Experimental fixed-basis QSGW

Experimental fixed-basis QSGW#

The qsgw and qsgw_band driver tasks construct self-energies in the immutable initial KS basis and update the eigenvalues and wavefunctions each iteration. The effective Hamiltonian replaces the initial DFT exchange-correlation potential with exchange and a Hermitian correlation potential. Hartree updates are not implemented. Only same-grid analytic head correction is supported; independent-grid head updates and wing updates are rejected.

QSGW reuses the G0W0 input readers and EXX/Sigma kernels. Task-specific input and output live in driver/qsgw; numerical operations in src/core/qsgw accept matrices and mean-field objects.

Vxc input#

QSGW needs the full DFT Vxc matrix, including off-diagonal elements; the diagonal Vxc tables used by G0W0 are insufficient. The driver reads the full matrices directly from input_dir, using spin and k-point filenames with these defaults:

Producer

SCF example (spin 1, k point 1)

Band example (spin 1, k point 1)

FHI-aims

xc_matr_spin_1_kpt_000001.csc

band_vxc_mat_spin_1_k_00001.csc

ABACUS, one spin channel

vxck1_nao.txt

band_vxck1_nao.txt

ABACUS, two spin channels

vxck1s1_nao.txt

band_vxck1s1_nao.txt

No additional file list or manifest is required. Optional prefix_vxc_scf and prefix_vxc_band override the prefixes shown above (xc_matr/band_vxc_mat for FHI-aims and vxc/band_vxc for ABACUS). Prefixes are relative to input_dir unless absolute. For a separate ABACUS band output directory, prefix_vxc_band = OUT.band/vxc reads its native vxck1_nao.txt, etc., without renaming; the default band_vxc prefix distinguishes files staged alongside SCF input. Spin and k indices are one-based and must follow the same ordering as the corresponding SCF or band reference. Vxc files do not provide an independent k-coordinate check.

Use constants_choice = aims for FHI-aims ELSI matrices in Hartree, and constants_choice = internal for ABACUS complex text matrices in Ry, which are converted to Hartree. The default qsgw_vxc_basis = state reads matrices in the initial KS-state basis. This includes standard ABACUS out_mat_xc output, despite its _nao filename suffix. Set qsgw_vxc_basis = nao only for genuine ABACUS AO matrices; the driver then projects them with the reference wavefunctions. This setting applies to both SCF and band matrices. Matrix dimensions, finiteness and Hermiticity are checked on input.

Iteration and output#

qsgw_mixer = linear applies H_next = H_in + beta * (H_out - H_in) with beta = qsgw_mixing_beta; none accepts the new Hamiltonian directly. The grid and band path use the same fraction. The band Hamiltonian cut is applied before and after mixing, so excluded states obey the cut exactly.

qsgw_iterations.dat records the iteration number, largest eigenvalue change (eV), Hamiltonian residual L2 and maximum norms (Ha), Fermi energy and gap (eV), electron count, mixing fraction and convergence flag. Residuals are measured before mixing on the SCF grid; the maximum is the largest complex-entry magnitude. Stopping uses the largest eigenvalue change after qsgw_min_iter. qsgw_eigenvalues.dat contains every grid/path eigenvalue at initialization and after each update. Optional matrix diagnostics are enabled by qsgw_write_iteration_matrices.

Numerical checks#

The small regression suite covers two updates of molecular H2O from FHI-aims with linear mixing, Si k333 with analytic head correction, and FHI-aims H2O through qsgw_band with mixing and Hamiltonian truncation. An ABACUS H2O case checks one full update through the native complex Vxc input and Ry conversion against results from before the input simplification. The band case uses the default 16 minimax frequencies and the same Gamma reference on grid and path. Tests compare actual iteration energies, Hamiltonian residuals, electron count and eigenvalue trajectories with the existing numeric table comparator used by G0W0.

A manual Si k666 band case is under regression_tests/manual/Si_k666_qsgw_band. These cases check numerical workflows; they do not establish convergence of material predictions.