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Crystal field theory

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The oxidation state of the metal also contributes to the size of Δ between the high and low energy levels. As the oxidation state increases for a given metal, the magnitude of Δ increases. A V complex will have a larger Δ than a V complex for a given set of ligands, as the difference in charge
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The use of these splitting diagrams can aid in the prediction of magnetic properties of co-ordination compounds. A compound that has unpaired electrons in its splitting diagram will be paramagnetic and will be attracted by magnetic fields, while a compound that lacks unpaired electrons in its
574:-orbitals are referred to as weak-field ligands. In this case, it is easier to put electrons into the higher energy set of orbitals than it is to put two into the same low-energy orbital, because two electrons in the same orbital repel each other. So, one electron is put into each of the five 344:
The size of the gap Δ between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the complex. Some ligands always produce a small value of Δ, while others always give a large splitting. The reasons behind this can be explained by
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set becomes lower in energy than the orbitals in the barycenter. As a result of this, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field relative to the barycenter by an amount known as the CFSE. Conversely, the
644:(for the same metal and same ligands). Therefore, the energy required to pair two electrons is typically higher than the energy required for placing electrons in the higher energy orbitals. Thus, tetrahedral complexes are usually high-spin. 488:
density allows the ligands to be closer to a V ion than to a V ion. The smaller distance between the ligand and the metal ion results in a larger Δ, because the ligand and metal electrons are closer together and therefore repel more.
530:. In complexes with these ligands, it is unfavourable to put electrons into the high energy orbitals. Therefore, the lower energy orbitals are completely filled before population of the upper sets starts according to the 232:, which will have higher energy, because the former group is farther from the ligands than the latter and therefore experiences less repulsion. The three lower-energy orbitals are collectively referred to as 263: 116:
arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand. The theory is developed by considering energy changes of the five
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The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands. It arises due to the fact that when the
135:-orbitals and those in the ligand repel each other due to repulsion between like charges. Thus the d-electrons closer to the ligands will have a higher energy than those further away which results in the 589:
In order for low spin splitting to occur, the energy cost of placing an electron into an already singly occupied orbital must be less than the cost of placing the additional electron into an e
1591: 698:-orbitals within a spherical negative electric field (center), and loss of degeneracy relative to the spherical field when ligands are treated as point charges in an octahedral geometry. 1141:
Schlapp, Robert; Penney, William G. (1932). "Influence of Crystalline Fields on the Susceptibilities of Salts of Paramagnetic Ions. II. The Iron Group, Especially Ni, Cr and Co".
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Penney, William G.; Schlapp, Robert (1932). "The Influence of Crystalline Fields on the Susceptibilities of Salts of Paramagnetic Ions. I. The Rare Earths, Especially Pr and Nd".
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upon being surrounded by an array of point charges consisting of the ligands. As a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the
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are split in a ligand field (as described above), some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five
779:) = 0 - in this case, the stabilization generated by the electrons in the lower orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals. 54:
orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used to describe various spectroscopies of
578:-orbitals in accord with Hund's rule, and "high spin" complexes are formed before any pairing occurs. For example, Br is a weak-field ligand and produces a small Δ 273:
Tetrahedral complexes are the second most common type; here four ligands form a tetrahedron around the metal ion. In a tetrahedral crystal field splitting, the
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in transition metal complexes. CFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of
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the nature of the ligands surrounding the metal ion. The stronger the effect of the ligands then the greater the difference between the high and low energy
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orbitals (in the octahedral case) are higher in energy than in the barycenter, so putting electrons in these reduces the amount of CFSE.
333:- opposite to the octahedral case. Furthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the 909: 627:
in octahedral complexes. If the energy required to pair two electrons is greater than Δ, the energy cost of placing an electron in an e
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is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see also
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in E. Pavarini, E. Koch, F. Anders, and M. Jarrell (eds.): Correlated Electrons: From Models to Materials, JĂĽlich 2012,
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can be explained by Crystal Field Theory. Often, however, the deeper colors of metal complexes arise from more intense
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structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists
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Van Vleck, J. (1932). "Theory of the Variations in Paramagnetic Anisotropy Among Different Salts of the Iron Group".
