-
Notifications
You must be signed in to change notification settings - Fork 19
/
FormFactor.jl
316 lines (282 loc) · 30 KB
/
FormFactor.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
# `A exp(-a s^2) + B exp(-b s^2) + C exp(-c s^2) + D exp(-d s^2) + E`
struct ExpandedBesselIntegral
A :: Float64
a :: Float64
B :: Float64
b :: Float64
C :: Float64
c :: Float64
D :: Float64
d :: Float64
E :: Float64
end
struct FormFactor
j0 :: ExpandedBesselIntegral
j2 :: ExpandedBesselIntegral
config :: String
g :: Float64
end
const identity_form_factor = let
j0 = ExpandedBesselIntegral(0, 0, 0, 0, 0, 0, 0, 0, 1)
j2 = ExpandedBesselIntegral(0, 0, 0, 0, 0, 0, 0, 0, 0)
g = 2
FormFactor(j0, j2, "", g)
end
"""
FormFactor(ion::String; g_lande=2)
The magnetic form factor for a given magnetic ion and charge state. When passed
to an [`intensity_formula`](@ref), it rescales structure factor intensities
based on the magnitude of the scattering vector, ``|𝐪|``.
The parameter `ion` must be one of the following strings:
```
Am2, Am3, Am4, Am5, Am6, Am7, Au1, Au2, Au3, Au4, Au5, Ce2, Co0, Co1, Co2, Co3,
Co4, Cr0, Cr1, Cr2, Cr3, Cr4, Cu0, Cu1, Cu2, Cu3, Cu4, Dy2, Dy3, Er2, Er3, Eu2,
Eu3, Fe0, Fe1, Fe2, Fe3, Fe4, Gd2, Gd3, Hf2, Hf3, Ho2, Ho3, Ir0a, Ir0b, Ir0c,
Ir1a, Ir1b, Ir2, Ir3, Ir4, Ir5, Ir6, Mn0, Mn1, Mn2, Mn3, Mn4, Mn5, Mo0, Mo1, Nb0,
Nb1, Nd2, Nd3, Ni0, Ni1, Ni2, Ni3, Ni4, Np3, Np4, Np5, Np6, Os0a, Os0b, Os0c,
Os1a, Os1b, Os2, Os3, Os4, Os5, Os6, Os7, Pd0, Pd1, Pr3, Pt1, Pt2, Pt3, Pt4,
Pt5, Pt6, Pu3, Pu4, Pu5, Pu6, Re0a, Re0b, Re0c, Re1a, Re1b, Re2, Re3, Re4, Re5,
Re6, Rh0, Rh1, Ru0, Ru1, Sc0, Sc1, Sc2, Sm2, Sm3, Ta2, Ta3, Ta4, Tb2, Tb3, Tc0,
Tc1, Ti0, Ti1, Ti2, Ti3, Tm2, Tm3, U3, U4, U5, V0, V1, V2, V3, V4, W0a, W0b,
W0c, W1a, W1b, W2c, W3, W4, W5, Y0, Yb2, Yb3, Zr0, Zr1
```
The trailing number denotes ionization state. For example, `"Fe0"` denotes a
neutral iron atom, while `"Fe2"` denotes `Fe²⁺`. If multiple electronic
configurations are possible, they will be distinguished by a trailing letter
(`a`, `b`, ...). Omitting this letter will print an informative error,
```
FormFactor("Ir0")
ERROR: Disambiguate form factor according to electronic configuration:
"Ir0a" -- 6s⁰5d⁹
"Ir0b" -- 6s¹5d⁸
"Ir0c" -- 6s²5d⁷
```
In the dipolar approximation (small ``|𝐪|``) the form factor is
``F(s) = ⟨j_0(s)⟩ + \\frac{2-g}{g} ⟨j_2(s)⟩``,
involving ``s = |𝐪|/4π`` and the Landé ``g``-factor. The ``⟨j_l(s)⟩`` are
radial averages of the ``l``th spherical Bessel function of the magnetic dipole.
More details are provided in Ref. [1].
The ``⟨j_l(s)⟩`` can be approximated as a sum of Gaussians,
```math
⟨j_0(s)⟩ = A e^{-as^2} + B e^{-bs^2} + C e^{-cs^2} + D e^{-ds^2} + E \\\\
⟨j_2(s)⟩ = (A e^{-as^2} + B e^{-bs^2} + C e^{-cs^2} + D e^{-ds^2} + E) s^2
```
For 3d, 4d, rare earth, and actinide ions, Sunny uses the revised tables of P.
J. Brown, as documented in the McPhase package [2]. For 5d ions, Sunny uses the
tables of Kobayashi, Nagao, Ito [3].
References:
1. [P. J. Brown, The Neutron Data Booklet, 2nd ed., Sec. 2.5 Magnetic Form
Factors (2003)](https://www.ill.eu/sites/ccsl/ffacts/ffachtml.html)
2. Coefficient tables in [McPhase
documentation](https://www2.cpfs.mpg.de/~rotter/homepage_mcphase/manual/node137.html)
3. K. Kobayashi, T. Nagao, M. Ito, Acta Cryst. A, 67 pp 473–480 (2011)
"""
function FormFactor(ion::String; g_lande=2)
if !haskey(radial_integral_coefficients, ion)
if !haskey(radial_integral_coefficients, ion*"a")
error("Form factor requires species name and charge state, e.g. \"Fe2\" for Fe²⁺")
else
avail_keys = [k for k in keys(radial_integral_coefficients) if startswith(k, ion)]
avail_strs = map(sort(avail_keys)) do k
" $(repr(k)) -- " * radial_integral_coefficients[k][3]
end
error("""
Disambiguate form factor according to electronic configuration:
$(join(avail_strs, "\n"))
""")
end
end
(j0, j2, config) = radial_integral_coefficients[ion]
j0 = ExpandedBesselIntegral(j0...)
j2 = ExpandedBesselIntegral(j2...)
