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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8"/>
<title>An overview of GW and its applications to core level spectroscopy</title>
<meta name="author" content="(Dr. Ramón L. Panadés Barrueta)"/>
<style type="text/css">
.underline { text-decoration: underline; }
</style>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/reveal.js/dist/reveal.css"/>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/reveal.js/dist/theme/serif.css" id="theme"/>
<link rel="stylesheet" href="./mod.css"/>
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<base target="_blank">
</head>
<body>
<div class="reveal">
<div class="slides">
<section id="sec-title-slide"><h1 class="title">An overview of GW and its applications to core level spectroscopy</h1>
<br>
<h3 class="author"> Dr. Ramón L. Panadés Barrueta</h3>
<h3 class="author"><a href="http://panadestein.github.io "target="_blank">panadestein.github.io</a></h3>
</section>
<section id="sec-table-of-contents"><div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#/slide-orgbe2674c">Why is it called GW anyway?</a></li>
<li><a href="#/slide-org3bdee20">Practical GW calculations</a></li>
<li><a href="#/slide-org5df0e4a">Example application to core level spectroscopy</a></li>
<li><a href="#/slide-org516b74f">Learning resources</a></li>
</ul>
</div>
</div>
</section>
<section>
<section id="slide-orgbe2674c">
<h2 id="orgbe2674c">Why is it called GW anyway?</h2>
<div class="outline-text-2" id="text-orgbe2674c">
</div>
</section>
<section id="slide-org9fb71f7">
<h3 id="org9fb71f7">GW in a nutshell</h3>
<aside class="notes">
<p>
There is a family of GW methods, the simplest one is the single-shot GoWo
You can use also for computing correlation energies of course
DFT and GW were developed almost at the same time, but the latter was computationally
more expensive, which delayed its widespread application
</p>
</aside>
<ul>
<li>Perturbative methods for solving the many-body problem.</li>
<li><p>
The main object in the method is the one-particle Green's function:
</p>
<div>
\begin{equation*}
\LARGE{G(\mathbf{r}, \mathbf{r'}; \omega) = \sum_n \frac{f_n(\mathbf{r})f_n^{*}(\mathbf{r'})}
{\hbar\omega - \epsilon_n +i\eta\hbar\text{sgn}(\epsilon_n-\mu)}}
\end{equation*}
</div></li>
<li>Excellent for charge excitations (IPs, EAs, fundamental gaps, CE)</li>
<li>Can be used for finite size or extended systems, up to hundreds of atoms.</li>
</ul>
</section>
<section id="slide-orgb7e6a05">
<h3 id="orgb7e6a05">Derivation</h3>
<aside class="notes">
<p>
The functional derivative method was developed by Schwinger. The Hedin's equations
are the first step in the GW derivation, which is a lengthy process
Beware that the numbers are a convenient abbreviation 1 -> (r<sub>1</sub>, t<sub>1</sub>)
</p>
</aside>
<p style="text-justify: auto; font-size: 70%">
GW is an approximation to an exact set of integro-differential equations
(<a href="https://journals.aps.org/pr/abstract/10.1103/PhysRev.139.A796">Hedin's equations</a>). The latter
can be derived using a diagrammatic approach, or alternatively the
<a href="#/slide-funcder">Schwinger's</a> functional derivative technique.
