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--- developers:pseudos:psp8_format [2015/02/25 13:30] – created Matteo Giantomassi
+++ developers:pseudos:psp8_format [2020/08/10 18:04] (current) – Xavier Gonze
@@ Line 1: / Line 1: @@
+==== Information on the format 8 for pseudopotentials ====
+(Note: the implementation of format 8 was done by D. R. Hamann).
+The format 8 for ABINIT pseudopotentials is designed to allow users
+who wish to experiment with pseudopotentials, possibly with non-standard
+features, to have great flexibility in doing so.
+It does not correspond to any publicly available tabulation.
+The open-source ONCVPSP package available at www.mat-simresearch.com produces pseudopotentials in this
+format.
+An annotated example is presented in detail below, followed by a second
+example incorporating spin-orbit coupling.  An extended discussion follows
+below the examples, with a separate section discussing spin-orbit as produced by ONCVPSP.
+When first producing a pseudopotential in this format, it would be a very
+good idea to do a well-converged calculation of an isolated atom in a big
+box to confirm that you are correctly recreating the atomic valence levels you intend.
+The format is best explained by an example, which is presented in
+detail below.  (The example is excerpted from Psps_for_tests/20ca_sic.drh.
+Another example of pspcod=8 is Psps_for_tests/8o_sic.drh.)
+All but the last data block of this file are read in subroutine psp8in.f.
+The "comment" (#) lines below are not permitted in the actual file.
+Nor are blank lines.
+<code bash>
+#Header
+# line 1 - Title
+# line 2 - atomic number, pseudoion charge, date
+# line 3 - pspcod=8 identifies this format
+#          pspxc=2 identifies the exchange-correlation functional (see
+#           ixc list in the input variables documentation)
+#          lmax=2 gives the largest angular momentum potential present
+#          lloc=4 (which is >lmax) indicates that the local potential
+#           is independent of that for any angular momentum.  In other
+#           cases, it can be <=lmax, and the local potential can be
+#           that of a particular angular momentum channel.  (The choice
+#           of 4 is arbitrary, but the index of the corresponding data block
+#           below must be consistent with the value assigned in the header.)
+#          mmax=313, giving the number of radial grid points (arbitrary).
+#          r2well=0 is an historical header holdover, and is not used
+# line 4 - rchrg=6.18.. is the radius beyond which the model core
+#           charge (if used) is zero or negligible.  The maximum
+#           radial mesh point must equal or exceed this value.
+#          fchrg=1.0 signals that a model core charge is present.  Any
+#           value >0.0 will do, and the value is not used otherwise.
+#          qchrg=0.0 is a historical holdover, not used.
+# line 5 - number of Bloechl-Kleinman-Bylander projectors nproj for each
+#          angular momentum l=0 to l=lmax.  The value of nproj for lloc
+#          must be 0 (if lloc <= lmax).
+# line 6 - extension_switch=0, not initially used, but values >0 but may
+#          be utilized to signal the presence of additonal lines of header
+#          information for special-purpose use in the future.
+#          The value 2 is now used to indicate the presence os spin-orbit
+#          projectors (see SPIN-ORBIT section below).
+</code>
+    self-intraction-corrected psp for calcium (D. R. Hamann)
+.0000      2.0000    040701    zatom,zion,pspd
+     2     2     4   313     0    pspcod,pspxc,lmax,lloc,mmax,r2well
+.18295050  1.00000000  0.00000000    rchrg fchrg qchrg
+     1     1     0     0    nproj
+                            extension_switch
+<code shell>
+#First data block
+# first line - angular momentum l=0, ekb(ii) for ii=1,2(=nproj(1))
+# following lines labeled 1,2,...,mmax -
+#    1st column: radial grid index
+#    2nd column: radial grid mesh point (LINEAR mesh starting at 0.0)
+#    3rd column: first  BKB projector for l=0
+#    4th column: second BKB projector for l=0
+# The projectors should go smoothly to zero, or decay to negligible
+#  values within the range of the radial grid.
+# In general there are nproj ekb and projector columns for each l, as
+#  many as you want.
+# If nproj is zero, AND lloc/= the current l, this block is omitted.
+# While some may be absent, l blocks must be in ascending order.
