GW

Element: gw

G0W0 calculation setup.

contains:	freqgrid (optional) selfenergy (optional) mixbasis (optional) barecoul (optional) scrcoul (optional)
XPath:	/input/gw

This element allows for specification of the following attributes: GBatchCount, coreflag, degeneracyAbsoluteTolerance, degeneracyRelativeTolerance, enforceCrystalSymmetryTetrahedron, enforceDegeneracy, ibgw, mblksiz, nbgw, nempty, ngridq, printKpoints, printSpectralFunction, qdepw, rpmat, skipgnd, symmetryBandstructure, taskname, vqloff

Attribute: GBatchCount

During the computation of expansion coefficients, operations on the interstitial part are processed in batches over G vectors for improved performance. For large unit cells or systems with significant vacuum, memory usage can become excessive. To reduce RAM pressure, the batch size can be limited from the full set of G vectors to a smaller value, defined by GBatchCount.

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/@GBatchCount

Attribute: coreflag

Option for treating core states in GW:

• all - All-electron treatment.
• xal - Both core and valence states are used to compute the exchange self-energy and only valence electrons for computing the correlation self-energy.
• val - Valence-electron treatment.
• vab - Valence-electron treatment where core states are also excluded from the construction of the mixed-product basis.

Type:	string
Default:	"all"
Use:	optional
XPath:	/input/gw/@coreflag

Attribute: degeneracyAbsoluteTolerance

When enforceDegeneracy is true, this controls the absolute tolerance for considering two states degenerate. Systems with flat bands and/or bunch of degenerate states in the vicinity of the Fermi level might require lower values.

Type:	fortrandouble
Default:	"1.0d-8"
Use:	optional
XPath:	/input/gw/@degeneracyAbsoluteTolerance

Attribute: degeneracyRelativeTolerance

When enforceDegeneracy is true, this controls the relative tolerance for considering two states degenerate. Systems with degenerate flat bands might require lower values.

Type:	fortrandouble
Default:	"1.0d-5"
Use:	optional
XPath:	/input/gw/@degeneracyRelativeTolerance

Attribute: enforceCrystalSymmetryTetrahedron

When true it enforces crystal symmetry for the tetrahedron method. It should be used when crystal symmetry is used to restrict the computation of the dielectric matrix to the irreducible wedge.

Type:	boolean
Default:	"false"
Use:	optional
XPath:	/input/gw/@enforceCrystalSymmetryTetrahedron

Attribute: enforceDegeneracy

When true, enforce a special treatment of degeneracy by:

• Adjusting the number of unoccupied bands downward to prevent truncating degenerate subspaces when computing the dielectric function and correlation self-energy.
• Internally enlarging the range of KS states over which the diagonal elements of the self-energy elements and exchange-correlation potential are evaluated, to allow for performing an average over degenerate subspaces.

Unless there is a good reason, it is not generally advisable to set enforceDegeneracy to false. For details, refer to Section 6 and Appendix A of this (https://doi.org/10.1016/j.cpc.2011.12.006) and this (https://doi.org/10.1103/PhysRevB.35.5585) papers, respectively.

Type:	boolean
Default:	"true"
Use:	optional
XPath:	/input/gw/@enforceDegeneracy

Attribute: ibgw

QP corrections are computed for states in the interval [ibgw, nbgw].

Type:	integer
Default:	"1"
Use:	optional
XPath:	/input/gw/@ibgw

Attribute: mblksiz

To reduce the memory usage, in summations over unoccupied states, big matrices are considered to be in a block form with a size of mblksiz.

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/@mblksiz

Attribute: nbgw

QP corrections are computed for states in the interval [ibgw, nbgw].

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/@nbgw

Attribute: nempty

Number of empty states to compute both the screened Coulomb potential and the self-energy.

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/@nempty

Attribute: ngridq

Size of the $\mathbf{k/q}$-point grids.

Type:	integertriple
Default:	"0 0 0"
Use:	optional
XPath:	/input/gw/@ngridq

Attribute: printKpoints

If true, detailed information about the k-points will be printed to the file GW_KPOINTS.OUT.

Type:	boolean
Default:	"false"
Use:	optional
XPath:	/input/gw/@printKpoints

Attribute: printSpectralFunction

Compute and output the spectral function.

