FAES: Factors of Atomic Electron Scattering

A computational tool which (a) enables Gaussian parameterization of elastic electron scattering factors [International Tables for Crystallography, Volume C, pp. 263-281 (2004)] into six analytical approximations and (b) derives fractionally charged scattering factors by computing weighted sums of adjacent integral neighbors. Curve-fitting is treated as a nonlinear least-squares optimization problem and implemented using a Levenberg-Marquardt algorithm in MATLAB.

where j = 4 or 5. Inclusion of the charge-correction term given by Peng [Acta Cryst. A54, 481-485 (1998)] yields a superior statistical fit for ionic electron scattering factors; however, this term is unsupported by crystallographic refinement programs like PHENIX, REFMAC, and SHELXL. For PHENIX, select 5 Gaussians + c; for REFMAC, 5 Gaussians; and for SHELXL, 4 Gaussians.

4 Gaussians f(s) = a1*exp(-b1*(s^2))+a2*exp(-b2*(s^2))+a3*exp(-b3*(s^2))+a4*exp(-b4*(s^2))

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE

H	1	0.129	0.036	0.127	0.236	0	37.737	0.553	3.772	13.518	0	0	0.001

H^-1	1	-37.647	-4.391	0.351	-13.954	0	1537.902	177.243	5.666	553.026	0	0	0.013

He	2	0.078	0.04	0.125	0.174	0	19.191	0.309	2.053	6.989	0	0	0

Li	3	1.39	0.119	0.394	1.379	0	117.035	0.588	6.083	36.687	0	0	0.003

Li¹⁺	3	23.445	0.3	1.344	6.07	0	697.333	1.661	26.504	160.375	0	0	0.017

Be	4	1.065	0.118	0.439	1.428	0	66.144	0.461	4.485	21.589	0	0	0.002

Be²⁺	4	47.441	0.486	2.899	12.592	0	719.569	2.261	30.72	171.613	0	0	0.028

B	5	0.765	0.13	0.521	1.377	0	51.783	0.419	3.927	16.688	0	0	0.002

C	6	0.6	0.136	0.547	1.225	0	40.938	0.374	3.278	13.013	0	0	0.001

N	7	0.482	0.135	0.519	1.075	0	31.526	0.324	2.607	10.017	0	0	0.001

O	8	0.392	0.144	0.511	0.937	0	25.675	0.306	2.272	8.27	0	0	0.001

O^-1	8	-23.228	0.383	1.281	-5.699	0	684.687	0.82	6.889	157.036	0	0	0.014

F	9	0.309	0.152	0.519	0.822	0	22.005	0.289	2.062	7.261	0	0	0.001

F^-1	9	-65.246	-5.474	1.383	-16.441	0	1913.852	150.335	3.163	573.682	0	0	0.056

Ne	10	0.256	0.158	0.504	0.733	0	19.19	0.272	1.841	6.313	0	0	0

Na	11	1.972	0.331	0.985	1.483	0	118.259	0.493	4.081	31.374	0	0	0.006

Na¹⁺	11	21.988	0.647	1.314	4.93	0	591.309	0.926	10.171	111.463	0	0	0.03

Mg	12	1.958	0.325	0.922	1.998	0	80.547	0.446	3.572	24.183	0	0	0.005

Mg²⁺	12	45.955	0.898	2.424	11.391	0	661.678	1.253	20.279	143.191	0	0	0.044

Al	13	1.913	0.359	0.974	2.638	0	80.5	0.454	3.78	23.357	0	0	0.006

Al³⁺	13	70.097	1.044	3.946	18.003	0	691.147	1.466	25.606	157.56	0	0	0.052

Si	14	1.762	0.362	0.974	2.725	0	64.441	0.428	3.553	19.406	0	0	0.005

Si⁴⁺	14	93.814	1.149	5.414	24.39	0	699.961	1.556	27.251	162.042	0	0	0.064

P	15	1.567	0.354	0.941	2.622	0	49.607	0.394	3.189	15.68	0	0	0.004

S	16	1.39	0.348	0.915	2.506	0	40.169	0.365	2.89	13.043	0	0	0.003

Cl	17	1.232	0.341	0.893	2.391	0	33.612	0.339	2.625	11.095	0	0	0.002

Cl^-1	17	-120.636	3.287	0.666	-21.071	0	2803.538	9.276	0.647	429.353	0	0	0.118

Ar	18	1.075	0.341	0.9	2.263	0	28.97	0.323	2.487	9.764	0	0	0.002

K	19	3.532	0.566	2.414	2.457	0	150.836	0.507	5.768	31.814	0	0	0.015

K¹⁺	19	21.404	0.813	3.119	4.603	0	551.389	0.729	8.788	92.632	0	0	0.04

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ca	20	3.88	0.547	2.281	3.194	0	109.54	0.47	5.048	29.73	0	0	0.012

Ca²⁺	20	43.972	1.016	3.338	9.863	0	590.914	0.879	10.27	111.139	0	0	0.06

Sc	21	3.431	0.539	2.211	3.117	0	98.119	0.444	4.574	26.467	0	0	0.011

Sc³⁺	21	67.922	1.556	3.959	16.329	0	637.938	1.408	15.853	132.285	0	0	0.072

Ti	22	3.078	0.539	2.158	2.992	0	90.552	0.428	4.223	24.193	0	0	0.01

Ti²⁺	22	44.391	1.378	3.305	10.205	0	605.298	1.172	11.843	117.047	0	0	0.057

Ti³⁺	22	68.102	1.636	3.967	16.436	0	640.957	1.411	16.042	133.181	0	0	0.073

Ti⁴⁺	22	92.443	1.843	5.142	23.098	0	669.282	1.626	20.734	146.166	0	0	0.085

V	23	2.792	0.542	2.109	2.854	0	84.561	0.414	3.932	22.411	0	0	0.009

V²⁺	23	43.753	1.173	3.249	9.725	0	583.132	0.885	9.79	107.432	0	0	0.064

V³⁺	23	68.061	1.7	3.933	16.367	0	639.296	1.398	16.111	132.795	0	0	0.073

V⁵⁺	23	116.315	2.025	6.558	29.693	0	684.515	1.734	24.066	154.335	0	0	0.095

Cr	24	1.989	0.548	2.072	2.352	0	87.861	0.403	3.698	20.054	0	0	0.009

Cr²⁺	24	44.348	1.493	3.173	10.163	0	603.76	1.16	11.729	116.79	0	0	0.058

Cr³⁺	24	68.055	1.747	3.882	16.334	0	638.559	1.374	16.077	132.403	0	0	0.073

Mn	25	2.354	0.555	2.013	2.579	0	75.291	0.394	3.485	19.714	0	0	0.008

Mn²⁺	25	43.699	1.257	3.106	9.674	0	581.489	0.871	9.523	106.837	0	0	0.065

Mn³⁺	25	68.103	1.793	3.844	16.397	0	640.24	1.352	16.202	132.923	0	0	0.074

Mn⁴⁺	25	92.167	1.968	5.049	22.918	0	665.233	1.513	20.603	144.881	0	0	0.085

Fe	26	2.177	0.563	1.966	2.453	0	71.621	0.387	3.307	18.67	0	0	0.007

Fe²⁺	26	43.687	1.292	3.029	9.662	0	581.141	0.861	9.421	106.746	0	0	0.065

Fe³⁺	26	67.162	1.603	3.65	15.701	0	618.91	1.091	13.661	123.602	0	0	0.082

Co	27	2.032	0.571	1.916	2.33	0	68.195	0.378	3.142	17.663	0	0	0.007

Co²⁺	27	43.661	1.323	2.952	9.644	0	580.545	0.848	9.327	106.584	0	0	0.065

Co³⁺	27	67.921	1.856	3.751	16.374	0	639.011	1.296	16.389	132.955	0	0	0.074

Ni	28	1.89	0.582	1.87	2.221	0	65.305	0.373	3.009	16.917	0	0	0.007

Ni²⁺	28	43.654	1.348	2.877	9.634	0	580.253	0.833	9.246	106.515	0	0	0.065

Ni³⁺	28	68.27	1.882	3.721	16.474	0	642.879	1.27	16.593	133.781	0	0	0.074

Cu	29	1.355	0.593	1.836	1.81	0	70.864	0.368	2.899	15.669	0	0	0.006

Cu¹⁺	29	21.11	1.128	2.534	4.419	0	532.756	0.673	6.703	84.838	0	0	0.045

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Cu²⁺	29	44.603	1.677	2.795	10.261	0	609.584	1.079	11.833	118.487	0	0	0.058

