Commit 108761af by Anoop Chandran

all tables fixed

parent 1f9f6376
 ... ... @@ -33,10 +33,10 @@ GCUT (MBASIS) --------------- If :math:{N} is the number of LAPW basis functions, one would naively expect the number of product functions to be roughly :math:{N^2}. In the case of the interstitial plane waves, this is not so, since, with a cutoff :math:{g_\mathrm{max}}, the maximum momentum of the product would be :math:{2g_\mathrm{max}}, leading to :math:{8N} as the number of product plane waves. Fortunately, it turns out that the basis size can be much smaller in practice. Therefore, we introduce a reciprocal cutoff radius :math:{G_\mathrm{max}} for the interstitial plane waves and find that, instead of :math:{G_\mathrm{max}=2g_\mathrm{max}}, good convergence is achieved already with :math:{G_\mathrm{max}=0.75g_\mathrm{max}}, the default value. The parameter :math:{G_\mathrm{max}} can be set to a different value with the keyword GCUT in the section MBASIS of the input file. +---------+--------------+--+------------------------------------------------+ +---------+--------------+---------------------------------------------------+ | Example | GCUT 2.9 | | Use a reciprocal cutoff radius of 2.9 | | | | | :math:Bohr^{-1} for the product plane waves. | +---------+--------------+--+------------------------------------------------+ +---------+--------------+---------------------------------------------------+ .. _lcut: ... ... @@ -54,14 +54,17 @@ In the LAPW basis, the matching conditions at the MT boundaries require large :m +----------+--------------------------------+------------------------------------------------------------------------------------------------------------------+ | Examples | SELECT 2;3 | | Use products of :math:{u_{lp} u_{l'p'}} with :math:{l\le 2} and :math:{l'\le 3} | | | | | for :math:{p=0} (so-called :math:{u}) and no function of :math:{p=1} (so-called :math:{\dot{u}}). | | | | | for :math:{p=0} (so-called :math:{u}) and no function | | | | | of :math:{p=1} (so-called :math:{\dot{u}}). | +----------+--------------------------------+------------------------------------------------------------------------------------------------------------------+ | | SELECT 2,1;3,2 | | Same as before but also include the :math:{\dot{u}} functions with :math:{l\le 2} and :math:{l'\le 3}. | | | SELECT 2,1;3,2 | | Same as before but also include the :math:{\dot{u}} functions | | | | | with :math:{l\le 2} and :math:{l'\le 3}. | +----------+--------------------------------+------------------------------------------------------------------------------------------------------------------+ | | SELECT 2,,1100;3,,1111 | | Same as first line but also include the local orbitals | | | | | :math:{p\ge 2}, which are selected (deselected) by "1" ("0"): | | | | | here, the first two and all four LOs, respectively. The default behavior is | | | | | to include semicore LOs but to exclude the ones at higher energies. | | | | | here, the first two and all four LOs, respectively. | | | | | The default behavior is to include semicore LOs but to | | | | | exclude the ones at higher energies. | +----------+--------------------------------+------------------------------------------------------------------------------------------------------------------+ | | SELECT 2,1,1100;3,2,1111 | | Same as second line with the LOs. | +----------+--------------------------------+------------------------------------------------------------------------------------------------------------------+ ... ... @@ -73,7 +76,8 @@ TOL (MBASIS) (*) The set of MT products selected by SELECT can still be highly linearly dependent. Therefore, in a subsequent optimization step one diagonalizes the MT overlap matrix and retains only those eigenfunctions whose eigenvalues exceed a predefined tolerance