tropt

TROPT

The TROPT module is one of three drivers (see Section Stepper for documentation on STEPPER and Section Driver module for documentation on DRIVER) to perform a geometry optimization function on the molecule defined by input using the GEOMETRY directive (see Section Geometry). Geometry optimization is either an energy minimization or a transition state optimization. The algorithm programmed in TROPT is a trust region quasi-newton optimization and approximate energy Hessian updates.

TROPT is not selected by default out of the two available modules to perform geometry optimization. In order to force use of TROPT (e.g., because a previous optimization used STEPPER or DRIVER) provide a TROPT input block (below) — even an empty block will force use of TROPT.

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

      TROPT 
        (LOOSE || DEFAULT || TIGHT)
        GMAX <real value>
        GRMS <real value>
        XMAX <real value>
        XRMS <real value>

        OPTTOL <real opttol default 3e-4>

        EPREC <real eprec default 1e-7>

        TRUST <real trust default 0.3>

        CLEAR
        REDOAUTOZ

        INHESS <integer inhess default 0>

        (MODDIR || VARDIR) <integer dir default 0>
        (FIRSTNEG || NOFIRSTNEG)

        MAXITER <integer maxiter default 20>

        BSCALE <real BSCALE default 1.0>
        ASCALE <real ASCALE default 0.25>
        TSCALE <real TSCALE default 0.1>
        HSCALE <real HSCALE default 1.0>
       
        PRINT ...

        XYZ [<string xyz default $file_prefix$>]
        NOXYZ

      END

###Convergence criteria

        (LOOSE || DEFAULT || TIGHT)
        GMAX <real value>
        GRMS <real value>
        XMAX <real value>
        XRMS <real value>
        
        OPTTOL  <real value>

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 being used (Z-matrix, redundant internals, or Cartesian). 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

Additionally the user may request a specific value for the tolerance with the keyword OPTTOL which will couple all the convergence criteria in the following way:

             GRMS   1.0*OPTTOL
             GMAX   1.5*OPTTOL
             XRMS   4.0*OPTTOL
             XMAX   6.0*OPTTOL

Note that GMAX and GRMS used for convergence of geometry may significantly vary in different coordinate systems such as Z-matrix, redundant internals, or Cartesian. The coordinate system is defined in the input file (default is Z-matrix). Therefore the choice of coordinate system may slightly affect converged energy. Although in most cases XMAX and XRMS are last to converge which are always done in Cartesian coordinates, which insures convergence to the same geometry in different coordinate systems.

The old criterion may be recovered with the input

       gmax 0.0008; grms 1; xrms 1; xmax 1

###Available precision

        EPREC <real eprec default 1e-7>

In performing a trust region optimization the precision of the energy is coupled to the convergence criteria. As mentioned above in most cases XMAX and XRMS are last to converge, thus, an accelerated converge is triggered in TROPT when GMAX and GRMS are already converged and the corresponding energy change with respect to the previous point is below the EPREC threshold, then, the structure is treated as optimized. This is used as an accelerated convergence criteria to avoid long tail in the optimization process. This will increase the speed of an optimization in most of the cases but it will be somehow cumbersome when dealing with flat energy surfaces, in this case a more tight EPREC value is recommended. Note that the default EPREC for DFT calculations is 5e-6 instead of 1e-7.

###Controlling the step length

        TRUST <real trust default 0.3>

A dynamic trust radius (trust) is used to control the step during optimization processes both minimization and saddle-point searches. It defaults to 0.3 for minimizations and 0.1 for saddle-point searches.

###Backstepping in TROPT

If a step taken during the optimization is too large or in the wrong direction (e.g., the step causes the energy to go up for a minimization), the TROPT optimizer will automatically “backstep” and reduce the current value of the trust radius in order to avoid a permanent “backsteping”.

###Maximum number of steps

        MAXITER <integer maxiter default 20>

By default at most 20 geometry optimization steps will be taken, but this may be modified with this directive.

###Discard restart information

        CLEAR

By default TROPT reuses Hessian information from a previous optimization, and, to facilitate a restart also stores which mode is being followed for a saddle-point search. This option deletes all restart data.

###Regenerate internal coordinates

        REDOAUTOZ

Deletes Hessian data and regenerates internal coordinates at the current geometry. Useful if there has been a large change in the geometry that has rendered the current set of coordinates invalid or non-optimal.

###Initial Hessian

        INHESS <integer inhess default 0>

0 = Default ... use restart data if available, otherwise use diagonal guess.
1 = Use diagonal initial guess.
2 = Use restart data if available, otherwise transform Cartesian Hessian from previous frequency calculation.

In addition, the diagonal elements of the initial Hessian for internal coordinates may be scaled using separate factors for bonds, angles and torsions with the following

        BSCALE <real bscale default 1.0>
        ASCALE <real ascale default 0.25>
        TSCALE <real tscale default 0.1>

These values typically give a two-fold speedup over unit values, based on about 100 test cases up to 15 atoms using 3-21g and 6-31g* SCF. However, if doing many optimizations on physically similar systems it may be worth fine tuning these parameters.

Finally, the entire Hessian from any source may be scaled by a factor using the directive

        HSCALE <real hscale default 1.0>

It might be of utility, for instance, when computing an initial Hessian using SCF to start a large MP2 optimization. The SCF vibrational modes are expected to be stiffer than the MP2, so scaling the initial Hessian by a number less than one might be beneficial.

###Mode or variable to follow to saddle point

        (MODDIR || VARDIR) <integer dir default 0>
        (FIRSTNEG || NOFIRSTNEG)

When searching for a transition state the program, by default, will take an initial step uphill and then do mode following using a fuzzy maximum overlap (the lowest eigen-mode with an overlap with the previous search direction of 0.7 times the maximum overlap is selected). Once a negative eigen-value is found, that mode is followed regardless of overlap.

The initial uphill step is appropriate if the gradient points roughly in the direction of the saddle point, such as might be the case if a constrained optimization was performed at the starting geometry. Alternatively, the initial search direction may be chosen to be along a specific internal variable (using the directive VARDIR) or along a specific eigen-mode (using MODDIR). Following a variable might be valuable if the initial gradient is either very small or very large. Note that the eigen-modes in the optimizer have next-to-nothing to do with the output from a frequency calculation. You can examine the eigen-modes used by the optimizer with

         tropt; print hvecs; end

The selection of the first negative mode is usually a good choice if the search is started in the vicinity of the transition state and the initial search direction is satisfactory. However, sometimes the first negative mode might not be the one of interest (e.g., transverse to the reaction direction). If NOFIRSTNEG is specified, the code will not take the first negative direction and will continue doing mode-following until that mode goes negative.

###Optimization history as XYZ file

        XYZ [<string xyz default $fileprefix>]
        NOXYZ

The XYZ directive causes the geometry at each step to be output into file in the permanent directory in XYZ format. The optional string will prefix the filename. The NOXYZ directive turns this off.

For example, the input

        tropt; xyz ; end

will cause a trajectory file filename.xyz to be created in the permanent directory.

###Print options

The UNIX command "egrep '^@' < output" will extract a pretty table summarizing the optimization.

If you specify the NWChem input

          scf; print none; end
          tropt; print low; end
          task scf optimize

you’ll obtain a pleasantly terse output.

For more control, these options for the standard print directive are recognized

debug - prints a large amount of data. Don’t use in parallel.
high - print the search direction in internals
default - prints geometry for each major step (not during the line search), gradient in internals (before and after application of constraints)
low - prints convergence and energy information. At convergence prints final geometry, change in internals from initial geometry

and these specific print options