An efficient and flexible approach for computing rovibrational polaritons from first principles.

A theoretical framework is presented for the computation of the rovibrational polaritonic states of a molecule in a lossless infrared (IR) microcavity. In the proposed approach, the quantum treatment of the rotational and vibrational motions of the molecule can be formulated using arbitrary approximations. The cavity-induced changes in electronic structure are treated perturbatively, which allows using the existing polished tools of standard quantum chemistry for determining electronic molecular properties. As a case study, the rovibrational polaritons and related thermodynamic properties of H2O in an IR microcavity are computed for varying cavity parameters, applying various approximations to describe the molecular degrees of freedom. The self-dipole interaction is significant for nearly all light-matter coupling strengths investigated, and the molecular polarizability proved important for the correct qualitative behavior of the energy level shifts induced by the cavity. On the other hand, the magnitude of polarization remains small, justifying the perturbative approach for the cavity-induced changes in electronic structure. Comparing results obtained using a high-accuracy variational molecular model with those obtained utilizing the rigid rotor and harmonic oscillator approximations revealed that as long as the rovibrational model is appropriate for describing the field-free molecule, the computed rovibropolaritonic properties can be expected to be accurate as well. Strong light-matter coupling between the radiation mode of an IR cavity and the rovibrational states of H2O leads to minor changes in the thermodynamic properties of the system, and these changes seem to be dominated by non-resonant interactions between the quantum light and matter.

Achieving high molecular alignment and orientation for CH[Formula: see text]F through manipulation of rotational states with varying optical and THz laser pulse parameters.

Increasing interest in the fields of high-harmonics generation, laser-induced chemical reactions, and molecular imaging of gaseous targets demands high molecular "alignment" and "orientation" (A&O). In this work, we examine the critical role of different pulse parameters on the field-free A&O dynamics of the CH[Formula: see text]F molecule, and identify experimentally feasible optical and THz range laser parameters that ensure maximal A&O for such molecules. Herein, apart from rotational temperature, we investigate effects of varying pulse parameters such as, pulse duration, intensity, frequency, and carrier envelop phase (CEP). By analyzing the interplay between laser pulse parameters and the resulting rotational population distribution, the origin of specific A&O dynamics was addressed. We could identify two qualitatively different A&O behaviors and revealed their connection with the pulse parameters and the population of excited rotational states. We report here the highest alignment of [Formula: see text] and orientation of [Formula: see text] for CH[Formula: see text]F molecule at 2 K using a single pulse. Our study should be useful to understand different aspects of laser-induced unidirectional rotation in heteronuclear molecules, and in understanding routes to tune/enhance A&O in laboratory conditions for advanced applications.

A quantum-chemical perspective on the laser-induced alignment and orientation dynamics of the CH3 X (X = F, Cl, Br, I) molecules.

Motivated by recent experiments, the laser-induced alignment-and-orientation (A&O) dynamics of the prolate symmetric top CH3 X (X = F, Cl, Br, I) molecules is investigated, with particular emphasis on the effect of halogen substitution on the rotational constants, dipole moments, and polarizabilities of these species, as these quantities determine the A&O dynamics. Insight into possible control schemes for preferred A&O dynamics of halogenated molecules and best practices for A&O simulations are provided, as well. It is shown that for accurate A&O -dynamics simulations it is necessary to employ large basis sets and high levels of electron correlation when computing the rotational constants, dipole moments, and polarizabilities. The benchmark-quality values of these molecular parameters, corresponding to the equilibrium, as well as the vibrationally averaged structures are obtained with the help of the focal-point analysis (FPA) technique and explicit electronic-structure computations utilizing the gold-standard CCSD(T) approach, basis sets up to quintuple-zeta quality, core-correlation contributions and, in particular, relativistic effects for CH3 Br and CH3 I. It is shown that the different A&O behavior of the CH3 X molecules in the optical regime is mostly caused by the differences in their polarizability anisotropy, in other terms, the size of the halogen atom. In contrast, the A&O dynamics of the CH3 X series induced by an intense few-cycle THz pulse is mostly governed by changes in the rotational constants, due to the similar dipole moments of the CH3 X molecules. The A&O dynamics is most sensitive to the B rotational constant: even the difference between its equilibrium and vibrationally-averaged values results in noticeably different A&O dynamics. The contribution of rotational states having different symmetry, weighted by nuclear-spin statistics, to the A&O dynamics is also studied.

