^{1,a)}, Michael Sanrey

^{2}, Fabien Gatti

^{2}and Frédéric Le Quéré

^{3}

### Abstract

We report on full-dimensional vibrational quantum dynamics of the highly excited ammonia isotopologue using a newly developed potential energy surface and the MCTDH program package. The calculations allow to realistically simulate an infrared laser induced stereomutation reaction at the pyramidal nitrogen atom in the femtosecond time domain. Our results allow for a thorough qualitative and quantitative understanding of infrared photoinduced stereomutation kinetics, the underlying quantum dynamics, and the reaction mechanisms. Comparison is made with a previous, reduced dimensionality study of the same reaction [R. Marquardt, M. Quack, I. Thanopulos, and D. Luckhaus, J. Chem. Phys.118, 643 (2003)], and it is shown that slight variances of reduced spaces lead to significantly different kinetics. Because the quantum dynamics depends subtly on variances of reduced spaces, reduced dimensionality treatments are not reliable even for qualitative predictions of the stereomutation kinetics. The first direct comparison between the Multiconfigurational Time Dependent Hartree [M. H. Beck, A. Jäckle, G. A. Worth *et al.*, Phys. Rep.324, 1 (2000)] and Unimolecular Reactions Induced by Monochromatic Infrared Radiation [M. Quack and E. Sutcliffe, QCPE Bulletin6, 98 (1986)] program packages on a specific, four dimensional quantum dynamical problem allows for their full validation in the present work.

This work has received financial support from the Agence Nationale de la Recherche (Project ANR blanc NT05-3_842315). The authors thank Professor H.-D. Meyer and Dr. D. Luckhaus for numerous discussions and help.

I. INTRODUCTION

II. METHODS

A. Solution of the time dependent Schrödinger equation

B. Hamiltonian and coordinates

1. 6D-theory

2. 4D-theory

C. Molecule-radiation coupling

III. RESULTS FROM 6D CALCULATIONS

A. Vibrational term values and discussion of MCTDH parameters

B. Absorptionspectrum and excitation pathways

C. Intramolecular kinetics and the underlying wave packet dynamics

1. Kinetics

2. Wave packet dynamics

D. Mechanisms

1. Population evolution of spectroscopic states

2. Mechanisms M2 and M4

3. After pulse mechanisms

IV. RESULTS FROM 4D CALCULATIONS

A. Test on PES

B. Test on reduced space dynamics

C. Test on methods

V. CONCLUSIONS

### Key Topics

- Tunneling
- 34.0
- Excited state reaction dynamics
- 16.0
- Laser induced chemistry
- 16.0
- Potential energy surfaces
- 13.0
- Absorption spectra
- 9.0

## Figures

Graphical definition of Radau coordinates for ammonia and isotopologues (see discussion in the text).

Graphical definition of Radau coordinates for ammonia and isotopologues (see discussion in the text).

Coherent absorption spectrum in the region of the NH stretching fundamental; , 6D calculations using the MCTDH code and based on the AMMPOT4 PES. Peaks labeled A–E are discussed in the text. (– – –) and (——) .

Coherent absorption spectrum in the region of the NH stretching fundamental; , 6D calculations using the MCTDH code and based on the AMMPOT4 PES. Peaks labeled A–E are discussed in the text. (– – –) and (——) .

Time evolution of the population of R-type molecules (reactant population evolution), according to Eq. (17), during excitation with a time averaged intensity at three different excitation wave numbers corresponding to peaks A, B, and C in Fig. 2. After 2 ps, two lines are shown for each excitation wave number, indicating evolutions at laser on/off conditions as follows: (A) , laser on (- - -), off (◇-◇); (B) , laser on (——), off (--); (C) , laser on (– –), off (○ –○).

Time evolution of the population of R-type molecules (reactant population evolution), according to Eq. (17), during excitation with a time averaged intensity at three different excitation wave numbers corresponding to peaks A, B, and C in Fig. 2. After 2 ps, two lines are shown for each excitation wave number, indicating evolutions at laser on/off conditions as follows: (A) , laser on (- - -), off (◇-◇); (B) , laser on (——), off (--); (C) , laser on (– –), off (○ –○).

Time evolution of the absorbed energy, Eq. (15), six-dimensional calculations; peaks A, B, and C as defined in Fig. 2. The horizontal, dashed, and dotted line indicates the classical barrier energy ( on AMMPOT4) (Ref. 32). (- - -) (peak A), (——) (peak B), and (– – –) (peak C).

Time evolution of the absorbed energy, Eq. (15), six-dimensional calculations; peaks A, B, and C as defined in Fig. 2. The horizontal, dashed, and dotted line indicates the classical barrier energy ( on AMMPOT4) (Ref. 32). (- - -) (peak A), (——) (peak B), and (– – –) (peak C).