Zn	30	1.665	0.6	1.776	2.018	0	60.12	0.36	2.769	15.492	0	0	0.006

Zn²⁺	30	43.655	1.395	2.733	9.631	0	580.403	0.805	9.176	106.588	0	0	0.065

Ga	31	1.931	0.671	1.849	2.649	0	74.503	0.388	3.024	19.106	0	0	0.008

Ga³⁺	31	68.062	1.916	3.603	16.389	0	640.291	1.178	16.907	133.581	0	0	0.072

Ge	32	2.039	0.668	1.77	2.894	0	62.774	0.375	2.852	17.377	0	0	0.007

Ge⁴⁺	32	92.523	2.024	4.808	23.271	0	670.285	1.228	20.484	145.151	0	0	0.084

As	33	2.015	0.651	1.665	2.985	0	50.642	0.355	2.611	15.035	0	0	0.006

Se	34	1.96	0.635	1.57	3.036	0	42.435	0.338	2.401	13.14	0	0	0.005

Br	35	1.861	0.624	1.495	3.075	0	36.786	0.323	2.244	11.727	0	0	0.004

Br^-1	35	-121.434	4.503	1.531	-22.068	0	2886.035	11.306	0.772	469.988	0	0	0.109

Kr	36	1.748	0.622	1.438	3.087	0	32.461	0.313	2.137	10.616	0	0	0.003

Rb	37	4.353	1.017	2.871	3.514	0	154.533	0.485	5.122	25.929	0	0	0.022

Rb¹⁺	37	20.889	1.376	4.168	4.551	0	517.741	0.658	8.758	75.721	0	0	0.052

Sr	38	5.135	1.01	2.938	4.007	0	116.292	0.47	4.963	26.868	0	0	0.019

Sr²⁺	38	43.433	1.508	4.499	9.526	0	572.429	0.708	9.667	102.522	0	0	0.07

Y	39	4.642	0.976	2.871	4.159	0	99.298	0.445	4.567	24.096	0	0	0.017

Y³⁺	39	66.164	1.653	4.839	14.877	0	593.682	0.766	10.642	111.893	0	0	0.089

Zr	40	4.151	0.957	2.852	4.178	0	89.731	0.426	4.312	22.129	0	0	0.015

Zr⁴⁺	40	88.832	1.831	5.326	20.406	0	606.834	0.84	12.06	118.203	0	0	0.108

Nb	41	2.985	0.937	2.822	3.909	0	85.635	0.409	4.069	19.497	0	0	0.013

Nb³⁺	41	65.614	1.697	5.089	14.628	0	583.555	0.754	10.283	107.761	0	0	0.093

Nb⁵⁺	41	112.142	2.063	6.066	26.373	0	622.554	0.946	14.178	125.342	0	0	0.126

Mo	42	2.625	0.934	2.866	3.825	0	82.593	0.4	3.959	18.676	0	0	0.012

Mo³⁺	42	65.604	1.727	5.141	14.542	0	581.818	0.753	10.108	106.792	0	0	0.096

Mo⁵⁺	42	112.011	2.063	6.104	26.21	0	619.479	0.923	13.553	123.537	0	0	0.126

Mo⁶⁺	42	136.072	2.31	7.109	32.755	0	639.79	1.063	16.752	133.099	0	0	0.141

Tc	43	3.114	0.929	2.894	3.897	0	74.66	0.389	3.828	18.356	0	0	0.012

Ru	44	2.2	0.916	2.873	3.548	0	74.517	0.377	3.643	16.48	0	0	0.011

Ru³⁺	44	65.252	1.747	5.147	14.384	0	576.705	0.732	9.45	104.994	0	0	0.097

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ru⁴⁺	44	88.372	1.935	5.52	20	0	597.49	0.819	11	113.874	0	0	0.115

Rh	45	1.932	0.921	2.958	3.413	0	75.303	0.371	3.603	16.371	0	0	0.014

Rh³⁺	45	65.214	1.765	5.112	14.324	0	575.193	0.725	9.174	104.318	0	0	0.097

Rh⁴⁺	45	88.302	1.96	5.487	19.894	0	595.487	0.813	10.722	112.857	0	0	0.116

Pd	46	1.413	0.784	2.175	3.199	0	37.395	0.31	2.588	9.848	0	0	0.005

Pd²⁺	46	42.759	1.623	4.835	9.139	0	549.867	0.651	7.858	92.114	0	0	0.079

Pd⁴⁺	46	87.908	1.986	5.438	19.778	0	592.089	0.808	10.466	111.946	0	0	0.118

Ag	47	1.713	0.907	2.939	3.105	0	70.45	0.353	3.325	14.732	0	0	0.009

Ag¹⁺	47	20.403	1.446	4.535	4.481	0	490.007	0.567	6.521	64.417	0	0	0.058

Ag²⁺	47	42.702	1.637	4.77	9.085	0	548.663	0.644	7.611	92.04	0	0	0.079

Cd	48	2.19	0.906	2.945	3.183	0	62.472	0.347	3.225	14.804	0	0	0.009

Cd²⁺	48	42.748	1.653	4.693	9.051	0	548.602	0.639	7.382	92.045	0	0	0.079

In	49	2.625	0.967	3.204	3.626	0	76.06	0.365	3.461	18.415	0	0	0.012

In³⁺	49	65.092	1.858	4.847	14.169	0	571.695	0.708	8.314	102.705	0	0	0.101

Sn	50	2.882	0.953	3.115	3.901	0	66.558	0.354	3.269	17.617	0	0	0.011

Sn²⁺	50	42.25	1.792	4.873	9.088	0	533.28	0.669	7.801	83.815	0	0	0.088

Sn⁴⁺	50	87.659	2.098	5.083	19.507	0	586.366	0.791	9.608	109.281	0	0	0.121

Sb	51	2.975	0.931	2.987	4.073	0	56.336	0.34	3.047	16.205	0	0	0.009

Sb³⁺	51	65.197	2.05	5.256	14.25	0	570.932	0.756	9.239	101.23	0	0	0.107

Sb⁵⁺	51	110.972	2.465	5.759	25.505	0	606.758	0.928	12.353	118.599	0	0	0.139

Te	52	3.074	0.905	2.841	4.167	0	48.129	0.325	2.817	14.617	0	0	0.008

I	53	2.929	0.892	2.745	4.334	0	43.268	0.315	2.663	13.708	0	0	0.007

I^-1	53	-122.763	6.91	2.734	-23.906	0	3032.171	14.365	1.01	542.917	0	0	0.133

Xe	54	2.872	0.875	2.63	4.412	0	38.584	0.305	2.498	12.603	0	0	0.006

Cs	55	5.641	1.295	3.87	5.663	0	168.782	0.445	4.325	24.179	0	0	0.033

Cs¹⁺	55	19.82	1.803	5.375	5.463	0	456.075	0.616	7.313	47.623	0	0	0.073

Ba	56	7.125	1.315	3.933	5.861	0	128.365	0.446	4.313	24.199	0	0	0.031

Ba²⁺	56	42.47	2.138	6.25	9.192	0	537.974	0.722	9.264	85.156	0	0	0.094

La	57	6.822	1.097	3.62	6.204	0	106.424	0.378	3.436	20.312	0	0	0.043

La³⁺	57	65.22	2.3	6.623	14.35	0	573.363	0.768	10.063	102.573	0	0	0.109

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ce	58	5.85	1.376	4.124	5.991	0	113.777	0.45	4.424	25.207	0	0	0.04

Ce³⁺	58	65.136	2.309	6.54	14.301	0	572.085	0.757	9.844	102.317	0	0	0.108

Ce⁴⁺	58	87.734	2.444	6.971	19.683	0	589.003	0.807	10.758	110.645	0	0	0.125

Pr	59	6.409	1.334	3.882	5.306	0	117.398	0.43	4.048	22.279	0	0	0.029

Pr³⁺	59	65.205	2.319	6.447	14.296	0	572.491	0.748	9.645	102.274	0	0	0.108

Pr⁴⁺	59	87.943	2.459	6.867	19.69	0	589.756	0.798	10.577	110.447	0	0	0.125

Nd	60	6.228	1.344	3.854	5.129	0	114.834	0.426	3.969	21.81	0	0	0.028

Nd³⁺	60	65.148	2.328	6.351	14.251	0	571.628	0.738	9.461	102.115	0	0	0.108

Pm	61	6.025	1.36	3.843	4.963	0	112.856	0.424	3.927	21.6	0	0	0.027

Pm³⁺	61	65.024	2.334	6.247	14.201	0	570.299	0.728	9.275	101.794	0	0	0.107

Sm	62	5.858	1.366	3.801	4.819	0	110.724	0.42	3.843	21.183	0	0	0.027

Sm³⁺	62	64.996	2.341	6.146	14.159	0	569.263	0.718	9.108	101.522	0	0	0.107

Eu	63	5.604	1.392	3.82	4.721	0	110.928	0.421	3.845	21.594	0	0	0.025

Eu²⁺	63	42.534	2.207	5.759	9.065	0	541.827	0.665	8.125	87.869	0	0	0.089

Eu³⁺	63	65.031	2.349	6.044	14.141	0	569.491	0.71	8.958	101.394	0	0	0.107

Gd	64	5.217	1.405	3.787	4.816	0	96.512	0.415	3.816	20.72	0	0	0.023

Gd³⁺	64	64.962	2.357	5.944	14.12	0	568.385	0.701	8.818	101.186	0	0	0.107

Tb	65	5.284	1.413	3.766	4.452	0	107.388	0.415	3.74	21.13	0	0	0.026

Tb³⁺	65	65.089	2.365	5.847	14.151	0	568.953	0.693	8.693	101.057	0	0	0.107

Dy	66	5.182	1.421	3.709	4.285	0	103.807	0.411	3.672	20.495	0	0	0.024

Dy³⁺	66	64.737	2.369	5.748	14.051	0	566.075	0.684	8.556	100.659	0	0	0.106

Ho	67	5.012	1.379	3.544	4.412	0	86.953	0.393	3.414	18.523	0	0	0.019

Ho³⁺	67	64.803	2.378	5.658	14.03	0	566.189	0.676	8.458	100.646	0	0	0.106

Er	68	4.894	1.443	3.639	4.061	0	100.711	0.405	3.581	20.167	0	0	0.023

Er³⁺	68	64.948	2.387	5.57	14.068	0	567.98	0.67	8.37	100.894	0	0	0.106

Tm	69	4.774	1.45	3.595	3.949	0	98.69	0.401	3.523	19.872	0	0	0.022

Tm³⁺	69	64.794	2.392	5.48	14.029	0	566.424	0.662	8.269	100.59	0	0	0.106

Yb	70	4.624	1.463	3.569	3.861	0	98.054	0.399	3.498	19.9	0	0	0.021

Yb²⁺	70	42.334	2.246	5.134	8.931	0	539.714	0.611	7.305	88.702	0	0	0.086

Yb³⁺	70	64.857	2.4	5.395	14.04	0	566.903	0.655	8.193	100.686	0	0	0.106

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Lu	71	4.45	1.444	3.478	4.079	0	84.664	0.389	3.351	18.906	0	0	0.019

