infdet

Summary

This code seeks to find the geometry that has the minimum energy under the constrain that its softest phonon mode(s)
has zero frequency.

The algorithm is described in:
A. van de Walle, S. Kadkhodaei, R. Sun, and Q.-J. Hong., 'Epicycle method for elasticity limit calculations.',
Phys. Rev. B, 95:144113, 2017. http://dx.doi.org/10.1103/PhysRevB.95.144113

A theoretical motivation for using such a quantity can be found in:
A. van de Walle, Q. Hong, S. Kadkhodaei, and R. Sun., 'The free energy of mechanically unstable phases',
Nature Commun. 6, 7559 (2015). http://dx.doi.org/10.1038/ncomms8559

This is code often invoked automatically within the script robustrelax_xxxx with the -id option. In this case,
all options are passed with -idop \"[any of the options described below]\". Also, all files described below
then reside in the 01 subdirectory and the log file is 01/infdet.log .

It is implemented as two nested optimization problems:
-an inner optimization problem to find the softest phonon mode using a modification of the dimer method
(called the epicycle method) and 
-an outer optimization problem to find the actual atomic geometry.
An epicycle differs from a dimer in that one of the system images lies in the center and the other one
is rotating around it while in a dimer the two images lie symmetrically about the center.

All options that pertain to the inner 'epicycle' optimization start with '-e' while
those that control ionic (and cell parameter) movement start with '-i'.
Both optimization are implemented via a conjugate gradient algorithm.

Parameters controlling the optimization

-el  (Epicycle Length, in Angstrom) specifies the distance between the two images of the epicycle.
-egt (Epicycle Gradient Tolerance, in eV/Ang^2) is the stopping criterion for the soft mode search algorithm.
-ets (Epicycle Trial Step, in radiant) trial step for the line minimizations.
     If this trial step fails to bracket the minimum, the step is size multiplied by the...
-eml (Epicycle Multiplier in Line minimization) until the minimum is bracketed.
     But the step size will never exceed the...
-ems (Epicycle Maximum Step multiplier).
     The actual maximum step is equal to trial step times the multiplier.
     Bracketing stops when a bracket is found or the
-ebl (Epicycle maximum number of Bracketing steps in Line minimizations) is reached.
     Once the bracketing step is done, the algorithm does a sequant search, finding the point most likely to have zero derivative
     based on the derivatives at the end points of the bracket. If the predicted point falls too close to the endpoints
     (not in the middle half of the bracket) a bisection step is taken instead, except the first 't' times this occurs,
     where 't' is the...
-ebf (Epicycle motion Bad step Forgiveness).
     This is repeated until either the gradiant tolerance is met (-egt divided by sqrt(number of degrees of freedom ) or the...
-eil (Epicycle maximum number of Iterations in Line minimizations) is reached.
     The line minimizations are embedded in a conjugate gradient proceedure which is repeated until
     the gradient tolerance (-egt) is met or the ...
-eic (Epicycle maximum number of Iterations in Conjugate gradient) is reached.
     As in any conjugate gradient method, the conjugate direction reset to steepest descent every...
-eir (Epicycle iterations between conjugate gradient reset) steps.

For the outer optimization problem (ion motion), the same parameters are available: with the initial '-e' replaced by '-i':
-igt,-its,-iml,-ims,-ibl,-ibf,-iil,-iic,iir.
     One difference is that -igt is in eV/Ang and -its and -ims are in Angstrom.
     Since the outer optimization takes into account two criteria (curvature and energy), it needs
     one multiplier to convert curvature gradient into force (so they can be combined into a single force):
-ics (Ion motion Curvature constraint Stiffness) If this is set to zero, the multiplier is automatically set to make
     the curvature gradient and the force equal at the first step and then kept constant thereafter.
     In addition, the outer optimization start with a few steps of steepest descent, indicated by the
-isi (Ion motion Steepest maximum number of Iterations) parameter.
     This helps because the outer optimization problem can be far from quadratic in behavior initially.
     The step size is equal to the force times the
-ism (Ion motion Steepest descent Multiplier, in Angstrom^2/eV).
     The outer optimization problem also optimizes cell shape in addition to ionic coordinates.
     To make cell degress of freedom comparable to atomic coordinates, the following scaling is used:
     The 'force' on the cell is Omega^(2/3) * (stress tensor) * f where Omega is the average atomic volume for the
     initial configuration and f is a constant set with:
 -ff (Force scale Factor, dimensionless).
     The cell shape is parametrized by n*Omega^(1/3)*strain/f where n is the number of atoms.
     This convention ensures that stress and cell parameters scale approriately with cell size and have units and magnitudes
     comparable to the atomic coordinates. Note that the atomic coordinates are stored internally as the coordinates for the
     initial cell shape (and are distorded according the strain acting on the cell).
-ds  indicates whether and how to relax the cell shape. 3 (the default) means fully general 3d strains are allowed,
     2 means means fully general 2d strains, etc.
     0 means no cell relaxations are allowed.
     The unique axis is x be default but can be changed by adding 4 (for y axis) or 8 (for z axis).
-st (Sleep Time between read access) is the time between each attempt to check if the calculation lauched has completed.

Input files
  str.in  The initial structure geometry in standard ATAT format (see mmaps -h)
 Optionally the following files can be read to continue a previous run (see below for a description):
  epidir.out
  epipos.out

Final output files
  cstr_relax.out  The optimized inflection point geometry at the end of the calculations.
  cenergy.out     The corresponding final energy.
  stdout          Log file (written to infdet.log if called by robustrelax_xxxx)

A few notes about the log file (assuming it is redirected to infdet.log):
  -The inner optimization problem output is bracketted by the phrases 'begin on_sphere' and 'end on_sphere'.
  -For a quick overview of the progress, use:      grep curv infdet.log
  -For a more detailed view (each c.g. step), use: grep norm infdet.log
   The inner optimization steps are indicated by s_gnorm while the outer by l_gnorm.
  -To see each function evaluation, use:           grep dfx infdet.log
  -To see the whole history of epicycle positions and directions:
                                                   grep -e epipos -e epidir infdet.log

Intermediate input/output files
 The infdet code relies on an external program to obtain its energy and force data. At each optimization step, it writes:
  busy            A semaphore file indicating that the external program should run now.
  str.out         The current geometry to be run by the external code
 When done, the external program deletes the busy file and infdet knows it has to read:
  force.out       the forces acting on each atom (one 3d vector per line)
  stress.out      the stress tensor acting on the cell
  energy          the total energy
  str_relax.out   the atomic coordinate (same as str.out but perhaps re-ordered - forces will be re-ordered accordingly)

 As the optimization progresses, the current status is written to various files:
  str_current.out   the current best approximation to the inflection point (in standard ATAT format)
  epipos.out        the current best approximation to the inflection point (as a vector, in internal format)
  epidir.out        the current direction of the epicycle (softest phonon mode)
                    Note that the whole history of these values are available in the log file, prefixed by
                    epipos= and epidir= , which can be used to restart an aborted or misbehaving run.