Nonadiabatic phenomena in molecular vibrational polaritons.

Nonadiabatic phenomena are investigated in the rovibrational motion of molecules confined in an infrared cavity. Conical intersections (CIs) between vibrational polaritons, similar to CIs between electronic polaritonic surfaces, are found. The spectral, topological, and dynamic properties of the vibrational polaritons show clear fingerprints of nonadiabatic couplings between molecular vibration, rotation, and the cavity photonic mode. Furthermore, it is found that for the investigated system, composed of two rovibrating HCl molecules and the cavity mode, breaking the molecular permutational symmetry, by changing 35Cl to 37Cl in one of the HCl molecules, the polaritonic surfaces, nonadiabatic couplings, and related spectral, topological, and dynamic properties can deviate substantially. This implies that the natural occurrence of different molecular isotopologues needs to be considered when modeling realistic polaritonic systems.

Spectroscopic signatures of HHe2+ and HHe3.

Using two different action spectroscopic techniques, a high-resolution quantum cascade laser operating around 1300 cm-1 and a cryogenic ion trap machine, the proton shuttle motion of the cations HHe2+ and HHe3+ has been probed at a nominal temperature of 4 K. For HHe3+, the loosely bound character of this complex allowed predissociation spectroscopy to be used, and the observed broad features point to a lifetime of a few ps in the vibrationally excited state. For He-H+-He, a fundamental linear molecule consisting of only three nuclei and four electrons, the method of laser-induced inhibition of complex growth (LIICG) enabled the measurement of three accurate rovibrational transitions, pinning down its molecular parameters for the first time.

Rotational-vibrational resonance states.

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L2, square integrable) or non-Hermitian (non-L2) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

Robust field-dressed spectra of diatomics in an optical lattice.

The absorption spectra of the cold Na2 molecule dressed by a linearly polarized standing laser wave is investigated with a theoretical model incorporating translational, electronic, vibrational as well as rotational degrees of freedom. In such a situation a light-induced conical intersection (LICI) can be formed (J. Phys. B: At. Mol. Opt. Phys., 2008, 41, 221001). To measure the spectra a weak field is used whose propagation direction is perpendicular to the direction of the dressing field but has identical polarization direction. Although LICIs are present in our model, the simulations demonstrate a very robust absorption spectrum, which is insensitive to the intensity and the wavelength of the dressing field and which does not reflect clear signatures of light-induced nonadiabatic phenomena related to the strong mixing between the electronic, vibrational, rotational and translational motions. However, by widening artificially the very narrow translational energy level gaps, the fingerprint of the LICI appears to some extent in the spectrum.

Infrared Signatures of the HHen+ and DHen+ (n = 3-6) Complexes.

Combination of a cryogenic ion-trap machine, operated at 4.7 K, with the free-electron-laser FELIX allows the first experimental characterization of the unusually bright antisymmetric stretch (ν3) and π-bending (ν2) fundamentals of the He-X+-He (X = H, D) chromophore of the in situ prepared HHen+ and DHen+ (n = 3-6) complexes. The band origins obtained are fully supported by first-principles quantum-chemical computations, performed at the MP2, the CCSD(T), and occasionally the CCSDTQ levels employing extended basis sets. Both the experiments and the computations are consistent with structures for the species with n = 3 and 6 being of T-shaped C2v and of D4h symmetry, respectively, while the species with n = 4 are suggested to exhibit interesting dynamical phenomena related to large-amplitude motions.

Toward Automated Variational Computation of Rovibrational Resonances, Including a Case Study of the H2 Dimer.

A general and semi-automatic technique, based on the complex absorbing potential (CAP) method, is developed for the variational computation and identification of rotational-vibrational resonance states. This technique is an extension of a method introduced by Tremblay and Carrington ( J. Chem. Phys. 2005, 122, 244107 ), and it employs the damped eigenvectors of a CAP-modified Hamiltonian as a basis to describe resonance wave functions. The low-lying resonances of the weakly bound Ar·NO+ complex are computed with the new and the traditional CAP techniques to test the new algorithm. As an additional, more challenging test case, the bound and resonance rovibrational states of the H2 dimer, the latter with both negative and positive binding energies, are determined, corresponding to different rotational excitations of the H2 monomers. Resonances above the first few dissociation channels of (H2)2 are computed with the new and the traditional CAP methods, revealing some new, assigned resonance quantum states not reported in the literature.

