Coherent states suitable for the description of molecular rotations are developed and their connection to similar coherent states in the literature are explored. In particular their quasiclassical properties are developed. The use of such coherent states in time-dependent electron nuclear dynamics studies of molecular collision processes is discussed.
Coherent states suitable for the description of molecular rotations are developed and their connection to similar coherent states in the literature are explored. In particular their quasiclassical properties are developed. The use of such coherent states in time-dependent electron nuclear dynamics studies of molecular collision processes is discussed.
We show that molecules and nuclei with well-expressed rotational degrees of freedom can be excited by means of a multistep process, initiated by a short and sufficiently strong electromagnetic pulse, into a coherent superposition of rotational states. Properties of a molecule or a nucleus in such a nonstationary state change (quasi-) periodically in time, due to the fact that the energies of the rotational states satisfy (approximately) the rule \ensuremath{\omega}J(J+1). Accordingly, their interaction with an electromagnetic field or with other particles changes (quasi-) periodically in time. A gas of molecules in a coherent state exhibits a (quasi-) periodic change of the refractive index, an effect which has been observed for the case of CS2 gas at 325 K. The nuclear case does not lead to direct experimental detection, because of its short coherence period.
We reformulate a previous rotational coherent state (CS) to obtain temporally stable (TS) CSs for the spherical rotor (SR) and linear rotor (LR): TSSR and TSLR CSs, respectively. Being TS, the new CSs remain within their own classes during dynamics by evolving exclusively through their CS parameters. The new TS CSs are now appropriate to reconstruct quantum rotational properties from classical-mechanics simulations of chemical reactions. Following literature precedents, we enforce temporal stability by incorporating action-angle-related phase factors into the parameters of the original CS. In addition, to elucidate CS quantum reconstruction procedures, we derive one more rotational CS from a quantum electron nuclear dynamics description of a diatomic rotor (DR). The DR CS and the TSLR CS are not identical but display similar structures and properties. We rigorously demonstrate and examine the key properties of the three CSs: continuity, resolution of unity, temporal stability, action identity, minimum uncertainty relationships, and quasi-classical behavior. Finally, we present computer simulations of the CSs dynamics and an application of them to predict CO rotational excitation probabilities in the Li+ + CO reaction. CS results agree satisfactorily with experimental ones and encourage future applications in chemical dynamics, statistical mechanics, spectroscopy, nuclear physics, quantum coherence, and quantum computing.
Following our preceding work on spherical and linear rotors [C. Stopera and J. A. Morales, J. Chem. Phys. 152, 134112 (2020)], we reformulate an earlier rotational coherent state (CS) set to obtain a temporally stable (TS) CS set for symmetric rotors. Being TS, the new CSs remain within its own set during dynamics by evolving exclusively through their parameters. The TS CS set is now appropriate to reconstruct quantum rotational properties from classical-mechanics simulations of chemical reactions. Following literature precedents, we enforce temporal stability by incorporating action-angle-related phase factors into two parameters of the original CS set. Proofs and final expressions of the symmetric-rotor CS turn out more intricate than those of its spherical-rotor counterpart. We demonstrate and examine the key properties of the new CS set: continuity, resolution of unity, temporal stability, action identity, minimum uncertainty relationships, and quasi-classical behavior. Regarding the last property, we demonstrate that the body-fixed z-component of the CS angular momentum average evolves exactly as its classical counterpart, and that the x- and y-components display an astonishing analogy with their classical counterparts in terms of functional form, precession angular velocities, amplitudes, and phases. We elucidate some of these properties via computer simulations of a rotating benzene molecule represented with the CS set. We discuss the utilization of this CS set to reconstruct quantum rotational properties of symmetric-rotor molecules from classical-mechanics simulations. The new CS set is appropriate to establish quantum-classical connections for rotational properties in chemical dynamics, statistical mechanics, spectroscopy, nuclear physics, and quantum computing.
A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow.
Using an optical centrifuge to control molecular rotation in an extremely broad range of angular momenta, we study coherent rotational dynamics of nitrogen molecules in the presence of collisions. We cover the range of rotational quantum numbers between J=8 and J=66 at room temperature and study a crossover between the adiabatic and nonadiabatic regimes of rotational relaxation, which cannot be easily accessed by thermal means. We demonstrate that the rate of rotational decoherence changes by more than an order of magnitude in this range of J values and show that its dependence on J can be described by a simplified scaling law.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.