RESPACK: An ab initio tool for derivation of effective low-energy model of material

Program summary

• RESPACK computes maximally localized Wannier functions, RPA response functions, and frequency-dependent screened direct and exchange interactions for deriving effective low-energy models.The method uses plane waves, fast Fourier transforms for matrix elements, and generalized tetrahedron integration for Brillouin-zone integrals.Source: PROGRAM SUMMARY · p. 1
• Current inputs must come from band-structure codes using norm-conserving pseudopotentials and plane-wave basis sets.Automatic conversion scripts are prepared for xTAPP and Quantum ESPRESSO.Source: PROGRAM SUMMARY · p. 1
• OpenMP and MPI hybrid parallelization lets RESPACK treat calculation cells containing a few hundred atoms.The code is written in Fortran and Python and uses LAPACK, BLAS, and MPI routines.Source: PROGRAM SUMMARY · p. 1

1. Introduction

• LDA often fails for strongly correlated systems, where local interactions and quantum fluctuations dominate low-energy properties.The introduction describes ab initio methods for these materials as an active research subject.Source: §1 · p. 1
• First-principles effective-model calculations derive a correlated-electron model and then analyze it with solvers capable of evaluating electronic correlations accurately.The paper notes that such software development and release are necessary to spread the approach beyond laboratory-level programs.Source: §1 · pp. 1–2
• RESPACK combines maximally localized Wannier-function and ab initio many-body perturbation programs to derive effective low-energy models.The paper focuses on model derivation; GW, spin-orbit interaction, and electron-lattice coupling extensions are identified as future reports.Source: §1 · p. 2

2.1. Effective low-energy model

• The effective model uses Wannier-orbital transfer integrals and screened direct-Coulomb and exchange integrals, whose static limits provide interaction parameters.The screened interaction W(r, r′, ω) is evaluated using RPA with a constraint on the polarization function.Source: §2.1 · p. 2

2.2. Wannier function

• Wannier functions are constructed from selected Kohn–Sham bands using a transformation matrix, and their centers and spreads characterize their spatial localization.The selected bands are determined from energy-window information.Source: §2.2 · pp. 2–3

2.3. Response function with random phase approximation

• The response calculation evaluates polarization in a plane-wave basis; constrained RPA uses Wannier-to-Bloch transition probabilities, while usual RPA sets those probabilities to zero.Optical properties are calculated from the inverse dielectric matrix; the non-local pseudopotential contribution is omitted, which may significantly affect optical response, especially in transition metals.Source: §2.3 · pp. 3–4

2.4. Direct-Coulomb and exchange integrals

• Screened direct and exchange integrals are evaluated using the inverse dielectric matrix and Wannier orbitals, with the direct integral also examined as a function of Wannier-center distance.The q-grid is the same as the k-grid, and the q → 0 divergence is removed using a cited prescription.Source: §2.4 · p. 4

3.1. Symmetry

• Symmetry operations generate Bloch functions at reducible k points from irreducible data, with rotation and fractional translation operators; the inverse dielectric matrix is likewise generated at reducible q points.A rewind vector returns the rotated irreducible k point to the first Brillouin zone.Source: §3.1 · p. 5

3.2. Frequency grid

• The polarization-frequency grid is logarithmic, with 70 points and a default spacing of 0.05 eV; its upper boundary reaches 3Emax.The default Nmax is 90% of the total grid count, and ωNmax = Emax.Source: §3.2 · p. 5, Figure 1 · p. 5

3.3. Interpolation treatment

• Using transfer data, RESPACK constructs the one-body Hamiltonian at requested k points, then derives band eigenvalues, density of states, density matrices, and Fermi surfaces.The lattice weight avoids double-counting transfers at periodic-system boundary edges.Source: §3.3 · pp. 5–6

3.4. Parallel calculation

• Polarization calculations parallelize over band pairs and irreducible q points; virtual-state data are exchanged between processes, while q-point communities also parallelize over band pairs.The illustrated q-point setup divides 64 MPI processes into four communities of 16.Source: §3.4 · pp. 6–7, Figure 2 · p. 6

4. Calculation flow

• The RESPACK workflow runs band calculations, converts their results into inputs, calculates Wannier functions, computes polarization and dielectric functions, and evaluates screened-interaction matrix elements.The Wannier calculation precedes chiqw because constrained RPA uses Wannier information to restrict the polarization process.Source: §4 · p. 7, Figure 4 · p. 7

