Coupling polyatomic molecules to lossy nanocavities: Lindblad vs Schrödinger description.

The use of cavities to impact molecular structure and dynamics has become popular. As cavities, in particular plasmonic nanocavities, are lossy and the lifetime of their modes can be very short, their lossy nature must be incorporated into the calculations. The Lindblad master equation is commonly considered an appropriate tool to describe this lossy nature. This approach requires the dynamics of the density operator and is thus substantially more costly than approaches employing the Schrödinger equation for the quantum wave function when several or many nuclear degrees of freedom are involved. In this work, we compare numerically the Lindblad and Schrödinger descriptions discussed in the literature for a molecular example where the cavity is pumped by a laser. The laser and cavity properties are varied over a range of parameters. It is found that the Schrödinger description adequately describes the dynamics of the polaritons and emission signal as long as the laser intensity is moderate and the pump time is not much longer than the lifetime of the cavity mode. Otherwise, it is demonstrated that the Schrödinger description gradually fails. We also show that the failure of the Schrödinger description can often be remedied by renormalizing the wave function at every step of time propagation. The results are discussed and analyzed.

Impact of Cavity on Molecular Ionization Spectra.

Ionization phenomena have been widely studied for decades. With the advent of cavity technology, the question arises how quantum light affects molecular ionization. As the ionization spectrum is recorded from the neutral ground state, it is usually possible to choose cavities which exert negligible effect on the neutral ground state, but have significant impact on the ion and the ionization spectrum. Particularly interesting are cases where the ion exhibits conical intersections between close-lying electronic states, which gives rise to substantial nonadiabatic effects. Assuming single-molecule strong coupling, we demonstrate that vibrational modes irrelevant in the absence of a cavity play a decisive role when the molecule is in the cavity. Here, dynamical symmetry breaking is responsible for the ion-cavity coupling and high symmetry enables control of the coupling via molecular orientation relative to the cavity field polarization. Significant impact on the spectrum by the cavity is found and shown to even substantially increase for less symmetric molecules.

Quantum Nuclear Delocalization and its Rovibrational Fingerprints.

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex HHe 3 + ${{\rm{HHe}}_3^ + }$ . The equilibrium structure of HHe 3 + ${{\rm{HHe}}_3^ + }$ is planar and T-shaped, one He atom solvating the quasi-linear He-H+ -He core. The dynamical structure of HHe 3 + ${{\rm{HHe}}_3^ + }$ , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent HHe 2 + ${{\rm{HHe}}_2^ + }$ chomophore, but freely orbits the central proton, forming a three-dimensional torus around the HHe 2 + ${{\rm{HHe}}_2^ + }$ chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.

Quantum-Chemical and Quantum-Graph Models of the Dynamical Structure of CH5.

Experimental and computational results about the structure, dynamics, and rovibrational spectra of protonated methane have challenged a considerable number of traditional chemical concepts. Hereby theoretical and computational results are provided about the dynamical structure of CH5+. It is shown that the ground vibrational state investigated thus far by computations, forbidden by nuclear-spin statistics, has a structure similar to the first allowed vibrational state and, in fact, the structures of all vibrational states significantly below 200 cm-1 are highly similar. Spatial delocalization of the nuclei, determined by nuclear densities computed from accurate variational vibrational wave functions, turns out to be limited when viewed in the body-fixed frame, confirming that the effective structure of CH5+ is well described as a CH3+ tripod with a H2 unit on top of it. The interesting and unusual qualitative aspects of the sophisticated state-dependent variational results receive full explanation via simple quantum-graph models.

Parity-pair-mixing effects in nonlinear spectroscopy of HDO.

A non-linear spectroscopic study of the HDO molecule is performed in the wavelength range of 1.36-1.42 µm using noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS). More than 100 rovibrational Lamb dips are recorded, with an experimental precision of 2-20 kHz, related to the first overtone of the O-H stretch fundamental of HD16O and HD18O. Significant perturbations, including distortions, shifts, and splittings, have been observed for a number of Lamb dips. These spectral perturbations are traced back to an AC-Stark effect, arising due to the strong laser field applied in all saturation-spectroscopy experiments. The AC-Stark effect mixes parity pairs, that is pairs of rovibrational states whose assignment differs solely in the Kc quantum number, where Kc is part of the standard J K a,K c asymmetric-top rotational label. Parity-pair mixing seems to be especially large for parity pairs with Ka ≥ 3, whereby their energy splittings become as small as a few MHz, resulting in multi-component asymmetric Lamb-dip profiles of gradually increasing complexity. These complex profiles often include crossover resonances. This effect is well known in saturation spectroscopy, but has not been reported in combination with parity-pair mixing. Parity-pair mixing is not seen in H2 16O and H2 18O, because their parity pairs correspond to ortho and para nuclear-spin isomers, whose interaction is prohibited. Despite the frequency shifts observed for HD16O and HD18O, the absolute accuracy of the detected transitions still exceeds that achievable by Doppler-limited techniques.

