233:
228:
In the first excited state, the two π* electrons are paired in the same orbital, so that there are no unpaired electrons. In the second excited state, however, the two π* electrons occupy different orbitals with opposite spin. Each is therefore an unpaired electron, but the total spin is zero and the
229:
multiplicity is 2S + 1 = 1 despite the two unpaired electrons. The multiplicity of the second excited state is therefore not equal to the number of its unpaired electrons plus one, and the rule which is usually true for ground states is invalid for this excited state.
122:
which favors the single filling of degenerate orbitals. The triplet consists of three states with spin components +1, 0 and –1 along the direction of the total orbital angular momentum, which is also 1 as indicated by the letter P. The
130:
However the multiplicity equals the number of spin orientations only if S ≤ L. When S > L there are only 2L+1 orientations of total angular momentum possible, ranging from S+L to S-L. The ground state of the
66:
of an atom or molecule, the unpaired electrons usually all have parallel spin. In this case the multiplicity is also equal to the number of unpaired electrons plus one.
147:= 3/2 due to three unpaired electrons. For an S state, L = 0 so that J can only be 3/2 and there is only one level even though the multiplicity is 4.
420:
159:
molecules have complete electron shells with no unpaired electrons and therefore have singlet ground states. This is true also for
119:
124:
214:
orbitals. In the ground state of dioxygen, this energy level is occupied by two electrons of the same spin, as shown in the
225:. Each has two electrons of opposite spin in the π* level so that S = 0 and the multiplicity is 2S + 1 = 1 in consequence.
44:
291:
carbenes, named for their spin multiplicities. Both have two non-bonding electrons; in singlet carbenes these exist as a
581:
562:
539:
514:
436:
295:
and have opposite spins so that there is no net spin, while in triplet carbenes these electrons have parallel spins.
279:
are molecules which have carbon atoms with only six electrons in their valence shells and therefore disobey the
82:
74:
The multiplicity is often equal to the number of possible orientations of the total spin relative to the total
215:
232:
600:
86:
75:
347:
315:
310:
531:
506:
320:
332:
199:
191:
176:
8:
325:
160:
525:
164:
577:
558:
535:
510:
500:
432:
342:
272:
236:
Molecular orbital diagram of two singlet excited states and triplet ground state of O
156:
115:
24:
424:
352:
195:
305:
218:. The molecule, therefore, has two unpaired electrons and is in a triplet state.
221:
In contrast, the first and second excited states of dioxygen are both states of
412:
222:
210:
The highest occupied orbital energy level of dioxygen is a pair of antibonding
594:
554:
288:
284:
101:
56:
52:
48:
428:
127:
J can vary from L+S = 2 to L–S = 0 in integer steps, so that J = 2, 1 or 0.
198:. A simple explanation of the spin states of such complexes is provided by
63:
32:
20:
476:
464:
524:
Clayden, Jonathan; Greeves, Nick; Warren, Stuart; Wothers, Peter (2001).
337:
97:
280:
292:
132:
276:
211:
184:
47:. States with multiplicity 1, 2, 3, 4, 5 are respectively called
371:
369:
168:
93:
366:
523:
482:
470:
452:
390:
388:
386:
384:
190:
However, higher spin ground states are very common in
381:
421:International Union of Pure and Applied Chemistry
592:
16:Property of an atomic or molecular energy level
498:
375:
240:. From left to right, the diagrams are for: Δ
571:
458:
253:singlet oxygen (second excited state), and Σ
572:Miessler, Gary L.; Tarr, Donald A. (1999).
417:IUPAC Compendium of Chemical Terminology
231:
499:Atkins, Peter; de Paula, Julio (2006).
407:
405:
403:
244:singlet oxygen (first excited state), Σ
593:
548:
394:
81:, and therefore to the number of near–
125:total angular momentum quantum number
400:
92:For example, the ground state of a
13:
413:"multiplicity (spin multiplicity)"
106:) indicates that the multiplicity
100:). The superscript three (read as
14:
612:
85:levels that differ only in their
283:. Carbenes generally split into
576:(2nd ed.). Prentice-Hall.
553:(4th ed.). United States:
505:(8th ed.). United States:
492:
262:triplet oxygen (ground state).
1:
359:
135:atom is a S state, for which
114:= 1. This spin is due to two
150:
110:= 3, so that the total spin
7:
298:
266:
205:
167:. Important exceptions are
45:total spin angular momentum
10:
617:
502:Atkins' Physical Chemistry
376:Atkins & de Paula 2006
163:molecules containing only
216:molecular orbital diagram
59:, quartets and quintets.
