v0+1 · built electron by electron · Z = 169 → 366 · model only past Z ≈ 170

Out to 366: where the rows close

Same method as the first build (element-168-build.html): each atom finds its own lowest-energy arrangement, with nothing assigned by a filling rule. This page runs from 169 to 366. Past Z ≈ 170 the innermost electron has dropped below the floor of empty space, so everything here is model-only: atoms this heavy cannot hold this form. AMBER throughout

The build, row by row

169: newest electron 9s, gap 0.51 eV, settled, code 144+21+3+1170: newest electron 9s, gap 0.58 eV, did not settle, code 144+21+5170171: newest electron 7f, gap 0.15 eV, did not settle, code 144+21+5+1172: newest electron 7f, gap 0.46 eV, did not settle, code 144+21+5+2173: newest electron 6g, gap 1.48 eV, did not settle, code 144+21+8174: newest electron 6g, gap 2.41 eV, did not settle, code 144+21+8+1175: newest electron 6g, gap 0.10 eV, did not settle, code 144+21+8+2176: newest electron 6g, gap 6.38 eV, did not settle, code 144+21+8+3177: newest electron 6g, gap 3.37 eV, did not settle, code 144+21+8+3+1178: newest electron 6g, gap 2.03 eV, did not settle, code 144+34179: newest electron 6g, gap 9.60 eV, did not settle, code 144+34+1180: newest electron 6g, gap 1.78 eV, did not settle, code 144+34+2180181: newest electron 9p, gap 0.42 eV, did not settle, code 144+34+3182: newest electron 6g, gap 2.23 eV, did not settle, code 144+34+3+1183: newest electron 9p, gap 0.79 eV, did not settle, code 144+34+5184: newest electron 8p, gap 7.81 eV, did not settle, code 144+34+5+1185: newest electron 9p, gap 0.72 eV, did not settle, code 144+34+5+2186: newest electron 6g, gap 2.12 eV, did not settle, code 144+34+8187: newest electron 9s, gap 0.94 eV, settled, code 144+34+8+1188: newest electron 7f, gap 0.18 eV, did not settle, code 144+34+8+2189: newest electron 7f, gap 0.35 eV, did not settle, code 144+34+8+3190: newest electron 7f, gap 0.68 eV, did not settle, code 144+34+8+3+1190191: newest electron 7f, gap 0.16 eV, did not settle, code 144+34+13192: newest electron 7f, gap 0.50 eV, did not settle, code 144+34+13+1193: newest electron 7f, gap 0.33 eV, did not settle, code 144+34+13+2194: newest electron 7f, gap 0.30 eV, did not settle, code 144+34+13+3195: newest electron 7f, gap 0.24 eV, settled, code 144+34+13+3+1196: newest electron 7f, gap 0.82 eV, settled, code 144+34+13+5197: newest electron 7f, gap 1.41 eV, settled, code 144+34+13+5+1198: newest electron 7f, gap 2.00 eV, settled, code 144+34+13+5+2199: newest electron 7f, gap 2.61 eV, settled, code 144+55200: newest electron 7f, gap 3.22 eV, settled, code 144+55+1200201: newest electron 9s, gap 1.32 eV, settled, code 144+55+2202: newest electron 9s, gap 0.35 eV, settled, code 144+55+3203: newest electron 8d, gap 1.79 eV, did not settle, code 144+55+3+1204: newest electron 8d, gap 1.71 eV, did not settle, code 144+55+5205: newest electron 8d, gap 0.29 eV, settled, code 144+55+5+1206: newest electron 8d, gap 0.83 eV, settled, code 144+55+5+2207: newest electron 8d, gap 1.38 eV, settled, code 144+55+8208: newest electron 8d, gap 1.95 eV, settled, code 144+55+8+1209: newest electron 8d, gap 2.53 eV, settled, code 144+55+8+2210: newest electron 8d, gap 3.12 eV, settled, code 144+55+8+3210211: newest electron 9s, gap 2.54 eV, settled, code 144+55+8+3+1212: newest electron 9s, gap 2.97 eV, settled, code 144+55+13213: newest electron 9p, gap 2.37 eV, settled, code 144+55+13+1214: newest electron 9p, gap 3.16 eV, settled, code 144+55+13+2215: newest electron 9p, gap 3.94 eV, settled, code 144+55+13+3216: newest electron 9p, gap 4.69 eV, settled, code 144+55+13+3+1217: newest electron 9p, gap 5.44 eV, settled, code 144+55+13+5218: newest electron 9p, gap 6.19 eV, settled, code 144+55+13+5+1218219: newest electron 10s, gap 0.01 eV, did not settle, code 144+55+13+5+2220: newest electron 7g, gap 0.94 eV, did not settle, code 144+55+21220221: newest electron 7g, gap 1.50 eV, did not settle, code 144+55+21+1222: newest electron 7g, gap 0.21 eV, did not settle, code 144+55+21+2223: newest electron 7g, gap 0.12 eV, did not settle, code 144+55+21+3224: newest electron 6h, gap 6.87 eV, did not settle, code 144+55+21+3+1225: newest electron 6h, gap 3.64 eV, did not settle, code 144+55+21+5226: newest electron 7g, gap 0.90 eV, did not settle, code 144+55+21+5+1227: newest electron 8f, gap 0.56 eV, did not settle, code 144+55+21+5+2228: newest electron 9d, gap 0.05 eV, did not settle, code 144+55+21+8229: newest electron 8f, gap 0.46 eV, did not settle, code 144+55+21+8+1230: newest electron 8f, gap 0.63 eV, did