+</code>
+                         1.8442549429363D+01 -1.5467656752626D+01
+  0.0000000000000D+00  0.0000000000000D+00  0.0000000000000D+00
+  2.0000000000000D-02  3.2695476840515D-03 -7.7803072439537D-05
+  4.0000000000000D-02  6.5413292698932D-03 -1.5573364986856D-04
+     .....
+     .....
+<code shell>
+#Second data block
+# first line - angular momentum l=1, ekb(ii) for ii=1,1(=nproj(2))
+# following lines labeled 1,2,...,mmax -
+#    1st column: radial grid index
+#    2nd column: radial grid mesh point
+#    3rd column: first (only)  BKB projector for l=1
+</code>
+                         1.0250215833500D+01
+  0.0000000000000D+00  0.0000000000000D+00
+  2.0000000000000D-02  4.1259561971920D-05
+  4.0000000000000D-02  1.6501618805883D-04
+     .....
+     .....
+<code shell>
+# Third data block
+# as above, for l=2
+</code>
+                        -4.9318560092991D-01
+  0.0000000000000D+00  0.0000000000000D+00
+  2.0000000000000D-02 -2.8426374194219D-04
+  4.0000000000000D-02 -2.2672423014226D-03
+   .....
+   .....
+<code shell>
+#Fourth data block
+# first line - index corresponding to lloc in header.  In this case,
+#  the local potential does not correspond to that for any angular
+#  momentum.  lloc can be arbitrary in this case, but MUST be >lmax,
+#  and this block must follow the blocks for projectors with l <=lmax.
+# following lines labeled 1,2,...,mmax -
+#    1st column: radial grid index
+#    2nd column: radial grid mesh point
+#    3rd column: local potential
+# If lloc<lmax, the corresponding block must occur in its proper l order
+#  among the blocks of nonlocal projectors.
+# The last line should, ideally, be equal to -zion/rad(mmax), and the
+#  numerical data should approach -zion/r as continuously as possible,
+#  since the Fourier transform is extended to infinity analytically
+#  assumming this functional form.  This isn't precisely satisfied for
+#  the expeimental potential in the example, and the result will be a
+#  small-amplitude Gibbs oscillation as a function of the Q of the
+#  Fourier-transformed local potenial with a period of 2*Pi/rad(mmax).
+</code>
+  0.0000000000000D+00 -9.3285752771727D-01
+  2.0000000000000D-02 -9.3284556214441D-01
+  4.0000000000000D-02 -9.3280966542583D-01
+     .....
+     .....
+  6.2400000000000D+00 -3.3275722650983D-01
+<code shell>
+#Fifth (last) data block (read in psp8cc.f)
+# lines labeled 1,2,...,mmax -
+#    1st column: radial grid index
+#    2nd column: radial grid mesh point (LINEAR mesh starting at 0.0)
+#    3rd column: rhoc = 4*Pi*model core charge density
+#    4th column: d rhoc / dr
+#    5th column: d^2 rhoc / dr^2
+#    6th column: d^3 rhoc / dr^3
+#    7th column: d^4 rhoc / dr^4
+# This block is only read if the header variable fchrg >0.0.
+</code>
+  0.0000000000000D+00  1.8263604328455D+00 -1.3822038662342D-06 -3.4248477651502D-05  2.2949926081983D-05 -1.3721984594931D+01
+  2.0000000000000D-02  1.8263581757935D+00 -1.8290946429655D-05 -2.7430630291457D-03 -2.7416158741933D-01 -1.3679142685104D+01
+  4.0000000000000D-02  1.8263568047539D+00 -1.4618869292620D-04 -1.0954897796014D-02 -5.4658870398836D-01 -1.3549201500559D+01
+     .....
+     .....
+SPIN-ORBIT
+----------
+Spin-orbit coupling is present in the file Psps_for_tests/78_Pt_r.oncvpsp.psp8.
+This pseudopotential treats the 5s and 5p core states as valence.  More
+details are given in the spin-orbit portion of the discussion section
+<code shell>
+#Header -  lines 1-4 as above
+# line 5 - number of Vanderbilt-Kleinman-Bylander projectors nproj for
+#          the scalar-relativistic non-local potential for each
+#          angular momentum l=0 to l=lmax. The value of nproj for lloc
+#          must be 0 (if lloc <= lmax).
