From 2a954d19dd376ece2a264989416d0982d55f57c4 Mon Sep 17 00:00:00 2001 From: Valerio Vitale Date: Wed, 27 Nov 2019 12:23:43 +0000 Subject: [PATCH 1/6] Tutorial for extracting SCDM parameters from projectability using projwfc.x --- doc/tutorial/W_bs.pdf | Bin 0 -> 170352 bytes doc/tutorial/W_fit.png | Bin 0 -> 100777 bytes doc/tutorial/tutorial.tex | 86 + doc/wannier90.bib | 26 +- examples/example31/W.nscf | 1035 ++ examples/example31/W.proj | 6 + examples/example31/W.pw2wan | 7 + examples/example31/W.scf | 31 + examples/example31/W.win | 1040 ++ examples/example31/generate_weights.sh | 14 + pseudo/W_pbe_v1.2.uspp.F.UPF | 12629 +++++++++++++++++++++++ 11 files changed, 14873 insertions(+), 1 deletion(-) create mode 100644 doc/tutorial/W_bs.pdf create mode 100644 doc/tutorial/W_fit.png create mode 100644 examples/example31/W.nscf create mode 100644 examples/example31/W.proj create mode 100644 examples/example31/W.pw2wan create mode 100644 examples/example31/W.scf create mode 100644 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v_KeD?r;3&L+f_$>&3y4(MsFb#u(=w;rvUg=Z4 Qhu}X65$PKl*X}(0KW^>nQUCw| literal 0 HcmV?d00001 diff --git a/doc/tutorial/tutorial.tex b/doc/tutorial/tutorial.tex index 8848f8d76..0d35085e5 100644 --- a/doc/tutorial/tutorial.tex +++ b/doc/tutorial/tutorial.tex @@ -6,6 +6,7 @@ \usepackage{amsmath} \usepackage{graphicx} \usepackage{fancyhdr} +\usepackage{subfig} \usepackage[T1]{fontenc} % important for having searchable underscores \usepackage{bm}% bold math \usepackage[sort&compress,numbers]{natbib} @@ -3518,6 +3519,91 @@ \subsection*{Notes} \end{quote} } \end{itemize} +\sectiontitle{31: Tungsten --- SCDM parameters from projectability} + +\begin{itemize} + \item{Outline: {\it Compute the Wannier interpolated band structure of tungsten (W) + using the SCDM method to calculate the initial guess (see Example 27 for more details). The free parameters + in the SCDM method, i.e., $\mu$ and $\sigma$, are obtained by fitting + a complementary error + function to the projectabilities. The number of MLWFs is given by the number + of pseudo-atomic orbitals (PAOs) in the pseudopotential, $21$ in this case. All the steps shown in this example have been automated in the AiiDA\cite{Pizzi_AiiDA} workflow that can be downloaded from the MaterialsCloud website\cite{MaterialsCloudArchiveEntry}}.} + \item{Directory: {\tt examples/example31/}} + \item{Input files} + \begin{itemize} + \item{ {\tt W.scf} {\it The \pwscf\ input file for ground state + calculation}} + \item{ {\tt W.nscf} {\it The \pwscf\ input file to obtain Bloch + states on a uniform grid}} + \item{ {\tt W.pw2wan} {\it The input file for {\tt pw2wannier90}}} + \item{ {\tt W.proj} {\it The input file for {\tt projwfc}}} + \item{ {\tt generate\_weights.sh} {\it The bash script to extract the projectabilities from the output of {\tt projwfc} }} + \item{ {\tt W.win} {\it The {\tt wannier90} input file}} + \end{itemize} +\end{itemize} + +\begin{enumerate} + \item Run \pwscf\ to obtain the ground state of tungsten\\ + {\tt pw.x -in W.scf > scf.out} + + \item Run \pwscf\ to obtain the Bloch states on a $10\times10\times10$ uniform $k$-point + grid\\ + {\tt pw.x -in W.nscf > nscf.out} + + \item Run \wannier\ to generate a list of the required overlaps (written + into the {\tt W.nnkp} file)\\ + {\tt wannier90.x -pp W} + + \item Run {\tt projwfc} to compute the projectabilities of the Bloch states + onto the Bloch sums obtained from the PAOs in the pseudopotential \\ + {\tt projwfc.x -in W.proj > proj.out} + + \item Run {\tt generate\_weights} to extract the projectabilitites from {\tt proj.out} + in a format suitable to be read by Xmgrace or gnuplot \\ + {\tt ./generate\_weights.sh} + + \item Plot the projectabilities and fit the data with the complementary error function + $$f(\epsilon;\mu,\sigma) = \frac{1}{2}\mathrm{erfc}(-\frac{\mu - \epsilon}{\sigma}).$$ + We are going Xmgrace to plot the projectabilities and perform the fitting. Open Xmgrace \\ + {\tt xmgrace } + + To Import the {\tt p\_vs\_e.dat} file, click on {\tt Data} from the top bar and then {\tt Import -> ASCII...}. + At this point a new window {\tt Grace: Read sets} should pop up . Select {\tt p\_vs\_e.dat} in the {\tt Files} section, click {\tt Ok} at the bottom and close the window. You should now be able to see a quite noisy function that is bounded between 1 and 0. You can modify the appearence of the plot by clicking on {\tt Plot} in the top bar and then {\tt Set appearance...