Generalization of the Badger Rule Based on the Use of Adiabatic Vibrational Modes

Computational Spectroscopy: Methods, Experiments and Applications

Volumn , Issue , 2010, Pages 105-149

  Kraka, Elfi ^a   Larsson, John Andreas ^a   Cremer, Dieter ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

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EID: 84882365565     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527633272.ch4     Document Type: Chapter

References (110)

1. Kratzer, A. (1920) Die ultraroten rotationsspektren der halogenwasserstoffe. Z. Physik, 3, 289-307.
2. Birge, R.T. (1925) The quantum structure of the OH bands, and notes on the quantum theory of band spectra. Phys. Rev., 25, 240-254.
3. Mecke, R. (1925) Zum aufbau der bandenspektra. Z. Physik, 32 (1925), 823-834.
4. Morse, P.M. (1929) Diatomic molecules according to the wave mechanics. II. Vibrational levls. Phys. Rev. 34, 57-64
5. Clark, C.H.D. (1934) The relation between vibration frequency and nuclear separation for some simple non-hydride diatomic molecules. Phil. Mag., 18, 459-470.
6. Badger, R.M. (1934) A relation between internuclear distances and bond force constants. J. Chem. Phys., 2, 128-132.
7. Badger, R.M. (1935) The relation between internuclear distances and the force constants of diatomic molecules. Phys. Rev., 48, 284-285.
8. Allen, H.S. and Longair, A.K. (1935) Internuclear distance and vibration frequency for diatomic molecules. Nature, 135, 764-764.
9. Badger, R.M. (1935) The relation between the internuclear distances and force constants of molecules and its application to polyatomic molecules. J. Chem. Phys., 3, 710-715.
10. Huggins, M.L. (1935) molecular constants and potential energy curves for diatomic molecules. J. Chem. Phys., 3, 473-479.
11. Huggins, M.L. (1936) Molecular constants and potential energy curves for diatomic molecules. J. Chem. Phys., 4, 308-312.
12. Sutherland, G.B.B.M. (1938) Proc. Indian Natl. Sci. Acad., 8, 341.
13. Sutherland, G.B.B.M. (1940) The determination of internuclear distances and of dissociation energies from force constants. J. Chem. Phys., 8, 161-165.
14. Newing, R.A. (1940) On the interrelation of molecular constants for diatomic molecules - II. Phil. Mag., 29, 298-301.
15. Linnett, J.W. (1940) The relation between potential energy and interatomic distance in some diatomic molecules. Trans. Faraday Soc., 36, 1123-1135.
16. Clark, C.H.D. and Webb, K.R. (1941) Systematics of band-spectral constants. Part VI. Interrelation of equilibrium bond constant and internuclear distance. Trans. Faraday Soc., 37, 293-298.
17. Linnett, J.W. (1942) The relation between potential energy and interatomic distance in some di-atomic molecules II. Trans. Faraday Soc., 38, 1-9.
18. Wu, C.K. and Yang, C.T. (1944) The relation between the force constant and the interatomic distance of a diatomic linkage. J. Phys. Chem., 48, 295-303.
19. Linnett, J.W. (1945) The force constants of some CH, NH and related bonds. Trans. Faraday Soc., 41, 223-232.
20. Gordy,W. (1946)Arelation between bond force constants, bond orders, bond lengths, and the electronegativities of the bonded atoms. J. Chem. Phys., 14, 305-321.
21. Guggenheimer, K.M. (1946) New regularities in vibrational spectra. Proc. Phys. Soc., 58, 456-468.
22. Guggenheimer, K.M. (1950) General discussion. Discuss. Faraday Soc., 9, 207-222.
23. Wu, C.K. and Chao, S.C. (1947) The relation between the force constant and the interatomic distance of a diatomic linkage. II. A modified Huggins relation. Phys. Rev., 71, 118-121.
24. Herzberg, G. (1950) Spectra of Diatomic Molecules, 2nd edn, D. Van Nostand Co. Inc., Princeton, NJ, p. 453.
25. Lovera, G. (1951) Regolarita nei dati spettroscopici di molecole biatomiche formate con atomi del 4 e 6 gruppo.Nuovo Cimento, 8, 1014-1015.
26. Siebert, H. (1953) Kraftkonstante und strukturchemie. I. Über die verwendung der molekularen kraftkonstanten zu strukturchemischen aussagen. Z. Anorg. Allg. Chem., 273, 170-182.