Type:	boolean
Default:	"false"
Use:	optional
XPath:	/input/gw/@printSpectralFunction

Attribute: qdepw

Method to compute k/q and frequency dependent weights in the expression for polarizability:

• tet - Using the tetrahedron method as implemented in LibBZInt library
• sum - Direct summation employing a smearing parameter eta of freqgrid

Type:	string
Default:	"tet"
Use:	optional
XPath:	/input/gw/@qdepw

Attribute: rpmat

Skip calculation of the momentum matrix elements, instead read them from files PMATVV.OUT and PMATCV.OUT (restart option).

Type:	boolean
Default:	"false"
Use:	optional
XPath:	/input/gw/@rpmat

Attribute: skipgnd

Skip the recalculation of KS eigenvalues and eigenvectors for the specified k/q-point grids (restart option).

Type:	boolean
Default:	"false"
Use:	optional
XPath:	/input/gw/@skipgnd

Attribute: symmetryBandstructure

When true, symmetry operations are taken into account during the Fourier interpolation used to construct the quasiparticle (QP) bandstructure (for taskname="band").

Type:	boolean
Default:	"true"
Use:	optional
XPath:	/input/gw/@symmetryBandstructure

Attribute: taskname

Tasks launcher:

• g0w0 - G0W0 calculations
• g0w0-x - Exchange only G0W0 calculations
• cohsex - Coulomb-hole and screened-exchange (COHSEX) approximation
• band - QP banstructure as obtained by Fourier interpolation
• dos - QP density of states
• emac - Calculate the macroscopic dielectric function
• pmat - Calculate matrix elements of the momentum operator
• acon - Perform analytic continuation of the correlation self-energy from imaginary to real frequency and calculate QP energies
• taskGroup - Execute the group of tasks defined in taskGroup.

Type:	string
Default:	"g0w0"
Use:	optional
XPath:	/input/gw/@taskname

Attribute: vqloff

The $\mathbf{k/q}$-point offset vector in lattice coordinates.

Type:	vect3d
Default:	"0.0d0 0.0d0 0.0d0"
Use:	optional
XPath:	/input/gw/@vqloff

Element: freqgrid

Frequency grid setup used for computing $W(q,omega)$ and $Sigma(k,omega)$.

Type:	no content
XPath:	/input/gw/freqgrid

This element allows for specification of the following attributes: eta, fconv, fgrid, freqmax, freqmin, nomeg

Attribute: eta

Numerical (complex) smearing parameter used for the real frequency convolution and qdepw=sum.

Type:	fortrandouble
Default:	"1.0d-3"
Use:	optional
XPath:	/input/gw/freqgrid/@eta

Attribute: fconv

Frequency convolution type:

• nofreq - skip frequency dependency (testing option).
• refreq - real frequency formalism (only for response functions).
• imfreq - imaginary frequency formalism.

Type:	string
Default:	"imfreq"
Use:	optional
XPath:	/input/gw/freqgrid/@fconv

Attribute: fgrid

Grid types (listed only the recommended ones, for more grids see the source subroutine mod_frequency.f90):

• eqdist - Equidistant grid from freqmin to freqmax.
• gaulag - Grid for the Gauss-Laguerre quadrature rule from 0 to $\infty$.
• gauleg - Grid for the Gauss-Lagendre quadrature rule from 0 to $\infty$.
• gauleg2 - Grid for the double Gauss-Lagendre quadrature rule from 0 to freqmax and freqmax to $\infty$.
• clencurt2 - Grid for the Clenshaw-Curtis quadrature rule from 0 to $\infty$. freqmax can be used to rescale the frequencies.

Type:	string
Default:	"gauleg2"
Use:	optional
XPath:	/input/gw/freqgrid/@fgrid

Attribute: freqmax

Upper limit for the grid interval.

Type:	fortrandouble
Default:	"1.0d0"
Use:	optional
XPath:	/input/gw/freqgrid/@freqmax

Attribute: freqmin

Lower limit for the grid interval.

Type:	fortrandouble
Default:	"0.0d0"
Use:	optional
XPath:	/input/gw/freqgrid/@freqmin

Attribute: nomeg

Number of grid points.

