEZEN <logical freezen default .false.>  

    TOL <float tol default 0.00045>  

    [IMPOSE]  
    [HASMIDDLE]  
    [XYZ_PATH <string xyzfilename>]  
    [RESET]  
    PRINT_SHIFT <integer print_shift default 0>  
 END

The following list describes the input for the STRING block

  • nbeads - number of beads (or images) used to represent the path
  • maxiter - maximum number of NEB path optimizations to be performed
  • stepsize - value for the stepsize used in the optimization. Typically less than 1.
  • nhist - number of histories to use for quasi-Newton optimization (algorithm =0)
  • tol - value for the maximum gradient used to determine convergence
  • freeze1 - .true.: first bead of simulation frozen, .false.:first bead of simulation not frozen.
  • freezeN - .true.:last bead of simulation frozen, .false.:last bead of simulation not frozen
  • interpol - 1: linear, 2: spline, 3: Akima spline
  • IMPOSE - if specified causes the initial geometries used to specify the path to be aligned with one another
  • HASMIDDLE - if specified causes the initial path to use the the “midgeom” geometry to be used as the midpoint, i.e. the initial path is defined as a linear morphing from “geometry” –> “midgeom” –> “endgeom”
  • XYZ_PATH - if specified the initial path is defined from the sequence of geometries contained in xyzfilename
  • RESET - if specified causes the NEB optimization and path to be started from scratch
  • print_shift - setting the PRINT_SHIFT directive causes the path energies and geometries to be outputed every <print_shift> steps. The current path energies are appended to the file jobname.neb_epath and the current geometries are appended to the file jobname.nebpath _"current iteration".xyz

Setting up the initial path

There are three different ways to define the initial path for NEB optimization.

  • Linear interpolation between two geometries

The geometries in the path are defined by

\[\vec{R}^i_{xyz} = \vec{R}^1_{xyz} + \frac{i-1}{nbeads-1} (\vec{R}^{nbeads}_{xyz}-\vec{R}^{1}_{xyz}), \ for \ i=1,nbeads\]

where the starting geometry \(\vec{R}^1_{xyz}\) is entered in the geometry block labeled geometry, e.g.

geometry nocenter noautosym noautoz  
O  0.00000000    -0.02293938     0.00000000  
H  0.00000000     0.55046969     0.75406534  
H  0.00000000     0.55046969    -0.75406534  
end

and the last geometry in the path \(\vec{R}^{nbeads}_{xyz}\) is entered in the geometry block label endgeom, e.g.

geometry endgeom nocenter noautosym noautoz  
O  0.00000000     0.02293938     0.00000000  
H  0.00000000    -0.55046969     0.75406534  
H  0.00000000    -0.55046969    -0.75406534  
end
  • Linear interpolation between three geometries

The geometries for this path are defined by

\[\vec{R}^i_{xyz} = \vec{R}^1_{xyz} + \frac{i-1}{nbeads/2-1} (\vec{R}^{nbeads/2}_{xyz}-\vec{R}^{1}_{xyz}), \ for \ i=1,nbeads/2\]

and

\[\vec{R}^i_{xyz} = \vec{R}^{nbeads/2}_{xyz} + \frac{i-nbeads/2}{nbeads/2-1} (\vec{R}^{nbeads}_{xyz}-\vec{R}^{nbeads/2}_{xyz}), \ for \ i=nbeads/2+1,nbeads\]

where the starting \(\vec{R}^{1}_{xyz}\) , middle \(\vec{R}^{nbeads/2}_{xyz}\) and last \(\vec{R}^{nbeads}_{xyz}\)” geometries are entered in the geometry blocks geometry, midgeom and endgeom respectively, e.g.

geometry nocenter noautosym noautoz  
O  0.00000000    -0.02293938     0.00000000  
H  0.00000000     0.55046969     0.75406534  
H  0.00000000     0.55046969    -0.75406534  
end

geometry midgeom nocenter noautosym noautoz  
O  0.00000000     0.00000000     0.00000000  
H  0.00000000     0.00000000     1.00000000  
H  0.00000000     0.00000000    -1.00000000  
end

geometry endgeom nocenter noautosym noautoz  
O  0.00000000     0.02293938     0.00000000  
H  0.00000000    -0.55046969     0.75406534  
H  0.00000000    -0.55046969    -0.75406534  
end
  • Using xyz_path to explicitly input a path of geometries

The xyz_path option can also be used to define the initial path, e.g.

...
STRING
   ...
  XYZ_PATH path.xyz
END
...

