1. International Symposium on Molecular Spectroscopy
64th Meeting - - June 22 – 26, 2009
WF06 in Dynamics

2. Chemistry Molecules Physics/ Technology Spectroscopic data
Quantum monodromy
as a lattice defect of
energy-momentum
maps
Theoretical
spectroscopy
GSRB Hamiltonian
Topology of
potential function
Mathematics
The purpose of computing is insight, not numbers. Richard Hamming

3. Ab initio equilibrium structure of NCNCS
CCSD(T)/cc-pV5Z level of theory
This work
J = 12 – 11 rotational transition
observed by H. W. Kroto et al.
J. Mol. Spectrosc. 113, 1 (1985)

4. 4 normalization functions as indicated in panel b
Re-scaling of the intensities for the NCNCS millimeter wave spectrum by using
4 normalization functions as indicated in panel b
Predicted peak intensities for a-type Ka = 0, 1
and 2 rotational transitions
Raw Data
Normalization functions
Normalized spectrum

5. Expanded screen dump of CAAARS display

6. 1) Frequency(J) / [2(J + 1)] = Beff – Deff 2(J + 1)2 + …
2) GSRB least squares fit to Beff and Deff is currently
limited to energy levels in the range from
J = Ka to J = 25
MMW
GSRB

7. Reduced Fortrat diagrams of the assigned rotational frequencies
for NCNCS in 7 bending states
Champagne bottle potential function
for quasi-linear two-dimensional
bending mode

8. <r2> Beff Quantum lattice
of the effective rotational constants Beff for NCNCS
Quantum lattice of expectation values <r2> of the
bending coordinate r calculated with the GSRB
wave functions
Experimental Data are connected
by solid lines. Circles are GSRB values
Circles are GSRB values connected by
dashed lines
Beff
<r2>

9. Three dimensional image of the quantum lattice for the end-over-end rotational energy contribution for NCNCS and OCCCS
Lattice defect due to
Champagne bottle potential
function
Lattice due to harmonic
potential function
NCNCS
OCCCS

10. Beff E(vb,Ka) Quantum lattice
of the effective rotational constants Beff for NCNCS
Two-dimensional energy-momentum lattice for NCNCS
representing GSRB bending-rotation term values
E(vb,Ka) plotted for J = Ka
Experimental Data are connected
by solid lines. Circles are GSRB values
Beff
E(vb,Ka)

11. with the GSRB wave functions
Quantum lattice of expectation values for <r> and <r2> of the bending coordinate r calculated
with the GSRB wave functions
<r>
<r2>

12. SRB wave functions for NCNCS
Expectation values of the permanent electric dipole moment components ma and mb over the CNC
SRB wave functions for NCNCS
<vb,Ka|ma(r)|vb,Ka>
<vb,Ka|mb(r)|vb,Ka>

13. Conclusions and Insight
Re-scaling of the experimental line intensities helps greatly in the
assignment of high Ka and vb rotational lines in the NCNCS spectrum
GSRB (including centrifugal distortion) analysis of monodromy in
NCNCS is illustrated in the quantum lattice of the Beff values and the energy-momentum lattice of the bending-rotation term values.
Both maps show clearly the effects of quantum monodromy as a lattice defect which depends on the topology of the bending potential function.
The quantum lattice of the expectation values for <r> and <r2> using
the GSRB wave functions show that all physical quantities that depend on the bending coordinate r exhibit similar quantum monodromy plots
including rotational constants, dipole moments etc.