The singlet and open shell high-spin states of [4], [6] and [8]-annulenes and their Kekule vibrational modes

State Method "Kekule"
Mode, cm-1
FC,
mDyne/Å
Reduced
mass, AMU
Bond
length, Å
Data DOI
Cyclobutadiene
3A1g CCSD/Def2-SVP 1422a 7.7848 6.5340 1.444 6634
1373b 7.9700 7.1807
3A1g CCSD(T)/Def-SVP 1395 7.2647 6.3381 1.449 6643
1345 7.6931 7.2202
3A1g CCSD/Def2-TZVPP 1392 6.9173 6.0600 1.438 6671
1342 8.0252 7.5582
3A1g CCSD(T)/Def2-TZVPP 1360 7.2647 6.3381 1.449 6672
1310 7.7044 7.6151

5B1g CCSD/Def2-SVP 1192 2.2102 2.6391 1.566 6635
1088 4.9656 7.1153
5B1g CCSD(T)/Def-SVP 1176 2.0739 2.5452 1.569 6644
1069 4.7829 7.0983
5B1g CCSD/Def-TZVPP 1177 1.8783 2.3023 1.563 6636
1067 5.0294 7.5000
5B1g CCSD(T)/Def-TZVPP 1157 1.7555 2.2253 1.568 6678
1045 4.8322 7.5073
Cyclobutadiene Di-anion (isoelectronic with benzene)
1A1g CCSD/Def2-SVP 1283 5.9023 6.0872 1.470 6652
1233 6.3831 7.1172
1A1g CCSD(T)/Def2-SVP 1258 5.5888 5.9952 1.475 6653
1209 6.1657 7.1565
1A1g CCSD/Def2-TZVPP 1216 4.3487 4.9883 1.467 6676
1165 6.2282 7.7827
1A1g CCSD(T)/Def2-TZVPP 1187 4.1223 4.9621 1.473 6679
1138 6.0103 7.8734
Benzene
1A1g CCSD/Def2-SVP 1337 4.9922 4.7425 1.401 6623
1308 10.7126 10.6244
1A1g CCSD(T)/Def2-SVP 1359 6.9812 6.4190 1.405 6647
1339 11.3860 10.7785
1A1g CCSD/Def2-TZVPP 1309 3.5714 3.5358 1.392 6646
1273 10.1936 10.6709
1A1g CCSD(T)/Def2-TZVPP 1328 5.6130 5.4004 1.398 6710
1306 10.9097 10.8588

5A1g CCSD/Def2-SVP 1600 17.4689 11.5855 1.463 6626
1597 17.4799 11.6274
5A1g CCSD/Def2-TZVPP 1572 17.1041 11.7511 1.455 6669
1571 17.1770 11.8198

7B1u CCSD/Def2-SVP 1361 11.0797 10.1574 1.550 6632
1355 12.4274 11.4839
Cyclo-octatetraene Dication (isoelectronic with benzene)
1A1g CCSD/Def2-SVP 1750 21.4531 11.8876 1.414 6648
1750 21.5770 11.9620
1A1g CCSD(T)/Def2-SVP 1707 20.4695 11.9226 1.420 6673
1707 20.5570 11.9773

5A1g CCSD/Def2-SVP 1702 20.4349 11.9684 1.444 6663
1702 20.4690 11.9899

7B1g CCSD/Def2-SVP 1460 14.8761 11.8407 1.511 6675
1460 15.0578 11.9890
Cyclo-octatetraene
3B2g CCSD/Def2-SVP 1777 22.3143 11.9956 1.409 6637
1777 22.3176 11.9976

7A1g CCSD/Def2-SVP 1637 18.9335 11.9851 1.484 6639
1637 18.9464 11.9941

9B1g CCSD/Def2-SVP 1441 14.6711 11.9988 1.553 6640
1441 14.6723 11.9998
9B1g CCSD(T)/Def2-SVP 1421 13.4795 11.3256 1.555 6677
Cyclo-octatetraene dianion
1A1g CCSD/Def2-SVP 1731 21.1621 11.9903 1.419 6695
1731 21.1668 11.9937

5A1g CCSD/Def2-SVP 1642 19.0214 11.9711 1.461 6698
1642 19.0408 11.9852

9B2u CCSD/Def2-SVP 1517 16.0290 11.8174 1.528 6700
1517 16.1516 11.9186

aUnprojected, with possible Dushinsky coupling bProjected from Dushinksky coupling.

Badger's rule for diatomics. ko(re - 0.68)3 = 1.86 x 105 Plot cube root of 1/ko vs bond length