# gw input variables¶

This document lists and provides the description of the name (keywords) of the gw input variables to be used in the input file for the abinit executable.

## awtr¶

Mnemonics: evaluate the Adler-Wiser expression of $\chi^{0}_{KS}$ assuming Time-Reversal
Mentioned in topic(s): topic_Susceptibility
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 3

Test list (click to open). Moderately used, [36/1095] in all abinit tests, [3/151] in abinit tutorials

This input variable defines whether the irreducible polarizability $\chi^{0}_{KS}$ is evaluated taking advantage of time-reversal symmetry or not.

• 0 → Use the “standard” Adler-Wiser expression without assuming time-reversal symmetry. In this case, the irreducible polarizability is calculated summing over all possible electronic transitions (both resonant and anti-resonant).
• 1 → Take advantage of time-reversal symmetry to halve the number of transitions to be explicitly considered. This method leads to a decrease in the CPU time by a factor two with respect to the awtr = 0 case.

Important

Note that the parallel algorithm gwpara = 2 is not compatible with the choice awtr = 0.

## bdgw¶

Mnemonics: BanDs for GW calculation
Mentioned in topic(s): topic_GW, topic_SelfEnergy
Variable type: integer
Dimensions: (2,nkptgw,nsppol)
Default value: 0
*Only relevant if:
optdriver in [4, 7]

Test list (click to open). Moderately used, [75/1095] in all abinit tests, [12/151] in abinit tutorials

For each k-point with number ikptgw in the range (1:nkptgw) and each spin index isppol, bdgw(1,ikptgw,isppol) is the number of the lowest band for which the self-energy computation must be done. bdgw(2,ikptgw,isppol) gives the index of the highest band for which the self-energy computation must be done.

Note

The initial values given in the input file might be changed inside the code so that all the degenerate states at a given k-point and spin are included. This might happen when symsigma = 1 is used or in the case of self-consistent GW calculations. When symsigma == 1, indeed, the diagonal matrix elements of the self-energy are obtained by averaging the unsymmetrized results in the subspace spanned by the degenerate states.

When gwcalctyp >= 20, the quasi-particle wavefunctions are computed and represented as linear combination of Kohn-Sham wavefunctions. In this case bdgw designates the range of KS wavefunctions used as basis set. For each k-point, indeed, the quasi-particle wavefunctions are expanded considering only the KS states between bdgw(1,ikptgw,isppol) and bdgw(2,ikptgw,isppol).

For self-consistent calculations, on the other hand, the basis set used to expand the GW wavefunctions should include all the degenerate states belonging to the same irreducible representation. Only in this case, indeed, the initial symmetries and energy degenerations are preserved.

## cd_customnimfrqs¶

Mnemonics: Contour Deformation CUSTOM IMaginary FReQuencieS
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: (optdriver ==3 or optdriver ==4) and gwcalctyp in [2,9,12,19,22,29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_customnimfrqs lets the user define the grid points along the imaginary axis by hand. Set this to the number of frequencies you want. The frequencies are specified with cd_imfrqs.

## cd_frqim_method¶

Mnemonics: Contour Deformation FReQuency integration on IMaginary axis Method
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver ==4 and gwcalctyp in [2, 9, 12, 19, 22, 29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_frqim_method defines the choice of integration method along the imaginary frequency axis for Contour Deformation calculations. The default method is very robust, fast and optimal for the vast majority of cases. However, for very accurate (“paranoid level”) convergence studies, ABINIT offers the possibility of a variety of methods and grids. Note that as one starts to change the defaults, one needs to carefully consider the grid used. Therefore we recommend that in addition to reading the information below, the user reads the description of the input variables freqim_alpha, nfreqim, ppmfrq, gw_frqim_inzgrid.

The integration to be performed for each matrix element of the self energy along the imaginary axis is of the form:

\langle i|\Sigma(\omega)|j \rangle \propto \sum_s C_s \int_0^\infty d(i\omega^\prime) \frac{(\omega - \epsilon_s)}{(\omega-\epsilon_s)^2 + i{\omega^\prime}^2} f(i\omega^\prime),

where $\omega$ is the frequency point along the real axis, $\epsilon_s$ is an eigenvalue, and $i\omega^\prime$ is the variable along the imaginary axis. Thus the function to be integrated is a Lorentzian weight function centred on the origin (whose FWHM is decided by $|\omega-\epsilon_s|$), times a function. The function is related to the inverse dielectric matrix. It might have a peaked structure near the origin and is very smooth otherwise. the function decays asymptotically as $1/i\omega^\prime$, so the whole integral converges as this to the third power.

• cd_frqim_method = 1 - Histogram: This is the default method where the function $f(i\omega^\prime)$ is approximated by a histogram, and the Lorentzian is integrated analytically in each sub-interval. See the section on grids below for a description of the default grid. This method combined with the default grid is the fastest and optimised for the use of few points along the imaginary axis.
• cd_frqim_method = 2 - Trapezoid: The next step up from the histogram approximation in the previous method. The integration region is transformed $[0, \infty] \rightarrow [0,1]$ with a proper weight depending on the width of the Lorentzian. In this space $f(i\omega^\prime)$ is approximated by a linear function between grid points (trapezoids), and the integrand is integrated analytically in each sub-interval. This method tends to slightly overestimate contributions while the default method tends to slightly underestimate them, so the results from methods 1 and 2 should bracket the converged values. The asymptotic behaviour is explicitly taken into account by a fit using the last two grid points.
• cd_frqim_method = 3, 4, 5 - Natural Spline: The function is transformed $[0, \infty] \rightarrow [0,1]$. In this space $f(i\omega^\prime)$ is approximated by a natural spline function whose starting and ending sections are linear. This transform is chosen so that the function should approach a linear function asymptotically as the integration interval approaches 1, so that the asymptotic behaviour is automatically taken into account. For each Lorentzian width (determined by $|\omega-\epsilon_s|$) the integrand is appropriately scaled in the interval $[0,1]$, and a nested Gauss-Kronrod (GK) numerical integration rule is performed. The integrand is evaluated at the GK nodes by means of a spline-fit. The order of the GK rule is controlled by the index of the method:
• 3 → Gauss 7 point, Kronrod 15 point rule.
• 4 → Gauss 11 point, Kronrod 23 point rule.
• 5 → Gauss 15 point, Kronrod 31 point rule. There is rarely any difference to machine precision between these rules, and the code will issue a warning if a higher-order rule is recommended.

Grids for the integral along the imaginary axis:

All the methods above should execute no matter what grid is used along the imaginary axis, so this is very much under the control of the user. The only requirement is that the grid be strictly increasing. The point at zero frequency is assumed to lie on the real axis, so the calculation of that point is controlled by nfreqre and corresponding variables. We highly recommend extracting various elements of the dielectric matrix from the _SCR file using the Mrgscr utility and plotting them for visual inspection.

• Default - The default grid is an exponentially increasing grid given by the formula:
i\omega^\prime_k = \frac{\omega_p}{\alpha-2}\left[ e^{\frac{2k}{N+1} \ln(\alpha-1)} -1 \right].

Here $\omega_p$ is the plasma frequency (by default determined by the average density of the system, but this can be overridden by setting ppmfrq). $N$ is the total number of grid points (set by nfreqim). $\alpha$ is a parameter which determines how far out the final grid point will lie. The final point will be at $\alpha*\omega_p$ (the default is $\alpha = 5$, and was hard-coded in older versions of ABINIT). This grid is designed so that approximately half the grid points are always distributed to values lower than the plasma frequency, in order to resolve any peaked structure. If one seeks to increase the outermost reach by increasing ppmfrq one must simultaneously take care to increase nfreqim in order to have the appropriate resolution for the low-frequency region. In more recent versions of ABINIT one can also simply adjust the parameter $\alpha$ by using freqim_alpha. This grid is optimised for speed and accurate results with few grid points for cd_frqim_method = 1.

• Inverse z transform - This grid is activated by the use of the variable gw_frqim_inzgrid. This is the standard $[0, \infty] \rightarrow [0,1]$ transform using the formula:
i\omega^\prime = \omega_p \frac{z}{1-z}.

Here $\omega_p$ is the plasma frequency (default can be overridden by setting ppmfrq). The grid points are then picked by an equidistant grid (number of points set by nfreqim) in the interval $z \subset [0,1]$. This grid can easily be uniquely converged by just increasing nfreqim. Again the points are distributed so that approximately half of them lie below the plasma frequency.

• User defined - The user can also define their own grid using the variables cd_customnimfrqs and cd_imfrqs. With great power comes great responsibility!

The mrgscr utility is handy in optimising the numerical effort expended in convergence studies. By estimating the densest grid one can afford to calculate in the SCR file, and successively removing frequencies from a single file (using the utility), one only needs to perform the screening calculation once on the dense mesh for a given convergence study. One can also use the utility to merge independent screening calculations over q-points and frequency sections.

## cd_full_grid¶

Mnemonics: Contour Deformation FULL GRID in complex plane
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3 and gwcalctyp in [2, 9, 12, 19, 22, 29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_full_grid enables the calculation of the screening [both chi0 and epsilon^(-1)] on a grid in the first quadrant of the complex plane. The grid is determined by the (tensor) product of the grid in real frequency and the grid in imaginary frequency. In the SUS and SCR files the grid points are stored as follows:

  **Index:**
1   . . .   nfreqre   nfrqre+1 . . . nfreqre+nfreqim   nfreqre+nfreqim+1 . . . nfreqre*nfreqim
**Entry:**
| purely real freq.  |     purely imaginary freq.     |      gridpoints in complex plane        |


The grid in the complex plane is stored looping over the real dimension as the inner loop and the imaginary as the outer loop. The contents of the generated SUS and SCR files can be extracted for visualisation and further analysis with the Mrgscr utility.