Lu³⁺	71	64.853	2.403	5.311	14.019	0	566.629	0.647	8.1	100.454	0	0	0.106

Hf	72	4.104	1.427	3.396	4.224	0	76.01	0.379	3.221	17.769	0	0	0.017

Hf⁴⁺	72	87.29	2.58	5.609	19.241	0	580.239	0.69	9.156	106.756	0	0	0.126

Ta	73	3.748	1.418	3.344	4.32	0	70.207	0.372	3.131	16.85	0	0	0.016

Ta⁵⁺	73	109.901	2.785	6.089	24.722	0	592.446	0.741	10.592	112.367	0	0	0.146

W	74	3.452	1.408	3.295	4.366	0	65.57	0.365	3.043	15.906	0	0	0.015

W⁶⁺	74	133.51	3.012	6.817	30.705	0	608.669	0.801	12.476	118.938	0	0	0.165

Re	75	3.248	1.391	3.231	4.373	0	60.608	0.356	2.934	14.832	0	0	0.013

Os	76	3.024	1.381	3.19	4.37	0	56.982	0.348	2.855	14.011	0	0	0.012

Os⁴⁺	76	87.218	2.643	6.105	19.188	0	578.131	0.676	9.24	105.412	0	0	0.131

Ir	77	2.811	1.376	3.166	4.348	0	54.223	0.343	2.797	13.352	0	0	0.011

Ir³⁺	77	64.538	2.5	5.947	13.891	0	559.455	0.629	8.252	96.897	0	0	0.112

Ir⁴⁺	77	87.02	2.643	6.175	19.083	0	575.789	0.668	9.112	104.72	0	0	0.131

Pt	78	2.174	1.348	3.066	4.212	0	50.387	0.332	2.657	12.009	0	0	0.01

Pt²⁺	78	42.137	2.356	5.806	8.903	0	529.169	0.584	7.376	82.518	0	0	0.093

Pt⁴⁺	78	87.2	2.763	6.244	19.119	0	578.334	0.694	9.592	106.04	0	0	0.155

Au	79	1.994	1.345	3.064	4.163	0	48.63	0.327	2.618	11.55	0	0	0.009

Au¹⁺	79	20.087	2.132	5.5	4.802	0	467.165	0.521	6.192	53.162	0	0	0.07

Au³⁺	79	64.738	2.501	6.026	13.886	0	560.803	0.616	7.991	97.01	0	0	0.112

Hg	80	2.27	1.357	3.134	4.195	0	47.992	0.326	2.641	11.706	0	0	0.009

Hg¹⁺	80	19.858	2.134	5.538	5.019	0	459.34	0.516	6.12	50.944	0	0	0.071

Hg²⁺	80	42.074	2.35	5.845	8.807	0	529.002	0.571	7.098	83.251	0	0	0.092

Tl	81	2.61	1.47	3.613	4.392	0	64.497	0.349	3.065	14.762	0	0	0.013

Tl¹⁺	81	19.862	2.141	5.593	5.176	0	456.484	0.512	6.077	48.994	0	0	0.072

Tl³⁺	81	64.437	2.494	6.029	13.765	0	557.836	0.602	7.657	96.348	0	0	0.112

Pb	82	2.909	1.469	3.636	4.573	0	60.255	0.345	3.03	14.85	0	0	0.013

Pb²⁺	82	41.858	2.407	6.081	8.854	0	520.104	0.573	7.23	78.061	0	0	0.097

Pb⁴⁺	82	86.775	2.649	6.254	18.872	0	571.412	0.635	8.317	102.692	0	0	0.133

Bi	83	3.192	1.465	3.644	4.784	0	56.775	0.34	2.982	14.85	0	0	0.012

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Bi³⁺	83	64.12	2.58	6.359	13.689	0	551.16	0.611	7.953	93.36	0	0	0.117

Bi⁵⁺	83	109.291	2.843	6.59	24.17	0	582.547	0.679	9.257	107.544	0	0	0.155

Po	84	3.462	1.435	3.539	4.91	0	50.424	0.33	2.83	13.958	0	0	0.011

At	85	3.529	1.413	3.459	5.057	0	45.684	0.321	2.71	13.301	0	0	0.01

Rn	86	3.43	1.4	3.411	5.244	0	42.34	0.315	2.628	12.899	0	0	0.009

Fr	87	5.517	1.776	4.694	6.663	0	155.254	0.398	4.016	23.122	0	0	0.035

Ra	88	7.244	1.762	4.678	6.81	0	120.872	0.392	3.911	22.345	0	0	0.033

Ra²⁺	88	41.351	2.641	7.209	9.13	0	504.452	0.596	8.009	69.61	0	0	0.111

Ac	89	7.04	1.735	4.601	7.051	0	102.298	0.382	3.749	21.186	0	0	0.03

Ac³⁺	89	64.108	2.84	7.716	13.747	0	547.157	0.639	8.895	90.147	0	0	0.129

Th	90	6.594	1.706	4.509	7.251	0	89.501	0.372	3.585	19.932	0	0	0.027

Pa	91	6.346	1.73	4.635	6.803	0	95.871	0.374	3.634	19.828	0	0	0.028

U	92	5.991	1.741	4.7	6.66	0	95.173	0.373	3.628	19.64	0	0	0.027

U³⁺	92	64.069	2.857	7.777	13.673	0	546.691	0.625	8.464	90.329	0	0	0.128

U⁴⁺	92	86.545	2.987	8.061	18.801	0	567.154	0.656	9.108	100.406	0	0	0.145

U⁶⁺	92	132.108	3.269	8.872	29.695	0	592.782	0.726	10.702	111.923	0	0	0.181

Np	93	5.86	1.728	4.672	6.45	0	91.511	0.367	3.528	18.791	0	0	0.026

Pu	94	5.615	1.75	4.789	5.987	0	100.875	0.368	3.565	18.854	0	0	0.027

Am	95	5.418	1.75	4.804	5.816	0	98.632	0.365	3.513	18.476	0	0	0.027

Cm	96	5.295	1.729	4.72	5.923	0	86.326	0.358	3.382	17.716	0	0	0.024

Bk	97	5.161	1.729	4.72	5.75	0	84.294	0.355	3.327	17.349	0	0	0.024

Cf	98	5.471	1.628	4.373	5.464	0	72.911	0.329	2.957	14.58	0	0	0.029

5 Gaussians + scalar constant f(s) = a1*exp(-b1*(s^2))+a2*exp(-b2*(s^2))+a3*exp(-b3*(s^2))+a4*exp(-b4*(s^2))+a5*exp(-b5*(s^2))+c

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE

H	1	0.098	0.267	-0.006	0.141	-10.25	47.316	15.011	252.987	3.601	-0.001	10.277	0.001

H^-1	1	-2.453	-27.017	0.109	-8.939	0.304	134.104	1054.39	2.218	374.597	12.019	0.011	0.001

He	2	0.144	0.158	0.019	0.076	-4.727	11.972	3.974	30.408	1.128	-0	4.747	0

Li	3	1.509	0.538	0.968	0.221	-15.607	51.84	13.909	137.241	2.356	-0.001	15.658	0.001

Li¹⁺	3	24.486	1.813	-95.176	0.445	6.952	785.535	44.319	-0	5.384	206.345	95.256	0.009

Be	4	1.412	0.668	0.698	0.22	-12.032	30.493	9.594	78.291	1.861	-0.001	12.087	0.001

Be²⁺	4	49.545	3.932	-91.085	0.854	14.43	812.306	50.286	-0	7.269	221.138	91.201	0.015

B	5	1.249	0.752	0.485	0.244	-10.72	23.248	7.732	62.096	1.72	-0.001	10.784	0

C	6	1.058	0.778	0.342	0.263	-7.859	18.872	6.351	51.228	1.528	-0.001	7.926	0

N	7	0.88	0.703	0.284	0.275	-5.513	14.404	5.11	38.644	1.352	-0.001	5.583	0

O	8	0.702	0.715	0.188	0.302	-5.592	13.03	4.691	33.445	1.266	-0.002	5.668	0

O^-1	8	-2.941	-26.666	0.568	-8.927	1.122	110.973	1012.845	1.886	342.122	9.084	0.072	0.002

F	9	0.601	0.651	0.152	0.316	-5.374	11.062	4.089	28.174	1.19	-0.002	5.455	0

F^-1	9	-2.581	-26.027	0.55	-8.411	0.974	91.814	948.981	1.635	302.518	7.477	0.073	0.002

Ne	10	0.447	0.623	0.113	0.373	-5.588	10.471	4.152	25.032	1.254	-0.002	5.684	0

Na	11	1.685	0.815	1.443	0.684	-17.304	47.943	9.288	138.848	1.983	-0.001	17.453	0.002

Na¹⁺	11	23.79	1.57	-105.861	1.045	6.365	725.957	30.94	-0	3.358	174.942	106.075	0.013

Mg	12	2.148	0.904	1.348	0.654	-15.145	35.081	8.794	95.246	1.795	-0.001	15.298	0.001

Mg²⁺	12	48.345	3.325	-137.356	1.152	13.358	757.814	38.263	-0	3.837	191.438	137.61	0.02

Al	13	2.609	1.223	1.205	0.681	-17.403	34.533	9.946	99.773	1.809	-0.001	17.573	0.002

Al³⁺	13	74.072	5.81	-216.771	1.491	21.435	805.606	49.066	-0.001	6.381	217.906	217.201	0.024

Si	14	2.573	1.347	1.084	0.65	-6.7	28.527	8.912	79.693	1.67	-0.004	6.874	0.001

Si⁴⁺	14	99.267	8.07	-127.122	1.9	29.177	820.025	52.227	-0.001	7.507	225.85	127.6	0.029

P	15	2.404	1.375	0.919	0.615	-13.374	23.079	7.68	61.621	1.523	-0.002	13.549	0.001

S	16	2.234	1.381	0.783	0.585	-10.504	19.233	6.679	50.219	1.411	-0.002	10.681	0.001

Cl	17	2.065	1.389	0.665	0.563	-17.763	16.482	5.901	42.348	1.303	-0.001	17.94	0.001

Cl^-1	17	-8.385	-127.084	1.025	-31.007	3.187	236.585	3715.557	1.725	966.444	12.821	0.122	0.018

Ar	18	1.912	1.373	0.587	0.534	-13.637	14.211	5.166	36.037	1.191	-0.001	13.812	0

K	19	2.508	2.439	2.622	1.137	-83.972	57.713	10.64	179.655	2.401	-0.001	84.247	0.005

K¹⁺	19	23.217	2.523	-169.924	1.915	5.905	679.674	19.568	-0	3.834	151.502	170.267	0.018

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ca	20	3.514	2.255	2.76	1.11	-14.222	46.02	9.367	129.442	2.199	-0.003	14.493	0.004

Ca²⁺	20	47.671	3.394	-112.042	2.342	12.795	728.525	30.172	-0.001	4.412	175.857	112.428	0.026

Sc	21	3.296	2.168	2.432	1.134	-30.908	40.717	8.767	116.067	2.112	-0.001	31.182	0.003

Sc³⁺	21	73.115	5.462	-247.188	2.672	20.681	780.212	43.643	-0.001	5.62	204.565	247.76	0.026