value. This tolerance is 0.0001 by default and can be changed with the keyword TOL in the input file. +---------+-----------------+-------------------------------------------------------------------------------+ | Example | TOL 0.00001 | Remove linear dependencies that fall below a tolerance of 0.00001 (see text). | | Example | TOL 0.00001 | | Remove linear dependencies that fall below a | | | | | tolerance of 0.00001 (see text). | +---------+-----------------+-------------------------------------------------------------------------------+ OPTIMIZE (MBASIS) ... ... @@ -81,13 +85,16 @@ OPTIMIZE (MBASIS) The mixed product basis can still be quite large. In the calculation of the screened interaction, each matrix element, when represented in the basis of Coulomb eigenfunctions, is multiplied by :math:{\sqrt{v_\mu v_\nu}} with the Coulomb eigenvalues :math:{\{v_\mu\}}. This gives an opportunity for reducing the basis-set size further by introducing a Coulomb cutoff :math:{v_\mathrm{min}}. The reduced basis set is then used for the polarization function, the dielectric function, and the screened interaction. The parameter :math:{v_\mathrm{min}} can be specified after the keyword OPTIMIZE MB in three ways: first, as a "pseudo" reciprocal cutoff radius :math:{\sqrt{4\pi/v_\mathrm{min}}} (which derives from the plane-wave Coulomb eigenvalues :math:{v_\mathbf{G}=4\pi/G^2}), second, directly as the parameter :math:{v_\mathrm{min}} by using a negative real number, and, finally, as the number of basis functions that should be retained when given as an integer. The so-defined basis functions are mathematically close to plane waves. For testing purposes, one can also enforce the usage of plane waves (or rather projections onto plane waves) with the keyword OPTIMIZE PW, in which case the Coulomb matrix is known analytically. No optimization of the basis is applied, if OPTIMIZE is omitted. +----------+-----------------------+-------------------------------------------------------------------------------------------------------------+ | Examples | OPTIMIZE MB 4.0 | Optimize the mixed product basis by removing eigenfunctions with eigenvalues below 4\pi/4.5^2. | | Examples | OPTIMIZE MB 4.0 | | Optimize the mixed product basis by removing eigenfunctions | | | | | with eigenvalues below 4\pi/4.5^2. | +----------+-----------------------+-------------------------------------------------------------------------------------------------------------+ | | OPTIMIZE MB -0.05 | Optimize the mixed product basis by removing eigenfunctions with eigenvalues below 0.05. | | | OPTIMIZE MB -0.05 | | Optimize the mixed product basis by removing eigenfunctions | | | | | with eigenvalues below 0.05. | +----------+-----------------------+-------------------------------------------------------------------------------------------------------------+ | | OPTIMIZE MB 80 | Retain only the eigenfunctions with the 80 largest eigenvalues. | +----------+-----------------------+-------------------------------------------------------------------------------------------------------------+ | | OPTIMIZE PW 4.5 | Use projected plane waves with the cutoff 4.5 \mathrm{Bohr}^{-1} (for testing only, can be quite slow). | | | OPTIMIZE PW 4.5 | | Use projected plane waves with the cutoff :math:{4.5 \mathrm{Bohr}^{-1}} | | | | | (for testing only, can be quite slow). | +----------+-----------------------+-------------------------------------------------------------------------------------------------------------+ In summary, there are a number of parameters that influence the accuracy of the basis set. Whenever a new physical system is investigated, it is recommendable to converge the basis set for that system. The parameters to consider in this respect are GCUT, LCUT, SELECT, and OPTIMIZE. ... ...
