797:, where nucleophiles with a lone pair of electrons on an atom adjacent to the nucleophilic center have enhanced reactivity. The alpha effect, basicity, and polarizability are still accepted as the main factors in determining nucleophilic reactivity. As such, the Edwards equation is applied in a qualitative sense much more frequently than in a quantitative one. In studying nucleophilic reactions, Edwards and Pearson noticed that for certain classes of nucleophiles most of the contribution of nucleophilic character originated from their basicity, resulting in large β values. For other nucleophiles, most of the nucleophilic character came from their high polarizability, with little contribution from basicity, resulting in large α values. This observation led Pearson to develop his
801:, which is arguably the most important contribution that the Edwards equation has made to current understanding of organic and inorganic chemistry. Nucleophiles, or bases, that were polarizable, with large α values, were categorized as “soft”, and nucleophiles that were non-polarizable, with large β and small α values, were categorized as “hard”.
518:
where 2.60 is the correction for the oxidative dimerization of water, obtained from a least-squares correlation of data in
Edwards’ first paper on the subject. α and β are then parameters unique to specific nucleophiles that relate the sensitivity of the substrate to the basicity and polarizability
239:
However, both the Swain–Scott equation and the Brønsted relationship make the rather inaccurate assumption that all nucleophiles have the same reactivity with respect to a specific reaction site. There are several different categories of nucleophiles with different attacking atoms (e.g. oxygen,
35:
The general idea is that most nucleophiles are also good bases because the concentration of negatively charged electron density that defines a nucleophile will strongly attract positively charged protons, which is the definition of a base according to
949:
Swain, C. Gardner; Scott, Carleton B. (January 1953). "Quantitative
Correlation of Relative Rates. Comparison of Hydroxide Ion with Other Nucleophilic Reagents toward Alkyl Halides, Esters, Epoxides and Acyl Halides".
523:
was determined to have some dependence on the basicity relative to protons (H) due to some factors that affect basicity also influencing the electrochemical properties of the nucleophile. To account for this,
461:
315:
792:
A later paper by
Edwards and Pearson, following research done by Jencks and Carriuolo in 1960 led to the discovery of an additional factor in nucleophilic reactivity, which Edwards and Pearson called the
204:
782:
651:
519:
factors. However, because some β's appeared to be negative as defined by the first generation of the
Edwards equation, which theoretically should not occur, Edwards adjusted his equation. The term E
240:
carbon, nitrogen) and each of these atoms has different nucleophilic characteristics. The
Edwards equation attempts to account for this additional parameter by introducing a polarizability term.
720:
123:
513:
374:
585:
1115:
Hudson, Michael J.; Laurence M. Harwood; Dominic M. Laventine; Frank W. Lewis (2013). "Use of Soft
Heterocyclic N‑Donor Ligands To Separate Actinides and Lanthanides".
139:
Swain and Scott later tried to define a more specific and quantitative relationship by correlating nucleophilic data with a single-parameter equation derived in 1953:
976:
784:, especially since it was republished in that form in a later paper of Edwards’, leading to confusion over which parameters are being defined.
725:
where A= αa and B = β + αb. However, because the second generation of the equation was also the final one, the equation is sometimes written as
56:
quantitatively. Brønsted and
Pederson first discovered the relationship between basicity, with respect to protons, and nucleophilicity in 1924:
804:
The
Edwards equation parameters have since been used to help categorize acids and bases as hard or soft, due to the approach's simplicity.
40:. Additionally, highly polarizable nucleophiles will have greater nucleophilic character than suggested by their basicity because their
405:
254:
145:
728:
590:
398:
is the term
Edwards introduced to account for the polarizability of the nucleophile. It is related to the oxidation potential (E
656:
The values of a and b, obtained by the method of least squares, are 3.60 and 0.0624 respectively. With this new definition of E
37:
823:
1211:
1015:
933:
666:
1088:
Jencks, William P.; Carriuolo, Joan (February 1960). "General Base
Catalysis of the Aminolysis of Phenyl Acetate".
63:
32:. This equation was first developed by John O. Edwards in 1954 and later revised based on additional work in 1956.
818:
1178:
Yingst, Austin; MacDaniel, Darl H. (1967). "Use of the Edwards Equation to Determine Hardness of Acids".
469:
1061:
Jencks, William P.; Carriuolo, Joan (April 1960). "Reactivity of Nucleophilic Reagents toward Esters".
328:
O). H is a measure of the basicity of the nucleophile relative to protons, as defined by the equation:
334:
848:
Edwards, J.O. (1954). "Correlation of Relative Rates and Equilibria with a Double Basicity Scale".