Radiative emission of polaritons controlled by light-induced geometric phase.

Polaritons - hybrid light-matter states formed in cavity - strongly change the properties of the underlying matter. In optical or plasmonic nanocavities, polaritons decay by radiative emission of the cavity, which is accessible experimentally. Due to the interaction of a molecule with the quantized radiation field, polaritons exhibit light-induced conical intersections (LICIs) which dramatically influence the nuclear dynamics of molecular polaritons. We show that ultrafast radiative emission from the lower polariton is controlled by the geometric phase imposed by the LICI. This finding provides insight into the process of emission and, furthermore, allows one to compute these signals by augmenting the Born-Oppenheimer approximation for polaritons with a geometric phase term.

Probing Light-Induced Conical Intersections by Monitoring Multidimensional Polaritonic Surfaces.

The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

The rovibrational Aharonov-Bohm effect.

Another manifestation of the Aharonov-Bohm effect is introduced to chemistry, in fact to nuclear quantum dynamics and high-resolution molecular spectroscopy. As demonstrated, the overall rotation of a symmetric-top molecule influences the dynamics of an internal vibrational motion in a way that is analogous to the presence of a solenoid carrying magnetic flux. To a good approximation, the low-energy rovibrational energy-level structure of the quasistructural molecular ion H+5 can be understood entirely in terms of this effect.

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane.

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 60-vertex graph Γ60 with a single edge length parameter. Within this model, the quantum states of CH5+ are obtained in analytic form and are related to combinatorial properties of Γ60. The bipartite structure of Γ60 gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH5+.

Signatures of light-induced nonadiabaticity in the field-dressed vibronic spectrum of formaldehyde.

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

High-resolution FTIR spectroscopy of benzaldehyde in the far-infrared region: probing the rotational barrier.

A discrepancy between theoretical and experimental values of the rotational barrier in benzaldehyde has been observed, which was attributed to inaccurate experimental results in part. Here, we report results on the -CHO torsion of benzaldehyde (C6H5CHO) based on a high resolution spectroscopic investigation in the far-infrared range in an effort to remove the experimental ambiguity. The rotationally-resolved vibrational spectra were measured with an unapodized resolution of 0.00064 cm-1 using synchrotron-based Fourier transform infrared (FTIR) spectroscopy at the Canadian Light Source. The torsional fundamental νt = 109.415429(20) cm-1 was unambiguously assigned via rovibrational analysis, followed by the tentative assignment of the first (2νt-νt) and second (3νt- 2νt) hot bands at 107.58 cm-1 and 105.61 cm-1, respectively, by comparison of the observed Q branch structures at high resolution with simulation based on a previous microwave study. This assignment is different from any previous low resolution infrared studies in which the intensity patterns were misleading. The key result of the assignment of the first three transitions allowed the determination of the barrier to internal rotation of (hc)1533.6 cm-1 (4.38 kcal mol-1). When compared with calculated results from vibrational second-order perturbation theory (VPT2) and the quasiadiabatic channel reaction path Hamiltonian (RPH) approach, the experimental value is still too low and this suggests that the discrepancy between theory and experiment remains despite the best experimental efforts.

Quantum light-induced nonadiabatic phenomena in the absorption spectrum of formaldehyde: Full- and reduced-dimensionality studies.

The coupling of a molecule to a cavity can induce conical intersections of the arising polaritonic potential energy surfaces. Such intersections give rise to the strongest possible nonadiabatic effects. By choosing an example that does not possess nonadiabatic effects in the absence of the cavity, we can study, for the first time, the emergence of these effects in a polyatomic molecule due to its coupling with the cavity taking into account all vibrational degrees of freedom. The results are compared with those of reduced-dimensionality models, and the shortcomings and merits of the latter are analyzed.

Striking Generic Impact of Light-Induced Non-Adiabaticity in Polyatomic Molecules.

Non-adiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing non-adiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.

Born-Oppenheimer approximation in optical cavities: from success to breakdown.

The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduced-dimensional models and the use of the Born-Oppenheimer approximation (BOA) may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a one-dimensional model and is generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity.

Controlling tunneling in ammonia isotopomers.

We report results of full-dimensional variational rovibrational quantum-dynamical computations for several ammonia isotopomers, based on selected potential energy and electric dipole moment hypersurfaces. The variational rovibrational eigenstates have been used as a basis for the solution of the time-dependent Schrödinger equation for nuclear motion including coherent infrared multiphoton excitation. The theoretical and computational framework developed during this study enables the investigation of the coherent inhibition or enhancement of tunneling in ammonia isotopomers by appropriately chosen laser fields. Our quantum-dynamical computations include all vibrational and rotational degrees of freedom and assume neither the alignment nor the orientation of the molecules under investigation. Specific results include accurate rotational-vibrational levels for NH2D, NHD2, NHDMu, and NHDT, probability densities for structural parameters as a function of time from the full-dimensional wavepacket results, time-dependent chirality for the isotopically chiral molecule NHDT, and detailed analyses of the enhancement and inhibition of stereomutation dynamics.