4.1. Preparation for RESPACK

• Interface scripts convert band-structure outputs from xTAPP or Quantum ESPRESSO into RESPACK inputs.The xTAPP script creates nine files in dir-wfn; qe2respack.py is provided for Quantum ESPRESSO.Source: §4.1 · p. 7

4.2. Wannier calculation

• The wannier calculation uses dir-wfn data and input.in conditions, then saves results in dir-wan and dir-model.It is run with the calc wannier executable.Source: §4.2 · p. 7

4.3. Chiqw calculation

• The chiqw calculation uses dir-wfn and dir-wan data to compute polarization and dielectric functions, saving results by irreducible q point under dir-eps.Its executable is calc chiqw.Source: §4.3 · p. 7, §4 · p. 7

4.4. Calc int calculation

• The calc int stage evaluates direct-Coulomb and exchange integrals with separate executables and a common input namelist.Results are saved in dir-intW, dir-intJ, and dir-model.Source: §4 · p. 7, §4.4 · p. 8

5.1. Download source files and compile

• The source archive contains installation materials and separate source directories for calc int, chiqw, and wannier.Each source directory has a Makefile.Source: §5.1 · p. 8
• Running make in a source directory generates its executable, and the same procedure applies to the other programs.The example builds calc chiqw.Source: §5.1 · p. 8

5.2. Compile using cmake

• CMake compilation uses a temporary build directory and runs cmake followed by make and make install.The example sets -DCONFIG=gcc and a configurable installation prefix.Source: §5.2 · p. 8
• The -DCONFIG option selects configuration files from RESPACK/config.The passage introduces available options but does not list them.Source: §5.2 · p. 8
• CMake places executables under RESPACK/build/src, while make install installs them under the chosen prefix or /usr/local/bin by default.Source: §5.2 · p. 8
• For a repeated CMake run, deleting the temporary build directory and restarting is recommended because prior settings may persist.Source: §5.2 · p. 8

6.1. Typical outputs

• The four principal t2g transfer integrals reproduce the original SrVO3 band structure.The benchmark compares the Kohn–Sham and Wannier-interpolated bands and illustrates the dxy Wannier function; equivalent transfers apply to dyz and dzx orbitals.Source: §6.1 · p. 8, Table 2 · p. 11, Figure 6 · p. 11
• Below 2–3 eV, constrained RPA and usual RPA dielectric spectra differ: usual RPA has a negative-diverging real part and Drude-like imaginary response, while constrained RPA converges to a finite real part.The constrained-RPA polarization excludes metallic charge excitation; the reported SrVO3 spectra neglect the nonlocal-pseudopotential transition-moment contribution, checked as insignificant here, though support remains future work.Source: §6.1 · p. 8, &param calc int · p. 11, Figure 9 · p. 11
• Usual RPA produces a low-energy t2g plasmon peak in EELS and a sharp reflectance drop, while constrained RPA lacks low-energy optical-conductivity intensity.The optical-conductivity trend follows the macroscopic dielectric function; the spectra differ below 2 eV.Source: &param calc int · pp. 11–12, Figure 10 · p. 12

6.2. Convergence check to calculation conditions

• Static interaction parameters converge around an 8 × 8 × 8 k-point grid; 50 bands suffice, and about 30 Ry for cRPA or 40 Ry for RPA gives onsite interactions converged within 0.01 eV.The polarization cutoff is important and larger cutoffs require more computation because of the double loop over G and G′ vectors.Source: §6.2 · pp. 12, 14, Table 3 · p. 13, Table 4 · p. 13
• Broadening δ does not affect static cRPA or RPA interactions, but increasing δ weakens the 1–2 eV EELS plasmon peak and shifts it lower, so dynamical properties require careful settings.The plasmon excitation is also sensitive to k-point density.Source: §6.2 · p. 14, Table 6 · p. 14, Figure 14 · p. 14

