This file describes the contents of the tarballs and lists compatible
version of the software they relate to.  Unless otherwise specified,
numbers in data files are in Hartree atomic units, and the various
quantities are defined as specified in the paper.

1D_quadrature.tar.gz
====================
This tarball contains the numerical one-dimensional quadrature grid
solver we have used in Section IV of the paper.

This tarball consists of a "1D_quadrature" directory containing the
following files:

* anh_quadrature.f90:
  Stand-alone Fortran 95 code.  Note that the code requires a LAPACK
  library installed that can be linked with "-llapack".

* compile.sh:
  Compilation script.  Note that the script may need to be adapted
  depending on the Fortran compiler to use.

The code is intended to be run interactively.  Given the polynomial
coefficients of a 1D potential, the code generates and tests
quadrature grids of up to 10 points.  The code also produces Grace
plots formatted like Figs. 1-5 of the paper.

NB, the potentials used for the tests reported in Figs. 1 and 2 of the
paper were defined with coefficient strings:
  0 0 -0.5 0 0.25
and
  0 0 0.5 0.25 0.125
respectively.

HF.tar.gz and NH3.tar.gz
========================
These tarballs contain the data for the n-dimensional tests carried
out in Section V of the paper.

These tarballs contain an "HF" and "NH3" base directory, respectively,
and these contain subdirectories named "Direct", "AllModes", and
"OneMode" or "TwoModes", matching the terminology used in the paper
for direct Monte Carlo integration, Monte Carlo sampling of
increasingly fine grids for all modes, and Monte Carlo sampling of
two-point grids for all modes and increasingly fine grids for modes
identified as non-quadratic.

Alongside these directories, each tarball also contains a "System"
directory containing the files:
* *.param, *.cell, *.castep, *.bands: CASTEP input/output files
  at the equilibrium atomic configuration.
* disp_patterns.dat: characterization of the normal modes of the
  system, listing normal-mode frequencies and associated atomic
  displacements obtained from the CASTEP output using the CAESAR
  development code.

The "AllModes", "OneMode", and "TwoModes" directories contain
subdirectories named "p<p>", where <p> is the number of points in
the grid -- note that "p2" is omitted in the "OneMode" and "TwoMode"
directories since the results are by definition identical to those
in AllModes/p2.

The Direct and {AllModes,OneMode,TwoModes}/p<p> directories contain
the following directories:

* Raw/
  This directory contains subdirectories named run.<n>, where <n>
  is an index, each of which contains CASTEP input and output files
  to compute the band gap at a different displaced nuclear
  configuration.  The CASTEP files are:
  - *.param, *.cell: CASTEP input parameters and atomic positions
  - *.castep: CASTEP output file
  - *.bands: CASTEP band structure data

* Stats/
  This directory contains data files, obtained from the system data
  and the CASTEP calculations, which are processed to produce the
  expectation values and variances reported in the paper.  The files
  are:
  * freqs_grid.dat: list of mode frequencies.  Note that the first
    lines correspond to acoustic modes of (numerically) zero
    frequency.
  * phonon_coords.dat: list of normal-mode coordinates sampled in the
    Monte Carlo run, with each line corresponding to a random nuclear
    configuration.  Where the first three numbers in all lines are
    *not* zero, acoustic modes have been omitted.
  * delta_gap.dat: list of values of the band gap obtained from the
    CASTEP calculations, with each line corresponding to a nuclear
    configuration matching the order in phonon_coords.dat.  In some
    cases there are fewer lines in delta_gap.dat than in
    phonon_coords.dat, implying that the unmatched configurations
    listed in phonon_coords.dat have not been used.

Software and versions
=====================
- CASTEP files are compatible with CASTEP version 6.11 and later.
  For information on how to get a copy of CASTEP visit:
    http://www.castep.org

- The anh_quadrature.f90 Fortran code is written in standard Fortran
  95 and it should be possible to compile it with any compliant
  Fortran compiler.  We used the gfortran compiler v7.2.0 and the
  Atlas LAPACK library v3.10.3.

- Plots produced by the and_quadrature.f90 Fortran code can be opened
  with Grace v5.1.25; for more information visit:
    http://plasma-gate.weizmann.ac.il/Grace/

- For information on the CAESAR anharmonic corrections research code
  email bm418 at cam.ac.uk .