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