Snapshots of the time dependent reduced probability densities (upper row) and (lower row) [see Eq. (18)] after 100 fs of excitation at and . Probability densities are represented by broad isodensity contour lines, drawn at monotonically darkening gray tones; the outermost lines give the lowest densities at (upper row) and (lower row), and all following lines are at constant increments of (upper row) and (lower row). Because of their width, contour lines become indistinguishable at higher densities, which are then indicated by the darkness of the region. Probability density contours are superimposed to 12 thin contour lines of sections of the potential energy surface AMMPOT4 (Ref. 32), ranging from 500 to , at increments of . Sections were calculated at equilibrium values of the remaining coordinates: , (upper row), , , and (lower row). Straight interrupted lines show key coordinate values (see also text).

Snapshots of the time dependent reduced probability densities (upper row) and (lower row) [see Eq. (18)] after 100 fs of excitation at and . Probability densities are represented by broad isodensity contour lines, drawn at monotonically darkening gray tones; the outermost lines give the lowest densities at (upper row) and (lower row), and all following lines are at constant increments of (upper row) and (lower row). Because of their width, contour lines become indistinguishable at higher densities, which are then indicated by the darkness of the region. Probability density contours are superimposed to 12 thin contour lines of sections of the potential energy surface AMMPOT4 (Ref. 32), ranging from 500 to , at increments of . Sections were calculated at equilibrium values of the remaining coordinates: , (upper row), , , and (lower row). Straight interrupted lines show key coordinate values (see also text).

Snapshots of the time dependent reduced probability densities (upper row) and (lower row) after 1238 fs of excitation at and (see also Fig. 5).

Snapshots of the time dependent reduced probability densities (upper row) and (lower row) after 1238 fs of excitation at and (see also Fig. 5).

Graphical representation of the laser induced stereomutation process at (pathway B); indicated are the section of the PES along the coordinate at equilibrium values for the remaining coordinates (see Fig. 5), the positions of spectroscopic states participating most importantly at the dynamics (with continuous, horizontal lines; see also Table I), and the reduced, 1D probability densities corresponding to the initial state and to the spectroscopic state at . Dashed horizontal lines and vertical arrows indicate the one- and two-photon resonance levels.

Graphical representation of the laser induced stereomutation process at (pathway B); indicated are the section of the PES along the coordinate at equilibrium values for the remaining coordinates (see Fig. 5), the positions of spectroscopic states participating most importantly at the dynamics (with continuous, horizontal lines; see also Table I), and the reduced, 1D probability densities corresponding to the initial state and to the spectroscopic state at . Dashed horizontal lines and vertical arrows indicate the one- and two-photon resonance levels.

Time evolution of populations of spectroscopic states, Eq. (19), during excitation at (column B) and (column C), and ; continuous lines are states of positive, interrupted lines are states of negative inversion parity. (a) Ground state doublet: (—) and (– – –) . (b) doublet: (– – –) and (—) . (c) doublet: (– – –) and (—) . (d) doublet: (—) and (– – –) .

Time evolution of populations of spectroscopic states, Eq. (19), during excitation at (column B) and (column C), and ; continuous lines are states of positive, interrupted lines are states of negative inversion parity. (a) Ground state doublet: (—) and (– – –) . (b) doublet: (– – –) and (—) . (c) doublet: (– – –) and (—) . (d) doublet: (—) and (– – –) .

Reactant population evolution, according to Eq. (17), but in the 4D model described in Sec. ???, during excitation at ; excitation wave numbers differ slightly for the two PES representations compared here (see text): (– – –) AMMPOT 1 , (—) AMMPOT4 , and (- - -) AMMPOT4 (, 6D calculation as in Fig. 3).

Reactant population evolution, according to Eq. (17), but in the 4D model described in Sec. ???, during excitation at ; excitation wave numbers differ slightly for the two PES representations compared here (see text): (– – –) AMMPOT 1 , (—) AMMPOT4 , and (- - -) AMMPOT4 (, 6D calculation as in Fig. 3).

Time evolution of state vector components , as obtained with MCTDH (left hand side) and URIMIR (right hand side), at and , for AMMPOT1. Continuous lines are states of positive, interrupted lines are states of negative inversion parity. (a) Population of ground state doublet: (—) and (– – –) . (b) Population of an excited doublet: (– – –) and (—) . (c) Relative phases of the excited doublet [line code as under (b)] (see text for definitions).

Time evolution of state vector components , as obtained with MCTDH (left hand side) and URIMIR (right hand side), at and , for AMMPOT1. Continuous lines are states of positive, interrupted lines are states of negative inversion parity. (a) Population of ground state doublet: (—) and (– – –) . (b) Population of an excited doublet: (– – –) and (—) . (c) Relative phases of the excited doublet [line code as under (b)] (see text for definitions).

## Tables

Experimental and calculated vibrational wavenumbers for . In Ref. 32 a complete list of theoretical term values to up to is given.

Experimental and calculated vibrational wavenumbers for . In Ref. 32 a complete list of theoretical term values to up to is given.

Run time parameters for MCTDH.

Run time parameters for MCTDH.

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