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1 (Picture courtesy of Python M)
2 Where is Wuppertal?
3 The Wuppertal monorail
4 The general scheme of things (at least in this lecture.) Potential energy surface(s) Dipole moment surface(s)... in general obtained from ab initio calculations PROGRAMS MORBID, RENNER, DR, TROVE Simulated rotation-vibration spectra
5 Nuclear-motion programs developed: MORBID (Morse Oscillator Rigid Bender Internal Dynamics, 1988) triatomic molecule in isolated electronic state RENNER (Renner Effect, 1995) triatomic molecule in Renner-degenerate states DR (Double Renner, 2004) triatomic molecule in double-renner-degenerate states TROVE (Theoretical ROtation-Vibration Energies, 2007) (in principle) any molecule in isolated electronic state
6 TROVE: Theoretical ROVibrational Energies: Variational calculations of rotationvibration for a general polyatomic molecule in an isolated electronic state S.N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc (2007)
7 Hamiltonian: Coordinate transformation Laboratory fixed Cartesian coordinate system Body fixed internal coordinate system
8 Different molecules different transformations?
9 Different molecules different transformations?
10 One transformation for all molecules? Laboratory fixed Cartesian coordinate system Body fixed internal coordinate system The coordinate transformation is part of the program
11 TROVE input/output: Example for PH3 (CALCULATION OF VIBRATION ENERGIES FOR PH3) KinOrder 4 (Max order in the kinetic energy expansion) PotOrder 8 (Max order in the potential energy expansion) Natoms 4 Nmodes 6 SYMGROUP C3v(M) MOLTYPE XY3 (Number of atoms) (Number of modes = 3*Natoms-6) ZMAT P H H H END (ACTIVE SPACE CUTOFFS:) PRIMITIVES Npolyads 12 (how many polyads we calculate) enercut (energy cut in the primitive matrix for the diagonalization) END CONTRACTION Npolyads 10 (how many polyads we calculate) enercut END DIAGONALIZER SYEVR uplimit END Equilibrium re alphae deg End POTEN NPARAM 304 POT_TYPE poten_xy3_morbid_10 COEFF list (powers or list) ve fa fa fa Gamma i value j k t quanta A ( A1 ; 0 0 0) ( A2 ; ) A ( A1 ; 0 0 0) ( A2 ; ) A ( A1 ; 0 0 0) ( A2 ; ) A ( A1 ; 0 0 0) ( A2 ; ) A ( A1 ; 0 0 0) ( A2 ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; ) E ( A1 ; 0 0 0) ( E ; )
12 TROVE: Summary Variational calculations Approximate kinetic energy operator OpenMP parallelization For a general molecule of arbitrary structure, arbitrary basis sets or coordinates FBR method (not DVR) Accuracy & Efficiency For one large amplitude motion Black-box program Intensity simulations Robust symmetrization Lanczos diagonalization (large matrices) Automatic labeling of the levels Vibrational contraction of the basis set Basis sets: Harmonic oscillator Morse oscillator Numerov-Cooley solutions
13 1D vibrational basis functions Harmonic oscillator functions Morse oscillator functions Numerical function generated by Numerov-Cooley integration
14 Other programs/contributors in this area (Not exhaustive. No ranking intended ) DEWE and GENIUSH (A. G. Császár and E. Mátyus) MULTIMODE (J. Bowman and S. Carter) T. Carrington H. Guo N. C. Handy and S. Carter D. Lauvergnat and A. Nauts D. W. Schwenke J. Tennyson
15 TROVE for NH 3 : Absorption intensities at T=300K, 3.25 million transitions HITRAN = EXPERIMENT TROVE = THEORY
16 Ammonia line list simulations S. N. Yurchenko, R. J. Barber, A. Yachmenev, W. Thiel, Per Jensen, J. Tennyson, J. Phys. Chem. (2009).
17 Absorption spectrum of NH 3 at T = 300 K HITRAN TROVE
18 Absorption spectrum of NH 3 at T = 300 K
19 Absorption spectrum of NH 3 at T = 300 K (2 2 / 4 bands)
20 Absorption spectrum of NH 3 at T = 300 K (2 2 / 4 bands) Improvements under way!
21 Torsional splittings and anomalous intensities in HSOH Two enantiomer minima Internal rotation about the SO bond, strongly coupled to the rotation about the a axis (associated with K a ) Torsional splittings K a =0 J 0,J d 0 torsional splitting
22 HSOH: Torsional potential cis trans cis r O H H S t HSOH s Torsional splittings show strong variation with K a
23 HOOH, HSSH, HNCNH: Splittings stagger with K a Example: HNCNH Experiment: M. Birk, M. Winnewisser, J. Mol. Spectrosc. 136, 402 (1989) Semi-empirical explanation by Hougen and co-workers for HOOH and HSSH: J.T. Hougen, Can. J. Phys. 62, 1392 (1984). J.T. Hougen, B.M. DeKoven, J. Mol. Spectrosc. 98, 375 (1983).