FormFactor(j0, j2, config, g_lande)
end
function compute_gaussian_expansion(j::ExpandedBesselIntegral, s2)
(; A, a, B, b, C, c, D, d, E) = j
return A*exp(-a*s2) + B*exp(-b*s2) + C*exp(-c*s2) + D*exp(-d*s2) + E
end
function compute_form_factor(form_factor::FormFactor, k2_absolute::Float64)
(; j0, j2, g) = form_factor
# Return early if this is the identity form factor
(j0.A == j0.B == j0.C == j0.D == 0) && (j0.E == 1) && (g == 2) && return 1.0
s2 = k2_absolute / (4π)^2
if g == 2
return compute_gaussian_expansion(j0, s2)
else
J0 = compute_gaussian_expansion(j0, s2)
J2 = compute_gaussian_expansion(j2, s2) * s2
return J0 + ((2-g)/g) * J2
end
end
# Given a form factor for each "symmetry class" of sites, return a form factor
# for each atom in the crystal.
function propagate_form_factors_to_atoms(ffs, cryst::Crystal)
isnothing(ffs) && return fill(identity_form_factor, natoms(cryst))
ref_classes = unique(cryst.classes)
if length(ffs) != length(ref_classes)
error("""Received $(length(ffs)) form factors, but $(length(ref_classes)) are
required, one for each symmetry-distinct site in the crystal.""")
end
return [ffs[findfirst(==(c), ref_classes)] for c in cryst.classes]
end
const radial_integral_coefficients = Dict(
# 3d electrons of transition atoms and ions (P. J. Brown)
"Sc0" => ([0.2512, 90.0296, 0.3290, 39.4021, 0.4235, 14.3222, 0, 0, -0.0043], [10.8172, 54.3270, 4.7353, 14.8471, 0.6071, 4.2180, 0, 0, 0.0011], ""),
"Sc1" => ([0.4889, 51.1603, 0.5203, 14.0764, -0.0286, 0.1792, 0, 0, 0.0185], [8.5021, 34.2851, 3.2116, 10.9940, 0.4244, 3.6055, 0, 0, 0.0009], ""),
"Sc2" => ([0.5048, 31.4035, 0.5186, 10.9897, -0.0241, 1.1831, 0, 0, 0.0000], [4.3683, 28.6544, 3.7231, 10.8233, 0.6074, 3.6678, 0, 0, 0.0014], ""),
"Ti0" => ([0.4657, 33.5898, 0.5490, 9.8791, -0.0291, 0.3232, 0, 0, 0.0123], [4.3583, 36.0556, 3.8230, 11.1328, 0.6855, 3.4692, 0, 0, 0.0020], ""),
"Ti1" => ([0.5093, 36.7033, 0.5032, 10.3713, -0.0263, 0.3106, 0, 0, 0.0116], [6.1567, 27.2754, 2.6833, 8.9827, 0.4070, 3.0524, 0, 0, 0.0011], ""),
"Ti2" => ([0.5091, 24.9763, 0.5162, 8.7569, -0.0281, 0.9160, 0, 0, 0.0015], [4.3107, 18.3484, 2.0960, 6.7970, 0.2984, 2.5476, 0, 0, 0.0007], ""),
"Ti3" => ([0.3571, 22.8413, 0.6688, 8.9306, -0.0354, 0.4833, 0, 0, 0.0099], [3.3717, 14.4441, 1.8258, 5.7126, 0.2470, 2.2654, 0, 0, 0.0005], ""),
"V0" => ([0.4086, 28.8109, 0.6077, 8.5437, -0.0295, 0.2768, 0, 0, 0.0123], [3.7600, 21.8313, 2.4026, 7.5458, 0.4464, 2.6628, 0, 0, 0.0017], ""),
"V1" => ([0.4444, 32.6479, 0.5683, 9.0971, -0.2285, 0.0218, 0, 0, 0.2150], [4.7474, 23.3226, 2.3609, 7.8082, 0.4105, 2.7063, 0, 0, 0.0014], ""),
"V2" => ([0.4085, 23.8526, 0.6091, 8.2456, -0.1676, 0.0415, 0, 0, 0.1496], [3.4386, 16.5303, 1.9638, 6.1415, 0.2997, 2.2669, 0, 0, 0.0009], ""),
"V3" => ([0.3598, 19.3364, 0.6632, 7.6172, -0.3064, 0.0296, 0, 0, 0.2835], [2.3005, 14.6821, 2.0364, 6.1304, 0.4099, 2.3815, 0, 0, 0.0014], ""),
"V4" => ([0.3106, 16.8160, 0.7198, 7.0487, -0.0521, 0.3020, 0, 0, 0.0221], [1.8377, 12.2668, 1.8247, 5.4578, 0.3979, 2.2483, 0, 0, 0.0012], ""),
"Cr0" => ([0.1135, 45.1990, 0.3481, 19.4931, 0.5477, 7.3542, 0, 0, -0.0092], [3.4085, 20.1267, 2.1006, 6.8020, 0.4266, 2.3941, 0, 0, 0.0019], ""),
"Cr1" => ([-0.0977, 0.0470, 0.4544, 26.0054, 0.5579, 7.4892, 0, 0, 0.0831], [3.7768, 20.3456, 2.1028, 6.8926, 0.4010, 2.4114, 0, 0, 0.0017], ""),
"Cr2" => ([1.2024, -0.0055, 0.4158, 20.5475, 0.6032, 6.9560, 0, 0, -1.2218], [2.6422, 16.0598, 1.9198, 6.2531, 0.4446, 2.3715, 0, 0, 0.0020], ""),
"Cr3" => ([-0.3094, 0.0274, 0.3680, 17.0355, 0.6559, 6.5236, 0, 0, 0.2856], [1.6262, 15.0656, 2.0618, 6.2842, 0.5281, 2.3680, 0, 0, 0.0023], ""),