Type:	integer
Default:	"16"
Use:	optional
XPath:	/input/gw/freqgrid/@nomeg

Element: selfenergy

Correlation self-energy setup.

contains:	wgrid (optional)
XPath:	/input/gw/selfenergy

This element allows for specification of the following attributes: actype, eqpsolver, eshift, method, nempty, singularity, swidth, tol

Attribute: actype

Analytical continuation scheme:

• pade - Pade's approximant (by H. J. Vidberg and J. W. Serence, J. Low Temp. Phys. 29, 179 (1977)).
• aaa - Y. Nakatsukasa, O. Sete, L. N. Trefethen, "The AAA algorithm for rational approximation", SIAM J. Sci. Comp. 40 (2018), A1494-A1522.

Type:	string
Default:	"pade"
Use:	optional
XPath:	/input/gw/selfenergy/@actype

Attribute: eqpsolver

Schemes to solve the quasiparticle (non-linear) equation:

• 0 - Perturbative solution.
• 1 - Z=1 calculations.
• 2 - Iterative solution.

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/selfenergy/@eqpsolver

Attribute: eshift

Alignment of the chemical potential:

• 0 - No alignment.
• 1 - Self-consistency at the Fermi level (iteratively).
• 2 - Self-consistency at the Fermi level (perturbatively).

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/selfenergy/@eshift

Attribute: method

Technique to compute the frequency convolution integral:

• ac - Analytical continuation
• cd - Contour deformation

Type:	string
Default:	"ac"
Use:	optional
XPath:	/input/gw/selfenergy/@method

Attribute: nempty

Number of empty states to calculate the correlation self energy (different from default).

Type:	integer
Default:	"0"
Use:	optional
XPath:	/input/gw/selfenergy/@nempty

Attribute: singularity

Treatment of the $\mathbf{q} \rightarrow 0$ singularity:

• none: No special treatment (test purpose only).
• mpb: Auxiliary function method by S. Massidda, M. Posternak, and A. Baldereschi, PRB 48, 5058 (1993)
• crg: Auxiliary function method by P. Carrier, S. Rohra, and A. Goerling, PRB 75, 205126 (2007).
• low_dim: Special treatment for low-dimensional cutoff by F. Rasmussen, P. Schmidt, K. Winther, and K. Thygesen, PRB 94, 155406 (2016).

Type:	choose from: none mpb crg low_dim
Default:	"mpb"
Use:	optional
XPath:	/input/gw/selfenergy/@singularity

Attribute: swidth

Smearing parameter for visualizing the spectral function.

Type:	fortrandouble
Default:	"1.0d-4"
Use:	optional
XPath:	/input/gw/selfenergy/@swidth

Attribute: tol

Tolerance factor used for generating support points in AAA-interpolation.

Type:	fortrandouble
Default:	"1.0d-12"
Use:	optional
XPath:	/input/gw/selfenergy/@tol

Element: wgrid

The real frequency grid (output) setup for computing and visualizing the correlation self-energy and the spectral function. For more detailed description see freqgrid.

Type:	no content
XPath:	/input/gw/selfenergy/wgrid

This element allows for specification of the following attributes: size, type, wmax, wmin

Attribute: size

Number of grid points.

Type:	integer
Default:	"1000"
Use:	optional
XPath:	/input/gw/selfenergy/wgrid/@size

Attribute: type

Grid type.

Type:	string
Default:	"eqdist"
Use:	optional
XPath:	/input/gw/selfenergy/wgrid/@type

Attribute: wmax

Upper limit for the grid interval.

Type:	fortrandouble
Default:	"1.0d0"
Use:	optional
XPath:	/input/gw/selfenergy/wgrid/@wmax

Attribute: wmin

Lower limit for the grid interval.

Type:	fortrandouble
Default:	"-1.0d0"
Use:	optional
XPath:	/input/gw/selfenergy/wgrid/@wmin

Element: mixbasis

Mixed-product basis setup.

Type:	no content
XPath:	/input/gw/mixbasis

This element allows for specification of the following attributes: epsmb, gmb, lmaxmb

Attribute: epsmb

Linear dependence tolerance factor: controls construction of the radial part of the mixed-product basis.