813:
542:
383:
is that of the conjugate acid of the nucleophile and the constant 1.74 is the correction for the pK
1034:
Edwards, J.O.; Pearson, Ralph G. (1962). "The Factors Determining Nucleophilic Reactivities".
1114:
917:
910:
213:, of a reaction, normalized to that of a standard reaction with water as the nucleophile (
8:
228:
that depends on the sensitivity of a substrate to nucleophilic attack (defined as 1 for
1216:
529:
52:
Prior to Edwards developing his equation, other scientists were also working to define
1152:
1132:
1011:
929:
986:
1187:
1160:
1124:
1097:
1070:
1043:
990:
981:
959:
921:
887:
857:
233:
41:
25:
53:
229:
29:
1205:
985:, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "
878:
Edwards, J.O. (1956). "Polarizability, Basicity and Nucleophilic Character".
994:
1136:
794:
925:
798:
21:
1191:
1164:
1101:
1074:
1047:
963:
891:
861:
1128:
132:
is the rate constant for nitramide decomposition by a base (B) and β
20:
in organic chemistry is a two-parameter equation for correlating
528:
was redefined in terms of basicity and polarizability (given as
456:{\displaystyle \mathrm {2X^{-}\rightleftharpoons X_{2}+2e^{-}} }
310:{\displaystyle \log {\frac {k}{k_{0}}}=\alpha E_{n}+\beta H\,}
44:
can be shifted with relative ease to concentrate in one area.
463:(oxidative dimerization of the nucleophile) by the equation:
1008:
Perspectives on Structure and Mechanism in Organic Chemistry
199:{\displaystyle \log _{10}\left({\frac {k}{k_{0}}}\right)=sn}
1150:
Pearson, Ralph G. (1963). "Hard and Soft Acids and Bases".
777:{\displaystyle \log {\frac {k}{k_{0}}}=\alpha P+\beta H\,}
646:{\displaystyle \ P\equiv \log {\frac {R_{N}}{R_{H_{2}0}}}}
324:
are the rate constants for a nucleophile and a standard (H
916:. Vol. 215. American Chemical Society. pp.
731:
669:
593:
545:
472:
408:
337:
257:
148:
66:
1010:(2 ed.). New Jersey: Wiley. pp. 506–507.
909:
776:
714:
645:
579:
507:
455:
423:
368:
309:
198:
117:
24:, as defined by relative rate constants, with the
1149:
248:The first generation of the Edwards equation was
224:for a given nucleophile and a substrate constant
28:of the nucleophile (relative to protons) and its
1203:
1177:
1087:
1060:
715:{\displaystyle \log {\frac {k}{k_{0}}}=AP+BH\,}
1033:
908:Harris, J. Milton; McManus, Samuel P. (1987).
907:
118:{\displaystyle \log k_{B}=\beta _{n}pK_{b}+C}
660:, the Edwards equation can be rearranged:
948:
773:
711:
306:
1090:Journal of the American Chemical Society
1063:Journal of the American Chemical Society
1036:Journal of the American Chemical Society
952:Journal of the American Chemical Society
903:
901:
880:Journal of the American Chemical Society
850:Journal of the American Chemical Society
209:This equation relates the rate constant
1005:
877:
847:
232:). This equation was modeled after the
1204:
1029:
1027:
898:
873:
871:
843:
841:
839:
243:
13:
1024:
982:Compendium of Chemical Terminology
868:
836:
508:{\displaystyle \ E_{n}=E_{0}+2.60}
443:
427:
414:
14:
1228:
136:is a parameter of the equation.
1171:
1143:
1108:
787:
369:{\displaystyle \ H=pK_{a}+1.74}
38:Brønsted–Lowry acid-base theory
1081:
1054:
999:
970:
942:
220:), to a nucleophilic constant
1:
829:
580:{\displaystyle \ E_{n}=aP+bH}
824:Bell–Evans–Polanyi principle
7:
819:Brønsted catalysis equation
807:
10:
1233:
1212:Physical organic chemistry
799:hard-soft acid-base theory
47:
814:Free-energy relationship
1006:Carroll, Felix (2010).