String Tutorial 1:HCN –> HNC path optimization

(input:HCN-string1.nw, output:HCN-string1.nwout, datafiles: HCN-string1.string_epath.dat HCN-string1.string_final_epath.dat )

(xyzfiles: HCN-string1.stringpath_000001.xyz HCN-string1.stringpath_000005.xyz HCN-string1.stringpath_000010.xyz HCN-string1.stringpath_000020.xyz HCN-string1.stringpath_000030.xyz HCN-string1.stringpath_final.xyz )

HCN-->HNC Reaction Pathway

400px

In this example, the path energy for the reaction HCN –> HNC is calculated.

#    
# The initial path has the Carbon moving through the Nitrogen.  
# So for this simulation to work that atom avoidance code needs to work.  
# Because the initial path is so stiff the wavefunction optimizer needs to requires  
# lots of iterations during the early stages of the path optimization.  
#  
#  
Title "HCN --> HNC Zero-Temperature String Simulation"  
echo  
start hcn-hnc-dft  

geometry noautoz noautosym  
C         0.00000000     0.00000000    -0.49484657  
N         0.00000000     0.00000000     0.64616359  
H         0.00000000     0.00000000    -1.56151539  
end  

geometry endgeom  noautoz noautosym  
C         0.00000000     0.00000000     0.73225318   
N         0.00000000     0.00000000    -0.42552059  
H         0.00000000     0.00000000    -1.42351006  
end  

#### Gaussian DFT ####  
basis  
* library 3-21G  
end  

dft  
  xc b3lyp  
  maxiter 501  
end  

string  
  nhist 10  
  nbeads 10  
  maxiter 10  
  stepsize 0.10  
  print_shift 1  

  # don't allow the end points of the path to move  
  freeze1 .true.  
  freezeN .true.  
end  
task dft string ignore

string  
  # increase the number of images  
  nbeads 20  
  maxiter 20  

  # allow the end points of the path to move  
  freeze1 .false.  
  freezeN .false.  
end  
task dft string ignore

After each optimization step the path energies are outputed as follows

 string: Path Energy #                    2  
 string:                     1  -92.906682492969779  
 string:                     2  -92.743446565848473  
 string:                     3  -92.751945829987775  
 string:                     4  -92.756507971834026  
 string:                     5  -92.726984154346979  
 string:                     6  -92.701651474021503  
 string:                     7  -92.672613497521183  
 string:                     8  -92.825096796032099  
 string:                     9  -92.716422030970662  
 string:                    10  -92.881713271394148

Another way to keep track of the optimization process is to run the following grep command on the output file.

