Add SAD_GTO guess with 3-21G instead of Hydrogen AOs

[stigrj]

• New SCF.guess_type = sad_gto which reads the 3-21G basis sets from share/sad_basis/ instead of setting up an AO basis of Hydrogen eigenfunctions. Not sure whether it's an improvement over the standard sad_dz, though...

• Added screening option for the evaluation of GTOs in various initial guesses. Controlled by input parameter SCF.guess_screen which is a float representing number of standard deviations, beyond which the GTO is evaluated to zero. Expected to speed up standard SAD guesses somewhat.

[codecov[bot]]

Codecov Report

Merging #400 (a565cc7) into master (ab262e1) will decrease coverage by 0.51%. The diff coverage is 0.82%.

:exclamation: Current head a565cc7 differs from pull request most recent head 5a5d2cb. Consider uploading reports for the commit 5a5d2cb to get more accurate results

@@            Coverage Diff             @@
##           master     #400      +/-   ##
==========================================
- Coverage   68.51%   68.00%   -0.52%     
==========================================
  Files         179      179              
  Lines       14300    14410     +110     
==========================================
+ Hits         9798     9799       +1     
- Misses       4502     4611     +109     

Impacted Files	Coverage Δ
src/initial_guess/gto.cpp	59.01% <0.00%> (-19.25%)	:arrow_down:
src/initial_guess/sad.cpp	67.93% <0.00%> (-32.07%)	:arrow_down:
src/qmfunctions/qmfunction_utils.cpp	81.02% <0.00%> (-5.79%)	:arrow_down:
src/driver.cpp	69.55% <50.00%> (-0.06%)	:arrow_down:
src/chemistry/Nucleus.h	73.91% <0.00%> (-26.09%)	:arrow_down:

---

Continue to review full report at Codecov.

Legend - Click here to learn more Δ = absolute <relative> (impact), ø = not affected, ? = missing data Powered by Codecov. Last update ab262e1...5a5d2cb. Read the comment docs.

[stigrj]

SAD_GTO convergence for some Ni complex:

===========================================================================
 Iter           MO residual             Total energy                Update
---------------------------------------------------------------------------
    0          9.486833e+00       -2871.133370005639         -2.871133e+03
    1          6.373926e-01       -2886.516418844161         -1.538305e+01
    2          2.557858e-01       -2887.134570848163         -6.181520e-01
    3          1.194583e-01       -2887.245656006424         -1.110852e-01
    4          7.999071e-02       -2887.286245156482         -4.058915e-02
    5          1.264002e-01       -2887.321871333240         -3.562618e-02
    6          6.671218e-02       -2887.334927415342         -1.305608e-02
    7          6.802234e-02       -2887.347317597009         -1.239018e-02
    8          4.746045e-02       -2887.353855939271         -6.538342e-03
    9          5.211014e-02       -2887.357988889306         -4.132950e-03
   10          2.794708e-02       -2887.360939947434         -2.951058e-03
   11          2.283775e-02       -2887.362321669932         -1.381722e-03
   12          1.505338e-02       -2887.362824301893         -5.026320e-04
---------------------------------------------------------------------------
                      SCF converged in 12 iterations!
===========================================================================

compared to the good ol' SAD_DZ:

