1861:, the energy needed to overcome the activation barrier, has a slightly different meaning in each theory. In practice, experimental data does not generally allow a determination to be made as to which is "correct" in terms of best fit. Hence, it must be remembered that all three are conceptual frameworks that make numerous assumptions, both realistic and unrealistic, in their derivations. As a result, they are capable of providing different insights into a system.
1534:
1626:, in which reactants are viewed as hard spheres with a particular cross-section, provided yet another common way to rationalize and model the temperature dependence of the rate constant, although this approach has gradually fallen into disuse. The equation for the rate constant is similar in functional form to both the Arrhenius and Eyring equations:
1283:
1618:
The biggest difference between the two theories is that
Arrhenius theory attempts to model the reaction (single- or multi-step) as a whole, while transition state theory models the individual elementary steps involved. Thus, they are not directly comparable, unless the reaction in question involves
568:
There are few examples of elementary steps that are termolecular or higher order, due to the low probability of three or more molecules colliding in their reactive conformations and in the right orientation relative to each other to reach a particular transition state. There are, however, some
1937:
Rate constant can be calculated for elementary reactions by molecular dynamics simulations. One possible approach is to calculate the mean residence time of the molecule in the reactant state. Although this is feasible for small systems with short residence times, this approach is not widely
353:
is a unimolecular rate constant. Since a reaction requires a change in molecular geometry, unimolecular rate constants cannot be larger than the frequency of a molecular vibration. Thus, in general, a unimolecular rate constant has an upper limit of
1954:
The theory is based on the assumption that the reaction can be described by a reaction coordinate, and that we can apply
Boltzmann distribution at least in the reactant state. A new, especially reactive segment of the reactant, called the
1529:{\displaystyle k(T)=\kappa {\frac {k_{\mathrm {B} }T}{h}}(c^{\ominus })^{1-M}e^{-\Delta G^{\ddagger }/RT}=\left(\kappa {\frac {k_{\mathrm {B} }T}{h}}(c^{\ominus })^{1-M}\right)e^{\Delta S^{\ddagger }/R}e^{-\Delta H^{\ddagger }/RT},}
1916:
Calculation of rate constants of the processes of generation and relaxation of electronically and vibrationally excited particles are of significant importance. It is used, for example, in the computer simulation of processes in
1243:, or frequency factor (not to be confused here with the reactant A) takes into consideration the frequency at which reactant molecules are colliding and the likelihood that a collision leads to a successful reaction. Here,
796:
2025:
961:
569:
termolecular examples in the gas phase. Most involve the recombination of two atoms or small radicals or molecules in the presence of an inert third body which carries off excess energy, such as O +
1182:
1839:
1080:
2048:
is the rate constant from the saddle domain. The first can be simply calculated from the free energy surface, the latter is easily accessible from short molecular dynamics simulations
452:
is a bimolecular rate constant. Bimolecular rate constants have an upper limit that is determined by how frequently molecules can collide, and the fastest such processes are limited by
1694:
695:
864:
830:
2219:→ 2 NOCl, etc.) have also been suggested as examples of termolecular elementary processes. However, other authors favor a two-step process, each of which is bimolecular: (NO +
641:
For a first-order reaction (including a unimolecular one-step process), there is a direct relationship between the unimolecular rate constant and the half-life of the reaction:
1749:
174:
2576:
West, Anthony M.A.; Elber, Ron; Shalloway, David (2007). "Extending molecular dynamics time scales with milestoning: Example of complex kinetics in a solvated peptide".
633:. In cases where a termolecular step might plausibly be proposed, one of the reactants is generally present in high concentration (e.g., as a solvent or diluent gas).
1964:
536:
423:
324:
214:
the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary, one would use moles of A or B per unit area instead.)
563:
450:
351:
1938:
applicable as reactions are often rare events on molecular scale. One simple approach to overcome this problem is
Divided Saddle Theory. Such other methods as the
728:
800:
a quantity that can be regarded as the free energy change needed to reach the transition state. In particular, this energy barrier incorporates both enthalpic
198:
51:
2113:
1574:. In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor
734:
876:
2560:
2270:
2156:
1089:
988:) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (Δ
1772:
2428:
2123:
2403:
2378:
2342:
1017:
1595:) ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher. Here,
1857:, and 1 give Arrhenius theory, collision theory, and transition state theory, respectively, although the imprecise notion of Δ
1631:
2516:
Chandler, David (1978). "Statistical mechanics of isomerization dynamics in liquids and the transition state approximation".