Ti	22	3.096	2.098	2.122	1.179	-12.635	37.924	8.458	108.552	2.055	-0.003	12.914	0.003

Ti²⁺	22	48.221	3.625	-105.6	2.548	13.258	752.899	35.963	-0.002	5.032	188.873	106.164	0.021

Ti³⁺	22	73.745	5.516	-125.517	2.682	20.974	788.821	43.521	-0.002	5.454	206.416	126.114	0.027

Ti⁴⁺	22	98.663	7.511	-139.544	2.802	28.218	797.226	46.584	-0.001	5.793	212.013	140.164	0.032

V	23	2.888	2.014	1.895	1.221	-12.421	35.556	8.174	102.102	2.007	-0.003	12.707	0.003

V²⁺	23	47.536	3.422	-113.53	2.387	12.674	722.713	29.254	-0.001	3.887	172.872	113.948	0.026

V³⁺	23	73.177	5.403	-125.343	2.645	20.601	776.893	42.187	-0.002	5.211	202.001	125.957	0.027

V⁵⁺	23	123.189	9.59	-161.547	2.98	35.599	802.448	48.247	-0.001	6.064	216.086	162.22	0.039

Cr	24	2.107	1.964	1.363	1.244	-28.087	33.775	7.853	107.995	1.935	-0.001	28.376	0.003

Cr²⁺	24	48.181	3.573	-109.521	2.512	13.26	751.677	35.593	-0.002	4.698	188.458	110.126	0.022

Cr³⁺	24	73.121	5.378	-259.633	2.626	20.527	774.973	41.971	-0.001	5.068	201.168	260.271	0.027

Mn	25	2.52	1.862	1.585	1.248	-26.379	31.498	7.481	91.292	1.849	-0.002	26.671	0.002

Mn²⁺	25	47.481	3.336	-114.692	2.362	12.627	720.565	28.938	-0.001	3.605	171.796	115.134	0.027

Mn³⁺	25	73.313	5.372	-55.711	2.597	20.624	777.9	41.899	-0.004	4.941	201.533	56.373	0.028

Mn⁴⁺	25	97.876	7.326	-149.194	2.725	27.746	785.151	44.858	-0.002	5.308	207.086	149.886	0.034

Fe	26	2.371	1.795	1.432	1.27	-25.253	30.349	7.3	87.796	1.797	-0.002	25.55	0.002

Fe²⁺	26	47.467	3.291	-116.793	2.34	12.617	719.965	28.88	-0.001	3.487	171.472	117.249	0.027

Fe³⁺	26	72.073	4.889	-134.412	2.455	19.66	744.827	34.989	-0.001	3.77	184.501	134.892	0.033

Co	27	2.239	1.718	1.314	1.28	-24.828	29.04	7.052	84.339	1.744	-0.002	25.131	0.002

Co²⁺	27	47.425	3.249	-118.039	2.312	12.597	718.952	28.84	-0.001	3.375	171.1	118.507	0.027

Co³⁺	27	72.887	5.315	-135.919	2.511	20.506	772.962	41.468	-0.002	4.708	200.054	136.627	0.028

Ni	28	2.097	1.651	1.221	1.291	-9.549	27.907	6.882	80.69	1.691	-0.004	9.856	0.002

Ni²⁺	28	47.41	3.208	-119.49	2.282	12.586	718.408	28.859	-0.001	3.279	170.884	119.971	0.027

Ni³⁺	28	73.38	5.298	-137.621	2.465	20.55	776.155	41.377	-0.002	4.616	199.952	138.352	0.028

Cu	29	1.511	1.59	0.895	1.29	-9.709	27.447	6.627	89.025	1.634	-0.004	10.022	0.002

Cu¹⁺	29	23.157	2.049	-185.583	2.082	5.856	674.758	20.002	-0	2.817	148.973	186.039	0.018

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Cu²⁺	29	48.64	3.435	-118.387	2.309	13.361	758.525	36.132	-0.002	4.155	189.279	119.101	0.022

Zn	30	1.872	1.521	1.078	1.274	-21.856	25.522	6.377	74.235	1.575	-0.002	22.174	0.001

Zn²⁺	30	47.443	3.152	-122.066	2.213	12.602	719.282	29.099	-0.001	3.115	171.129	122.575	0.027

Ga	31	2.512	1.669	1.185	1.395	-28.624	30.741	7.767	95.727	1.676	-0.002	28.97	0.002

Ga³⁺	31	72.722	5.238	-285.931	2.315	20.312	767.627	41.111	-0.001	4.402	198.112	286.727	0.028

Ge	32	2.755	1.683	1.244	1.348	-10.945	26.984	7.369	79.355	1.587	-0.004	11.291	0.002

Ge⁴⁺	32	96.524	6.363	-134.252	2.326	26.369	752.012	39.046	-0.002	4.458	187.662	135.073	0.044

As	33	2.845	1.651	1.212	1.275	-8.946	22.688	6.637	63.33	1.465	-0.005	9.284	0.001

Se	34	2.859	1.625	1.172	1.215	-18.051	19.486	6.073	52.563	1.369	-0.002	18.384	0.001

Br	35	2.838	1.657	1.06	1.173	-15.219	17.488	5.75	46.021	1.297	-0.003	15.55	0.001

Br^-1	35	-9.525	-127.67	1.896	-32.307	4.293	279.393	3853.868	1.642	1063.346	14.92	0.233	0.028

Kr	36	2.775	1.737	0.915	1.139	-14.015	16.162	5.544	41.518	1.24	-0.003	14.346	0.001

Rb	37	2.893	3.487	3.307	1.606	-58.708	53.394	10.892	185.721	1.945	-0.001	59.188	0.007

Rb¹⁺	37	22.788	3.863	-119.582	2.177	5.593	646.465	16.333	-0.001	2.826	134.927	120.169	0.022

Sr	38	4.103	3.331	3.655	1.543	-21.808	47.269	9.706	139.566	1.827	-0.003	22.281	0.006

Sr²⁺	38	46.626	4.12	-157.739	2.662	11.945	686.717	21.072	-0.001	3.464	154.868	158.393	0.033

Y	39	4.173	3.29	3.23	1.507	-19.952	40.821	8.957	120.559	1.748	-0.003	20.42	0.005

Y³⁺	39	71.385	5.072	-389.05	3.113	18.925	720.435	28.058	-0	4.014	170.877	389.761	0.041

Zr	40	4.047	3.275	2.863	1.498	-45.27	36.675	8.47	109.151	1.72	-0.002	45.744	0.005

Zr⁴⁺	40	95.928	6.593	-216.852	3.403	26.089	741.571	33.837	-0.001	4.328	182.663	217.601	0.047

Nb	41	3.352	3.317	2.039	1.486	-18.149	32.59	8.043	106.309	1.684	-0.004	18.626	0.004

Nb³⁺	41	70.983	5.313	-196.362	3.333	18.844	716.554	27.948	-0.001	4.024	170.254	197.094	0.041

Nb⁵⁺	41	120.906	8.449	-233.963	3.62	33.492	759.002	37.934	-0.001	4.528	191.873	234.741	0.053

Mo	42	3.173	3.306	1.794	1.499	-42.351	30.645	7.736	101.819	1.679	-0.002	42.836	0.004

Mo³⁺	42	71.269	5.389	-196.6	3.434	18.973	721.207	28.256	-0.001	4.008	172.164	197.342	0.04

Mo⁵⁺	42	120.395	8.196	-231.716	3.708	32.902	748.991	36.575	-0.001	4.481	186.758	232.503	0.057

Mo⁶⁺	42	145.57	10.298	-104.269	3.788	40.565	766.166	40.04	-0.002	4.642	196.073	105.071	0.058

Tc	43	3.486	3.253	2.099	1.521	-17.485	30.037	7.445	91.857	1.669	-0.004	17.975	0.004

Ru	44	2.797	3.248	1.491	1.523	-16.636	27.29	7.096	93.374	1.641	-0.004	17.129	0.003

Ru³⁺	44	70.847	5.205	-196.415	3.594	18.801	715.206	27.774	-0.001	3.929	169.8	197.173	0.041

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ru⁴⁺	44	96.07	6.657	-218.813	3.764	26.07	741.022	33.155	-0.001	4.19	181.803	219.598	0.048

Rh	45	2.637	3.304	1.124	1.658	-19.003	29.676	7.405	103.988	1.748	-0.004	19.519	0.01

Rh³⁺	45	70.797	5.122	-195.63	3.653	18.737	713.473	27.73	-0.001	3.871	169.127	196.395	0.041

Rh⁴⁺	45	95.926	6.589	-217.178	3.811	25.898	737.793	32.927	-0.001	4.112	180.461	217.969	0.048

Pd	46	2.295	2.8	0.777	1.26	-18.422	16.377	5.183	49.432	1.312	-0.003	18.867	0.002

Pd²⁺	46	46.737	4.06	-171.024	3.47	12.016	689.932	22.03	-0.001	3.509	156.003	171.764	0.033

Pd⁴⁺	46	95.578	6.566	-434.772	3.858	25.946	737.281	33.055	-0	4.047	180.884	435.571	0.047

Ag	47	2.271	3.099	1.154	1.632	-37.933	24.945	6.535	88.467	1.649	-0.002	38.445	0.003

Ag¹⁺	47	22.663	3.481	-294.317	3.168	5.583	641.01	16.576	-0	3.074	132.634	295.02	0.023

Ag²⁺	47	46.75	3.942	-352.677	3.524	12.058	691.458	22.176	-0	3.465	156.931	353.424	0.033

Cd	48	2.616	2.993	1.469	1.641	-35.272	24.494	6.249	76.72	1.611	-0.002	35.783	0.002

Cd²⁺	48	46.741	3.818	-169.238	3.55	12.002	689.509	22.101	-0.001	3.393	156.233	169.991	0.033

In	49	3.276	3.021	1.663	1.924	-19.432	30.409	7.199	96.803	1.798	-0.004	19.978	0.003

In³⁺	49	71.329	4.903	-196.823	3.792	18.995	721.937	28.696	-0.001	3.617	171.819	197.619	0.041

Sn	50	3.658	2.895	1.827	1.932	-18.376	27.836	6.921	83.115	1.756	-0.004	18.922	0.003

Sn²⁺	50	46.688	4.589	-345.454	3.57	12.028	688.922	22.871	-0	3.278	155.599	346.224	0.033