995:10.1351/goldbook.S06201
22:nucleophilic reactivity
778:
716:
647:
581:
509:
457:
370:
311:
200:
119:
779:
717:
648:
582:
510:
458:
371:
312:
201:
120:
987:Swain–Scott equation
926:10.1021/ba-1987-0215
729:
667:
591:
543:
470:
406:
335:
255:
146:
64:
1192:10.1021/ic50051a051
1180:Inorganic Chemistry
1165:10.1021/ja00905a001
1117:Inorganic Chemistry
1102:10.1021/ja01488a044
1075:10.1021/ja01492a058
1048:10.1021/ja00860a005
964:10.1021/ja01097a041
892:10.1021/ja01590a012
862:10.1021/ja01635a021
774:
712:
643:
577:
530:molar refractivity
505:
453:
402:) of the reaction
366:
307:
196:
115:
1159:(22): 3533–3539.
1153:J. Am. Chem. Soc.
1129:10.1021/ic3008848
753:
691:
641:
596:
548:
475:
340:
279:
244:Edwards equations
181:
1224:
1196:
1195:
1186:(5): 1067–1068.
1175:
1169:
1168:
1147:
1141:
1140:
1123:(7): 3414–3428.
1112:
1106:
1105:
1085:
1079:
1078:
1069:(7): 1778–1786.
1058:
1052:
1051:
1031:
1022:
1021:
1003:
997:
974:
968:
967:
946:
940:
939:
915:
905:
896:
895:
886:(9): 1819–1820.
875:
866:
865:
856:(6): 1540–1547.
845:
783:
781:
780:
775:
754:
752:
751:
739:
721:
719:
718:
713:
692:
690:
689:
677:
652:
650:
649:
644:
642:
640:
639:
635:
634:
620:
619:
610:
594:
586:
584:
583:
578:
558:
557:
546:
514:
512:
511:
506:
498:
497:
485:
484:
473:
462:
460:
459:
454:
452:
451:
450:
435:
434:
422:
421:
375:
373:
372:
367:
359:
358:
338:
316:
314:
313:
308:
296:
295:
280:
278:
277:
265:
234:Hammett equation
205:
203:
202:
197:
186:
182:
180:
179:
167:
158:
157:
124:
122:
121:
116:
108:
107:
95:
94:
82:
81:
42:electron density
18:Edwards equation
1232:
1231:
1227:
1226:
1225:
1223:
1222:
1221:
1202:
1201:
1200:
1199:
1176:
1172:
1148:
1144:
1113:
1109:
1086:
1082:
1059:
1055:
1032:
1025:
1018:
1004:
1000:
975:
971:
947:
943:
936:
912:Nucleophilicity
906:
899:
876:
869:
846:
837:
832:
810:
790:
747:
743:
738:
730:
727:
726:
685:
681:
676:
668:
665:
664:
659:
630:
626:
625:
621:
615:
611:
609:
592:
589:
588:
553:
549:
544:
541:
540:
535:
527:
522:
493:
489:
480:
476:
471:
468:
467:
446:
442:
430:
426:
417:
413:
409:
407:
404:
403:
401:
397:
390:
386:
382:
354:
350:
336:
333:
332:
327:
323:
291:
287:
273:
269:
264:
256:
253:
252:
246:
219:
175:
171:
166:
162:
153:
149:
147:
144:
143:
135:
131:
103:
99:
90:
86:
77:
73:
65:
62:
61:
54:nucleophilicity
50:
12:
11:
5:
1230:
1220:
1219:
1214:
1198:
1197:
1170:
1142:
1107:
1096:(3): 675–681.
1080:
1053:
1023:
1017:978-0470276105
1016:
998:
969:
958:(1): 141–147.