}. In the {\tt Main} section of the pop-up window change the symbol type from {\tt None} to {\tt Circle} and symbol size from 100 to 25. Also change symbol color from black to blue. Change the line type from straight to none. Move to the {\tt Symbols} section and change the filling pattern from none to full (indentified by a full black square) and then close the window. For the fitting, go to {\tt Data -> Transformations -> Non-linear curve fitting}. In this window, select the source from the {\tt Set} box and in the {\tt Formula} box insert the following \\ + + {\tt y = 0.5 * erfc( ( x - A0 ) / A1 )} \\ + +Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ + + \item Open {\tt W.pw2wan} and append the following lines + {\tt + + scdm\_entanglement = erfc + + scdm\_mu = 20.0169 + + scdm\_proj = .true. + + scdm\_sigma = 6.6529 + + /} + + \item Run {\tt pw2wannier90} to compute the overlaps between Bloch + states and the projections for the starting guess (written in the + {\tt W.mmn} and {\tt W.amn} files)\\ + {\tt pw2wannier90.x -in W.pw2wan > pw2wan.out} + + \item Run \wannier\ to obtain the interpolated bandstructure (see Fig. \ref{fig:W_fit}-(b)).\\ + {\tt wannier90.x W} +\end{enumerate} + +\begin{figure} +\centering +\subfloat[]{\includegraphics[width=0.45\columnwidth]{./W_fit.png}} +\subfloat[]{\includegraphics[width=0.45\columnwidth]{./W_bs.pdf}} +\caption{ a) Each blue dot represents the projectability as defined in Eq. (22) of Ref. \cite{Vitale2019automated} of the state +$\vert n\mathbf{k} \rangle$ as a function of the corresponding energy $\epsilon_{n\mathbf{k}}$ for tungsten. The yellow line shows the fitted complementary error function. The vertical red line represents the value of $\sigma_{fit}$ while the vertical green line represents the optimal value of $\mu_{SCDM}$, i.e. $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit}$. b) Band structure of tungsten on the $\Gamma$-H-N-$\Gamma$ path from DFT calculations (solid black) and Wannier interpolation using the SCDM method to construct the initial guess (red dots).} +\label{fig:W_fit} +\end{figure} %\cleardoublepage \bibliographystyle{apsrev4-1} diff --git a/doc/wannier90.bib b/doc/wannier90.bib index 2d85d9aa7..fbaed14ea 100644 --- a/doc/wannier90.bib +++ b/doc/wannier90.bib @@ -651,4 +651,28 @@ @article{guo-prl2008 url = {https://link.aps.org/doi/10.1103/PhysRevLett.100.096401} } - +@misc{vitale2019automated, + title={Automated high-throughput wannierisation}, + author={Valerio Vitale and Giovanni Pizzi and Antimo Marrazzo and Jonathan Yates and Nicola Marzari and Arash Mostofi}, + year={2019}, + eprint={1909.00433}, + archivePrefix={arXiv} +} + +@article{MaterialsCloudArchiveEntry, + title = {Automated high-throughput Wannierisation}, + author = {V. Vitale and G. Pizzi and A. Marrazzo and J. R. Yates and N. Marzari and A. A. Mostofi}, + journal = {Materials Cloud Archive}, + volume = {}, + year = {2019}, + note = {doi:\href{http://doi.org/10.24435/materialscloud:2019.0044/v2}{10.24435/materialscloud:2019.0044/v2}} +} + +@article{Pizzi_AiiDA, +title = "AiiDA: automated interactive infrastructure and database for computational science", +journal = "Computational Materials Science", +volume = "111", +pages = "218 - 230", +year = "2016", +author = "Giovanni Pizzi and Andrea Cepellotti and Riccardo Sabatini and Nicola Marzari and Boris Kozinsky" +} diff --git a/examples/example31/W.nscf b/examples/example31/W.nscf new file mode 100644 index 000000000..28c62f893 --- /dev/null +++ b/examples/example31/W.nscf @@ -0,0 +1,1035 @@ +&CONTROL + calculation = 'nscf' + outdir = './out' + prefix = 'W' + pseudo_dir = '../../pseudo/' + restart_mode = 'restart' + wf_collect = .true. +/ +&SYSTEM + degauss = 2.0000000000d-02 + ecutrho = 2.4000000000d+02 + ecutwfc = 3.0000000000d+01 + ibrav = 0 + nat = 1 + nbnd = 21 + nosym = .true. + ntyp = 1 + occupations = 'smearing' + smearing = 'marzari-vanderbilt' +/ +&ELECTRONS + conv_thr = 1.0000000000d-10 + diago_full_acc = .true. + diagonalization = 'cg' +/ +ATOMIC_SPECIES +W 183.85 W_pbe_v1.2.uspp.F.UPF +ATOMIC_POSITIONS angstrom +W 0.0000000000 0.0000000000 0.0000000000 +K_POINTS crystal +1000 + 0.00000000 0.00000000 0.00000000 1.000000e-03 + 0.00000000 0.00000000 0.10000000 1.000000e-03 + 0.00000000 0.00000000 0.20000000 1.000000e-03 + 0.00000000 0.00000000 0.30000000 1.000000e-03 + 0.00000000 0.00000000 0.40000000 1.000000e-03 + 0.00000000 0.00000000 0.50000000 1.000000e-03 + 0.00000000 0.00000000 0.60000000 1.000000e-03 + 0.00000000 0.00000000 0.70000000 1.000000e-03 + 0.00000000 0.00000000 0.80000000 1.000000e-03 + 0.00000000 0.00000000 0.90000000 1.000000e-03 + 0.00000000 0.10000000 0.00000000 1.000000e-03 + 0.00000000 0.10000000 0.10000000 1.000000e-03 + 0.00000000 0.10000000 0.20000000 1.000000e-03 + 0.00000000 0.10000000 0.30000000 1.000000e-03 + 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b/examples/example31/W.pw2wan new file mode 100644 index 000000000..5aedf20d3 --- /dev/null +++ b/examples/example31/W.pw2wan @@ -0,0 +1,7 @@ +&inputpp + outdir = './out' + prefix = 'W' + seedname = 'W' + write_amn = .true. + write_mmn = .true. + write_unk = .false. diff --git a/examples/example31/W.scf b/examples/example31/W.scf new file mode 100644 index 000000000..dafe4d7dc --- /dev/null +++ b/examples/example31/W.scf @@ -0,0 +1,31 @@ +&CONTROL + calculation = 'scf' + max_seconds = 1710 + outdir = './out/' + prefix = 'W' + pseudo_dir = '../../pseudo/' + restart_mode = 'from_scratch' +/ +&SYSTEM + degauss = 2.0000000000d-02 + ecutrho = 2.4000000000d+02 + ecutwfc = 3.0000000000d+01 + ibrav = 0 + nat = 1 + ntyp = 1 + occupations = 'smearing' + smearing = 'marzari-vanderbilt' +/ +&ELECTRONS + conv_thr = 1.0000000000d-10 +/ +ATOMIC_SPECIES +W 183.85 W_pbe_v1.2.uspp.F.UPF +ATOMIC_POSITIONS angstrom +W 0.0000000000 0.0000000000 0.0000000000 +K_POINTS automatic +14 14 14 0 0 0 +CELL_PARAMETERS angstrom + -1.5915572711 1.5915572711 1.5915572711 + 1.5915572711 -1.5915572711 1.5915572711 + 1.5915572711 1.5915572711 -1.5915572711 diff --git a/examples/example31/W.win b/examples/example31/W.win new file mode 100644 index 000000000..90af1c9dd --- /dev/null +++ b/examples/example31/W.win @@ -0,0 +1,1040 @@ +bands_plot = .true. +conv_tol = 8.0000000000d-06 +conv_window = 3 +dis_num_iter = 0 +auto_projections = .true. +num_bands = 21 +num_iter = 10000 +num_wann = 13 +use_ws_distance = .true. +wannier_plot = .false. +write_xyz = .false. + +begin atoms_cart +ang +W 0.0 0.0 0.0 +end atoms_cart + +begin kpoint_path +G 0.0 0.0 0.0 H 0.5 -0.5 0.5 +H 0.5 -0.5 0.5 N 0.0 0.0 0.5 +N 0.0 0.0 0.5 G 0.0 0.0 0.0 +G 0.0 0.0 0.0 P 0.25 0.25 0.25 +P 0.25 0.25 0.25 H 0.5 -0.5 0.5 +P 0.25 0.25 0.25 N 0.0 0.0 0.5 +end kpoint_path + +mp_grid: 10 10 10 + +begin kpoints + 0.00000000 0.00000000 0.00000000 + 0.00000000 0.00000000 0.10000000 + 0.00000000 0.00000000 0.20000000 + 0.00000000 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a/pseudo/W_pbe_v1.2.uspp.F.UPF b/pseudo/W_pbe_v1.2.uspp.F.UPF new file mode 100644 index 000000000..ad3d5a8bc --- /dev/null +++ b/pseudo/W_pbe_v1.2.uspp.F.UPF @@ -0,0 +1,12629 @@ + +Generated using Vanderbilt code, version 7 3 6 +Author: kfg Generation date: 3 2 2014 +Automatically converted from original format + 1 The Pseudo was generated with a Scalar-Relativistic Calculation + 2.00000000000E+00 Local Potential cutoff radius +nl pn l occ Rcut Rcut US E pseu +5S 5 0 2.00 0.00000000000 1.45000000000 -5.87786794000 +5P 5 1 6.00 0.00000000000 1.50000000000 -3.24146052300 +5D 5 2 3.90 0.00000000000 1.70000000000 -0.38902219300 +6S 6 0 2.00 0.00000000000 1.45000000000 -0.46971592100 +6P 6 1 0.00 0.00000000000 1.50000000000 -0.13888875900 + + + + + 0 Version Number + W Element + US Ultrasoft pseudopotential + T Nonlinear Core Correction +SLA PW PBE PBE PBE Exchange-Correlation functional + 14.00000000000 Z valence + -158.26726038400 Total energy + 0.00000 0.00000 Suggested cutoff for wfc 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-2.20475942576E-03 -2.35720009982E-03 + -2.52009655709E-03 -2.69415699690E-03 -2.88013659806E-03 -3.07884059230E-03 + -3.29112740465E-03 -3.51791210625E-03 -3.76016994455E-03 -4.01894021533E-03 + -4.29533022709E-03 -4.59051963557E-03 -4.90576488154E-03 -5.24240404106E-03 + -5.60186179108E-03 -5.98565479067E-03 -6.39539728721E-03 -6.83280701146E-03 + -7.29971150278E-03 -7.79805460758E-03 -8.32990350717E-03 -8.89745592176E-03 + -9.50304787711E-03 -1.01491616639E-02 -1.08384343939E-02 -1.15736667638E-02 + -1.23578324490E-02 -1.31940877064E-02 -1.40857816481E-02 -1.50364667204E-02 + -1.60499098803E-02 -1.71301039690E-02 -1.82812798052E-02 -1.95079184618E-02 + -2.08147642308E-02 -2.22068378716E-02 -2.36894502842E-02 -2.52682167430E-02 + -2.69490712423E-02 -2.87382815175E-02 -3.06424640213E-02 -3.26685995372E-02 + -3.48240486176E-02 -3.71165675626E-02 -3.95543240518E-02 -4.21459131947E-02 + -4.49003729841E-02 -4.78271999972E-02 -5.09363642175E-02 -5.42383238190E-02 + -5.77440387381E-02 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5.58481658722E-01 4.06345635691E-01 2.59268745500E-01 1.31655247636E-01 + 3.96454892486E-02 1.72946626215E-03 6.49275333284E-04 0.00000000000E+00 + 0.00000000000E+00 0.00000000000E+00 0.00000000000E+00 0.00000000000E+00 + 0.00000000000E+00 0.00000000000E+00 0.00000000000E+00 + + + 13 Number of nonzero Dij + 1 1 -2.67174298137E+00 + 1 2 -2.56975645438E-01 + 1 3 1.33331803328E+00 + 2 2 -6.03093784613E+00 + 2 3 -5.35820637962E+00 + 3 3 -7.53674462494E+00 + 4 4 -3.51377250508E+00 + 4 5 -1.21630354481E+00 + 5 5 -1.44295753093E+00 + 6 6 -1.45933985611E+00 + 6 7 -5.33419212864E-01 + 7 7 1.94160213405E+00 + 8 8 2.92701868924E+00 + + + 6 nqf. If not zero, Qij's inside rinner are computed using qfcoef's + + 1 1.35000000000E+00 + 2 1.35000000000E+00 + 3 1.35000000000E+00 + 4 1.35000000000E+00 + 5 1.35000000000E+00 + 6 1.35000000000E+00 + 7 1.35000000000E+00 + + 1 1 0 i j (l(j)) + -2.13784822386E-01 Q_int + 0.00000000000E+00 -9.29389040198E-13 -3.78137415448E-12 -8.65456163801E-12 + -1.56515100745E-11 -2.48788760512E-11 -3.64475650598E-11 -5.04728877640E-11 + -6.70747218223E-11 -8.63776794604E-11 -1.08511280993E-10 -1.33610134508E-10 + -1.61814121916E-10 -1.93268591610E-10 -2.28124557938E-10 -2.66538907753E-10 + -3.08674614269E-10 -3.54700958487E-10 -4.04793758458E-10 -4.59135606642E-10 + -5.17916115665E-10 -5.81332172753E-10 -6.49588203152E-10 -7.22896442848E-10 + -8.01477220901E-10 -8.85559251746E-10 -9.75379937796E-10 -1.07118568271E-09 + -1.17323221567E-09 -1.28178492716E-09 -1.39711921644E-09 -1.51952085134E-09 + -1.64928634073E-09 -1.78672331994E-09 -1.93215094994E-09 -2.08590033036E-09 + -2.24831492714E-09 -2.41975101512E-09 -2.60057813626E-09 -2.79117957379E-09 + -2.99195284321E-09 -3.20331020028E-09 -3.42567916700E-09 -3.65950307595E-09 + -3.90524163369E-09 -4.16337150397E-09 -4.43438691128E-09 -4.71880026560E-09 + -5.01714280898E-09 -5.32996528479E-09 -5.65783863033E-09 -6.00135469372E-09 + -6.36112697580E-09 -6.73779139805E-09 -7.13200709729E-09 -7.54445724813E-09 + -7.97584991425E-09 -8.42691892932E-09 -8.89842480873E-09 -9.39115569314E-09 + -9.90592832496E-09 -1.04435890589E-08 -1.10050149079E-08 -1.15911146253E-08 + -1.22028298249E-08 -1.28411361403E-08 -1.35070444241E-08 -1.42016019894E-08 + -1.49258938947E-08 -1.56810442725E-08 -1.64682177059E-08 -1.72886206515E-08 + -1.81435029129E-08 -1.90341591650E-08 -1.99619305319E-08 -2.09282062189E-08 + -2.19344252021E-08 -2.29820779761E-08 -2.40727083634E-08 -2.52079153857E-08 + -2.63893552013E-08 -2.76187431088E-08 -2.88978556214E-08 -3.02285326130E-08 + -3.16126795387E-08 -3.30522697327E-08 -3.45493467859E-08 -3.61060270065E-08 + 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Subject: [PATCH 2/6] Tutorial and example for extracting SCDM parameters from projectability --- doc/tutorial/tutorial.tex | 129 +- examples/example31/W.win | 1040 ----------------- examples/{example31 => example32}/W.nscf | 0 examples/{example31 => example32}/W.proj | 0 examples/{example31 => example32}/W.pw2wan | 0 examples/{example31 => example32}/W.scf | 0 examples/example32/W.win | 1040 +++++++++++++++++ .../generate_weights.sh | 0 8 files changed, 1104 insertions(+), 1105 deletions(-) delete mode 100644 examples/example31/W.win rename examples/{example31 => example32}/W.nscf (100%) rename examples/{example31 => example32}/W.proj (100%) rename examples/{example31 => example32}/W.pw2wan (100%) rename examples/{example31 => example32}/W.scf (100%) create mode 100644 examples/example32/W.win rename examples/{example31 => example32}/generate_weights.sh (100%) diff --git a/doc/tutorial/tutorial.tex b/doc/tutorial/tutorial.tex index 0d6615997..05dfdca98 100644 --- a/doc/tutorial/tutorial.tex +++ b/doc/tutorial/tutorial.tex @@ -3519,7 +3519,70 @@ \subsection*{Notes} \end{quote} } \end{itemize} -\sectiontitle{31: Tungsten --- SCDM parameters from projectability} + +\sectiontitle{31: Platinum -- Selected columns of density matrix algorithm for spinor wavefunctions} + +Note: This example requires a recent version of the {\tt pw2wannier90.x} post-processing code of {\tt Quantum ESPRESSO} (v6.3 or above). + +\begin{itemize} +\item Outline: {\it For bulk crystalline platinum with spin-orbit coupling, generate the $A_{mn}$ matrices via the selected columns of density matrix (SCDM) algorithm and the corresponding spinor-MLWFs. To better understand the input files and the results of these calculations, it is crucial that the Reader has familiarized with the concepts and methods explained in Ref.~\cite{LinLin-ArXiv2017}. More info on the keywords related to the SCDM method may be found in the user\_guide.} + +This example focuses on the use of the SCDM method for spin-noncollinear systems. For the overview of the use of SCDM method to spinless systems, please refer to example27. +\item Directory: {\tt examples/example31/} + +The input files for this examples are similar to the ones in example 29, except that a coarser k-point grid is used and that the keywords related to {\tt postw90.x} are removed. +\item Input Files: +\begin{itemize} +\item {\tt Pt.scf} {\it The \pwscf\ input file for the ground state calculation} +\item {\tt Pt.nscf} {\it The \pwscf\ input file to obtain Bloch states on a uniform grid} +\item {\tt Pt.pw2wan} {\it The input file for {\tt pw2wannier90} with keywords related to the SCDM method} +\item {\tt Pt.win} {\it The {\tt wannier90} input file} +\end{itemize} +\end{itemize} + + +We will compute 18 localized WFs. Since the band structure of platinum is metallic, the low-lying bands are entangled with other high-energy bands, and the columns of the density matrix are not exponentially localized by construction. +Thus, we use a modified density matrix \cite{LinLin-ArXiv2017}, with the function $f(\varepsilon_{n,\mathbf{k}})$ defined as a complementary error function. Refer to example 27 for the definition of the modified density matrix and the functional form of $f(\varepsilon_{n,\mathbf{k}})$. + +\begin{enumerate} + \item Run \pwscf\ to obtain the ground state of platinum\\ + {\tt pw.x < Pt.scf > scf.out} + + \item Run \pwscf\ to obtain the Bloch states on a uniform $7\times 7\times 7$ $k$-point + grid\\ + {\tt pw.x < Pt.nscf > nscf.out} + + \item Inspect the {\tt Pt.win} input file and make sure that the {\tt auto\_projections} flag is set to {\tt .true.