27. Lippincott, E.R. and Schroeder, R. (1955) General relation between potential energy and internuclear distance for diatomic and polyatomic molecules. I. J. Chem. Phys., 23, 1131-1142.
28. Jenkins, H.O. (1955) Bond energies, internuclear distances, and force constants in series of related molecules. Trans. Faraday Soc., 51, 1042-1051.
29. Varshni, Y.P. (1958) Correlation of molecular constants. I. Deduction of relations. J. Chem. Phys., 28, 1078-1081.
30. Varshni, Y.P. (1958) Correlation of molecular constants. II. Relation between force constant and equilibrium internuclear distance. J. Chem. Phys., 28, 1081-1089.
31. Hershbach, D.R. and Laurie, V.W. (1961) Anharmonic potential constants and their dependence upon bond length. J. Chem. Phys., 35, 458-463.
32. Johnston, H.S. (1964) Continuity of bond force constants between normal molecules and Lennard-Jones pairs. J. Am. Chem. Soc., 86, 1643-1645.
33. Ladd, J.A., Orville-Thomas, W.J., and Cox, B.C. (1964) Molecular parameters and bond structure III. Carbon-oxygen bonds. Spectrochim. Acta, 20, 1771-1780.
34. Ladd, J.A. and Orville-Thomas, W.J. (1966) Molecular parameters and bond structure V. Nitrogenoxygen bonds. Spectrochim. Acta, 22, 919-925.
35. Dewar, M.J.S. and Gleicher, G.J. (1966) Ground states of conjugated molecules. VII. Compounds containing nitrogen and oxygen. J. Chem. Phys., 44, 759-774.
36. Decius, J.C. (1966) Relation between force constant and bond length for the nitrogen-nitrogen bond. J. Chem. Phys., 45, 1069-1071.
37. Goubeau, J. and Sawodny, W. (1966) Kraftkonstanten und bindungsgrade von stickstoffverbindungen. Angew. Chem., 78, 565-576.
38. Borkman, R.F. and Parr, R.G. (1968) Toward an understanding of potential-energy functions for diatomic molecules. J. Chem. Phys., 48, 1116-1127.
39. Roy, R.S. (1968) New relationship between bond length and force constant. Proc. Phys. Soc. Ser., 2 (1), 445-448.
40. Stals, J. (1970) Empirical correlations of molecular constants for carbon-carbon, carbon-nitrogen, carbon-oxygen, nitrogen-nitrogen, nitrogen-oxygen and oxygen-oxygen bonds. Rev. Pure Appl. Chem., 20, 2-5.
41. McKean, D.C. (1978) IndividualCHbond strengths in simple organic compounds: effects of conformation and substitution. Chem. Soc. Rev., 7, 399-422.
42. Schlegel, H.B. (1984) Estimating the Hessian for gradient-type geometry optimizations. Theor. Chim. Acta., 66, 333-340.
43. Byler, D.M., Susi, H., and Damert, W.C. (1987) Relation between force constant and bond length for carbon nitrogen bonds. Spectrochim. Acta A, 43, 861-863.
44. Bürgi, H.B. and Dunitz, J.D. (1987) Fractional bonds: relations among their lengths, strengths, and stretching force constants. J. Am. Chem. Soc., 109, 2924-2926.
45. Swanton, D.J. and Henry, B.R. (1987) A theoretical basis for the correlation between bond length and local mode frequency. J. Chem. Phys., 86, 4801-4808.
46. Zavitsas, A.A. (1987) Quantitative relationship between bond dissociation energies, infrared stretching frequencies, and force constants in polyatomic molecules. J. Phys. Chem., 91, 5573-5577.
47. Miskowski, V.M., Dallinger, R.F., Christoph, G.G., Morris, D.E., Spies, G.H., and Woodruff, W.H. (1987) Assignment of the rhodium-rhodium stretching frequency in Rh2(O2CCH3)4L2 complexes and the crystal and molecular structure of [C(NH2)3]2[Rh2(O2CCH3) 4Cl2]. Relationship between vibrational spectra and structure. Inorg. Chem., 26, 2127-2139.
