#
# Description of the basis set:
#
# Double-zeta plus polarization for the valence states.
# Single-zeta for the semicore states.
#
# For Ba: 
#    5s: one radial function   | semicore
#    5p: one radial function   | semicore
#    6s: two radial functions
#    5d: one radial functions
#    6p: 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 Ba has been optimized for 
# bulk cubic BaTiO3 at the experimental lattice constant (4.000 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:
# 3.981982 Ang = 7.5248584122136828 bohr
# Compared with the experimental lattice constant, 4.000 Ang,
# the deviation is of -0.4%.
#
# Compared with other simulations, using the same XC functional
#
# Siesta:  3.982 Ang
# Crystal: 3.990 Ang (both with Ti pseudopotentials and without Ti pseudopot.)
# Differences smaller than 0.2 %
# 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          ABINIT    Expt.
#                 400 Ry    1200 Ry  Ti all electron  Ti pseudo
#
# a (Ang)         3.964072  3.962131    3.982         3.978     3.973      3.986
# c (Ang)         4.073185  4.076979    4.030         4.049     4.063      4.026
# c/a             1.0275    1.0290      1.012         1.018     1.023      1.010
# Volume (Ang**3) 64.005    64.0024     63.9          64.1      64.13      64.0 
# delta Ti        0.0182    0.0182      0.013         0.016     0.015      0.015
# delta O_para   -0.0323   -0.0329     -0.022        -0.025    -0.030     -0.023
# delta O_perp   -0.0183   -0.0187     -0.013        -0.016    -0.019     -0.014
#------------------------------------------------------------------------------
# Structure of the rhombohedral phase:
#   Data for Wu-Cohen taken from 
#   Z. Wu and R. E. Cohen, Physical Review B 73, 235116 (2006).
#
#                  SIESTA        Wu-Cohen          Expt.
#                 400 Ry    
#
# a (Ang)         4.005433                       
# alpha           89.8026        89.86   (-0.06 %)  89.87
# Volume (Ang**3) 64.2600        64.04   (+0.34 %)  64.04
# u_z Ba          0.00000        0.0000             0.0000
# u_z Ti          0.48694        0.4883  (-0.27 %)  0.487
# u_z O1O1        0.51196        0.5116  (+0.07 %)  0.511
# u_z O2          0.01988        0.0184  (+8.04 %)  0.018
#
#------------------------------------------------------------------------------
# Eggbox effect for a mesh cutoff of 400 Ry
#
# For the bulk tetragonal structure, we computed the effect of the
# eggbox effect.
# The peak-to-peak difference in energy is of the order of 0.000502 eV,
# and the peak-to-peak difference in the maximum component of the force
# on any atom is of the order of 0.022 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
# 
#                              SIESTA                     CRYSTAL          Expt.
#                                              No Ti pseudo. Ti  pseudo. 
#  eigenvalue # 1  omega= -221.86794316303744         128i      192i       Soft
#  eigenvalue # 2  omega= -221.86791386994904
#  eigenvalue # 3  omega= -221.86773816855853
#  eigenvalue # 4  omega= -0.03606287570996306         0         0           0
#  eigenvalue # 5  omega= -0.028509148263777297
#  eigenvalue # 6  omega= -0.028318535012277844
#  eigenvalue # 7  omega= 190.95091727982336          186       186         182
#  eigenvalue # 8  omega= 190.95183284633507
#  eigenvalue # 9  omega= 190.9539755565065
#  eigenvalue # 10  omega= 297.637902774628           282       280         306
#  eigenvalue # 11  omega= 297.6381444000293
#  eigenvalue # 12  omega= 297.63961264092103
#  eigenvalue # 13  omega= 466.7180888732863          469       463         482
#  eigenvalue # 14  omega= 466.71813993557527
#  eigenvalue # 15  omega= 466.7186898335554
#
#------------------------------------------------------------------------------
# For the bulk theoretical cubic structure, we have computed 
# the Born effective charges
#
#                       SIESTA                         CRYSTAL: 
#           Direct result    Normalized        No pseudo Ti       pseudo Ti
# For Ba:      2.7031          2.7040             2.76              2.73
# For Ti:      7.2590          7.2599             7.10              7.31
# For O para: -5.8722         -5.8713            -5.66             -5.82
# For O perp: -2.0471         -2.0463            -2.10             -2.11
#            --------------------------         ---------------------------
# Sum:        -0.0043          0.0000             0.00              0.00 