}. Also, make sure that no projection block is present. + + \item Run \wannier\ to generate a list of the required overlaps (written + into the {\tt Pt.nnkp} file)\\ + {\tt wannier90.x -pp Pt} + + \item Inspect the {\tt Pt.nnkp} file and make sure you find the {\tt auto\_projections} block and that no projections have been written in the {\tt projections} block. + + \item Inspect the {\tt Pt.pw2wan} input file. You will find four SCDM-related keywords: {\tt scdm\_proj}, {\tt scdm\_entanglement}, {\tt scdm\_mu} and {\tt scdm\_sigma}. + In particular, the keyword {\tt scdm\_proj} will instruct {\tt pw2wannier90.x} to use the SCDM method when generating the $A_{mn}$ matrix. + The remaining three keywords defines the formula and parameters to define the function $f(\varepsilon_{n\mathbf{k}})$ (see Ref.~\cite{LinLin-ArXiv2017} and example 27). + + \item Run {\tt pw2wannier90} to compute the overlap between Bloch + states and the projections via the SCDM method (written in the + {\tt Pt.mmn} and {\tt Pt.amn} respectively).\\ + {\tt pw2wannier90.x < Pt.pw2wan > pw2wan.out} + + \item Inspect the {\tt pw2wan.out} output file. + Compared to the spinless case, you will find the following two additional lines. + \begin{verbatim} + Number of pivot points with spin up : 9 + Number of pivot points with spin down: 9 + \end{verbatim} + These lines give information on the pivots obtained by the QR decomposition with column pivoting (QRCP) in the SCDM algorithm. Each pivot determines a point in the real-space grid and a spin state. The basis of the spin state is determined by the basis used in the electronic structure code. In \pwscf, the basis states are spin up and down states along the Cartesian $z$-axis. + + \item Run \wannier\ to compute the MLWFs\\ + {\tt wannier90.x Pt}\\ + +\end{enumerate} + +\sectiontitle{32: Tungsten --- SCDM parameters from projectability} \begin{itemize} \item{Outline: {\it Compute the Wannier interpolated band structure of tungsten (W) @@ -3604,70 +3667,6 @@ \subsection*{Notes} $\vert n\mathbf{k} \rangle$ as a function of the corresponding energy $\epsilon_{n\mathbf{k}}$ for tungsten. The yellow line shows the fitted complementary error function. The vertical red line represents the value of $\sigma_{fit}$ while the vertical green line represents the optimal value of $\mu_{SCDM}$, i.e. $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit}$. b) Band structure of tungsten on the $\Gamma$-H-N-$\Gamma$ path from DFT calculations (solid black) and Wannier interpolation using the SCDM method to construct the initial guess (red dots).} \label{fig:W_fit} \end{figure} -======= - -\sectiontitle{31: Platinum -- Selected columns of density matrix algorithm for spinor wavefunctions} - -Note: This example requires a recent version of the {\tt pw2wannier90.x} post-processing code of {\tt Quantum ESPRESSO} (v6.3 or above). - -\begin{itemize} -\item Outline: {\it For bulk crystalline platinum with spin-orbit coupling, generate the $A_{mn}$ matrices via the selected columns of density matrix (SCDM) algorithm and the corresponding spinor-MLWFs. To better understand the input files and the results of these calculations, it is crucial that the Reader has familiarized with the concepts and methods explained in Ref.~\cite{LinLin-ArXiv2017}. More info on the keywords related to the SCDM method may be found in the user\_guide.} - -This example focuses on the use of the SCDM method for spin-noncollinear systems. For the overview of the use of SCDM method to spinless systems, please refer to example27. -\item Directory: {\tt examples/example31/} - -The input files for this examples are similar to the ones in example 29, except that a coarser k-point grid is used and that the keywords related to {\tt postw90.x} are removed. -\item Input Files: -\begin{itemize} -\item {\tt Pt.scf} {\it The \pwscf\ input file for the ground state calculation} -\item {\tt Pt.nscf} {\it The \pwscf\ input file to obtain Bloch states on a uniform grid} -\item {\tt Pt.pw2wan} {\it The input file for {\tt pw2wannier90} with keywords related to the SCDM method} -\item {\tt Pt.win} {\it The {\tt wannier90} input file} -\end{itemize} -\end{itemize} - - -We will compute 18 localized WFs. Since the band structure of platinum is metallic, the low-lying bands are entangled with other high-energy bands, and the columns of the density matrix are not exponentially localized by construction. -Thus, we use a modified density matrix \cite{LinLin-ArXiv2017}, with the function $f(\varepsilon_{n,\mathbf{k}})$ defined as a complementary error function. Refer to example 27 for the definition of the modified density matrix and the functional form of $f(\varepsilon_{n,\mathbf{k}})$. - -\begin{enumerate} - \item Run \pwscf\ to obtain the ground state of platinum\\ - {\tt pw.x < Pt.scf > scf.out} - - \item Run \pwscf\ to obtain the Bloch states on a uniform $7\times 7\times 7$ $k$-point - grid\\ - {\tt pw.x < Pt.nscf > nscf.out} - - \item Inspect the {\tt Pt.win} input file and make sure that the {\tt auto\_projections} flag is set to {\tt .true.