2475:
2625:
101:
117:
1939:
1608:
1012:
at which a reaction proceeds. The rate constant as a function of thermodynamic temperature is then given by:
1275:
698:
644:
1240:
1221:
839:
805:
2337:. Treichel, Paul., Townsend, John R. (7th ed.). Belmont, Calif.: Thomson Brooks/ Cole. p. 703.
1543:
1267:
981:. As useful rules of thumb, a first-order reaction with a rate constant of 10 s will have a half-life (
1713:
2585:
2525:
2453:
2299:
2062:
1925:. First-principle based models should be used for such calculation. It can be done with the help of
2087:
1926:
1877:
203:
1943:
1599:
is the standard concentration, generally chosen based on the unit of concentration used (usually
1001:
978:
273:
242:
226:
276:. Almost all elementary steps are either unimolecular or bimolecular. For a unimolecular step
1607:
is the molecularity of the transition state. Lastly, κ, usually set to unity, is known as the
2601:
2556:
2498:
2434:
2424:
2399:
2374:
2348:
2338:
2315:
2266:
2258:
2152:
2129:
2119:
1870:
1194:
1005:
56:
20:
1004:
is an elementary treatment that gives the quantitative basis of the relationship between the
475:
373:
285:
2593:
2533:
2490:
2366:
2307:
1922:
1918:
1623:
541:
428:
329:
1271:
970:
869:
704:
630:
2589:
2529:
2303:
211:
183:
36:
1542:
is the free energy of activation, a parameter that incorporates both the enthalpy and
2619:
2057:
1009:
265:
109:
2067:
1612:
1202:
791:{\displaystyle {\Delta G^{\ddagger }=\Delta H^{\ddagger }-T\Delta S^{\ddagger }}}
2020:{\displaystyle k=k_{\mathrm {SD} }\cdot \alpha _{\mathrm {RS} }^{\mathrm {SD} }}
1214:
207:
1213:
are experimentally determined partial orders in and , respectively. Since at
2352:
2319:
2118:. Richardson, Kathleen Schueller (3rd ed.). New York: Harper & Row.
2041:
is the conversion factor between the reactant state and saddle domain, while
1546:
change needed to reach the transition state. The temperature dependence of Δ
202:
is the reaction rate constant that depends on temperature, and and are the
55:) is a proportionality constant which quantifies the rate and direction of a
2133:
956:{\textstyle k(T)={\frac {k_{\mathrm {B} }T}{h}}e^{-\Delta G^{\ddagger }/RT}}
453:
2605:
2502:
2438:
272:
a relationship between stoichiometry and rate law, as determined by the
2265:. Comprehensive Chemical Kinetics. Vol. 6. Elsevier. p. 174.
1710:
is energy input required to overcome the activation barrier. Of note,
1224:, one can expect the proportion of collisions with energy greater than
456:. Thus, in general, a bimolecular rate constant has an upper limit of
2597:
2494:
2394:
Steinfeld, Jeffrey I.; Francisco, Joseph S.; Hase, William L. (1999).
2311:
2537:
2259:"5. Reactions of the Oxides of Nitrogen §5.5 Reactions with Chlorine"
868:
changes that need to be achieved for the reaction to take place: The
2553:
Algorithms for
Chemical Computations, ACS Symposium Series No. 46
2476:"Divided Saddle Theory: A New Idea for Rate Constant Calculation"
1550:
is used to compute these parameters, the enthalpy of activation Δ
1904:
For order three, the rate constant has units of L·mol·s (or M·s)
1907:
For order four, the rate constant has units of L·mol·s (or M·s)
1895:
For order zero, the rate constant has units of mol·L·s (or M·s)
1266:
Another popular model that is derived using more sophisticated
617:. One well-established example is the termolecular step 2 I +
1901:
For order two, the rate constant has units of L·mol·s (or M·s)
62:
For a reaction between reactants A and B to form a product C,
2257:
Compton, R.G.; Bamford, C. H.; Tipper, C.F.H., eds. (2014) .
2171:
The reactions of nitric oxide with the diatomic molecules
1946:
have also been developed for rate constant calculations.
1763:
All three theories model the temperature dependence of
1755:
different from both the
Arrhenius and Eyring models.
879:
647:
1967:
1869:
The units of the rate constant depend on the overall
1775:
1716:
1634:
1286:
1092:
1020:
842:
808:
737:
707:
544:
478:
431:
376:
332:
288:
186:
120:
39:
1959:, is introduced, and the rate constant is factored:
1177:{\displaystyle r=Ae^{-E_{\mathrm {a} }/RT}^{m}^{n},}
59:
by relating it with the concentration of reactants.