</p>
<img src="./Figures/gweq.svg" width="35%" style="padding: 29px; border: 0px;">
<img src="./Figures/hedin_eqs.jpg" width="30%" style="padding: 29px; border: 0px;">
<p style="font-size: 40%">Image from
<a href="https://www.frontiersin.org/articles/10.3389/fchem.2019.00377/full" target="_blank">GW compendium</a></p>
</section>
<section id="slide-org2296966">
<h3 id="org2296966">From Hedin's equations to GW</h3>
<img src="./Figures/hedin_pentagon.svg" width="30%" style="border: 0px;">
<img class="fragment" data-fragment-index="1" src="./Figures/gw_pentagon.svg" width="45%" style="border: 0px;">
<p class="fragment" data-fragment-index="1" style="font-size: 40%">Images from
<a href="https://docs.abinit.org/theory/mbt/" target="_blank">ABINIT</a> website</p>
</section>
</section>
<section>
<section id="slide-org3bdee20">
<h2 id="org3bdee20">Practical GW calculations</h2>
<div class="outline-text-2" id="text-org3bdee20">
</div>
</section>
<section id="slide-orgc171c04">
<h3 id="orgc171c04">Quasiparticle equation</h3>
<aside class="notes">
<p>
Practical GW calculations usually start from a DFT calculation
</p>
</aside>
<p>
Starting from Dyson's equation in differential form:
</p>
<div>
\begin{equation*}
[i\hbar\frac{\partial}{\partial t_1} - h(1)]G(1,2)-\int d3\Sigma(1,3)G(3,2)=\delta(1,2)
\end{equation*}
</div>
<p>
Taking the Fourier transform to the energy domain and using the eigenvalue expansion of the Green's function:
</p>
<div class="r-stack DIV" id="org3939e58">
<div data-fragment-index="1" class="fragment fade-out">
\begin{equation*}
[-\omega -h(r_1)]G(r_1,r_2;\omega)-\int dr_3\Sigma(r_1,r_3;\omega)G(r_3,r_2;\omega) = \delta(r_1-r_2)
\end{equation*}
</div>
<div data-fragment-index="1" class="fragment fade-in-then-out">
\begin{equation*}
G(r_1,r_2;\omega) = \sum_s \frac{\phi_{s\sigma}^0(r_1)\phi_{s\sigma}^{0*}(r_2)}
{\omega-\epsilon^{0}_{s\sigma}-i\eta\text{sgn}(E_F-\epsilon^0_{s\sigma})}
\end{equation*}
</div>
<div data-fragment-index="2" class="fragment appear">
\begin{equation*}
h(r_1)\phi_{s\sigma}(r_1) -\int dr_3\Sigma(r_1,r_3)\phi_{s\sigma}(r_3) = \phi_{s\sigma}(r_1)\epsilon_{s\sigma}
\end{equation*}
</div>
</div>
</section>
<section id="slide-orgf513640">
<h3 id="orgf513640">Typical G<sub>0</sub>W<sub>0</sub> algorithm</h3>
<img src="./Figures/algo.svg" width="60%" style="border: 0px;">
<p style="font-size: 60%">
GW typically scales as \(\color{red}{\mathbf{O(N^4)}}\), we are working on
reducing the scaling to \(\color{green}{\mathbf{O(N^3)}}\)
</p>
</section>
<section id="slide-org86e714e">
<h3 id="org86e714e">The contour deformation approach for the self-energy</h3>
<p style="font-size: 70%;">
A clever application of <a href="https://en.wikipedia.org/wiki/Jordan%27s_lemma">Jordan's Lemma</a> and
<a href="https://en.wikipedia.org/wiki/Residue_theorem">Cauchy's residue theorem</a>.
Integral self-energy expression is a consequence of
the <a href="https://en.wikipedia.org/wiki/Convolution_theorem">Convolution theorem</a>.
</p>
<img src="./Figures/cd_mine.svg" width="45%" style="border: 0px; float: left;">
<img src="./Figures/cd_eq.svg" width="45%" style="border: 0px; float: right; margin-top: 75px;">
<p style="font-size: 40%; clear: both;">
<a href="https://pubs.acs.org/doi/10.1021/acs.jctc.8b00458" target="_blank">
Golze et al. JCTC 14.9 (2018)</a></p>
</section>
</section>
<section>
<section id="slide-org5df0e4a">
<h2 id="org5df0e4a">Example application to core level spectroscopy</h2>
<div class="outline-text-2" id="text-org5df0e4a">
</div>
</section>
<section id="slide-org3a75d4c">
<h3 id="org3a75d4c">Software packages implementing GW methods</h3>
<table style="margin-left: 20%; margin-right:auto;">
<tbody>
<td>
<a href="https://www.abinit.org/">
<img src="./Figures/abinit.svg" width="20%" style="padding: 15px; border: 0px;"></a>
<a href="https://berkeleygw.org/">
<img src="./Figures/bgw.png" width="23%" style="padding: 15px; border: 0px;"></a>
<a href="http://perso.neel.cnrs.fr/xavier.blase/fiesta/">
<img src="./Figures/logofiesta.png" width="13%" style="padding: 15px; border: 0px;"></a>
</td>
<tbody>
</table>
<table style="margin-left: 20%; margin-right:auto;">
<tbody>
<td>
<a href="https://vasp.at/">
<img src="./Figures/vasp.png" width="15%" style="padding: 15px; border: 0px;"></a>
<a href="https://aims-web.rz-berlin.mpg.de/">
<img src="./Figures/aims.png" width="27%" style="padding: 15px; border: 0px;"></a>