+# line 6 - extension_switch=2 indicating spin-orbit projectors are present
+# line 7 - number of Vanderbilt-Kleinman-Bylander projectors nprojso for
+#          the spin-orbit non-local potential for each angular momentum
+#          l=1 to l=lmax.
+</code>
+  Pt    NOPTPSP  r_core=  2.21  2.52  2.40  3.02
+.0000     18.0000      140202    zatom,zion,pspd
+     2     3     4   500     0    pspcod,pspxc,lmax,lloc,mmax,r2well
+.99000000  0.00000000  0.00000000    rchrg fchrg qchrg
+     4     3     3    nproj
+                 extension_switch
+     4     3    nprojso
+<code shell>
+#Data blocks 1-4 are as-above for the scalar-relativistic non-local projector
+# coefficients ("ekb"), grid indices, grid points, and projectors.
+#Data block 5 is the local potential lloc=4 as above.
+#Data blocks 6-8 are as-above for the spin-orbit non-local projector
+# coefficients ("ekb"), grid indices, grid points, and projectors.
+#Non-linear core corrections are not used in this example, but if they
+#were, the model core charge and its derivatives would be the last data
+#block
+</code>
+DISCUSSION
+----------
+This introduces a norm-conserving pseudopotential input file format
+designed by D. R. Hamann which offers additional flexibility over
+previously available Abinit psp formats, as well as possible improvements
+in performance in certain respects.  Its new features are:
+(1)
+Numerical psp's, which offer the ability to experiment beyond existing
+tabulated collections.  Available psp's given as basis function sums
+are easily convertible to this format.
+(2)
+Linear radial grids, which have the following advantages:
+    (a) Computational efficiency compared to log grids because the
+        core region of those grids is highly redundant for psp's.
+    (b) Increased accuracy at large ecut values.  The spacing of
+        mesh points for log grids at larger radii, where there are
+	usually still significant contributions to the psp's, becomes
+	too large and introduces aliasing noise into the Fourier-
+	transform psp's.  In fact, this code is written to double,
+	triple, etc. the linear grid and interpolate prior to performing
+	the transform to ensure accuracy, based on ecut.
+    (c) Storage economy (probably not important in modern computers, but
+        the files are easier to read).
+    (d) While redundant, repeating the grid in the data block with each
+        function facilitates inspection and plotting of the various inputs.
+(3)
+Allowance for any number of nonlocal projectors for each anugular
+momentum channel, previously available for several formats but without
+the current flexibility.
+(4)
+Direct input of the Bloechl-Kleinman-Bylander projectors rather
+than wave functions and semi-local potentials.  This allows greater
+flexibility important for some exploratory applications such
+as self-interaction-corrected psp's.  The projectors are applied
+to the wave functions as the following operators
+                   Sum_(nlm)    |fkb(n,l),m> ekb(n,l) <fkb(n,l),m|
+The conventional Kleinman-Bylander choice for a single projector (single n) would be
+                   fkb(r,l) = (V(r,l)-V_loc(r))u(r,l),
+where V(r,l) is the semi-local norm-conserving pseudopotential for
+angular momentum l, V_loc(r) is the local potential, and u(r,l) is
+the radial Schroedinger equation solution (bound or scattering).[1,2]
+Note that u(r) has the conventional "r" factor, u(r)=r*psi(r).
+In this case, the "energies" ekb (which have dimensions 1/energy
+for the above definition of fkb) are
+                   ekb(l) = 1 / [Integral_(0, inf) fkb(r,l)*u(r,l) dr]
+(no 4*Pi factor).  For the Bloechl generalization, see [3].
+Other possible generalizations include the treatment of self-
+interaction corrections as additional projectors.[4]
+Finally, creating numerical projectors as part of the psp generation
+process (rather than within Abinit) allows one to solve the radial
+Schrodinger equation in its fully nonlocal form and compare logarithmic
+derivatives of the pseudo and all-electron wave functions over a wide
+energy range.  This is a superior test of transferability, and will
+locate shallow "ghost resonances" above the reference valence
+states, which would be missed in the standard ghost tests [5] but
+can lead to poor results.