Conical Intersections Induced by Quantum Light: Field-Dressed Spectra from the Weak to the Ultrastrong Coupling Regimes.

In classical laser fields with frequencies resonant with the electronic excitation in molecules, it is by now known that conical intersections are induced by the field and are called light-induced conical intersections (LICIs). As optical cavities have become accessible, the question arises whether their quantized modes could also lead to the appearance of LICIs. A theoretical framework is formulated for the investigation of LICIs of diatomics in such quantum light. The eigenvalue spectrum of the dressed states in the cavity is studied, putting particular emphasis on the investigation of absorption spectra of the Na2 molecule, that is, on the transitions between dressed states, measured by employing a weak probe pulse. The dependence of the spectra on the light-matter coupling strength in the cavity and on the frequency of the cavity mode is studied in detail. The computations demonstrate strong nonadiabatic effects caused by the appearing LICI.

Direct Signatures of Light-Induced Conical Intersections on the Field-Dressed Spectrum of Na2.

Rovibronic spectra of the field-dressed homonuclear diatomic Na2 molecule are investigated to identify direct signatures of the light-induced conical intersection (LICI) on the spectrum. The theoretical framework formulated allows the computation of the (1) field-dressed rovibronic states induced by a medium-intensity continuous-wave laser light and the (2) transition amplitudes between these field-dressed states with respect to an additional weak probe pulse. The field-dressed spectrum features absorption peaks resembling the field-free spectrum as well as stimulated emission peaks corresponding to transitions not visible in the field-free case. By investigating the dependence of the field-dressed spectra on the dressing-field wavelength, in both full- and reduced-dimensional simulations, direct signatures of the LICI can be identified. These signatures include (1) the appearance of new peaks and the splitting of peaks for both absorption and stimulated emission and (2) the manifestation of an intensity-borrowing effect in the field-dressed spectrum.

Rovibrational Resonances in H2He.

The nuclear dynamics of the metastable H2He+ complex is explored by symmetry considerations and angular momentum addition rules as well as by accurate quantum chemical computations with complex coordinate scaling, complex absorbing potential, and stabilization techniques. About 200 long-lived rovibrational resonance states of the complex are characterized and selected long-lived states are analyzed in detail. The stabilization mechanism of these long-lived resonance states is discussed on the basis of probability density plots of the wave functions. Overlaps of wave functions derived by a reduced-dimensional model with the full-dimensional wave functions reveal dissociation pathways for the long-lived resonance states and allow the calculation of their branching ratios.

A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2⋠CO systems.

The quasi-variational quantum chemical protocol and code GENIUSH [E. Mátyus et al., J. Chem. Phys. 130, 134112 (2009) and C. Fábri et al., J. Chem. Phys. 134, 074105 (2011)] has been augmented with the complex absorbing potential (CAP) technique, yielding a method for the determination of rovibrational resonance states. Due to the effective implementation of the CAP technique within GENIUSH, the GENIUSH-CAP code is a powerful tool for the study of important dynamical features of arbitrary-sized molecular systems with arbitrary composition above their first dissociation limit. The GENIUSH-CAP code has been tested and validated on the H2He+ cation: the computed resonance energies and lifetimes are compared to those obtained with a previously developed triatomic rovibrational resonance-computing code, D2FOPI-CCS [T. Szidarovszky and A. G. Császár Mol. Phys. 111, 2131 (2013)], utilizing the complex coordinate scaling method. A unique feature of the GENIUSH-CAP protocol is that it allows the simple implementation of reduced-dimensional dynamical models. To prove this, resonance energies and lifetimes of the H2⋅CO van der Waals complex have been computed utilizing a four-dimensional model (freezing the two monomer stretches), and a related potential energy surface, of the complex.

Complex rovibrational dynamics of the Ar·NO+ complex.