<a href="https://www.cp2k.org/">
<img src="./Figures/cp2k.png" width="15%" style="padding: 15px; border: 0px;"></a>
</td>
<tbody>
</table>
<p style="font-size: 60%">
See Table 1 in the <a href="https://www.frontiersin.org/articles/10.3389/fchem.2019.00377/full">
GW compendium</a> for a complete list
</p>
</section>
<section id="slide-org8ea8e7f">
<h3 id="org8ea8e7f">Computation of the spectral function of the H<sub>2</sub>O 1s orbital</h3>
<ul style="line-height: 45px">
<li>Showcase FHI-aims workflow with a small application</li>
<li><p>
The contour deformation technique has a larger scaling for
core levels \(\color{red}{O(N^5)}\) due to the number of residues:
</p>
<div>
\begin{equation*}
\color{red}{N_{res}N_{occ}N_{virt}N^2_{aux}} \qquad \color{blue}{N_{\omega}N_{occ}N_{virt}N^2_{aux}}
\end{equation*}
</div></li>
<li>Description of satellite structure is expensive due to spectral function</li>
</ul>
</section>
<section id="slide-org7c078e0">
<h4 id="org7c078e0"></h4>
<p>
The <font color="green"> geometry.in</font> file
</p>
<div class="org-src-container">
<pre class="src src-example" ><code trim>atom 0.00000000 -0.00000000 -0.00614048 O
atom 0.76443318 -0.00000000 0.58917024 H
atom -0.76443318 0.00000000 0.58917024 H
</code></pre>
</div>
</section>
<section id="slide-orgf976221">
<h4 id="orgf976221"></h4>
<p>
The <font color="green"> control.in</font> file
</p>
<div class="org-src-container">
<pre class="src src-example" ><code trim>####################################################
# H2O molecule calculation
# Using def2-QVPZ basis for light and heavy elements
####################################################
#-------------------General options----------------------------
xc pbe # DFT functional
hybrid_xc_coeff 0.45 # Exchange mixing parameter
qpe_calc gw # Single shot GoWo
KS_method serial # Solve the geneigenval problem serial algorithm
override_illconditioning .true. # Override safe options for overlap matrix
RI_method v # Resolution of the identity for GW
prodbas_threshold 1.e-5 # Prevent ill-conditioning of auxiliary basis set
spin none # No spin specified, why?
partition_type rho_r2 # Patition type for integration grids
occupation_type gaussian 0.000001 # Broadening scheme used to find Fermi level
empty_states 25000 # Kohn-Sham states beyond the occupied levels
density_update_method density_matrix # Density matrix updating scheme
sc_accuracy_rho 1E-5 # SCF options
sc_accuracy_eev 1E-5
sc_accuracy_etot 1E-5
sc_iter_limit 400
#--------------------------------------------------------------
#-------------------GW specific options------------------------
anacon_type 1 # Pade analytic continuation
n_anacon_par 16 # Number of parameters in the Pade approximation
frequency_points 200 # Number of imaginary frequency points in \Sigma
contour_def_gw 1 1 # Range of states for which CD is applied
contour_eta 0.002 # Infinitesimal in Lehmann representation
state_lower_limit 1 # Lowest single-particle eigenstate
calc_spectral_func -560 -500 0.001 # Compute spectral function
#--------------------------------------------------------------
#-------------------Relativistic options-----------------------
relativistic none # Non-relativistic calculation
override_relativity .true. # Do not stop the code when questionable input
#--------------------------------------------------------------
#-------------------Density mixing options---------------------
mixer pulay
n_max_pulay 10
charge_mix_param 0.2
#--------------------------------------------------------------
################################################################################
#
# FHI-aims code project
# VB, Fritz-Haber Institut, 2007
#
# Suggested "safe" defaults for H atom (to be pasted into control.in file)
#
################################################################################
species H
include_min_basis false
pure_gauss true
cut_pot 6.0 2.5 1.0
l_hartree 8
basis_dep_cutoff 0.d0
radial_base 100 7.0
radial_multiplier 8
angular_grids auto
angular 1202
angular_acc 1.0e-08
angular_min 110
basis_acc 1.0e-5
# global species definitions
nucleus 1
mass 1.00794
#
#
#
################################################################################
#
# Definition of "minimal" basis
#
################################################################################
# valence basis states
valence 1 s 1.