233:generally equal to the stoichiometric coefficients
2286:Sullivan, John H. (1967-01-01). "Mechanism of the
2019:
1892:), the rate constant has units of mol·L·s (or M·s)
1833:
1743:
1688:
1528:
1176:
1074:
955:
858:
824:
790:
722:
689:
557:
530:
444:
417:
345:
318:
192:
168:
45:
2551:Bennett, C. H. (1977). Christofferson, R. (ed.).
1834:{\displaystyle k(T)=CT^{\alpha }e^{-\Delta E/RT}}
1588:gives the frequency of molecular collision.
2555:. Washington, D.C.: American Chemical Society.
2373:(3rd ed.). Harper & Row. p. 113.
1898:For order one, the rate constant has units of s
701:gives a relationship between the rate constant
1075:{\displaystyle k(T)=Ae^{-E_{\mathrm {a} }/RT}}
2263:Reactions of Non-metallic Inorganic Compounds
1611:, a parameter which essentially serves as a "
8:
2421:Determination of organic reaction mechanisms
2398:(2nd ed.). Prentice Hall. p. 301.
2151:(3rd ed.). John Wiley. pp. 226–7.
1880:of mol·L (sometimes abbreviated as M), then
1220:the molecules have energies according to a
256:) is called the overall order of reaction.
2147:Moore, John W.; Pearson, Ralph G. (1981).
1702:is the steric (or probability) factor and
16:Coefficient of rate of a chemical reaction
2115:Mechanism and theory in organic chemistry
2007:
2006:
1997:
1996:
1979:
1978:
1966:
1818:
1808:
1798:
1774:
1731:
1727:
1715:
1670:
1660:
1633:
1510:
1504:
1493:
1479:
1473:
1465:
1444:
1434:
1411:
1410:
1403:
1379:
1373:
1362:
1346:
1336:
1313:
1312:
1305:
1285:
1165:
1156:
1147:
1138:
1122:
1115:
1114:
1106:
1091:
1059:
1052:
1051:
1043:
1019:
940:
934:
923:
903:
902:
895:
878:
850:
841:
816:
807:
781:
762:
746:
738:
736:
706:
669:
656:
652:
646:
549:
543:
520:
509:
498:
489:
477:
436:
430:
407:
396:
387:
375:
337:
331:
308:
299:
287:
185:
160:
151:
142:
133:
119:
38:
1689:{\displaystyle k(T)=PZe^{-\Delta E/RT},}
730:and the Gibbs free energy of activation
2079:
1751:, making the temperature dependence of
690:{\textstyle t_{1/2}={\frac {\ln 2}{k}}}
245:and can be determined experimentally.
2474:Daru, János; Stirling, András (2014).
2469:
2467:
7:
859:{\displaystyle \Delta S^{\ddagger }}
825:{\displaystyle \Delta H^{\ddagger }}
2335:Chemistry & chemical reactivity
870:result from transition state theory
2011:
2008:
2001:
1998:
1983:
1980:
1812:
1664:
1615:" for transition state theory.
1497:
1466:
1412:
1366:
1314:
1235:. The constant of proportionality
1157:
1139:
1116:
1053:
927:
904:
843:
809:
774:
755:
739:
521:
510:
499:
472:the reaction rate is described by
408:
397:
370:the reaction rate is described by
309:
282:the reaction rate is described by
152:
134:
14:
1706:is the collision frequency, and Δ
1558:, based on the defining formula Δ
565:is a termolecular rate constant.
112:is often found to have the form:
1876:If concentration is measured in
1744:{\displaystyle Z\propto T^{1/2}}
992:) is approximately 23 kcal/mol.
637:Relationship to other parameters
2578:The Journal of Chemical Physics
2292:The Journal of Chemical Physics
1619:only a single elementary step.
1554:and the entropy of activation Δ
1247:has the same dimensions as an (
1084:The reaction rate is given by:
2396:Chemical Kinetics and Dynamics
1785:
1779:
1767:using an equation of the form
1644:
1638:
1441:
1427:
1343:
1329:
1296:
1290:
1162:
1153:
1144:
1135:
1030:
1024:
889:
883:
717:
711:
525:
517:
514:
506:
503:
495:
412:
404:
401:
393:
313:
305:
157:
148:
139:
130:
1:
241:. Instead they depend on the
210:per unit volume of solution,
2419:Carpenter, Barry K. (1984).
2290:Hydrogen—Iodine Reaction".
169:{\displaystyle r=k^{m}^{n}}
102:stoichiometric coefficients
2642:
1940:Bennett Chandler procedure
1933:Rate constant calculations
248:Sum of m and n, that is, (
2112:Lowry, Thomas H. (1987).