[WE24397:NWChem/NEB/Example2] bylaska% grep @ HCN-dft.out  
@zts  
@zts String method.  
@zts Temperature          =   0.00000  
@zts Covergence Tolerance =   0.00010  
@zts Step Size            =   0.10000  
@zts Maximum Time Steps   =        10  
@zts Number of replicas   =        10  
@zts Number of histories  =        10  
@zts String Interpolator  =         1  
@zts First Replica        = frozen  
@zts Last Replica         = frozen  
@zts  
@zts  Step     xrms     xmax        E start       E middle          E end          E max      E average  
@zts     1 0.460700 2.602234    -92.9066825    -83.4767173    -92.8817133    -83.4767173    -91.6169775  
@zts     2 0.862226 5.405612    -92.9066825    -92.3028437    -92.8817133    -92.3028437    -92.6631831  
@zts     3 0.105285 0.530157    -92.9066825    -92.3289676    -92.8817133    -92.3289676    -92.6702949  
@zts     4 0.134687 0.740991    -92.9066825    -92.3512584    -92.8817133    -92.3512584    -92.6821949  
@zts     5 0.117113 0.916210    -92.9066825    -92.3767826    -92.8817133    -92.3767826    -92.6899234  
@zts     6 0.124464 0.844439    -92.9066825    -92.4195957    -92.8817133    -92.4195957    -92.7045117  
@zts     7 0.092105 0.731434    -92.9066825    -92.4510785    -92.8817133    -92.4510785    -92.7156403  
@zts     8 0.049227 0.330651    -92.9066825    -92.4690983    -92.8817133    -92.4690983    -92.7288274  
@zts     9 0.032819 0.177356    -92.9066825    -92.4827444    -92.8817133    -92.4827444    -92.7344806  
@zts    10 0.076249 0.444246    -92.9066825    -92.4930430    -92.8817133    -92.4930430    -92.7381477  
@zts The string calculation failed to converge  
@zts Bead number    1  Potential Energy =     -92.906682487840  
@zts Bead number    2  Potential Energy =     -92.850640135623  
@zts Bead number    3  Potential Energy =     -92.819370566454  
@zts Bead number    4  Potential Energy =     -92.680821335407  
@zts Bead number    5  Potential Energy =     -92.505231918657  
@zts Bead number    6  Potential Energy =     -92.493042984646  
@zts Bead number    7  Potential Energy =     -92.637367419044  
@zts Bead number    8  Potential Energy =     -92.775376312982  
@zts Bead number    9  Potential Energy =     -92.831230727986  
@zts Bead number   10  Potential Energy =     -92.881713271394  
@zts  
@zts String method.  
@zts Temperature          =   0.00000  
@zts Covergence Tolerance =   0.00010  
@zts Step Size            =   0.10000  
@zts Maximum Time Steps   =        20  
@zts Number of replicas   =        20  
@zts Number of histories  =        10  
@zts String Interpolator  =         1  
@zts First Replica        = moves  
@zts Last Replica         = moves  
@zts  
@zts  Step     xrms     xmax        E start       E middle          E end          E max      E average  
@zts     1 1.039809 5.039486    -92.9071472    -92.4998400    -92.8820628    -92.4998400    -92.7500136  
@zts     2 0.192562 0.999019    -92.9073958    -92.5259828    -92.8821500    -92.5259828    -92.7624061  
@zts     3 0.244943 1.236459    -92.9075306    -92.5735140    -92.8821223    -92.5735140    -92.7816692  
@zts     4 0.207031 1.093667    -92.9075888    -92.6229190    -92.8821177    -92.6154678    -92.7979112  
@zts     5 0.056648 0.293829    -92.9075975    -92.6672565    -92.8821033    -92.6507897    -92.8101666  
@zts     6 0.078950 0.555245    -92.9076044    -92.7245122    -92.8822536    -92.7014407    -92.8241914  
@zts     7 0.065564 0.521110    -92.9076101    -92.7539982    -92.8822915    -92.7376310    -92.8326007  
@zts     8 0.050188 0.319477    -92.9076113    -92.7695725    -92.8824219    -92.7612604    -92.8378464  
@zts     9 0.055301 0.322130    -92.9076168    -92.7754581    -92.8825732    -92.7740099    -92.8408900  
@zts    10 0.038769 0.195102    -92.9076177    -92.7775695    -92.8826652    -92.7775695    -92.8425440  
@zts    11 0.064900 0.273480    -92.9076215    -92.7800330    -92.8827175    -92.7800330    -92.8443574  
@zts    12 0.062593 0.266337    -92.9076224    -92.7823972    -92.8826993    -92.7823972    -92.8458976  
@zts    13 0.205437 0.948190    -92.9076243    -92.7842034    -92.8826408    -92.7842034    -92.8469810  
@zts    14 0.015025 0.068924    -92.9076247    -92.7844362    -92.8826536    -92.7844362    -92.8472227  
@zts    15 0.129208 0.602636    -92.9076254    -92.7849856    -92.8826676    -92.7849856    -92.8477169  
@zts    16 0.013479 0.056561    -92.9076260    -92.7855201    -92.8826783    -92.7855201    -92.8481626  
@zts    17 0.472858 2.220715    -92.9076271    -92.7878088    -92.8826913    -92.7878088    -92.8497919  
@zts    18 0.162617 0.766201    -92.9076273    -92.7879912    -92.8826934    -92.7879912    -92.8499197  
@zts    19 0.013204 0.060562    -92.9076276    -92.7885097    -92.8826994    -92.7885097    -92.8502675  
@zts    20 0.718205 3.423813    -92.9076278    -92.7905066    -92.8827009    -92.7895258    -92.8514863  
@zts The string calculation failed to converge  
@zts Bead number    1  Potential Energy =     -92.907627751439  
@zts Bead number    2  Potential Energy =     -92.905047596626  
@zts Bead number    3  Potential Energy =     -92.897944354806  
@zts Bead number    4  Potential Energy =     -92.887494117302  
@zts Bead number    5  Potential Energy =     -92.874059841858  
@zts Bead number    6  Potential Energy =     -92.857382758537  
@zts Bead number    7  Potential Energy =     -92.837207959079  
@zts Bead number    8  Potential Energy =     -92.815902497386  
@zts Bead number    9  Potential Energy =     -92.798474907121  
@zts Bead number   10  Potential Energy =     -92.789525765222  
@zts Bead number   11  Potential Energy =     -92.790506632257  
@zts Bead number   12  Potential Energy =     -92.799861168980  
@zts Bead number   13  Potential Energy =     -92.814252430183  
@zts Bead number   14  Potential Energy =     -92.830704548760  
@zts Bead number   15  Potential Energy =     -92.847248091296  
@zts Bead number   16  Potential Energy =     -92.861557132126  
@zts Bead number   17  Potential Energy =     -92.871838446832  
@zts Bead number   18  Potential Energy =     -92.878543965696  
@zts Bead number   19  Potential Energy =     -92.881844751735  
@zts Bead number   20  Potential Energy =     -92.882700859222