## cd_halfway_freq¶

Mnemonics: Contour Deformation tangent grid HALFWAY FREQuency
Characteristics: ENERGY
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: scalar
Default value: 100.0 eV
Only relevant if: (optdriver == 3 or optdriver == 4) and gwcalctyp in [2,9,12,19,22,29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_halfway_freq determines the frequency where half of the number of points defined in nfreqre are used up. The tangent transformed grid is approximately linear up to this point. To be used in conjunction with gw_frqre_tangrid.

## cd_imfrqs¶

Mnemonics: Contour Deformation IMaginary FReQuencieS
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: (cd_customnimfrqs)
Default value: None
Only relevant if: optdriver == 3 and gwcalctyp in [2, 9, 12, 19, 22, 29] and cd_customnimfrqs != 0

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_imfrqs specifies the grid points for the imaginary axis. The number of frequencies is set by the value of cd_customnimfrqs. For example,

cd_customnimfrqs   5
nfreqim            5
cd_imfrqs          0.1  0.2  0.5  1.0  5.0


If nfreqim is not equal to cd_customnimfrqs a warning will be issued.

Use at own risk! The use of a custom grid makes it your responsibility that the SUS and SCR files are valid in self-energy (i.e. optdriver = 4) calculations, so caution is advised. Note that frequencies have to be strictly increasing, and the point at zero frequency is not considered to be part of the imaginary grid, but rather the grid along the real axis. The calculation of that point should be controlled by nfreqre and related variables.

## cd_max_freq¶

Mnemonics: Contour Deformation grid MAXimum FREQuency
Characteristics: ENERGY
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: scalar
Default value: 1000.0 eV
Only relevant if: (optdriver == 3 or optdriver == 4) and gwcalctyp in [2,9,12,19,22,29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

cd_max_freq determines the frequency where all the points defined in nfreqre are used up. To be used in conjunction with gw_frqre_tangrid.

## cd_subset_freq¶

Mnemonics: Contour Deformation grid calculate SUBSET of FREQuencies
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: (2)
Default value: [1, ‘nfreqre’]
Only relevant if: optdriver == 3 and gwcalctyp in [2, 9, 12, 19, 22, 29] and gw_frqre_tangrid == 0

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

cd_subset_freq Specifies that only a subset of the frequencies defined by nfreqre are to be calculated. The first index is the start and the second the end, with index number 1 always being the origin. For example a calculation with nfreqre = 100 could be separated into two datasets with:

subset_freq1   1   50
subset_freq2   51  100


Any resulting susceptibility (_SUS) and screening (_SCR) files can then be merged with the mrgscr utility.

## ecuteps¶

Mnemonics: Energy CUT-off for EPSilon (the dielectric matrix)
Characteristics: ENERGY
Mentioned in topic(s): topic_Susceptibility, topic_RandStopPow
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver in [3, 4]

Test list (click to open). Moderately used, [96/1095] in all abinit tests, [13/151] in abinit tutorials

ecuteps determines the cut-off energy of the planewave set used to represent the independent-particle susceptibility $\chi^{0}_{KS}$, the dielectric matrix $\epsilon$, and its inverse. It is not worth to take ecuteps bigger than four times ecutwfn, this latter limit corresponding to the highest Fourier components of a wavefunction convoluted with itself. Usually, even twice the value of ecutwfn might overkill. A value of ecuteps between 5 and 10 Hartree often (but not always) leads to converged results (at the level of 0.01 eV for the energy gap). In any case, a convergence study is worth.

## ecutsigx¶

Mnemonics: Energy CUT-off for SIGma eXchange
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 4

Test list (click to open). Moderately used, [80/1095] in all abinit tests, [8/151] in abinit tutorials

ecutsigx determines the cut-off energy of the planewave set used to generate the exchange part of the self-energy operator. For norm-conserving calculations, it is pointless to have ecutsigx bigger than 4*ecut, while for PAW calculations, the maximal useful value is pawecutdg. Thus, if you do not care about CPU time, please use these values. If you want to spare some CPU time, you might try to use a value between ecut and these upper limits.

ecutsigx is actually used to initialize the internal variable %npwsigx.

## ecutwfn¶

Mnemonics: Energy CUT-off for WaveFunctioNs
Characteristics: ENERGY
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: ecut if optdriver in [3, 4], 0.0 otherwise.

Only relevant if: optdriver in [3, 4]

Test list (click to open). Moderately used, [87/1095] in all abinit tests, [7/151] in abinit tutorials

ecutwfn determines the cut-off energy of the planewave set used to represent the wavefunctions in the formula that generates the independent- particle susceptibility $\chi^{0}_{KS}$ (for optdriver = 3), or the self- energy (for optdriver = 4). Usually, ecutwfn is smaller than ecut, so that the wavefunctions are filtered, and some components are ignored. As a side effect, the wavefunctions are no more normalized, and also, no more orthogonal. Also, the set of plane waves can be much smaller for optdriver = 3, than for optdriver = 4, although a convergence study is needed to choose correctly both values.

The size of this set of planewaves is %npwwfn.

## fftgw¶

Mnemonics: FFT for GW calculation
Mentioned in topic(s): topic_GW, topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 21
Only relevant if: optdriver in [3, 4]

Test list (click to open). Moderately used, [14/1095] in all abinit tests, [0/151] in abinit tutorials

The basic ingredients needed to perform both a screening and a sigma calculation are the so-called oscillator matrix elements defined as

\langle \mathbf{k-q},b_1 | e^{-i (\mathbf{q+G)} \mathbf{r}} | \mathbf{k}, b_2 \rangle

In reciprocal space, this expression is evaluated by a convolution in which the number of reciprocal lattice vectors employed to describe the wavefunctions is given by ecutwfn. In the case of screening calculations, the number of G vectors in the above expression is defined by ecuteps, while ecutsigx defines the number of G used in sigma calculations. To improve the efficiency of the code, the oscillator matrix elements are evaluated in real space through FFT techniques, and the fftgw input variable is used to select the FFT mesh to be used.

fftgw is the concatenation of two digits, labelled (A) and (B) whose value is internally used to define the value of ngfft(1:3) (see the setmesh.F90 routine).

The first digit (A) defines the augmentation of the FFT grid. Possible values are 1, 2 and 3.

• 0 → Use the FFT grid specified by the user through ngfft(1:3)
• 1 → Use a coarse FFT grid which encloses a sphere in reciprocal space whose radius depends on the largest value between ecutwfn and ecuteps
• 2 → Use a slightly augmented FFT which is sufficient for the correct treatment of the convolution
• 3 → Doubled FFT grid (same mesh as that used for GS calculations).

The second digit (B) can be chosen between 0 and 1. It defines whether a FFT grid compatible with all the symmetries of the space group must be enforced or not:

• 0 → Use the smallest FFT mesh which is compatible with the FFT library (faster, save memory but is less accurate)
• 1 → Enforce a FFT grid which is compatible with all the symmetry operations of the space group. This method leads to an increase both of CPU time and memory, but the matrix elements are more accurate since the symmetry properties of the system are preserved.

The behaviour of ABINIT before v5.5 corresponds to the default value 11.

## freqim_alpha¶

Mnemonics: FREQuencies along the IMaginary axis ALPHA parameter
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 5.0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

freqim_alpha is used only for numerical integration of the GW self-energy (gwcalctyp in [2, 12, 22, 9, 19, 29]). freqim_alpha determines the location of the maximum frequency point along the imaginary axis if the default grid is used in Contour Deformation (numerical integration) calculations. It is set as $\alpha*\omega_p$, where $\omega_p$ is the plasma frequency determined by the average density of the system (this can be set by hand by using the variable ppmfrq). See the section on grids in the descriptive text for cd_frqim_method for a detailed

## freqremax¶

Mnemonics: FREQuencies along the Real axis MAXimum
Characteristics: ENERGY
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 3

Test list (click to open). Moderately used, [16/1095] in all abinit tests, [3/151] in abinit tutorials

freqremax is used only for numerical integration of the GW self-energy (gwcalctyp in [2, 12, 22, 9, 19, 29]). freqremax sets the maximum real frequency used to calculate the dielectric matrix in order to perform the numerical integration of the GW self-energy. freqremax , freqremin and nfreqre define the spacing of the frequency mesh along the real axis.

## freqremin¶

Mnemonics: FREQuencies along the Real axis MINimum
Characteristics: ENERGY
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 3

Test list (click to open). Rarely used, [6/1095] in all abinit tests, [1/151] in abinit tutorials

freqremin is used only for numerical integration of the GW self-energy (gwcalctyp in [2, 12, 22, 9, 19, 29]). freqremin sets the minimum real frequency used to calculate the dielectric matrix in order to perform the numerical integration of the GW self-energy. freqremin can be used to split a wide frequency interval into smaller subintervals that can be calculated independently. The different subintervals can then be merged together with the mrgscr utility thus obtaining a single screening file that can used for self-energy calculations. Note that freqremax, freqremin and nfreqre define the spacing of the frequency mesh along the real axis.

## freqspmax¶

Mnemonics: FREQuencies for the SPectral function MAXimum
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 4

Test list (click to open). Moderately used, [12/1095] in all abinit tests, [3/151] in abinit tutorials

freqspmax sets the maximum real frequency used to calculate the spectral function from the GW Green’s function. freqspmin, freqspmax and nfreqsp define the spacing of an equidistant frequency mesh along the real axis. Alternatively, the variables gw_customnfreqsp and gw_freqsp can be used to make a user-defined grid.

## freqspmin¶

Mnemonics: FREQuencies for the SPectral function MINimum
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: -freqspmax
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [7/1095] in all abinit tests, [1/151] in abinit tutorials

freqspmin sets the minimum real frequency used to calculate the spectral function from the GW Green’s function. freqspmin is set to -freqspmax if left undefined. freqspmin , freqspmax, and nfreqsp define the spacing of an equidistant frequency mesh along the real axis. Alternatively, the variables gw_customnfreqsp and gw_freqsp can be used to make a user-defined grid.

