Accurate prediction of experimental free energy of activation barriers for the aliphatic-Claisen rearrangement through DFT calculations

Computational and Theoretical Chemistry

Volumn 976, Issue 1-3, 2011, Pages 167-182

  Ramadhar, Timothy R ^a   Batey, Robert A ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Benchmarking study; DFT calculations; Free energy of activation; Kinetic isotope effect; Pericyclic reaction; Sigmatropic rearrangement

Indexed keywords

EID: 84555197171     PISSN: 2210271X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.comptc.2011.08.022     Document Type: Article

References (105)

1. Castro A.M.M. Claisen rearrangement over the past nine decades. Chem. Rev. 2004, 104:2939-3002.
2. The Claisen Rearrangement: Methods and Applications 2007, Wiley-VCH, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
3. Claisen L. über umlagerung von phenol-allyläthern in C-allyl-phenole. Chem. Ber. 1912, 45:3157-3167.
4. Ichikawa H., Maruoka K. Aliphatic Claisen rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 45-85. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
5. Ito H., Taguchi T. Aromatic Claisen rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 86-116. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
6. Chai Y., Hong S.-P., Lindsay H.A., McFarland C., McIntosh M.C. New aspects of the Ireland and related Claisen rearrangements. Tetrahedron 2002, 58:2905-2928.
7. McFarland C.M., McIntosh M.C. The Ireland-Claisen rearrangement (1972-2004). The Claisen Rearrangement: Methods and Applications 2007, 117-120. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hier semann, U. Nubbemeyer (Eds.).
8. Langlois Y. Claisen-Johnson orthoester rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 301-366. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
9. Gradl S.N., Trauner D. The Meerwein-Eschenmoser-Claisen rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 367-396. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
10. Ganem B. The mechanism of the Claisen rearrangement: déjà vu all over again. Angew. Chem. Int. Ed. 1996, 35:936-945.
11. Ganem B. Catalysis by chorismate mutases. Comput. Nat. Prod. Chem. 1999, 5:343-370.
12. Guo H., Rao N. Chorismate-mutase-catalyzed Claisen rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 1-23. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
13. Rehbein J., Hiersemann M. Mechanistic aspects of the aliphatic Claisen rearrangement. The Claisen Rearrangement: Methods and Applications 2007, 525-557. Wiley-VCH Verlag GmbH & Co., KGaA, Weinheim, Germany. M. Hiersemann, U. Nubbemeyer (Eds.).
14. Dewar M.S., Healy E.F. Ground states of molecules. 68. MNDO study of the Claisen rearrangement. J. Am. Chem. Soc. 1984, 106:7127-7131.
15. Gul S., Schoenbeck F., Aviyente V., Houk K.N. Computational study of factors controlling the boat and chair transition states of Ireland-Claisen rearrangements. J. Org. Chem. 2010, 75:2115-2118.
16. Acevedo O., Armacost K. Claisen rearrangements: insight into solvent effects and " on water" reactivity from QM/MM simulations. J. Am. Chem. Soc. 2010, 132:1966-1975.
17. Uyeda C., Jacobsen E.N. Transition-state charge stabilization through multiple non-covalent interactions in the guanidinium-catalyzed enantioselective claisen rearrangement. J. Am. Chem. Soc. 2011, 133:5062-5075.
18. Lee E.E., Batey R.A. Palladium-catalyzed [3,3] sigmatropic rearrangement of (allyloxy)iminodiazaphospholidines: allylic transposition of C-O and C-N functionality. Angew. Chem. Int. Ed. 2004, 43:1865-1868.
19. Lee E.E., Batey R.A. Palladium-catalyzed allylic transposition of (allyloxy) iminodiazaphospholidines: a formal [3,3]-aza-phospha-oxa-Cope sigmatropic rearrangement for the stereoselective synthesis of allylic amines. J. Am. Chem. Soc. 2005, 127:14887-14893.
20. Rodrigues A., Lee E.E., Batey R.A. Enantioselective palladium(II)-catalyzed formal [3,3]-sigmatropic rearrangement of 2-allyloxypyridines and related heterocycles. Org. Lett. 2010, 12:260-263.
21. Ramadhar T.R., Kawakami J., Lough A.J., Batey R.A. Stereocontrolled synthesis of contiguous C(sp3)-C(aryl) bonds by lanthanide(III)-catalyzed domino aryl-Claisen [3,3]-sigmatropic rearrangements. Org. Lett. 2010, 12:4446-4449.