Sn⁴⁺	50	95.847	6.448	-216.07	3.932	26.021	740.165	34.16	-0.001	3.749	182.266	216.902	0.048

Sb	51	3.922	2.763	1.884	1.868	-15.79	24.494	6.379	69.25	1.661	-0.004	16.325	0.003

Sb³⁺	51	71.168	5.475	-192.273	3.748	18.669	712.452	26.317	-0.001	3.443	166.509	193.081	0.042

Sb⁵⁺	51	119.831	8.134	-225.38	3.977	32.792	745.276	36.053	-0.001	3.776	186.015	226.236	0.054

Te	52	4.088	2.636	1.97	1.782	-31.101	21.406	5.796	58.553	1.55	-0.002	31.621	0.002

I	53	4.243	2.588	1.75	1.803	-29.025	20.092	5.731	53.444	1.524	-0.002	29.546	0.002

I^-1	53	-12.09	-129.292	3.326	-35.761	6.367	361.413	4182.968	2.089	1279.06	18.53	0.375	0.05

Xe	54	4.3	2.509	1.707	1.765	-11.034	18.192	5.425	47.391	1.456	-0.006	11.547	0.001

Cs	55	3.822	4.979	4.323	2.7	-185.271	53.143	12.353	205.854	2.175	-0.001	185.945	0.01

Cs¹⁺	55	22.505	5.776	-145.2	3.264	5.538	625.532	17.079	-0.001	2.73	123.101	145.971	0.026

Ba	56	5.143	4.86	5.055	2.562	-31.152	50.164	11.041	157.662	1.988	-0.003	31.792	0.01

Ba²⁺	56	46.327	5.968	-174.557	3.558	11.638	670.638	18.879	-0.001	2.996	146.145	175.384	0.037

La	57	5.391	4.929	4.482	2.618	-0.001	44.309	10.094	137.318	1.597	-1.156	0.375	0.028

La³⁺	57	70.034	6.344	-206.979	3.883	17.947	687.974	21.346	-0.001	3.284	155.238	207.863	0.048

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ce	58	5.638	4.526	4.243	2.348	-16.373	41.462	9.17	137.779	1.76	-0.005	16.991	0.028

Ce³⁺	58	69.931	6.206	-210.482	3.923	17.93	686.947	21.313	-0.001	3.275	155.116	211.382	0.048

Ce⁴⁺	58	93.949	7.088	-103.287	4.268	24.647	704.222	25.058	-0.002	3.625	164.244	104.233	0.058

Pr	59	4.719	4.617	4.42	2.552	-72.699	47.534	10.189	147.304	1.908	-0.001	73.366	0.008

Pr³⁺	59	70.049	6.064	-213.204	3.954	17.93	687.479	21.305	-0.001	3.261	154.93	214.118	0.048

Pr⁴⁺	59	94.331	6.977	-246.881	4.295	24.682	706.183	25.219	-0.001	3.607	164.379	247.843	0.058

Nd	60	4.521	4.49	4.384	2.53	-69.971	45.68	9.828	142.342	1.863	-0.001	70.641	0.008

Nd³⁺	60	70.063	5.938	-216.916	3.985	17.962	688.306	21.405	-0.001	3.254	155.409	217.846	0.049

Pm	61	4.438	4.402	4.192	2.523	-69.644	45.366	9.605	140.73	1.832	-0.001	70.319	0.008

Pm³⁺	61	69.95	5.808	-220.788	4.008	17.955	687.886	21.515	-0.001	3.245	155.521	221.734	0.049

Sm	62	4.357	4.306	4.023	2.518	-28.796	44.991	9.391	139.102	1.802	-0.003	29.476	0.008

Sm³⁺	62	69.923	5.691	-223.29	4.025	17.948	687.42	21.635	-0.001	3.233	155.618	224.251	0.049

Eu	63	4.238	4.166	3.911	2.544	-29.716	44.057	9.301	136.807	1.809	-0.003	30.413	0.008

Eu²⁺	63	46.074	5.002	-362.512	3.686	11.464	663.625	17.773	-0	2.871	143.094	363.432	0.038

Eu³⁺	63	70.019	5.576	-226.27	4.035	17.941	688.24	21.765	-0.001	3.218	155.665	227.246	0.049

Gd	64	4.442	4.154	3.606	2.389	-23.524	38.684	8.462	119.303	1.654	-0.004	24.189	0.006

Gd³⁺	64	70.002	5.48	-230.041	4.046	17.993	688.846	21.984	-0.001	3.208	156.182	231.032	0.049

Tb	65	4.222	4.039	3.406	2.569	-73.636	45.692	9.202	139.592	1.793	-0.001	74.356	0.01

Tb³⁺	65	70.204	5.388	-98.284	4.047	18.019	689.868	22.159	-0.002	3.19	156.096	99.288	0.049

Dy	66	3.95	3.923	3.574	2.478	-27.406	42.033	8.617	129.672	1.699	-0.004	28.111	0.007

Dy³⁺	66	69.693	5.289	-233.862	4.041	17.949	686.781	22.269	-0.001	3.172	156.094	234.88	0.048

Ho	67	3.852	3.708	3.822	2.31	-21.81	32.422	7.542	101.578	1.555	-0.004	22.486	0.006

Ho³⁺	67	69.893	5.217	-234.775	4.037	18.011	689.126	22.502	-0.001	3.156	156.914	235.807	0.049

Er	68	3.797	3.745	3.347	2.46	-27.137	41.074	8.327	126.217	1.659	-0.004	27.858	0.007

Er³⁺	68	70.241	5.147	-239.624	4.038	18.112	693.467	22.833	-0.001	3.153	157.898	240.673	0.048

Tm	69	3.724	3.665	3.228	2.454	-27.05	40.788	8.217	124.285	1.643	-0.004	27.778	0.007

Tm³⁺	69	69.99	5.073	-239.748	4.018	18.067	691.345	22.933	-0.001	3.126	157.612	240.807	0.048

Yb	70	3.639	3.573	3.169	2.432	-62.927	39.826	8.024	122.596	1.616	-0.002	63.661	0.006

Yb²⁺	70	45.793	4.236	-204.331	3.695	11.478	662.546	18.148	-0.001	2.785	144.385	205.345	0.038

Yb³⁺	70	70.304	5.032	-103.076	4.015	18.223	696.143	23.347	-0.002	3.119	159.195	104.149	0.049

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Lu	71	3.899	3.502	2.975	2.373	-10.203	35.353	7.612	105.821	1.559	-0.009	10.929	0.005

Lu³⁺	71	70.185	4.955	-487.356	3.989	18.124	693.886	23.417	-0	3.097	158.444	488.442	0.048

Hf	72	3.967	3.478	2.676	2.326	-22.887	32.062	7.325	95.666	1.518	-0.004	23.614	0.005

Hf⁴⁺	72	94.609	6.257	-274.074	4.186	25.058	715.457	28.549	-0.001	3.328	169.764	275.215	0.055

Ta	73	3.969	3.482	2.384	2.287	-52.148	29.668	7.089	89.259	1.486	-0.002	52.877	0.005

Ta⁵⁺	73	118.911	7.865	-127.023	4.32	32.057	729.899	32.328	-0.002	3.488	177.798	128.204	0.062

W	74	3.905	3.509	2.135	2.259	-50.636	27.876	6.915	84.457	1.461	-0.002	51.368	0.004

W⁶⁺	74	144.136	9.623	-135.079	4.435	39.203	743.517	34.992	-0.002	3.623	183.787	136.295	0.069

Re	75	3.79	3.467	2.101	2.186	-7.812	24.889	6.462	76.112	1.393	-0.011	8.527	0.003

Os	76	3.7	3.508	1.88	2.167	-18.517	23.834	6.344	72.918	1.381	-0.005	19.242	0.004

Os⁴⁺	76	94.783	6.58	-121.416	4.378	25.048	715.06	27.393	-0.002	3.39	168.528	122.609	0.057

Ir	77	3.599	3.503	1.765	2.121	-83.61	22.267	6.083	69.025	1.351	-0.001	84.338	0.003

Ir³⁺	77	70.188	5.534	-109.913	4.238	18.115	692.941	22.688	-0.002	3.175	157.6	111.077	0.049

Ir⁴⁺	77	94.38	6.563	-581.352	4.437	24.891	711.038	27.137	-0	3.404	167.515	582.558	0.057

Pt	78	3.191	3.553	1.258	2.087	-16.266	20.607	5.885	67.589	1.32	-0.005	16.99	0.003

Pt²⁺	78	46.217	4.906	-227.347	4.029	11.599	668.2	18.481	-0.001	2.925	145.051	228.475	0.04

Pt⁴⁺	78	95.629	6.991	-117.11	4.428	25.814	730.808	27.889	-0.002	3.313	175.516	118.306	0.081

Au	79	3.079	3.551	1.178	2.045	-15.081	19.365	5.639	63.89	1.285	-0.006	15.801	0.002

Au¹⁺	79	22.573	4.615	-186.645	3.7	5.432	618.312	14.647	-0.001	2.594	118.033	187.718	0.029

Au³⁺	79	70.547	5.427	-261.685	4.373	18.142	695.15	22.567	-0.001	3.206	157.588	262.872	0.049

Hg	80	3.22	3.564	1.382	2.062	-15.386	19.56	5.609	61.516	1.299	-0.006	16.122	0.002

Hg¹⁺	80	22.313	4.751	-191.711	3.786	5.479	611.776	15.092	-0.001	2.633	115.746	192.801	0.03

Hg²⁺	80	45.907	4.708	-474.597	4.131	11.472	662.662	17.996	-0	2.925	143.889	475.742	0.039

Tl	81	3.547	3.832	1.648	2.276	-22.02	24.73	6.405	83.815	1.454	-0.005	22.819	0.004

Tl¹⁺	81	22.33	4.914	-194.169	3.846	5.439	607.753	15.348	-0.001	2.649	113.569	195.271	0.03

Tl³⁺	81	70.23	5.278	-537.074	4.511	18.117	693.947	22.724	-0	3.226	157.878	538.283	0.049

Pb	82	3.9	3.787	1.839	2.274	-8.696	24.097	6.235	76.222	1.433	-0.011	9.49	0.004

Pb²⁺	82	46.004	5.192	-231.564	4.241	11.47	662.542	18.61	-0.001	2.944	143.205	232.731	0.04