## gw1rdm¶

Mnemonics: GW 1-Reduced Density Matrix
Mentioned in topic(s): topic_GW, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [4/1095] in all abinit tests, [0/151] in abinit tutorials

gw1rdm governs the calculation of the density matrix within the linearized GW approximation. It must be used with gwcalctyp=21.

*  **gw1rdm**  = 0: Do not update the density matrix.
*  **gw1rdm**  = 1: Compute the update of the density matrix for the k-point list specified with the keyword [[kptgw]].
*  **gw1rdm**  = 2: Same as 1 but also compute the correction to the Fock operator and update total energies.


## gw_customnfreqsp¶

Mnemonics: GW CUSTOM FREQuencies for SPectral function
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4 and gwcalctyp in [2, 9, 12, 19, 22, 29]

Test list (click to open). Rarely used, [3/1095] in all abinit tests, [0/151] in abinit tutorials

gw_customnfreqsp lets the user define the grid points along the real frequency axis by hand for the calculation of the self-energy along the real axis. Set this to the number of frequencies you want. The frequencies are specified with gw_freqsp.

## gw_freqsp¶

Mnemonics: GW SPectral FREQuencies
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: real
Dimensions: (gw_customnfreqsp)
Default value: [ {‘start’: 1, ‘stop’: ‘gw_customnfreqsp’}; ->
Only relevant if: optdriver == 4 and gw_customnfreqsp > 0

Test list (click to open). Rarely used, [3/1095] in all abinit tests, [0/151] in abinit tutorials

gw_freqsp specifies the grid points for the real frequency axis when the real and imaginary (spectral function) parts of sigma are calculated explicitly for post-processing or plotting. Only activated if gw_customnfreqsp is not equal to 0. The number of frequencies is set by the value of gw_customnfreqsp. Example:

gw_customnfreqsp   5
nfreqsp            5
gw_freqsp         -0.5  -0.1  0.0  1.0  10.0 eV


If nfreqsp is not equal to gw_customnfreqsp a warning will be issued.

## gw_frqim_inzgrid¶

Mnemonics: GW Contour Deformation FReQuencies on IMaginary axis Inverse Z Grid
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3,4] and gwcalctyp in [2, 9, 12, 19, 22, 29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gw_frqim_inzgrid creates grid points along the imaginary frequency axis by using an equidistant grid in the variable $z \subset [0,1]$ where the transform is:

i\omega^\prime = w_p \frac{z}{1-z}.

Here $\omega_p$ is the plasma frequency (default can be overridden by setting ppmfrq). The equidistant grid in z is determined uniquely by nfreqim) and the points are distributed so that half of them lie below the plasma frequency.

## gw_frqre_inzgrid¶

Mnemonics: GW Contour Deformation FReQuencies on REal axis Inverse Z Grid
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3, 4] and gwcalctyp in [2, 9, 12, 19, 22, 29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gw_frqre_inzgrid creates grid points along the real frequency axis by using an equidistant grid in the variable $z \subset [0, 1]$ where the transform is:

\omega = \omega_p \frac{z}{1-z}.

Here $\omega_p$ is the plasma frequency (default can be overridden by setting ppmfrq). The equidistant grid in z is determined uniquely by nfreqre ) and the points are distributed so that half of them lie below the plasma frequency. This is useful in conjunction with gw_frqim_inzgrid if one needs to use a grid which maps $[0, \infty] \rightarrow [0,1]$. Note that typically many more points are needed along the real axis in order to properly resolve peak structures. In contrast, both the screening and self-energy are very smooth along the imaginary axis. Also, please note that this is not an efficient grid for standard Contour Deformation calculations, where typically only a smaller range of frequencies near the origin is required. The maximum value needed along the real frequency axis is output in the logfile during Contour Deformation sigma calculations.

## gw_frqre_tangrid¶

Mnemonics: GW Contour Deformation FReQencies on REal axis - Use Tangent Grid
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3,4] and gwcalctyp in [2,9,12,19,22,29]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gw_frqre_tangrid defines a nonuniform grid to be used in frequency, with stepsize increasing proportional to $\tan(x)$. This makes the grid approximately linear to start with, with a rapid increase towards the end. Also, this is the grid which gives equal importance to each point used in the integration of a function which decays as $1/x^2$. To be used in conjunction with nfreqre, cd_max_freq and cd_halfway_freq which determine the parameters of the transformed grid.

## gw_icutcoul¶

Mnemonics: GW CUT-off for COULomb interaction
Mentioned in topic(s): topic_GWls, topic_Susceptibility, topic_Coulomb, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 6
Only relevant if: optdriver in [3,4]

Test list (click to open). Moderately used, [67/1095] in all abinit tests, [4/151] in abinit tutorials

Many-body calculations for fully periodic systems are problematic due to the presence of the integrable Coulomb singularity at $\mathbf{G}=0$ that hinders the convergence with respect to the number of q-points used to sample the Brillouin zone. The convergence can be accelerated by integrating accurately the zone in the neighborhood of $\mathbf{G}=0$.

gw_icutcoul defines the particular expression to be used for such integration. It can be used in conjunction with its equivalent for the ground state electronic structure cut-off icutcoul.

• 0 → sphere (molecules, but also 3D-crystals, see below).
• 1 → cylinder (nanowires, nanotubes).
• 2 → surface.
• 3 → Integration in a spherical mini-Brillouin Zone, legacy value.
• 4 → ERF, long-range only Coulomb interaction.
• 5 → ERFC, short-range only Coulomb interaction (e.g. as used in the HSE functional).
• 6 → auxiliary function integration for 3D systems from [Carrier2007].
• 7 → auxiliary function for 3D systems of Gygi and Baldereschi [Gygi1986].
• 14 → Monte-Carlo integration in the mini-Brillouin zone for ERF, long-range only Coulomb interaction.
• 15 → Monte-Carlo integration in the mini-Brillouin zone for ERFC, short-range only Coulomb interaction.
• 16 → Monte-Carlo integration in the mini-Brillouin zone for Full Coulomb interaction.

## gw_invalid_freq¶

Mnemonics: GW treatment of INVALID FREQuency for Hybertsen-Louie PPM
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3,4] and ppmodel in [2]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gw_invalid_freq sets the procedure to follow when a PPM frequency is invalid (negative or imaginary).

• gw_invalid_freq = 0: Drop them as proposed in Appendix B of [Hybertsen1986].
• gw_invalid_freq = 1: Set them to 1 hartree, as done for the PPM of Godby-Needs [Godby1989].
• gw_invalid_freq = 2: Set them to infinity.

## gw_nqlwl¶

Mnemonics: GW, Number of Q-points for the Long Wave-Length Limit
Mentioned in topic(s): topic_GW, topic_BSE, topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver in [3,4,99]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Only relevant if optdriver = 3,4,99 that is, screening, sigma or Bethe- Salpeter calculations, although the actual meaning of the variable depends on the particular run-level (see discussion below).

gw_nqlwl defines the number of directions in reciprocal space used to describe the non-analytical behaviour of the heads ($G = G'=0$) and the wings ($G=0$ or $G'=0$) of the dielectric matrix in the optical limit (i.e. for $q$ tending to zero). The number of directions is specified by the additional variable gw_qlwl.

When optdriver = 3, gw_nqlwl and gw_qlwl define the set of “small” $q$ that will be calculated and stored in the final SCR file. Therefore, the two variables can be used to analyze how the optical spectra depend on the direction of the incident phonon (useful especially in anisotropic systems).

When optdriver = 4, gw_nqlwl and gw_qlwl can be used to specify the heads and the wings to be used to perform the quadrature of the correlated part of the self-energy in the small region around the origin. (NB: not yet available, at present the quadrature is performed using a single direction in q-space)

When optdriver = 99, gw_nqlwl and gw_qlwl define the set of directions in q-space along which the macroscopic dielectric function is evaluated. By default the Bethe-Salpeter code calculates the macroscopic dielectric function using six different directions in q-space (the three basis vectors of the reciprocal lattice and the three Cartesian axis).

## gw_nstep¶

Mnemonics: GW Number of self-consistent STEPs
Mentioned in topic(s): topic_GW
Variable type: integer
Dimensions: scalar
Default value: 30
Only relevant if: optdriver == 8

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

Gives the maximum number of self-consistent GW cycles (or “iterations”) in which G and/or W will be updated until the quasi-particle energies are converged within gw_toldfeig. gwcalctyp and gw_sctype are used to define the type of self-consistency.

## gw_qlwl¶

Mnemonics: GW, Q-points for the Long Wave-Length limit
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy, topic_BSE
Variable type: real
Dimensions: (3,gw_nqlwl)
Default value: [1e-05, 2e-05, 3e-05]
Only relevant if: optdriver in [3,4,99]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

When optdriver = 3, gw_qlwl defines the set of q-points around Gamma that are considered during the evaluation of the non-analytical behaviour of the dielectric matrix. Optical spectra (with and without non-local field effects) are evaluated for each direction specified by gw_qlwl .

## gw_qprange¶

Mnemonics: GW QuasiParticle RANGE policy
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [10/1095] in all abinit tests, [0/151] in abinit tutorials

gw_qprange is active only when nkptgw is equal to zero (default value). This variable simplifies the specification of the list of kpoints and of the bands to be used for the computation of the quasi-particle corrections. The possible values are:

• 0 → Compute the QP corrections only for the fundamental and the optical gap
• +num → Compute the QP corrections for all the k-points in the irreducible zone, and include num bands above and below the Fermi level.
• -num → Compute the QP corrections for all the k-points in the irreducible zone. Include all occupied states and num empty states.