22. Becke A.D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98:5648-5652.
23. Lee C., Yang W., Parr R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37:785-789.
24. Wiest O., Black K.A., Houk K.N. Density functional theory isotope effects and activation energies for the Cope and Claisen rearrangements. J. Am. Chem. Soc. 1994, 116:10336-10337.
25. Aviyente V., Yoo H.Y., Houk K.N. Analysis of substituent effects on the Claisen rearrangement with ab initio and density functional theory. J. Org. Chem. 1997, 62:6121-6128.
26. Aviyente V., Houk K.N. Cyano, amino, and trifluoromethyl substituent effects on the Claisen rearrangement. J. Phys. Chem. A 2001, 105:383-391.
27. Hayden A.E., Xu H., Nicolaou K.C., Houk K.N. Origins of selectivity in pericyclic reaction cascades for the synthesis of Gambogin and Lateriflorone. Org. Lett. 2006, 8:2989-2992.
28. Sauer E.L.O., Hooper J., Woo T., Barriault L. Origin of diastereoselectivity in the tandem oxy-Cope/Claisen/ene reaction: experimental and theoretical studies of the ring inversion mechanism. J. Am. Chem. Soc. 2007, 129:2112-2119.
29. Kirsten M., Rehbein J., Hiersemann M., Strassner T. Organocatalytic Claisen rearrangement: theory and experiment. J. Org. Chem. 2007, 72:4001-4011.
30. Uyeda C., Jacobsen E.N. Enantioselective Claisen rearrangements with a hydrogen-bond donor catalyst. J. Am. Chem. Soc. 2008, 130:9228-9229.
31. Rehbein J., Hiersemann M. Gosteli-Claisen rearrangement: DFT study of substituent - rate effects. J. Org. Chem. 2009, 74:4336-4342.
32. Voute N., Philp D., Slawin A.M.Z., Westwood N.J. Studies on the Claisen rearrangements in the indolo23-b]quinoline system. Org. Biomol. Chem. 2010, 8:442-450.
33. Uyeda C., Roetheli A.R., Jacobsen E.N. Catalytic enantioselective Claisen rearrangements of O-allyl β-ketoesters. Angew. Chem. Int. Ed. 2010, 49:9753-9756.
34. Zahedi E., Shiroudi A., Ali-Asgari S., Keley V. A DFT study of NBO and NICS analysis of the allylic rearrangements (the Claisen and thio-Claisen rearrangements) of 3-(vinyloxy)prop-1-ene and allyl vinyl sulfide. Phosphorus Sulfur Silicon Related Elements 2011, 186:159-170.
35. Khaledy M.M., Kalani M.Y.S., Khuong K.S., Houk K.N., Aviyente V., Neier R., Soldermann N., Velker J. Origins of boat or chair preferences in the Ireland-Claisen rearrangements of cyclohexenyl esters: a theoretical study. J. Org. Chem. 2003, 68:572-577.
36. Yamabe S., Okumoto S., Hayashi T. Transition structures for the aromatic Claisen rearrangements by the molecular orbital method. J. Org. Chem. 1996, 61:6218-6226.
37. Arnaud R., Dillet V., Pelloux-Leon N., Vallee Y. Theoretical study of the thio-Claisen rearrangement. Can vinylthioethanimine undergo a [3,3]-sigmatropic shift?. J. Chem. Soc., Perkin Trans. 1996, 2:2065-2071.
38. Gómez B., Chattaraj P.K., Chamorro E., Contreras R., Fuentealba P. A density functional study of the Claisen rearrangement of allyl aryl ether, allyl arylamine, allyl aryl thio ether, and a series of meta-substituted molecules through reactivity and selectivity profiles. J. Phys. Chem. A 2002, 106:11227-11233.
39. Gozzo F.C., Fernandes S.A., Rodrigues D.C., Eberlin M.N., Marsaioli A.J. Regioselectivity in aromatic Claisen rearrangements. J. Org. Chem. 2003, 68:5493-5499.
40. Emamian S.R., Aghaie M., Zardoost M.R., Zahedi E., Zare K. Kinetic and thermodynamic study of the substituent effect on the amino-Claisen rearrangement of para-substituted N-allyl-N-arylamine: a Hammett study via DFT. Mol. Simulat. 2010, 36:978-985.
