1872:, 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.
1545:
1637:, 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:
1294:
1629:
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
579:
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
1948:
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
364:
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
1965:
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
1540:{\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},}
1927:
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
1254:, 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,
807:
2036:
972:
580:
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 +
1193:
1850:
1091:
2059:
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
463:
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
1705:
706:
875:
841:
2230:→ 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 +
652:
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:
1760:
185:
2587:
West, Anthony M.A.; Elber, Ron; Shalloway, David (2007). "Extending molecular dynamics time scales with milestoning: Example of complex kinetics in a solvated peptide".
644:. 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).
1975:
547:
434:
335:
225:
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.)
574:
461:
362:
1949:
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
739:
811:
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
209:
62:
2124:
1585:. In effect, the free energy of activation takes into account both the activation energy and the likelihood of successful collision, while the factor
745:
887:
2571:
2281:
2167:
1100:
999:) of approximately 2 hours. For a one-step process taking place at room temperature, the corresponding Gibbs free energy of activation (Δ
1783:
2439:
2134:
2414:
2389:
2353:
1028:
1606:) ensures the dimensional correctness of the rate constant when the transition state in question is bimolecular or higher. Here,
1868:, and 1 give Arrhenius theory, collision theory, and transition state theory, respectively, although the imprecise notion of Δ
1642:
2527:
Chandler, David (1978). "Statistical mechanics of isomerization dynamics in liquids and the transition state approximation".
2486:
2636:
112:
128:
1950:
1619:
1023:
at which a reaction proceeds. The rate constant as a function of thermodynamic temperature is then given by:
1286:
709:
655:
1251:
1232:
850:
816:
2348:. Treichel, Paul., Townsend, John R. (7th ed.). Belmont, Calif.: Thomson Brooks/ Cole. p. 703.
1554:
1278:
992:. As useful rules of thumb, a first-order reaction with a rate constant of 10 s will have a half-life (
1724:
2596:
2536:
2464:
2310:
2073:
1936:. First-principle based models should be used for such calculation. It can be done with the help of
2098:
1937:
1888:
214:
1954:
1610:
is the standard concentration, generally chosen based on the unit of concentration used (usually
1012:
989:
284:
253:
237:
287:. Almost all elementary steps are either unimolecular or bimolecular. For a unimolecular step
1618:
is the molecularity of the transition state. Lastly, κ, usually set to unity, is known as the
2612:
2567:
2509:
2445:
2435:
2410:
2385:
2359:
2349:
2326:
2277:
2269:
2163:
2140:
2130:
1881:
1205:
1016:
67:
31:
1015:
is an elementary treatment that gives the quantitative basis of the relationship between the
486:
384:
296:
2604:
2544:
2501:
2377:
2318:
1933:
1929:
1634:
552:
439:
340:
1282:
981:
880:
715:
641:
2600:
2540:
2314:
222:
194:
47:
1553:
is the free energy of activation, a parameter that incorporates both the enthalpy and
2630:
2068:
1020:
276:
120:
2078:
1623:
1213:
802:{\displaystyle {\Delta G^{\ddagger }=\Delta H^{\ddagger }-T\Delta S^{\ddagger }}}
2031:{\displaystyle k=k_{\mathrm {SD} }\cdot \alpha _{\mathrm {RS} }^{\mathrm {SD} }}
1225:
218:
1224:
are experimentally determined partial orders in and , respectively. Since at
2363:
2330:
2129:. Richardson, Kathleen Schueller (3rd ed.). New York: Harper & Row.
2052:
is the conversion factor between the reactant state and saddle domain, while
1557:
change needed to reach the transition state. The temperature dependence of Δ
213:
is the reaction rate constant that depends on temperature, and and are the
66:) is a proportionality constant which quantifies the rate and direction of a
17:
2144:
967:{\textstyle k(T)={\frac {k_{\mathrm {B} }T}{h}}e^{-\Delta G^{\ddagger }/RT}}
464:
2616:
2513:
2449:
283:
a relationship between stoichiometry and rate law, as determined by the
2276:. Comprehensive Chemical Kinetics. Vol. 6. Elsevier. p. 174.