Type:	fortrandouble
Default:	"1.0d-4"
Use:	optional
XPath:	/input/gw/mixbasis/@epsmb

Attribute: gmb

Plane-wave energy cutoff (in units of $G_{max}^{LAPW}$): controls construction of the plane-wave part of the mixed-product basis.

Type:	fortrandouble
Default:	"1.0"
Use:	optional
XPath:	/input/gw/mixbasis/@gmb

Attribute: lmaxmb

Maximal angular momentum: controls construction of the radial part of the mixed-product basis.

Type:	integer
Default:	"3"
Use:	optional
XPath:	/input/gw/mixbasis/@lmaxmb

Element: barecoul

The bare Coulomb potential setup.

Type:	no content
XPath:	/input/gw/barecoul

This element allows for specification of the following attributes: barcevtol, basis, cutofftype, pwm, stctol

Attribute: barcevtol

Matrix elements of the polarizability, the screened Coulomb potential, and the self-energy are computed in the basis that diagonalize the bare Coulomb potential. This tolerance factor is used to reduce the size of the $V_c$-diagonal product basis when computing the screened Coulomb potential and the correlation self-energy.

Type:	fortrandouble
Default:	"0.1d0"
Use:	optional
XPath:	/input/gw/barecoul/@barcevtol

Attribute: basis

Two approaches to compute the bare Coulomb potential:

• mb - The Coulomb potential is computed in the mixed-product basis.
• pw - The Coulomb potential is computed in the plane-wave basis and then converted into the mixed-product basis. This option is used only when the potential truncation technique cutofftype is employed. From practical point, usage of this approach requires to set a higher value of pwm (typically = 4.0)

Type:	string
Default:	"mb"
Use:	optional
XPath:	/input/gw/barecoul/@basis

Attribute: cutofftype

Trigger the usage of the Coulomb potential truncation technique (S. Ismail-Beigi, "Truncation of Periodic Image Interactions for Confined Systems. Phys. Rev. B 73, 233103 (2006)).

• none - 3D periodic crystal.
• 0d - Isolated atom or molecule.
• 1d - 1D chain (periodicity along z-axis)
• 2d - 2D surface (vacuum separation along z-direction)

Type:	string
Default:	"none"
Use:	optional
XPath:	/input/gw/barecoul/@cutofftype

Attribute: pwm

Plane-wave energy cutoff (in units of gmaxvr*gmb) for computing the plane-wave part of the Coulomb potential.

Type:	fortrandouble
Default:	"2.0d0"
Use:	optional
XPath:	/input/gw/barecoul/@pwm

Attribute: stctol

Tolerance factor for computing the structure factor in Ewald summation scheme.

Type:	fortrandouble
Default:	"1.0d-15"
Use:	optional
XPath:	/input/gw/barecoul/@stctol

Element: scrcoul

Dynamically screened Coulomb potential setup.

Type:	no content
XPath:	/input/gw/scrcoul

This element allows for specification of the following attributes: averaging, omegap, q0eps, scrtype

Attribute: averaging

Averaging of the inverse dielectric function in the q $\to$ 0 limit.

Type:	choose from: isotropic 2d anisotropic anisotropic-2d
Default:	"isotropic"
Use:	optional
XPath:	/input/gw/scrcoul/@averaging

Attribute: omegap

Plasmon-pole frequency (fitting parameter).

Type:	fortrandouble
Default:	"1.0d0"
Use:	optional
XPath:	/input/gw/scrcoul/@omegap

Attribute: q0eps

q0eps - averaging direction q $\to$ 0. Default: (1,1,1)

Type:	vect3d
Default:	"1.0d0 1.0d0 1.0d0"
Use:	optional
XPath:	/input/gw/scrcoul/@q0eps

Attribute: scrtype

Approximation:

• rpa - Full-frequency Random-Phase Approximation.
• ppm - Godby-Needs plasmon-pole model.

Type:	string
Default:	"rpa"
Use:	optional
XPath:	/input/gw/scrcoul/@scrtype

Reused Elements

The following elements can occur more than once in the input file. There for they are listed separately.

Data Types

The Input definition uses derived data types. These are described here.