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the metal's oxidation state. A higher oxidation state leads to a larger splitting relative to the spherical field.
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It is useful to note that the ligands producing the most splitting are those that can engage in metal to ligand
1521: 1485: 1390: 1367: 1000: 853: 89: 85: 43: 968: 876: 792: 559: 508: 167:, in which six ligands form the vertices of an octahedron around the metal ion. In octahedral symmetry the 1666: 1551: 527: 350: 1586: 922: 542:-electrons, would have the octahedral splitting diagram shown at right with all five electrons in the 1541: 1150: 1107: 1072: 1029: 788: 636:
The crystal field splitting energy for tetrahedral metal complexes (four ligands) is referred to as Δ
586:-electrons, would have an octahedral splitting diagram where all five orbitals are singly occupied. 1661: 1480: 1454: 1409: 995: 899: 346: 255: 93: 58: 1346: 17: 1475: 1429: 1295: 1288: 463: 247: 118: 70: 66: 992:
seen in materials containing high-spin magnetic impurities, often due to crystal field splitting
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configurations shown further up the page. The low-spin (top) example has five electrons in the
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G. L. Miessler and D. A. Tarr “Inorganic Chemistry” 2nd Ed. (Prentice Hall 1999), p.379
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splitting diagram will be diamagnetic and will be weakly repelled by a magnetic field.
553: 520: 481: 452: 421: 121: 1681: 1607: 989: 938: 139:-orbitals splitting in energy. This splitting is affected by the following factors: 823: 425: 538:
is a strong-field ligand and produces a large Δ. The octahedral ion , which has 5
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According to crystal field theory, the interaction between a transition metal and
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The optical properties (details of absorption and emission spectra) of many
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Conversely, ligands (like I and Br) which cause a small splitting Δ of the
337:-orbitals, the energy splitting will be lower than in the octahedral case. 433: 394: 376: 73: 62: 470: 456: 437: 402: 380: 368: 364: 152:
the coordination number of the metal (i.e. tetrahedral, octahedral...)
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are referred to as strong-field ligands, such as CN and CO from the
277:-orbitals again split into two groups, with an energy difference of 1347:
Crystal-field Theory, Tight-binding Method, and Jahn-Teller Effect
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An introduction to transition-metal chemistry: Ligand-Field theory
685: 668:-orbitals are degenerate. For example, in an octahedral case, the 558: 507: 387: 690:
Octahedral crystal field stabilization energy. Degenerate atomic
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and other complex geometries can also be described by CFT.
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Arene complexes of univalent gallium, indium, and thallium
694:-orbitals of a free metal ion (left), destabilization of 171:-orbitals split into two sets with an energy difference, 1294:(4th ed.). New York: McGraw Hill Company. pp.  717:
orbitals are stabilized relative to the barycenter by /
763:. In the high-spin (lower) example, the CFSE is (3 x / 189:
for ten times the "differential of quanta") where the
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level. This low spin state therefore does not follow
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Chemistry: The Molecular Nature of Matter and Change
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the arrangement of the ligands around the metal ion.