1721:
is energy input required to overcome the activation barrier. Of note,
1235:, one can expect the proportion of collisions with energy greater than
467:. Thus, in general, a bimolecular rate constant has an upper limit of
2608:
2505:
2405:
Steinfeld, Jeffrey I.; Francisco, Joseph S.; Hase, William L. (1999).
2322:
2548:
2270:"5. Reactions of the Oxides of Nitrogen §5.5 Reactions with Chlorine"
879:
changes that need to be achieved for the reaction to take place: The
2564:
Algorithms for
Chemical Computations, ACS Symposium Series No. 46
2487:"Divided Saddle Theory: A New Idea for Rate Constant Calculation"
1561:
is used to compute these parameters, the enthalpy of activation Δ
1915:
For order three, the rate constant has units of L·mol·s (or M·s)
1918:
For order four, the rate constant has units of L·mol·s (or M·s)
1906:
For order zero, the rate constant has units of mol·L·s (or M·s)
1277:
Another popular model that is derived using more sophisticated
628:. One well-established example is the termolecular step 2 I +
1912:
For order two, the rate constant has units of L·mol·s (or M·s)
73:
For a reaction between reactants A and B to form a product C,
2268:
Compton, R.G.; Bamford, C. H.; Tipper, C.F.H., eds. (2014) .
2182:
The reactions of nitric oxide with the diatomic molecules
1957:
have also been developed for rate constant calculations.
1774:
All three theories model the temperature dependence of
1766:
different from both the
Arrhenius and Eyring models.
890:
658:
1978:
1880:
The units of the rate constant depend on the overall
1786:
1727:
1645:
1297:
1103:
1031:
853:
819:
748:
718:
555:
489:
442:
387:
343:
299:
197:
131:
50:
1970:, is introduced, and the rate constant is factored:
1188:{\displaystyle r=Ae^{-E_{\mathrm {a} }/RT}^{m}^{n},}
70:
by relating it with the concentration of reactants.
244:generally equal to the stoichiometric coefficients
2297:Sullivan, John H. (1967-01-01). "Mechanism of the
2030:
1903:), the rate constant has units of mol·L·s (or M·s)
1844:
1754:
1699:
1539:
1187:
1085:
966:
869:
835:
801:
733:
700:
568:
541:
455:
428:
356:
329:
203:
179:
56:
2562:Bennett, C. H. (1977). Christofferson, R. (ed.).
1845:{\displaystyle k(T)=CT^{\alpha }e^{-\Delta E/RT}}
1599:gives the frequency of molecular collision.
2566:. Washington, D.C.: American Chemical Society.
2384:(3rd ed.). Harper & Row. p. 113.
1909:For order one, the rate constant has units of s
712:gives a relationship between the rate constant
1086:{\displaystyle k(T)=Ae^{-E_{\mathrm {a} }/RT}}
2274:Reactions of Non-metallic Inorganic Compounds
1622:, a parameter which essentially serves as a "
8:
2432:Determination of organic reaction mechanisms
2409:(2nd ed.). Prentice Hall. p. 301.
2162:(3rd ed.). John Wiley. pp. 226–7.
1891:of mol·L (sometimes abbreviated as M), then
1231:the molecules have energies according to a
267:) is called the overall order of reaction.
2158:Moore, John W.; Pearson, Ralph G. (1981).
1713:is the steric (or probability) factor and
27:Coefficient of rate of a chemical reaction
2126:Mechanism and theory in organic chemistry
2018:
2017:
2008:
2007:
1990:
1989:
1977:
1829:
1819:
1809:
1785:
1742:
1738:
1726:
1681:
1671:
1644:
1521:
1515:
1504:
1490:
1484:
1476:
1455:
1445:
1422:
1421:
1414:
1390:
1384:
1373:
1357:
1347:
1324:
1323:
1316:
1296:
1176:
1167:
1158:
1149:
1133:
1126:
1125:
1117:
1102:
1070:
1063:
1062:
1054:
1030:
951:
945:
934:
914:
913:
906:
889:
861:
852:
827:
818:
792:
773:
757:
749:
747:
717:
680:
667:
663:
657:
560:
554:
531:
520:
509:
500:
488:
447:
441:
418:
407:
398:
386:
348:
342:
319:
310:
298:
196:
171:
162:
153:
144:
130:
49:
1700:{\displaystyle k(T)=PZe^{-\Delta E/RT},}
741:and the Gibbs free energy of activation
2090:
1762:, making the temperature dependence of
701:{\textstyle t_{1/2}={\frac {\ln 2}{k}}}
256:and can be determined experimentally.