The default value is 0 and is very handy for one-shot calculations. It is important to stress, however, that the position of the optical/fundamental gaps is deduced from the energies computed on the k-mesh used for the WFK file. Therefore the computed gaps might differ from the correct ones that can only be obtained with an appropriate sampling of the irreducible zone. Positive values are useful if we do not know the position of the GW HOMO, LOMO and we want to investigate the effect of the GW corrections on the states close to the gap Negative values are usually used for self-consistent calculations Note that, in the case of self-consistency or symsigma == 1, the code might change the bands range so that all the degenerate states are included. Note also that kptgw, and bdgw are ignored when this options is used. If you want to select manually the list of k-points and bands, you have to provide the three variables nkptgw, kptgw, and bdgw.

## gw_sctype¶

Mnemonics: GW, Self-Consistency TYPE
Mentioned in topic(s): topic_GW
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver in [3,4]

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

This variable is used to partially define the kind of self-consistency for GW calculations. The other piece of information is given by gwcalctyp that defines the particular approximation for the self-energy operator as well as whether the wavefunctions have to replaced by quasi-particle amplitudes.

If gw_sctype is specified in the input file, the code will perform an iterative update of the quantities entering the GW equations until the quasi- particle energies are converged within gw_toldfeig. The maximum number of iterations is specified by gw_nstep. Possible values are:

• 1 → standard one-shot method (one screening calculation followed by a single sigma run)
• 2 → self-consistency only on W (iterative update of W followed by a sigma run in which G is approximated with the Kohn-Sham independent-particle Green’s function G0)
• 3 → self-consistency only of G (a single screening calculation to obtain the Kohn-Sham polarizability followed by an iterative update of the Green’s functions in the self-energy)
• 4 → fully self-consistent algorithm (iterative update of both G and W)

It is possible to initialize the self-consistent procedure by reading a previously calculated SCR or SUSC file via the variables getscr or getsuscep, respectively. getqps can be used to read a previous QPS file thus initializing the Green functions to be used in the first self- consistent iteration.

## gw_sigxcore¶

Mnemonics: GW, SIGma (self-energy) for the CORE contribution
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4 and %usepaw == 1

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Only available for PAW and relevant if optdriver = 4 that is, sigma calculations.

Theoretical introduction: GW calculations performed on top of electronic calculations relying when the frozen-core approximation is used to separate inner-core electrons from valence electrons, only the contribution to the self-energy arising from valence electrons is explicitly accounted for. In the standard approach based on pseudopotentials the contribution to the self- energy due to core electrons is approximated by means of the KS exchange- correlation potential generated by the core density. In the case of GW calculations employing the PAW method, the core contribution to the self- energy can be more accurately estimated in terms of the Fock operator generated by the core wavefunctions. In the simplest approach, the only ingredients required for this more refined treatment are the wave functions of the core electrons in the reference atomic configuration that are calculated during the generation of the PAW setup. This is a good approximation provided that the core wave functions are strictly localized inside the PAW spheres.

gw_sigxcore defines the approximation used to evaluate the core contribution to sigma.

• gw_sigxcore = 0, standard approach, the core contribution is approximated with vxc.
• gw_sigxcore = 1, the core term is approximated with the Fock operator inside the PAW spheres.

## gw_toldfeig¶

Mnemonics: GW TOLerance on the DiFference of the EIGenvalues
Characteristics: ENERGY
Mentioned in topic(s): topic_GW
Variable type: real
Dimensions: scalar
Default value: 0.1 eV
Only relevant if: optdriver == 8

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

Sets a tolerance for absolute differences of QP energies that will cause one self-consistent GW cycle to stop. Can be specified in Ha (the default), Ry, eV or Kelvin, since toldfe has the ENERGY characteristics (1 Ha = 27.2113845 eV)

## gwaclowrank¶

Mnemonics: GW Analytic Continuation LOW RANK approximation
Mentioned in topic(s): topic_GW, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gwaclowrank governs the number of eigenvectors of epsm1(iw’) that will be retained in the calculation. The default value gwaclowrank = 0 means all eigenvectors are retained and therefore no approximation is made. gwaclowrank is by definition lower than the number of planewaves used for epsm1, which is set by %npweps or indirectly by ecuteps. The lower gwaclowrank, the faster the calculation.

## gwcalctyp¶

Mnemonics: GW CALCulation TYPe
Mentioned in topic(s): topic_GW, topic_SelfEnergy, topic_RPACorrEn
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3,4]

Test list (click to open). Moderately used, [54/1095] in all abinit tests, [5/151] in abinit tutorials

gwcalctyp governs the choice between the different capabilities of the GW code.

• 0 <= gwcalctyp <= 9: standard “1 shot” quasi-particle method.
• 10 <= gwcalctyp <= 19: self-consistent quasi-particle method on energies only.
• 20 <= gwcalctyp <= 29: self-consistent quasi-particle method on energies and wavefunctions.

• gwcalctyp = 0, 10, or 20: standard Plasmon-Pole model GW calculation.

• gwcalctyp = 1: GW calculation where the self-energy along the real axis is obtained by performing the analytic continuation from the imaginary axis to the full complex plane via the Pade approximant. Only available for standard “1 shot” quasi-particle method.
• gwcalctyp = 2, 12, or 22: GW calculation using numerical integration (contour deformation method, see e.g. [Lebegue2003]).
• gwcalctyp = 5, 15, or 25: Hybrid functional or Hartree-Fock calculation, with the identifier of the functional given by ixc_sigma. See the latter for the definition of other related variables.
• gwcalctyp = 6, 16, or 26: Screened Exchange calculation.
• gwcalctyp = 7, 17, or 27: COHSEX calculation.
• gwcalctyp = 8, 18, or 28: model GW calculation following [Faleev2004] using a Plasmon-Pole model.
• gwcalctyp = 9, 19, or 29: model GW calculation following [Faleev2004] using numerical integration (contour deformation method).

## gwcomp¶

Mnemonics: GW COMPleteness
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [3,4]

Test list (click to open). Rarely used, [10/1095] in all abinit tests, [0/151] in abinit tutorials

gwcomp governs the use of an extrapolar approximation. If gwcomp == 1, one improves the completeness in a truncated sum over states. In practice, this permits one to reduce quite much the number of bands required in the calculation of the screening or of the self-energy. The energy parameter needed in the extrapolar approximation is set by gwencomp. See [Bruneval2008] for a description of the methodology.

## gwencomp¶

Mnemonics: GW ENergy for COMPleteness
Mentioned in topic(s): topic_SelfEnergy, topic_Susceptibility
Variable type: real
Dimensions: scalar
Default value: 2.0
Only relevant if: optdriver in [3,4] and gwcomp == 1

Test list (click to open). Rarely used, [10/1095] in all abinit tests, [0/151] in abinit tutorials

gwencomp sets the energy parameter used in the extrapolar approximation used to improve completeness and make the convergence against the number of bands much faster.

See [Bruneval2008] for a description of the methodology.

## gwgamma¶

Mnemonics: GW GAMMA
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver = 3 or 4 (Sigma calculations)

Test list (click to open). Rarely used, [4/1095] in all abinit tests, [0/151] in abinit tutorials

If gwgamma is 1, the vertex correction will be included leading to what is known as “GW-Gamma” approximation. see R. Del Sole, L. Reining, and R. W. Godby, Phys. Rev. B 49, 8024 (1994). Note that, in order to include the vertex correction in W, one has to start the sigma calculation from the susceptibility file_SUSC instead of the _SCR file (see getsuscep and irdsuscep ) Not available for PAW calculations.

gwgamma = -4 activates the bootstrap kernel of Sharma et al. [Sharma2011] in the test-charge-test-charge dielectric function [Chen2015].

gwgamma = -6 uses the same bootstrap kernel as with gwgamma = -4 but with only the head of the kernel. As such, the self-consistent iteration in the kernel can be disregarded [Chen2016].

gwgamma = -8 activates the RPA bootstrap-like kernel (one-shot) (see [Berger2015] and [Rigamonti2015]).

## gwgmcorr¶

Mnemonics: GW Galitskii-Migdal CORRelation energy
Mentioned in topic(s): topic_RPACorrEn, topic_GW, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

gwgmcorr ==1 allows to compute the GW correlation energy with the Galitskii-Migdal (GM) formula. It must be used with gwrpacorr>0. For gwrpacorr=1 it will be obtained for free, while for gwrpacorr>1 it will require an extra inversion of the polarizability matrix.

## gwls_band_index¶

Mnemonics: GWLS BAND INDEX
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

Governs the DFT eigenstate $|e\rangle$ in which the self-energy will be evaluated, as shown in Eq. (7) of [Laflamme2015]. That is, it is the state to be corrected in the G0W0 scheme.

## gwls_correlation¶

Mnemonics: GWLS CORRELATION
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 3
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Governs the use of a dielectric model (as explained in Sec. V of [Laflamme2015] and the use of the Lanczos scheme to solve Eqs. (30) and (35) of the same reference at all external gw_freqsp and integration (as generated from gwls_npt_gauss_quad) frequencies. The different choices are:

• gwls_correlation == 1: GWLS calculation with the dielectric model and without the shift Lanczos technique,
• gwls_correlation == 2: GWLS calculation without the dielectric model and without the shift Lanczos technique,
• gwls_correlation == 3: GWLS calculation with the dielectric model and with the shift Lanczos technique,
• gwls_correlation == 4: GWLS calculation without the dielectric model and with the shift Lanczos technique,
• gwls_correlation == 5: Not a GWLS calculation; just calculate and print the eigenvalues of the (static) dielectric matrix (for debugging purposes).

The default, ( gwls_correlation == 3), is the most performant option and should be kept by the user. Option 1, 2 and 5 are deprecated and will be removed.

## gwls_diel_model¶

Mnemonics: GWLS dielectric model
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 2
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Not used yet.

## gwls_exchange¶

Mnemonics: GWLS exact EXCHANGE
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Governs whether the exact exchange for the state to be corrected (gwls_band_index) is calculated ( gwls_exchange == 1) or not ( gwls_exchange = =0).

