Add WFN-history backend for Gamma-only NAO calculations

[Growl1234]

This PR introduces an optional WFN-based initialization path for NAO calculations.

A new wfc_extrap use_prev_wf path is added. It stores the converged wavefunction from the previous ionic step, rebuilds the current overlap matrix, reorthonormalizes the previous wavefunction with the current overlap matrix, and then reconstructs the density matrix and charge density before entering the normal SCF cycle. When this path is enabled, the existing charge-density extrapolation is skipped, so the initial density is generated from the WFN-history backend instead of being extrapolated directly in real space.

The implementation currently focuses on the Gamma-only backend, including MPI-distributed matrices. This is intended as a common backend for future improvements and more WFN-based predictors such as ASPC and GExt_PROJ.

Here's a simple test that shows the accuracy and effectiveness of the WFN-based path: test.zip. The regtesting is left for a next commit.

What's planned to resolve in the future PRs:

• Further reducing SCF iterations requires a more accurate WFN prediction, which would probably be more involved because the wavefunction coefficients live in a nonorthogonal moving NAO basis. The backend therefore has to handle wavefunction history ownership, current-overlap reconstruction, distributed matrix layout, S-orthonormalization, occupation handling, and density reconstruction consistently.
• For k-point case it's even more complicated because the backend has to handle complex per-k wavefunctions, k-dependent overlap matrices $S(k)$, local/global k-point ownership, density-matrix reconstruction from all k-points, and PBC phase or convention corrections between ionic steps.

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Adds Gamma-only LCAO wavefunction-history extrapolation (use_prev_wf) by snapshotting the previous step’s coefficients and reorthonormalizing them against the current overlap matrix before SCF.

Changes:

• Introduces LCAO wavefunction snapshot/history helpers and a Gamma-only reorthonormalization routine.
• Wires extrapolation into the LCAO ESolver flow and adds wfc_extrap input validation/handling (including skipping charge extrapolation when enabled).
• Updates CMake to enforce a minimum C++ standard and adds a new module_extrap subdirectory target.

Reviewed changes

Copilot reviewed 14 out of 14 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
source/source_lcao/module_extrap/wf_snapshot_lcao.h	Stores/restores full Psi coefficient snapshots plus occupations.
source/source_lcao/module_extrap/wf_orthonormalize_lcao.h	Declares Gamma-only reorthonormalization API + diagnostic result struct.
source/source_lcao/module_extrap/wf_orthonormalize_lcao.cpp	Implements MPI-aware assembly + Cholesky-based reorthonormalization.
source/source_lcao/module_extrap/wf_history_lcao.h	Defines wavefunction history class and apply-result diagnostics.
source/source_lcao/module_extrap/wf_history_lcao.cpp	Implements history management and use_prev_wf apply path.
source/source_lcao/module_extrap/wf_extrap_method.h	Adds extrapolation method/status enums and string conversions.
source/source_lcao/module_extrap/CMakeLists.txt	Adds lcao_extrap object library target for new module sources.
source/source_lcao/CMakeLists.txt	Enables module_extrap subdir and adds new sources to LCAO objects list.
source/source_io/module_parameter/read_input_item_system.cpp	Adds wfc_extrap input item, docs, and validation checks.
source/source_io/module_parameter/input_parameter.h	Adds wfc_extrap parameter with default "none".
source/source_esolver/esolver_ks_lcao.h	Adds wf_history_lcao_ member to ESolver.
source/source_esolver/esolver_ks_lcao.cpp	Initializes history, prepares overlap early, applies extrapolation, rebuilds density, updates history after SCF.
source/source_esolver/esolver_fp.cpp	Skips charge extrapolation when wfc_extrap is enabled (LCAO, istep>0).
CMakeLists.txt	Enforces a minimum C++ standard globally (now 14).

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.