2485:Daru, János; Stirling, András (2014).
2480:
2478:
7:
870:{\displaystyle \Delta S^{\ddagger }}
836:{\displaystyle \Delta H^{\ddagger }}
2346:Chemistry & chemical reactivity
881:result from transition state theory
2022:
2019:
2012:
2009:
1994:
1991:
1823:
1675:
1626:" for transition state theory.
1508:
1477:
1423:
1377:
1325:
1246:. The constant of proportionality
1168:
1150:
1127:
1064:
938:
915:
854:
820:
785:
766:
750:
532:
521:
510:
483:the reaction rate is described by
419:
408:
381:the reaction rate is described by
320:
293:the reaction rate is described by
163:
145:
25:
1717:is the collision frequency, and Δ
1569:, based on the defining formula Δ
576:is a termolecular rate constant.
123:is often found to have the form:
1887:If concentration is measured in
1755:{\displaystyle Z\propto T^{1/2}}
1003:) is approximately 23 kcal/mol.
648:Relationship to other parameters
2589:The Journal of Chemical Physics
2303:The Journal of Chemical Physics
1630:only a single elementary step.
1565:and the entropy of activation Δ
1258:has the same dimensions as an (
1095:The reaction rate is given by:
2407:Chemical Kinetics and Dynamics
1796:
1790:
1778:using an equation of the form
1655:
1649:
1452:
1438:
1354:
1340:
1307:
1301:
1173:
1164:
1155:
1146:
1041:
1035:
900:
894:
728:
722:
536:
528:
525:
517:
514:
506:
423:
415:
412:
404:
324:
316:
168:
159:
150:
141:
1:
252:. Instead they depend on the
221:per unit volume of solution,
2430:Carpenter, Barry K. (1984).
2301:Hydrogen—Iodine Reaction".
180:{\displaystyle r=k^{m}^{n}}
113:stoichiometric coefficients
2653:
1951:Bennett Chandler procedure
1944:Rate constant calculations
259:Sum of m and n, that is, (
2123:Lowry, Thomas H. (1987).
2099:"Chemical Kinetics Notes"
1007:Dependence on temperature
217:of substances A and B in
40:reaction rate coefficient
2465:"Differential Rate Laws"
1620:transmission coefficient
642:hydrogen-iodine reaction
477:For a termolecular step
1287:transition state theory
1266:)-order rate constant (
710:Transition state theory
542:{\displaystyle r=k_{3}}
429:{\displaystyle r=k_{2}}
375:For a bimolecular step
330:{\displaystyle r=k_{1}}
2494:J. Chem. Theory Comput
2344:Kotz, John C. (2009).
2160:Kinetics and Mechanism
2032:
1846:
1756:
1701:
1633:Finally, in the past,
1614:= 1 mol L = 1 M), and
1541:
1281:considerations is the
1279:statistical mechanical
1252:pre-exponential factor
1233:Boltzmann distribution
1189:
1087:
968:
871:
837:
803:
735:
702:
570:
543:
457:
430:
358:
331:
205:
181:
58:
36:reaction rate constant
2266:+ NO → 2 NOCl). See:
2033:
1961:Divided saddle theory
1847:
1757:
1702:
1542:
1190:
1088:
969:
872:
838:
804:
736:
703:
571:
569:{\displaystyle k_{3}}
544:
458:
456:{\displaystyle k_{2}}
431:
359:
357:{\displaystyle k_{1}}
332:
206:
182:
94:A and B are reactants
59:
2103:www.chem.arizona.edu
2074:Equilibrium constant
1976:
1784:
1770:Comparison of models
1725:
1643:
1295:
1101:
1029:
888:
851:
817:
746:
734:{\displaystyle k(T)}
716:
656:
553:
487:
440:
385:
341:
297:
215:molar concentrations
195:
129:
48:
2601:2007JChPh.126n5104W
2541:1978JChPh..68.2959C
2434:. New York: Wiley.