6.3. Pseudopotential dependence

• Changing the vanadium pseudopotential cutoff radius rloc leaves the five t2g band structures nearly identical but changes Wannier localization and bare onsite direct interactions.Smaller rloc shifts pseudo-wavefunction amplitude toward the ion core, yields smaller Wannier spreads and larger bare onsite U and U′; bare exchange J and nearest-neighbor V show no discernible effects.Source: §6.3 · pp. 14–15, Table 7 · p. 15, Figure 15 · p. 15
• Pseudopotential details hardly affect constrained- and usual-RPA interaction values, unlike bare interactions; a sufficiently large Eϵ cutoff is desirable for safer quantitative discussion, especially for usual RPA.Table 8 varies the local-pseudopotential cutoff radius rloc and examines Eϵ-cutoff dependence for SrVO3.Source: §6.3 · p. 15, Table 8 · p. 15
• Even at the same rloc, pseudopotential functional forms can produce quantitatively different results; ONCV and RRKJ are among the noted types.The passage cautions users to account for this dependence when choosing pseudopotentials.Source: §6.3 · p. 15
• RRKJ-QE gives significantly smaller screened direct-Coulomb U and U′ values than TM-xTAPP and ONCV-QE.TM-xTAPP uses xTAPP; ONCV-QE and RRKJ-QE use Quantum Espresso. TM results include valence and semicore configurations, while ONCV and RRKJ use semicore configurations.Source: §6.3 · p. 16, Table 9 · p. 16

• RESPACK provides programs for computing maximally localized Wannier functions, RPA response functions, and screened-interaction matrix elements for deriving effective low-energy models.Source: §7 · p. 16
• Interface scripts convert band-calculation results from xTAPP and Quantum Espresso into RESPACK inputs, which currently require norm-conserving pseudopotentials.Source: §7 · p. 16
• The software has been extended to GW calculations, spin-orbit interactions, and electron-lattice coupling evaluation, with those features slated for future reporting.Source: §7 · p. 16

• The RESPACK input file, input.in, uses Fortran namelist format to specify calculation conditions.Source: Appendix A · p. 16
• Six namelists cover Wannier-function calculations, band interpolation, visualization, polarization and dielectric functions, and direct-Coulomb and exchange-integral calculations.Source: Appendix A · p. 16, Table A.10 · p. 17
• The Wannier, chiqw, and calc int namelists are read by calc wannier, calc chiqw, and the calc w3d/calc j3d executables, respectively.Source: Appendix A · p. 16

Appendix A.1. &param wannier

• Wannier construction uses an energy window, Wannier-function count, and Gaussian initial guesses specified by orbital type, exponent, and fractional position.Source: Appendix A.1 · p. 17, Table A.11 · p. 17

Appendix A.2. &param interpolation

• Band interpolation takes symmetric k-point coordinates along the dispersion path, usually matching the points used in the DFT band calculation.Source: Appendix A.2 · p. 17, Table A.12 · p. 17

Appendix A.3. &param visualization

• Real-space Wannier visualization is skipped by default; setting Flg vis wannier to 1 generates data drawable with VESTA.Source: Appendix A.3 · p. 17, Table A.13 · p. 17

Appendix A.4. &param chiqw

• The chiqw namelist sets polarization and dielectric-function conditions, including the polarization cutoff and frequency-grid size.Source: Appendix A.4 · p. 17, Table A.14 · p. 18
• The default chiqw frequency grid has 70 logarithmically spaced points, and its range extends to three times the estimated maximum excitation energy.Source: Appendix A.4 · p. 18
• chiqw parallelizes polarization over q-point communities and performs constrained RPA only when Flg cRPA is enabled; its default is usual RPA.Source: Appendix A.4 · p. 18

Appendix A.5. &param calc int

• The calc int namelist controls direct-Coulomb and exchange-integral calculations, while Calc ifreq selects which effective-interaction frequencies are output.Source: Appendix A.5 · p. 18

Appendix B. transfer analysis

• A completed RESPACK job creates dir-model, which contains transfer-integral data such as zvo_hr.dat for transfer analysis.The passage notes that nine files are generated in the directory but does not enumerate them here.Source: Appendix B · p. 18
• The tr.py script sorts transfer data and can calculate band dispersion, density of states, and Fermi surfaces while varying transfer energy or spatial cutoffs and k-grid size.It uses calc tr internally and operates on data in dir-model.Source: Appendix B · pp. 18–19, Figure B.16 · p. 19, Table B.16 · p. 19
• With --ecut=0.1 eV, only nearest-neighbor transfers are included, appreciably changing the SrVO3 band dispersion and density of states.Figure B.17 compares energy cutoffs of 0.00, 0.01, 0.05, and 0.1 eV.Source: Figure B.17 · p. 19, Appendix B · p. 19
• Accurately describing Al’s small red Fermi-surface region requires a dense k-grid.Figure B.18 compares grids from 8 × 8 × 8 to 48 × 48 × 48; n, m, and l specify grid counts along reciprocal vectors b1, b2, and b3.Source: Appendix B · p. 20, Figure B.18 · p. 20