Hoping Threshold Frequencies

The work function data were taken from "Mechtly, Eugene A. "Properties of Materials." pp. 4–1 to 4–33 in Reference Data For Engineers: Radio, Electronics, Computer, and Communications. By Mac E. Van Valkenburg, edited by Wendy M. Middleton. Woburn, MA: Butterworth-Heinemann, 2002. doi:10.1016/B978-075067291-7/50006-6"

Atomic Number	Name	Symbol	Work Function (eV)	Freq (Hz)	Density g/cm^-3	Cal. Freq (Hz)	R_Error
13	Aluminum	Al	4.08	9.8654E+14	2.698	3.5941E+14	0.364
51	Antimony	Sb	4.01	9.6961E+14	6.685	1.1206E+15	1.156
33	Arsenic	As	5.11	1.2356E+15	5.776	8.3786E+14	0.678
56	Barium	Ba	2.48	5.9966E+14	3.594	8.6096E+14	1.436
4	Beryllium	Be	3.92	9.4785E+14	1.85	1.6509E+14	0.174
83	Bismuth	Bi	4.25	1.0276E+15	9.807	1.7314E+15	1.685
5	Boron	B	4.5	1.0881E+15	2.34	2.0758E+14	0.191
48	Cadmium	Cd	4	9.6720E+14	8.69	1.2395E+15	1.281
55	Caesium	Cs	1.92	4.6425E+14	1.873	6.1596E+14	1.327
20	Calcium	Ca	2.706	6.5431E+14	1.54	3.3680E+14	0.515
6	Carbon	C	4.81	1.1631E+15	3.513	2.7862E+14	0.240
58	Cerium	Ce	2.84	6.8671E+14	6.77	1.2026E+15	1.751
24	Chromium	Cr	4.37	1.0567E+15	7.15	7.9498E+14	0.752
27	Cobalt	Co	4.2	1.0156E+15	8.86	9.3864E+14	0.924
29	Copper	Cu	4.18	1.0107E+15	8.96	9.7826E+14	0.968
32	Germanium	Ge	4.5	1.0881E+15	5.323	7.9205E+14	0.728
79	Gold	Au	4.82	1.1655E+15	19.282	2.3686E+15	2.032
53	Iodine	I	6.8	1.6442E+15	4.93	9.8098E+14	0.597
26	Iron	Fe	4.33	1.0470E+15	7.874	8.6833E+14	0.829
82	Lead	Pb	4.05	9.7929E+14	11.342	1.8508E+15	1.890
3	Lithium	Li	2.35	5.6823E+14	0.534	7.6812E+13	0.135
12	Magnesium	Mg	3.68	8.8982E+14	1.738	2.7715E+14	0.311
25	Manganese	Mn	3.76	9.0916E+14	7.44	8.2767E+14	0.910
80	Mercury	Hg	4.53	1.0953E+15	13.5336	1.9969E+15	1.823
42	Molybdenum	Mo	4.25	1.0276E+15	10.22	1.2573E+15	1.224
28	Nickel	Ni	5.01	1.2114E+15	8.912	9.5866E+14	0.791
41	Niobium	Nb	4.5	1.0881E+15	8.57	1.1376E+15	1.045
46	Palladium	Pd	4.97	1.2017E+15	12.02	1.4270E+15	1.187
78	Platinum	Pt	5.22	1.2622E+15	21.46	2.4829E+15	1.967
19	Potassium	K	2.24	5.4163E+14	0.862	2.4560E+14	0.453
75	Rhenium	Re	5	1.2090E+15	21.02	2.4096E+15	1.993
45	Rhodium	Rh	4.57	1.1050E+15	12.41	1.4341E+15	1.298
37	Rubidium	Rb	2.09	5.0536E+14	1.532	4.5691E+14	0.904
34	Selenium	Se	4.8	1.1606E+15	4.809	7.7601E+14	0.669
14	Silicon	Si	4.52	1.0929E+15	2.3296	3.4658E+14	0.317
47	Silver	Ag	4.73	1.1437E+15	10.501	1.3482E+15	1.179
11	Sodium	Na	2.28	5.5130E+14	0.971	1.9834E+14	0.360
38	Strontium	Sr	2.74	6.6253E+14	2.64	6.0785E+14	0.917
73	Tantalum	Ta	4.14	1.0010E+15	16.654	2.1160E+15	2.114
52	Tellurium	Te	4.76	1.1510E+15	6.232	1.0925E+15	0.949
81	Thallium	Tl	3.68	8.8982E+14	11.85	1.8802E+15	2.113
90	Thorium	Th	3.47	8.3904E+14	11.72	1.9710E+15	2.349
50	Tin	Sn	4.38	1.0591E+15	7.287	1.1584E+15	1.094
22	Titanium	Ti	4.06	9.8170E+14	4.54	6.0651E+14	0.618
74	Tungsten	W	4.49	1.0857E+15	19.25	2.2905E+15	2.110
92	Uranium	U	3.63	8.7773E+14	18.95	2.5340E+15	2.887
23	Vanadium	V	3.77	9.1158E+14	6.11	7.1942E+14	0.789
30	Zinc	Zn	3.73	9.0191E+14	7.134	8.8782E+14	0.984
40	Zirconium	Zr	3.82	9.2367E+14	6.506	9.7901E+14	1.060

Error is taken as a ratio \(R\_error=\cfrac{Cal.\,Freq}{Freq}\), to indicate constants that might have been missed.  There seems to be none.

Below is a series plot of sorted experimental data, in ascending order, together with the corresponding calculated threshold frequencies.  The x-axis is just a numerical ordering.  The y-axis is in \(\times 10^{15}\,Hz\).

and the calculated data hop up and down the experimental threshold frequencies line.

Just a lucky guess.