2315:1967JChPh..46...73S
2027:
1938:computer simulation
236:are called partial
2028:
2003:
1854:for some constant
1842:
1752:
1697:
1537:
1185:
1083:
1013:Arrhenius equation
990:molar gas constant
964:
867:
833:
799:
731:
698:
566:
539:
453:
426:
354:
327:
285:law of mass action
254:reaction mechanism
238:orders of reaction
201:
177:
54:
2637:Chemical kinetics
2609:10.1063/1.2716389
2573:978-0-8412-0371-6
2506:10.1021/ct400970y
2469:Chemical Kinetics
2382:Chemical Kinetics
2378:Laidler, Keith J.
2323:10.1063/1.1840433
2283:978-0-08-086801-1
2169:978-0-471-03558-9
1882:order of reaction
1436:
1338:
1206:activation energy
1017:activation energy
928:
696:
204:{\displaystyle k}
68:chemical reaction
57:{\displaystyle k}
32:chemical kinetics
16:(Redirected from
2644:
2621:
2620:
2584:
2578:
2577:
2559:
2553:
2552:
2549:10.1063/1.436049
2524:
2518:
2517:
2500:(3): 1121–1127.
2491:
2482:
2473:
2472:
2460:
2454:
2453:
2427:
2421:
2420:
2402:
2396:
2395:
2374:
2368:
2367:
2341:
2335:
2334:
2294:
2288:
2287:
2265:
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2251:
2241:
2240:
2239:
2229:
2228:
2227:
2217:
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2205:
2204:
2203:
2193:
2192:
2191:
2180:
2174:
2173:
2155:
2149:
2148:
2120:
2114:
2113:
2111:
2109:
2095:
2051:
2050:
2037:
2035:
2034:
2029:
2026:
2025:
2016:
2015:
1999:
1998:
1997:
1934:microelectronics
1930:plasma chemistry
1923:Plasma and gases
1867:
1866:
1862:
1851:
1849:
1848:
1843:
1841:
1840:
1833:
1814:
1813:
1761:
1759:
1758:
1753:
1751:
1750:
1746:
1706:
1704:
1703:
1698:
1693:
1692:
1685:
1635:collision theory
1546:
1544:
1543:
1538:
1533:
1532:
1525:
1520:
1519:
1499:
1498:
1494:
1489:
1488:
1471:
1467:
1466:
1465:
1450:
1449:
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1432:
1428:
1427:
1426:
1415:
1402:
1401:
1394:
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1388:
1368:
1367:
1352:
1351:
1339:
1334:
1330:
1329:
1328:
1317:
1194:
1192:
1191:
1186:
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1180:
1171:
1163:
1162:
1153:
1145:
1144:
1137:
1132:
1131:
1130:
1092:
1090:
1089:
1084:
1082:
1081:
1074:
1069:
1068:
1067:
975:
973:
971:
970:
965:
963:
962:
955:
950:
949:
929:
924:
920:
919:
918:
907:
878:
876:
874:
873:
868:
866:
865:
844:
842:
840:
839:
834:
832:
831:
810:
808:
806:
805:
800:
798:
797:
796:
778:
777:
762:
761:
740:
738:
737:
732:
707:
705:
704:
699:
697:
692:
681:
676:
675:
671:
639:
638:
637:
627:
626:
625:
615:
614:
613:
603:
602:
601:
591:
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572:
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564:
548:
546:
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540:
535:
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513:
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504:
462:
460:
459:
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452:
451:
435:
433:
432:
427:
422:
411:
403:
402:
363:
361:
360:
355:
353:
352:
336:
334:
333:
328:
323:
315:
314:
271:Elementary steps
212:
210:
208:
207:
202:
186:
184:
183:
178:
176:
175:
166:
158:
157:
148:
65:
63:
61:
60:
55:
21:
2652:
2651:
2647:
2646:
2645:
2643:
2642:
2641:
2627:
2626:
2625:
2624:
2586:
2585:
2581:
2574:
2561:
2560:
2556:
2526:
2525:
2521:
2489:
2484:
2483:
2476:
2463:Blauch, David.