A plotting program (e.g. gnuplot, xmgrace) can be used to look at final path as well as the the convergence of the path i.e.,

[WE24397:NEB/Example2/perm] bylaska% gnuplot  

   G N U P L O T  
   Version 4.6 patchlevel 0    last modified 2012-03-04   
   Build System: Darwin x86_64  

   Copyright (C) 1986-1993, 1998, 2004, 2007-2012  
   Thomas Williams, Colin Kelley and many others  

   gnuplot home:     <http://www.gnuplot.info>  
   faq, bugs, etc:   type "help FAQ"  
   immediate help:   type "help"  (plot window: hit 'h')  

Terminal type set to 'aqua'  
gnuplot> set xlabel "Reaction Coordinate"  
gnuplot> set ylabel "Energy (kcal/mol)"  
gnuplot> set yrange [0:100]  
gnuplot> set grid  
gnuplot> set style data linespoints  
gnuplot> plot "hcn-hnc-dft.string_epath" using 1:($2+92.908)*27.2116*23.06,"hcn-hnc-dft.string_final_epath" using 1:($2+92.908)*27.2116*23.06  
gnuplot> 

400px

String Tutorial 2:

Title "2SiO4H4 --> H3O3Si-O-SiO3H3 + H2O"  
echo  
start sio4h4-dimer  

geometry noautoz noautosym  
Si        -3.90592       -0.11789        0.03791   
O         -2.32450       -0.24327       -0.05259  
O         -4.45956       -1.13247        1.13159  
O         -4.53584       -0.45118       -1.38472  
O         -4.28179        1.37363        0.44838  
Si         1.27960        0.06912        0.14555  
O          2.85122        0.23514        0.32761  
O          0.54278        0.38513        1.52092  
O          0.94484       -1.42248       -0.29913  
O          0.75605        1.07390       -0.97272  
H         -1.66762       -0.74425       -0.29362  
H         -4.05734        2.06481        0.90983  
H         -4.30983       -1.85807        1.57116  
H         -4.43621       -0.88060       -2.12508  
H          3.59374       -0.16315        0.50572  
H          0.36896        0.10990        2.31839  
H          0.53993       -2.15495       -0.09488  
H          0.43207        1.85525       -1.13531  
end  

geometry endgeom  noautoz noautosym  
Si        -3.07373        0.18232       -0.24945  
O         -1.50797        0.23823       -0.53062  
O         -3.36758       -0.93058        0.85023  
O         -3.83958       -0.20093       -1.59101  
O         -3.57993        1.59735        0.27471  
Si        -0.05186        0.25441        0.11277  
O          0.94679       -0.58168       -0.80206  
O         -0.10091       -0.40972        1.55838  
O          1.41035       -3.75872        1.22931  
O          0.47135        1.75206        0.24209  
H          1.03624       -4.62405        0.92620  
H         -3.81554        2.06192        0.96069  
H         -3.97094       -1.38510        1.26383  
H         -4.39754       -0.73964       -1.96563  
H          1.45990       -0.57144       -1.49361  
H         -0.44444       -0.37536        2.34765  
H          2.15751       -4.00850        1.82933  
H          0.77180        2.44229       -0.17616  
end  

nwpw  
  simulation_cell  
     SC 18.0  
  end  
  cutoff 30.0  
  lmbfgs  
end  

string  
  nhist 10  
  nbeads 10  
  maxiter 10  
  stepsize 0.10  
  print_shift 1  

  # don't allow the end points of the path to move  
  freeze1 .true.  
  freezeN .true.  
end  
task pspw string ignore

string  
  # increase the number of images  
  nbeads 20  
  maxiter 20  

  # allow the end points of the path to move  
  freeze1 .false.  
  freezeN .false.  
end  
task pspw string ignore

String Tutorial 3: Combining NEB and String path optimizations