Refactor&Fix: remove normalization of numerical atomic orbitals in psi_initializer

[kirk0830]

Result

Previous:

Now:

Reminder

• Have you linked an issue with this pull request?
• Have you noticed possible changes of behavior below or in the linked issue?
• Have you explained the changes of codes in core modules of ESolver, HSolver, ElecState, Hamilt, Operator or Psi? (ignore if not applicable)

Linked Issue

Fix #3713

What's changed?

• Change the normalization of numerical atomic orbital from incomplete |k+G>-spanned space to |r>, make it in accord with module_nao
• Annotation change: previous annotation is somewhat difficult to read, all functions mess up with their annotations. Therefore annotations are rewritten. Additionally more annotations are added in ESolver_KS_PW, recording present development progress and future to implement design.
• Remove redundant virtual functions in psi_initializer: previously all functions are declared in base class psi_initializer, while it is actually not needed, because some functions will only be called inside class. After removal, now psi_initializer does not have too many functions and become much easier to maintain.
• Rename member function of psi_initializer: cal_psig -> proj_ao_onkG, create_ovlpjlqX -> allocate_table, ...
• Change to use STL container with algorithm: to meet the requirement of RAII, STL is used to replace all raw pointer or dynamic array based on raw pointer. This will be more parallel-safe and more strictly prevent the memory leaking problem.
• Use smart pointer to manage memory of psig, psi_initializer in esolver: use smart pointer to manage the variable lifespan, no manual delelte is needed anymore.

Any changes of core modules? (ignore if not applicable)

• Yes, change to use smart pointer to manage lifespan of psi_initializer in esolver_ks_pw, also add abundant annotations, illustrating consideration and develop progress.

[dyzheng]

Will this PR affect the result of examples/wannier90 or examples/berryphase ?

[kirk0830]

Will this PR affect the result of examples/wannier90 or examples/berryphase ?

@dyzheng for wannier90, I guess you mean examples/interface_wannier90. If so, my answer would be yes, the result I posted is the comparison between before and after removal of normalization after projecting onto |k+G> basis.
For berry phase, I am not sure about the reference value, but I had a look into the TIME_STATISTICS table in running_nscf.log, I did not find the psi_initializer_nao related items:

TIME STATISTICS
------------------------------------------------------------------------------------
     CLASS_NAME                 NAME            TIME(Sec)  CALLS   AVG(Sec) PER(%)
------------------------------------------------------------------------------------
                     total                        5.03           7   0.72   100.00
Driver               reading                      0.00           1   0.00     0.04
Input                Init                         0.00           1   0.00     0.02
Input_Conv           Convert                      0.00           1   0.00     0.01
Driver               driver_line                  5.03           1   5.03    99.96
UnitCell             check_tau                    0.00           1   0.00     0.00
PW_Basis_Sup         setuptransform               0.01           1   0.01     0.22
PW_Basis_Sup         distributeg                  0.00           1   0.00     0.00
mymath               heapsort                     0.00           3   0.00     0.03
PW_Basis_K           setuptransform               0.02           1   0.02     0.31
PW_Basis_K           distributeg                  0.00           1   0.00     0.00
PW_Basis             setup_struc_factor           0.02           1   0.02     0.31
NOrbital_Lm          extra_uniform                0.22         661   0.00     4.41
Mathzone_Add1        SplineD2                     0.01         661   0.00     0.17
Mathzone_Add1        Cubic_Spline_Interpolation   0.07         661   0.00     1.42
ppcell_vl            init_vloc                    0.00           1   0.00     0.04
Ions                 opt_ions                     4.65           1   4.65    92.50
ESolver_KS_LCAO      othercalculation             4.65           1   4.65    92.49
ESolver_KS_LCAO      beforesolver                 0.04           1   0.04     0.73
ESolver_KS_LCAO      set_matrix_grid              0.02           1   0.02     0.48
atom_arrange         search                       0.00           1   0.00     0.01
Grid_Technique       init                         0.00           1   0.00     0.07
Grid_BigCell         grid_expansion_index         0.00           2   0.00     0.02
Record_adj           for_2d                       0.02           1   0.02     0.38
Grid_Driver          Find_atom                    0.00          55   0.00     0.01
LCAO_Hamilt          grid_prepare                 0.00           1   0.00     0.00
Veff                 initialize_HR                0.00           1   0.00     0.02
OverlapNew           initialize_SR                0.00           1   0.00     0.02
EkineticNew          initialize_HR                0.00           1   0.00     0.02
NonlocalNew          initialize_HR                0.00           1   0.00     0.10
Charge               set_rho_core                 0.00           1   0.00     0.00
ModuleIO             read_rhog                    0.00           1   0.00     0.00
Potential            init_pot                     0.06           1   0.06     1.10
Potential            update_from_charge           0.06           1   0.06     1.10
Potential            cal_fixed_v                  0.01           1   0.01     0.12
PotLocal             cal_fixed_v                  0.01           1   0.01     0.12
PW_Basis_Sup         recip2real                   0.03           6   0.00     0.56
PW_Basis_Sup         gathers_scatterp             0.00           6   0.00     0.01
Potential            cal_v_eff                    0.05           1   0.05     0.97
H_Hartree_pw         v_hartree                    0.01           1   0.01     0.16
PW_Basis_Sup         real2recip                   0.02           6   0.00     0.49
PW_Basis_Sup         gatherp_scatters             0.00           6   0.00     0.00
PotXC                cal_v_eff                    0.04           1   0.04     0.82
XC_Functional        v_xc                         0.04           1   0.04     0.82
Potential            interpolate_vrs              0.00           1   0.00     0.00
HSolverLCAO          solve                        1.67           1   1.67    33.32
HamiltLCAO           updateHk                     1.03         128   0.01    20.55
OperatorLCAO         init                         0.92         384   0.00    18.39
Veff                 contributeHR                 0.35           1   0.35     7.05
Gint_interface       cal_gint                     0.35           1   0.35     7.02
Gint_interface       cal_gint_vlocal              0.35           1   0.35     7.02
Gint_Tools           cal_psir_ylm                 0.01          51   0.00     0.12
Gint_k               transfer_pvpR                0.00           1   0.00     0.03
OverlapNew           calculate_SR                 0.09           1   0.09     1.79
OverlapNew           contributeHk                 0.02         128   0.00     0.37
EkineticNew          contributeHR                 0.20           1   0.20     3.96
EkineticNew          calculate_HR                 0.19           1   0.19     3.83
NonlocalNew          contributeHR                 0.34           1   0.34     6.69
NonlocalNew          calculate_HR                 0.34           1   0.34     6.67
OperatorLCAO         contributeHk                 0.03         128   0.00     0.67
HSolverLCAO          hamiltSolvePsiK              0.64         128   0.01    12.73
DiagoElpa            elpa_solve                   0.62         128   0.00    12.43
Local_Orbital_wfc    wfc_2d_to_grid               0.00         128   0.00     0.02
ORB_gaunt_table      init_Gaunt_CH                0.00           1   0.00     0.02
ORB_gaunt_table      Calc_Gaunt_CH                0.00        1631   0.00     0.01
ORB_gaunt_table      init_Gaunt                   0.01           1   0.01     0.13
ORB_gaunt_table      Get_Gaunt_SH                 0.00       25313   0.00     0.07
ORB_table_phi        cal_ST_Phi12_R               0.66        1617   0.00    13.11
------------------------------------------------------------------------------------

Thus I think it would not affect result of berryphase calculation inside ABACUS.

[dyzheng]

Thanks for your fixing, I think this change will not affect the result of SCF with LCAO_in_PW, and I hope it can help the correctness of wannier90 interface.