# ion occupancy
ion_occ 1 s 0.5
################################################################################
#
# Suggested additional basis functions. For production calculations,
# uncomment them one after another (the most important basis functions are
# listed first).
#
# Basis constructed for dimers: 0.5 A, 0.7 A, 1.0 A, 1.5 A, 2.5 A
#
################################################################################
# H cc-pVQZ
gaussian 0 3
82.6400000 0.0020060
12.4100000 0.0153430
2.8240000 0.0755790
gaussian 0 1 0.7977000
gaussian 0 1 0.2581000
gaussian 0 1 0.0898900
gaussian 1 1 2.2920000
gaussian 1 1 0.8380000
gaussian 1 1 0.2920000
gaussian 2 1 2.0620000
gaussian 2 1 0.6620000
gaussian 3 1 1.3970000
################################################################################
#
# FHI-aims code project
# VB, Fritz-Haber Institut, 2007
#
# Suggested "safe" defaults for O atom (to be pasted into control.in file)
#
################################################################################
species O
include_min_basis false
pure_gauss true
cut_pot 6.0 2.5 1.0
l_hartree 8
basis_dep_cutoff 0.d0
radial_base 100 7.0
radial_multiplier 8
angular_grids auto
angular 1202
angular_acc 1.0e-08
angular_min 110
basis_acc 1.0e-5
# global species definitions
nucleus 8
mass 15.9994
#
#
#
################################################################################
#
# Definition of "minimal" basis
#
################################################################################
# valence basis states
valence 2 s 2.
valence 2 p 4.
# ion occupancy
ion_occ 2 s 1.
ion_occ 2 p 3.
################################################################################
#
# Suggested additional basis functions. For production calculations,
# uncomment them one after another (the most important basis functions are
# listed first).
#
# Constructed for dimers: 1.0 A, 1.208 A, 1.5 A, 2.0 A, 3.0 A
#
################################################################################
# O cc-pVQZ
gaussian 0 9
61420.0000000 0.0000900
9199.0000000 0.0006980
2091.0000000 0.0036640
590.9000000 0.0152180
192.3000000 0.0524230
69.3200000 0.1459210
26.9700000 0.3052580
11.1000000 0.3985080
4.6820000 0.2169800
gaussian 0 9
61420.0000000 -0.0000200
9199.0000000 -0.0001590
2091.0000000 -0.0008290
590.9000000 -0.0035080
192.3000000 -0.0121560
69.3200000 -0.0362610
26.9700000 -0.0829920
11.1000000 -0.1520900
4.6820000 -0.1153310
gaussian 0 1 1.4280000
gaussian 0 1 0.5547000
gaussian 0 1 0.2067000
gaussian 1 3
63.4200000 0.0060440
14.6600000 0.0417990
4.4590000 0.1611430
gaussian 1 1 1.5310000
gaussian 1 1 0.5302000
gaussian 1 1 0.1750000
gaussian 2 1 3.7750000
gaussian 2 1 1.3000000
gaussian 2 1 0.4440000
gaussian 3 1 2.6660000
gaussian 3 1 0.8590000
gaussian 4 1 1.8460000
</code></pre>
</div>
</section>
<section id="slide-org25a6586">
<h4 id="org25a6586"></h4>
<p>
The <font color="green"> aims.out</font> file
</p>
<div class="org-src-container">
<pre class="src src-example" ><code trim>------------------------------------------------------------
Invoking FHI-aims ...
When using FHI-aims, please cite the following reference:
Volker Blum, Ralf Gehrke, Felix Hanke, Paula Havu,
Ville Havu, Xinguo Ren, Karsten Reuter, and Matthias Scheffler,
'Ab Initio Molecular Simulations with Numeric Atom-Centered Orbitals',
Computer Physics Communications 180, 2175-2196 (2009)
In addition, many other developments in FHI-aims are likely important for
your particular application. A partial list of references is given at the end of
this file. Thank you for giving credit to the authors of these developments.
For any questions about FHI-aims, please visit our slack channel at
https://fhi-aims.slack.com
and our main development and support site at
https://aims-git.rz-berlin.mpg.de .
The latter site, in particular, has a wiki to collect information, as well
as an issue tracker to log discussions, suggest improvements, and report issues
or bugs. https://aims-git.rz-berlin.mpg.de is also the main development site
of the project and all new and updated code versions can be obtained there.
Please send an email to [email protected] and we will add
you to these sites. They are for you and everyone is welcome there.
------------------------------------------------------------
Date : 20210920, Time : 144849.255
Time zero on CPU 1 : 0.120000000000000E-01 s.
Internal wall clock time zero : 401381329.255 s.