not settle, code 144+55+21+8+2230231: newest electron 8f, gap 0.75 eV, did not settle, code 144+55+21+8+3232: newest electron 10p, gap 0.67 eV, did not settle, code 144+55+21+8+3+1233: newest electron 10p, gap 0.50 eV, did not settle, code 233234: newest electron 6h, gap 5.02 eV, did not settle, code 233+1235: newest electron 7g, gap 3.13 eV, did not settle, code 233+2236: newest electron 9p, gap 0.97 eV, did not settle, code 233+3237: newest electron 9p, gap 2.54 eV, did not settle, code 233+3+1238: newest electron 7g, gap 1.33 eV, did not settle, code 233+5239: newest electron 7g, gap 1.24 eV, did not settle, code 233+5+1240: newest electron 6h, gap 7.91 eV, did not settle, code 233+5+2240241: newest electron 8f, gap 0.30 eV, did not settle, code 233+8242: newest electron 8f, gap 0.33 eV, did not settle, code 233+8+1243: newest electron 8f, gap 0.21 eV, did not settle, code 233+8+2244: newest electron 8f, gap 0.48 eV, did not settle, code 233+8+3245: newest electron 7g, gap 0.83 eV, did not settle, code 233+8+3+1246: newest electron 7g, gap 2.00 eV, did not settle, code 233+13247: newest electron 7g, gap 1.37 eV, did not settle, code 233+13+1248: newest electron 9d, gap 0.10 eV, did not settle, code 233+13+2249: newest electron 7g, gap 8.20 eV, did not settle, code 233+13+3250: newest electron 7g, gap 3.98 eV, did not settle, code 233+13+3+1250251: newest electron 7g, gap 2.13 eV, did not settle, code 233+13+5252: newest electron 7g, gap 3.14 eV, did not settle, code 233+13+5+1253: newest electron 7g, gap 0.60 eV, did not settle, code 233+13+5+2254: newest electron 7g, gap 2.93 eV, did not settle, code 233+21255: newest electron 9p, gap 10.01 eV, did not settle, code 233+21+1256: newest electron 9p, gap 7.24 eV, did not settle, code 233+21+2257: newest electron 7g, gap 4.35 eV, did not settle, code 233+21+3258: newest electron 7g, gap 0.02 eV, settled, code 233+21+3+1259: newest electron 10s, gap 0.82 eV, settled, code 233+21+5260: newest electron 8f, gap 0.09 eV, did not settle, code 233+21+5+1260261: newest electron 8f, gap 0.27 eV, did not settle, code 233+21+5+2262: newest electron 8f, gap 0.39 eV, did not settle, code 233+21+8263: newest electron 8f, gap 0.94 eV, did not settle, code 233+21+8+1264: newest electron 8f, gap 1.16 eV, did not settle, code 233+21+8+2265: newest electron 8f, gap 1.86 eV, did not settle, code 233+21+8+3266: newest electron 8f, gap 0.60 eV, settled, code 233+21+8+3+1267: newest electron 8f, gap 1.21 eV, settled, code 233+34268: newest electron 8f, gap 1.83 eV, settled, code 233+34+1269: newest electron 8f, gap 2.45 eV, settled, code 233+34+2270: newest electron 8f, gap 3.08 eV, settled, code 233+34+3270271: newest electron 8f, gap 3.71 eV, settled, code 233+34+3+1272: newest electron 8f, gap 4.34 eV, settled, code 233+34+5273: newest electron 10s, gap 1.18 eV, settled, code 233+34+5+1274: newest electron 10s, gap 0.08 eV, settled, code 233+34+5+2275: newest electron 9d, gap 1.53 eV, did not settle, code 233+34+8276: newest electron 9d, gap 0.01 eV, settled, code 233+34+8+1277: newest electron 9d, gap 0.53 eV, settled, code 233+34+8+2278: newest electron 9d, gap 1.06 eV, settled, code 233+34+8+3279: newest electron 9d, gap 1.61 eV, settled, code 233+34+8+3+1280: newest electron 9d, gap 2.16 eV, settled, code 233+34+13280281: newest electron 9d, gap 2.73 eV, settled, code 233+34+13+1282: newest electron 9d, gap 3.30 eV, settled, code 233+34+13+2283: newest electron 10s, gap 2.41 eV, settled, code 233+34+13+3284: newest electron 10s, gap 2.81 eV, settled, code 233+34+13+3+1285: newest electron 10p, gap 2.36 eV, settled, code 233+34+13+5286: newest electron 10p, gap 3.12 eV, settled, code 233+34+13+5+1287: newest electron 10p, gap 3.86 eV, settled, code 233+34+13+5+2288: newest electron 10p, gap 4.58 eV, settled, code 233+55289: newest electron 10p, gap 5.29 eV, settled, code 233+55+1290: newest electron 10p, gap 6.00 eV, settled, code 233+55+2290291: newest electron 8g, gap 0.04 eV, did not settle, code 233+55+3292: newest electron 8g, gap 1.99 eV, did not settle, code 233+55+3+1293: newest electron 8g, gap 0.89 eV, did not settle, code 233+55+5294: newest electron 7h, gap 1.97 eV, did not settle, code 233+55+5+1295: newest electron 7h, gap 0.29 eV, did not settle, code 233+55+5+2296: newest electron 7h, gap 1.45 eV, did not settle, code 233+55+8297: newest electron 10d, gap 0.23 eV, did not settle, code 233+55+8+1298: newest electron 7h, gap 3.18 eV, did not settle, code 233+55+8+2299: newest electron 7h, gap 0.14 eV, did not settle, code 233+55+8+3300: newest electron 7h, gap 3.99 eV, did