Information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes. However, normal vibrational modes result from a coupling of local vibrational modes, which means that only the latter can provide detailed insight into bonding and other structural features. In this work, it is proven that the adiabatic internal coordinate vibrational modes of Konkoli and Cremer [Int. J. Quantum Chem. 67, 29 (1998)] https://doi.org/10.1002/(SICI)1097-461X(1998)67:1<29::AID-QUA3>3.0.CO;2-0 represent a unique set of local modes that is directly related to the normal vibrational modes. The missing link between these two sets of modes are the compliance constants of Decius, which turn out to be the reciprocals of the local mode force constants of Konkoli and Cremer. Using the compliance constants matrix, the local mode frequencies of any molecule can be converted into its normal mode frequencies with the help of an adiabatic connection scheme that defines the coupling of the local modes in terms of coupling frequencies and reveals how avoided crossings between the local modes lead to changes in the character of the normal modes.
REFERENCES
1.
2.
R.
Daudel
, Quantum Theory of the Chemical Bond
(Kluwer Academic
, Netherlands
, 1974
).3.
Z. B.
Maksic
, Theoretical Models of Chemical Bonding, Parts 1 and 2
(Springer
, Heidelberg
, 1990
).4.
E.
Kraka
and D.
Cremer
, in Theoretical Models of Chemical Bonding: The Concept of the Chemical Bond
(Springer
, Heidelberg
, 1990
), pp. 453
–542
.5.
R. F. W.
Bader
, Atoms in Molecules: A Quantum Theory
(Oxford University Press
, Oxford
, 1995
), Vol. 22.6.
A. H.
Zewail
, Femtochemistry, Ultrafast Dynamics of the Chemical Bond
(World Scientific
, Singapore
, 1994
).7.
R. F.
Nalewajski
, Information Origins of the Chemical Bond
(Nova Science
, Hauppauge, New York
, 2010
).8.
9.
Y.-R.
Luo
, Handbook of Bond Dissociation Energies in Organic Compounds
(CRC
, Boca Raton
, 2003
).10.
E.
Kraka
, J. A.
Larsson
, and D.
Cremer
, in Computational Spectroscopy: Methods, Experiments and Applications
, edited by J.
Grunenberg
(Wiley
, New York
, 2010
), pp. 105
–149
.11.
D.
Cremer
, A.
Wu
, A.
Larsson
, and E.
Kraka
, J. Mol. Model.
6
, 396
(2000
).12.
E. B.
Wilson
, J. C.
Decius
, and P. C.
Cross
, Molecular Vibrations
(McGraw-Hill
, New York
, 1955
).13.
14.
W. J.
Taylor
and K. S.
Pitzer
, J. Res. Natl. Bur. Stand.
38
, 1
(1947
).15.
J. C.
Decius
, J. Chem. Phys.
21
, 1121
(1953
).16.
S. J.
Cyvin
and N. B.
Slater
, Nature (London)
188
, 485
(1960
).17.
J.
Decius
, J. Chem. Phys.
38
, 241
(1963
).18.
D. C.
McKean
, Chem. Soc. Rev.
7
, 399
(1978
).19.
D. C.
McKean
, I.
Torto
, and A. R.
Morrisson
, J. Phys. Chem.
86
, 307
(1982
).20.
B. R.
Henry
, Acc. Chem. Res.
20
, 429
(1987
).21.
J.
Larsson
and D.
Cremer
, J. Mol. Struct.
485
, 385
(1999
).22.
D. C.
McKean
, Spectrochim. Acta A
31
, 1167
(1975
).23.
D. C.
McKean
and I.
Torto
, J. Mol. Struct.
81
, 51
(1982
).24.
D. C.
McKean
, Int. J. Chem. Kinet.
21
, 445
(1989
).25.
W. F.
Murphy
, F.
Zerbetto
, J. L.
Duncan
, and D. C.
McKean
, J. Phys. Chem.
97
, 581
(1993
).26.
J. L.
Duncan
, J. L.
Harvie
, D. C.
McKean
, and C.
Cradock
, J. Mol. Struct.
145
, 225
(1986
).27.
J.
Caillod
, O.
Saur
, and J.-C.
Lavalley
, Spectrochim. Acta A
36
, 185
(1980
).28.
R. G.
Snyder
, A. L.
Aljibury
, H. L.
Strauss
, H. L.
Casal
, K. M.
Gough
, and W. J.
Murphy
, J. Chem. Phys.
81
, 5352
(1984
).29.
A. L.
Aljibury
, R. G.
Snyder
, H. L.
Strauss
, and K.
Raghavachari
, J. Chem. Phys.
84
, 6872
(1986
).30.
Z.
Konkoli
and D.
Cremer
, Int. J. Quantum Chem.
67
, 1
(1998
).31.
Z.
Konkoli
and D.