 ... ... @@ -41,13 +41,14 @@ Each Spex run needs a job definition, which defines what Spex should do, e.g.,  Details of these jobs are explained in subsequent sections. The job definition must not be omitted but may be empty: JOB, in which case Spex will just read the wavefunctions and energies, perform some checks and some elemental calculations (e.g., Wannier interpolation), and stop. In principle, Spex supports multiple jobs such as JOB GW 1:(1-5) DIELEC 1:{0:1,0.01}. This feature is, however, seldom used and is not guaranteed to work correctly in all versions. +----------+------------------------------------------+----------------------------------------------------------------------+ | Examples | JOB COSX 1:(1-5) | Perform COHSEX calculation. | +----------+------------------------------------------+----------------------------------------------------------------------+ | | JOB COSX 1:(1-5) SCREEN 2:{0:1,0.01} | Subsequently, calculate the screened interaction on a frequency mesh | +----------+------------------------------------------+----------------------------------------------------------------------+ | | JOB | Just perform some checks and stop | +----------+------------------------------------------+----------------------------------------------------------------------+ +----------+------------------------------------------+--------------------------------------------+ | Examples | JOB COSX 1:(1-5) | Perform COHSEX calculation. | +----------+------------------------------------------+--------------------------------------------+ | | JOB COSX 1:(1-5) SCREEN 2:{0:1,0.01} | | Subsequently, calculate the screened | | | | | interaction on a frequency mesh | +----------+------------------------------------------+--------------------------------------------+ | | JOB | Just perform some checks and stop | +----------+------------------------------------------+--------------------------------------------+ BZ ----- ... ... @@ -68,6 +69,7 @@ This is an important keyword. It enables (a) continuing a calculation that has, +----------+---------------+----------------------------------------------+ | Examples | RESTART | Read/write restart file | +----------+---------------+----------------------------------------------+ | | RESTART 2 | Try to reuse data from standard output files | +----------+---------------+----------------------------------------------+ ... ... @@ -116,19 +118,19 @@ BANDINFO -------- (*) In some cases, it may be necessary to replace the energy eigenvalues, provided by the mean-field (DFT) code, by energies (e.g., GW quasiparticle energies) obtained in a previous Spex calculation, for example, to determine the GW Fermi energy or to perform energy-only self-consistent calculations. This can be achieved with the keyword ENERGY file, where file contains the new energies in eV. The format of file corresponds to the output of the spex.extr utility: spex.extr g spex.out > file. It must be made sure that file contains energy values for the whole irreducible Brillouin zone. Band energies not contained in file will be adjusted so that the energies are in accending order (provided that there is at least one energy value for the particular k point). +---------+-----------------------+-----------------------------------------------------------------------------------------------+ | Example | ENERGY energy.inp | | Replace the mean-field energy eigenvalues by the | | | | | energies provided in the file energy.inp | +---------+-----------------------+-----------------------------------------------------------------------------------------------+ +---------+-----------------------+---------------------------------------------------------+ | Example | ENERGY energy.inp | | Replace the mean-field energy eigenvalues by the | | | | | energies provided in the file energy.inp | +---------+-----------------------+---------------------------------------------------------+ DELTAEX ------- (*) This keyword modifies the exchange splitting of a collinear magnetic system, i.e., it shifts spin-up and spin-down energies relative to to each other so as to increase or decrease the exchange splitting. With DELTAEX x, the spin-up (spin-down) energies are lowered (elevated) by x/2. The parameter x can be used to enforce the Goldstone condition in spin-wave calculations [Phys. Rev. B 94, 064433 (2016)] +---------+-------------------+---------------------------------------------------------------------------------------------------+ | Example | DELTAEX 0.2eV | | Increase the exchange splitting by 0.2eV | | | | | (spin-up/down energies are decreased/increased by 0.1eV) | +---------+-------------------+---------------------------------------------------------------------------------------------------+ +---------+-------------------+---------------------------------------------------------------+ | Example | DELTAEX 0.2eV | | Increase the exchange splitting by 0.2eV | | | | | (spin-up/down energies are decreased/increased by 0.1eV) | +---------+-------------------+---------------------------------------------------------------+ PLUSSOC ------- ... ... @@ -138,17 +140,18 @@ ITERATE ------- (*) If specified, Spex only reads the LAPW basis set from the input data, provided by the mean-field (DFT) code, but performs the diagonalization of the Hamiltonian at the k points itself. This calculation effectively replaces the second run of the DFT code. In this sense, the name of the keyword is a bit misleading, as the calculation is non-iterative. The keyword ITERATE is mostly intended for testing and debugging. It is not available for executables compiled with -DLOAD (configured with --enable-load). +----------+---------------------+----------------------------------------------------------------------------------+ | Examples | ITERATE NR | Diagonalize a non-relativistic Hamiltonian | +----------+---------------------+----------------------------------------------------------------------------------+ | | ITERATE SR | Use scalar-relativity | +----------+---------------------+----------------------------------------------------------------------------------+ | | ITERATE FR | Also include SOC | +----------+---------------------+----------------------------------------------------------------------------------+ | | ITERATE SR -1 | Diagonalize scalar-relativistic Hamiltonian and neglect eigenvalues below -1 htr | +----------+---------------------+----------------------------------------------------------------------------------+ | | ITERATE FR STOP | Diagonalize relativistic Hamiltonian (including SOC), then stop | +----------+---------------------+----------------------------------------------------------------------------------+ +----------+---------------------+-------------------------------------------------------------------+ | Examples | ITERATE NR | Diagonalize a non-relativistic Hamiltonian | +----------+---------------------+-------------------------------------------------------------------+ | | ITERATE SR | Use scalar-relativity | +----------+---------------------+-------------------------------------------------------------------+ | | ITERATE FR | Also include SOC | +----------+---------------------+-------------------------------------------------------------------+ | | ITERATE SR -1 | | Diagonalize scalar-relativistic Hamiltonian and | | | | | neglect eigenvalues below -1 htr | +----------+---------------------+-------------------------------------------------------------------+ | | ITERATE FR STOP | Diagonalize relativistic Hamiltonian (including SOC), then stop | +----------+---------------------+-------------------------------------------------------------------+ Parallelized version ==================== ... ...