## gwls_first_seed¶

Mnemonics: GWLS FIRST SEED vector
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: gwls_band_index
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable sets the band index to be used to generate the first seed vector to be used in the construction of the Lanczos basis for the (static) dielectric matrix in a GWLS calculation. See Sec. IV of [Laflamme2015]. Together with gwls_nseeds, this defines the seeds for the Lanczos procedure. That is, the states associated to band index gwls_first_seed to gwls_first_seed +gwls_nseeds-1 are used to generate the seed vectors.

The default gwls_first_seed == gwls_band_index and gwls_nseeds == 1 has been thoroughly tested and seems to be the most performant. Users should therefore keep the default value.

## gwls_kmax_analytic¶

Mnemonics: GWLS KMAX for the ANALYTIC term
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 8
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Governs the number of iterations to be done in the shift Lanczos solution of Eq. (35) of [Laflamme2015] to solve it at all external frequencies requested by the user (gw_freqsp). The default value is converged to a few 10s of meV for all molecules studied so far.

## gwls_kmax_complement¶

Mnemonics: GWLS KMAX for the COMPLEMENT space.
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

The G0W0 formalism involves the calculation of a summation conceptually linked to the trace of the dielectric matrix [see Eq. (38) of [Laflamme2015]]. Since the eigenvalues spectrum of the dielectric matrix of formed by a few large discrete eigenvalues and an integrable divergence in the density of eigenvalues around 0, it is expensive to sample accurately this divergence using the exact dielectric operator. It this becomes interesting to calculate the ‘trace’ of the ‘exact - model’ dielectric matrix in a small basis and add it to the ‘trace’ of the ‘model’ dielectric matrix obtained in a large basis. In the context where the model dielectric matrix is used in the calculations, gwls_stern_kmax determines the size of the ‘small’ basis and gwls_kmax_complement determines the size of the ‘large’ basis.

For more information on the exact role of these bases and on the model dielectric operator used, see Sec. V of [Laflamme2015].

## gwls_kmax_numeric¶

Mnemonics: GWLS KMAX for the NUMERIC term
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 16
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Governs the number of iterations to be done in the shift Lanczos solution of Eq. (30) of [Laflamme2015] to solve it simultaneously at all integration frequencies (generated automatically by the number of points gwls_npt_gauss_quad to use in the gaussian quadrature) and all external frequencies requested by the user (gw_freqsp). The default value is converged to a few 10s of meV for all molecules studied so far.

## gwls_kmax_poles¶

Mnemonics: GWLS KMAX for the calculation of the POLES residue
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 4
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

The contour deformation technique, in the G0W0 context, will involve the calculation of pole residues associated to states lying between the one corrected (gwls_band_index) and the Fermi level. These residues take the form of a matrix element of the inverse dielectric matrix at a real frequency [see Eq. (11) of [Laflamme2015]]. Therefore, the dielectric matrix must be constructed in some basis at these frequencies and inverted to calculate the matrix element. The present input variable sets the size of the Lanczos basis to be constructed for this purpose. The default value has proven to be very robust for many molecular systems and should therefore be left to the default value by the user.

For more information on the Lanczos basis constructed for the calculation of the residues, see Sec. IV of [Laflamme2015].

## gwls_list_proj_freq¶

Mnemonics: GWLS LIST of the PROJection FREQuencies
Mentioned in topic(s): topic_GWls
Variable type: real
Dimensions: (gwls_n_proj_freq)
Default value: 0.0
*Only relevant if:
optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable sets the frequencies to be used to construct the basis in which the Hamiltonian is projected to accelerate the solution of the Sternheimer equations involved by the construction of the dielectric matrix at finite frequencies. See Sec. VI of [Laflamme2015]. For most cases, since the frequencies $\infty$ and 0.0 (if gwls_recycle > 0) are used at no computational cost, gwls_n_proj_freq == 0 (which means no ADDITIONAL frequency is to be used) is fine and no frequencies need to be picked up.

## gwls_model_parameter¶

Mnemonics: GWLS MODEL PARAMETER
Characteristics: ENERGY
Mentioned in topic(s): topic_GWls
Variable type: real
Dimensions: scalar
Default value: 1.0
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This is the width of the lorentzian, in Ha, used to model the frequency dependence of the dielectric matrix in the GWLS calculation [see Eqs. (12-16) and (34) of [Laflamme2015]]. More precisely, this parameter is the value of $\alpha$ used in Eq. (34). This model is then used to separate the integration over frequencies into a ‘model’ part [second term of Eq. (12)] and an ‘exact - model’ part [first term of Eq. (12)]. Since the ‘model’ part can be integrated analytically [see Eqs. (15), (16) and (34)], only the ‘exact - model’ part needs to be integrated numerically.

The only effect of this model is therefore to alleviate the numerical cost of the integration over frequencies in the G0W0 calculation. The value of the associated parameter has thus an impact on the convergence rate of the GWLS calculation with respect to the number of frequencies of integration (gwls_npt_gauss_quad), but no impact on the converged result of the GWLS calculation. Typically, the default ( gwls_model_parameter == 1.0) is optimal.

## gwls_n_proj_freq¶

Mnemonics: GWLS Number of PROJection FREQuencies
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable sets the number of frequencies, on top of $\infty$ and 0.0 (if gwls_recycle > 0), to be used for the construction of the basis in which the Hamiltonian is projected to accelerate the solution of the Sternheimer equations involved in the construction of the dielectric matrix at finite frequencies. See Sec. VI of [Laflamme2015]. For most cases, the default ( gwls_n_proj_freq == 0) is fine.

Mnemonics: GWLS Number of PoinTs to use for the GAUSSian QUADrature
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 10
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable defines the number of points used for the numerical integration of the self-energy over frequencies in GWLS computations [see Eq. (12) of [Laflamme2015]]. The default is fine for most cases.

## gwls_nseeds¶

Mnemonics: GWLS Number of SEED vectorS
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable sets the number of seed vectors to be used in the construction of the Lanczos basis for the (static) dielectric matrix in a GWLS calculation. See Sec. IV of [Laflamme2015]. Only gwls_nseeds == 1 has been tested for now and users should keep this value.

## gwls_print_debug¶

Mnemonics: GWLS PRINT level for DEBUGging
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Influences the level of verbosity for debugging purposes in a GWLS calculation. Users should keep its value at the default.

## gwls_recycle¶

Mnemonics: GWLS RECYCLE
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 2
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

This variable let the user choose if and how he wants to recycle the solutions of the Sternheimer equations involved in the construction of the static dielectric matrix.

• gwls_recycle = 0: No recycling of the solutions.
• gwls_recycle = 1: Recycle the solutions. To do so, store them in RAM.
• gwls_recycle = 2: Recycle the solutions. To do so, store them on disk.

If the user choose to recycle the solutions, they are used to construct the basis in which the Hamiltonian is projected for the solution of the Sternheimer equations involved by the calculation of the dielectric matrix at finite frequencies. The other solutions used will be those at $\omega \to \infty$ (always used) and those at $\omega=$gwls_list_proj_freq. For more information of the basis constructed, see Sec. IV of [Laflamme2015].

It is important to note that the solutions rapidly take much space to store. Therefore, it is often not possible to store them in RAM in production calculations, yet still desirable to retain them. This is when it becomes interesting to store them on disk. It is particularly efficient to choose the path of the file to be on disk space local to the processor in large MPI calculations, since each processor need only his own solutions in the construction of the basis.

## gwls_stern_kmax¶

Mnemonics: GWLS Kmax
Mentioned in topic(s): topic_GWls
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 66

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

This variable sets the dimension of the dielectric matrix used in a GWLS calculation [see Sec. IV of [Laflamme2015]]. Typically converged at a value of a few hundreds to a few thousands for a convergence criterion of 50 meV on the eigenenergies.

## gwmem¶

Mnemonics: GW MEMory
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy, topic_GW, topic_TuningSpeedMem
Variable type: integer
Dimensions: scalar
Default value: 11
Only relevant if: optdriver in [3,4]

Test list (click to open). Rarely used, [8/1095] in all abinit tests, [0/151] in abinit tutorials

gwmem governs the memory strategy during a screening and/or a sigma run.

• gwmem = 1x, the screening matrix are read for all q-vectors and stored in the memory.
• gwmem = 0x, the screening matrix are read just a q-vector after another.

• gwmem = x1, the real-space wavefunctions are stored in the memory.

• gwmem = x0, the real-space wavefunctions are not stored, but rather recalculated on-fly each abinit needs them using FFTs.

The default is gwmem = 11, which is the fastest, but also the most memory consuming. When experiencing memory shortage, one should try gwmem = 0. The first digit is only meaningful when performing sigma calculations.

## gwrpacorr¶

Mnemonics: GW RPA CORRelation energy
Mentioned in topic(s): topic_RPACorrEn
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3 and gwcalctyp in [1,11,21]

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

gwrpacorr governs the calculation of the RPA correlation energy.

• gwrpacorr = 0, no RPA correlation energy is calculated.
• gwrpacorr = 1, the RPA correlation energy is calculated using an exact integration over the coupling constant: it requires one diagonalization of the polarizability matrix.
• gwrpacorr = $n$ > 1, the RPA correlation energy is calculated using $n$ values for the coupling constant: it requires $n$ inversions of the polarizability matrix.

## inclvkb¶

Mnemonics: INCLude VKB
Mentioned in topic(s): topic_Susceptibility, topic_BSE
Variable type: integer
Dimensions: scalar
Default value: 2
Only relevant if: optdriver in [3,99]

Test list (click to open). Moderately used, [66/1095] in all abinit tests, [6/151] in abinit tutorials

Possible values of inclvkb are 0,1,2. If inclvkb is 1 or 2, the commutator of the non-local part of the pseudopotential with the position operator is correctly included in the q → 0 contribution. This is unfortunately time-consuming and in particular when the old algorithm implemented by inclvkb = 1 is used ( inclvkb = 2 is the recommended option). When inclvkb is 0, this contribution is incorrectly omitted, but the computation is much faster.