}. Also, make sure that no projection block is present. - - \item Run \wannier\ to generate a list of the required overlaps (written - into the {\tt Pt.nnkp} file)\\ - {\tt wannier90.x -pp Pt} - - \item Inspect the {\tt Pt.nnkp} file and make sure you find the {\tt auto\_projections} block and that no projections have been written in the {\tt projections} block. - - \item Inspect the {\tt Pt.pw2wan} input file. You will find four SCDM-related keywords: {\tt scdm\_proj}, {\tt scdm\_entanglement}, {\tt scdm\_mu} and {\tt scdm\_sigma}. - In particular, the keyword {\tt scdm\_proj} will instruct {\tt pw2wannier90.x} to use the SCDM method when generating the $A_{mn}$ matrix. - The remaining three keywords defines the formula and parameters to define the function $f(\varepsilon_{n\mathbf{k}})$ (see Ref.~\cite{LinLin-ArXiv2017} and example 27). - - \item Run {\tt pw2wannier90} to compute the overlap between Bloch - states and the projections via the SCDM method (written in the - {\tt Pt.mmn} and {\tt Pt.amn} respectively).\\ - {\tt pw2wannier90.x < Pt.pw2wan > pw2wan.out} - - \item Inspect the {\tt pw2wan.out} output file. - Compared to the spinless case, you will find the following two additional lines. - \begin{verbatim} - Number of pivot points with spin up : 9 - Number of pivot points with spin down: 9 - \end{verbatim} - These lines give information on the pivots obtained by the QR decomposition with column pivoting (QRCP) in the SCDM algorithm. Each pivot determines a point in the real-space grid and a spin state. The basis of the spin state is determined by the basis used in the electronic structure code. In \pwscf, the basis states are spin up and down states along the Cartesian $z$-axis. - - \item Run \wannier\ to compute the MLWFs\\ - {\tt wannier90.x Pt}\\ - -\end{enumerate} - %\cleardoublepage diff --git a/examples/example31/W.win b/examples/example31/W.win deleted file mode 100644 index 90af1c9dd..000000000 --- a/examples/example31/W.win +++ /dev/null @@ -1,1040 +0,0 @@ -bands_plot = .true. -conv_tol = 8.0000000000d-06 -conv_window = 3 -dis_num_iter = 0 -auto_projections = .true. -num_bands = 21 -num_iter = 10000 -num_wann = 13 -use_ws_distance = .true. -wannier_plot = .false. -write_xyz = .false. - -begin atoms_cart -ang -W 0.0 0.0 0.0 -end atoms_cart - -begin kpoint_path -G 0.0 0.0 0.0 H 0.5 -0.5 0.5 -H 0.5 -0.5 0.5 N 0.0 0.0 0.5 -N 0.0 0.0 0.5 G 0.0 0.0 0.0 -G 0.0 0.0 0.0 P 0.25 0.25 0.25 -P 0.25 0.25 0.25 H 0.5 -0.5 0.5 -P 0.25 0.25 0.25 N 0.0 0.0 0.5 -end kpoint_path - -mp_grid: 10 10 10 - -begin kpoints - 0.00000000 0.00000000 0.00000000 - 0.00000000 0.00000000 0.10000000 - 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b/examples/example32/W.scf similarity index 100% rename from examples/example31/W.scf rename to examples/example32/W.scf diff --git a/examples/example32/W.win b/examples/example32/W.win new file mode 100644 index 000000000..2b332f0c1 --- /dev/null +++ b/examples/example32/W.win @@ -0,0 +1,1040 @@ +bands_plot = .true. +conv_tol = 8.0000000000d-06 +conv_window = 3 +dis_num_iter = 0 +auto_projections = .true. +num_bands = 21 +num_iter = 10000 +num_wann = 13 +use_ws_distance = .true. +wannier_plot = .false. +write_xyz = .false. + +begin atoms_cart +ang +W 0.0 0.0 0.0 +end atoms_cart + +begin kpoint_path +G 0.0 0.0 0.0 H 0.5 -0.5 0.5 +H 0.5 -0.5 0.5 N 0.0 0.0 0.5 +N 0.0 0.0 0.5 G 0.0 0.0 0.0 +G 0.0 0.0 0.0 P 0.25 0.25 0.25 +P 0.25 0.25 0.25 H 0.5 -0.5 0.5 +P 0.25 0.25 0.25 N 0.0 0.0 0.5 +end kpoint_path + +mp_grid: 10 10 10 + +begin kpoints + 0.00000000 0.00000000 0.00000000 + 0.00000000 0.00000000 0.10000000 + 0.00000000 0.00000000 0.20000000 + 0.00000000 0.00000000 0.30000000 + 0.00000000 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0.90000000 0.90000000 0.60000000 + 0.90000000 0.90000000 0.70000000 + 0.90000000 0.90000000 0.80000000 + 0.90000000 0.90000000 0.90000000 +end kpoints + +begin projections +end projections + +begin unit_cell_cart +ang + -1.5915572711 1.5915572711 1.5915572711 + 1.5915572711 -1.5915572711 1.5915572711 + 1.5915572711 1.5915572711 -1.5915572711 +end unit_cell_cart diff --git a/examples/example31/generate_weights.sh b/examples/example32/generate_weights.sh similarity index 100% rename from examples/example31/generate_weights.sh rename to examples/example32/generate_weights.sh From 193a64765657e2233d7613fec9a7897e355fa496 Mon Sep 17 00:00:00 2001 From: Valerio Vitale Date: Fri, 29 Nov 2019 15:22:33 +0000 Subject: [PATCH 3/6] Changed text in example32 as suggested by Pizzi --- doc/tutorial/tutorial.