 ... ... @@ -93,13 +93,13 @@ in the section SENERGY of the input file. This option does not require the  the keyword SPECTRAL in the section SENERGY, in the examples below from -10 eV to 1 eV in steps of 0.01 eV. If there is no explicit mesh, Spex chooses one automatically. The spectral function is then written to the file "spectral", one block of data for each k point given in the job definition. There is another optional parameter given at the end of the line (second example below), which can be used to bound the imaginary part of the self-energy and, thus, the quasiparticle peak widths from below by this value (unset if not given). This can be helpful in the case of very sharp quasiparticle peaks that are otherwise hard to catch with the frequency mesh. +----------+---------------------------------------+--------------------------------------------------------------------------------------------------------+ | Examples | SPECTRAL {-10eV:1eV,0.01eV} | | Write spectral function :math:{\text{Im}G(\omega)} on the | | | | | specified frequency mesh to the file "spectral". | +----------+---------------------------------------+--------------------------------------------------------------------------------------------------------+ | | SPECTRAL {-10eV:1eV,0.01eV} 0.002 | | Bound imaginary part from below by 0.02, preventing | | | | | peak widths to become too small to be plotted. | +----------+---------------------------------------+--------------------------------------------------------------------------------------------------------+ +----------+---------------------------------------+-----------------------------------------------------------------+ | Examples | SPECTRAL {-10eV:1eV,0.01eV} | | Write spectral function :math:{\text{Im}G(\omega)} on the | | | | | specified frequency mesh to the file "spectral". | +----------+---------------------------------------+-----------------------------------------------------------------+ | | SPECTRAL {-10eV:1eV,0.01eV} 0.002 | | Bound imaginary part from below by 0.02, preventing | | | | | peak widths to become too small to be plotted. | +----------+---------------------------------------+-----------------------------------------------------------------+ Alhough GW calculations can be readily performed with the default settings, the user should be familiar to some degree with the details of the computation and how he/she can influence each step of the program run. Also note that the default settings might work well for one physical system but be unsuitable for another. ... ... @@ -142,19 +142,19 @@ CONTINUE (SENERGY) ------------------- The keyword CONTINUE in the section SENERGY chooses the analytic continuation method. It can have optional parameters. If given without parameters (or if not specified at all), Pade approximants are used. An integer number, such as CONTINUE 2, lets Spex perform a fit to an n-pole function (here, n=2) with the Newton method. The latter approach is somewhat obsolete by now and recommended only for test calculations. The argument can have additional flags +c*. Any combination is possible. They are explained in the examples. +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ | Examples | CONTINUE | Use Pade approximants (Default). | +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ | | CONTINUE 2 | Fit to the two-pole function :math:{a_1/(\omega-b_1)+a_2/(\omega-b_2)} | +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ | | CONTINUE 2+ | Include a constant in the fit function :math:{a_1/(\omega-b_1)+a_2/(\omega-b_2)+c} | +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ | | CONTINUE 2c | | Take constraints (continuity of value and gradient at :math:{\omega=0}) | | | | | into account when fitting | +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ | | CONTINUE 2* | | Allow parameters :math:{b_i} with positive imaginary parts | | | | | (should be negative) to contribute. (Default with Pade method.) | +----------+-----------------+------------------------------------------------------------------------------------------------------------------------------+ +----------+-----------------+-----------------------------------------------------------------------------------------+ | Examples | CONTINUE | Use Pade approximants (Default). | +----------+-----------------+-----------------------------------------------------------------------------------------+ | | CONTINUE 2 | Fit to the two-pole function :math:{a_1/(\omega-b_1)+a_2/(\omega-b_2)} | +----------+-----------------+-----------------------------------------------------------------------------------------+ | | CONTINUE 2+ | Include a constant in the fit function :math:{a_1/(\omega-b_1)+a_2/(\omega-b_2)+c} | +----------+-----------------+-----------------------------------------------------------------------------------------+ | | CONTINUE 2c | | Take constraints (continuity of value and gradient at :math:{\omega=0}) | | | | | into account when fitting | +----------+-----------------+-----------------------------------------------------------------------------------------+ | | CONTINUE 2* | | Allow parameters :math:{b_i} with positive imaginary parts | | | | | (should be negative) to contribute. (Default with Pade method.) | +----------+-----------------+-----------------------------------------------------------------------------------------+ The second method is contour integration, in which the frequency integration is performed explicitly, however not along the real frequency axis but on a deformed integration contour that avoids the real frequency axis as well as possible. This integration contour starts from :math:{-\infty}, describes an infinite quarter circle to :math:{-i\infty}, then runs along the imaginary frequency axis to :math:{i\infty}, and finishes, again with an infinite quarter circle, to :math:{\infty}. The two quarter circles do not contribute to the integral (because the integrand behaves as :math:{\propto \omega^{-2}}). Furthermore, depending on the frequency argument :math:{\omega} of the self-energy, one has to add a few residues coming from the poles of the Green function in the interval [:math:{0,\omega-\epsilon_\mathrm{F}}] if :math:{\omega>\epsilon_\mathrm{F}} and [:math:{\epsilon_\mathrm{F}-\omega,0}] otherwise, which requires the correlation screened interaction :math:{W^\mathrm{c}(\omega)} to be evaluated on this interval of the real axis. As a consequence, the calculations are more demanding in terms of computational complexity and cost (time and memory). Also, contour integration requires additional input parameters and is therefore somewhat more difficult to apply. However, the results are more accurate. In particular, they are not affected by the "ill-definedness" of the analytic continuation. ... ... @@ -163,18 +163,20 @@ CONTOUR (SENERGY) The corresponding keyword is called CONTOUR and belongs to the section SENERGY. Obviously, CONTOUR and CONTINUE must not be given at the same time. The keyword CONTOUR expects two arguments. The first defines the frequencies :math:{\omega}, for which the self-energy :math:{\Sigma^\mathrm{xc}(\omega)} is to be evaluated. At least, two frequencies are needed to approximate the self-energy as a linear function in :math:{\omega} and, thus, to calculate the ''linearized'' solution of the quasiparticle equation (see above). For this, a single value suffices (example 0.01), with which the self-energy for a state :math:{\mathbf{k}n} is evaluated at two frequencies (:math:{\epsilon_{\mathbf{k}n}-0.01} and :math:{\epsilon_{\mathbf{k}n}+0.01}). The more accurate ''direct'' solution is only available if we specify a range of frequencies for the self-energy instead of a single number. This is possible by an argument such as :math:{-0.1:0.15,0.01}. Here, the range of values is relative to :math:{\epsilon_{\mathbf{k}n}}. Note that the range is flipped (to :math:{-0.15:0.1,0.01} in the example) for occupied states :math:{\mathbf{k}n} to reflect the fact that occupied and unoccupied states tend to shift in opposite directions by the renormalization. One can also specify an absolute frequency mesh by [:math:{...}], i.e., relative to the Fermi energy. This is mandatory for FULL calculations. It is sometimes a bit inconvenient to determine suitable values for the upper and lower bound of [:math:{...