===========================================================================
 Iter           MO residual             Total energy                Update
---------------------------------------------------------------------------
    0          9.486833e+00       -2851.355144659785         -2.851355e+03
    1          1.652298e+00       -2866.293443194611         -1.493830e+01
    2          1.124413e+00       -2873.238534223135         -6.945091e+00
    3          7.123881e-01       -2876.870289729848         -3.631756e+00
    4          6.979813e-01       -2879.453487196854         -2.583197e+00
    5          6.689936e-01       -2881.418573873416         -1.965087e+00
    6          4.042748e-01       -2882.406062604978         -9.874887e-01
    7          1.513471e+00       -2884.282844013223         -1.876781e+00
    8          5.992928e-01       -2884.997568455024         -7.147244e-01
    9          7.527686e-01       -2885.971568578544         -9.740001e-01
   10          3.291256e-01       -2886.427363244316         -4.557947e-01
   11          4.072887e-01       -2886.719450121097         -2.920869e-01
   12          4.008856e-01       -2886.953903769770         -2.344536e-01
   13          2.179256e-01       -2887.054556525391         -1.006528e-01
   14          5.348428e-01       -2887.128757250646         -7.420073e-02
   15          3.394773e-01       -2887.158681634962         -2.992438e-02
   16          4.588629e-01       -2887.239357284327         -8.067565e-02
   17          1.602679e-01       -2887.293899982501         -5.454270e-02
   18          8.510131e-02       -2887.316638160011         -2.273818e-02
   19          1.805406e-01       -2887.333276527359         -1.663837e-02
   20          7.475968e-02       -2887.345227063257         -1.195054e-02
   21          1.382609e-01       -2887.355325514161         -1.009845e-02
   22          3.819932e-02       -2887.359147728878         -3.822215e-03
   23          6.187910e-02       -2887.362356608575         -3.208880e-03
   24          2.858246e-02       -2887.364267834016         -1.911225e-03
   25          3.096303e-02       -2887.365610029450         -1.342195e-03
   26          1.981330e-02       -2887.366463058896         -8.530294e-04
   27          1.537261e-02       -2887.367044335408         -5.812765e-04
---------------------------------------------------------------------------
                      SCF converged in 27 iterations!
===========================================================================

[Brakjen]

Very nice! :)

Here is sad_gto for Xe (world_prec = guess_prec = 1e-5) Walltime: 18 minutes

===========================================================================
 Iter           MO residual             Total energy                Update
---------------------------------------------------------------------------
    0          5.196152e+00       -7202.619249713141         -7.202619e+03
    1          1.160183e-01       -7233.031488098271         -3.041224e+01
    2          3.283643e-02       -7234.076552256704         -1.045064e+00
    3          1.667258e-02       -7234.196645609136         -1.200934e-01
    4          1.310087e-02       -7234.220586582349         -2.394097e-02
    5          1.170140e-02       -7234.231655376288         -1.106879e-02
    6          4.885828e-03       -7234.232218701658         -5.633254e-04
    7          3.572509e-03       -7234.232818258200         -5.995565e-04
    8          1.560652e-03       -7234.232917946327         -9.968813e-05
    9          8.057152e-04       -7234.232964806587         -4.686026e-05
   10          5.494256e-04       -7234.232990455595         -2.564901e-05
   11          3.050460e-04       -7234.232993350029         -2.894434e-06
   12          1.277010e-04       -7234.232994278396         -9.283676e-07
---------------------------------------------------------------------------
                      SCF converged in 12 iterations!
===========================================================================

and the same with sad_dz Walltime: 25 minutes

===========================================================================
 Iter           MO residual             Total energy                Update
---------------------------------------------------------------------------
    0          5.196152e+00       -7134.586380860554         -7.134586e+03
    1          1.946345e+00       -7218.310867616008         -8.372449e+01
    2          1.058071e+00       -7228.682418878908         -1.037155e+01
    3          6.361629e-01       -7232.392158178065         -3.709739e+00
    4          2.130290e-01       -7233.398960646703         -1.006802e+00
    5          1.850029e-01       -7233.982924021013         -5.839634e-01
    6          1.041522e-01       -7234.176739783486         -1.938158e-01
    7          5.698223e-02       -7234.214943367646         -3.820358e-02
    8          2.991435e-02       -7234.225195276479         -1.025191e-02
    9          1.881444e-02       -7234.230164071142         -4.968795e-03
   10          9.468968e-03       -7234.231917155496         -1.753084e-03
   11          1.053953e-02       -7234.232192296029         -2.751405e-04
   12          5.704532e-03       -7234.232711716407         -5.194204e-04
   13          3.340135e-03       -7234.232850554931         -1.388385e-04
   14          2.414959e-03       -7234.232918021183         -6.746625e-05
   15          1.892349e-03       -7234.232948312133         -3.029095e-05
   16          1.297262e-03       -7234.232964464264         -1.615213e-05
   17          6.341829e-04       -7234.232969582814         -5.118550e-06
   18          4.916449e-04       -7234.232971318601         -1.735787e-06
   19          3.021556e-04       -7234.232972460484         -1.141883e-06
   20          2.148755e-04       -7234.232973139436         -6.789514e-07
---------------------------------------------------------------------------
                      SCF converged in 20 iterations!
===========================================================================