Based on extensive ab initio calculations and the time-propagation of the nuclear Schrödinger equation, we study the vibrational relaxation dynamics and resulting spectral signatures of the OH stretch vibration of a hydrogen-bonded complex, HCO. Despite their smallness, it has been shown experimentally by Johnson and coworkers that the gas-phase infrared spectra of these types of complexes exhibit much of the complexity commonly observed for hydrogen-bonded systems. That is, the OH stretch band exhibits a significant red shift together with an extreme broadening and a pronounced substructure, which reflects its very strong anharmonicity. Employing an adiabatic separation of time scales between the three intramolecular high-frequency modes of the water molecule and the three most important intermolecular low-frequency modes of the complex, we calculate potential energy surfaces (PESs) of the ground and the first excited states of the high-frequency modes and identify a vibrational conical intersection between the PESs of the OH stretch fundamental and the HOH bend overtone. By performing a time-dependent propagation of the resulting system, we show that the conical intersection affects a coherent population transfer between the two states, the first step of which being ultrafast (60 fs) and irreversible. The subsequent relaxation of vibrational energy into the HOH bend and ground state occurs incoherently but also quite fast (1 ps), although the corresponding PESs are well separated in energy. Owing to the smaller effective mass difference between light and heavy degrees of freedom, the adiabatic ansatz is consequently less significant for vibrations than in the electronic case. Based on the model, we consider several approximations to calculate the measured Ar-tag action spectrum of HCO and achieve semiquantitative agreement with the experiment.
REFERENCES
Q2 represents a linear translation with a kinetic energy operator , whose DVR representation is given by Eq. (A6) of Ref. 41. On the other hand, Q1 and Q3 are linear combinations of rotations of the two molecules (Fig. 1). Since we consider only 1D rotations due to restricting the problem to modes that stay in the plane of the complex, the corresponding kinetic energy operator remains simple with (where αi are the rotation angles of the two molecules). In principle, a DVR exists for that operator that takes its periodicity into account.41 Since we, however, combine two angles with different scaling factors into one mode (so that their linearisations for small displacements reveal the corresponding normal mode coordinates), the overall coordinates Q1 and Q3 are no longer periodic. We therefore use Eq. (A6) of Ref. 41 for the angle coordinates as well. Since the maximum rotation in the considered region is still significantly smaller than 2π, that approximation appears to be acceptable.
Apart from convergence issues, it is in fact irrelevant for both the adiabatic and the diabatic representation whether or not the minimum energy positions in Eq. (10) are considered (discarding them actually leads to slightly better convergence with respect to basis size). On the other hand, for the numerically exact time-propagation, it is mandatory to expand Eq. (10) and to consider the minimum energy positions explicitly. We have found that it is the variation of the minimum energy positions as a function of inter-molecular coordinates Q that dominates the non-adiabtic couplings between the excited states to the bend fundamental and the ground state.