2462:
2461:
2457:
2442:
2429:
2428:
2424:
2417:
2404:
2403:
2399:
2392:
2376:
2375:
2371:
2356:
2343:
2342:
2338:
2296:
2295:
2291:
2284:
2267:
2262:
2259:
2258:
2257:
2255:
2250:
2247:
2246:
2245:
2243:
2238:
2235:
2234:
2233:
2231:
2226:
2223:
2222:
2221:
2219:
2214:
2211:
2210:
2209:
2207:
2202:
2199:
2198:
2197:
2195:
2190:
2187:
2186:
2185:
2183:
2181:
2177:
2170:
2157:
2156:
2152:
2137:
2122:
2121:
2117:
2107:
2105:
2097:
2096:
2092:
2087:
2065:
2058:
2049:
2046:
2045:
2044:
1985:
1974:
1973:
1963:
1946:
1925:
1878:
1864:
1860:
1859:
1858:, where α = 0,
1815:
1805:
1782:
1781:
1772:
1734:
1723:
1722:
1667:
1641:
1640:
1591:
1511:
1500:
1480:
1472:
1451:
1441:
1417:
1416:
1410:
1406:
1380:
1369:
1353:
1343:
1319:
1318:
1293:
1292:
1283:Eyring equation
1241:
1203:
1172:
1154:
1121:
1113:
1099:
1098:
1058:
1050:
1027:
1026:
1009:
998:
982:Planck constant
941:
930:
909:
908:
886:
885:
884:
857:
849:
848:
846:
823:
815:
814:
812:
788:
769:
753:
744:
743:
742:
714:
713:
682:
659:
654:
653:
650:
636:
633:
632:
631:
629:
624:
621:
620:
619:
617:
612:
609:
608:
607:
605:
600:
597:
596:
595:
593:
588:
585:
584:
583:
581:
556:
551:
550:
496:
485:
484:
481:
473:
443:
438:
437:
394:
383:
382:
379:
371:
344:
339:
338:
306:
295:
294:
291:
277:elementary step
273:
193:
192:
190:
167:
149:
127:
126:
88:
46:
45:
43:
28:
23:
22:
15:
12:
11:
5:
2650:
2648:
2640:
2639:
2629:
2628:
2623:
2622:
2595:(14): 145104.
2579:
2572:
2554:
2519:
2474:
2455:
2441:978-0471893691
2440:
2422:
2415:
2397:
2390:
2369:
2354:
2336:
2289:
2282:
2260:
2248:
2236:
2224:
2218:(e.g., 2 NO +
2212:
2200:
2188:
2175:
2168:
2150:
2136:978-0060440848
2135:
2115:
2089:
2088:
2086:
2083:
2082:
2081:
2076:
2071:
2064:
2061:
2056:
2047:
2024:
2021:
2014:
2011:
2006:
2002:
1996:
1993:
1988:
1984:
1981:
1962:
1959:
1945:
1942:
1924:
1921:
1920:
1919:
1916:
1913:
1910:
1907:
1904:
1877:
1874:
1839:
1836:
1832:
1828:
1825:
1822:
1818:
1812:
1808:
1804:
1801:
1798:
1795:
1792:
1789:
1771:
1768:
1749:
1745:
1741:
1737:
1733:
1730:
1696:
1691:
1688:
1684:
1680:
1677:
1674:
1670:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1589:
1536:
1531:
1528:
1524:
1518:
1514:
1510:
1507:
1503:
1497:
1493:
1487:
1483:
1479:
1475:
1470:
1464:
1461:
1458:
1454:
1448:
1444:
1440:
1435:
1431:
1425:
1420:
1413:
1409:
1405:
1400:
1397:
1393:
1387:
1383:
1379:
1376:
1372:
1366:
1363:
1360:
1356:
1350:
1346:
1342:
1337:
1333:
1327:
1322:
1315:
1312:
1309:
1306:
1303:
1300:
1239:
1201:
1184:
1179:
1175:
1170:
1166:
1161:
1157:
1152:
1148:
1143:
1140:
1136:
1129:
1124:
1120:
1116:
1112:
1109:
1106:
1080:
1077:
1073:
1066:
1061:
1057:
1053:
1049:
1046:
1043:
1040:
1037:
1034:
1008:
1005:
996:
961:
958:
954:
948:
944:
940:
937:
933:
927:
923:
917:
912:
905:
902:
899:
896:
893:
864:
860:
856:
830:
826:
822:
795:
791:
787:
784:
781:
776:
772:
768:
765:
760:
756:
752:
730:
727:
724:
721:
695:
691:
688:
685:
679:
674:
670:
666:
662:
649:
646:
640:→ 2 HI in the
634:
622:
610:
598:
586:
563:
559:
538:
534:
530:
527:
523:
519:
516:
512:
508:
503:
499:
495:
492:
479:
471:
450:
446:
425:
421:
417:
414:
410:
406:
401:
397:
393:
390:
377:
369:
351:
347:
326:
322:
318:
313:
309:
305:
302:
289:
272:
269:
228:The exponents
200:
174:
170:
165:
161:
156:
152:
147:
143:
140:
137:
134:
117:
116:
98:
97:C is a product
95:
75:
53:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2649:
2638:
2635:
2634:
2632:
2618:
2614:
2610:
2606:
2602:
2598:
2594:
2590:
2583:
2580:
2575:
2569:
2565:
2558:
2555:
2550:
2546:
2542:
2538:
2534:
2530:
2529:J. Chem. Phys
2523:
2520:
2515:
2511:
2507:
2503:
2499:
2495:
2488:
2481:
2479:
2475:
2470:
2466:
2459:
2456:
2451:
2447:
2443:
2437:
2433:
2426:
2423:
2418:
2416:0-13-737123-3
2412:
2408:
2401:
2398:
2393:
2391:0-06-043862-2
2387:
2383:
2379:
2373:
2370:
2365:
2361:
2357:
2355:9780495387039
2351:
2347:
2340:
2337:
2332:
2328:
2324:
2320:
2316:
2312:
2308:
2304:
2300:
2293:
2290:
2285:
2279:
2275:
2271:
2179:
2176:
2171:
2165:
2161:
2154:
2151:
2146:
2142:
2138:
2132:
2128:
2127:
2119:
2116:
2104:
2100:
2094:
2091:
2084:
2080:
2077:
2075:
2072:
2070:
2069:Reaction rate
2067:
2066:
2062:
2060:
2055:
2043:
2038:
2004:
2000:
1986:
1982:
1979:
1971:
1969:
1968:saddle domain
1960:
1958:
1956:
1952:
1943:
1941:
1939:
1935:
1931:
1922:
1917:
1914:
1911:
1908:
1905:
1902:
1898:
1894:
1893:
1892:
1890:
1885:
1883:
1875:
1873:
1871:
1857:
1852:
1837:
1834:
1830:
1826:
1820:
1816:
1810:
1806:
1802:
1799:
1793:
1787:
1779:
1777:
1769:
1767:
1765:
1747:
1743:
1739:
1735:
1731:
1728:
1720:
1716:
1712:
1707:
1694:
1689:
1686:
1682:
1678:
1672:
1668:
1664:
1661:
1658:
1652:
1646:
1638:
1636:
1631:
1627:
1625:
1621:
1617:
1613:
1609:
1605:
1600:
1598:
1594:
1588:
1584:
1580:
1576:
1572:
1568:
1564:
1560:
1556:
1552:
1547:
1534:
1529:
1526:
1522:
1516:
1512:
1505:
1501:
1495:
1491:
1485:
1481:
1473:
1468:
1462:
1459:
1456:
1446:
1442:
1433:
1429:
1418:
1411:
1407:
1403:
1398:
1395:
1391:
1385:
1381:
1374:
1370:
1364:
1361:
1358:
1348:
1344:
1335:
1331:
1320:
1313:
1310:
1304:
1298:
1290:
1288:
1284:
1280:
1275:
1273:
1269:
1265:
1261:
1257:
1253:
1249:
1245:
1242:to vary with
1238:
1234:
1230:
1227:
1223:
1219:
1215:
1211:
1207:
1200:
1195:
1182:
1177:
1159:
1141:
1138:
1134:
1122:
1118:
1114:
1110:
1107:
1104:
1096:
1093:
1078:
1075:
1071:
1059:
1055:
1051:
1047:
1044:
1038:
1032:
1024:
1022:
1021:reaction rate
1018:
1014:
1006:
1004:
1002:
995:
991:
987:
983:
979:
959:
956:
952:
946:
942:
935:
931:
925:
921:
910:
903:
897:
891:
882:
862:
858:
845:and entropic
828:
824:
793:
789:
782:
779:
774:
770:
763:
758:
754:
725:
719:
711:
693:
689:
686:
683:
677:
672:
668:
664:
660:
647:
645:
643:
577:
561:
557:
501:
497:
493:
490:
480:A + B + C → P
478:
475:
470:
466:
448:
444:
399:
395:
391:
388:
376:
373:
368:
349:
345:
311:
307:
303:
300:
288:
286:
282:
278:
270:
268:
266:
262:
257:
255:
251:
247:
243:
239:
235:
231:
226:
224:
220:
216:
198:
187:
172:
154:
138:
135:
132:
124:
122:
121:reaction rate
114:
110:
106:
102:
99:
96:
93:
92:
91:
86:
82:
78:
74:
71:
69:
51:
41:
37:
33:
19:
18:Rate constant
2592:
2588:
2582:
2563:
2557:
2532:
2528:
2522:
2497:
2493:
2468:
2458:
2431:
2425:
2406:
2400:
2381:
2372:
2345:
2339:
2309:(1): 73–78.