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/doc/tutorial/tutorial.tex b/doc/tutorial/tutorial.tex index 05dfdca98..a5b52e42c 100644 --- a/doc/tutorial/tutorial.tex +++ b/doc/tutorial/tutorial.tex @@ -3631,11 +3631,11 @@ \subsection*{Notes} {\tt xmgrace } To Import the {\tt p\_vs\_e.dat} file, click on {\tt Data} from the top bar and then {\tt Import -> ASCII...}. - At this point a new window {\tt Grace: Read sets} should pop up . Select {\tt p\_vs\_e.dat} in the {\tt Files} section, click {\tt Ok} at the bottom and close the window. You should now be able to see a quite noisy function that is bounded between 1 and 0. You can modify the appearence of the plot by clicking on {\tt Plot} in the top bar and then {\tt Set appearance...}. In the {\tt Main} section of the pop-up window change the symbol type from {\tt None} to {\tt Circle} and symbol size from 100 to 25. Also change symbol color from black to blue. Change the line type from straight to none. Move to the {\tt Symbols} section and change the filling pattern from none to full (indentified by a full black square) and then close the window. For the fitting, go to {\tt Data -> Transformations -> Non-linear curve fitting}. In this window, select the source from the {\tt Set} box and in the {\tt Formula} box insert the following \\ + At this point a new window {\tt Grace: Read sets} should pop up. Select {\tt p\_vs\_e.dat} in the {\tt Files} section, click {\tt Ok} at the bottom and close the window. You should now be able to see a quite noisy function that is bounded between 1 and 0. You can modify the appearence of the plot by clicking on {\tt Plot} in the top bar and then {\tt Set appearance...}. For the fitting, go to {\tt Data -> Transformations -> Non-linear curve fitting}. In this window, select the source from the {\tt Set} box and in the {\tt Formula} box insert the following \\ {\tt y = 0.5 * erfc( ( x - A0 ) / A1 )} \\ -Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ +Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV.The motivation for this specific choice of $\mu_{fit}$ and $\sigma_{fit}$ may be found in Ref.~\cite{Vitale2019Automated}, where the authors also show validation of this approach on a dataset of 200 materials. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ \item Open {\tt W.pw2wan} and append the following lines {\tt @@ -3657,6 +3657,8 @@ \subsection*{Notes} \item Run \wannier\ to obtain the interpolated bandstructure (see Fig. \ref{fig:W_fit}-(b)).\\ {\tt wannier90.x W} + +Please cite Ref.~\cite{Vitale2019Automated} in any publication employing the procedure outlined in this example to obtain $\mu$ and $\sigma$. \end{enumerate} \begin{figure} From e145ae8768522afc732b41eba84a0bbfda66a702 Mon Sep 17 00:00:00 2001 From: Valerio Vitale Date: Fri, 29 Nov 2019 15:25:27 +0000 Subject: [PATCH 4/6] typo-fix in citation in example32 --- doc/tutorial/tutorial.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/tutorial/tutorial.tex b/doc/tutorial/tutorial.tex index a5b52e42c..cb9c73746 100644 --- a/doc/tutorial/tutorial.tex +++ b/doc/tutorial/tutorial.tex @@ -3635,7 +3635,7 @@ \subsection*{Notes} {\tt y = 0.5 * erfc( ( x - A0 ) / A1 )} \\ -Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV.The motivation for this specific choice of $\mu_{fit}$ and $\sigma_{fit}$ may be found in Ref.~\cite{Vitale2019Automated}, where the authors also show validation of this approach on a dataset of 200 materials. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ +Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV.The motivation for this specific choice of $\mu_{fit}$ and $\sigma_{fit}$ may be found in Ref.~\cite{Vitale2019automated}, where the authors also show validation of this approach on a dataset of 200 materials. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ \item Open {\tt W.pw2wan} and append the following lines {\tt @@ -3658,7 +3658,7 @@ \subsection*{Notes} \item Run \wannier\ to obtain the interpolated bandstructure (see Fig. \ref{fig:W_fit}-(b)).\\ {\tt wannier90.x W} -Please cite Ref.~\cite{Vitale2019Automated} in any publication employing the procedure outlined in this example to obtain $\mu$ and $\sigma$. +Please cite Ref.~\cite{Vitale2019automated} in any publication employing the procedure outlined in this example to obtain $\mu$ and $\sigma$. \end{enumerate} \begin{figure} From 41f91a19af8b242523ba5375b3bb5282a42ffa41 Mon Sep 17 00:00:00 2001 From: Valerio Vitale Date: Fri, 29 Nov 2019 19:18:34 +0000 Subject: [PATCH 5/6] Further changes to tutorial.tex requested by G. Pizzi --- doc/tutorial/tutorial.tex | 4 ++-- examples/example32/generate_weights.sh | 23 +++++++++++++++++++++++ 2 files changed, 25 insertions(+), 2 deletions(-) diff --git a/doc/tutorial/tutorial.tex b/doc/tutorial/tutorial.tex index cb9c73746..fe6fa40d1 100644 --- a/doc/tutorial/tutorial.tex +++ b/doc/tutorial/tutorial.tex @@ -3631,11 +3631,11 @@ \subsection*{Notes} {\tt xmgrace } To Import the {\tt p\_vs\_e.dat} file, click on {\tt Data} from the top bar and then {\tt Import -> ASCII...