41. Ghadari R., Shaabani A. Investigation of substituent effect on the Johnson-Claisen rearrangement: a DFT approach. J. Mol. Struct. Theochem. 2010, 961:83-87.
42. Lucas C.L., Lygo B., Blake A.J., Lewis W., Moody C.J. Regioselectivity of the Claisen rearrangement in meta-allyloxy aryl ketones: an experimental and computational study, and application in the synthesis of (R)-(-)-Pestalotheol D. Chem. Eur. J. 2011, 17:1972-1978.
43. Wiest O., Houk K.N. Stabilization of the transition state of the chorismate-prephenate rearrangement: an ab initio study of enzyme and antibody catalysis. J. Am. Chem. Soc. 1995, 117:11628-11639.
44. Kast O., Tewari Y.B., Wiest O., Hilvert D., Houk K.N., Goldberg R.N. Thermodynamics of the conversion of chorismate to prephenate: experimental results and theoretical predictions. J. Phys. Chem. B 1997, 101:10976-10982.
45. Khanjin N.A., Snyder J.P., Menger F.M. Mechanism of chorismate mutase: contribution of conformational restriction to catalysis in the Claisen rearrangement. J. Am. Chem. Soc. 1999, 121:11831-11846.
46. Guo H., Cui Q., Lipscomb W.N., Karplus M. Substrate conformational transitions in the active site of chorismate mutase: their role in the catalytic mechanism. Proc. Natl. Acad. Sci. USA 2001, 98:9032-9037.
47. Martí S., Andrés J., Moliner V., Silla E., Tuñón I., Bertrán J., Field M.J. A hybrid potential reaction path and free energy study of the chorismate mutase reaction. J. Am. Chem. Soc. 2001, 123:1709-1712.
48. Hur S., Bruice T.C. The mechanism of catalysis of the chorismate to prephenate reaction by the Escherichia coli mutase enzyme. Proc. Natl. Acad. Sci. USA 2002, 99:1176-1181.
49. Crespo A., Scherlis D.A., Martí M.A., Ordejón P., Roitberg A.E., Estrin D.A. A DFT-based QM-MM approach designed for the treatment of large molecular systems: application to chorismate mutase. J. Phys. Chem. B 2003, 107:13728-13736.
50. Woodcock H.L., Hodošček M., Sherwood P., Lee Y.S., Schaefer H.F., Brooks B.R. Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase. Theor. Chem. Acc. 2003, 109:140-148.
51. Martí S., Andrés J., Moliner V., Silla E., Tuñón I., Bertrán J. A comparative study of Claisen and Cope rearrangements catalyzed by chorismate mutase. An insight into enzymatic efficiency: Transition state stabilization or substrate preorganization?. J. Am. Chem. Soc. 2004, 126:311-319.
52. Martí S., Moliner V., Tuñón I., Williams I.H. Computing kinetic isotope effects for chorismate mutase with high accuracy. A new DFT/MM strategy. J. Phys. Chem. B 2005, 109:3707-3710.
53. Woodcock H.L., Hodoscek M., Gilbert A.T.B., Gill P.M.W., Schaefer H.F., Brooks B.R. Interfacing Q-Chem and CHARMM to perform QM/MM reaction path calculations. J. Comp. Chem. 2007, 28:1485-1502.
54. Benighaus T., Thiel W. Long-range electrostatic effects in QM/MM studies of enzymatic reactions: application of the solvated macromolecule boundary potential. J. Chem. Theory Comput. 2011, 7:238-249.
55. Balta B., öztürk C., Aviyente V., Vincent M.A., Hillier I.H. Claisen rearrangement of aliphatic allyl vinyl ethers in the presence of copper(II) bisoxazoline. J. Org. Chem. 2008, 73:4800-4809.
56. Zhao Y., Truhlar D.G. Hybrid meta density functional theory methods for thermochemistry, thermochemical kinetics, and noncovalent interactions: the MPW1B95 and MPWB1K models and comparative assessments for hydrogen bonding and van der Waals interactions. J. Phys. Chem. A 2004, 108:6908-6918.
57. Zhao Y., Truhlar D.G. Benchmark databases for nonbonded interactions and their use to test density functional theory. J. Chem. Theory Comput. 2005, 1:415-432.
