Feature: Add orthonormalization for PW RT-TDDFT

[AsTonyshment]

Summary

Single-precision PW RT-TDDFT propagation can accumulate electron-count errors, causing dipole drift and spurious low-frequency dielectric response. This PR adds explicit wavefunction orthonormalization before density construction to control this drift.

• Add td_orthonormal with Cholesky (cholesky, default), Löwdin (lowdin), Newton-Schulz (newton_schulz), and none options.
• Use the current electronic density for shared dipole output.

Validation

Benzene propagation over 10 fs, comparing single-precision calculations against a double-precision reference.

Dipole and dielectric response. Without orthonormalization, the default lin_thr produces electron-count drift that contaminates the dipole and low-frequency dielectric response. All three orthonormalization methods restore agreement with the double-precision reference. Tightening lin_thr also improves the response.

Timing. Orthonormalization preserves efficiency in this benchmark: the three methods take 40.34-40.90 min, slightly less than 41.14 min without correction. Tightening lin_thr to 1e-6 or 1e-7 without orthonormalization increases the runtime to 42.52 and 47.33 min, respectively.

Electron conservation. The error is measured against benzene's 30 valence electrons, $\Delta N_{\psi}=N_{\psi}-30$. Explicit orthonormalization keeps the error near zero during propagation; tightening the linear-solver tolerance alone does not systematically enforce electron conservation.

Orthogonality. The maximum elementwise deviation of $\boldsymbol{\Psi}^{\dagger}\boldsymbol{\Psi}$ from the identity remains below 1e-6 after correction for all tested orthonormalization methods.

[AsTonyshment]

We found that the densities (e.g., rho and rho_save) are rather chaotic in the code. This should be addressed and refactored in a separate PR in the near future. This PR focused on RT-TDDFT, and is ready to merge.