1646: 1600: 1504: 1468: 1397: 1321:(5th ed.). Houghton Mifflin Company. pp.  1020:Bethe, H. (1929). "Termaufspaltung in Kristallen". 802: 1314: 1287: 1226: 96:(LFT), which delivers insight into the process of 595:orbital at an energy cost of Δ. As noted above, e 88:in the 1930s. CFT was subsequently combined with 519:Ligands which cause a large splitting Δ of the 1375: 8: 1476:Oxidative addition / reductive elimination 1382: 1368: 1360: 246:. These labels are based on the theory of 210:orbitals will be lower in energy than the 1206:Housecroft, C. E.; Sharpe, A. G. (2004). 306:, and the higher energy orbitals will be 1425:Polyhedral skeletal electron pair theory 239:, and the two higher-energy orbitals as 1233:(3rd ed.). Pearson Prentice Hall. 1012: 92:to form the more realistic and complex 1267:Shriver, D. F.; Atkins, P. W. (2001). 1225:Miessler, G. L.; Tarr, D. A. (2003). 706:-orbitals in an octahedral field is Δ 623:which are higher in energy than the t 7: 1532:Transition metal fullerene complexes 751:orbitals, so the total CFSE is 5 x / 284:. The lower energy orbitals will be 46:of electron orbital states, usually 163:The most common type of complex is 104:(ILFT) to better describe bonding. 1567:Transition metal carbyne complexes 1562:Transition metal carbene complexes 1527:Transition metal indenyl complexes 27:Theory in condensed matter physics 25: 18:Crystal field stabilization energy 1577:Transition metal alkyne complexes 1572:Transition metal alkene complexes 799:Geometries and splitting diagrams 180:crystal-field splitting parameter 1582:Transition-metal allyl complexes 960: 937: 914: 891: 868: 845: 822: 740:. As examples, consider the two 582:. So, the ion , again with five 1557:Transition metal acyl complexes 1210:(2nd ed.). Prentice Hall. 732:orbitals are destabilized by / 640:, and is roughly equal to 4/9Δ 633:, high spin splitting occurs. 1: 1286:Silberberg, Martin S (2006). 143:the nature of the metal ion. 102:inverted ligand field theory 42:) describes the breaking of 1633:Shell higher olefin process 1440:Dewar–Chatt–Duncanson model 988:— low temperature spike in 793:charge-transfer excitations 252:irreducible representations 182:, also commonly denoted by 1724: 1522:Cyclopentadienyl complexes 1486:β-hydride elimination 1460:Metal–ligand multiple bond 1313:Zumdahl, Steven S (2005). 501: 495: 1587:Transition metal carbides 1248:Orgel, Leslie E. (1960). 498:Spin states (d electrons) 1688:Condensed matter physics 1391:Organometallic chemistry 1042:10.1002/andp.19293950202 1001:Molecular orbital theory 702:If the splitting of the 250:: they are the names of 90:molecular orbital theory 86:John Hasbrouck van Vleck 1552:Half sandwich compounds 1703:Coordination chemistry 1667:Bioinorganic chemistry 1163:10.1103/PhysRev.42.666 1120:10.1103/PhysRev.41.194 1085:10.1103/PhysRev.41.208 972: 949: 926: 903: 880: 857: 841:Pentagonal bipyramidal 834: 789:coordination complexes 699: 567: 528:spectrochemical series 516: 492:High-spin and low-spin 351:spectrochemical series 256:octahedral point group 59:coordination complexes 1638:Ziegler–Natta process 1542:Metal tetranorbornyls 971: 948: 925: 902: 879: 856: 833: 689: 566:crystal field diagram 562: 515:crystal field diagram 511: 1647:Related branches of 1405:Crystal field theory 956:Trigonal bipyramidal 864:Square antiprismatic 652:Stabilization