FHI-aims created a unique identifier for this run for later identification
aims_uuid : 1834686C-6A3D-44DB-AA67-5CBBADA1A125
Build configuration of the current instance of FHI-aims
-------------------------------------------------------
FHI-aims version : 210802
Commit number : 8af8a52de
CMake host system : Linux-4.9.0-14-amd64
CMake version : 3.7.2
Fortran compiler : /usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries/linux/mpi/intel64/bin/mpiifort (Intel) version 17.0.4.20170411
Fortran compiler flags: -O3 -ip -fp-model precise
C compiler : /usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries/linux/bin/intel64/icc (Intel) version 17.0.4.20170411
C compiler flags : -O3 -ip -fp-model precise -std=gnu99
ELPA2 kernel : AVX2
Using MPI
Using ScaLAPACK
Using LibXC
Using i-PI
Using RLSY
Linking against: /usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries_2017/linux/mkl/lib/intel64/libmkl_intel_lp64.so
/usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries_2017/linux/mkl/lib/intel64/libmkl_sequential.so
/usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries_2017/linux/mkl/lib/intel64/libmkl_core.so
/usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries_2017/linux/mkl/lib/intel64/libmkl_scalapack_lp64.so
/usr/local/share/intel/parallel_studio_xe_2017/compilers_and_libraries_2017/linux/mkl/lib/intel64/libmkl_blacs_intelmpi_lp64.so
Using 8 parallel tasks.
Task 0 on host cpch06 reporting.
Task 1 on host cpch06 reporting.
Task 2 on host cpch06 reporting.
Task 3 on host cpch06 reporting.
Task 4 on host cpch06 reporting.
Task 5 on host cpch06 reporting.
Task 6 on host cpch06 reporting.
Task 7 on host cpch06 reporting.
Performing system and environment tests:
| Environment variable OMP_NUM_THREADS correctly set to 1.
| Checking for ScaLAPACK...
| Testing pdtran()...
| All pdtran() tests passed.
Obtaining array dimensions for all initial allocations:
-----------------------------------------------------------------------
Parsing control.in (first pass over file, find array dimensions only).
The contents of control.in will be repeated verbatim below
unless switched off by setting 'verbatim_writeout .false.' .
in the first line of control.in .
-----------------------------------------------------------------------
####################################################
# H2O molecule calculation
# Using def2-QVPZ basis for light and heavy elements
####################################################
#-------------------General options----------------------------
xc pbe # DFT functional
qpe_calc gw # Single shot GoWo
KS_method serial # Solve the geneigenval problem serial algorithm
override_illconditioning .true. # Override safe options for overlap matrix
RI_method v # Resolution of the identity for GW
prodbas_threshold 1.e-5 # Prevent ill-conditioning of auxiliary basis set
spin none # No spin specified, why?
partition_type rho_r2 # Patition type for integration grids
occupation_type gaussian 0.000001 # Broadening scheme used to find Fermi level
empty_states 25000 # Kohn-Sham states beyond the occupied levels
density_update_method density_matrix # Density matrix updating scheme
sc_accuracy_rho 1E-5 # SCF options
sc_accuracy_eev 1E-5
sc_accuracy_etot 1E-5
sc_iter_limit 400
#--------------------------------------------------------------
#-------------------GW specific options------------------------
anacon_type 1 # Pade analytic continuation
n_anacon_par 16 # Number of parameters in the Pade approximation
frequency_points 200 # Number of imaginary frequency points in \Sigma
#contour_def_gw 5 5 # Range of states for which CD is applied
#contour_eta 0.001 # Infinitesimal in Lehmann representation
state_lower_limit 1 # Lowest single-particle eigenstate
#--------------------------------------------------------------
#-------------------Relativistic options-----------------------
relativistic none # Non-relativistic calculation
override_relativity .true. # Do not stop the code when questionable input
#--------------------------------------------------------------
#-------------------Density mixing options---------------------
mixer pulay
n_max_pulay 10
charge_mix_param 0.2
#--------------------------------------------------------------
################################################################################
#
# FHI-aims code project
# VB, Fritz-Haber Institut, 2007
#
# Suggested "safe" defaults for H atom (to be pasted into control.in file)
#
################################################################################
species H
include_min_basis false
pure_gauss true
cut_pot 6.0 2.5 1.0
l_hartree 8
basis_dep_cutoff 0.d0
radial_base 100 7.0
radial_multiplier 8
angular_grids auto
angular 1202
angular_acc 1.0e-08
angular_min 110
basis_acc 1.0e-5
# global species definitions
nucleus 1
mass 1.00794
#
#
#
################################################################################
#
# Definition of "minimal" basis
#
################################################################################
# valence basis states
valence 1 s 1.