Pb⁴⁺	82	94.618	6.401	-297.09	4.773	24.991	713.908	27.641	-0.001	3.44	168.409	298.347	0.057

Bi	83	4.258	3.731	2.004	2.292	-21.076	23.582	6.151	71.227	1.444	-0.005	21.884	0.003

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Bi³⁺	83	69.891	5.786	-543.024	4.558	18.001	688.72	22.241	-0	3.186	156.291	544.245	0.049

Bi⁵⁺	83	119.243	7.907	-646.283	4.941	32.016	729.868	31.583	-0	3.574	176.601	647.575	0.064

Po	84	4.523	3.595	2.244	2.208	-18.211	21.312	5.682	61.972	1.369	-0.005	19	0.003

At	85	4.782	3.513	2.184	2.198	-87.133	20.192	5.511	56.866	1.356	-0.001	87.926	0.003

Rn	86	4.991	3.456	2.073	2.186	-16.157	19.127	5.346	52.418	1.327	-0.006	16.942	0.002

Fr	87	4.652	5.462	4.325	3.259	-114.597	43.69	10.85	188.927	2.01	-0.001	115.597	0.013

Ra	88	5.593	5.497	5.263	3.201	-107.437	44.286	10.365	148.553	1.946	-0.001	108.427	0.011

Ra²⁺	88	45.934	6.966	-235.738	4.409	11.464	658.602	18.342	-0.001	2.876	140.278	236.951	0.041

Ac	89	6.084	5.407	4.893	3.112	-97.44	39.974	9.694	126.834	1.864	-0.001	98.414	0.009

Ac³⁺	89	69.798	7.3	-111.104	4.685	17.675	679.262	20.011	-0.002	3.065	150.692	112.363	0.052

Th	90	6.322	5.337	4.437	3.042	-37.487	36.091	9.16	111.734	1.795	-0.004	38.446	0.008

Pa	91	5.702	5.415	4.37	3.094	-202.793	37.407	9.162	119.457	1.812	-0.001	203.766	0.008

U	92	5.521	5.408	4.094	3.111	-89.961	36.982	9.003	118.142	1.804	-0.002	90.94	0.008

U³⁺	92	69.619	7.03	-519.36	4.882	17.574	675.776	19.482	-0	3.074	149.272	520.65	0.053

U⁴⁺	92	93.42	7.637	-300.004	5.167	24.053	690.81	22.27	-0.001	3.308	157.205	301.34	0.063

U⁶⁺	92	142.495	9.895	-711.89	5.676	37.888	720.453	28.6	-0	3.76	171.549	713.309	0.08

Np	93	5.317	5.363	3.995	3.101	-36.766	35.918	8.722	114.677	1.768	-0.004	37.737	0.008

Pu	94	4.699	5.352	3.971	3.174	-37.906	37.554	8.754	125.515	1.792	-0.004	38.891	0.008

Am	95	4.577	5.303	3.754	3.2	-89.843	37.533	8.635	124.118	1.789	-0.002	90.836	0.008

Cm	96	4.853	5.164	3.571	3.132	-183.069	34.177	8.159	108.745	1.727	-0.001	184.049	0.007

Bk	97	4.723	5.09	3.462	3.138	-178.451	33.645	7.972	106.388	1.707	-0.001	179.431	0.007

Cf	98	4.235	4.348	4.814	2.675	-5.588	21.248	5.948	78.856	1.421	-0.018	6.464	0.026

5 Gaussians f(s) = a1*exp(-b1*(s^2))+a2*exp(-b2*(s^2))+a3*exp(-b3*(s^2))+a4*exp(-b4*(s^2))+a5*exp(-b5*(s^2))

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE

H	1	0.041	0.266	0.154	-0.009	0.075	0.619	17.116	4.462	214.422	57.283	0	0.001

H^-1	1	0.351	-4.391	-199.271	-37.48	-13.95	5.666	177.241	4975.51	1536.194	552.975	0	0.013

He	2	0.029	0.155	0.076	0.017	0.141	0.229	4.185	1.328	31.441	12.292	0	0

Li	3	0.077	0.582	0.232	0.88	1.516	0.394	16.16	3.044	142.201	55.581	0	0.001

Li¹⁺	3	2.143	0.534	25.106	7.518	0.153	57.161	8.962	843.171	238.033	0.744	0	0.006

Be	4	0.079	0.7	0.226	0.654	1.392	0.318	10.489	2.296	80.004	31.845	0	0.001

Be²⁺	4	4.576	1.096	50.718	15.53	0.219	63.429	11.406	868.725	252.676	0.838	0	0.01

B	5	0.091	0.783	0.257	0.449	1.213	0.3	8.465	2.127	63.745	24.397	0	0

C	6	0.094	0.796	0.275	0.318	1.026	0.26	6.842	1.832	52.535	19.684	0	0

N	7	0.093	0.706	0.282	0.273	0.857	0.223	5.39	1.556	39.145	14.786	0	0

O	8	0.101	0.718	0.307	0.176	0.68	0.215	4.938	1.448	34.137	13.464	0	0

O^-1	8	1.292	0.42	-27.455	-9.809	-3.525	7.436	0.893	1093.626	386.901	124.108	0	0.007

F	9	0.109	0.647	0.319	0.144	0.582	0.208	4.295	1.355	28.652	11.38	0	0

F^-1	9	1.383	-5.454	-139.58	-50.629	-16.025	3.163	150.116	4996.255	1774.931	567.743	0	0.058

Ne	10	0.132	0.625	0.387	0.097	0.411	0.229	4.532	1.468	26.086	11.251	0	0

Na	11	0.222	0.779	0.711	1.355	1.709	0.344	10.886	2.452	142.697	51.04	0	0.002

Na¹⁺	11	1.724	1.031	24.201	6.715	0.36	38.664	4.527	761.383	193.654	0.53	0	0.01

Mg	12	0.223	0.911	0.661	1.27	2.143	0.316	9.975	2.162	97.421	36.79	0	0.001

Mg²⁺	12	3.79	1.182	49.273	14.177	0.459	47.404	5.88	799.542	214.025	0.61	0	0.016

Al	13	0.246	1.277	0.676	1.126	2.563	0.323	11.1	2.188	102.506	36.274	0	0.001

Al³⁺	13	6.713	1.695	75.717	22.984	0.684	60.95	10.056	858.057	247.055	0.901	0	0.018

Si	14	0.254	1.423	0.645	0.999	2.506	0.31	9.927	2.047	82.154	30.137	0	0.001

Si⁴⁺	14	9.212	2.26	101.327	31.135	0.741	63.953	11.383	870.175	253.93	0.92	0	0.021

P	15	0.257	1.496	0.619	0.804	2.313	0.293	8.718	1.901	64.584	24.936	0	0.001

S	16	0.257	1.463	0.582	0.709	2.151	0.275	7.382	1.739	51.912	20.367	0	0.001

Cl	17	0.249	1.434	0.551	0.623	2.001	0.252	6.333	1.567	43.243	17.115	0	0

Cl^-1	17	0.839	3.407	-127.402	-31.676	-8.978	0.834	11.178	3780.327	1009.429	251.832	0	0.034

Ar	18	0.249	1.409	0.522	0.548	1.852	0.238	5.528	1.446	36.797	14.742	0	0

K	19	0.401	2.287	1.316	2.418	2.56	0.361	12.307	3.209	186.495	63.87	0	0.004

K¹⁺	19	2.31	2.189	23.641	6.25	0.52	25.002	5.125	713.099	168.005	0.465	0	0.014

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ca	20	0.389	2.139	1.269	2.545	3.569	0.336	10.834	2.873	133.835	49.43	0	0.003

Ca²⁺	20	3.638	2.522	48.598	13.584	0.605	39.078	5.769	768.396	196.901	0.519	0	0.02

Sc	21	0.384	2.07	1.258	2.283	3.31	0.318	9.927	2.655	119.109	43.135	0	0.002

Sc³⁺	21	5.992	2.703	74.091	21.6	0.861	51.235	7.102	811.935	222.445	0.772	0	0.021

Ti	22	0.389	2.011	1.294	1.984	3.098	0.309	9.577	2.546	111.565	40.23	0	0.002

Ti²⁺	22	3.874	2.566	48.916	13.87	0.841	43.37	6.314	784.553	206.22	0.723	0	0.017

Ti³⁺	22	6.071	2.697	74.943	22	0.911	51.347	6.992	823.99	225.369	0.782	0	0.022

Ti⁴⁺	22	8.281	2.858	100.1	29.509	0.968	54.337	7.64	830.714	230.646	0.829	0	0.026

V	23	0.396	1.934	1.327	1.767	2.879	0.303	9.276	2.461	105.031	37.788	0	0.002

V²⁺	23	3.612	2.471	48.29	13.309	0.654	36.076	4.984	754.704	189.626	0.497	0	0.021

V³⁺	23	5.947	2.642	74.269	21.593	0.949	49.978	6.769	810.775	220.696	0.78	0	0.022

V⁵⁺	23	10.725	3.126	125.268	37.541	1.091	57.112	8.458	841.931	237.926	0.89	0	0.031

Cr	24	0.399	1.884	1.336	1.277	2.072	0.294	8.838	2.342	111.237	36.158	0	0.002

Cr²⁺	24	3.842	2.486	48.923	13.918	0.921	43.158	6.014	785.101	206.532	0.728	0	0.018

Cr³⁺	24	5.933	2.604	74.208	21.524	0.993	49.855	6.659	809.067	220.092	0.781	0	0.022

Mn	25	0.4	1.798	1.324	1.483	2.501	0.285	8.404	2.214	93.776	33.389	0	0.002

Mn²⁺	25	3.533	2.4	48.224	13.251	0.699	35.537	4.651	751.857	188.091	0.492	0	0.021

Mn³⁺	25	5.958	2.56	74.526	21.687	1.04	50.073	6.601	814.302	221.36	0.785	0	0.023

Mn⁴⁺	25	8.173	2.744	99.382	29.163	1.111	53.305	7.361	821.535	227.526	0.835	0	0.027

Fe	26	0.406	1.738	1.333	1.337	2.351	0.28	8.173	2.132	90.264	32.17	0	0.002

Fe²⁺	26	3.493	2.356	48.203	13.234	0.723	35.407	4.517	750.904	187.56	0.49	0	0.022

Fe³⁺	26	5.381	2.471	73.203	20.636	0.789	42.263	5.041	777.91	202.198	0.532	0	0.027