459:Miessler & Tarr 1999
348:Effective nuclear charge
316:Azimuthal quantum number
311:Principal quantum number
76:orbital angular momentum
69:
549:Levine, Ira N. (1991).
532:Oxford University Press
507:Oxford University Press
429:10.1351/goldbook.M04062
321:Magnetic quantum number
263:
192:coordination complexes
87:spin–orbit interaction
235:
333:Exchange interaction
200:crystal field theory
574:Inorganic Chemistry
483:Clayden et al. 2001
471:Clayden et al. 2001
326:Spin quantum number
165:main-group elements
264:
116:unpaired electrons
601:Quantum chemistry
551:Quantum Chemistry
530:. United States:
527:Organic Chemistry
273:organic chemistry
196:transition metals
118:, as a result of
25:quantum chemistry
608:
587:
568:
545:
520:
486:
480:
474:
468:
462:
456:
450:
449:
447:
445:
409:
398:
392:
379:
373:
353:Shielding effect
261:
260:
252:
251:
616:
615:
611:
610:
609:
607:
606:
605:
591:
590:
584:
565:
542:
517:
495:
490:
489:
485:, p. 1061.
481:
477:
473:, p. 1055.
469:
465:
457:
453:
443:
441:
439:
411:
410:
401:
393:
382:
374:
367:
362:
357:
306:Quantum numbers
301:
269:
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182:
174:
153:
72:
17:
12:
11:
5:
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563:
546:
540:
521:
515:
494:
491:
488:
487:
475:
463:
451:
437:
399:
397:, p. 308.
380:
378:, p. 353.
364:
363:
361:
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355:
350:
345:
343:Slater's rules
340:
335:
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329:
328:
323:
318:
313:
302:
300:
297:
268:
265:
257:
248:
241:
237:
223:singlet oxygen
207:
204:
180:
172:
152:
149:
71:
68:
35:is defined as
15:
9:
6:
4:
3:
2:
613:
602:
599:
598:
596:
585:
583:0-13-841891-8
579:
575:
570:
566:
564:0-205-12770-3
560:
556:
555:Prentice-Hall
552:
547:
543:
541:0-19-850346-6
537:
533:
529:
528:
522:
518:
516:0-7167-8759-8
512:
508:
504:
503:
497:
496:
484:
479:
472:
467:
461:, p. 33.
460:
455:
440:
438:0-9678550-9-8
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324:
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319:
317:
314:
312:
309:
308:
307:
304:
303:
296:
294:
290:
287:carbenes and
286:
282:
278:
274:
234:
230:
226:
224:
219:
217:
213:
203:
201:
197:
193:
188:
186:
178:
175:) as well as
170:
166:
162:
158:
148:
146:
142:
138:
134:
128:
126:
121:
117:
113:
109:
105:
104:
99:
95:
90:
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50:
46:
42:
38:
34:
30:
26:
22:
573:
550:
526:
501:
493:Bibliography
478:
466:
454:
442:. Retrieved
416:
270:
227:
220:
209:
189:
183:) and other
155:Most stable
154:
144:
140:
136:
129:
111:
107:
102:
91:
78:
73:
64:ground state
61:
40:
36:
33:energy level
29:multiplicity
28:
21:spectroscopy
18:
395:Levine 1991
338:Term symbol
120:Hund's rule
98:Term symbol
96:atom is P (
360:References
281:octet rule
83:degenerate
423:). 2006.
419:. IUPAC (
293:lone pair
177:methylene
161:inorganic
151:Molecules
139:= 4 in a
595:Category
444:30 March
299:See also
277:carbenes
267:Carbenes
206:Dioxygen
185:carbenes
169:dioxygen
133:nitrogen
89:energy.
57:triplets
53:doublets
49:singlets
39:, where
289:triplet
285:singlet
157:organic
143:state,
141:quartet
103:triplet
62:In the
43:is the
580:
561:
538:
513:
435:
137:2S + 1
94:carbon
31:of an
27:, the
70:Atoms
578:ISBN
559:ISBN
536:ISBN
511:ISBN
446:2018
433:ISBN
108:2S+1
37:2S+1
23:and
425:doi
271:In
194:of
179:(CH
19:In
597::
557:.
534:.
509:.
431:.
415:.
402:^
383:^
368:^
275:,
212:π*
202:.
187:.
171:(O
55:,
51:,
586:.
567:.
544:.
519:.
448:.
427::
258:g
249:g
242:g
238:2
181:2
173:2
145:S
112:S
79:L
41:S
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