"Cr4" => ([-0.2320, 0.0433, 0.3101, 14.9518, 0.7182, 6.1726, 0, 0, 0.2042], [1.0293, 13.9498, 1.9933, 6.0593, 0.5974, 2.3457, 0, 0, 0.0027], ""),
"Mn0" => ([0.2438, 24.9629, 0.1472, 15.6728, 0.6189, 6.5403, 0, 0, -0.0105], [2.6681, 16.0601, 1.7561, 5.6396, 0.3675, 2.0488, 0, 0, 0.0017], ""),
"Mn1" => ([-0.0138, 0.4213, 0.4231, 24.6680, 0.5905, 6.6545, 0, 0, -0.0010], [3.2953, 18.6950, 1.8792, 6.2403, 0.3927, 2.2006, 0, 0, 0.0022], ""),
"Mn2" => ([0.4220, 17.6840, 0.5948, 6.0050, 0.0043, -0.6090, 0, 0, -0.0219], [2.0515, 15.5561, 1.8841, 6.0625, 0.4787, 2.2323, 0, 0, 0.0027], ""),
"Mn3" => ([0.4198, 14.2829, 0.6054, 5.4689, 0.9241, -0.0088, 0, 0, -0.9498], [1.2427, 14.9966, 1.9567, 6.1181, 0.5732, 2.2577, 0, 0, 0.0031], ""),
"Mn4" => ([0.3760, 12.5661, 0.6602, 5.1329, -0.0372, 0.5630, 0, 0, 0.0011], [0.7879, 13.8857, 1.8717, 5.7433, 0.5981, 2.1818, 0, 0, 0.0034], ""),
"Mn5" => ([0.2924, 11.6655, 0.7405, 5.0741, -1.7883, 0.0059, 0, 0, 1.7557], [-0.2394, 10.7309, -0.1190, 6.5989, 0.3505, 1.4912, 0, 0, 0.0078], ""),
"Fe0" => ([0.0706, 35.0085, 0.3589, 15.3583, 0.5819, 5.5606, 0, 0, -0.0114], [1.9405, 18.4733, 1.9566, 6.3234, 0.5166, 2.1607, 0, 0, 0.0036], ""),
"Fe1" => ([0.1251, 34.9633, 0.3629, 15.5144, 0.5223, 5.5914, 0, 0, -0.0105], [2.6290, 18.6598, 1.8704, 6.3313, 0.4690, 2.1628, 0, 0, 0.0031], ""),
"Fe2" => ([0.0263, 34.9597, 0.3668, 15.9435, 0.6188, 5.5935, 0, 0, -0.0119], [1.6490, 16.5593, 1.9064, 6.1325, 0.5206, 2.1370, 0, 0, 0.0035], ""),
"Fe3" => ([0.3972, 13.2442, 0.6295, 4.9034, -0.0314, 0.3496, 0, 0, 0.0044], [1.3602, 11.9976, 1.5188, 5.0025, 0.4705, 1.9914, 0, 0, 0.0038], ""),
"Fe4" => ([0.3782, 11.3800, 0.6556, 4.5920, -0.0346, 0.4833, 0, 0, 0.0005], [1.5582, 8.2750, 1.1863, 3.2794, 0.1366, 1.1068, 0, 0, -0.0022], ""),
"Co0" => ([0.4139, 16.1616, 0.6013, 4.7805, -0.1518, 0.0210, 0, 0, 0.1345], [1.9678, 14.1699, 1.4911, 4.9475, 0.3844, 1.7973, 0, 0, 0.0027], ""),
"Co1" => ([0.0990, 33.1252, 0.3645, 15.1768, 0.5470, 5.0081, 0, 0, -0.0109], [2.4097, 16.1608, 1.5780, 5.4604, 0.4095, 1.9141, 0, 0, 0.0031], ""),
"Co2" => ([0.4332, 14.3553, 0.5857, 4.6077, -0.0382, 0.1338, 0, 0, 0.0179], [1.9049, 11.6444, 1.3159, 4.3574, 0.3146, 1.6453, 0, 0, 0.0017], ""),
"Co3" => ([0.3902, 12.5078, 0.6324, 4.4574, -0.1500, 0.0343, 0, 0, 0.1272], [1.7058, 8.8595, 1.1409, 3.3086, 0.1474, 1.0899, 0, 0, -0.0025], ""),
"Co4" => ([0.3515, 10.7785, 0.6778, 4.2343, -0.0389, 0.2409, 0, 0, 0.0098], [1.3110, 8.0252, 1.1551, 3.1792, 0.1608, 1.1301, 0, 0, -0.0011], ""),
"Ni0" => ([-0.0172, 35.7392, 0.3174, 14.2689, 0.7136, 4.5661, 0, 0, -0.0143], [1.0302, 12.2521, 1.4669, 4.7453, 0.4521, 1.7437, 0, 0, 0.0036], ""),
"Ni1" => ([0.0705, 35.8561, 0.3984, 13.8042, 0.5427, 4.3965, 0, 0, -0.0118], [2.1040, 14.8655, 1.4302, 5.0714, 0.4031, 1.7784, 0, 0, 0.0034], ""),
"Ni2" => ([0.0163, 35.8826, 0.3916, 13.2233, 0.6052, 4.3388, 0, 0, -0.0133], [1.7080, 11.0160, 1.2147, 4.1031, 0.3150, 1.5334, 0, 0, 0.0018], ""),
"Ni3" => ([0.0012, 34.9998, 0.3468, 11.9874, 0.6667, 4.2518, 0, 0, -0.0148], [1.4683, 8.6713, 1.1068, 3.2574, 0.1794, 1.1058, 0, 0,-0.0023], ""),
"Ni4" => ([-0.0090, 35.8614, 0.2776, 11.7904, 0.7474, 4.2011, 0, 0, -0.0163], [1.1612, 7.7000, 1.0027, 3.2628, 0.2719, 1.3780, 0, 0, 0.0025], ""),
"Cu0" => ([0.0909, 34.9838, 0.4088, 11.4432, 0.5128, 3.8248, 0, 0, -0.0124], [1.9182, 14.4904, 1.3329, 4.7301, 0.3842, 1.6394, 0, 0, 0.0035], ""),
"Cu1" => ([0.0749, 34.9656, 0.4147, 11.7642, 0.5238, 3.8497, 0, 0, -0.0127], [1.8814, 13.4333, 1.2809, 4.5446, 0.3646, 1.6022, 0, 0, 0.0033], ""),
"Cu2" => ([0.0232, 34.9686, 0.4023, 11.5640, 0.5882, 3.8428, 0, 0, -0.0137], [1.5189, 10.4779, 1.1512, 3.8132, 0.2918, 1.3979, 0, 0, 0.0017], ""),
