CTMQC, a module for excited-state nonadiabatic dynamics


CTMQC is a module for excited-state nonadiabatic dynamics. It is used to simulate the coupled dynamics of electrons and nuclei (ideally in gas phase molecular systems) in response to, for instance, an initial electronic excitation.

The CTMQC module is based on the coupled-trajectory mixed quantum-classical (CT-MQC) algorithm [1,2] that has been derived starting from the evolution equations in the framework the exact factorization of the electron-nuclear wavefunction [3,4,5]. The CTMQC algorithm belongs to the family of quantum-classical methods, as the time evolution of the nuclear degrees of freedom is treated within the classical approximation, whereas electronic dynamics is treated fully quantum mechanically. Basically, the nuclei evolve as point particles, following classical trajectories, while the electrons generate the potential inducing such time evolution.

In its current implementation (used in Refs. [6,7]), the module cannot deal with arbitrary nuclear dimensions, but it is restricted to treat up to 3-dimensional problems, which gives the possibility to compare quantum-classical results easily and directly with quantum wavepacket dynamics. CTMQC has been analyzed and benchmarked against exact propagation results on typical low-dimensional model systems [1,2,6,7], and applied for the simulation of the photo-initiated ring-opening process of Oxirane [8]. For this study, CTMQC has been implemented in a developer version of the CPMD electronic structure package based on time-dependent density functional theory. Concerning electronic input properties, the CTMQC module requires a grid representation of the adiabatic potential energy surfaces and of the nonadiabatic coupling vectors, since the electronic dynamics is represented and solved in the adiabatic basis.

This feature allows the algorithm to be easily adaptable, in the current form, to any quantum chemistry electronic structure package. The number of electronic states to be included is not limited and can be specified as input.

Practical application and exploitation of the code
The purpose of the module is to familiarize the user with a new simulation technique, i.e., the CTMQC method, for treating problems where electronic excited states are populated during the molecular dynamics. Photo-activated ultrafast processes are typical situations in which an approach like CTMQC can be used to predict molecular properties, like structures, quantum yields, or quantum coherence.
The module is designed to apply the CTMQC procedure to one-, two-, and three-dimensional model systems where an arbitrary number of electronic states are coupled via the nuclear dynamics. Tully model systems [9] are within the class of problems that can be treated by the module, as well as a wide class of multidimensional problems involving, for instance, ultrafast radiationless relaxation of photo-excited molecules [10] through conical intersections.


Software documentation can be found in our E-CAM software Library here.


[1] S. K. Min, F. Agostini, E. K. U. Gross Coupled-trajectory quantum-classical approach to electronic decoherence in nonadiabatic processes Phys. Rev. Lett. 115 (2015) 073001
[2] F. Agostini, S. K. Min, A. Abedi, E. K. U. Gross Quantum-classical nonadiabatic dynamics: Coupled- vs independent-trajectory methods J. Chem. Theory Comput. 12 (2016) 2127
[3] A. Abedi, N. T. Maitra, E. K. U. Gross Exact factorization of the time-dependent electron-nuclear wave function Phys. Rev. Lett. 105 (2010) 123002
[4] A. Abedi, F. Agostini, Y. Suzuki, E. K. U. Gross Dynamical steps that bridge piecewise adiabatic shapes in the exact time-dependent potential energy surface Phys. Rev. Lett. 110 (2013) 263001
[5] F. Agostini, B. F. E. Curchod, R. Vuilleumier, I. Tavernelli, E. K. U. Gross, TDDFT and Quantum-Classical Dynamics: A Universal Tool Describing the Dynamics of Matter Springer International Publishing (2018) 1
[7] G. H. Gossel, F. Agostini, N. T. Maitra Coupled-trajectory mixed quantum-classical algorithm: A deconstruction J. Chem. Theory Comput. 14 (2018) 4513
[8] S. K. Min, F. Agostini, I. Tavernelli, E. K. U. Gross Ab initio nonadiabatic dynamics with coupled trajectories: A rigorous approach to quantum (de)coherence J. Phys. Chem. Lett. 8 (2017) 3048
[9] J. C. Tully Molecular dynamics with electronic transitions J. Chem. Phys. 93 (1990) 1061
[10] B. F. E. Curchod, F. Agostini On the dynamics through a conical intersection J. Phys. Chem. Lett. 8 (2017) 831