48. Weisshaar, J.C. (1989) Application of badger rule to third row metal diatomics. J. Chem. Phys., 90, 1429-1434.
49. Mallick, P.K., Strommen, D.P., and Kincaid, J.R. (1990) Molecular structure determination of transient species from vibrational frequency data. Application to the 3MLCT state of tris(bipyridine) ruthenium(II). J. Am. Chem. Soc., 112, 1686-1690.
50. Fischer, T.H. and Almlöf, J. (1992) General methods for geometry and wave function optimization. J. Phys. Chem., 96, 9768-9774.
51. Rutkowski, A., Rutkowska, D., and Schwarz, W.H.E. (1992) Relativistic perturbation theory of molecular structure. Theor. Chem. Acc.. Theor. Comput. Model., 84, 105-114.
52. Pearson, R.G. (1993) Bond-energies, force-constants and electronegativities. J. Mol. Struct., 300, 519-525.
53. Lindh, R., Bernhardsson, A., Karlström, G., and Malmqvist, P.-Å. (1995) On the use of a Hessian model function in molecular-geometry optimizations. Chem. Phys. Lett., 241, 423-428.
54. Harvey, P.D. (1996) Reparameterized Herschbach-Laurie empirical relationships between metal-metal distances and force constants applied to homonuclear bi- and polynuclear complexes (M = Cr, Mo, Rh, Pd, Ag, W, Re, Ir, P, A, Hg). Coord. Chem. Rev., 153, 175-198.
55. Wittbrodt, J.M. and Schlegel, H.B. (1997) Estimating stretching force constants for geometry optimization. J. Mol. Struct. (Theochem), 398-399, 55-61.
56. Stichler, M. and Menzel, D. (1999) A systematic investigation of the geometric structures of four oxygen/nitric oxide coadsorbate layers on Ru(001). Surf. Sci., 419, 272-290.
57. Larsson, J.A. and Cremer, D. (1999) Theoretical verification and extension of the McKean relationship between bond lengths and stretching frequencies. J. Mol. Struct., 485, 385-408.
58. Cioslowski, J., Liu, G., and Castro, A.M. (2000) Badger rule revised. Chem. Phys. Lett., 331, 497-501.
59. Hermann, H.L., Boche, G., and Schwerdtfeger, P. (2001) Metallophilic interactions in closed-shell copper(I) compounds: a theoretical study. Chem. Eur. J., 24, 5333-5342.
60. Jules, J.L. and Lombardi, J.R. (2003) Transition metal dimer internuclear distances from measured force constants. J. Phys. Chem. A, 107, 1268-1273.
61. Kurita, E., Matsuura, H., and Ohno, K. (2004) Relationship between force constants and bond lengths for CX (X=C, Si, Ge, N, P, As, O, S, Se, F, Cl, and Br) single and multiple bonds: formulation of Badger?s rule for universal use. Spectrochim. Acta A, 60, 3013-3023.
62. Stone, K.L., Behan, R.K., andGreen, M.T. (2006) Resonance Raman spectroscopy of chloroperoxidase compound II provides direct evidence for the existence of an iron(IV)-hydroxide. Proc. Natl. Acad. Sci. USA, 103, 12307-12310.
63. Behan, R.K. and Green, M.T. (2006) On the status of ferryl protonation, J. Inorg. Biochem, 100, pp. 448-459.
64. Lin, Y.W., Nie, C.M., and Liao, L.F. (2007) Probing the weak interactions between amino acids and carbon monoxide. Chin. Chem. Lett., 19, 119-122.
65. Das, U. and Raghavachari, R. (2008) Predicting PH vibrations of gas phase molecules and surface-adsorbed species usingbondlength-frequency correlations. J. Comp. Chem., 30, 1872-1881.
66. Oomens, J., Kraka, E., Nguyen, M.K., and Morton, T.H. (2008) Structure, vibrational spectra, and unimolecular dissociation of gaseous 1-fluoro-1- phenethyl cations. J. Phys. Chem. A, 112, 10774-10783.
67. Kraka, E. and Cremer, D. (2009) Characterization of CF bond with multiple-bond character: bond lengths, stretching force constants, and bond dissociation energies. Chem. Phys. Chem., 10, 689-698.
68. Xie, R.-H. and Gong, J. (2005) Simple three-parameter model potential for diatomic systems: from weakly to strongly bound molecules to metastable molecular ions. Phys. Rev. Lett., 95, 263202-1-263202-4.