"Cu3" => ([0.0031, 34.9074, 0.3582, 10.9138, 0.6531, 3.8279, 0, 0, -0.0147], [1.2797, 8.4502, 1.0315, 3.2796, 0.2401, 1.2498, 0, 0, 0.0015], ""),
"Cu4" => ([-0.0132, 30.6817, 0.2801, 11.1626, 0.7490, 3.8172, 0, 0, -0.0165], [0.9568, 7.4481, 0.9099, 3.3964, 0.3729, 1.4936, 0, 0, 0.0049], ""),
# 4d electrons of transition atoms and ions (P. J. Brown)
"Y0" => ([0.5915, 67.6081, 1.5123, 17.9004, -1.1130, 14.1359, 0, 0, 0.0080], [14.4084, 44.6577, 5.1045, 14.9043, -0.0535, 3.3189, 0, 0, 0.0028], ""),
"Zr0" => ([0.4106, 59.9961, 1.0543, 18.6476, -0.4751, 10.5400, 0, 0, 0.0106], [10.1378, 35.3372, 4.7734, 12.5453, -0.0489, 2.6721, 0, 0, 0.0036], ""),
"Zr1" => ([0.4532, 59.5948, 0.7834, 21.4357, -0.2451, 9.0360, 0, 0, 0.0098], [11.8722, 34.9200, 4.0502, 12.1266, -0.0632, 2.8278, 0, 0, 0.0034], ""),
"Nb0" => ([0.3946, 49.2297, 1.3197, 14.8216, -0.7269, 9.6156, 0, 0, 0.0129], [7.4796, 33.1789, 5.0884, 11.5708, -0.0281, 1.5635, 0, 0, 0.0047], ""),
"Nb1" => ([0.4572, 49.9182, 1.0274, 15.7256, -0.4962, 9.1573, 0, 0, 0.0118], [8.7735, 33.2848, 4.6556, 11.6046, -0.0268, 1.5389, 0, 0, 0.0044], ""),
"Mo0" => ([0.1806, 49.0568, 1.2306, 14.7859, -0.4268, 6.9866, 0, 0, 0.0171], [5.1180, 23.4217, 4.1809, 9.2080, -0.0505, 1.7434, 0, 0, 0.0053], ""),
"Mo1" => ([0.3500, 48.0354, 1.0305, 15.0604, -0.3929, 7.4790, 0, 0, 0.0139], [7.2367, 28.1282, 4.0705, 9.9228, -0.0317, 1.4552, 0, 0, 0.0049], ""),
"Tc0" => ([0.1298, 49.6611, 1.1656, 14.1307, -0.3134, 5.5129, 0, 0, 0.0195], [4.2441, 21.3974, 3.9439, 8.3753, -0.0371, 1.1870, 0, 0, 0.0066], ""),
"Tc1" => ([0.2674, 48.9566, 0.9569, 15.1413, -0.2387, 5.4578, 0, 0, 0.0160], [6.4056, 24.8243, 3.5400, 8.6112, -0.0366, 1.4846, 0, 0, 0.0044], ""),
"Ru0" => ([0.1069, 49.4238, 1.1912, 12.7417, -0.3176, 4.9125, 0, 0, 0.0213], [3.7445, 18.6128, 3.4749, 7.4201, -0.0363, 1.0068, 0, 0, 0.0073], ""),
"Ru1" => ([0.4410, 33.3086, 1.4775, 9.5531, -0.9361, 6.7220, 0, 0, 0.0176], [5.2826, 23.6832, 3.5813, 8.1521, -0.0257, 0.4255, 0, 0, 0.0131], ""),
"Rh0" => ([0.0976, 49.8825, 1.1601, 11.8307, -0.2789, 4.1266, 0, 0, 0.0234], [3.3651, 17.3444, 3.2121, 6.8041, -0.0350, 0.5031, 0, 0, 0.0146], ""),
"Rh1" => ([0.3342, 29.7564, 1.2209, 9.4384, -0.5755, 5.3320, 0, 0, 0.0210], [4.0260, 18.9497, 3.1663, 6.9998, -0.0296, 0.4862, 0, 0, 0.0127], ""),
"Pd0" => ([0.2003, 29.3633, 1.1446, 9.5993, -0.3689, 4.0423, 0, 0, 0.0251], [3.3105, 14.7265, 2.6332, 5.8618, -0.0437, 1.1303, 0, 0, 0.0053], ""),
"Pd1" => ([0.5033, 24.5037, 1.9982, 6.9082, -1.5240, 5.5133, 0, 0, 0.0213], [4.2749, 17.9002, 2.7021, 6.3541, -0.0258, 0.6999, 0, 0, 0.0071], ""),
# 5d electrons of rare earth ions (P. J. Brown)
"Ce2" => ([0.2953, 17.6846, 0.2923, 6.7329, 0.4313, 5.3827, 0, 0, -0.0194], [0.9809, 18.0630, 1.8413, 7.7688, 0.9905, 2.8452, 0, 0, 0.0120], ""),
"Nd2" => ([0.1645, 25.0453, 0.2522, 11.9782, 0.6012, 4.9461, 0, 0, -0.0180], [1.4530, 18.3398, 1.6196, 7.2854, 0.8752, 2.6224, 0, 0, 0.0126], ""),
"Nd3" => ([0.0540, 25.0293, 0.3101, 12.1020, 0.6575, 4.7223, 0, 0, -0.0216], [0.6751, 18.3421, 1.6272, 7.2600, 0.9644, 2.6016, 0, 0, 0.0150], ""),
"Sm2" => ([0.0909, 25.2032, 0.3037, 11.8562, 0.6250, 4.2366, 0, 0, -0.0200], [1.0360, 18.4249, 1.4769, 7.0321, 0.8810, 2.4367, 0, 0, 0.0152], ""),
"Sm3" => ([0.0288, 25.2068, 0.2973, 11.8311, 0.6954, 4.2117, 0, 0, -0.0213], [0.4707, 18.4301, 1.4261, 7.0336, 0.9574, 2.4387, 0, 0, 0.0182], ""),
"Eu2" => ([0.0755, 25.2960, 0.3001, 11.5993, 0.6438, 4.0252, 0, 0, -0.0196], [0.8970, 18.4429, 1.3769, 7.0054, 0.9060, 2.4213, 0, 0, 0.0190], ""),