}. - At this point a new window {\tt Grace: Read sets} should pop up. Select {\tt p\_vs\_e.dat} in the {\tt Files} section, click {\tt Ok} at the bottom and close the window. You should now be able to see a quite noisy function that is bounded between 1 and 0. You can modify the appearence of the plot by clicking on {\tt Plot} in the top bar and then {\tt Set appearance...}. For the fitting, go to {\tt Data -> Transformations -> Non-linear curve fitting}. In this window, select the source from the {\tt Set} box and in the {\tt Formula} box insert the following \\ + At this point a new window {\tt Grace: Read sets} should pop up. Select {\tt p\_vs\_e.dat} in the {\tt Files} section, click {\tt Ok} at the bottom and close the window. You should now be able to see a quite noisy function that is bounded between 1 and 0. You can modify the appearence of the plot by clicking on {\tt Plot} in the top bar and then {\tt Set appearance...}. In the {\tt Main} section of the pop-up window change the symbol type from {\tt None} to {\tt Circle}. Change the line type from straight to none, since the lines added by default by Xmgrace are not meaningful. For the fitting, go to {\tt Data -> Transformations -> Non-linear curve fitting}. In this window, select the source from the {\tt Set} box and in the {\tt Formula} box insert the following \\ {\tt y = 0.5 * erfc( ( x - A0 ) / A1 )} \\ -Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV.The motivation for this specific choice of $\mu_{fit}$ and $\sigma_{fit}$ may be found in Ref.~\cite{Vitale2019automated}, where the authors also show validation of this approach on a dataset of 200 materials. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ +Select 2 as number of parameters, give 40 as initial condition for {\tt A0} and 7 for {\tt A1}. Click {\tt Apply}. A new window should pop up with the stats of the fitting. In particular you should find a {\tt Correlation coefficient} of 0.96 and a value of $39.9756$ for {\tt A0} and $6.6529$ for {\tt A1}. These are the value of $\mu_{fit}$ and $\sigma_{fit}$ we are going to use for the SCDM method. In particular, $\mu_{SCDM} = \mu_{fit} - 3\sigma_{fit} = 20.0169$ eV and $\sigma_{SCDM} = \sigma_{fit} = 6.6529$ eV. The motivation for this specific choice of $\mu_{fit}$ and $\sigma_{fit}$ may be found in Ref.~\cite{Vitale2019automated}, where the authors also show validation of this approach on a dataset of 200 materials. You should now see the fitting function, as well as the projectabilities, in the graph (see Fig. \ref{fig:W_fit}-(a)).\\ \item Open {\tt W.pw2wan} and append the following lines {\tt diff --git a/examples/example32/generate_weights.sh b/examples/example32/generate_weights.sh index cbba8d51d..c22d3b7b2 100755 --- a/examples/example32/generate_weights.sh +++ b/examples/example32/generate_weights.sh @@ -1,4 +1,25 @@ #!/bin/bash +# This script is used to extract the projectability from +# the output of projwfc.x (proj.out) and it works only +# for this specific system with 21 bands. + +# Remove temporary files if exist +if [ -f "e.dat" ]; then + rm e.dat; +fi + +if [ -f "p.dat" ]; then + rm p.dat; +fi + +if [ -f "p_vs_e.dat" ]; then + rm p_vs_e.dat; +fi + +# Check proj.out exists +[[ -f "proj.out" ]] || { echo "proj.out not found!"; echo "Aborting!"; exit; } + +# Start loop over bands for i in {1..21}; do echo $i if [ $i -lt 10 ]; then @@ -11,4 +32,6 @@ for i in {1..21}; do paste e.dat p.dat >> tmp.dat; done sort -k1n tmp.dat > p_vs_e.dat + +# Clean workspace rm e.dat p.dat tmp.dat From 5c97870f10ff329161dfefb1a2e90cabc5adf643 Mon Sep 17 00:00:00 2001 From: Valerio Vitale Date: Sat, 30 Nov 2019 11:05:10 +0000 Subject: [PATCH 6/6] Update generate_weights.sh --- examples/example32/generate_weights.sh | 17 +++++------------ 1 file changed, 5 insertions(+), 12 deletions(-) diff --git a/examples/example32/generate_weights.sh b/examples/example32/generate_weights.sh index c22d3b7b2..0c328065e 100755 --- a/examples/example32/generate_weights.sh +++ b/examples/example32/generate_weights.sh @@ -4,20 +4,13 @@ # for this specific system with 21 bands. # Remove temporary files if exist -if [ -f "e.dat" ]; then - rm e.dat; -fi - -if [ -f "p.dat" ]; then - rm p.dat; -fi - -if [ -f "p_vs_e.dat" ]; then - rm p_vs_e.dat; -fi +rm -f e.dat +rm -f p.dat +rm -f tmp.dat +rm -f p_vs_e.dat # Check proj.out exists -[[ -f "proj.out" ]] || { echo "proj.out not found!"; echo "Aborting!"; exit; } +[[ -f "proj.out" ]] || { echo "proj.out not found!"; echo "Aborting!"; exit 1; } # Start loop over bands for i in {1..21}; do