The importance of this contribution depends on the number of k points. Turning off inclvkb is to let to the choice of the user.

In general, the use of inclvkb = 0 is fine for GW calculations in crystalline systems provided that the k-point sampling is sufficiently converged.

Important

The use of inclvkb = 2 is strongly recommended for the calculation of optical properties.

## ixc_sigma¶

Mnemonics: Index of eXchange-Correlation functional used for self-energy calculations (SIGMA)
Mentioned in topic(s): topic_xc, topic_Hybrids
Variable type: integer
Dimensions: scalar
Default value: 1
Comment: Default corresponds to Teter parametrization.
Only relevant if: mod(gwcalctyp,10)==5

Test list (click to open). Moderately used, [15/1095] in all abinit tests, [0/151] in abinit tutorials

When gwcalctyp == 5, 15 or 25, ixc_sigma gives the identifier of the advanced functional (usually a hybrid) that is used perturbatively or self- consistently to obtain the improved electronic structure.

The meaning of the values of ixc_sigma is the same as the ones of ixc, so we refer to the latter for the list of possible values.

This input variable is introduced because in such calculation with gwcalctyp == 5, 15 or 25, there is an underlying primary exchange- correlation functional, that was used to obtain the starting wavefunctions and eigenenergies, whose identified is ixc. The definition of both ixc and ixc_sigma allows one to bypass possible sources of confusion.

Note however that in the case where gwcalctyp == 5, 15 or 25, the values of the input variables auxc_ixc, hyb_mixing, hyb_mixing_sr, hyb_range_fock and hyb_range_dft refers to the advanced functional, and not the primary one. Also, icutcoul and rcut have precedence over hyb_mixing, hyb_mixing_sr, hyb_range_fock and hyb_range_dft to define the parameters of the hybrid functional.

## kptgw¶

Mnemonics: K-PoinTs for GW calculations
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: (3,nkptgw)
Default value: 0.0
*Only relevant if:
optdriver in [4, 7]

Test list (click to open). Moderately used, [81/1095] in all abinit tests, [13/151] in abinit tutorials

For each k-point with number igwpt in the range (1:nkptgw), kptgw (1,igwpt) is the reduced coordinate of the k-point where the self-energy corrections are required while bdgw (1:2,igwpt) specifies the range of bands to be considered.

At present, not all k-points are possible. Only those corresponding to the k-point grid defined with the same repetition parameters ( kptrlatt, or ngkpt ) than the GS one, but without any shift, are allowed.

## mbpt_sciss¶

Mnemonics: Many Body Perturbation Theory SCISSor operator
Characteristics: ENERGY
Mentioned in topic(s): topic_GW, topic_Susceptibility, topic_SelfEnergy, topic_ElPhonInt
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver in [3,4,7,99]

Test list (click to open). Moderately used, [18/1095] in all abinit tests, [3/151] in abinit tutorials

The scissor operator energy added to the conductions states. In some cases, it mimics a second iteration self-consistent GW calculation.

## mdf_epsinf¶

Mnemonics: Model Dielectric Function, EPSilon INFinity
Mentioned in topic(s): topic_BSE
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 99 and bs_coulomb_term in [20,21] (Bethe-Salpeter calculations with a model dielectric function

Test list (click to open). Moderately used, [11/1095] in all abinit tests, [0/151] in abinit tutorials

mdf_epsinf specifies the value of the macroscopic dielectric function used to model the screening function (see [Bechstedt1992]). The proper spatial symmetry of the screening $W(\mathbf{r},\mathbf{r}^\prime)$ is enforced using Eq. (7) of [vonderLinden1988].

## nbandkss¶

Mnemonics: Number of BANDs in the KSS file
Mentioned in topic(s): topic_GW, topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Moderately used, [12/1095] in all abinit tests, [3/151] in abinit tutorials

This input variable is used for the preparation of a GW calculation: it is used in a GS run (where optdriver = 0) to generate a _KSS file. In this run, nbandkss should be non-zero. The generated _KSS file can be subsequently used to calculate the irreducible polarizabilty $\chi^{(0)}_{KS}$ using optdriver = 3 or to calculate GW corrections setting optdriver = 4.

• If nbandkss = 0, no _KSS file is created.
• If nbandkss = -1, all the available eigenstates (energies and eigenfunctions) are stored in the abo_KSS file at the end of the ground state calculation. The number of states is forced to be the same for all k-points: it will be the minimum of the number of plane waves over all k-points.
• If nbandkss is greater than 0, abinit stores (about) nbandkss eigenstates in the abo_KSS file. This number of states is forced to be the same for all k-points.

See npwkss for the selection of the number of the planewave components of the eigenstates to be stored. The input variable iomode can be used to read and write KSS files according to different fileformat (presently only iomode = 0 and 3 are available in the GW part). The precision of the KSS file can be tuned through the input variable kssform. For more details about the format of the abo_KSS file, see the routine outkss.F90.

Warning

For the time being, istwfk must be 1 for all the k-points in order to generate a _KSS file.

## nfreqim¶

Mnemonics: Number of FREQuencies along the IMaginary axis
Mentioned in topic(s): topic_FrequencyMeshMBPT, topic_RPACorrEn
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3 and gwcalctyp in [2,12,22,9,19,29]

Test list (click to open). Moderately used, [31/1095] in all abinit tests, [4/151] in abinit tutorials

nfreqim sets the number of pure imaginary frequencies used to calculate the dielectric matrix in order to perform the numerical integration of the GW self-energy.

## nfreqmidm¶

Mnemonics: Nth FREQuency Moment of the Imaginary part of the Dielectric Matrix
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: None
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

depending on the value of nfreqmidm will calculate the frequency moment of the dielectric matrix or its inverse,

• if nfreqmidm is positive: calculate (nth= nfreqmidm ) frequency moment of the dielectric matrix.
• if nfreqmidm is negative: calculate (nth= nfreqmidm ) frequency moment of the inverse dielectric matrix.
• if nfreqmidm = 0: calculate first frequency moment of the full polarizability.

See [Taut1985].

## nfreqre¶

Mnemonics: Number of FREQuencies along the REal axis
Mentioned in topic(s): topic_FrequencyMeshMBPT
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3 and gwcalctyp in [2,12,22,9,19,29]

Test list (click to open). Moderately used, [26/1095] in all abinit tests, [4/151] in abinit tutorials

nfreqre sets the number of real frequencies used to calculate the dielectric matrix in order to perform the numerical integration of the GW self-energy.

It can be used also in case of GW calculations with plasmon-pole models, i.e. gwcalctyp<10, to reduce the number of frequencies used to evaluate the dielectric matrix from the (default) two to one frequency (omega=0) by setting nfreqre = 1. This might be a good idea in case one is planning to use ppmodel > 1. This will force the calculation of the screening on a single frequency ($\omega=0$) and hence reduce memory and disk space requirement. The only draw back is that the user will not be able to perform self energy calculation using ppmodel = 1, since in the last case the dielectric matrix calculated on two frequencies is required. If the user is not sure which ppmodel to use, then s/he is not advised to use this input variable. Using the default values, one must be able to get a screening file that can be used with any ppmodel.

## nfreqsp¶

Mnemonics: Number of FREQuencies for the SPectral function
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Moderately used, [14/1095] in all abinit tests, [3/151] in abinit tutorials

nfreqsp defines the number of real frequencies used to calculate the spectral function of the GW Green’s function.

## nkptgw¶

Mnemonics: Number of K-PoinTs for GW corrections
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Moderately used, [81/1095] in all abinit tests, [13/151] in abinit tutorials

nkptgw gives the number of k-points for which the GW calculation must be done. It is used to dimension kptgw.

## nomegasf¶

Mnemonics: Number of OMEGA to evaluate the Spectral Function
Characteristics: ENERGY
Mentioned in topic(s): topic_Susceptibility
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3 and spmeth!=0

Test list (click to open). Rarely used, [6/1095] in all abinit tests, [1/151] in abinit tutorials

nomegasf defines the number of real frequencies used to describe the spectral function associated to the irreducible polarizability $\chi^{(0)}_{KS}$. The frequency mesh will cover the interval between 0 and the maximum (positive) transition energy between occupied and empty states. The delta function entering the expression defining the spectral function is approximated using two different methods according to the value of the spmeth input variable.

It is important to notice that an accurate description of the imaginary part of $\chi^{(0)}_{KS}$ requires an extremely dense frequency mesh. It should be kept in mind, however, that the memory required grows fast with the value of nomegasf .

## nomegasi¶

Mnemonics: Number of OMEGA(S) along the Imaginary axis
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 12
Only relevant if: optdriver == 4 and gwcalctyp == 1

Test list (click to open). Rarely used, [6/1095] in all abinit tests, [0/151] in abinit tutorials

nomegasi defines the number of frequency points used to sample the self- energy along the imaginary axis. The frequency mesh is linear and covers the interval between omegasimin=0.01 Hartree and omegasimax.

## nomegasrd¶

Mnemonics: Number of OMEGA to evaluate the Sigma Real axis Derivative
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 9
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

The number of real frequencies around the KS energy where the self-energy $\Sigma$ is evaluated. From these values, the derivative of $\Sigma$ at the KS energy is numerically estimated through linear interpolation.

## npvel¶

Mnemonics: Number of Particle VELocities
Mentioned in topic(s): topic_RandStopPow
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

In the context of the electronic stopping power of impinging ion in matter, npvel sets the number of the ion velocities to be calculated via linear response. When npvel = 0, no stopping power calculation is performed. The direction and the velocity maximum are set with the input variable pvelmax. Note that the results are output for a $Z=1$ impinging ion, i.e. a proton.

