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

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 1915 - 1998

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 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

Expanded screen dump of CAAARS display

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

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

<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>

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

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)

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>

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>

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.