2088:"Chemical Kinetics Notes"
996:Dependence on temperature
206:of substances A and B in
29:reaction rate coefficient
2454:"Differential Rate Laws"
1609:transmission coefficient
631:hydrogen-iodine reaction
466:For a termolecular step
1276:transition state theory
1255:)-order rate constant (
699:Transition state theory
531:{\displaystyle r=k_{3}}
418:{\displaystyle r=k_{2}}
364:For a bimolecular step
319:{\displaystyle r=k_{1}}
2483:J. Chem. Theory Comput
2333:Kotz, John C. (2009).
2149:Kinetics and Mechanism
2021:
1835:
1745:
1690:
1622:Finally, in the past,
1603:= 1 mol L = 1 M), and
1530:
1270:considerations is the
1268:statistical mechanical
1241:pre-exponential factor
1222:Boltzmann distribution
1178:
1076:
957:
860:
826:
792:
724:
691:
559:
532:
446:
419:
347:
320:
194:
170:
47:
25:reaction rate constant
2255:+ NO → 2 NOCl). See:
2022:
1950:Divided saddle theory
1836:
1746:
1691:
1531:
1179:
1077:
958:
861:
827:
793:
725:
692:
560:
558:{\displaystyle k_{3}}
533:
447:
445:{\displaystyle k_{2}}
420:
348:
346:{\displaystyle k_{1}}
321:
195:
171:
83:A and B are reactants
48:
2092:www.chem.arizona.edu
2063:Equilibrium constant
1965:
1773:
1759:Comparison of models
1714:
1632:
1284:
1090:
1018:
877:
840:
806:
735:
723:{\displaystyle k(T)}
705:
645:
542:
476:
429:
374:
330:
286:
204:molar concentrations
184:
118:
37:
2590:2007JChPh.126n5104W
2530:1978JChPh..68.2959C
2423:. New York: Wiley.
2304:1967JChPh..46...73S
2016:
1927:computer simulation
225:are called partial
2017:
1992:
1843:for some constant
1831:
1741:
1686:
1526:
1174:
1072:
1002:Arrhenius equation
979:molar gas constant
953:
856:
822:
788:
720:
687:
555:
528:
442:
415:
343:
316:
274:law of mass action
243:reaction mechanism
227:orders of reaction
190:
166:
43:
2626:Chemical kinetics
2598:10.1063/1.2716389
2562:978-0-8412-0371-6
2495:10.1021/ct400970y
2458:Chemical Kinetics
2371:Chemical Kinetics
2367:Laidler, Keith J.
2312:10.1063/1.1840433
2272:978-0-08-086801-1
2158:978-0-471-03558-9
1871:order of reaction
1425:
1327:
1195:activation energy
1006:activation energy
917:
685:
193:{\displaystyle k}
57:chemical reaction
46:{\displaystyle k}
21:chemical kinetics
2633:
2610:
2609:
2573:
2567:
2566:
2548:
2542:
2541:
2538:10.1063/1.436049
2513:
2507:
2506:
2489:(3): 1121–1127.
2480:
2471:
2462:
2461:
2449:
2443:
2442:
2416:
2410:
2409:
2391:
2385:
2384:
2363:
2357:
2356:
2330:
2324:
2323:
2283:
2277:
2276:
2254:
2253:
2252:
2242:
2241:
2240:
2230:
2229:
2228:
2218:
2217:
2216:
2206:
2205:
2204:
2194:
2193:
2192:
2182:
2181:
2180:
2169:
2163:
2162:
2144:
2138:
2137:
2109:
2103:
2102:
2100:
2098:
2084:
2040:
2039:
2026:
2024:
2023:
2018:
2015:
2014:
2005:
2004:
1988:
1987:
1986:
1923:microelectronics
1919:plasma chemistry
1912:Plasma and gases
1856:
1855:
1851:
1840:
1838:
1837:
1832:
1830:
1829:
1822:
1803:
1802:
1750:
1748:
1747:
1742:
1740:
1739:
1735:
1695:
1693:
1692:
1687:
1682:
1681:
1674:
1624:collision theory
1535:
1533:
1532:
1527:
1522:
1521:
1514:
1509:
1508:
1488:
1487:
1483:
1478:
1477:
1460:
1456:
1455:
1454:
1439:
1438:
1426:
1421:
1417:
1416:
1415:
1404:
1391:
1390:
1383:
1378:
1377:
1357:
1356:
1341:
1340:
1328:
1323:
1319:
1318:
1317:
1306:
1183:
1181:
1180:
1175:
1170:
1169:
1160:
1152:
1151:
1142:
1134:
1133:
1126:
1121:
1120:
1119:
1081:
1079:
1078:
1073:
1071:
1070:
1063:
1058:
1057:
1056:
964:
962:
960:
959:
954:
952:
951:
944:
939:
938:
918:
913:
909:
908:
907:
896:
867:
865:
863:
862:
857:
855:
854:
833:
831:
829:
828:
823:
821:
820:
799:
797:
795:
794:
789:
787:
786:
785:
767:
766:
751:
750:
729:
727:
726:
721:
696:
694:
693:
688:
686:
681:
670:
665:
664:
660:
628:
627:
626:
616:
615:
614:
604:
603:
602:
592:
591:
590:
580:
579:
578:
564:
562:
561:
556:
554:
553:
537:
535:
534:
529:
524:
513:
502:
494:
493:
451:
449:
448:
443:
441:
440:
424:
422:
421:
416:
411:
400:
392:
391:
352:
350:
349:
344:
342:
341:
325:
323:
322:
317:
312:
304:
303:
260:Elementary steps
201:
199:
197:
196:
191:
175:
173:
172:
167:
165:
164:
155:
147:
146:
137:
54:
52:
50:
49:
44:
2641:
2640:
2636:
2635:
2634:
2632:
2631:
2630:
2616:
2615:
2614:
2613:
2575:
2574:
2570:
2563:
2550:
2549:
2545:
2515:
2514:
2510:
2478:
2473:
2472:
2465:
2452:Blauch, David.