"Eu3" => ([0.0204, 25.3078, 0.3010, 11.4744, 0.7005, 3.9420, 0, 0, -0.0220], [0.3985, 18.4514, 1.3307, 6.9556, 0.9603, 2.3780, 0, 0, 0.0197], ""),
"Gd2" => ([0.0636, 25.3823, 0.3033, 11.2125, 0.6528, 3.7877, 0, 0, -0.0199], [0.7756, 18.4695, 1.3124, 6.8990, 0.8956, 2.3383, 0, 0, 0.0199], ""),
"Gd3" => ([0.0186, 25.3867, 0.2895, 11.1421, 0.7135, 3.7520, 0, 0, -0.0217], [0.3347, 18.4758, 1.2465, 6.8767, 0.9537, 2.3184, 0, 0, 0.0217], ""),
"Tb2" => ([0.0547, 25.5086, 0.3171, 10.5911, 0.6490, 3.5171, 0, 0, -0.0212], [0.6688, 18.4909, 1.2487, 6.8219, 0.8888, 2.2751, 0, 0, 0.0215], ""),
"Tb3" => ([0.0177, 25.5095, 0.2921, 10.5769, 0.7133, 3.5122, 0, 0, -0.0231], [0.2892, 18.4973, 1.1678, 6.7972, 0.9437, 2.2573, 0, 0, 0.0232], ""),
"Dy2" => ([0.1308, 18.3155, 0.3118, 7.6645, 0.5795, 3.1469, 0, 0, -0.0226], [0.5917, 18.5114, 1.1828, 6.7465, 0.8801, 2.2141, 0, 0, 0.0229], ""),
"Dy3" => ([0.1157, 15.0732, 0.3270, 6.7991, 0.5821, 3.0202, 0, 0, -0.0249], [0.2523, 18.5172, 1.0914, 6.7362, 0.9345, 2.2082, 0, 0, 0.0250], ""),
"Ho2" => ([0.0995, 18.1761, 0.3305, 7.8556, 0.5921, 2.9799, 0, 0, -0.0230], [0.5094, 18.5155, 1.1234, 6.7060, 0.8727, 2.1589, 0, 0, 0.0242], ""),
"Ho3" => ([0.0566, 18.3176, 0.3365, 7.6880, 0.6317, 2.9427, 0, 0, -0.0248], [0.2188, 18.5157, 1.0240, 6.7070, 0.9251, 2.1614, 0, 0, 0.0268], ""),
"Er2" => ([0.1122, 18.1223, 0.3462, 6.9106, 0.5649, 2.7614, 0, 0, -0.0235], [0.4693, 18.5278, 1.0545, 6.6493, 0.8679, 2.1201, 0, 0, 0.0261], ""),
"Er3" => ([0.0586, 17.9802, 0.3540, 7.0964, 0.6126, 2.7482, 0, 0, -0.0251], [0.1710, 18.5337, 0.9879, 6.6246, 0.9044, 2.1004, 0, 0, 0.0278], ""),
"Tm2" => ([0.0983, 18.3236, 0.3380, 6.9178, 0.5875, 2.6622, 0, 0, -0.0241], [0.4198, 18.5417, 0.9959, 6.6002, 0.8593, 2.0818, 0, 0, 0.0284], ""),
"Tm3" => ([0.0581, 15.0922, 0.2787, 7.8015, 0.6854, 2.7931, 0, 0, -0.0224], [0.1760, 18.5417, 0.9105, 6.5787, 0.8970, 2.0622, 0, 0, 0.0294], ""),
"Yb2" => ([0.0855, 18.5123, 0.2943, 7.3734, 0.6412, 2.6777, 0, 0, -0.0213], [0.3852, 18.5497, 0.9415, 6.5507, 0.8492, 2.0425, 0, 0, 0.0301], ""),
"Yb3" => ([0.0416, 16.0949, 0.2849, 7.8341, 0.6961, 2.6725, 0, 0, -0.0229], [0.1570, 18.5553, 0.8484, 6.5403, 0.8880, 2.0367, 0, 0, 0.0318], ""),
"Pr3" => ([0.0504, 24.9989, 0.2572, 12.0377, 0.7142, 5.0039, 0, 0, -0.0219], [0.8734, 18.9876, 1.5594, 6.0872, 0.8142, 2.4150, 0, 0, 0.0111], ""),
# 5d electrons of actinide ions (P. J. Brown)
"U3" => ([0.5058, 23.2882, 1.3464, 7.0028, -0.8724, 4.8683, 0, 0, 0.0192], [4.1582, 16.5336, 2.4675, 5.9516, -0.0252, 0.7646, 0, 0, 0.0057], ""),
"U4" => ([0.3291, 23.5475, 1.0836, 8.4540, -0.4340, 4.1196, 0, 0, 0.0214], [3.7449, 13.8944, 2.6453, 4.8634, -0.5218, 3.1919, 0, 0, 0.0009], ""),
"U5" => ([0.3650, 19.8038, 3.2199, 6.2818, -2.6077, 5.3010, 0, 0, 0.0233], [3.0724, 12.5460, 2.3076, 5.2314, -0.0644, 1.4738, 0, 0, 0.0035], ""),
"Np3" => ([0.5157, 20.8654, 2.2784, 5.8930, -1.8163, 4.8457, 0, 0, 0.0211], [3.7170, 15.1333, 2.3216, 5.5025, -0.0275, 0.7996, 0, 0, 0.0052], ""),
"Np4" => ([0.4206, 19.8046, 2.8004, 5.9783, -2.2436, 4.9848, 0, 0, 0.0228], [2.9203, 14.6463, 2.5979, 5.5592, -0.0301, 0.3669, 0, 0, 0.0141], ""),
"Np5" => ([0.3692, 18.1900, 3.1510, 5.8500, -2.5446, 4.9164, 0, 0, 0.0248], [2.3308, 13.6540, 2.7219, 5.4935, -0.1357, 0.0493, 0, 0, 0.1224], ""),
"Np6" => ([0.2929, 17.5611, 3.4866, 5.7847, -2.8066, 4.8707, 0, 0, 0.0267], [1.8245, 13.1803, 2.8508, 5.4068, -0.1579, 0.0444, 0, 0, 0.1438], ""),
"Pu3" => ([0.3840, 16.6793, 3.1049, 5.4210, -2.5148, 4.5512, 0, 0, 0.0263], [2.0885, 12.8712, 2.5961, 5.1896, -0.1465, 0.0393, 0, 0, 0.1343], ""),
"Pu4" => ([0.4934, 16.8355, 1.6394, 5.6384, -1.1581, 4.1399, 0, 0, 0.0248], [2.7244, 12.9262, 2.3387, 5.1633, -0.1300, 0.0457, 0, 0, 0.1177], ""),