energy 36:crystal field theory 1693:Inorganic chemistry 1662:Inorganic chemistry 1481:Migratory insertion 1455:Agostic interaction 1410:Ligand field theory 1317:Chemical Principles 1269:Inorganic Chemistry 1229:Inorganic Chemistry 1208:Inorganic Chemistry 1155:1932PhRv...42..666S 1112:1932PhRv...41..194P 1077:1932PhRv...41..208V 1034:1929AnP...395..133B 996:Ligand field theory 347:ligand field theory 94:ligand field theory 1547:Sandwich compounds 1505:Types of compounds 1430:Isolobal principle 1022:Annalen der Physik 973: 950: 927: 904: 881: 858: 835: 783:Optical properties 700: 568: 517: 248:molecular symmetry 1708:Transition metals 1675: 1674: 1657:Organic chemistry 1628:Olefin metathesis 1618:Grignard reaction 1517:Grignard reagents 1355:978-3-89336-796-2 1332:978-0-669-39321-7 1305:978-0-8151-8505-5 1278:978-0-8412-3849-7 1240:978-0-13-035471-6 1217:978-0-13-039913-7 977: 976: 32:molecular physics 16:(Redirected from 1715: 1698:Chemical bonding 1623:Monsanto process 1420:d electron count 1415:18-electron rule 1384: 1377: 1370: 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494: 467: 460: 449:2,2'-bipyridine 441: 429: 417: 410: 406: 391: 384: 332: 323: 314: 305: 292: 282: 268:character table 267: 261: 244: 237: 231: 218: 208: 201: 194: 176: 110: 28: 23: 22: 15: 12: 11: 5: 1721: 1719: 1711: 1710: 1705: 1700: 1695: 1690: 1680: 1679: 1673: 1672: 1670: 1669: 1664: 1659: 1653: 1651: 1644: 1643: 1641: 1640: 1635: 1630: 1625: 1620: 1615: 1613:Cativa process 1610: 1604: 1602: 1598: 1597: 1595: 1594: 1589: 1584: 1579: 1574: 1569: 1564: 1559: 1554: 1549: 1544: 1539: 1534: 1529: 1524: 1519: 1514: 1508: 1506: 1502: 1501: 1499: 1498: 1493: 1488: 1483: 1478: 1472: 1470: 1466: 1465: 1463: 1462: 1457: 1452: 1447: 1442: 1437: 1432: 1427: 1422: 1417: 1412: 1407: 1401: 1399: 1395: 1394: 1389: 1387: 1386: 1379: 1372: 1364: 1358: 1357: 1342: 1341:External links 1339: 1338: 1337: 1331: 1310: 1304: 1283: 1277: 1264: 1259:978-0416634402 1258: 1245: 1239: 1222: 1216: 1201: 1198: 1195: 1194: 1177: 1149:(5): 666–686. 1133: 1106:(2): 194–207. 1090: 1071:(2): 208–215. 1055: 1028:(2): 133–208. 1011: 1010: 1008: 1005: 1004: 1003: 998: 993: 981: 978: 975: 974: 965: 958: 952: 951: 942: 935: 929: 928: 919: 912: 906: 905: 896: 889: 883: 882: 873: 866: 860: 859: 850: 843: 837: 836: 827: 820: 814: 813: 810: 807: 800: 797: 784: 781: 776: 772: 768: 764: 760: 756: 752: 747: 737: 733: 728: 722: 718: 713: 707: 679: 671: 653: 650: 641: 637: 628: 624: 614: 605: 601:refers to the 596: 590: 579: 546: 535: 496:Main article: 493: 490: 465: 458: 439: 427: 415: 408: 404: 389: 382: 328: 319: 310: 297: 288: 280: 265: 259: 242: 235: 223: 214: 206: 199: 192: 174: 161: 160: 153: 150: 147: 144: 109: 106: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 1720: 1709: 1706: 1704: 1701: 1699: 1696: 1694: 1691: 1689: 1686: 1685: 1683: 1668: 1665: 1663: 1660: 1658: 1655: 1654: 1652: 1650: 1645: 1639: 1636: 1634: 1631: 1629: 1626: 1624: 1621: 1619: 1616: 1614: 1611: 1609: 1608:Carbonylation 1606: 1605: 1603: 1599: 1593: 1590: 1588: 1585: 1583: 1580: 1578: 1575: 1573: 1570: 1568: 1565: 1563: 1560: 1558: 1555: 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103: 99: 95: 91: 87: 83: 79: 75: 72: 68: 64: 60: 57: 53: 49: 45: 41: 37: 33: 19: 1601:Applications 1537:Metallocenes 1404: 1316: 1289: 1268: 1249: 1228: 1207: 1180: 1146: 1142: 1136: 1103: 