2451:
2450:
2446:
2431:
2418:
2417:
2413:
2406:
2393:
2392:
2388:
2381:
2365:
2364:
2360:
2345:
2332:
2331:
2327:
2285:
2284:
2280:
2273:
2256:
2251:
2248:
2247:
2246:
2244:
2239:
2236:
2235:
2234:
2232:
2227:
2224:
2223:
2222:
2220:
2215:
2212:
2211:
2210:
2208:
2203:
2200:
2199:
2198:
2196:
2191:
2188:
2187:
2186:
2184:
2179:
2176:
2175:
2174:
2172:
2170:
2166:
2159:
2146:
2145:
2141:
2126:
2111:
2110:
2106:
2096:
2094:
2086:
2085:
2081:
2076:
2054:
2047:
2038:
2035:
2034:
2033:
1974:
1963:
1962:
1952:
1935:
1914:
1867:
1853:
1849:
1848:
1847:, where α = 0,
1804:
1794:
1771:
1770:
1761:
1723:
1712:
1711:
1656:
1630:
1629:
1580:
1500:
1489:
1469:
1461:
1440:
1430:
1406:
1405:
1399:
1395:
1369:
1358:
1342:
1332:
1308:
1307:
1282:
1281:
1272:Eyring equation
1230:
1192:
1161:
1143:
1110:
1102:
1088:
1087:
1047:
1039:
1016:
1015:
998:
987:
971:Planck constant
930:
919:
898:
897:
875:
874:
873:
846:
838:
837:
835:
812:
804:
803:
801:
777:
758:
742:
733:
732:
731:
703:
702:
671:
648:
643:
642:
639:
625:
622:
621:
620:
618:
613:
610:
609:
608:
606:
601:
598:
597:
596:
594:
589:
586:
585:
584:
582:
577:
574:
573:
572:
570:
545:
540:
539:
485:
474:
473:
470:
462:
432:
427:
426:
383:
372:
371:
368:
360:
333:
328:
327:
295:
284:
283:
280:
266:elementary step
262:
182:
181:
179:
156:
138:
116:
115:
77:
35:
34:
32:
17:
12:
11:
5:
2639:
2637:
2629:
2628:
2618:
2617:
2612:
2611:
2584:(14): 145104.