24 HSOH: No staggering, more complicated variation Experiment Cologne Terahertz spectrometer First observation (for K a 3) in 2003 M. Behnke, J. Suhr, S. Thorwirth, F. Lewen, H. Lichau, J. Hahn, J. Gauss, K.M.T. Yamada, G. Winnewisser, J. Mol. Spectrosc. 221, 121 (2003) G. Winnewisser, F. Lewen, S. Thorwirth, M. Behnke, J. Hahn, J. Gauss, and E. Herbst, Chem. Eur. J 9, 5501 (2003) O. Baum, M. Koerber, O. Ricken, G. Winnewisser, S. N. Yurchenko, S. Schlemmer, K. M. T. Yamada, and T. F. Giesen, J. Chem. Phys. 129, (2008).
25 Ab initio potential energy surface + TROVE calculation of torsional splittings Ab initio potential energy surface: CCSD(T) method data points with aug-cc-pvtz basis set, energies up to cm -1 above equilibrium data points with aug-cc-pv(q+d)z basis set, energies up to cm -1 above equilibrium Simultaneous, weighted fitting to all data points, 762 parameters varied, standard error 2.8 cm -1 R. I. Ovsyannikov, V.V. Melnikov, W. Thiel, Per Jensen, O. Baum, T. F. Giesen, and S. N. Yurchenko, J. Chem. Phys. 129, (2008). S. N. Yurchenko, A. Yachmenev, W. Thiel, O. Baum, T. F. Giesen, V. V. Melnikov, and Per Jensen: J. Mol. Spectrosc. 257, 57 (2009).
26 HSOH: Ab initio ~12000 points CCSD(T)/aug-cc-pV(Q+d)Z TROVE J = 0 40, v HSOH 42 Full 6D calculations SRB approach s SRB approach: expansion around MEP S. N. Yurchenko, A. Yachmenev, W. Thiel, O. Baum, T. F. Giesen, V. V. Melnikov, and Per Jensen: J. Mol. Spectrosc. 257, 57 (2009).
27 HSOH rotation-torsion levels: experiment vs TROVE Term values (cm -1 ) Splitting (cm -1 ) J K a K c obs calc exp-calc calc exp exp-calc A' A" A" A' A' A" A" A' A' A" A' A" A" A' A' A" A" A' Basis set: HSOH 42
28 HSOH torsional splittings Experiment Cologne Terahertz spectrometer Theory TROVE calculations R. I. Ovsyannikov, V.V. Melnikov, W. Thiel, Per Jensen, O. Baum, T. F. Giesen, and S. N. Yurchenko, J. Chem. Phys. 129, (2008). O. Baum, M. Koerber, O. Ricken, G. Winnewisser et al., J. Chem. Phys. 129, (2008).
29 Semi-empirical alternative approach, following ideas of Hougen: J.T. Hougen, Can. J. Phys. 62, 1392 (1984). J.T. Hougen, B.M. DeKoven, J. Mol. Spectrosc. 98, 375 (1983). Ratio of I a moments of inertia I SH /I total 1/3. Pretend that t HSOH [-3,3 ] Molecule formally has C 3v (M) symmetry Do quantum mechanics under this assumption. Subject results to reality check : A 2 rotation of the SH moiety relative to OH moiety must leave wavefunction unchanged. K.M.T. Yamada, G. Winnewisser, and P. Jensen, J. Mol. Struct., , 323 (2004)
30 Semi-empirical alternative approach, following ideas of Hougen: t HSOH [-3,3 ] 6 6 matrix: K.M.T. Yamada, G. Winnewisser, and P. Jensen, J. Mol. Struct., , 323 (2004)
31 HSOH splittings (2009): K. M. T. Yamada, Per Jensen, S. C. Ross, O. Baum, T. F. Giesen, and S. Schlemmer, J. Mol. Structure 927, (2009).
32 Thanks & Acknowledgments The principal doer: Sergei N. Yurchenko, Wuppertal, Ottawa, Mülheim, Dresden, London Other doers: Oliver Baum, Cologne Vladlen Melnikov, Wuppertal Roman Ovsyannikov, Wuppertal Andrei Yachmenev, Mülheim Fellow ponderers: Thomas Giesen, Cologne Walter Thiel, Mülheim Thanks for support from the European Commission, the German Research Council (DFG), and the Foundation of the German Chemical Industry (Fonds der Chemie).
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