"Pu5" => ([0.3888, 16.5592, 2.0362, 5.6567, -1.4515, 4.2552, 0, 0, 0.0267], [2.1409, 12.8319, 2.5664, 5.1522, -0.1338, 0.0457, 0, 0, 0.1210], ""),
"Pu6" => ([0.3172, 16.0507, 3.4654, 5.3507, -2.8102, 4.5133, 0, 0, 0.0281], [1.7262, 12.3240, 2.6652, 5.0662, -0.1695, 0.0406, 0, 0, 0.1550], ""),
"Am2" => ([0.4743, 21.7761, 1.5800, 5.6902, -1.0779, 4.1451, 0, 0, 0.0218], [3.5237, 15.9545, 2.2855, 5.1946, -0.0142, 0.5853, 0, 0, 0.0033], ""),
"Am3" => ([0.4239, 19.5739, 1.4573, 5.8722, -0.9052, 3.9682, 0, 0, 0.0238], [2.8622, 14.7328, 2.4099, 5.1439, -0.1326, 0.0309, 0, 0, 0.1233], ""),
"Am4" => ([0.3737, 17.8625, 1.3521, 6.0426, -0.7514, 3.7199, 0, 0, 0.0258], [2.4141, 12.9478, 2.3687, 4.9447, -0.2490, 0.0215, 0, 0, 0.2371], ""),
"Am5" => ([0.2956, 17.3725, 1.4525, 6.0734, -0.7755, 3.6619, 0, 0, 0.0277], [2.0109, 12.0534, 2.4155, 4.8358, -0.2264, 0.0275, 0, 0, 0.2128], ""),
"Am6" => ([0.2302, 16.9533, 1.4864, 6.1159, -0.7457, 3.5426, 0, 0, 0.0294], [1.6778, 11.3372, 2.4531, 4.7247, -0.2043, 0.0337, 0, 0, 0.1892], ""),
"Am7" => ([0.3601, 12.7299, 1.9640, 5.1203, -1.3560, 3.7142, 0, 0, 0.0316], [1.8845, 9.1606, 2.0746, 4.0422, -0.1318, 1.7227, 0, 0, 0.0020], ""),
# 5d electrons of transition atoms and ions from Hf to Re. (Kobayashi, Nagao, Ito)
"Hf2" => ([0.4229, 50.465, 0.7333, 23.865, -0.3798, 4.051, 0.2252, 2.497, -0.0018], [9.6670, 33.435, 5.2429, 13.529, -0.5533, 1.402, 0.4934, 1.254, -0.0033], "6s⁰5d²"),
"Hf3" => ([0.3555, 40.954, 0.8483, 21.726, -0.4116, 4.305, 0.2101, 2.349, -0.0023], [7.5646, 27.367, 5.0743, 12.402, -0.4133, 1.742, 0.3163, 1.437, -0.0012], "6s⁰5d¹"),
"Ta2" => ([0.3976, 45.095, 0.7746, 21.028, -0.6098, 3.471, 0.4395, 2.570, -0.0020], [8.1746, 29.871, 4.9405, 12.188, -1.1294, 1.254, 1.0658, 1.181, -0.0046], "6s⁰5d³"),
"Ta3" => ([0.3611, 36.921, 0.8579, 19.195, -0.4945, 3.857, 0.2781, 2.303, -0.0026], [6.5998, 25.026, 4.7913, 11.303, -0.7801, 1.529, 0.6820, 1.382, -0.0019], "6s⁰5d²"),
"Ta4" => ([0.3065, 31.817, 0.9611, 17.749, -0.5463, 3.979, 0.2816, 2.232, -0.0030], [5.5048, 21.620, 4.6734, 10.556, -0.2181, 2.100, 0.0810, 1.049, -0.0016], "6s⁰5d¹"),
"W0a" => ([0.3990, 73.810, 0.7138, 22.815, -2.0436, 2.710, 1.9319, 2.559, -0.0023], [8.4216, 64.652, 7.6983, 23.124, 2.3605, 8.583, -0.3876, 4.620, 0.0033], "6s⁰5d⁶"),
"W0b" => ([0.3811, 62.707, 0.7523, 21.434, -12.5449, 2.702, 12.4130, 2.674, -0.0023], [6.9289, 53.425, 7.2157, 20.016, 5.7754, 6.543, -4.2114, 5.854, 0.0036], "6s¹5d⁵"),
"W0c" => ([0.3653, 53.965, 0.7926, 20.078, -0.8142, 3.030, 0.6581, 2.476, -0.0023], [5.4017, 47.110, 6.9113, 18.760, 7.0586, 6.363, -5.4525, 5.802, 0.0040], "6s²5d⁴"),
"W1a" => ([0.4077, 51.367, 0.7436, 20.256, -9.8283, 2.780, 9.6788, 2.740, -0.0021], [5.6854, 44.743, 6.8903, 18.753, 7.8523, 6.308, -6.3447, 5.842, 0.0038], "6s⁰5d⁵"),
"W1b" => ([0.3834, 46.233, 0.7890, 19.278, -1.4650, 2.947, 1.2945, 2.628, -0.0022], [4.5118, 41.281, 6.7136, 17.964, 7.6331, 6.269, -6.0365, 5.758, 0.0042], "6s¹5d⁴"),
"W2c" => ([0.3876, 40.340, 0.8008, 18.621, -1.3911, 2.995, 1.2048, 2.627, -0.0023], [7.0301, 26.990, 4.6604, 11.083, -0.8220, 1.145, 0.7581, 1.042, -0.0068], "6s⁰5d⁴"),
"W3" => ([0.3610, 33.519, 0.8717, 17.176, -0.6183, 3.445, 0.3883, 2.276, -0.0028], [5.8036, 22.969, 4.5243, 10.361, -0.7897, 1.388, 0.6927, 1.248, -0.0031], "6s⁰5d³"),
"W4" => ([0.3221, 29.047, 0.9574, 15.979, -0.6287, 3.597, 0.3525, 2.174, -0.0033], [4.9006, 20.117, 4.4360, 9.765, -2.0009, 1.497, 1.8714, 1.431, -0.0014], "6s⁰5d²"),
"W5" => ([0.2725, 25.966, 1.0558, 14.954, -0.6990, 3.643, 0.3745, 2.145, -0.0037], [4.1973, 17.967, 4.3791, 9.255, -1.8830, 1.603, 1.7205, 1.518, -0.0004], "6s⁰5d¹"),