Cremer
, Int. J. Quantum Chem.
67
, 29
(1998
).32.
Z.
Konkoli
, J. A.
Larsson
, and D.
Cremer
, Int. J. Quantum Chem.
67
, 11
(1998
).33.
Z.
Konkoli
, J.
Larsson
, and D.
Cremer
, Int. J. Quantum Chem.
67
, 41
(1998
).34.
D.
Cremer
, J. A.
Larsson
, and E.
Kraka
, in Theoretical and Computational Chemistry, Volume 5, Theoretical Organic Chemistry
, edited by C.
Parkanyi
(Elsevier
, Amsterdam
, 1998
), p. 259
.35.
E.
Kraka
and D.
Cremer
, ChemPhysChem
10
, 686
(2009
).36.
J.
Oomens
, E.
Kraka
, M. K.
Nguyen
, and T. H.
Morton
, J. Phys. Chem. A
112
, 10774
(2008
).37.
R. M.
Badger
, J. Chem. Phys.
2
, 128
(1934
).38.
Z.
Konkoli
, E.
Kraka
, and D.
Cremer
, J. Phys. Chem. A
101
, 1742
(1997
).39.
E.
Kraka
, in Encyclopedia of Computational Chemistry, Vol 4
, edited by P. v. R.
Schleyer
, N. L.
Allinger
, T.
Clark
, J.
Gasteiger
, P. A.
Kollman
, H. F.
Schaefer
III, and P. R.
Schreiner
(Wiley
, Chichester, UK
, 1998
), p. 2437
.40.
E.
Kraka
, in Wiley Interdisciplinary Reviews: Computational Molecular Science, Reaction Path Hamiltonian and the Unified Reaction Valley Approach
, edited by W.
Allen
, and P. R.
Schreiner
(Wiley
, New York
, 2011
), pp. 531
–556
.41.
E.
Kraka
and D.
Cremer
, Acc. Chem. Res.
43
, 591
(2010
).42.
D.
Cremer
and E.
Kraka
, Curr. Org. Chem.
14
, 1524
(2010
).43.
D.
Cremer
and J. A.
Pople
, J. Am. Chem. Soc.
97
, 1354
(1975
).44.
W.
Zou
, D.
Izotov
, and D.
Cremer
, J. Phys. Chem.
115
, 8731
(2011
).45.
C. R.
Jacob
, S.
Luber
, and M.
Reiher
, Chem.-Eur. J.
15
, 13491
(2009
).46.
C. R.
Jacob
and M.
Reiher
, J. Chem. Phys.
130
, 084106
(2009
).47.
V.
Liégeois
, C. R.
Jacob
, B.
Champagne
, and M.
Reiher
, J. Phys. Chem. A
114
, 7198
(2010
).48.
J.
Grunenberg
and N.
Goldberg
, J. Am. Chem. Soc.
122
, 6045
(2000
).49.
S. J.
Cyvin
, in Molecular Vibrations and Mean Square Amplitudes
(Universitetsforlaget
, 1971
), pp. 68
–73
.50.
M.
Vijay Madhav
and S.
Manogaran
, J. Chem. Phys.
131
, 174112
(2009
).51.
K.
Brandhorst
and J.
Grunenberg
, Chem. Soc. Rev.
37
, 1558
(2008
).52.
J.
Grunenberg
, R.
Streubel
, G.
von Frantzius
, and W.
Marten
, J. Chem. Phys.
119
, 165
(2003
).53.
J.
Grunenberg
, J. Am. Chem. Soc
126
, 16310
(2004
).54.
C. A.
Pignedoli
, A.
Curioni
, and W.
Andreoni
, ChemPhysChem
6
, 1795
(2005
).55.
J.
Baker
and P.
Pulay
, J. Am. Chem. Soc.
128
, 11324
(2006
).56.
A.
Espinosa
and R.
Streubel
, Chem.-Eur. J.
17
, 3166
(2011
).57.
E. B.
Wilson
Jr., J. Chem. Phys.
7
, 1047
(1939
).58.
N.
Neto
, Chem. Phys.
91
, 89
(1984
).59.
B.
Winnewisser
and J. K. G.
Watson
, J. Mol. Spectrosc.
205
, 227
(2001
).60.
C.
Lee
, W.
Yang
, and R. G.
Parr
, Phys. Rev. B
37
, 785
(1988
).61.
A. D.
Becke
, J. Chem. Phys.
98
, 5648
(1993
).62.
P. J.
Stevens
, F. J.
Devlin
, C. F.
Chablowski
, and M. J.
Frisch
, J. Phys. Chem.
98
, 11623
(1994
).63.
Z.
Konkoli
, D.
Cremer
, and E.
Kraka
, J. Comput. Chem.
18
, 1282
(1997
).© 2012 American Institute of Physics.
2012
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