2568:
2561:
2543:
2508:
2463:
2444:
2430:978-0471893691
2429:
2411:
2404:
2386:
2379:
2358:
2343:
2325:
2278:
2271:
2249:
2237:
2225:
2213:
2207:(e.g., 2 NO +
2201:
2189:
2177:
2164:
2157:
2139:
2125:978-0060440848
2124:
2104:
2078:
2077:
2075:
2072:
2071:
2070:
2065:
2060:
2053:
2050:
2045:
2036:
2013:
2010:
2003:
2000:
1995:
1991:
1985:
1982:
1977:
1973:
1970:
1951:
1948:
1934:
1931:
1913:
1910:
1909:
1908:
1905:
1902:
1899:
1896:
1893:
1866:
1863:
1828:
1825:
1821:
1817:
1814:
1811:
1807:
1801:
1797:
1793:
1790:
1787:
1784:
1781:
1778:
1760:
1757:
1738:
1734:
1730:
1726:
1722:
1719:
1685:
1680:
1677:
1673:
1669:
1666:
1663:
1659:
1655:
1652:
1649:
1646:
1643:
1640:
1637:
1578:
1525:
1520:
1517:
1513:
1507:
1503:
1499:
1496:
1492:
1486:
1482:
1476:
1472:
1468:
1464:
1459:
1453:
1450:
1447:
1443:
1437:
1433:
1429:
1424:
1420:
1414:
1409:
1402:
1398:
1394:
1389:
1386:
1382:
1376:
1372:
1368:
1365:
1361:
1355:
1352:
1349:
1345:
1339:
1335:
1331:
1326:
1322:
1316:
1311:
1304:
1301:
1298:
1295:
1292:
1289:
1228:
1190:
1173:
1168:
1164:
1159:
1155:
1150:
1146:
1141:
1137:
1132:
1129:
1125:
1118:
1113:
1109:
1105:
1101:
1098:
1095:
1069:
1066:
1062:
1055:
1050:
1046:
1042:
1038:
1035:
1032:
1029:
1026:
1023:
997:
994:
985:
950:
947:
943:
937:
933:
929:
926:
922:
916:
912:
906:
901:
894:
891:
888:
885:
882:
853:
849:
845:
819:
815:
811:
784:
780:
776:
773:
770:
765:
761:
757:
754:
749:
745:
741:
719:
716:
713:
710:
684:
680:
677:
674:
668:
663:
659:
655:
651:
638:
635:
629:→ 2 HI in the
623:
611:
599:
587:
575:
552:
548:
527:
523:
519:
516:
512:
508:
505:
501:
497:
492:
488:
484:
481:
468:
460:
439:
435:
414:
410:
406:
403:
399:
395:
390:
386:
382:
379:
366:
358:
340:
336:
315:
311:
307:
302:
298:
294:
291:
278:
261:
258:
217:The exponents
189:
163:
159:
154:
150:
145:
141:
136:
132:
129:
126:
123:
106:
105:
87:
86:C is a product
84:
64:
42:
15:
13:
10:
9:
6:
4:
3:
2:
2638:
2627:
2624:
2623:
2621:
2607:
2603:
2599:
2595:
2591:
2587:
2583:
2579:
2572:
2569:
2564:
2558:
2554:
2547:
2544:
2539:
2535:
2531:
2527:
2523:
2519:
2518:J. Chem. Phys
2512:
2509:
2504:
2500:
2496:
2492:
2488:
2484:
2477:
2470:
2468:
2464:
2459:
2455:
2448:
2445:
2440:
2436:
2432:
2426:
2422:
2415:
2412:
2407:
2405:0-13-737123-3
2401:
2397:
2390:
2387:
2382:
2380:0-06-043862-2
2376:
2372:
2368:
2362:
2359:
2354:
2350:
2346:
2344:9780495387039
2340:
2336:
2329:
2326:
2321:
2317:
2313:
2309:
2305:
2301:
2297:
2293:
2289:
2282:
2279:
2274:
2268:
2264:
2260:
2168:
2165:
2160:
2154:
2150:
2143:
2140:
2135:
2131:
2127:
2121:
2117:
2116:
2108:
2105:
2093:
2089:
2083:
2080:
2073:
2069:
2066:
2064:
2061:
2059:
2058:Reaction rate
2056:
2055:
2051:
2049:
2044:
2032:
2027:
1993:
1989:
1975:
1971:
1968:
1960:
1958:
1957:saddle domain
1949:
1947:
1945:
1941:
1932:
1930:
1928:
1924:
1920:
1911:
1906:
1903:
1900:
1897:
1894:
1891:
1887:
1883:
1882:
1881:
1879:
1874:
1872:
1864:
1862:
1860:
1846:
1841:
1826:
1823:
1819:
1815:
1809:
1805:
1799:
1795:
1791:
1788:
1782:
1776:
1768:
1766:
1758:
1756:
1754:
1736:
1732:
1728:
1724:
1720:
1717:
1709:
1705:
1701:
1696:
1683:
1678:
1675:
1671:
1667:
1661:
1657:
1653:
1650:
1647:
1641:
1635:
1627:
1625:
1620:
1616:
1614:
1610:
1606:
1602:
1598:
1594:
1589:
1587:
1583:
1577:
1573:
1569:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1536:
1523:
1518:
1515:
1511:
1505:
1501:
1494:
1490:
1484:
1480:
1474:
1470:
1462:
1457:
1451:
1448:
1445:
1435:
1431:
1422:
1418:
1407:
1400:
1396:
1392:
1387:
1384:
1380:
1374:
1370:
1363:
1359:
1353:
1350:
1347:
1337:
1333:
1324:
1320:
1309:
1302:
1299:
1293:
1287:
1279:
1277:
1273:
1269:
1264:
1262:
1258:
1254:
1250:
1246:
1242:
1238:
1234:
1231:to vary with
1227:
1223:
1219:
1216:
1212:
1208:
1204:
1200:
1196:
1189:
1184:
1171:
1166:
1148:
1130:
1127:
1123:
1111:
1107:
1103:
1099:
1096:
1093:
1085:
1082:
1067:
1064:
1060:
1048:
1044:
1040:
1036:
1033:
1027:
1021:
1013:
1011:
1010:reaction rate
1007:
1003:
995:
993:
991:
984:
980:
976:
972:
968:
948:
945:
941:
935:
931:
924:
920:
914:
910:
899:
892:
886:
880:
871:
851:
847:
834:and entropic
817:
813:
782:
778:
771:
768:
763:
759:
752:
747:
743:
714:
708:
700:
682:
678:
675:
672:
666:
661:
657:
653:
649:
636:
634:
632:
566:
550:
546:
490:
486:
482:
479:
469:A + B + C → P
467:
464:
459:
455:
437:
433:
388:
384:
380:
377:
365:
362:
357:
338:
334:
300:
296:
292:
289:
277:
275:
271:
267:
259:
257:
255:
251:
246:
244:
240:
236:
232:
228:
224:
220:
215:
213:
209:
205:
187:
176:
161:
143:
127:
124:
121:
113:
111:
110:reaction rate
103:
99:
95:
91:
88:
85:
82:
81:
80:
75:
71:
67:
63:
60:
58:
40:
30:
26:
22:
2581:
2577:
2571:
2552:
2546:
2521:
2517:
2511:
2486:
2482:
2457:
2447:
2420:
2414:
2395:
2389:
2370:
2361:
2334:
2328:
2298:(1): 73–78.
2295:
2291:
2287:
2281:
2262:
2167:
2148:
2142:
2114:
2107:
2095:. Retrieved
2091:
2082:
2068:Molecularity
2042:
2030:
2028:
1961:
1956:
1953:
1936:
1915:
1889:
1885:
1875:
1868:
1858:
1844:
1842:
1769:
1764:
1762:
1752:
1707:
1703:
1699:
1697:
1628:
1621:
1617:
1613:fudge factor
1604:
1600:
1596:
1592:
1591:The factor (
1590:
1585:
1581:
1575:
1571:
1567:
1563:
1559:
1555:
1551:
1547:
1539:
1537:
1280:
1265:
1260:
1256:
1252:
1248:
1244:
1236:
1232:
1225:
1217:
1210:
1206:
1203:gas constant
1198:
1187:
1185:
1086:
1083:
1014:
999:
989:
982:
974:
966:
640:
567:
471:
465:
463:≤ ~10 Ms.
457:
369:
363:
355:
281:
269:
263:
253:
249:
247:
238:
234:
230:
222:
218:
216:
177:
114:
107:
97:
93:
89:
78:
73:
69:
65:
61:
28:
24:
18:
2524:(6): 2959.
2288:Bimolecular
1944:Milestoning
1884:For order (
1215:temperature
361:≤ ~10 s.
2074:References
1929:software.
72: B →
68: A +
2353:220756597
2320:0021-9606
1994:α
1990:⋅
1813:Δ
1810:−
1800:α
1721:∝
1665:Δ
1662:−
1506:‡
1498:Δ
1495:−
1475:‡
1467:Δ
1449:−
1436:⊖
1401:κ
1375:‡
1367:Δ
1364:−
1351:−
1338:⊖
1303:κ
1108:−
1045:−
936:‡
928:Δ
925:−
852:‡
844:Δ
818:‡
810:Δ
783:‡
775:Δ
769:−
764:‡
756:Δ
748:‡
740:Δ
676:
454:diffusion
367:A + B → P
2620:Category
2606:17444753
2503:26580187
2369:(1987).
2134:14214254
2052:See also
1008:and the
538:, where
425:, where
326:, where
268:, there
229:and are
212:assuming
2586:Bibcode
2526:Bibcode
2439:9894996
2300:Bibcode
1852:⁄
1544:entropy
1538:where Δ
1239:is the
1201:is the
1193:is the
969:is the
264:For an
200:
180:
76: C
53:
33:
2604:
2559:
2501:
2437:
2427:
2402:
2377:
2351:
2341:
2318:
2269:
2155:
2132:
2122:
2029:where
1942:, and
1698:where
1259:Units
1205:, and
1197:, and
1186:where
965:where
96:, and
79:where
2479:(PDF)
2097:5 May
1878:units
1865:Units
1274:from
1261:below
279:A → P
208:moles
178:Here
2602:PMID
2557:ISBN
2499:PMID
2435:OCLC
2425:ISBN
2400:ISBN
2375:ISBN
2349:OCLC
2339:ISBN
2316:ISSN
2267:ISBN
2245:NOCl
2233:NOCl
2153:ISBN
2130:OCLC
2120:ISBN
2099:2018
1209:and
1000:The
977:the
973:and
237:and
221:and
108:the
100:are
23:, a
2594:doi
2582:126
2534:doi
2491:doi
2308:doi
2195:or
1921:or
1562:= Δ
1263:).
