Semi-experimental (rs/re) Structures for the Heavy
Atom Backbones of Two Moderately Large
Molecules Obtained from Microwave
Spectroscopy and Quantum Chemical
Calculations
NORMAN C. CRAIG,Department of Chemistry and Biochemistry, Oberlin College,
Oberlin, OH 44074, USA [email protected]
ALBERTO LESARRI, Departamento de Quîmica Fîsica y Quîmica Inorgánica,
Facultad de Ciencias, Universidad de Valladolid, E-47011 Valladolid, Spain
EMILIO J. COCINERO, Departamento de Quîmica Fîsica, Facultad de Ciencia y
Tecnología, Universidad del País Vasco, Ap. 644, E-48080 Bilbao, Spain
JENS-UWE GRABOW, Institut für Physikalische Chemie und Elektrochemie,
Gottfried-Wilhelm-Leibniz-Universität, Callinstrasse 3A, D30167 Hannover,
Germany

Method: Semi-Experimental
Equilibrium Structures
• Obtain ground state rotational constants from
MW spectra for polar molecules.
• Do so for a full series of isotopologues.
• Use quantum chemistry (triple zeta level) to
compute vibration-rotation constants (alphas).
• Find equilibrium rotational
constants (k = a,b,c)
n
Be, k  B0, k 1/ 2k,
i 1
• Obtain an re structure from a global fit of all
the equilibrium rotational constants.
rs/re Structures
MW spectroscopy yields ground state rotational constants for
single substitution with heavy atoms (13C, 18O, 15N) in
natural abundance. Do we have a general method for
finding rs/re structures of heavy atom backbones?
Use Kraitchman equations (rs method) to find semiexperimental equilibrium structures (re) for heavy atom
backbones from equilibrium rotational constants.
Tested for ethylene, 1,1-difluoroethylene, 1,1difluorocyclopropane, and butadiene. (Columbus ‘10, TC05)
Applied to cis-hexatriene (3C) and the equatorial conformer of
glycidol I (3C, 2O, 1H). (Columbus ‘10, TC05)
Application to Equatorial Conformers of
N-Methyl-piperidone (4C, 1O, 1N) and
Tropinone (5C, 1O, 1N)
MW spectra
N-Methyl-piperidone. L. Evangelisti, A. Lesarri, M. Jahn, E. Cocinero,
W. Caminati, J.-U. Grabow J. Phys. Chem. A, in press.
Tropinone. E. J. Cocinero, A. Lesarri, P. Écija, J.-U. Grabow, J. A.
Fernández, F. Castaño PCCP 2010, 12, 6076-6083.
rs/re Cartesian Coordinates for N-Methyl-piperidone from
Equilibrium Rotational Constantsa and Kraitchman Equations
a/Å
b/Å
c/Å
O
-2.618
0.022b
0.397
C4
-1.498
0.012b
-0.066
C3
-0.737
1.267
-0.370
C2
0.677
1.193
0.197
N
1.363
0.023b
-0.278
C7
2.744
0.012ib
0.169
a
Alphas compu ted with force consta nts from B3LYP/
cc-pVTZ and scaling of harmonic for ce constants by 0.95.
b
Set to 0.0 before computi ng internal coordinates.
Comparison of Bond Parameters for
N-Methyl-piperidone
rs/re Cartesian Coordinates for Tropinone from Equilibrium
Rotational Constantsa and Kraitchman Equations
a/Å
b/Å
c/Å
O
-2.791
0.073ib
0.055
C3
-1.644
0.086b
-0.308
C2
-0.882
1.276
-0.551
C1
0.569
1.140
-0.065
C7
0.619
0.767
1.423
N
1.172
0.108b
-0.775
C9
2.624
0.022b
-0.658
a
Alphas compu ted with force consta nts from B3LYP/
cc-pVTZ and scaling of harmonic for ce constants by 0.95.
b
Set to 0.0 before computi ng internal coordinates.
Comparison of Bond Parameters for Tropinone
Kraitchman Equations
1/ 2
P 



P
P
y
z
x   x 
1

1





   Py  Px  Pz  Px 

Px  (1/2)(Ix  Iy  Iz )
Py  (1/2)(Iy  Iz  Ix )
Pz  (1/2)(Iz  Ix  Iy )

Mm
M  m
W. Gordy and R. L. Cook, Microwave Molecular Spectra,
third ed., 1984, Techniques of Chemistry, Vol. XVIII,
Interscience, New York, p. 663.
Conclusions
The rs/re method has been applied for determining the
equilibrium structures of two moderately large molecules.
The method falters as molecular size increases.
Molecular symmetry is not obtained for the Cartesian
coordinates.
Small coordinates are problematic with the rs method.
The “mixed estimation” method, as championed by Jean
Demaison, is probably a solution. (Recent success was
achieved with cis,trans-1,4-difluorobutadiene.1)
1. J. F. Demaison, N. C. Craig, J. Phys. Chem. A, in press.
Acknowledgement
Peter Groner used VIBROT to compute the
alphas.
Support
Dreyfus Foundation
National Science Foundation
Oberlin College
Kraitchman' s equations give exact results for equilibriu m
rotational constants. (Past use with ground state rotational
constants has been approximate.)
However, testing is needed to evaluate the impa ct of
approximations.
1) In fitting MW lines, some centrifugal distortion constants
may be from calculated values.
2) QC model s used to compute alphas are imperfect.
3) Alph as are only the linear term in an expansion.
4) Kraitchman' s equations involve differences between
mome nts of inertia; hence, good values for equilibrium
mome nts of inertia are needed.