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[WIP] Add cusp correction based on atomic orbitals #4901

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[WIP] Add cusp correction based on atomic orbitals #4901

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930ba5d
Add atomic-orbital based cusp correction
markdewing Jan 13, 2024
24556d1
Add comment
markdewing Jan 13, 2024
d759aab
Add script for computing cusp parameters
markdewing Jan 16, 2024
60c644a
Correct all the s-type orbitals
markdewing Jan 22, 2024
e0cda53
Fix bugs
markdewing Jan 29, 2024
6e917d2
Add adaptive rc
markdewing Jan 29, 2024
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Add adaptive rc 
Sometimes a crossing in the 2nd derivative is not found.  In that case,
increase the initial fitting range and try again.

n may not be quantum number, but we can treat it like one, especially
for 1s and 2s orbitals.

Move the lower bound for computing the reference values to 0.1.
That is, the range of values used for the initial fit is [0.1, 0.2].
This seems to work better.
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@markdewing
markdewing committed Jan 29, 2024
commit 6e917d2b44d313d61ca8bd670baeb0ce826e2bc4
38 changes: 21 additions & 17 deletions utils/compute_cusp_correction.py
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Original file line number Diff line number Diff line change
Expand Up @@ -181,7 +181,7 @@ def find_s_orbitals(fname):
bas_group = atbs["basisGroup" + str(ig)]
l = bas_group["l"][0]
n = bas_group["n"][0]
if l == 0:
if l == 0 and n in [0, 1]:
print(" ", ig, n, l)
s_orbs.append((ib, elem, ig, n, l))

Expand Down Expand Up @@ -302,7 +302,8 @@ def get_reference_vals(basis, rc=0.2):
npts = 80
uplim = np.log(rc) / np.log(10)
# xpts = np.logspace(-2.0, uplim, npts)
xpts = np.linspace(0.01, rc, npts)
# Get better results if the fit starts from 0.1 rather than a smaller value.
xpts = np.linspace(0.1, rc, npts)
vals = np.zeros(npts)

for i, x in enumerate(xpts):
Expand Down Expand Up @@ -385,10 +386,6 @@ def find_roots(initial_rc, popt, basis):

roots.sort()

# This is a big hack - not sure if it works
if len(roots) == 0:
roots = [initial_rc]

return roots


Expand Down Expand Up @@ -422,22 +419,29 @@ def compute_cusp_correction(fname_in, s_orbs, fname_out=None, root_idx=None):
if fname_out:
fout = h5py.File(fname_out, "a")

initial_rc = 0.2
for (ib, elem, bs_idx, n, l) in s_orbs:
print(f"Processing {elem} orbital {bs_idx} n = {n} l = {l}")
if elem == "H":
initial_rc = 4.0
initial_rc = 0.2
basis = bs[elem]
xpts, vals = get_reference_vals(basis[bs_idx], initial_rc)
res = optimize.curve_fit(target_f, xpts, vals, maxfev=3000)
popt = res[0]
a, alpha, c = popt
print(f" optimized a = {a} alpha = {alpha} c = {c}")

# Find possible roots to choose for actual r_c
# to keep the second derivative continuous
# Find initial_rc adaptively, so it results in at least one root
for itry in range(5):
xpts, vals = get_reference_vals(basis[bs_idx], initial_rc)
res = optimize.curve_fit(target_f, xpts, vals, maxfev=3000)
popt = res[0]
a, alpha, c = popt
print(f" optimized a = {a} alpha = {alpha} c = {c}")

# Find possible roots to choose for actual r_c
# to keep the second derivative continuous

roots = find_roots(initial_rc, popt, basis[bs_idx])

if len(roots) > 0:
break

roots = find_roots(initial_rc, popt, basis[bs_idx])
initial_rc *= 2
print("No roots found, try rc = ", initial_rc)

# print('roots',sorted(roots))
# print('roots',roots)
Expand Down