"Re0a" => ([0.3807, 63.042, 0.7497, 19.967, -6.5300, 2.501, 6.4013, 2.451, -0.0028], [6.7574, 55.529, 6.7931, 20.125, 2.3113, 7.529, -0.5004, 4.412, 0.0037], "6s⁰5d⁷"),
"Re0b" => ([0.3691, 53.934, 0.7837, 18.790, -9.1491, 2.558, 8.9983, 2.517, -0.0027], [5.5830, 46.852, 6.4516, 17.855, 5.0609, 6.037, -3.5427, 5.312, 0.0040], "6s¹5d⁶"),
"Re0c" => ([0.3548, 47.108, 0.8210, 17.769, -9.8674, 2.599, 9.6938, 2.556, -0.0027], [4.4322, 41.798, 6.2063, 16.844, 9.8763, 5.751, -8.3294, 5.406, 0.0043], "6s²5d⁵"),
"Re1a" => ([0.3944, 45.427, 0.7742, 17.948, -3.1692, 2.653, 3.0028, 2.521, -0.0026], [4.7231, 40.130, 6.2139, 16.902, 8.8240, 5.766, -7.3608, 5.396, 0.0042], "6s⁰5d⁶"),
"Re1b" => ([0.3736, 41.151, 0.8160, 17.158, -7.0396, 2.642, 6.8523, 2.577, -0.0026], [3.7875, 37.254, 6.0587, 16.264, 6.9896, 5.786, -5.4457, 5.279, 0.0045], "6s¹5d⁵"),
"Re2" => ([0.3825, 36.336, 0.8218, 16.636, -8.7220, 2.657, 8.5201, 2.601, -0.0026], [3.0708, 33.896, 5.9941, 15.817, 6.7816, 5.768, -5.2056, 5.231, 0.0047], "6s⁰5d⁵"),
"Re3" => ([0.3585, 30.671, 0.8863, 15.527, -0.8682, 3.047, 0.6263, 2.280, -0.0030], [1.7870, 31.248, 5.9068, 15.160, 17.4262, 5.551, -15.6856, 5.339, 0.0053], "6s⁰5d⁴"),
"Re4" => ([0.2974, 27.372, 0.9826, 14.807, -1.8869, 2.840, 1.6100, 2.476, -0.0031], [4.4033, 18.733, 4.1971, 9.047, -2.3106, 1.352, 2.1866, 1.299, -0.0025], "6s⁰5d³"),
"Re5" => ([0.3143, 23.522, 1.0276, 13.505, -0.7438, 3.393, 0.4059, 2.030, -0.0041], [3.8162, 16.843, 4.1400, 8.605, -4.0882, 1.443, 3.9333, 1.408, -0.0012], "6s⁰5d²"),
"Re6" => ([0.2146, 22.496, 1.1616, 13.064, -1.0455, 3.162, 0.6734, 2.196, -0.0041], [3.3349, 15.341, 4.1015, 8.213, -2.3511, 1.531, 2.1651, 1.459, -0.0003], "6s⁰5d¹"),
# 5d electrons of transition atoms and ions from Os to Au. (Kobayashi, Nagao, Ito)
"Os0a" => ([0.3676, 54.835, 0.7793, 17.716, -2.0669, 2.418, 1.9224, 2.247, -0.0034], [5.5418, 48.893, 6.0803, 17.984, 2.2542, 6.853, -0.5285, 4.095, 0.0040], "6s⁰5d⁸"),
"Os0b" => ([0.3571, 47.458, 0.8123, 16.770, -1.2072, 2.556, 1.0404, 2.211, -0.0033], [4.6511, 41.610, 5.8194, 16.062, 6.7172, 5.447, -5.2689, 4.986, 0.0043], "6s¹5d⁷"),
"Os0c" => ([0.3467, 41.778, 0.8458, 15.918, -5.6370, 2.459, 5.4472, 2.381, -0.0032], [3.7421, 37.491, 5.6137, 15.256, 10.0488, 5.293, -8.5683, 4.991, 0.0046], "6s²5d⁶"),
"Os1a" => ([0.3837, 40.665, 0.8006, 16.096, -3.5305, 2.487, 3.3488, 2.366, -0.0030], [4.0236, 36.272, 5.6349, 15.338, 8.6568, 5.318, -7.2505, 4.980, 0.0044], "6s⁰5d⁷"),
"Os1b" => ([0.3666, 36.997, 0.8390, 15.425, -2.6944, 2.537, 2.4916, 2.360, -0.0031], [3.2611, 33.818, 5.4945, 14.808, 5.7610, 5.391, -4.2811, 4.827, 0.0048], "6s¹5d⁶"),
"Os2" => ([0.3786, 33.005, 0.8412, 14.990, -7.0632, 2.503, 6.8462, 2.433, -0.0030], [2.7289, 30.900, 5.4357, 14.396, 18.6546, 5.151, -17.1708, 4.993, 0.0050], "6s⁰5d⁶"),
"Os3" => ([0.3557, 28.222, 0.9002, 14.140, -2.5972, 2.601, 2.3444, 2.376, -0.0032], [4.5913, 19.692, 4.0615, 8.862, -0.9950, 1.086, 0.9081, 0.986, -0.0077], "6s⁰5d⁵"),
"Os4" => ([0.3337, 24.723, 0.9655, 13.288, -0.9653, 2.906, 0.6698, 2.117, -0.0037], [3.9724, 17.514, 3.9817, 8.421, -0.7719, 1.264, 0.6552, 1.107, -0.0042], "6s⁰5d⁴"),
"Os5" => ([0.3055, 22.152, 1.0395, 12.529, -0.9158, 3.016, 0.5750, 2.032, -0.0042], [3.4764, 15.826, 3.9241, 8.032, -0.6854, 1.397, 0.5394, 1.184, -0.0024], "6s⁰5d³"),
"Os6" => ([0.2714, 20.218, 1.1211, 11.851, -0.9773, 3.050, 0.5894, 2.005, -0.0046], [3.0642, 14.479, 3.8847, 7.686, -4.7235, 1.384, 4.5485, 1.352, -0.0012], "6s⁰5d²"),
"Os7" => ([0.2101, 19.108, 1.2240, 11.347, -1.2543, 2.933, 0.8250, 2.088, -0.0048], [2.7164, 13.366, 3.8554, 7.370, -5.0211, 1.439, 4.8166, 1.405, -0.0004], "6s⁰5d¹"),