Rotational-vibrational states of the Ar·NO+ cationic complex are computed, below, above, and well above the complex's first dissociation energy, using variational nuclear motion and close-coupling scattering computations. The HSLH potential energy surface used in this study (J. Chem. Phys., 2011, 135, 044312) is characterized by a first dissociation energy of D0 = 887.0 cm-1 and supports 200 bound vibrational states. The bound-state vibrational energies and the corresponding wave functions allow the interpretation of the scarcely available experimental results about the intermonomer vibrational motion of the complex. A very large number of long-lived quasibound combination states of the three vibrational modes, exhibiting a very similar energy-level structure as that of the bound states, are found embedded in the continuum. Additional short-lived resonance states are also identified and their properties are analyzed.

Toward accurate thermochemistry of the (24)MgH, (25)MgH, and (26)MgH molecules at elevated temperatures: corrections due to unbound states.

The total partition functions QT and their first two moments Q(')T and Q(″)T, together with the isobaric heat capacities CpT, are computed a priori for three major MgH isotopologues on the temperature range of T = 100-3000 K using the recent highly accurate potential energy curve, spin-rotation, and non-adiabatic correction functions of Henderson et al. [J. Phys. Chem. A 117, 13373 (2013)]. Nuclear motion computations are carried out on the ground electronic state to determine the (ro)vibrational energy levels and the scattering phase shifts. The effect of resonance states is found to be significant above about 1000 K and it increases with temperature. Even very short-lived states, due to their relatively large number, have significant contributions to QT at elevated temperatures. The contribution of scattering states is around one fourth of that of resonance states but opposite in sign. Uncertainty estimates are given for the possible error sources, suggesting that all computed thermochemical properties have an accuracy better than 0.005% up to 1200 K. Between 1200 and 2500 K, the uncertainties can rise to around 0.1%, while between 2500 K and 3000 K, a further increase to 0.5% might be observed for Q(″)T and CpT, principally due to the neglect of excited electronic states. The accurate thermochemical data determined are presented in the supplementary material for the three isotopologues of (24)MgH, (25)MgH, and (26)MgH at 1 K increments. These data, which differ significantly from older standard data, should prove useful for astronomical models incorporating thermodynamic properties of these species.

Modelling non-adiabatic effects in H3⁺: solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces.

Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.

Grid-based empirical improvement of molecular potential energy surfaces.

A grid-based method designed to refine adiabatic potential energy surfaces (PES) of molecules via minimizing a suitable objective function is described. The objective function contains deviations from the reference (experimental) (ro)vibrational energy levels and is based on PES correction values determined at the grid points within a discrete-variable-representation nuclear-motion algorithm and first-order perturbation theory (PT). The proposed PES refinement technique is tested on the ground electronic state of the MgH molecule. The large number of numerical test results obtained suggest the following: (1) first-order PT is able to yield accurate correction values at the grid points representing the PES, and for practical cases there seems to be no need to go to higher orders of PT; (2) with the number of grid points greatly exceeding the number of experimental energy levels included in the refinement procedure, terms additional to the "obs-calc" term, including numerical first and second derivatives of the correction surface, are necessary in the objective function to arrive at a physically meaningful, "smooth" correction surface; (3) for a given J rotational quantum number, the corrected PES is able to reproduce experimental (ro)vibrational energies to within tenths of cm(-1) if they are included in the refinement or interpolated between states that are involved in the optimization, whereas extrapolated states tend to have somewhat larger remaining discrepancies; (4) the PES refined only for the J = 0 states introduces a minor systematic error for J > 0 states, with discrepancies growing with J; (5) when the number of experimental energies included in the refinement greatly exceeds the number of grid points upon which the PES is optimized, the systematic error of treating states with different J rotational quantum numbers can be reduced and an impressive average accuracy can be achieved for all rovibrational states; and (6) in the case of quasibound (also known as resonance) rovibrational states, energies can be computed to accuracies similar to those of the bound states and excellent lifetimes (widths) can also be determined. Changes in thermochemical functions upon inclusion of quasibound states during direct summation is discussed.

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.

Spectroscopy of H3+ based on a new high-accuracy global potential energy surface.

The molecular ion H(3)(+) is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro-vibrational spectrum of H(3)(+) is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm(-1) relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm(-1). Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro-vibrational data show that an accuracy of the order of 0.1 cm(-1) is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.