# ion occupancy
ion_occ 1 s 0.5
################################################################################
#
# Suggested additional basis functions. For production calculations,
# uncomment them one after another (the most important basis functions are
# listed first).
#
# Basis constructed for dimers: 0.5 A, 0.7 A, 1.0 A, 1.5 A, 2.5 A
#
################################################################################
# H cc-pVQZ
gaussian 0 3
82.6400000 0.0020060
12.4100000 0.0153430
2.8240000 0.0755790
gaussian 0 1 0.7977000
gaussian 0 1 0.2581000
gaussian 0 1 0.0898900
gaussian 1 1 2.2920000
gaussian 1 1 0.8380000
gaussian 1 1 0.2920000
gaussian 2 1 2.0620000
gaussian 2 1 0.6620000
gaussian 3 1 1.3970000
################################################################################
#
# FHI-aims code project
# VB, Fritz-Haber Institut, 2007
#
# Suggested "safe" defaults for O atom (to be pasted into control.in file)
#
################################################################################
species O
include_min_basis false
pure_gauss true
cut_pot 6.0 2.5 1.0
l_hartree 8
basis_dep_cutoff 0.d0
radial_base 100 7.0
radial_multiplier 8
angular_grids auto
angular 1202
angular_acc 1.0e-08
angular_min 110
basis_acc 1.0e-5
# global species definitions
nucleus 8
mass 15.9994
#
#
#
################################################################################
#
# Definition of "minimal" basis
#
################################################################################
# valence basis states
valence 2 s 2.
valence 2 p 4.
# ion occupancy
ion_occ 2 s 1.
ion_occ 2 p 3.
################################################################################
#
# Suggested additional basis functions. For production calculations,
# uncomment them one after another (the most important basis functions are
# listed first).
#
# Constructed for dimers: 1.0 A, 1.208 A, 1.5 A, 2.0 A, 3.0 A
#
################################################################################
# O cc-pVQZ
gaussian 0 9
61420.0000000 0.0000900
9199.0000000 0.0006980
2091.0000000 0.0036640
590.9000000 0.0152180
192.3000000 0.0524230
69.3200000 0.1459210
26.9700000 0.3052580
11.1000000 0.3985080
4.6820000 0.2169800
gaussian 0 9
61420.0000000 -0.0000200
9199.0000000 -0.0001590
2091.0000000 -0.0008290
590.9000000 -0.0035080
192.3000000 -0.0121560
69.3200000 -0.0362610
26.9700000 -0.0829920
11.1000000 -0.1520900
4.6820000 -0.1153310
gaussian 0 1 1.4280000
gaussian 0 1 0.5547000
gaussian 0 1 0.2067000
gaussian 1 3
63.4200000 0.0060440
14.6600000 0.0417990
4.4590000 0.1611430
gaussian 1 1 1.5310000
gaussian 1 1 0.5302000
gaussian 1 1 0.1750000
gaussian 2 1 3.7750000
gaussian 2 1 1.3000000
gaussian 2 1 0.4440000
gaussian 3 1 2.6660000
gaussian 3 1 0.8590000
gaussian 4 1 1.8460000
-----------------------------------------------------------------------
Completed first pass over input file control.in .
-----------------------------------------------------------------------
-----------------------------------------------------------------------
Parsing geometry.in (first pass over file, find array dimensions only).
The contents of geometry.in will be repeated verbatim below
unless switched off by setting 'verbatim_writeout .false.' .
in the first line of geometry.in .
-----------------------------------------------------------------------
atom 0.00000000 -0.00000000 -0.00614048 O
atom 0.76443318 -0.00000000 0.58917024 H
atom -0.76443318 0.00000000 0.58917024 H
-----------------------------------------------------------------------
Completed first pass over input file geometry.in .
-----------------------------------------------------------------------
Basic array size parameters:
| Number of species : 2
| Number of atoms : 3
| Max. basis fn. angular momentum : 4
| Max. atomic/ionic basis occupied n: 2
| Max. number of basis fn. types : 1
| Max. radial fns per species/type : 22
| Max. logarithmic grid size : 1430
| Max. radial integration grid size : 807
| Max. angular integration grid size: 1202
| Max. angular grid division number : 8
| Radial grid for Hartree potential : 1430
| Number of spin channels : 1
------------------------------------------------------------
Reading file control.in.
------------------------------------------------------------
XC: Using PBE gradient-corrected functionals.
GW quasiparticle calculation of excited states will be started after the DFT/HF calculation.
Kohn-Sham eigenvalues and eigenfunctions calculated by LAPACK via ELSI.
override_illconditioning: Explicitly overriding any built-in checks for an ill-conditioned overlap matrix.
*** WARNING: If you use this flag, you should really know what you are doing.
*** DO NOT keep this flag set by default in all your control.in files.
The 'V' version of RI (resolution of identity) technique is used.
Threshold for auxiliary basis singularities: 0.1000E-04
Spin treatment: No spin polarisation.