941:
934:
897:
867:
834:
833:
831:
828:
827:
826:
821:
816:
809:
806:
789:
786:
772:
769:
766:
763:
760:
757:
750:
746:
742:
737:
734:
723:
722:
710:
707:
704:
701:
698:
695:
688:
684:
680:
675:
672:
657:
654:
653:
638:
633:
629:
624:
618:
614:
608:
605:
602:
599:
576:
573:
570:
567:
564:
561:
556:
552:
533:
525:
520:
516:
515:
504:
501:
496:
492:
488:
483:
479:
449:
445:
441:
438:
433:
429:
425:
420:
416:
412:
399:
395:
388:
384:
380:
377:
376:
365:
362:
357:
353:
349:
346:
343:
325:
321:
318:
317:
305:
302:
299:
294:
290:
286:
283:
276:
272:
268:
263:
260:
245:
242:
230:methyl bromide
217:
207:
206:
195:
192:
189:
185:
178:
174:
170:
165:
161:
156:
152:
133:
129:
126:
125:
114:
111:
106:
102:
98:
93:
89:
85:
80:
76:
72:
69:
49:
46:
30:polarizability
9:
6:
4:
3:
2:
1229:
1218:
1215:
1213:
1210:
1209:
1207:
1193:
1189:
1185:
1181:
1174:
1166:
1162:
1158:
1155:
1154:
1146:
1138:
1134:
1130:
1126:
1122:
1118:
1111:
1103:
1099:
1095:
1091:
1084:
1076:
1072:
1068:
1064:
1057:
1049:
1045:
1041:
1037:
1030:
1028:
1019:
1013:
1009:
1002:
996:
992:
988:
984:
983:
978:
973:
965:
961:
957:
953:
945:
937:
935:9780841209527
931:
927:
923:
919:
914:
913:
904:
902:
893:
889:
885:
881:
874:
872:
863:
859:
855:
851:
844:
842:
840:
835:
825:
822:
820:
817:
815:
812:
811:
805:
802:
800:
796:
785:
770:
767:
764:
761:
758:
755:
748:
744:
740:
735:
732:
708:
705:
702:
699:
696:
693:
686:
682:
678:
673:
670:
663:
662:
661:
636:
631:
627:
622:
616:
612:
606:
603:
600:
597:
574:
571:
568:
565:
562:
559:
554:
550:
539:
538:
537:
531:
502:
499:
494:
490:
486:
481:
477:
466:
465:
464:
447:
439:
436:
431:
418:
410:
392:
363:
360:
355:
351:
347:
344:
341:
331:
330:
329:
320:where k and k
303:
300:
297:
292:
288:
284:
281:
274:
270:
266:
261:
258:
251:
250:
249:
241:
237:
235:
231:
227:
223:
216:
212:
193:
190:
187:
183:
176:
172:
168:
163:
159:
154:
150:
142:
141:
140:
137:
112:
109:
104:
100:
96:
91:
87:
83:
78:
74:
70:
67:
59:
58:
57:
55:
45:
43:
39:
33:
31:
27:
23:
19:
1183:
1179:
1173:
1156:
1151:
1145:
1120:
1116:
1110:
1093:
1089:
1083:
1066:
1062:
1056:
1042:(1): 16–24.
1039:
1035:
1007:
1001:
980:
972:
955:
951:
944:
911:
883:
879:
853:
849:
803:
795:alpha effect
791:
788:Significance
724:
655:
517:
393:
379:where the pK
378:
319:
247:
238:
225:
221:
214:
210:
208:
138:
127:
51:
34:
17:
15:
1206:Categories
830:References
1217:Equations
768:β
759:α
736:
674:
607:
601:≡
448:−
424:⇌
419:−
301:β
285:α
262:
160:
88:β
71:
1137:22867058
808:See also
587:where
26:basicity
128:where k
48:History
1135:
1014:
932:
595:
547:
474:
339:
60:where
977:IUPAC
1133:PMID
1012:ISBN
930:ISBN
503:2.60
387:of H
364:1.74
16:The
1188:doi
1161:doi
1125:doi
1098:doi
1071:doi
1044:doi
991:doi
989:".
960:doi
922:doi
918:7–8
888:doi
858:doi
733:log
671:log
604:log
536:):
532:, R
391:O.
259:log
151:log
68:log
1208::
1182:.
1157:85
1131:.
1121:52
1119:.
1094:82
1092:.
1067:82
1065:.
1040:84
1038:.
1026:^
979:,
956:75
954:.
928:.
920:.
900:^
884:78
882:.
870:^
854:76
852:.
838:^
236:.
155:10
1194:.
1190::
1184:6
1167:.
1163::
1139:.
1127::
1104:.
1100::
1077:.
1073::
1050:.
1046::
1020:.
993::
966:.
962::
938:.
924::
894:.
890::
864:.
860::
771:H
765:+
762:P
756:=
749:0
745:k
741:k
709:H
706:B
703:+
700:P
697:A
694:=
687:0
683:k
679:k
658:n
637:0
632:2
628:H
623:R
617:N
613:R
598:P
575:H
572:b
569:+
566:P
563:a
560:=
555:n
551:E
534:N
526:n
524:E
521:n
500:+
495:0
491:E
487:=
482:n
478:E
444:e
440:2
437:+
432:2
428:X
415:X
411:2
400:0
396:n
394:E
389:3
385:a
381:a
361:+
356:a
352:K
348:p
345:=
342:H
326:2
322:0
304:H
298:+
293:n
289:E
282:=
275:0
271:k
267:k
226:s
222:n
218:0
215:k
211:k
194:n
191:s
188:=
184:)
177:0
173:k
169:k
164:(
134:N
130:b
113:C
110:+
105:b
101:K
97:p
92:n
84:=
79:B
75:k
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