Co	27	0.417	1.662	1.34	1.221	2.214	0.278	7.952	2.074	86.874	30.905	0	0.002

Co²⁺	27	3.457	2.309	48.152	13.208	0.744	35.303	4.39	749.588	187.03	0.486	0	0.022

Co³⁺	27	5.915	2.442	74.078	21.589	1.116	49.736	6.443	809.769	220.192	0.778	0	0.023

Ni	28	0.42	1.604	1.334	1.136	2.074	0.27	7.696	1.987	83.05	29.636	0	0.001

Ni²⁺	28	3.423	2.26	48.132	13.194	0.767	35.304	4.287	748.87	186.734	0.483	0	0.022

Ni³⁺	28	5.907	2.383	74.644	21.633	1.153	49.742	6.404	813.457	220.225	0.774	0	0.023

Cu	29	0.433	1.529	1.329	0.834	1.474	0.27	7.428	1.933	91.897	29.494	0	0.001

Cu¹⁺	29	2.01	2.072	23.509	6.138	0.699	24.345	3.581	702.137	162.367	0.429	0	0.015

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Cu²⁺	29	3.754	2.184	49.481	14.041	1.099	43.974	5.569	793.743	207.96	0.715	0	0.018

Zn	30	0.441	1.475	1.309	0.995	1.844	0.267	7.214	1.866	76.667	27.316	0	0.001

Zn²⁺	30	3.385	2.157	48.174	13.214	0.814	35.577	4.127	749.958	187.059	0.479	0	0.022

Ga	31	0.48	1.655	1.399	1.105	2.468	0.282	8.701	1.969	98.693	32.462	0	0.002

Ga³⁺	31	5.86	2.207	73.864	21.387	1.239	49.518	6.301	804.207	218.518	0.749	0	0.022

Ge	32	0.483	1.703	1.348	1.145	2.698	0.274	8.315	1.873	82.053	28.631	0	0.002

Ge⁴⁺	32	6.883	2.262	97.382	27.055	1.266	45.667	6.473	773.183	200.367	0.743	0	0.04

As	33	0.472	1.694	1.272	1.106	2.776	0.261	7.505	1.73	65.527	24.093	0	0.001

Se	34	0.464	1.673	1.204	1.084	2.78	0.25	6.799	1.61	54.031	20.526	0	0.001

Br	35	0.455	1.696	1.146	0.997	2.766	0.238	6.271	1.502	46.972	18.178	0	0.001

Br^-1	35	1.664	4.602	-128.478	-34.083	-10.881	0.85	12.618	4012.566	1164.818	310.817	0	0.062

Kr	36	0.458	1.784	1.104	0.853	2.699	0.232	6.003	1.438	42.456	16.799	0	0.001

Rb	37	0.718	3.427	1.637	3.105	2.888	0.349	12.162	2.576	191.842	59.38	0	0.006

Rb¹⁺	37	3.554	2.396	23.225	5.922	0.91	19.562	4.1	679.274	150.71	0.436	0	0.018

Sr	38	0.699	3.264	1.564	3.424	4.154	0.332	10.733	2.387	143.599	50.651	0	0.005

Sr²⁺	38	3.942	3.067	47.677	12.809	1.036	28.779	5.232	728.76	175.864	0.482	0	0.026

Y	39	0.685	3.233	1.529	3.032	4.192	0.317	9.869	2.261	123.952	43.434	0	0.004

Y³⁺	39	5.461	3.461	73.106	20.341	1.118	38.594	5.837	768.32	195.905	0.509	0	0.031

Zr	40	0.687	3.219	1.529	2.687	4.036	0.31	9.343	2.218	112.202	38.981	0	0.004

Zr⁴⁺	40	7.42	3.674	97.998	27.873	1.166	44.147	6.084	787.189	207.14	0.52	0	0.035

Nb	41	0.689	3.267	1.529	1.905	3.281	0.303	8.898	2.177	109.753	34.934	0	0.004

Nb³⁺	41	5.604	3.633	72.414	20.072	1.121	36.657	5.586	757.586	191.786	0.489	0	0.031

Nb⁵⁺	41	9.562	3.858	123.305	35.594	1.212	47.421	6.278	801.851	214.954	0.529	0	0.04

Mo	42	0.696	3.247	1.56	1.674	3.081	0.3	8.594	2.173	105.121	32.914	0	0.003

Mo³⁺	42	5.59	3.652	72.419	19.957	1.11	35.326	5.346	754.113	189.478	0.475	0	0.031

Mo⁵⁺	42	9.482	4.018	123.051	35.219	1.239	47.454	6.328	796.909	212.923	0.531	0	0.044

Mo⁶⁺	42	11.601	4.033	148.138	42.867	1.255	48.83	6.44	805.384	217.511	0.537	0	0.045

Tc	43	0.699	3.182	1.601	1.942	3.427	0.294	8.315	2.157	95.02	32.269	0	0.003

Ru	44	0.699	3.175	1.619	1.375	2.683	0.288	7.963	2.124	97.061	29.668	0	0.003

Ru³⁺	44	5.458	3.818	72.104	19.884	1.134	35.427	5.21	751.235	188.637	0.467	0	0.032

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ru⁴⁺	44	7.296	3.954	97.84	27.562	1.188	41.517	5.569	778.962	201.891	0.49	0	0.037

Rh	45	0.73	3.199	1.815	0.978	2.52	0.294	8.492	2.28	111.656	33.099	0	0.009

Rh³⁺	45	5.367	3.843	71.96	19.746	1.138	35.045	5.066	747.161	186.882	0.461	0	0.032

Rh⁴⁺	45	7.194	3.973	97.553	27.279	1.192	40.873	5.406	773.127	199.373	0.483	0	0.037

Pd	46	0.621	2.769	1.292	0.717	2.179	0.245	5.651	1.642	51.028	17.378	0	0.002

Pd²⁺	46	3.974	3.663	47.486	12.62	1.075	27.45	4.514	719.819	171.002	0.427	0	0.026

Pd⁴⁺	46	7.159	3.99	97.129	27.297	1.2	40.692	5.268	771.535	199.166	0.477	0	0.037

Ag	47	0.711	2.981	1.777	1.057	2.143	0.276	7.413	2.102	92.261	27.449	0	0.002

Ag¹⁺	47	3.219	3.368	23.059	5.877	0.999	20.017	3.896	671.582	147.599	0.39	0	0.018

Ag²⁺	47	3.879	3.69	47.518	12.68	1.085	27.656	4.422	721.877	172.044	0.424	0	0.026

Cd	48	0.704	2.869	1.782	1.346	2.53	0.267	7.072	2.033	79.643	26.643	0	0.002

Cd²⁺	48	3.768	3.687	47.464	12.595	1.09	27.472	4.295	718.469	170.748	0.419	0	0.026

In	49	0.746	2.88	2.07	1.528	3.208	0.279	8.184	2.226	100.518	32.626	0	0.003

In³⁺	49	5.199	3.857	72.493	19.951	1.175	35.415	4.585	753.86	188.222	0.445	0	0.033

Sn	50	0.743	2.786	2.089	1.656	3.584	0.273	7.998	2.171	86.56	30.004	0	0.002

Sn²⁺	50	4.56	3.634	47.309	12.522	1.108	26.735	4.081	713.694	168.047	0.412	0	0.027

Sn⁴⁺	50	7.099	3.95	97.362	27.332	1.25	41.388	4.791	773.378	199.974	0.465	0	0.039

Sb	51	0.729	2.684	2.03	1.687	3.844	0.263	7.451	2.054	72.252	26.438	0	0.002

Sb³⁺	51	5.609	3.82	72.159	19.461	1.201	31.365	4.407	738.821	179.9	0.44	0	0.035

Sb⁵⁺	51	8.897	3.982	121.412	34.219	1.304	42.512	4.887	774.228	201.741	0.477	0	0.044

Te	52	0.703	2.564	1.917	1.802	4.01	0.249	6.679	1.894	60.513	22.778	0	0.002

I	53	0.697	2.55	1.912	1.595	4.151	0.243	6.549	1.833	55.192	21.25	0	0.001

I^-1	53	2.819	6.962	-139.481	-45.551	-15.569	1.05	15.017	4996.293	1615.268	430.449	0	0.122

Xe	54	0.689	2.485	1.862	1.564	4.193	0.236	6.192	1.749	48.799	19.172	0	0.001

Cs	55	0.936	5.015	2.75	4.098	3.701	0.322	13.712	2.639	212.049	59.506	0	0.008

Cs¹⁺	55	5.605	3.323	22.851	5.744	1.112	18.835	3.426	651.038	135.624	0.383	0	0.022

Ba	56	0.882	4.855	2.582	4.788	5.156	0.301	12.009	2.373	161.687	53.915	0	0.008

Ba²⁺	56	5.725	3.717	46.952	12.118	1.239	21.681	3.951	694.144	157.489	0.419	0	0.032

La	57	0.563	4.923	2.553	4.373	5.384	0.164	10.489	1.8	138.906	45.628	0	0.028

La³⁺	57	6.157	4.198	71.14	18.844	1.381	26.309	4.594	717.04	169.646	0.458	0	0.04

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Ce	58	0.818	4.468	2.294	4.187	5.607	0.267	9.537	2.003	138.654	42.216	0	0.028

Ce³⁺	58	6.026	4.244	71.065	18.865	1.41	26.577	4.604	717.128	170.132	0.46	0	0.04

Ce⁴⁺	58	7.276	4.718	95.872	26.29	1.529	33.293	5.3	744.53	184.891	0.498	0	0.046

Pr	59	0.922	4.574	2.563	4.168	4.75	0.298	11.073	2.286	151.43	51.036	0	0.007

Pr³⁺	59	5.897	4.273	71.227	18.887	1.435	26.838	4.598	718.552	170.392	0.461	0	0.039

Pr⁴⁺	59	7.201	4.718	96.298	26.316	1.551	33.607	5.258	746.677	185.136	0.497	0	0.046