Rovibrational quantum dynamics of the vinyl radical and its deuterated isotopologues.

Rotational-vibrational states up to 3200 cm-1, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H2Cß[double bond, length as m-dash]CαH, and the following deuterated isotopologues of VR: CH2[double bond, length as m-dash]CD, CHD[double bond, length as m-dash]CH, and CD2[double bond, length as m-dash]CD. The height of the CαH tunneling rocking barrier of VR, partially responsible for the complex nuclear dynamics of VR and its isotopologues, is determined to be 1641 ± 25 cm-1 by the focal-point analysis approach. The definitive nuclear-motion computations performed utilize two previously published potential energy hypersurfaces and reveal interesting energy-level and tunneling patterns characterizing the internal motions of the four isotopologues. A full assignment, including symmetry labels, of the vibrational states computed for CH2[double bond, length as m-dash]CH is provided, whenever feasible, based on the analysis of wave functions and the related one- and two-mode reduced density matrices. The computed vibrational states of CH2[double bond, length as m-dash]CD and CD2[double bond, length as m-dash]CD are characterized up to slightly above the top of the barrier. Interestingly, it is the interplay of the ν6 (formally CH2 rock) and ν7 (formally CH rock) modes that determines the tunneling dynamics; thus, the description of tunneling in VR needs, as a minimum, the consideration of two in-plane bending motions at the two ends of the molecule. When feasible, the computed results are compared to their experimental counterparts as well as to previous computational results. Corrections to the placement of the ν4 and ν6 fundamentals of VR are proposed. Tunneling switching, a unique phenomenon characterizing tunneling in slightly asymmetric effective double-well potentials, is observed and discussed for CHD[double bond, length as m-dash]CH. Despite the extensive tunneling dynamics, the rotational energy-level structure of VR exhibits rigid-rotor-type behavior.

Vibrational quantum graphs and their application to the quantum dynamics of CH5.

The first application of quantum graphs to the vibrational quantum dynamics of molecules is reported. The quantum-graph model is applied to the quasistructural molecular ion CH5+, whose nuclear dynamics challenges the traditional understanding of chemical structures and molecular spectra. The vertices of the quantum graph represent versions of the equilibrium structure with distinct atom numbering, while the edges refer to collective nuclear motions transforming the versions of the equilibrium structure into one another. These definitions allow the mapping of the complex vibrational quantum dynamics of CH5+ onto the motion of a particle confined in a quantum graph. The quantum-graph model provides a simple understanding of the low-energy vibrational quantum dynamics of CH5+ and is able to reproduce the low-lying vibrational energy levels of CH5+ (and CD5+) with remarkable accuracy.

A molecular quantum switch based on tunneling in meta-d-phenol C6H4DOH.

We introduce the concept of a molecular quantum switch and demonstrate it with the example of meta-d-phenol, based on recent theoretical and high-resolution spectroscopic results for this molecule. We show that in the regime of tunneling switching with localized low-energy states and delocalized high-energy states the molecular quantum switch can be operated in two different ways: (i) a quasiclassical switching by coherent infrared radiation between the two isomeric structures syn- and anti-m-d-phenol; and (ii) a highly nonclassical switching making use of bistructural quantum superposition states of the syn and anti structures, which can be observed by their time-dependent spectra after preparation.

On the use of nonrigid-molecular symmetry in nuclear motion computations employing a discrete variable representation: A case study of the bending energy levels of CH5.

A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric CH5+ molecular ion, a prototypical astructural system. While the numerical results obtained and the symmetry labels of the computed rovibrational states of CH5+ are of considerable utility by themselves, it must also be noted that the present study confirms that the nearly unconstrained motion of the five hydrogen atoms orbiting around the central carbon atom results in highly complex rotational-vibrational quantum dynamics and renders the understanding of the high-resolution spectra of CH5+ extremely challenging.

Isotope effects on the resonance interactions and vibrational quantum dynamics of fluoroform 12,13CHF3.

We report a comparison of the analysis of the low energy spectrum of 13CHF3 and 12CHF3 from the THz (FIR) range to the ν1 fundamental at high resolution (δ[small nu, Greek, tilde] < 0.001 cm-1 or otherwise Doppler limited) on the basis of FTIR spectra taken both with ordinary light sources and with the synchrotron radiation from the Swiss Light Source. Several vibrational levels are accurately determined including, in particular, the 2ν4 CH-bending overtone and the ν1 CH-stretching fundamental of 13CHF3. Comparison of experimental results with those from accurate full dimensional vibrational calculations allows for a study of the time-dependent quantum dynamics of intramolecular vibrational redistribution (IVR) in the CH chromophore both on short time scales (fs) and longer time scales (ps) when coupling to the lower frequency modes becomes important and where the 12C/13C isotope effects are very large.