Quantum tunnel effect: dynamics of molecules with quantum nuclei

Support: Croatian Science Foundation

Grant number: IP-2020-02-9932

Project duration: 18. 1. 2021. - 17. 1. 2025. (48 months)

Principal investigator: Marko T. Cvitaš

Project team members:
Nina Tokić
Mihael Eraković
Marin Sapunar
Ivan Ljubić
Marko T. Cvitaš
Nađa Došlić
Darko Babić


Brief description:
The goal of the project is to develop new computational methods for describing quantum nuclear effects in chemistry. Our approach is based on instanton theory and the emphasis is on studying the tunnel effect in molecular systems. In particular, we have generalized the method of Mil'nikov and Nakamura (J. Chem. Phys. 122, 124311, (2005)) to calculate tunnelling splittings in vibrationally excited states of molecules with multiple wells. We have also extended the formulation to include the wells that are asymmetric in shape and energy, and calculated tunnelling matrix elements due to coupling of inequivalent states on the opposite sides of the barrier [5]. The developed theory will be applied to study rearrangement dynamics of water clusters and its signature in the vibrational spectrum.  We also aim to apply the instanton method in new contexts: to calculate nonadiabatic tunnelling rates of proton-coupled electron transfer reactions in aqueous media and tunnelling rates in some photo-excited systems.


We have developed numerical algorithms for locating instanton paths and for increasing computational efficiency of the calculations of tunnelling splittings in molecules. The example below shows the located instanton path in malonaldehyde.

We have used instanton theory to explain the tunnelling splitting pattern of 320 states in the ground state of water pentamer, and interpreted it in terms of five rearrangements pathways (a simultaneous flip and bifuraction of hydrogen bonds is shown below).

Recently, we calculated the low-lying vibrational tunnelling spectrum of partially deuterated malonaldehyde [5]. The system features asymmetry of the two wells due to zero-point energy difference and the calculation of tunnelling matrix elements between inequivalent states.

Vibrational tunneling spectrum of partially deuterated malonaldehyde.


[5] M. Eraković, M.T. Cvitaš, https://arxiv.org/abs/2201.06654
[4] B. Milovanović, J. Novak, M. Etinski, W. Domcke, N. Došlić, submitted
[3] J. Coonjobeeharry, K.E. Spinlove, C. Sanz Sanz, M. Sapunar, N. Došlić, G.A. Worth, accepted in Philos. Trans. R. Soc. A
[2] R. Totani, I. Ljubić, A. Ciavardini, C. Grazioli, F. Galdenzi, M. de Simone, M. Coreno, Phys. Chem. Chem. Phys. 24, 1993 (2022).
[1] I. Sviben, I. Džeba, M. Bonifačić, I. Ljubić, Phys. Chem. Chem. Phys. 23, 10429 (2021).