69. Xie, R.-H. and Hsu, P.S. (2006) Universal reduced potential function for diatomic systems. Phys. Rev. Lett., 96, 243201- 1-243201-4.
70. Hooydonk, G.V. (1999) A universal two-parameter Kratzer-potential and its superiority over Morse?s for calculating and scaling first-order spectroscopic constants of 300 diatomic bonds. Eur. J. Inorg. Chem., 1617-1642.
71. Huber, K.P. and Herzberg, G. (1979) Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, Van Nostrand Rheinhold, London.
72. Henry, B.R. (1989) The frequency bond length correlation in local-mode overtone spectra. J. Mol. Struct. (Theochem), 202, 193-201.
73. Hess, B.A., Jr., Schaad, L., Carsky, R., and Zahradnik, J.P. (1986) Ab initio calculations of vibrational-spectra and their use in the identification of unusual molecules. Chem. Rev., 86, 709-730.
74. Wilson, S. ed. (1992) Methods in Computational Chemistry: Molecular Vibrations, vol. 4, Plenum Press, New York.
75. Wilson, E.B., Jr., Decius, J.C., and Cross, P.C. (1955) Molecular Vibrations, McGraw-Hill, New York.
76. Konkoli, Z., Larsson, J.A., andCremer, D. (1997) A new way of analyzing vibrational spectra. II. Comparison of internal mode frequencies. Int. J. Quantum Chem., 67, 11-27.
77. Herzberg, G. (1946) Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold Co., New York.
78. Califano, S. (1976) Vibrational States, John Wiley & Sons, Inc., New York.
79. Konkoli. Z and Cremer, D. (1998) A new way of analyzing vibrational spectra. 1. Derivation of adiabatic internal modes. Int. J. Quantum Chem., 67, 1-9.
80. Torkington, P. (1949) The general solution of the secular equation of second degree, with application to the class-A1 vibrations of the symmetrical triatomic molecule. J. Chem. Phys., 17, 357-369.
81. Morino, Y. and Kuchitsu, K. (1952) A note on the classification of normal vibrations of molecules. J. Chem. Phys., 20, 1809-1810.
82. Pulay, P. and Török, F. (1966) On parameter form of matrix F. 2. Investigation of assignment with aid of parameter form. Acta Chim. Hung., 47, 273-279.
83. Keresztury, G. and Jalsovszky, G. (1971) Alternative calculation of vibrational potential energy distribution. J. Mol. Struct., 10, 304.
84. Cremer, D., Larsson, J.A., and Kraka, E. (1998) New developments in the analysis of vibrational spectra: on the use of adiabatic internal vibrational modes, in Theoretical Organic Chemistry Theoretical and Computational Chemistry, vol. 5 (ed. C. Parkany), Elsevier Science, New York, pp. 259-327.
85. Konkoli, Z. and Cremer, D. (1998) A new way of analyzing vibrational spectra. III. Characterization of normal vibrational modes in terms of internal vibrational modes. Int. J. Quantum Chem., 67, 29-40.
86. Kraka, E. (1998) Reaction path Hamiltonian and its use for investigating reaction mechanism, in Encyclopedia of Computational Chemistry, vol. 4 (eds E.V.R. Schleyer, N.L. Allinger, T. Clark, J. Gasteiger, E.A. Kollman, H.F. Schaefer, III, and E.R. Schreiner), John Wiley & Sons Ltd., Chichester, UK, p. 2437.
87. Konkoli, Z., Kraka, E., and Cremer, D. (1997) Unified reaction valley approach mechanism of the reaction CH3 + H2 ! CH4 + H. J. Phys. Chem. A, 101, 1742-1757.
88. Vijay, A. and Sathyanarayana, D.N. (1994) Use of L-matrix to obtain reliable ab-initio force-constants of polyatomic molecules: ethylene as a test. J. Mol. Struct., 328, 269-276.
89. McKean, D.C. (1975) CH stretching frequencies, bond lengths and strengths in halogenated ethylenes. Spectrochim. Acta A, 31, 1167-1186.
90. McKean, D.C. (1989) CH bond dissociation energies, isolated stretching frequencies, and radical stabilization energy. Int. J. Chem. Kinet., 21, 445-464.
91. McKean, D.C. and Torto, I. (1982) CH stretching frequencies and bond strengths, and methyl-group geometry in CH3CXO compounds (X=H, Me, F, Cl, Br, CN, OMe) and CH3CH2CN. J. Mol. Struct., 81, 51-60.