}]. Therefore, Spex allows the usage of wildcards for one of the boundaries or both (see below). The second argument to CONTOUR gives the increment of the (equidistant) real-frequency mesh for :math:{W(\omega')}. The lower and upper boundaries of this mesh are predetermined already by the first argument. As a third method, Spex also allows to omit the second argument altogether. Then, it uses a ''hybrid'' method where the screened interaction is analytically continued from the imaginary (where it has to be known for the integral along this axis, see above) to the real axis, thereby obviating the need of calculating and storing ''W'' on a real-frequency mesh. The disadvantage is that the badly controlled Pade extrapolation introduces an element of randomness (also see keyword SMOOTH below). Our experience so far is that the ''hybrid'' method is in-between the two other methods in terms of both computational cost and numerical accuracy. +----------+------------------------------------+----------------------------------------------------------------------------------------------------+ | Examples | CONTOUR 0.01 0.005 | | Use contour integration to obtain the two values :math:{\Sigma^\mathrm{xc}(\epsilon\pm 0.01)}, | | | | | giving :math:{\Sigma^\mathrm{xc}} as a linear function. | +----------+------------------------------------+----------------------------------------------------------------------------------------------------+ | | CONTOUR {-0.1:0.15,0.01} 0.005 | | Calculate :math:{\Sigma^\mathrm{xc}(\omega)} on a frequency mesh relative to | | | | | the KS energy :math:{\epsilon}. | +----------+------------------------------------+----------------------------------------------------------------------------------------------------+ | | CONTOUR [{*:*,0.01}] 0.005 | | Use an absolute frequency mesh (relative to the Fermi energy) instead. | | | | | Wildcards are used for the upper and lower bounds. | +----------+------------------------------------+----------------------------------------------------------------------------------------------------+ | | CONTOUR [{*:*,0.01}] | Use hybrid method. | +----------+------------------------------------+----------------------------------------------------------------------------------------------------+ +----------+------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | Examples | CONTOUR 0.01 0.005 | | Use contour integration to obtain the two | | | | | values :math:{\Sigma^\mathrm{xc}(\epsilon\pm 0.01)}, giving :math:{\Sigma^\mathrm{xc}} as a linear | | | | | function. | +----------+------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | | CONTOUR {-0.1:0.15,0.01} 0.005 | | Calculate :math:{\Sigma^\mathrm{xc}(\omega)} on a frequency mesh relative to | | | | | the KS energy :math:{\epsilon}. | +----------+------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | | CONTOUR [{*:*,0.01}] 0.005 | | Use an absolute frequency mesh | | | | | (relative to the Fermi energy) instead. | | | | | Wildcards are used for the upper and lower bounds. | +----------+------------------------------------+--------------------------------------------------------------------------------------------------------------------+ | | CONTOUR [{*:*,0.01}] | Use hybrid method. | +----------+------------------------------------+--------------------------------------------------------------------------------------------------------------------+ FREQINT (SENERGY) (*) Independently of whether :math:{\Sigma^\mathrm{xc}(i\omega_n)} (CONTINUE) or :math:{\Sigma^\mathrm{xc}(\omega_n)} (CONTOUR) is evaluated, an important step in the calculation of the self-energy is to perform the frequency convolution :math:{\int_{-\infty}^\infty G(z+i\omega')W(i\omega')d\omega'} with :math:{z=i\omega} or :math:{z=\omega}. For this frequency integration, we interpolate W and then perform the convolution with the Green function analytically. The keyword FREQINT determines how the interpolation should be done. It can take two values, SPLINE and PADE for spline [after the transformation :math:{\omega\rightarrow \omega/(1+\omega)}] and Pade interpolation. The default is SPLINE. In the case of GT calculations, there is a similar frequency integration with the T matrix replacing W. There, the default is PADE. ... ... @@ -208,9 +210,11 @@ ALIGNVXC (SENERGY) +----------+--------------------+---------------------------------------------------------------------------------+ | Examples | ALIGNVXC | | Align exchange-correlation potential in such a way that the | | | | | ionization potential remains unchanged by the quasiparticle correction. | | | | | ionization potential remains unchanged by the quasiparticle | | | | | correction. | +----------+--------------------+---------------------------------------------------------------------------------+ | | ALIGNVXC 0.2eV | Apply a constant positive shift of 0.2 eV to the exchange-correlation potential.