2306:
2302:
2298:
2292:
2273:
2178:
2159:
2153:
2125:
2118:
2106:. Retrieved
2102:
2093:
2079:Molecularity
2053:
2041:
2039:
1972:
1967:
1964:
1947:
1926:
1900:
1896:
1886:
1879:
1869:
1855:
1853:
1780:
1775:
1773:
1763:
1718:
1714:
1710:
1708:
1639:
1632:
1628:
1624:fudge factor
1615:
1611:
1607:
1603:
1602:The factor (
1601:
1596:
1592:
1586:
1582:
1578:
1574:
1570:
1566:
1562:
1558:
1550:
1548:
1291:
1276:
1271:
1267:
1263:
1259:
1255:
1247:
1243:
1236:
1228:
1221:
1217:
1214:gas constant
1209:
1198:
1196:
1097:
1094:
1025:
1010:
1000:
993:
985:
977:
651:
578:
482:
476:
474:≤ ~10 Ms.
468:
380:
374:
366:
292:
280:
274:
264:
260:
258:
249:
245:
241:
233:
229:
227:
188:
125:
118:
108:
104:
100:
89:
84:
80:
76:
72:
39:
35:
29:
2535:(6): 2959.
2299:Bimolecular
1955:Milestoning
1895:For order (
1226:temperature
372:≤ ~10 s.
2085:References
1940:software.
83: B →
79: A +
2364:220756597
2331:0021-9606
2005:α
2001:⋅
1824:Δ
1821:−
1811:α
1732:∝
1676:Δ
1673:−
1517:‡
1509:Δ
1506:−
1486:‡
1478:Δ
1460:−
1447:⊖
1412:κ
1386:‡
1378:Δ
1375:−
1362:−
1349:⊖
1314:κ
1119:−
1056:−
947:‡
939:Δ
936:−
863:‡
855:Δ
829:‡
821:Δ
794:‡
786:Δ
780:−
775:‡
767:Δ
759:‡
751:Δ
687:
465:diffusion
378:A + B → P
2631:Category
2617:17444753
2514:26580187
2380:(1987).
2145:14214254
2063:See also
1019:and the
549:, where
436:, where
337:, where
279:, there
240:and are
223:assuming
2597:Bibcode
2537:Bibcode
2450:9894996
2311:Bibcode
1863:⁄
1555:entropy
1549:where Δ
1250:is the
1212:is the
1204:is the
980:is the
275:For an
211:
191:
87: C
64:
44:
2615:
2570:
2512:
2448:
2438:
2413:
2388:
2362:
2352:
2329:
2280:
2166:
2143:
2133:
2040:where
1953:, and
1709:where
1270:Units
1216:, and
1208:, and
1197:where
976:where
107:, and
90:where
2490:(PDF)
2108:5 May
1889:units
1876:Units
1285:from
1272:below
290:A → P
219:moles
189:Here
2613:PMID
2568:ISBN
2510:PMID
2446:OCLC
2436:ISBN
2411:ISBN
2386:ISBN
2360:OCLC
2350:ISBN
2327:ISSN
2278:ISBN
2256:NOCl
2244:NOCl
2164:ISBN
2141:OCLC
2131:ISBN
2110:2018
1220:and
1011:The
988:the
984:and
248:and
232:and
119:the
111:are
34:, a
2605:doi
2593:126
2545:doi
2502:doi
2319:doi
2206:or
1932:or
1573:= Δ
1274:).
