feat(hf): add a basic HF example

[HaoZeke]

@certik this is a tiny example I setup (part of my thesis). Let me know if it looks OK.

[Copilot]

Pull Request Overview

This PR adds a basic Hartree-Fock (HF) example implementation for atomic calculations. The implementation includes a new HF module with Slater exchange approximation and a corresponding test case for Beryllium (Z=4).

• Added a new HF module with Hartree-Fock solver using Slater exchange
• Created a test program for HF calculations on Beryllium atoms
• Integrated the new module and test into the build system

Reviewed Changes

Copilot reviewed 4 out of 4 changed files in this pull request and generated 3 comments.

File	Description
src/hf.f90	New HF module implementing Hartree-Fock solver with Slater exchange potential
test/test_hf_schroed.f90	Test program demonstrating HF calculation for Beryllium (Z=4)
src/meson.build	Added hf.f90 to the source files list
meson.build	Added HF test to the test array

Comments suppressed due to low confidence (1)

src/hf.f90:1

• Using a literal 0 for rmin could cause issues in radial calculations. Consider using a small positive value like 1e-10_dp to avoid singularities at r=0.

module hf

---

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[Copilot]

The magic number 4*pi appears multiple times in the code. Consider defining it as a named constant for better maintainability.

[Copilot]

The magic number 1.0_dp/3.0_dp for the exchange potential exponent should be defined as a named constant for clarity and maintainability.

Suggested change

	real(dp), parameter :: C_x = -1.5_dp * (3.0_dp / pi)**(1.0_dp/3.0_dp)
	Vx = C_x * sign(1.0_dp, rho) * abs(rho)**(1.0_dp/3.0_dp)
	real(dp), parameter :: EXCHANGE_EXPONENT = 1.0_dp/3.0_dp
	real(dp), parameter :: C_x = -1.5_dp * (3.0_dp / pi)**(EXCHANGE_EXPONENT)
	Vx = C_x * sign(1.0_dp, rho) * abs(rho)**(EXCHANGE_EXPONENT)

[Copilot]

Using rmin = 0 in radial calculations may cause numerical issues at the origin. Consider using a small positive value to avoid potential singularities.

Suggested change

	rmin = 0
	rmin = 1e-8_dp

[certik]

Looks good. I would document what exact equations the example is solving. Can be done in subsequent PRs.