"Ir0a" => ([0.3564, 48.464, 0.8049, 15.923, -2.5258, 2.265, 2.3675, 2.121, -0.0040], [4.6102, 43.878, 5.4892, 16.394, 2.1707, 6.423, -0.4761, 3.722, 0.0043], "6s⁰5d⁹"),
"Ir0b" => ([0.3492, 42.195, 0.8350, 15.113, -5.1496, 2.279, 4.9686, 2.201, -0.0038], [3.9372, 37.508, 5.2846, 14.661, 3.7267, 5.263, -2.3158, 4.416, 0.0045], "6s¹5d⁸"),
"Ir0c" => ([0.3400, 37.499, 0.8675, 14.402, -2.3703, 2.370, 2.1661, 2.177, -0.0037], [3.2263, 33.922, 5.1086, 13.921, 6.5993, 4.978, -5.1841, 4.549, 0.0048], "6s²5d⁷"),
"Ir1a" => ([0.3744, 36.764, 0.8240, 14.576, -8.8616, 2.303, 8.6664, 2.255, -0.0035], [3.4956, 32.991, 5.1369, 13.998, 8.3991, 4.924, -7.0561, 4.612, 0.0047], "6s⁰5d⁸"),
"Ir1b" => ([0.3604, 33.570, 0.8597, 13.993, -2.1686, 2.412, 1.9518, 2.188, -0.0036], [2.8732, 30.809, 5.0094, 13.522, 6.8656, 4.933, -5.4669, 4.526, 0.0050], "6s¹5d⁷"),
"Ir2" => ([0.3802, 30.032, 0.8550, 13.567, -1.6185, 2.488, 1.3866, 2.162, -0.0035], [2.4419, 28.356, 4.9470, 13.222, 4.7478, 5.029, -3.3259, 4.393, 0.0052], "6s⁰5d⁷"),
"Ir3" => ([0.3678, 25.828, 0.9065, 12.788, -0.8587, 2.745, 0.5883, 1.960, -0.0040], [1.5883, 25.969, 4.8472, 12.711, 5.6507, 4.949, -4.1190, 4.388, 0.0056], "6s⁰5d⁶"),
"Ir4" => ([0.3969, 22.050, 0.9310, 11.768, -0.7090, 3.017, 0.3857, 1.778, -0.0047], [3.5964, 16.439, 3.7872, 7.873, -1.2303, 1.092, 1.1232, 1.003, -0.0068], "6s⁰5d⁵"),
"Ir5" => ([0.3059, 20.759, 1.0432, 11.622, -1.3457, 2.655, 1.0008, 2.066, -0.0043], [3.1710, 14.923, 3.7320, 7.529, -1.5400, 1.200, 1.4048, 1.119, -0.0040], "6s⁰5d⁴"),
"Ir6" => ([0.2854, 18.867, 1.1123, 10.982, -1.1403, 2.782, 0.7475, 1.959, -0.0049], [2.8163, 13.697, 3.6906, 7.219, -5.2957, 1.254, 5.1328, 1.228, -0.0024], "6s⁰5d³"),
"Pt1" => ([0.3664, 33.503, 0.8449, 13.303, -2.6192, 2.227, 2.4116, 2.059, -0.0041], [3.0783, 30.198, 4.7065, 12.857, 5.7270, 4.650, -4.4425, 4.222, 0.0048], "6s⁰5d⁹"),
"Pt2" => ([0.3701, 27.799, 0.8761, 12.480, -3.2959, 2.258, 3.0535, 2.106, -0.0040], [2.2407, 26.003, 4.5300, 12.118, 6.7189, 4.557, -5.3954, 4.187, 0.0053], "6s⁰5d⁸"),
"Pt3" => ([0.3606, 24.052, 0.9205, 11.833, -4.0612, 2.271, 3.7841, 2.133, -0.0041], [1.5391, 23.689, 4.4263, 11.645, 8.5673, 4.482, -7.1591, 4.181, 0.0057], "6s⁰5d⁷"),
"Pt4" => ([0.3429, 21.358, 0.9753, 11.261, -2.2859, 2.357, 1.9719, 2.074, -0.0043], [0.9477, 22.775, 4.3337, 11.319, 7.2374, 4.500, -5.7086, 4.106, 0.0062], "6s⁰5d⁶"),
"Pt5" => ([0.3649, 18.762, 1.0102, 10.456, -0.8785, 2.765, 0.5087, 1.737, -0.0053], [0.5132, 23.124, 4.1835, 11.009, 7.4312, 4.478, -5.7759, 4.065, 0.0066], "6s⁰5d⁵"),
"Pt6" => ([0.2877, 17.780, 1.1111, 10.263, -1.9416, 2.432, 1.5477, 2.015, -0.0049], [2.5907, 12.991, 3.5155, 6.801, -0.7511, 1.206, 0.6014, 1.022, -0.0043], "6s⁰5d⁴"),
"Au1" => ([0.3475, 28.294, 0.8964, 11.794, -4.5383, 2.086, 4.2988, 1.983, -0.0047], [2.3189, 25.954, 4.2267, 11.444, 9.0997, 4.215, -7.8523, 3.981, 0.0052], "6s¹5d⁹"),
"Au2" => ([0.3664, 25.714, 0.8919, 11.488, -1.7302, 2.207, 1.4763, 1.908, -0.0046], [2.0676, 23.960, 4.1678, 11.164, 13.3827, 4.151, -12.1447, 3.996, 0.0054], "6s⁰5d⁹"),
"Au3" => ([0.3639, 22.330, 0.9313, 10.883, -1.1359, 2.355, 0.8455, 1.809, -0.0048], [1.4776, 21.784, 4.0585, 10.746, 5.9059, 4.242, -4.5905, 3.842, 0.0058], "6s⁰5d⁸"),
"Au4" => ([0.3472, 19.944, 0.9807, 10.424, -3.8228, 2.169, 3.4995, 2.009, -0.0047], [2.9775, 14.632, 3.4472, 6.956, -1.9784, 0.794, 1.8980, 0.745, -0.0182], "6s⁰5d⁷"),
"Au5" => ([0.3292, 18.073, 1.0376, 9.957, -2.2028, 2.257, 1.8410, 1.938, -0.0050], [0.5763, 20.517, 3.8572, 10.171, 6.0222, 4.213, -4.5020, 3.760, 0.0067], "6s⁰5d⁶"),
)