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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Tunneling and Parity Violation in Trisulfane (HSSSH): An Almost Ideal Molecule for Detecting Parity Violation in Chiral Molecules.

Measuring the parity-violating energy difference Δpv E between the enantiomers of chiral molecules is a major challenge of current physical-chemical stereochemistry. An important step towards this goal is to identify suitable molecules for such experiments by means of theory. This step has been made by calculations for the complex dynamics of tunneling and electroweak quantum chemistry of parity violation in the "classic" molecule trisulfane, HSSSH, which satisfies the relevant conditions for experiments almost ideally, as the molecule is comparatively simple and parity violation clearly dominates over tunneling in the ground state. At the same time, the barrier for stereomutation is easily overcome by the S-H infrared chromophore.

Communication: rigidity of the molecular ion H(+)(5).

The fourth-age quantum chemical code GENIUSH is used for the variational determination of rotational-vibrational energy levels corresponding to reduced- and full-dimensional models of H(+)(5), a molecular ion exhibiting several strongly coupled large-amplitude motions. The computations are supplemented with one- and two-dimensional analytic results which help to understand the peculiar rovibrational energy-level structure computed correctly for the first time. An unusual aspect of the results is that the canonical Eckart-embedding of molecule-fixed axes, a cornerstone of the computational spectroscopy of semirigid molecules, is found to be inadequate. Furthermore, it is shown that while the 1D "active torsion" model provides proper results when compared to the full, 9D treatment, models excluding the torsion have limited physical significance. The structure of the rovibrational energy levels of H(+)(5) proves that this is a prototypical astructural molecule: the rotational and vibrational level spacings are of the same order of magnitude and the level structure drastically deviates from that computed via perturbed rigid-rotor and harmonic-oscillator models.

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.

MARVEL analysis of the rotational-vibrational states of the molecular ions H2D+ and D2H+.

Critically evaluated rotational-vibrational line positions and energy levels, with associated critically reviewed labels and uncertainties, are reported for two deuterated isotopologues of the H3(+) molecular ion: H2D(+) and D2H(+). The procedure MARVEL, standing for Measured Active Rotational-Vibrational Energy Levels, is used to determine the validated levels and lines and their self-consistent uncertainties based on the experimentally available information. The spectral ranges covered for the isotopologues H2D(+) and D2H(+) are 5.2-7105.5 and 23.0-6581.1 cm(-1), respectively. The MARVEL energy levels of the ortho and para forms of the ions are checked against ones determined from accurate variational nuclear motion computations employing the best available adiabatic ab initio potential energy surfaces of these isotopologues. The number of critically evaluated, validated and recommended experimental (levels, lines) are (109, 185) and (104, 136) for H2D(+) and D2H(+), respectively. The lists of assigned MARVEL lines and levels and variational levels obtained for H2D(+) and D2H(+) as part of this study are deposited in the ESI to this paper.

Reduced-dimensional quantum computations for the rotational-vibrational dynamics of F(-)-CH4 and F(-)-CH2D2.

Variational rotational-vibrational quantum chemical computations are performed for the F(-)-CH4 and F(-)-CH2D2 anion complexes using several reduced-dimensional models in a curvilinear polyspherical coordinate system and utilizing an accurate ab initio potential energy surface (PES). The implementation of the models is made practical by using the general rovibrational code GENIUSH, which constructs the complicated form of the exact rovibrational kinetic energy operator in reduced and full dimensions in any user-specified coordinates and body-fixed frames. A one-dimensional CF stretch, 1D(RCF), a two-dimensional intermolecular bend, 2D(θ,φ), and a three-dimensional intermolecular, 3D(RCF,θ,φ), rigid methane model provide vibrational energies for the low-frequency, large-amplitude modes in good agreement with full-dimensional MCTDH results for F(-)-CH4. The 2D(θ,φ) and 3D(RCF,θ,φ) four-well computations, describing equally the four possible CH-F(-) bonds, show that the ground-state tunneling splitting is less than 0.01 cm(-1). For the hydrogen-bonded CH stretching fundamental a local-mode model is found to have almost spectroscopic accuracy, whereas a harmonic frequency analysis performs poorly. The 2D(θ,φ) and 3D(RCF,θ,φ) rotational-vibrational computations on the Td-symmetric four-well PES reveal that in most cases F(-)-CH4 behaves as a semirigid C3v symmetric top. For the degenerate intermolecular bending vibrational states substantial splittings of the rigid rotor levels are observed. For F(-)-CH2D2 the rotational levels guide the assignment of the vibrational states to either F(-)-H or F(-)-D connectivity.

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.

The fourth age of quantum chemistry: molecules in motion.

Developments during the last two decades in nuclear motion theory made it possible to obtain variational solutions to the time-independent, nuclear-motion Schrödinger equation of polyatomic systems as "exact" as the potential energy surface (PES) is. Nuclear motion theory thus reached a level whereby this branch of quantum chemistry started to catch up with the well developed and widely applied other branch, electronic structure theory. It seems to be fair to declare that we are now in the fourth age of quantum chemistry, where the first three ages are principally defined by developments in electronic structure techniques (G. Richards, Nature, 1979, 278, 507). In the fourth age we are able to incorporate into our quantum chemical treatment the motion of nuclei in an exact fashion and, for example, go beyond equilibrium molecular properties and compute accurate, temperature-dependent, effective properties, thus closing the gap between measurements and electronic structure computations. In this Perspective three fundamental algorithms for the variational solution of the time-independent nuclear-motion Schrödinger equation employing exact kinetic energy operators are presented: one based on tailor-made Hamiltonians, one on the Eckart-Watson Hamiltonian, and one on a general internal-coordinate Hamiltonian. It is argued that the most useful and most widely applicable procedure is the third one, based on a Hamiltonian containing a kinetic energy operator written in terms of internal coordinates and an arbitrary embedding of the body-fixed frame of the molecule. This Hamiltonian makes it feasible to treat the nuclear motions of arbitrary quantum systems, irrespective of whether they exhibit a single well-defined minimum or not, and of arbitrary reduced-dimensional models. As a result, molecular spectroscopy, an important field for the application of nuclear motion theory, has almost black-box-type tools at its disposal. Variational nuclear motion computations, based on an exact kinetic energy operator and an arbitrary PES, can now be performed for about 9 active vibrational degrees of freedom relatively straightforwardly. Simulations of high-resolution spectra allow the understanding of complete rotational-vibrational spectra up to and beyond the first dissociation limits. Variational results obtained for H(2)O, H, NH(3), CH(4), and H(2)CCO are used to demonstrate the power of the variational techniques for the description of vibrational and rotational excitations. Some qualitative features of the results are also discussed.