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Example: vibrational states of CH 3

Recent methodological developments in the MCTDH approach and their application to reactive and vibrational dynamics Uwe Manthe Theoretische Chemie, Universität Bielefeld The state-averaged MCTDH approach Examples: vibrational states of CH3 Thermal flux eigenstates for H+CH4

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Example: vibrational states of CH 3

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  1. Recent methodological developments in the MCTDH approach and their application to reactive and vibrational dynamics Uwe Manthe Theoretische Chemie, Universität Bielefeld The state-averaged MCTDH approach Examples: vibrational states of CH3 Thermal flux eigenstates for H+CH4 The multi-layer MCTDH/CDVR approch Examples: photodissociation of NOCl Reaction rates for H+CH4 →H2+CH3

  2. Example: vibrational states of CH3 potential energy surface of Medvedev, Harding, Gray curvilinear coordinate, quasi-exact kinetic energy operator single-particle function basis required is independent of the number of wavepackets (vibrational levels)

  3. Thermal flux eigenstates for H+CH4 iterative (Lanczos) diagonalization State averaged MCTDH for standard MCTDH based iteration scheme

  4. A simple example: NOCl photodissociation NOCl → NO + Cl standard MCTDH calculations without and with CDVR quadrature compared to exact results conclusion: CDVR error irrelevant for typical standard MCTDH calculations

  5. NOCl → NO + Cl mode combination MCTDH: combining R and r calculations without and with CDVR quadrature compared to exact results conclusion: CDVR errors are of similar size as the MCTDH representation errors

  6. NOCl → NO + Cl multi-layer MCTDH: calculations without and with CDVR quadrature compared to exact results CDVR errors comparable to mode-combination MCTDH

  7. H+CH4 → H2+CH3 : cumulative reaction probabilities state-averaged MCTDH (Jordan-Gilbert PES, transition state normal coordinates) converged standard MCTDH representation: n 6 5 33 3 3 3 2 2 2 2 2 N 48 48 3215 15 10 10 6 6 8 8 8 Q1 Q9 Q4Q2 Q3 Q5 Q6 Q7 Q8 Q10 Q11 Q12 H-H-CH3 CH3 H-H-CH3CH3 CH3 stretches umbrella bends bends stretches multi-layer MCTDH representation: n1 6 5 33 3 3 3 n n2 2 2 2 2 2 N 48 48 3215 15 10 10 6 6 8 8 8 Q1 Q9 Q4Q2 Q3 Q5 Q6 Q7 Q8 Q10 Q11 Q12 H-H-CH3 CH3 H-H-CH3CH3 CH3 stretches umbrellabends bends stretches

  8. CPU times required: standard MCTDH 47 h ML-MCTDH n=1 7 h n=2 12 h n=3 16 h next multi-layer MCTDH representation: n1n3 3 3 3 3 n2 6 5 3 2 2 2 2 2 N 48 48 3215 15 10 10 6 6 8 8 8 Q1 Q9 Q4Q2 Q3 Q5 Q6 Q7 Q8 Q10 Q11 Q12 H-H-CH3 CH3 H-H-CH3CH3 CH3 stretches umbrellabends bends stretches

  9. Thanks: Rob van Harrevelt Chris Evenhuis, Gerd Schiffel, Thorsten Hammer, Gloria Moyano Gunnar Nyman, Alexandra Viel, Fermin Huarte

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