| | | ALIGNVXC 0.2eV | | Apply a constant positive shift of 0.2 eV to the | | | | | exchange-correlation potential. | +----------+--------------------+---------------------------------------------------------------------------------+ ... ... @@ -229,15 +233,15 @@ RESTART --------- Spex can reuse data from a previous GW run that has finished successfully, crashed, or has been stopped by the user. A GW calculation consists mainly of a loop over the irreducible k points. For each k point, Spex (a) calculates the matrix W('k') and (b) updates the self-energy matrix (or expectation values) :math:{\Sigma^{xc}} with the contribution of the current k point (and its symmetry-equivalent k points). After completion of step (b), the current self-energy is always written to the (binary) files "spex.sigx" and "spex.sigc". If the RESTART option is specified (independently of its argument), Spex also writes the matrix W(k) (in addition to some other data) to the (HDF5) file "spex.cor" unless it is already present in that file. If it is present, the corresponding data is read instead of being calculated. In this way, the keyword RESTART enables reusage of the calculated W(k) from a previous run. The matrix W(k) does not depend on the k points and band indices defined after JOB. So, these parameters can be changed before a run with RESTART, in which the W data is then reused. For example, band structures can be calculated efficiently in this way (see below). Especially for long calculations, it is recommended to use the RESTART option. Spex can also restart a calculation using self-energy data contained in "spex.sigx" and "spex.sigc". To this end, an argument is added: RESTART 2. Spex then starts with the k point, at which the calculation was interrupted before. In contrast to "spex.cor", the files "spex.sigx" and "spex.sigc" do depend on the job definition, which must therefore not be changed before a run with RESTART 2. However, there are few parameters (see below) that may be changed before a rerun with RESTART 2. These concern details of solving the quasiparticle equation, which follows after completion of the self-energy calculation. The following logical table gives an overview. +--+---------------+-----------------------+ | | "spex.cor" | "spex.sigx/c" | +==+===============+=======================+ | | -- | write | +--+---------------+-----------------------+ | | RESTART | read-write write | +--+---------------+-----------------------+ | | RESTART 2 | read-write read-write | +--+---------------+-----------------------+ +---------------+--------------+-----------------+ | | spex.cor | spex.sigx/c | +===============+==============+=================+ | -- | -- | write | +---------------+--------------+-----------------+ | RESTART | read-write | write | +---------------+--------------+-----------------+ | RESTART 2 | read-write | read-write | +---------------+--------------+-----------------+ The different rules for "spex.cor" and "spex.sigx/c" are motivated by the facts that (a) the file "spex.cor" is much bigger than "spex.sigx/c" (so, writing of "spex.cor" to harddisc should not be the default), (b) the files "spex.sigx/c" include the updated self-energy (requiring more computation than for W, thus representing "more valuable" data). ... ... @@ -431,7 +435,8 @@ The most important keyword in the calculation of the polarization function is  | | | | and an accumulated stretching factor of 30 at 5 htr. | +----------+------------------------+----------------------------------------------------------------------------------------+ | | HILBERT 0.01 1.05 | | Use Hilbert mesh with a first step size of :math:{\omega_2-\omega_1=} 0.01 htr | | | | | and a stretching factor of :math:{a=1.05}. (First argument is real-valued.) | | | | | and a stretching factor of :math:{a=1.05}. | | | | | (First argument is real-valued.) | +----------+------------------------+----------------------------------------------------------------------------------------+ MULTDIFF (SUSCEP) ... ... @@ -446,7 +451,8 @@ MULTDIFF (SUSCEP) | | MULTDIFF INT | | Use default behavior (separate for k=0, do not for k≠0) | | | | | but stick energy difference into integration weights.a | +-------------------+--------------------+------------------------------------------------------------------------------+ | | MULTDIFF INTON | Always separate energy difference by sticking them into integration weights. | | | MULTDIFF INTON | | Always separate energy difference by sticking them into | | | | | integration weights. | +-------------------+--------------------+------------------------------------------------------------------------------+ PLASMA (SUSCEP) ... ...
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