[OFDFT] Non-unit TF weight is missing from single-spin total energy #8243

Describe the bug

For nspin = 1, KEDF_TF::get_energy() omits tf_weight_, although tf_potential() and get_energy_density() already apply it. As a result, the reported energy and its functional derivative describe different functionals when of_tf_weight != 1.

Reproduced on develop at 64463eb3d using CPU unit tests. Relevant implementation: kedf_tf.cpp.

Expected behavior

For a prescribed density, the weighted TF energy in Ry is

$$ T_w[\rho]=w C_{\mathrm{TF}}\Delta V\sum_i\rho_i^{5/3},\qquad C_{\mathrm{TF}}=5.742468000376382. $$

For two grid values rho = {1, 8} and dV = 0.25, the integral is 33 * dV:

At weight zero the TF potential vanishes, but the current total energy still depends on density. For a particle-conserving perturbation eta = {1, -1}, weight 0.4 gives a central energy difference of approximately -7.178085, while dV * sum(v_TF * eta) is approximately -2.871234.

To reproduce

Append this small prescribed-density test to source/source_pw/module_ofdft/test/test_kedf_tf.cpp:

TEST_F(TestKEDFTF, ReproduceNonUnitTFWeight)
{
    const double density[] = {1.0, 8.0};
    const double* rho[] = {density};
    const double weight = 0.4;
    const double dV = 0.25;
    kedf.set_para(2, dV, weight);
    const double energy = kedf.get_energy(rho);
    const double expected = 18.950144401242063;
    EXPECT_NEAR(energy, expected, 1e-12);
}

Configure a CPU testing build, then run:

cmake -S . -B build -DBUILD_TESTING=ON -DENABLE_MPI=ON \
  -DENABLE_LCAO=OFF -DENABLE_ELPA=OFF -DENABLE_LIBXC=OFF \
  -DENABLE_LIBRI=OFF -DENABLE_FFT_TWO_CENTER=OFF
cmake --build build --target MODULE_PW_OfDFT -j 6
OMP_NUM_THREADS=1 build/source/source_pw/module_ofdft/test/MODULE_PW_OfDFT \
  --gtest_filter=TestKEDFTF.ReproduceNonUnitTFWeight

The test runs with the default single spin channel. This is an analytic API reproducer, not a material-dependent reference calculation.

Additional regression tests confirm the same inconsistency through KEDF_Manager for both TF and complete WT energies with a fixed-electron-number density perturbation. The WT kernel does not compensate for the missing factor in the TF energy.

Environment

• Ubuntu 24.04.4 LTS
• GCC 13.3.0, CMake 3.28.3
• CPU, MPI-enabled build; test executed as one process with OMP_NUM_THREADS=1
• FFTW3, OpenBLAS/ScaLAPACK, system GoogleTest

Scope and proposed fix

Apply the stored TF weight in the single-spin energy integral and add energy/derivative, energy-density integral, and cached-stress regressions. get_stress() uses the cached TF energy, so its TF contribution also needs the corrected energy.

The nspin = 2 total-energy branch already includes the weight, and the default weight of 1 is unchanged. The potential formula already includes the weight. This report does not imply that all OFDFT densities, forces, or previous calculations are wrong: the effect depends on the actual parameters, convergence path, and quantity being used.

The existing tests/07_OFDFT/11_OF_TF_weight case uses of_tf_weight = 1.1; its reference values need to be regenerated and explained with the fix. Other kinetic-energy-density/ELF semantics are separate from this narrowly scoped energy issue.