## npwkss¶

Mnemonics: Number of PlaneWaves in the KSS file
Mentioned in topic(s): topic_Susceptibility, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0

Test list (click to open). Rarely used, [0/1095] in all abinit tests, [0/151] in abinit tutorials

This input variable is used for the preparation of a GW calculation: the GS run (where optdriver = 1 and nbandkss/=0) should be followed with a run where optdriver = 3. Also, if nbandkss = 0, no use of npwkss .

npwkss defines the number of planewave components of the Kohn-Sham states to build the Hamiltonian, in the routine outkss.F90, and so, the size of the matrix, the size of eigenvectors, and the number of available states, to be stored in the abo_KSS file. If it is set to 0, then, the planewave basis set defined by the usual Ground State input variable ecut is used to generate the superset of all planewaves used for all k points. Note that this (large) planewave basis is the same for all k points.

Warning

For the time being, istwfk must be 1 for all the k points.

## nqptdm¶

Mnemonics: Number of Q-PoinTs for the Dielectric Matrix
Mentioned in topic(s): topic_Susceptibility
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 3

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

If nqptdm is equal to 0, the set of q points for computing the dielectric matrix is determined automatically considering all the possible differences between the k-points contained in the _KSS file. When nqptdm is non-zero, the list of q points is read from qptdm. This allows one to split the big calculation of all the dielectric matrices into smaller calculations that can be performed independently. The _SCR files generated in different runs can be merged thanks to the Mrgscr utility. If nqptdm is equal to -1, the code reports the list of q-points in the log file (YAML format) and then stops.

## omegasimax¶

Mnemonics: OMEGA to evaluate Sigma along the Imaginary axis D: MAXimal value
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 50 eV
Only relevant if: optdriver == 4 and gwcalctyp == 1

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

omegasimax defines the maximum frequency along the imaginary the axis. In conjunction with nomegasi, omegasimax uniquely defines the linear mesh employed to sample the self-energy along the imaginary axis.

## omegasrdmax¶

Mnemonics: OMEGA to evaluate the Sigma Real axis Derivative: MAXimal value
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 1.0 eV
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

The maximum distance from the KS energy where to evaluate Sigma. Sigma is evaluated at [ KS_energy - omegasrdmax , KS_energy + omegasrdmax ] sampled nomegasrd times.

## ppmfrq¶

Mnemonics: Plasmon Pole Model FReQuency
Characteristics: ENERGY
Mentioned in topic(s): topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 0.0 Ha
Only relevant if: optdriver in [3,4]

Test list (click to open). Moderately used, [29/1095] in all abinit tests, [5/151] in abinit tutorials

In plasmon-pole calculations

Usually only effective if GW corrections are evaluated using the plasmon-pole model of Godby-Needs (ppmodel == 1).

In the present status of the GW code, the convolution in frequency space defining the self-energy operator can be evaluated using two different approaches: numerical integration and plasmon-pole models. Methods based on the numerical integration (contour deformation, analytic continuation) require the knowledge of the screened interaction for several frequencies. These approaches give the most accurate results but at the price of an increase in the CPU time required. Alternatively, it is possible to approximate the dynamical behaviour of the screened interaction through simple analytical expressions, the so-called plasmon-pole models. In the plasmon-pole model proposed by Godby-Needs (ppmodel = 1), the screening must be available at zero frequency, as well as at another imaginary frequency, of the order of the plasmon frequency (the peak in the EELS spectrum). This information is used to model the behaviour of the dielectric matrix for all frequencies. During the calculation of the screening, ppmfrq defines the imaginary frequency where the dielectric matrix is evaluated, in addition to the zero frequency. During the self-energy run, ppmfrq can be used to define the second frequency to be used to calculate the plasmon-pole parameters. This is particularly useful when the SCR file contains several frequencies along the imaginary axis. In this case the frequency whose value is the closest one to ppmfrq will be selected. Note that, if the plasmon-pole approximation is good, then, the choice of ppmfrq should have no influence on the final result. One should check whether this is the case. In general, the plasmon frequencies of bulk solids are of the order of 0.5 Hartree.

In Contour Deformation calculations

ppmfrq is here used to override the default value calculated from the average electronic density per unit cell. This can affect the distribution of gridpoints along the imaginary and real frequency axes. See cd_frqim_method, gw_frqim_inzgrid and gw_frqre_inzgrid for more details.

## ppmodel¶

Mnemonics: Plasmon Pole MODEL
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver in [3,4]

Test list (click to open). Moderately used, [18/1095] in all abinit tests, [0/151] in abinit tutorials

Please note the difference between ppmodel 1 and ppmodel 2,3,4. In the first case (ppmodel = 1), the plasmon-pole parameters are determined in order to reproduce the behaviour of the dielectric matrix at two calculated frequencies: the static limit ($\omega=0$) and the imaginary frequency defined by ppmfrq. In the last three cases, instead, the plasmon-pole parameters are found by using the dielectric matrix calculated only at $\omega=0$ and enforcing the so-called f-sum rule. See also nfreqre.

Please note also that in the case of ppmodel 4, the plasmon energies are not simple mathematical parameters, but rather have a physical meaning (at least the lowest ones). Thus the calculated plasmon band structure (plasmon energy vs q vector) is reported in the output file for the lowest 10 bands.

## pvelmax¶

Mnemonics: Particle VELocity MAXimum
Mentioned in topic(s): topic_RandStopPow
Variable type: real
Dimensions: (3)
Default value: 3 * 1.0
Only relevant if: optdriver == 3

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

When npvel is larger than 0, it performs electronic stopping power calculations on a velocity grid along the direction determined by pvelmax . The vector pvelmax defines both the direction and the maximum velocity. pvelmax is input in Cartesian coordinates.

## qptdm¶

Mnemonics: Q-PoinTs for the Dielectric Matrix
Mentioned in topic(s): topic_Susceptibility
Variable type: real
Dimensions: (3,nqptdm)
Default value: 0.0
*Only relevant if:
optdriver == 3 and nqptdm!=0

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

qptdm contains the set of q points used in the screening part of ABINIT, instead of the automatic generation of the q points when nqptdm = 0. These q points are given in terms of reciprocal space primitive translations (not in cartesian coordinates!). For further explanation, see the input variable nqptdm.

## rcut¶

Mnemonics: Radius of the CUT-off for coulomb interaction
Mentioned in topic(s): topic_GWls, topic_Susceptibility, topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 0.0

Test list (click to open). Moderately used, [16/1095] in all abinit tests, [0/151] in abinit tutorials

Truncation of the Coulomb interaction in real space. The meaning of rcut is governed by the cutoff shape option icutcoul.

If rcut is negative, the cutoff is automatically calculated so to enclose the same volume inside the cutoff as the volume of the primitive cell.

## rhoqpmix¶

Mnemonics: RHO QuasiParticle MIXing
Mentioned in topic(s): topic_GW
Variable type: real
Dimensions: scalar
Default value: 1.0

Test list (click to open). Rarely used, [9/1095] in all abinit tests, [0/151] in abinit tutorials

For self-consistent GW runs, rhoqpmix sets the mixing coefficient between the new and the previous electronic densities. This mixing damps the spurious oscillations in the Hartree potential when achieving self-consistency. rhoqpmix is meaningful only when doing self-consistency on the wavefunctions with gwcalctyp >= 20.

## sigma_bsum_range¶

Mnemonics: SIGMA: Band SUM RANGE
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: (2)
Default value: [0, 0]
Only relevant if: optdriver in [7]

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

This variable allows the user to specify the range of bands in the sum over states for the e-ph self-energy $\Sigma_{n\kk}$. If not specified, the code includes all the states from 1 up to nband. Note that this option can be used only when computing both the real and imaginary part of the self-energy. In the calculation of electron linewidths, indeed, the states are automatically selected using an energy window that takes into account the maximum phonon frequency.

## sigma_ngkpt¶

Mnemonics: SIGMA: Number of Grid points for K PoinTs generation
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: (3)
Default value: 0
Only relevant if: optdriver in [4, 7]

Test list (click to open). Rarely used, [6/1095] in all abinit tests, [3/151] in abinit tutorials

This variable allows the user to specify the list of k-points in the self-energy $\Sigma_{n\kk}$ in terms of a homogeneous mesh in the IBZ instead of the traditional approach based on nkptgw, kptgw, bdgw.

The specification in terms of sigma_ngkpt is easier to use in particular when the self-energy is needed on a sub-mesh used to generate the input WFK file.

The set of bands can be specified either with sigma_erange or gw_qprange. sigma_erange is the recommended approach when computing transport properties.

Important

sigma_ngkpt and nkptgw and are mutually exclusive.

## sigma_nshiftk¶

Mnemonics: SIGMA: Number of SHIFTs for K point grids
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver in [4, 7] and sigma_shiftk

Test list (click to open). Rarely used, [3/1095] in all abinit tests, [1/151] in abinit tutorials

The number of shifts in sigma_shiftk.

## sigma_shiftk¶

Mnemonics: SHIFT for K points
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: (3,sigma_nshiftk)
Default value: [0, 0, 0]
Only relevant if: optdriver in [4, 7] and sigma_nshiftk
The use of this variable forbids the use of: sigma_erange or nkptgw

Test list (click to open). Rarely used, [4/1095] in all abinit tests, [2/151] in abinit tutorials

The shifts of the k-mesh used to define the list of k-points for the computation of the electron self-energy $\Sigma_{n\kk}$. See also sigma_nshiftk.

Important

This variable is not compatible with nkptgw and sigma_erange.

Characteristics: ENERGY
Mentioned in topic(s): topic_Susceptibility
Variable type: real
Dimensions: scalar
Default value: 0.0
Only relevant if: optdriver == 3 and spmeth == 2

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

When a screening calculation (optdriver == 3) uses a spectral representation of the irreducible polarizability in which the delta function is replaced by the gaussian approximant (spmeth == 2), the standard deviation of the gaussian is given by spbroad .

## spmeth¶

Mnemonics: SPectral METHod
Mentioned in topic(s): topic_Susceptibility
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [6/1095] in all abinit tests, [1/151] in abinit tutorials

The spmeth input variable defines the method used to calculate the irreducible polarizability $\chi^{(0)}_{KS}$.