not settle, code 233+55+8+3+1300301: newest electron 7h, gap 4.41 eV, did not settle, code 233+55+13302: newest electron 9f, gap 0.20 eV, did not settle, code 233+55+13+1303: newest electron 9f, gap 0.94 eV, did not settle, code 233+55+13+2304: newest electron 7h, gap 17.84 eV, did not settle, code 233+55+13+3305: newest electron 10s, gap 6.31 eV, did not settle, code 233+55+13+3+1306: newest electron 10s, gap 4.41 eV, did not settle, code 233+55+13+5307: newest electron 8g, gap 0.07 eV, did not settle, code 233+55+13+5+1308: newest electron 7h, gap 4.88 eV, did not settle, code 233+55+13+5+2309: newest electron 10p, gap 6.66 eV, did not settle, code 233+55+21310: newest electron 8g, gap 2.06 eV, did not settle, code 233+55+21+1310311: newest electron 10p, gap 3.50 eV, did not settle, code 233+55+21+2312: newest electron 7h, gap 0.46 eV, did not settle, code 233+55+21+3313: newest electron 9f, gap 0.07 eV, did not settle, code 233+55+21+3+1314: newest electron 8g, gap 0.71 eV, did not settle, code 233+55+21+5315: newest electron 8g, gap 0.52 eV, did not settle, code 233+55+21+5+1316: newest electron 8g, gap 3.10 eV, did not settle, code 233+55+21+5+2317: newest electron 8g, gap 1.49 eV, did not settle, code 233+55+21+8318: newest electron 8g, gap 0.58 eV, did not settle, code 233+55+21+8+1319: newest electron 8g, gap 0.61 eV, did not settle, code 233+55+21+8+2320: newest electron 8g, gap 0.27 eV, settled, code 233+55+21+8+3320321: newest electron 8g, gap 1.16 eV, settled, code 233+55+21+8+3+1322: newest electron 8g, gap 2.04 eV, settled, code 233+89323: newest electron 8g, gap 2.91 eV, settled, code 233+89+1324: newest electron 8g, gap 7.73 eV, did not settle, code 233+89+2325: newest electron 8g, gap 4.63 eV, settled, code 233+89+3326: newest electron 8g, gap 5.48 eV, settled, code 233+89+3+1327: newest electron 8g, gap 6.33 eV, settled, code 233+89+5328: newest electron 8g, gap 4.95 eV, did not settle, code 233+89+5+1329: newest electron 8g, gap 5.79 eV, did not settle, code 233+89+5+2330: newest electron 10p, gap 6.81 eV, settled, code 233+89+8330331: newest electron 11s, gap 0.47 eV, settled, code 233+89+8+1332: newest electron 9f, gap 0.12 eV, did not settle, code 233+89+8+2333: newest electron 9f, gap 0.54 eV, did not settle, code 233+89+8+3334: newest electron 9f, gap 0.28 eV, did not settle, code 233+89+8+3+1335: newest electron 9f, gap 0.37 eV, settled, code 233+89+13336: newest electron 9f, gap 1.04 eV, settled, code 233+89+13+1337: newest electron 9f, gap 1.70 eV, settled, code 233+89+13+2338: newest electron 9f, gap 2.35 eV, settled, code 233+89+13+3339: newest electron 9f, gap 3.00 eV, settled, code 233+89+13+3+1340: newest electron 9f, gap 3.66 eV, settled, code 233+89+13+5340341: newest electron 9f, gap 4.31 eV, settled, code 233+89+13+5+1342: newest electron 9f, gap 4.96 eV, settled, code 233+89+13+5+2343: newest electron 9f, gap 5.61 eV, settled, code 233+89+21344: newest electron 9f, gap 6.27 eV, settled, code 233+89+21+1345: newest electron 11s, gap 0.82 eV, settled, code 233+89+21+2346: newest electron 11s, gap 0.07 eV, did not settle, code 233+89+21+3347: newest electron 10d, gap 1.42 eV, did not settle, code 233+89+21+3+1348: newest electron 10d, gap 0.36 eV, settled, code 233+89+21+5349: newest electron 10d, gap 0.88 eV, settled, code 233+89+21+5+1350: newest electron 10d, gap 1.41 eV, settled, code 233+89+21+5+2350351: newest electron 10d, gap 1.94 eV, settled, code 233+89+21+8352: newest electron 10d, gap 2.48 eV, settled, code 233+89+21+8+1353: newest electron 10d, gap 3.03 eV, settled, code 233+89+21+8+2354: newest electron 10d, gap 3.58 eV, settled, code 233+89+21+8+3355: newest electron 11s, gap 2.20 eV, settled, code 233+89+21+8+3+1356: newest electron 11s, gap 2.57 eV, settled, code 233+89+34357: newest electron 11p, gap 2.34 eV, settled, code 233+89+34+1358: newest electron 11p, gap 3.06 eV, settled, code 233+89+34+2359: newest electron 11p, gap 3.76 eV, settled, code 233+89+34+3360: newest electron 11p, gap 4.44 eV, settled, code 233+89+34+3+1360361: newest electron 11p, gap 5.11 eV, settled, code 233+89+34+5362: newest electron 11p, gap 4.65 eV, did not settle, code 233+89+34+5+1362363: newest electron 7i, gap 2.61 eV, did not settle, code 233+89+34+5+2364: newest electron 7i, gap 4.18 eV, did not settle, code 233+89+34+8365: newest electron 11d, gap 0.32 eV, did not settle, code 233+89+34+8+1366: newest electron 11d, gap 0.19 eV, did not settle, code 233+89+34+8+2
spdfghitall = p shell closes · outlined = any subshell closes · faded = did not settle · ● = no 1 in the Fibonacci code

