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Feature: RI-Hartree for LR-TDDFT benchmark with FHI-aims (#5084)
* read and write Cs, Vs * ri-j for benchmark (R-summation unfinished) CV: io index consistent with aims ri-j for benchmark continue update RI_benchmark * non-hermitian eigensolver * fix bug in OperatorLREXX * Support different basis number from aims * add an example for RI-J-benchmark * fix compile without LibRI * include headers to prevent the bot from changing varable names * fix after rebase * rearrange CV files * [pre-commit.ci lite] apply automatic fixes --------- Co-authored-by: pre-commit-ci-lite[bot] <117423508+pre-commit-ci-lite[bot]@users.noreply.github.com>
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‎docs/advanced/input_files/input-main.md‎

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- [exx\_real\_number](#exx_real_number)
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- [exx\_symmetry\_realspace](#exx_symmetry_realspace)
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- [rpa\_ccp\_rmesh\_times](#rpa_ccp_rmesh_times)
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- [out\_ri\_cv](#out_ri_cv)
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- [Molecular dynamics](#molecular-dynamics)
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- [md\_type](#md_type)
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- [md\_nstep](#md_nstep)
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- [abs\_wavelen\_range](#abs_wavelen_range)
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- [out\_wfc\_lr](#out_wfc_lr)
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- [abs\_broadening](#abs_broadening)
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- [ri\_hartree\_benchmark](#ri_hartree_benchmark)
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- [aims_nbasis](#aims_nbasis)
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[back to top](#full-list-of-input-keywords)
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## System variables
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- True: rotate both D(k) and Hexx(R) to accelerate both diagonalization and EXX calculation
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- **Default**: True
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### out_ri_cv
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- **Type**: Boolean
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- **Description**: Whether to output the coefficient tensor C(R) and ABFs-representation Coulomb matrix V(R) for each atom pair and cell in real space.
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- **Default**: false
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[back to top](#full-list-of-input-keywords)
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## Molecular dynamics
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- **Description**: The broadening factor $\eta$ for the absorption spectrum calculation.
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- **Default**: 0.01
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### ri_hartree_benchmark
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- **Type**: String
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- **Description**: Whether to use the localized resolution-of-identity (LRI) approximation for the **Hartree** term of kernel in the $A$ matrix of LR-TDDFT for benchmark (with FHI-aims or another ABACUS calculation). Now it only supports molecular systems running with a single processor, and a large enough supercell should be used to make LRI C, V tensors contain only the R=(0 0 0) cell.
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- `aims`: The `OUT.${suffix}`directory should contain the FHI-aims output files: RI-LVL tensors`Cs_data_0.txt` and `coulomb_mat_0.txt`, and KS eigenstates from FHI-aims: `band_out`and `KS_eigenvectors.out`. The Casida equation will be constructed under FHI-aims' KS eigenpairs.
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- LRI tensor files (`Cs_data_0.txt` and `coulomb_mat_0.txt`)and Kohn-Sham eigenvalues (`bands_out`): run FHI-aims with periodic boundary conditions and with `total_energy_method rpa` and `output librpa`.
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- Kohn-Sham eigenstates under aims NAOs (`KS_eigenvectors.out`): run FHI-aims with `output eigenvectors`.
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- If the number of atomic orbitals of any atom type in FHI-aims is different from that in ABACUS, the `aims_nbasis` should be set.
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- `abacus`: The `OUT.${suffix}`directory should contain the RI-LVL tensors `Cs` and `Vs` (written by setting `out_ri_cv` to 1). The Casida equation will be constructed under ABACUS' KS eigenpairs, with the only difference that the Hartree term is constructed with RI approximation.
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- `none`: Construct the Hartree term by Poisson equation and grid integration as usual.
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- **Default**: none
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### aims_nbasis
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- **Type**: A number(ntype) of Integers
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- **Availability**: `ri_hartree_benchmark` = `aims`
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- **Description**: Atomic basis set size for each atom type (with the same order as in `STRU`) in FHI-aims.
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- **Default**: {} (empty list, where ABACUS use its own basis set size)
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[back to top](#full-list-of-input-keywords)

‎examples/lr-tddft/H2-RI-J-aims-benchmark/INPUT‎

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INPUT_PARAMETERS
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#Parameters (1.General)
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suffix aims-benchmark-tdhf
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pseudo_dir /home/fortneu49/LR-TDDFT/abacus-develop/tests/PP_ORB
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orbital_dir /home/fortneu49/LR-TDDFT/abacus-develop/tests/PP_ORB
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calculation scf
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nbands 4
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symmetry 0
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#Parameters (2.Iteration)
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ecutwfc 50
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scf_thr 1e-6
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scf_nmax 100
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#Parameters (3.Basis)
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basis_type lcao
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gamma_only 1
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nspin 2
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#Parameters (4.Smearing)
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smearing_method gaussian
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smearing_sigma 0.02
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#Parameters (5.Mixing)
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mixing_type pulay
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mixing_beta 0.4
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mixing_gg0 0.0
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exx_real_number 1
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lr_nstates 3
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nvirt 3
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xc_kernel hf
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lr_solver lapack
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esolver_type lr
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ri_hartree_benchmark aims
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aims_nbasis 5
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read_file_dir aims-files

‎examples/lr-tddft/H2-RI-J-aims-benchmark/KPT‎

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K_POINTS
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0
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Gamma
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1 1 1 0 0 0

‎examples/lr-tddft/H2-RI-J-aims-benchmark/STRU‎

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ATOMIC_SPECIES
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H 1.008 H_ONCV_PBE-1.0.upf
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NUMERICAL_ORBITAL
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H_gga_8au_60Ry_2s1p.orb
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LATTICE_CONSTANT
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1.889725989
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LATTICE_VECTORS
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30 0 0
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0 30 0
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0 0 30
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ATOMIC_POSITIONS
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Cartesian
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H
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0
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2
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0 0 10.37 0 0 0
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0 0 9.63 0 0 0

‎examples/lr-tddft/H2-RI-J-aims-benchmark/aims-files/Cs_data_0.txt‎

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‎examples/lr-tddft/H2-RI-J-aims-benchmark/aims-files/KS_eigenvectors.out‎

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‎examples/lr-tddft/H2-RI-J-aims-benchmark/aims-files/band_out‎

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