#
# Description of the basis set:
#
# Double-zeta plus polarization for the valence states.
# Single-zeta for the semicore states.
#
# For Pb: 
#    5d: one radial functions  | semicore
#    6s: two radial function   
#    6p: two radial function   
#    6d: one radial function
#    5f: one radial function
# For Ti:
#    3s: one radial functions  | semicore
#    3p: one radial functions  | semicore
#    4s: two radial functions
#    3d: two radial function
#    4p: one radial function
# For O:
#    2s: two radial functions
#    2p: two radial functions
#    3d: one radial function
#
# The basis set for Pb has been optimized for 
# bulk cubic PbTiO3 at the experimental lattice constant (3.93 Ang) 
# with a pressure of 0.03 GPa
# The basis set for Ti and O has been frozen to the optimized one for SrTiO3
#
#------------------------------------------------------------------------------
#
# Tests performed on the basis set:
# 
#------------------------------------------------------------------------------
#
# Theoretical lattice constant of the cubic structure:
# 3.919505 Ang = 7.406793946070974 bohr
# Compared with the experimental lattice constant, 3.93 Ang,
# the deviation is of -0.26 %.
#
# Compared with other simulations, using the same XC functional
#
# Siesta:  3.919505 Ang
# Crystal: 3.923 Ang (all electron)
# Crystal: 3.921 Ang (Ti pseudopotentials) 
# Differences smaller than 0.09 %
# Reference for Crystal simulation taken from
#  D. Bilc et al., Physical Review B 77, 165107 (2008).
#
#------------------------------------------------------------------------------
# Structure of the tetragonal phase:
#   Data for CRYSTAL taken from 
#   D. Bilc et al., Physical Review B 77, 165107 (2008).
#   Data for ABINIT results obtained by Eric Bousquet.
# 
#                      SIESTA                   CRYSTAL         Wu-Cohen   Expt.
#                 400 Ry    1200 Ry  Ti all electron  Ti pseudo
#
# a (Ang)         3.864880  3.865590    3.870         3.840     3.890      3.88 
# c (Ang)         4.218389  4.215373    4.203         4.343     4.194      4.155
# c/a             1.0915    1.0905      1.086         1.131     1.078      1.071
# Volume (Ang**3) 63.0113   62.9894     62.9          64.1      63.47      62.6 
# delta Ti        0.0315    0.0313      0.044         0.047     0.0324     0.040
# delta O_para    0.1118    0.1111      0.121         0.141     0.1083     0.112
# delta O_perp    0.1157    0.1151      0.133         0.148     0.1106     0.112
#
# Deviations of SIESTA (400 Ry) with respect
#                   Wu-Cohen     Experiment
#
# a (Ang)           -0.64 %      -0.38 %
# c (Ang)           +0.58 %      +1.52 %
# c/a               +1.25 %      +1.91 %
# Volume (Ang**3)   -0.72 %      +0.65 %
# delta Ti          -2.77 %     -21.25 %
# delta O_para      +3.23 %      -0.18 %
# delta O_perp      +4.61 %      +3.30 %
#------------------------------------------------------------------------------
# Eggbox effect for a mesh cutoff of 400 Ry
#
# For the bulk tetragonal structure, we performed the effect of the
# eggbox effect.
# The peak-to-peak difference in energy is of the order of 0.000328 eV,
# and the peak-to-peak difference in the maximum component of the force
# on any atom is of the order of 0.028 eV/Ang.
# 
# The combination pseudo-basis set seems to be very well converged
# for this value of the MeshCutoff
#
#------------------------------------------------------------------------------
# For the bulk theoretical cubic structure, we have computed 
# the phonons at Gamma, X, M, and R.
# See the file in the directory Phonons-border-zone/phonons.tex
#
#------------------------------------------------------------------------------
# For the bulk theoretical cubic structure, we have computed 
# the Born effective charges
#
#                       SIESTA                         CRYSTAL: 
#           Direct result    Normalized        No pseudo Ti       pseudo Ti
# For Pb:      3.8986          3.8990             3.85              3.83
# For Ti:      7.1825          7.1828             6.70              7.17
# For O para: -6.0333         -6.0328            -5.81             -5.95
# For O perp: -2.5250         -2.5245            -2.52             -2.53
#            --------------------------         ---------------------------
# Sum:        -0.0022          0.0000            -0.30             -0.01 