Nd	60	0.925	4.44	2.532	4.162	4.538	0.295	10.652	2.226	145.866	48.842	0	0.006

Nd³⁺	60	5.792	4.303	71.31	18.977	1.463	27.285	4.608	721.14	171.684	0.462	0	0.04

Pm	61	0.936	4.342	2.521	3.97	4.464	0.294	10.415	2.194	144.37	48.498	0	0.007

Pm³⁺	61	5.689	4.322	71.242	19.018	1.49	27.754	4.614	722.215	172.574	0.464	0	0.04

Sm	62	0.945	4.24	2.514	3.799	4.388	0.292	10.204	2.163	142.893	48.154	0	0.007

Sm³⁺	62	5.598	4.322	71.222	19.03	1.512	28.085	4.594	722.287	173.024	0.463	0	0.039

Eu	63	0.977	4.086	2.542	3.702	4.251	0.298	10.162	2.189	140.273	47.141	0	0.007

Eu²⁺	63	4.703	3.892	46.822	12.047	1.408	21.766	3.944	692.018	156.842	0.426	0	0.031

Eu³⁺	63	5.512	4.317	71.357	19.041	1.534	28.469	4.579	723.907	173.501	0.463	0	0.039

Gd	64	0.917	4.088	2.342	3.473	4.437	0.276	9.014	1.953	121.387	40.383	0	0.006

Gd³⁺	64	5.449	4.307	71.367	19.122	1.555	28.888	4.558	725.372	174.423	0.462	0	0.039

Tb	65	1.026	3.946	2.597	3.08	4.309	0.304	10.298	2.226	146.379	50.215	0	0.009

Tb³⁺	65	5.392	4.289	71.6	19.15	1.574	29.277	4.534	726.868	174.623	0.46	0	0.039

Dy	66	0.986	3.832	2.449	3.388	3.975	0.288	9.35	2.046	132.944	44.728	0	0.006

Dy³⁺	66	5.311	4.258	71.002	19.071	1.589	29.417	4.492	723.135	174.528	0.458	0	0.038

Ho	67	0.937	3.642	2.274	3.705	3.812	0.269	8.145	1.852	103.001	34.058	0	0.006

Ho³⁺	67	5.275	4.236	71.28	19.183	1.608	29.882	4.475	727.008	175.982	0.457	0	0.039

Er	68	1.013	3.645	2.426	3.163	3.826	0.287	9.07	2.01	129.586	43.764	0	0.006

Er³⁺	68	5.235	4.211	71.666	19.275	1.628	30.34	4.459	731.523	177.01	0.456	0	0.038

Tm	69	1.026	3.561	2.419	3.035	3.76	0.287	8.977	1.998	127.898	43.592	0	0.006

Tm³⁺	69	5.18	4.168	71.36	19.212	1.638	30.431	4.409	728.779	176.558	0.452	0	0.038

Yb	70	1.031	3.465	2.386	3.007	3.659	0.284	8.73	1.959	125.627	42.262	0	0.005

Yb²⁺	70	4.021	3.835	46.617	12.167	1.544	23.345	3.872	695.378	160.423	0.421	0	0.03

Yb³⁺	70	5.18	4.144	71.786	19.428	1.657	31.079	4.4	735.508	178.841	0.451	0	0.038

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Lu	71	1.026	3.409	2.326	2.808	3.908	0.279	8.32	1.898	108.582	37.468	0	0.005

Lu³⁺	71	5.112	4.095	71.557	19.258	1.666	31.026	4.347	731.214	177.408	0.447	0	0.037

Hf	72	1.02	3.404	2.275	2.522	3.954	0.273	7.994	1.84	98.172	33.887	0	0.004

Hf⁴⁺	72	6.837	4.245	96.432	26.62	1.753	37.109	4.67	754.646	190.345	0.464	0	0.043

Ta	73	1.025	3.421	2.243	2.226	3.936	0.271	7.781	1.812	91.965	31.488	0	0.004

Ta⁵⁺	73	8.771	4.357	121.048	33.956	1.818	40.853	4.908	768.248	198.357	0.475	0	0.048

W	74	1.031	3.464	2.222	1.972	3.853	0.269	7.627	1.79	87.424	29.747	0	0.004

W⁶⁺	74	10.792	4.48	146.689	41.409	1.876	43.307	5.136	781.066	203.981	0.484	0	0.053

Re	75	1.017	3.429	2.147	1.956	3.711	0.262	7.137	1.717	78.502	26.544	0	0.003

Os	76	1.027	3.485	2.139	1.723	3.606	0.26	7.048	1.71	75.701	25.619	0	0.003

Os⁴⁺	76	7.031	4.509	96.676	26.607	1.806	35.438	4.748	753.943	188.473	0.455	0	0.044

Ir	77	1.029	3.475	2.092	1.631	3.488	0.258	6.735	1.674	71.405	23.83	0	0.003

Ir³⁺	77	5.563	4.41	71.531	19.204	1.739	29.245	4.404	728.502	175.316	0.433	0	0.039

Ir⁴⁺	77	6.995	4.581	96.18	26.426	1.814	35.133	4.744	749.136	187.266	0.452	0	0.044

Pt	78	1.03	3.534	2.06	1.147	3.042	0.255	6.523	1.645	70.461	22.192	0	0.003

Pt²⁺	78	4.648	4.224	47.124	12.298	1.658	23.204	3.998	702.193	161.323	0.408	0	0.032

Pt⁴⁺	78	7.095	4.357	96.519	26.549	1.703	31.685	4.196	748.876	184.65	0.419	0	0.074

Au	79	1.021	3.521	2.01	1.09	2.931	0.249	6.199	1.595	66.077	20.672	0	0.002

Au¹⁺	79	4.239	3.91	23.136	5.761	1.556	17.853	3.506	656.944	136.241	0.378	0	0.022

Au³⁺	79	5.447	4.554	71.909	19.21	1.753	29.194	4.389	730.293	175.037	0.427	0	0.039

Hg	80	1.04	3.52	2.038	1.281	3.085	0.25	6.181	1.619	63.491	20.88	0	0.002

Hg¹⁺	80	4.411	3.995	22.893	5.808	1.575	18.438	3.544	652.623	134.993	0.379	0	0.023

Hg²⁺	80	4.426	4.339	46.727	12.142	1.665	22.731	3.952	694.792	159.533	0.401	0	0.031

Tl	81	1.134	3.747	2.313	1.504	3.406	0.269	7.228	1.856	87.578	26.844	0	0.003

Tl¹⁺	81	4.605	4.038	22.873	5.728	1.582	18.572	3.532	646.433	132.356	0.376	0	0.023

Tl³⁺	81	5.321	4.676	71.561	19.189	1.765	29.475	4.346	729.054	175.382	0.42	0	0.038

Pb	82	1.129	3.701	2.318	1.672	3.776	0.265	7.058	1.831	79.449	26.059	0	0.003

Pb²⁺	82	4.951	4.402	46.762	12.068	1.675	22.654	3.897	692.053	157.744	0.394	0	0.031

Pb⁴⁺	82	6.846	4.871	96.334	26.426	1.839	35.351	4.594	749.848	187.049	0.434	0	0.044

Bi	83	1.139	3.647	2.357	1.812	4.14	0.264	7.011	1.843	74.242	25.463	0	0.003

	Z	a1	a2	a3	a4	a5	b1	b2	b3	b4	b5	c	RMSE
Bi³⁺	83	5.75	4.712	71.02	18.94	1.77	27.7	4.247	719.19	171.542	0.413	0	0.039

Bi⁵⁺	83	8.659	4.988	121.244	33.71	1.893	39.192	4.743	764.318	194.834	0.443	0	0.05

Po	84	1.109	3.507	2.26	2.068	4.415	0.254	6.433	1.739	64.027	22.729	0	0.003

At	85	1.102	3.427	2.244	2.019	4.678	0.249	6.206	1.704	58.596	21.353	0	0.002

Rn	86	1.097	3.382	2.241	1.897	4.874	0.245	6.062	1.675	54.122	20.242	0	0.002

Fr	87	1.392	5.555	3.389	4.05	4.317	0.31	12.711	2.569	196.741	50.441	0	0.01

Ra	88	1.362	5.52	3.282	4.866	5.518	0.3	11.796	2.438	154.439	49.505	0	0.009

Ra²⁺	88	6.698	4.534	46.584	11.948	1.72	20.916	3.736	683.224	152.265	0.382	0	0.034

Ac	89	1.328	5.426	3.16	4.549	6.012	0.289	10.861	2.299	131.211	43.597	0	0.007

Ac³⁺	89	7.046	4.901	70.767	18.443	1.82	23.61	4.098	704.109	162.844	0.401	0	0.043

Th	90	1.301	5.365	3.069	4.142	6.224	0.28	10.168	2.191	115.212	38.839	0	0.007

Pa	91	1.315	5.399	3.125	4.102	5.616	0.281	10.126	2.208	123.017	40.335	0	0.006

U	92	1.322	5.375	3.145	3.84	5.434	0.28	9.938	2.197	121.621	39.84	0	0.006

U³⁺	92	6.736	5.147	70.619	18.374	1.863	23.379	4.109	701.575	161.901	0.4	0	0.044

U⁴⁺	92	7.543	5.507	94.908	25.291	1.966	27.848	4.539	720.882	172.295	0.423	0	0.051

U⁶⁺	92	10.608	6.096	145.281	40.223	2.143	37.1	5.311	759.582	191.955	0.462	0	0.063

Np	93	1.31	5.321	3.133	3.747	5.24	0.275	9.607	2.147	118.146	38.705	0	0.006

Pu	94	1.326	5.269	3.213	3.751	4.624	0.276	9.629	2.174	129.083	40.607	0	0.006

Am	95	1.334	5.208	3.248	3.521	4.518	0.275	9.514	2.17	128.065	40.732	0	0.007

Cm	96	1.31	5.079	3.163	3.363	4.787	0.267	8.934	2.076	111.801	36.61	0	0.006

Bk	97	1.308	4.996	3.169	3.257	4.665	0.265	8.725	2.048	109.425	36.04	0	0.006

Cf	98	1.162	4.249	2.638	4.776	4.124	0.23	6.322	1.664	79.157	21.827	0	0.025

If you found FAES helpful, a suitable citation is A. Saha, S. S. Nia, and J. A. Rodriguez, Chem. Rev. 122, 13883-13914 (2022). FAES was first introduced in A. Saha, M. Evans, T. Holton, and J. Rodriguez, Acta Cryst. 77, a50 (2020).