The complete si.castep file can be found in the link. The file begins with a header
which contains the details of the version of castep which was compiled into the executable. Authors and contributors are
acknowledged and copyright and licensing information is summarised. The details of a publication which should be cited
in any work arising from use of CASTEP are given.
A full summary of all of the parameters (even those left to default) to be used in the calculation are listed in groups;
general parameters, Exchange-Correlation parameters, Pseudopotential parameters, Basis Set parameters, Electronic parameters,
Electronic Minimization parameters, Density Mixing, Population Analysis parameters, Geometry Optimization parameters.
Notice that our request for medium basis set precision has produced the default cutoff energy of 120eV.
The cell parameters follow, including a list of the k-point co-ordinates
-------------------------------
k-Points For BZ Sampling
-------------------------------
MP grid size for SCF calculation is 2 2 2
Number of kpoints used = 3
+++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Number Fractional coordinates Weight +
+-----------------------------------------------------+
+ 1 0.250000 0.250000 0.250000 0.2500000 +
+ 2 -0.250000 -0.250000 0.250000 0.2500000 +
+ 3 0.250000 -0.250000 0.250000 0.5000000 +
+++++++++++++++++++++++++++++++++++++++++++++++++++++++
After symmetry and constraint information the results of the calculation begin. For the initial configuration of the atoms in the supercell the electronic minimisation begins
------------------------------------------------------------------------ <-- SCF
SCF loop Energy Energy gain Timer <-- SCF
per atom (sec) <-- SCF
------------------------------------------------------------------------ <-- SCF
Initial 0.00000000E+000 1.13 <-- SCF
The iterations in the electronic structure continue until 2 consecutive iterations fall within the electron convergence window
1 -2.09000140E+002 1.04500070E+002 1.23 <-- SCF
2 -2.15287289E+002 3.14357473E+000 1.34 <-- SCF
3 -2.14863841E+002 -2.11724154E-001 1.45 <-- SCF
4 -2.14844155E+002 -9.84322032E-003 1.55 <-- SCF
5 -2.14844793E+002 3.19055641E-004 1.62 <-- SCF
6 -2.14844863E+002 3.53437051E-005 1.69 <-- SCF
7 -2.14844865E+002 6.42301690E-007 1.75 <-- SCF
8 -2.14844864E+002 -1.44644986E-007 1.81 <-- SCF
------------------------------------------------------------------------ <-- SCF
Final energy = -214.8448643011 eV
The electronic minisation for this ionic configuration is now complete. A convergence check is performed
******************************** Forces ********************************* * * * Cartesian components (eV/A) * * --------------------------------------------------------------------- * * x y z * * * * Si 1 0.00000 0.00000 0.08113 * * Si 2 0.00000 0.00000 -0.08113 * * * ************************************************************************* BFGS: finished iteration 0 with enthalpy= -2.14844864E+002 eV +-----------+-----------------+-----------------+------------+-----+ <-- BFGS | Parameter | value | tolerance | units | OK? | <-- BFGS +-----------+-----------------+-----------------+------------+-----+ <-- BFGS | dE/ion | 0.000000E+000 | 2.000000E-005 | eV | No | <-- BFGS | |F|max | 8.113133E-002 | 5.000000E-002 | eV/A | No | <-- BFGS | |dR|max | 0.000000E+000 | 1.000000E-003 | A | Yes | <-- BFGS +-----------+-----------------+-----------------+------------+-----+ <-- BFGS
|F|max is the maximum allowed force on any atom and |dR|max is the tolerance for the change in any atomic position between iterations. Since the calculation has not converged a new set of ionic co-ordinates must be generated. A new BFGS iteration is started and a summary of the previous BFGS step is given
================================================================================ Starting BFGS iteration 1 ... ================================================================================ +------------+-------------+-------------+-----------------+ <-- min BFGS | Step | lambda | F.delta | enthalpy | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS | previous | 0.000000 | 0.000002 | -214.844864 | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS
What is meant by lambda and F.delta ?
F.delta is the search direction in BFGS and this doesn't change during a BFGS iteration. F is the force vector. Ideally, the step length lambda should take the value that makes F.delta = 0 (to ensure conjugacy of the search directions). In practice, the value of F.delta for which the energy is lowest is chosen and so F.delta is not necessarily equal to zero at the end of each BFGS step. By default a step of lambda = 1 is taken first
-------------------------------------------------------------------------------- BFGS: starting iteration 1 with trial guess (lambda= 1.000000) --------------------------------------------------------------------------------
The electronic minimisation is performed and the total energy calculated. Now the line minimisation is performed
+------------+-------------+-------------+-----------------+ <-- min BFGS | Step | lambda | F.delta | enthalpy | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS | previous | 0.000000 | 0.000002 | -214.844864 | <-- min BFGS | trial step | 1.000000 | 0.000001 | -214.844908 | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS -------------------------------------------------------------------------------- BFGS: improving iteration 1 with line minimization (lambda= 6.048479) --------------------------------------------------------------------------------
Which results in
+------------+-------------+-------------+-----------------+ <-- min BFGS | Step | lambda | F.delta | enthalpy | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS | previous | 0.000000 | 0.000002 | -214.844864 | <-- min BFGS | trial step | 1.000000 | 0.000001 | -214.844908 | <-- min BFGS | line step | 6.048479 | 0.000000 | -214.845023 | <-- min BFGS +------------+-------------+-------------+-----------------+ <-- min BFGS BFGS: finished iteration 1 with enthalpy= -2.14845023E+002 eV
This is repeated for each BFGS step. The calculation proceeds until the end of BFGS iteration 2, after which the change in the energy falls within the convergence tolerance and
BFGS: finished iteration 2 with enthalpy= -2.14845023E+002 eV +-----------+-----------------+-----------------+------------+-----+ <-- BFGS | Parameter | value | tolerance | units | OK? | <-- BFGS +-----------+-----------------+-----------------+------------+-----+ <-- BFGS | dE/ion | 1.709020E-008 | 2.000000E-005 | eV | Yes | <-- BFGS | |F|max | 3.838766E-003 | 5.000000E-002 | eV/A | Yes | <-- BFGS | |dR|max | 7.445744E-005 | 1.000000E-003 | A | Yes | <-- BFGS +-----------+-----------------+-----------------+------------+-----+ <-- BFGS BFGS: Geometry optimization completed successfully.
All that is left to do is to print the final supercell configuration
================================================================================
BFGS: Final Configuration:
================================================================================
-------------------------------
Cell Contents
-------------------------------
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x Element Atom Fractional coordinates of atoms x
x Number u v w x
x----------------------------------------------------------x
x Si 1 0.249792 0.249792 0.250624 x
x Si 2 0.000208 0.000208 -0.000624 x
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BFGS: Final Enthalpy = -2.14845023E+002 eV
The bonding information is revealing
Atomic Populations
------------------
Species Ion s p d f Total Charge (e)
==============================================================
Si 1 1.22 2.78 0.00 0.00 4.00 0.00
Si 2 1.22 2.78 0.00 0.00 4.00 0.00
==============================================================
Bond Population Length (A)
====================================
Si 1--Si 2 3.22 2.13974
====================================
We can see that the bonds are sp hybridised as we might expect in Si. The bond length is 2.13974 Å. The accepted value for the Si-Si bulk bond length is 2.332 Å. Our calculation is 8% out. More about this in a later section.