One-dimensional quantum description of the bending vibrations of HCN/CNH

Quantum dynamics with curvilinear coordinates: models and kinetic energy operator

In order to simplify the numerical solution of the time-dependent or time-independent Schrödinger equations associated with atomic and molecular motions, the use of well-adapted coordinates is essential. Usually, this set of curvilinear coordinates leads to a Hamiltonian operator that is as separable as possible. Although their corresponding kinetic energy operator (KEO) expressions can be derived analytically for small systems or special kinds of coordinates, a numerical and exact approach allows one to compute them in terms of sophisticated curvilinear coordinates. Furthermore, the numerical approach enables one to easily define reduced-dimensionality or constrained models. We present here a recent implementation of this numerical approach that allows nested coordinate transformations, therefore leading to great flexibility in the definition of the curvilinear coordinates. Furthermore, this implementation has no limitations in terms of numbers of atoms or coordinate transformations. The quantum dynamics of the cis-trans photoisomerization of part of the retinal chromophore illustrates the construction of the coordinates and KEO part of a three-dimensional model. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.

Interplay of Rotational and Pseudorotational Motions in Flexible Cyclic Molecules

Solutions to the time-independent nuclear Schrödinger equation associated with the pseudorotational motion of three flexible cyclic molecules are presented and discussed. Structural relaxations related to the pseudorotational motion are described as functions of a pseudorotation angle ϕ which is formulated according to the definition of ring-puckering coordinates originally proposed by Cremer and Pople ( J. Am. Chem. Soc. 1975, 97 (6), 1354-1358). In order to take into account the interplay between pseudorotational and rotational motions, the rovibrational Hamiltonian matrices are formulated for the rotational quantum numbers J = 0 and J = 1. The rovibrational Hamiltonian matrices are constructed and diagonalized using a Python program developed by the authors. Suitable algorithms for (i) the construction of one-dimensional cuts of potential energy surfaces along the pseudorotation angle ϕ and (ii) the assignment of the vibrorotational wave functions (which are needed for the automatic calculation of rotational transition energies J = 0 → J = 1) are described and discussed.

Cumulative isomerization probability studied by various transition state wave packet methods including the MCTDH algorithm. Benchmark: HCN→CNH isomerization

The 3D cumulative isomerization probability N(E) for the transfer of a light particle between two atoms is computed by one time-independent and two time-dependent versions of the transition state wave packet (TSWP) method. The time-independent method is based on the direct expansion of the microcanonical projection operator on Chebyshev polynomials. In the time-dependent TSWP methods, the propagations are carried out by the split operator scheme and the multiconfiguration time-dependent Hartree (MCTDH) algorithm. This is the very first implementation of the TSWP method in the Heidelberg MCTDH package [G. W. Worth, M. H. Beck, A. Jackle, and H.-D. Meyer, The MCDTH package, Version 8.2 (2000); H.-D Meyer, Version 8.3 (2002). See http://www.pci.uni-heidelberg.de/tc/usr/mctdh/]. The benchmark is the HCN-->CNH isomerization for zero total angular momentum. Particular insights are given into the tunneling region. In larger systems, the time-dependent version of TSWP making use of the MCTDH algorithm will permit to treat more and more modes quantum mechanically, for very accurate results. Therefore, it was important to calibrate the implementation. Besides, we also assess the efficiency of a reduced dimensionality approach by comparing the new exact 3D calculations of N(E) for the HCN-->CNH isomerization with results obtained via 1D or 2D active subspaces. This suggests that, it should be possible to take directly benefit of the present 3D approaches, adapted for triatomic Jacobi coordinates to compute N(E) for H-transfer in larger systems, via three active coordinates. The prerequisite is then the simplification of the reduced 3D kinetic energy operator with rigid constraint to take the form corresponding to a pseudo triatomic system in Jacobi coordinates with effective masses. This last step is checked in the methoxy radical and malonaldehyde. Finally, different ways to obtain reliable eigenvectors of the flux operator associated with a dividing surface are revisited.

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).