58. Zhao Y., Truhlar D.G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120:215-241.
59. Zhao Y., Truhlar D.G. Density functionals with broad applicability in chemistry. Acc. Chem. Res. 2008, 41:157-167.
60. Guner V., Khuong K.S., Leach A.G., Lee P.S., Bartberger M.D., Houk K.N. A standard set of pericyclic reactions of hydrocarbons for the benchmarking of computational methods: the performance of ab initio, density functional, CASSCF, CASPT2, and CBS-QB3 methods for the prediction of activation barriers, reaction energetics, and transition state geometries. J. Phys. Chem. A 2003, 107:11445-11459.
61. Guner V.A., Khuong K.S., Houk K.N., Chuma A., Pulay P. The performance of the Handy/Cohen functionals, OLYP and O3LYP, for the computation of hydrocarbon pericyclic reaction activation barriers. J. Phys. Chem. A 2004, 108:2959-2965.
62. Quintal M.M., Karton A., Iron M.A., Boese A.D., Martin J.M.K. Benchmark study of DFT functionals for late-transition-metal reactions. J. Phys. Chem. A 2006, 110:709-716.
63. De Jong G.T., Bickelhaupt F.M. Oxidative addition of the chloromethane C-Cl bond to Pd, an ab initio benchmark and DFT validation study. J. Chem. Theory Comput. 2006, 2:322-335.
64. Amin E.A., Truhlar D.G. Zn coordination chemistry: development of benchmark suites for geometries, dipole moments, and bond dissociation energies and their use to test and validate density functionals and molecular orbital theory. J. Chem. Theory Comput. 2008, 4:75-85.
65. Valdes H., Pluháčková K., Pitonák M., řezáč J., Hobza P. Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field. Phys. Chem. Chem. Phys. 2008, 10:2747-2757.
66. Aguilera-Iparraguirre J., Curran H.J., Klopper W., Simmie J.M. Accurate benchmark calculation of the reaction barrier height for hydrogen abstraction by the hydroperoxyl radical from methane. Implications for CnH2n+2 where n=2→4. J. Phys. Chem. A 2008, 112:7047-7054.
67. Karton A., Gruzman D., Martin J.M.L. Benchmark thermochemistry of the CnH2n+2 alkane isomers (n=2-8) and performance of DFT and composite ab initio methods for dispersion-driven isomeric equilibria. J. Phys. Chem. A 2009, 113:8434-8447.
68. He X., Fursti-Molnar L., Merz K.M. Accurate benchmark calculations on the gas-phase basicities of small molecules. J. Phys. Chem. A 2009, 113:10096-10103.
69. Zhao Y., Schultz N.E., Truhlar D.G. Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions. J. Chem. Phys. 2005, 123:161103.
70. Zhao Y., Schultz N.E., Truhlar D.G. Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions. J. Chem. Theory Comput. 2006, 2:364-382.
71. Zhao Y., Truhlar D.G. Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states. J. Phys. Chem. A 2006, 110:13126-13150.
72. Zhao Y., Truhlar D.G. A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions. J. Chem. Phys. 2006, 125:194101.
73. Zhao Y., Truhlar D.G. Exploring the limit of accuracy of the global hybrid meta density functional for main-group thermochemistry, kinetics, and noncovalent interactions. J. Chem. Theory Comput. 2008, 4:1849-1868.
74. Perdew J.P., Ruzsinszky A., Tao J., Staroverov V.N., Scuseria G.E., Csonka G.I. Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. J. Chem. Phys. 2005, 123:062201.
75. Bigeleisen J., Mayer M.G. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 1947, 15:261-267.
76. Wolfsberg M. Theoretical evaluation of experimentally observed isotope effects. Acc. Chem. Res. 1972, 5:225-233.
77. Meyer M.P., DelMonte A.J., Singleton D.A. Reinvestigation of the isotope effects for the Claisen and aromatic Claisen rearrangements: the nature of the Claisen transition states. J. Am. Chem. Soc. 1999, 121:10865-10874.
78. Schuler F.W., Murphy G.W. The kinetics of the rearrangement of vinyl allyl ether. J. Am. Chem. Soc. 1950, 72:3155-3159.
79. Stein L., Murphy G.W. Kinetics of the rearrangement of isopropenyl allyl ether. J. Am. Chem. Soc. 1952, 74:1041-1043.
80. Frey H.M., Montague D.C. Thermal unimolecular isomerization of 1-methylallyl vinyl ether in the gas phase and in solution. Trans. Faraday Soc. 1968, 64:2369-2374.
