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 →H
2+CH
3
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)
Thermal flux eigenstates for H+CH4
iterative (Lanczos) diagonalization State averaged MCTDH for standard MCTDH based iteration scheme
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
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
NOCl → NO + Cl
multi-layer MCTDH:
calculations without and
with CDVR quadrature
compared to exact results
CDVR errors comparable to
mode-combination MCTDH
H+CH4 → H
2+CH
3 : cumulative reaction probabilities
state-averaged MCTDH (Jordan-Gilbert PES, transition state normal coordinates)
converged standard MCTDH representation:
n 6 5 3 3 3 3 3 2 2 2 2 2
N 48 48 32 15 15 10 10 6 6 8 8 8
Q1
Q9
Q4
Q2
Q3
Q5
Q6
Q7
Q8
Q10
Q11
Q12
H-H-CH3 CH3 H-H-CH3 CH3 CH3
stretches umbrella bends bends stretches
multi-layer MCTDH representation:
n1
6 5 3 3 3 3 3 n
n2
2 2 2 2 2
N 48 48 32 15 15 10 10 6 6 8 8 8
Q1
Q9
Q4
Q2
Q3
Q5
Q6
Q7
Q8
Q10
Q11
Q12
H-H-CH3 CH3 H-H-CH3 CH3 CH3
stretches umbrella bends bends stretches
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:
n1
n 3 3 3 3 3
n2
6 5 3 2 2 2 2 2
N 48 48 32 15 15 10 10 6 6 8 8 8
Q1
Q9
Q4
Q2
Q3
Q5
Q6
Q7
Q8
Q10
Q11
Q12
H-H-CH3 CH3 H-H-CH3 CH3 CH3
stretches umbrella bends bends stretches
Thanks:
Rob van Harrevelt
Chris Evenhuis, Gerd Schiffel, Thorsten Hammer,Gloria Moyano
Gunnar Nyman,Alexandra Viel,Fermin Huarte
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