1099: 1093: 1068: 1064: 1058: 1025: 1021: 1015: 786: 745: 741: 726: 711: 710:, the three 703: 701: 695: 691: 677: 669: 665: 659: 655: 646: 635: 629: 619: 615: 611: 606: 602: 597: 591: 588: 583: 575: 571: 569: 563: 548: 543: 539: 521: 518: 512: 486: 482:back-bonding 479: 359: 343: 334: 329: 325: 320: 316: 311: 307: 302: 298: 294: 289: 285: 278: 274: 272: 240: 233: 228: 224: 220: 215: 211: 204: 197: 190: 185: 183: 172: 168: 162: 156: 136: 132: 128: 122: 111: 65:properties, 51: 47: 44:degeneracies 39: 35: 29: 1450:spin states 1252:. Methuen. 933:Tetrahedral 554:Hund's rule 1682:Categories 1398:Principles 1007:References 818:Octahedral 771:) - (2 x / 725:, and the 502:See also: 355:this table 262:.(see the 165:octahedral 119:degenerate 82:Hans Bethe 74:enthalpies 1649:chemistry 1469:Reactions 1445:Hapticity 1296:1028–1034 1171:0031-899X 1128:0031-899X 1050:1521-3889 662:-orbitals 564:High Spin 524:-orbitals 125:-orbitals 71:hydration 980:See also 513:Low Spin 108:Overview 63:magnetic 1151:Bibcode 1108:Bibcode 1073:Bibcode 1030:Bibcode 254:of the 159:groups. 114:ligands 1353:  1329:  1302:  1275:  1256:  1237:  1214:  1188:  1169:  1126:  1048:  349:. The 78:spinel 76:, and 67:colors 809:Shape 473:< 469:< 462:< 455:< 451:< 447:< 443:< 436:< 432:< 420:< 412:< 401:< 397:< 393:< 386:< 379:< 371:< 367:< 363:< 178:(the 1351:ISBN 1327:ISBN 1300:ISBN 1273:ISBN 1254:ISBN 1235:ISBN 1212:ISBN 1186:ISBN 1167:ISSN 1124:ISSN 1046:ISSN 806:Name 759:= 2Δ 610:and 453:phen 324:and 293:and 219:and 203:and 84:and 1159:doi 1116:doi 1081:doi 1038:doi 1026:395 777:oct 769:oct 761:oct 757:oct 738:oct 723:oct 708:oct 642:oct 638:tet 580:oct 464:PPh 422:NCS 373:SCN 357:): 281:tet 258:, O 175:oct 50:or 40:CFT 30:In 1684:: 1325:. 1298:. 1165:. 1157:. 1147:42 1145:. 1122:. 1114:. 1104:41 1102:. 1079:. 1069:41 1067:. 1044:. 1036:. 795:. 748:2g 714:2g 672:2g 625:2g 556:. 484:. 477:. 475:CO 471:CN 457:NO 445:en 438:NH 434:py 430:CN 426:CH 399:OH 381:NO 377:Cl 365:Br 330:yz 321:xz 315:, 312:xy 236:2g 207:yz 200:xz 196:, 193:xy 186:Dq 184:10 69:, 34:, 1383:e 1376:t 1369:v 1335:. 1308:. 1281:. 1262:. 1243:. 1220:. 1192:. 1175:\ 1173:. 1161:: 1153:: 1130:. 1118:: 1110:: 1087:. 1083:: 1075:: 1052:. 1040:: 1032:: 775:Δ 773:5 767:Δ 765:5 755:Δ 753:5 746:t 742:d 736:Δ 734:5 729:g 727:e 721:Δ 719:5 712:t 704:d 696:d 692:d 680:g 678:e 670:t 666:d 660:d 630:g 620:y 618:- 616:x 612:d 607:z 603:d 598:g 592:g 584:d 576:d 572:d 549:g 547:2 544:t 540:d 536:2 522:d 466:3 459:2 440:3 428:3 418:O 416:2 414:H 409:4 407:O 405:2 403:C 395:F 390:3 388:N 383:3 369:S 361:I 335:d 326:d 317:d 308:d 303:y 301:- 299:x 295:d 290:z 286:d 279:Δ 275:d 266:h 264:O 260:h 243:g 241:e 234:t 229:y 227:- 225:x 221:d 216:z 212:d 205:d 198:d 191:d 173:Δ 169:d 157:d 137:d 133:d 129:d 123:d 52:f 48:d 38:( 20:)

Index

Crystal field stabilization energy
molecular physics
degeneracies
transition metal
coordination complexes
magnetic
colors
hydration
enthalpies
spinel
Hans Bethe
John Hasbrouck van Vleck
molecular orbital theory
ligand field theory
chemical bonding
inverted ligand field theory
ligands
degenerate
d-orbitals
octahedral
crystal-field splitting parameter
molecular symmetry
irreducible representations
octahedral point group
Oh character table
Square planar
ligand field theory
spectrochemical series
this table
I

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