198 atoms built. 114 of them did not settle — more than half. The solver keeps swapping electrons between near-equal g, h, f and i levels. Only the settled atoms carry weight; the closures at the end of each row settled best. Colours are my legend and carry no physical meaning.

The closures

ZclosesgapsettledFibonacci coderulerrow rule
2189p⁶6.19 eVyes144+55+13+5+1missyes
29010p⁶6.00 eVyes233+55+2hityes
33010p⁶6.81 eVyes233+89+8hitno
36211p⁶4.65 eVno233+89+34+5+1missyes

Gold, silver and the Planck scale

Gold (79) and silver (47) are both a full d shell plus one s electron. In this run the matching atoms would be 211, 283 and 355 (a full d shell, then one s electron). They are not 218 or 362, so the electrum label has no number behind it yet. One real coincidence: 47 + 79 = 126, which is a closed-shell number for nuclei. AMBER

Zsize of the innermost electron cloudpowers of ten above the Planck length
1684.72e-13 m22.5
2183.64e-13 m22.4
2902.74e-13 m22.2
3622.19e-13 m22.1

Even the most crushed-in electron in the heaviest atom is about 22 powers of ten bigger than the Planck length. Nothing in an atom gets to 1% under Planck. DEAD

For the smallest reader. We kept adding beads up to 366. The atom's coat buttoned up at 218, 290 and 362, just where the counting rule said. The golden ruler guessed wrong at 218 and 362, but the coats buttoned anyway. And even the tightest bead is still enormous next to the tiniest length there is.

Record

method    as v0, grid 4000 pts to 100 bohr, l up to 6 (i), up to 13 levels per l
atoms     169–366 (198), unconverged 114 (convergence above 1e-4)
p-shell closures  218, 290, 330, 362
limit     non-relativistic; ignores the dive at Z≈170; nuclei this heavy are not computed