81. Frey H.M., Pope B.M. The thermal unimolecular isomerisation of 2-methylallyl vinyl ether. J. Chem. Soc. B 1966, 209-210.
82. Hansen H.-J., Schmid H. Stereochemie von [3.3]- und [5.5]-sigmatropischen umlagerungen. Tetrahedron 1974, 30:1959-1969.
83. Vittorelli P., Hansen H.-J., Schmid H. Kinetik und stereochemischer verlauf der thermischen umlagerung der vier stereoisomeren propenyl-(but-2'-enyl)-äther. Helv. Chim. Acta. 1975, 58:1293-1309.
84. M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian, Inc., Gaussian 03, Revision E.01, Wallingford, CT, 2004.
85. Schmidt M.W., Baldridge K.K., Boatz J.A., Elbert S.T., Gordon M.S., Jensen J.H., Koseki S., Matsunaga N., Nguyen K.A., Su S., Windus T.L., Dupuis M., Montgomery J.A. General atomic and molecular electronic structure system. J. Comput. Chem. 1993, 14:1347-1363.
86. Gordon M.S., Schmidt M.W. Advances in electronic structure theory: GAMESS a decade later. Theory and Applications of Computational Chemistry: The First Forty Years 1993, 1347-1363. Elsevier, Amsterdam. C.E. Dykstra, G. Frenking, K.S. Kim, G.E. Scuseria (Eds.).
87. Császár P., Pulay P. Geometry optimization by direct inversion in the iterative subspace. J. Mol. Struct. 1984, 114:31-34.
88. Farkas ö., Schlegel H.B. Methods for optimizing large molecules. II. Quadratic search. J. Chem. Phys. 1999, 111:10806-10814.
89. Boese A.D., Martin J.M.L. Development of density functionals for thermochemical kinetics. J. Chem. Phys. 2004, 121:3405-3416.
90. Becke A.D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38:3098-3103.
91. Perdew J.P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 1986, 33:8822-8824.
92. Lynch B.J., Fast P.L., Harris M., Truhlar D.G. Adiabatic connection for kinetics. J. Phys. Chem. A 2000, 104:4811-4815.
93. Adamo C., Barone V. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 1999, 110:6158-6170.
94. Vosko S.H., Wilk L., Nusair M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 1980, 58:1200-1211.
95. Slater J.C. Quantum Theory of Molecules and Solids. The Self-Consistent Field for Molecules and Solids 1974, vol. 4. McGraw-Hill, New York.
96. Adamo C., Barone V. Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: the mPW and mPW1PW models. J. Chem. Phys. 1998, 108:664-675.
97. Perdew J.P. Unified theory of exchange and correlation beyond the local density approximation. Electronic Structure of Solids '91 1991, 11-20. Akademie Verlag, Berlin, Germany. P. Ziesche, H. Eschig (Eds.).
98. Becke A.D. Density-functional thermochemistry. IV. A new dynamical correlation functional and implications for exact-exchange mixing. J. Chem. Phys. 1996, 104:1040-1046.
99. Zhao Y., Truhlar D.G. A density functional that accounts for medium-range correlation energies in organic chemistry. Org. Lett. 2006, 8:5753-5755.
100. Voorhis T.V., Scuseria G.E. A novel form for the exchange-correlation energy functional. J. Chem. Phys. 1998, 109:400-410.
101. Saunders M., Laidig K.E., Wolfsberg M. Theoretical calculation of equilibrium isotope effects using ab initio force constants: application to NMR isotope perturbation studies. J. Am. Chem. Soc. 1989, 111:8989-8994.
102. Merrick J.P., Moran D., Radom L. An evaluation of harmonic vibrational frequency scale factors. J. Phys. Chem. A 2007, 111:11683-11700.
103. Bell R.P. The Tunnel Effect in Chemistry 1980, Chapman and Hall, London, pp. 60-63.
104. Singleton D.A., Merrigan S.R., Liu J., Houk K.N. Experimental geometry of the epoxidation transition state. J. Am. Chem. Soc. 1997, 119:3385-3386.
105. DelMonte A.J., Haller J., Houk K.N., Sharpless K.B., Singleton D.A., Strassner T., Thomas A.A. Experimental and theoretical kinetic isotope effects for asymmetric dihydroxylation. Evidence supporting a rate-limiting " (3 + 2)" cycloaddition. J. Am. Chem. Soc. 1997, 119:9907-9908.