1268:see
997:1/2
883:is
242:not
38:or
30:In
2633::
2611:.
2603:.
2591:.
2543:.
2533:68
2531:.
2508:.
2498:10
2496:.
2492:.
2477:^
2467:.
2444:.
2358:.
2325:.
2317:.
2307:46
2305:.
2272:.
2254:,
2242:⇄
2232:Cl
2220:Cl
2196:Br
2194:,
2184:Cl
2139:.
2101:.
2057:SD
2048:RS
1899:+
1884:.
1577:−
1289::
1262:+
708:.
684:ln
616:+
604:→
592:+
281:is
263:+
103:,
2619:.
2607::
2599::
2576:.
2551:.
2547::
2539::
2516:.
2504::
2471:.
2452:.
2419:.
2394:.
2366:.
2333:.
2321::
2313::
2286:.
2261:2
2249:2
2237:2
2225:2
2213:2
2208:O
2201:2
2189:2
2172:.
2147:.
2112:.
2054:k
2042:α
2023:D
2020:S
2013:S
2010:R
1995:D
1992:S
1987:k
1983:=
1980:k
1901:n
1897:m
1870:E
1865:2
1861:1
1856:C
1838:T
1835:R
1831:/
1827:E
1817:e
1807:T
1803:C
1800:=
1797:)
1794:T
1791:(
1788:k
1776:k
1764:k
1748:2
1744:/
1740:1
1736:T
1729:Z
1719:E
1715:Z
1711:P
1695:,
1690:T
1687:R
1683:/
1679:E
1669:e
1665:Z
1662:P
1659:=
1656:)
1653:T
1650:(
1647:k
1616:M
1612:c
1608:c
1604:c
1597:h
1595:/
1593:T
1590:B
1587:k
1583:S
1581:Δ
1579:T
1575:H
1571:G
1567:S
1563:H
1559:G
1551:G
1535:,
1530:T
1527:R
1523:/
1513:H
1502:e
1496:R
1492:/
1482:S
1474:e
1469:)
1463:M
1457:1
1453:)
1443:c
1439:(
1434:h
1430:T
1424:B
1419:k
1408:(
1404:=
1399:T
1396:R
1392:/
1382:G
1371:e
1365:M
1359:1
1355:)
1345:c
1341:(
1336:h
1332:T
1326:B
1321:k
1311:=
1308:)
1305:T
1302:(
1299:k
1264:n
1260:m
1256:A
1248:A
1244:e
1240:a
1237:E
1229:T
1222:n
1218:m
1210:R
1202:a
1199:E
1183:,
1178:n
1174:]
1169:B
1165:[
1160:m
1156:]
1151:A
1147:[
1142:T
1139:R
1135:/
1128:a
1123:E
1115:e
1111:A
1108:=
1105:r
1079:T
1076:R
1072:/
1065:a
1060:E
1052:e
1048:A
1045:=
1042:)
1039:T
1036:(
1033:k
1001:G
994:t
986:R
978:h
974:,
960:T
957:R
953:/
943:G
932:e
926:h
922:T
916:B
911:k
904:=
901:)
898:T
895:(
892:k
877:)
859:S
847:(
843:)
825:H
813:(
809:,
790:S
783:T
771:H
764:=
755:G
729:)
726:T
723:(
720:k
694:k
690:2
678:=
673:2
669:/
665:1
661:t
635:2
630:H
623:2
618:N
611:3
606:O
599:2
594:N
587:2
582:O
562:3
558:k
537:]
533:C
529:[
526:]
522:B
518:[
515:]
511:A
507:[
502:3
498:k
494:=
491:r
472:2
469:k
449:2
445:k
424:]
420:B
416:[
413:]
409:A
405:[
400:2
396:k
392:=
389:r
370:1
367:k
350:1
346:k
325:]
321:A
317:[
312:1
308:k
304:=
301:r
265:n
261:m
250:b
246:a
234:n
230:m
199:k
173:n
169:]
164:B
160:[
155:m
151:]
146:A
142:[
139:k
136:=
133:r
115:,
109:c
105:b
101:a
85:c
81:b
77:a
52:k
42:(
20:)
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