Partition function in integrals calculations: rho / r^2
Occupation type: Gaussian broadening, width = 0.100000E-05 eV.
Number of empty states per atom: 25000
Convergence accuracy of self-consistent charge density: 0.1000E-04
Convergence accuracy of sum of eigenvalues: 0.1000E-04
Convergence accuracy of total energy: 0.1000E-04
Maximum number of s.-c. iterations : 400
Using Pade approximation for analytical continuation.
Number of fitting parameters for analytical continuation : 16
Number of frequency points used for the self-energy calculation: 200
Lower limit of the eigenstates for the self-energy correction : 1
Non-relativistic treatment of kinetic energy.
override_relativity: Explicitly overriding any built-in relativity checks.
If you use this flag, you should really know what you are doing.
Using pulay charge density mixing.
Pulay mixing - number of memorized iterations: 10
Charge density mixing - mixing parameter: 0.2000
Reading configuration options for species H .
| Found request to include minimal basis fns. : F
| Found request to include pure gaussian fns. : T
| Found cutoff potl. onset [A], width [A], scale factor : 6.00000 2.50000 1.00000
| Found l_max for Hartree potential : 8
| Threshold for basis-dependent cutoff potential is 0.000000E+00
| Found data for basic radial integration grid : 100 points, outermost radius = 7.000 A
| Found multiplier for basic radial grid : 8
| Found angular grid specification: automatic.
| Found max. number of angular integration points per radial shell : 1202
| Found accuracy criterion for angular integrations : 0.1000E-07
| Will adapt angular grid densities automatically.
| Found min. number of angular integration points per radial shell : 110
| Found basis singularity cutoff : 0.1000E-04
| Found nuclear charge : 1.0000
| Found atomic mass : 1.00794000000000 amu
| Found free-atom valence shell : 1 s 1.000
| No ionic wave fns used. Skipping ion_occ.
| Found contracted cartesian Gaussian basis function : L = 0 , 3 elementary Gaussians:
| alpha = 0.826400E+02 weight = 0.200600E-02
| alpha = 0.124100E+02 weight = 0.153430E-01
| alpha = 0.282400E+01 weight = 0.755790E-01
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.797700E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.258100E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.898900E-01
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 1 0.229200E+01
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 1 0.838000E+00
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 1 0.292000E+00
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 2 0.206200E+01
| In terms of angular momentum, this radial function adds:
| 5 d-type basis functions
| Found primitive cartesian Gaussian basis function : 2 0.662000E+00
| In terms of angular momentum, this radial function adds:
| 5 d-type basis functions
| Found primitive cartesian Gaussian basis function : 3 0.139700E+01
| In terms of angular momentum, this radial function adds:
| 7 f-type basis functions
Species H : Missing cutoff potential type.
Defaulting to exp(1/x)/(1-x)^2 type cutoff potential.
Species H : No 'logarithmic' tag. Using default grid for free atom:
| Default logarithmic grid data [bohr] : 0.1000E-03 0.1000E+03 0.1012E+01
Species H : Using default innermost maximum threshold i_radial= 2 for radial functions.
Species H : Default cutoff onset for free atom density etc. is infinite
since the product basis is used (hybrid functionals, Hartree-Fock, GW etc.).
Species H : Basic radial grid will be enhanced according to radial_multiplier = 8, to contain 807 grid points.
Reading configuration options for species O .
| Found request to include minimal basis fns. : F
| Found request to include pure gaussian fns. : T
| Found cutoff potl. onset [A], width [A], scale factor : 6.00000 2.50000 1.00000
| Found l_max for Hartree potential : 8
| Threshold for basis-dependent cutoff potential is 0.000000E+00
| Found data for basic radial integration grid : 100 points, outermost radius = 7.000 A
| Found multiplier for basic radial grid : 8
| Found angular grid specification: automatic.
| Found max. number of angular integration points per radial shell : 1202
| Found accuracy criterion for angular integrations : 0.1000E-07
| Will adapt angular grid densities automatically.
| Found min. number of angular integration points per radial shell : 110
| Found basis singularity cutoff : 0.1000E-04
| Found nuclear charge : 8.0000
| Found atomic mass : 15.9994000000000 amu
| Found free-atom valence shell : 2 s 2.000
| Found free-atom valence shell : 2 p 4.000
| No ionic wave fns used. Skipping ion_occ.
| No ionic wave fns used. Skipping ion_occ.