1257:see
986:1/2
872:is
231:not
27:or
19:In
2622::
2600:.
2592:.
2580:.
2532:.
2522:68
2520:.
2497:.
2487:10
2485:.
2481:.
2466:^
2456:.
2433:.
2347:.
2314:.
2306:.
2296:46
2294:.
2261:.
2243:,
2231:⇄
2221:Cl
2209:Cl
2185:Br
2183:,
2173:Cl
2128:.
2090:.
2046:SD
2037:RS
1888:+
1873:.
1566:−
1278::
1251:+
697:.
673:ln
605:+
593:→
581:+
270:is
252:+
92:,
2608:.
2596::
2588::
2565:.
2540:.
2536::
2528::
2505:.
2493::
2460:.
2441:.
2408:.
2383:.
2355:.
2322:.
2310::
2302::
2275:.
2250:2
2238:2
2226:2
2214:2
2202:2
2197:O
2190:2
2178:2
2161:.
2136:.
2101:.
2043:k
2031:α
2012:D
2009:S
2002:S
1999:R
1984:D
1981:S
1976:k
1972:=
1969:k
1890:n
1886:m
1859:E
1854:2
1850:1
1845:C
1827:T
1824:R
1820:/
1816:E
1806:e
1796:T
1792:C
1789:=
1786:)
1783:T
1780:(
1777:k
1765:k
1753:k
1737:2
1733:/
1729:1
1725:T
1718:Z
1708:E
1704:Z
1700:P
1684:,
1679:T
1676:R
1672:/
1668:E
1658:e
1654:Z
1651:P
1648:=
1645:)
1642:T
1639:(
1636:k
1605:M
1601:c
1597:c
1593:c
1586:h
1584:/
1582:T
1579:B
1576:k
1572:S
1570:Δ
1568:T
1564:H
1560:G
1556:S
1552:H
1548:G
1540:G
1524:,
1519:T
1516:R
1512:/
1502:H
1491:e
1485:R
1481:/
1471:S
1463:e
1458:)
1452:M
1446:1
1442:)
1432:c
1428:(
1423:h
1419:T
1413:B
1408:k
1397:(
1393:=
1388:T
1385:R
1381:/
1371:G
1360:e
1354:M
1348:1
1344:)
1334:c
1330:(
1325:h
1321:T
1315:B
1310:k
1300:=
1297:)
1294:T
1291:(
1288:k
1253:n
1249:m
1245:A
1237:A
1233:e
1229:a
1226:E
1218:T
1211:n
1207:m
1199:R
1191:a
1188:E
1172:,
1167:n
1163:]
1158:B
1154:[
1149:m
1145:]
1140:A
1136:[
1131:T
1128:R
1124:/
1117:a
1112:E
1104:e
1100:A
1097:=
1094:r
1068:T
1065:R
1061:/
1054:a
1049:E
1041:e
1037:A
1034:=
1031:)
1028:T
1025:(
1022:k
990:G
983:t
975:R
967:h
963:,
949:T
946:R
942:/
932:G
921:e
915:h
911:T
905:B
900:k
893:=
890:)
887:T
884:(
881:k
866:)
848:S
836:(
832:)
814:H
802:(
798:,
779:S
772:T
760:H
753:=
744:G
718:)
715:T
712:(
709:k
683:k
679:2
667:=
662:2
658:/
654:1
650:t
624:2
619:H
612:2
607:N
600:3
595:O
588:2
583:N
576:2
571:O
551:3
547:k
526:]
522:C
518:[
515:]
511:B
507:[
504:]
500:A
496:[
491:3
487:k
483:=
480:r
461:2
458:k
438:2
434:k
413:]
409:B
405:[
402:]
398:A
394:[
389:2
385:k
381:=
378:r
359:1
356:k
339:1
335:k
314:]
310:A
306:[
301:1
297:k
293:=
290:r
254:n
250:m
239:b
235:a
223:n
219:m
188:k
162:n
158:]
153:B
149:[
144:m
140:]
135:A
131:[
128:k
125:=
122:r
104:,
98:c
94:b
90:a
74:c
70:b
66:a
41:k
31:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.