+(5)
+Ability to use an arbitrary local potential rather than that for
+one particular angular momentum channel.  This can be helpful in
+eliminating ghost states.[5]
+In the example above, a calcium pseudopotential, the "conventional"
+choice of the d-channel (lloc=2) for the local potential is particuarly
+bad because the incipient d shell represented by a shallow d
+resonance leads to a very deep d potential.  With this potential as
+local, it is nearly impossible to avoid ghost states.  Using p as
+the local potential would avoid this, but would place a spurious
+core-orthogonalization repulsive term in channels for higher angular
+momenta (f, g, h, ...) which could lead to errors in, for example,
+lattice constants.  The local potential here was formed by a
+smooth (polynomial) extrapolation of the tail-region all-electron
+potential to the origin.  While some other Abinit psp formats
+include the ability to form the local potential as a simple average
+over semi-local potentials, the d potential would likely still cause
+problems in this case.
+(6)
+Spherical bessel functions for Fourier transforms in the psp8*.f
+routines are computed by a highly accurate recursion method in sbf8.f,
+and all angular momentum channels are treated simultaneously,
+increasing accuracy and efficiency compared to sin/cos formulations,
+especially for large and small arguments.
+(7)
+The ability to experiment with various model core charges for the
+non-linear core correction[6] is advantageous.  Functions that are
+not sufficiently smooth can lead to potentially severe convergence
+errors, especially in response function calculations.  For other
+formats, Abinit internally generates higher derivatives of the model
+core charge up to the 4th derivative, and piecewise-constructed
+model functions that LOOK smooth can cause havoc.  The requirement
+that all the derivatives to be present in the input file permits
+early detection of such problems, and aids their remediation.
+(8)
+Release 7.x introduces the ablity to include spin-orbit coupling.  The
+Pt pseudopotential used as an example above was initially generated
+with two non-local projectors each from Dirac wave functions with j=l+1/2
+and j=l-1/2 using Vanderbilt generalized norm conservation, which
+gives much greater accuracy than the Bloechl construction discussed
+above.[7]  Weighted sums and differences of these non-local operators
+were separately re-diagonalized to produce efficient orthonormal
+projectors for the scalar-relativistic and spin-orbit terms which are
+required internally by abinit.  For a detailed description of the
+projectors, see Ref. 7.  The operation of SR and SO terms on the
+spinor wave functions is a straightforward generalization of
+                   Sum_(nlm)    |fkb(n,l),m> ekb(n,l) <fkb(n,l),m|
+where "fkb" and "ekb" are appropriately reinterpreted.  Since the
+"fkb" for the Pt example are orthonormal, the "ekb" have the
+dimensions energy.  Projectors with negligibly small energies
+(<2E-5 Ha at present) are neglected.  There is full flexibiltiy
+to use other methods to generate the SR and SO terms.
+REFERENCES
+   [1] "Generalized Norm-Conserving pseudopotentials," D. R. Hamann,
+       Phys. Rev. B 40, 2980 (1989); "Norm-Conserving Pseudopotentials,"
+       D. R. Hamann, M. Schlueter, and C. Chiang, Phys. Rev. Lett. 43,
+(1979).
+   [2] "Efficacious Form for Model Pseudopotentials," L. Kleinman
+       and D. M. Bylander, Phys. Rev. Lett. 48, 1425 (1982).
+   [3] "Generalized Separable Potentials for Electronic-Structure
+       Calculations," P. E. Bloechl, Phys. Rev. B 41, 5414 (1990).
+   [4] "Ab Initio Electronic-Structure Calculations for II-VI
+       Semiconductors Using Self-Interaction-Corrected Pseudopotentials,"
+       D. Vogel, P. Krueger, and J. Pollmann, Phys. Rev. B 52, 14316 (1995).
+   [5] "Ghost States for Separable, Norm-Conserving, ab initio
+       Pseudopotentials," X. Gonze, P. Kaeckell, and M. Scheffler,
+       Phys. Rev. B 41, 12,264 (1990); "Analysis of Separable Potentials,"
+       X. Gonze, Phys. Rev. B 44, 8503 (1991).
+   [6] "Nonlinear Ionic Pseudopotentials in Spin-Density-Functional
+       Calculations," S. G. Louie, S. Froyen, and M. L. Cohen, Phys.
+       Rev. B26, 1738 (1982).
+   [7] "Optimized norm-conserving Vanderbilt pseudopotentials", D. R.
+       Hamann, Phys. Rev. B 88, 085177 (1913), and references therein.