By default $\chi^{(0)}_{KS}$ is calculated employing the Adler-Wiser expression ( spmeth = 0) with a CPU effort that scales linearly with the number of frequencies. This approach is convenient when few frequencies are required, and is usually used in conjunction with plasmon-pole models in which only one or two frequencies are calculated, according to the value of ppmodel. Unfortunately a calculation based on the Adler-Wiser expression might be quite CPU demanding if the matrix elements of the self-energy operator are evaluated by performing numerically the convolution defining the self-energy. The integrand function, indeed, has poles above and below the real axis, and the screened interaction has to be evaluated on a dense frequency mesh in order to obtain accurate results.

In the spectral method ( spmeth = 1 or 2) the irreducible polarizability is expressed as the Hilbert transform of the imaginary part. The advantage in using this approach consists in the fact that, once the spectral function is known, the irreducible polarizability for an arbitrary frequency can be easily obtained through inexpensive integrations. On the other hand, an accurate evaluation of the imaginary part requires a dense frequency mesh due to the presence of delta functions. Two different approaches can be used to approximate these delta functions thus allowing the use of affordable frequency grids.

Summarizing:

• 0 → use Adler-Wiser expression to calculate $\chi^{(0)}_{KS}$
• 1 → use the spectral method approximating the delta function with a triangular approximant as proposed in REF TO BE ADDED
• 2 → use spectral method but approximating the delta function with a Taylor expansion of the exponential as proposed in REF TO BE ADDED

## symchi¶

Mnemonics: SYMmetryze $\chi_0$
Characteristics: DEVELOP
Mentioned in topic(s): topic_Susceptibility
Variable type: integer
Dimensions: scalar
Default value: 1
Only relevant if: optdriver == 3

Test list (click to open). Moderately used, [35/1095] in all abinit tests, [4/151] in abinit tutorials

The evaluation of the irreducible polarizability for a given q point requires an integration over the Brillouin zone (BZ) which is approximated by a discrete sum over k points. In principle the integrand function should be evaluated for each k-point in the BZ, however it is possible to reduce the number of points to be explicitly considered by taking advantage of symmetry properties. The development input variable symchi is used to choose between these two equivalent methods:

• 0 → the summation over k points is performed considering all the points in the BZ (useful for testing and debugging).
• 1 → the summation is restricted to the k points belonging to the irreducible wedge defined by the little group associated to the external vector q.

## symsigma¶

Mnemonics: SYMmetrization of SIGMA matrix elements
Mentioned in topic(s): topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 1
Comment: The default value changed in Abinitv9 from 0 to 1
Only relevant if: optdriver in [4, 7]

Test list (click to open). Moderately used, [69/1095] in all abinit tests, [3/151] in abinit tutorials

This option activates the symmetrization of the self-energy matrix elements ( symsigma = 1). In this case the BZ integration defining the self-energy matrix elements is reduced to an appropriate irreducible wedge defined by the point group of the wave-vector k specified in the kptgw list.

The symmetrized expression leads to a considerable speedup of the run, especially for high-symmetry k points e.g. $\Gamma$. Unfortunately, this option is not yet compatible with self-consistent GW calculations (see gwcalctyp).

The code constructs a symmetric invariant for the diagonal matrix elements of the self-energy by averaging the self-energy matrix elements within the degenerate subspace. Therefore, particular care has to be taken in the presence of accidental degeneracies. Since calculations performed with symsigma = 1 will not be able to remove the initial accidental degeneracy. This is the reason why this option is not activated by default.

## ucrpa¶

Mnemonics: calculation of the screened interaction U with the Constrained RPA method
Mentioned in topic(s): topic_CRPA
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: nspinor == 1

Test list (click to open). Rarely used, [7/1095] in all abinit tests, [2/151] in abinit tutorials

When equal to one or two, this variable allows one to calculate U with the cRPA method. An explicit test is shown in automatic tests v7[23], v7[24], v7[25], v7[68], and v7[69]. The present implementation is parallelized (as for usual GW calculations), use symmetry over k points only for calculations involving one correlated atom, and can be use when correlated bands are entangled or not. The constrained calculation of the polarisability can be done by eliminating transition betweens correlated bands (and not orbitals) with the variable ucrpa_bands.

For ucrpa = 1, two solutions are possible. The first one is to specify (with the variable ucrpa_bands) the bands to exclude from the polarisability calculation. The second solution is to provide an energy window (with the variable ucrpa_window). The electronic transitions inside this window will not be taken into account in the polarisability calculation.

For ucrpa = 2, the ucrpa_bands should be equal to the dmftbandi and dmftbandf values, and the polarisability of the correlated subspace is constructed with a band and k point dependent weight.

The implementation is restricted to the case of nspinor = 1 (collinear case).

A short presentation of the method and some aspect of the implementation can be found in Sec. II and Appendix A of [Amadon2014].

## ucrpa_bands¶

Mnemonics: For the calculation of U with the Constrained RPA method, gives correlated BANDS
Mentioned in topic(s): topic_CRPA
Variable type: integer
Dimensions: (2)
Default value: [-1, -1]
Comment: That is, the default includes no band.

Test list (click to open). Rarely used, [5/1095] in all abinit tests, [1/151] in abinit tutorials

Gives the first and last correlated bands for the cRPA calculation of the polarisability.

## ucrpa_window¶

Mnemonics: For the calculation of U with the Constrained RPA method, gives energy WINDOW
Mentioned in topic(s): topic_CRPA
Variable type: real
Dimensions: (2)
Default value: [-1, -1]
Comment: That is, the energy window is empty by default.

Test list (click to open). Rarely used, [1/1095] in all abinit tests, [0/151] in abinit tutorials

Specify a window of energy for the cRPA calculation of the polarisability. The transition inside this window will not be taken into account in the constrained polarisabilty calculations.

The lower bound and the upper bound energies must be specified (two real numbers) with respect to the position of the Fermi level.

## vcutgeo¶

Mnemonics: V (potential) CUT-off GEOmetry
Mentioned in topic(s): topic_GWls, topic_Susceptibility, topic_SelfEnergy
Variable type: real
Dimensions: (3)
Default value: 3 * 0.0
Only relevant if: icutcoul in [1,2]

Test list (click to open). Rarely used, [2/1095] in all abinit tests, [0/151] in abinit tutorials

vcutgeo is used in conjunction with icutcoul to specify the geometry used to truncate the Coulomb interaction, as well as the particular approach to be used. It has a meaning only for a periodic one-dimensional system, typically a nanowire, nanotube or polymer surrounded by vacuum separating the system from images in neighbouring cells (icutcoul = 1) or in the case of periodic two-dimensional system, typically a slab with vacuum separating it from images in neighbouring cells ((icutcoul = 2). For each geometry, two different definitions of the cutoff region are available (see [Ismail-Beigi2006] and [Rozzi2006] for a complete description of the methods)

In the method of Ismail-Beigi [Ismail-Beigi2006] for one-dimensional systems, the cutoff region is given by the Wigner-Seitz cell centered on the axis of the cylinder. The cutoff region is thus automatically defined by the unit cell and there is no need to specify the value of rcut.

To define a cylinder along the z-axis use the following lines:

icutcoul 1
vcutgeo  0 0 1


Please note that the method of Ismail-Beigi is implemented only in the case of an orthorhombic Bravais lattice. For hexagonal lattices, one has to use the method of Rozzi [Rozzi2006]. In this case, the interaction is truncated in a finite cylinder. Contrarily to the first approach, the user has to specify both the radius of the cylinder with rcut as well as the length of the cylinder along the periodic dimension, that should always be smaller than the extension of the Born von Karman box. The length of the cylinder is given in terms of a multiple of the primitive vector along the periodic direction. Another option provided by Rozzi [Rozzi2006] is the infinite length cylinder. In order to activate it in ABINIT, one needs to use a very large negative vcutgeo value on the third direction (i.e. vcutgeo(3) <= -999).

For example, in order to define a finite cylinder along z of radius 2.5 Bohr and length 3*R3,

icutcoul 1
vcutgeo  0 0 -3.0 # note the minus sign
rcut     2.5


For two-dimensional systems (icutcoul = 2), vcutgeo is used to define the two periodic directions. Also in this case two different techniques are available. In the method of Ismail-Beigi, the (positive) non-zero components of vcutgeo define the periodic directions of the infinite surface. The interaction is truncated within a slab of width L where L is the length of the primitive vector of the lattice along the non-periodic dimension. For example:

icutcoul 2
vcutgeo  1 1 0

At present, the implementation of the Beigi technique for two-dimensional systems is restricted to the periodic directions being in the x-y plane.

In Rozzi’s method, it is also possible to define a finite range for the Coulomb interaction in the periodic directions by employing negative values. For example:

icutcoul 2
vcutgeo -3 -2 0


Note that not all k-point grids are allowed in these 1D and 2D cases: the k point vector component(s) along non-periodic direction(s) must vanish. So, if the 2D Ismail-Beigi technique is used, the z-component of the k points must vanish.

## x1rdm¶

Mnemonics: EXchange-only 1-Reduced Density Matrix
Mentioned in topic(s): topic_GW, topic_SelfEnergy
Variable type: integer
Dimensions: scalar
Default value: 0
Only relevant if: optdriver == 4

Test list (click to open). Rarely used, [3/1095] in all abinit tests, [0/151] in abinit tutorials

x1rdm ==1 forces the update of the density-matrix using only the exchange operator (instead of exchange and GW correlation). It must be used with gwcalctyp==21 and gw1rdm>0.

## zcut¶

Mnemonics: Z-CUT
Characteristics: ENERGY
Mentioned in topic(s): topic_Susceptibility, topic_BSE, topic_SelfEnergy
Variable type: real
Dimensions: scalar
Default value: 0.0036749326
Comment: 0.1 eV (0.0036749326 Ha)
Only relevant if: optdriver in [3, 4, 7, 99]