| Found contracted cartesian Gaussian basis function : L = 0 , 9 elementary Gaussians:
| alpha = 0.614200E+05 weight = 0.900000E-04
| alpha = 0.919900E+04 weight = 0.698000E-03
| alpha = 0.209100E+04 weight = 0.366400E-02
| alpha = 0.590900E+03 weight = 0.152180E-01
| alpha = 0.192300E+03 weight = 0.524230E-01
| alpha = 0.693200E+02 weight = 0.145921E+00
| alpha = 0.269700E+02 weight = 0.305258E+00
| alpha = 0.111000E+02 weight = 0.398508E+00
| alpha = 0.468200E+01 weight = 0.216980E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found contracted cartesian Gaussian basis function : L = 0 , 9 elementary Gaussians:
| alpha = 0.614200E+05 weight = -.200000E-04
| alpha = 0.919900E+04 weight = -.159000E-03
| alpha = 0.209100E+04 weight = -.829000E-03
| alpha = 0.590900E+03 weight = -.350800E-02
| alpha = 0.192300E+03 weight = -.121560E-01
| alpha = 0.693200E+02 weight = -.362610E-01
| alpha = 0.269700E+02 weight = -.829920E-01
| alpha = 0.111000E+02 weight = -.152090E+00
| alpha = 0.468200E+01 weight = -.115331E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.142800E+01
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.554700E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found primitive cartesian Gaussian basis function : 0 0.206700E+00
| In terms of angular momentum, this radial function adds:
| 1 s-type basis function
| Found contracted cartesian Gaussian basis function : L = 1 , 3 elementary Gaussians:
| alpha = 0.634200E+02 weight = 0.604400E-02
| alpha = 0.146600E+02 weight = 0.417990E-01
| alpha = 0.445900E+01 weight = 0.161143E+00
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 1 0.153100E+01
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 1 0.530200E+00
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 1 0.175000E+00
| In terms of angular momentum, this radial function adds:
| 3 p-type basis functions
| Found primitive cartesian Gaussian basis function : 2 0.377500E+01
| In terms of angular momentum, this radial function adds:
| 5 d-type basis functions
| Found primitive cartesian Gaussian basis function : 2 0.130000E+01
| In terms of angular momentum, this radial function adds:
| 5 d-type basis functions
| Found primitive cartesian Gaussian basis function : 2 0.444000E+00
| In terms of angular momentum, this radial function adds:
| 5 d-type basis functions
| Found primitive cartesian Gaussian basis function : 3 0.266600E+01
| In terms of angular momentum, this radial function adds:
| 7 f-type basis functions
| Found primitive cartesian Gaussian basis function : 3 0.859000E+00
| In terms of angular momentum, this radial function adds:
| 7 f-type basis functions
| Found primitive cartesian Gaussian basis function : 4 0.184600E+01
| In terms of angular momentum, this radial function adds:
| 9 g-type basis functions
Species O : Missing cutoff potential type.
Defaulting to exp(1/x)/(1-x)^2 type cutoff potential.
Species O : No 'logarithmic' tag. Using default grid for free atom:
| Default logarithmic grid data [bohr] : 0.1000E-03 0.1000E+03 0.1012E+01
Species O : Using default innermost maximum threshold i_radial= 2 for radial functions.
Species O : Default cutoff onset for free atom density etc. is infinite
since the product basis is used (hybrid functionals, Hartree-Fock, GW etc.).
Species O : Basic radial grid will be enhanced according to radial_multiplier = 8, to contain 807 grid points.
Finished reading input file 'control.in'.
------------------------------------------------------------
------------------------------------------------------------
Reading geometry description geometry.in.
------------------------------------------------------------
| The smallest distance between any two atoms is 0.96889264 AA.
| The first atom of this pair is atom number 1 .
| The second atom of this pair is atom number 2 .
Input structure read successfully.
The structure contains 3 atoms, and a total of 10.000 electrons.
Input geometry:
| No unit cell requested.
| Atomic structure:
| Atom x [A] y [A] z [A]
| 1: Species O 0.00000000 0.00000000 -0.00614048
| 2: Species H 0.76443318 0.00000000 0.58917024
| 3: Species H -0.76443318 0.00000000 0.58917024
Finished reading input file 'control.in'.
------------------------------------------------------------
Reading geometry description geometry.in.
------------------------------------------------------------
Consistency checks for stacksize environment parameter are next.
| Maximum stacksize for task 0: unlimited
| Maximum stacksize for task 1: unlimited
| Maximum stacksize for task 2: unlimited
| Maximum stacksize for task 3: unlimited
| Maximum stacksize for task 4: unlimited
| Maximum stacksize for task 5: unlimited
| Maximum stacksize for task 6: unlimited
| Maximum stacksize for task 7: unlimited
| Current stacksize for task 0: unlimited