92. Duncan, J.L., Harvie, J.L., McKean, D.C., and Cradock, S. (1986) The ground-state structures of disilane, methyl silane and the silyl halides, and an SiH bond length correlation with stretching frequency. J. Mol. Struct., 145, 225-242.
93. McKean, D.C. (1989) CH bonddissociation energies, isolated stretching frequencies, and radical stabilization energy. Int. J. Chem. Kinet., 21, 445-464.
94. Murphy,W.F., Zerbetto, F., Duncan, J.L., and McKean, D.C. (1993) Vibrationalspectrum and harmonic force-field of trimethylamine. J. Phys. Chem., 97, 581-595.
95. Caillod, J., Saur, O., and Lavalley, J.-C. (1980) Etude par spectroscopie infrarouge des vibrations (CH) de composes cycliques: dioxanne-1,4, dithianne-1,4, oxathianne-1,4 et cyclohexane. Spectrochim. Acta A, 36, 185-191.
96. Snyder, R.G., Aljibury, A.L., Strauss, H.L., Casal, H.L., Gough, K.M., and Murphy, W.J. (1984) Isolated C-H stretching vibrations of N-alkanes: assignments and relation to structure. J. Chem. Phys., 81, 5352-5361.
97. Aljibury, A.L., Snyder, R.G., Strauss, H.L., and Raghavachari, K. (1986) The structure of N-alkanes: high-precision ab initio calculations and relation to vibrational-spectra. J. Chem. Phys., 84, 6872-6878.
98. Henry, B.R. (1987) The local mode model and overtone spectra: a probe of molecular-structure and conformation. Acc. Chem. Res., 20, 429-435 and references therein.
99. Pople, J.A., Schlegel, H.B., Krishnan, R., DeFrees, D.J., Binkley, J.S., Frisch, M.J., Whiteside, R.A., Hout, R.F., and Hehre, W.J. (1981) Molecular-orbital studies of vibrational frequencies. Int. J. Quantum Chem. Quant. Chem. Symp., 15, 269-278.
100. Mizugai, Y. and Katayama, M. (1980) The 5th overtone of the C-H stretching vibrations and the bond lengths in some heterocyclic-compounds. Chem. Phys. Lett., 73, 240-243.
101. Wong, J.S. and Moore, C.B. (1982) Inequivalent C-H oscillators of gaseous alkanes and alkenes in laser photoacoustic overtone spectroscopy. J. Chem. Phys., 77, 603-615.
102. Sbrana, G. and Muniz-Miranda, M. (1998) High overtones of C-H stretching vibrations in isoxazole, thiazole, and related methyl and dimethyl derivatives. J. Phys. Chem. A, 102, 7603-7608.
103. Hippler, M. and Quack, M. (1997) Intramolecular energy transfer from isotope selective overtone spectroscopy by vibrationally assisted dissociation and photofragment ionization. Ber. Bunsenges. Phys. Chem., 101, 356-362.
104. Hollensteun, H., Luckhaus, D., and Quack, M. (1993) Dynamics of the CH chromophore in CHX3: a combined treatment for a set of isotopic-species. J. Mol. Struct., 294, 65-70.
105. Boatz, J.A. and Gordon, M.S. (1989) Decomposition of normal-coordinate vibrational frequencies. J. Phys. Chem., 93, 1819-1826.
106. Decius, J.C. (1963) Compliance matrix and molecular vibrations. J. Chem. Phys., 38, 241-248.
107. Brandhorst, K. and Grunenberg, J. (2008) How strong is a bond? The interpretation of force and compliance constants as bond strength descriptors. Chem. Soc. Rev., 37, 1558-1567.
108. Grunenberg, J. and Goldberg, N. (2000) How strong is the gallium gallium triple bond? Theoretical compliance matrices as a probe for intrinsic bond strengths. J. Am. Chem. Soc., 122, 6046-6047.
109. Grunenberg, J., Streubel, R., Frantzius, G.V., andMarten,W. (2003) The strongest bond in the universe? Accurate calculation of compliance matrices for the ions N2H+, HCO+, and HOC+. J. Chem. Phys., 119, 165-169.
110. Grunenberg, J. (2004) Direct assessment of interresidue force in Watson-Crick base pairs using theoretical compliance constants. J. Am. Chem. Soc., 126, 16310-16311.