Irén Simkó

A method for automatic generation of flexible-monomer three-body (3B) nonadditive contribution to intermolecular force fields (FFs) has been developed. It is an extension of the method developed earlier for two-body contributions. Together with one-body contributions and a polarization model accounting for four- and higher-body contributions, these components form a complete FF that can be used to simulate molecular clusters and condensed phases. The method was used to develop 3B potential energy surfaces for (H2O)3, (HF)3, and HF–(H2O)2, enabling simulations of water, hydrogen fluoride, and some mixtures of the two. The fitting errors of these 3B surfaces are generally smaller than those of the published analytic expansion fits and on par with the best neural network model for the water trimer. The properties of small clusters predicted by the FFs developed here are more accurate than those given by the published benchmarks from single-point ab initio calculations for such clusters, and we had to compute more accurate benchmarks of this type to evaluate the quality of our FFs.

Noncovalently bound molecular trimers, held together by hydrogen-bonded and van der Waals interactions, are the smallest clusters in which the three-body interactions can manifest. Accurate description of these nonadditive interactions is of great importance since they play a crucial role in shaping the energetics, structural, and dynamical properties of condensed phases. Molecular trimers offer a unique opportunity for quantifying the three-body interactions through the comparison of the trimer vibration-tunneling states and spectra computed accurately on a high-level many-body potential energy surface with the high-resolution spectroscopic data. However, until just a couple of years ago, the methodology for high-dimensional fully coupled quantum bound-state calculations of molecular trimers was not available. The situation has changed profoundly as a result of the recent methodological developments described in this perspective. For trimers of diatomic molecules, e.g., (HF)3 and (HCl)3, they have made it possible for the first time rigorous full-dimensional (12D) quantum calculations of their coupled intra- and intermolecular vibrational states. Very recently, this methodology was extended to vibration-rotation states of trimers of diatomics. In a parallel development, the same advances have resulted in a theoretical approach capable of the first rigorous 12D quantum calculations of the intermolecular vibrational states and elaborate tunneling splittings of the water trimer, (H2O)3 and (D2O)3, where the monomers are treated as rigid. The computed eigenstates are utilized in the simulations of realistic low-frequency absorption spectra of water trimers, which can be directly compared with the measured far-infrared spectrum of (H2O)3 in helium nanodroplets.

Understanding whether a polaritonic phenomenon is fundamentally quantum or classical is essential for building accurate theoretical models and guiding experimental design. Here, we address this question in the context of polaritonic spectra and report an intriguing new feature: the twin polariton, an additional splitting beyond the primary resonant polariton splitting originating from vacuum field fluctuations. We show that the twin polariton persists in the many-molecule limit under permutationally symmetrical initial-state constraint and that it follows the same linear dependence on coupling strength as the primary polariton splitting. This establishes a novel mechanism by which a quantum feature (the twin polariton) can be tuned through a classical one (the primary polariton), offering new opportunities to probe and control the fundamental nature of polaritonic systems.

We present the first rigorous 12D quantum calculations of the intermolecular vibration-tunneling (VT) states of (D2O)3, in which the monomers are treated as rigid. They are performed using the recently developed methodology [Simkó, Felker, and Bačić, J. Chem. Phys. 162, 034301 (2025)], which was utilized in the 12D quantum treatment of (H2O)3. A high-quality ab initio 2 + 3-body water potential is employed. The 12D eigenstates of (D2O)3 are used to simulate the low-frequency absorption spectrum of this trimer. Through the comparison of the results obtained here for (D2O)3 with those computed previously for (H2O)3, we elucidate the effects of the substitution of all H atoms of water trimer with D atoms on the VT states and the low-frequency spectrum. They are substantial particularly for the large-amplitude torsional vibrations, whose energy levels in (D2O)3 are, by a factor of two, lower than those of (H2O)3. The entire low-frequency absorption spectrum of (D2O)3, which is dominated by the bending transitions, is strongly redshifted in comparison with the spectrum of (H2O)3. The deuteration of the intermolecular stretching vibrations lowers their energy by only a few wave numbers, since it does not change much the masses of the water monomers. In addition, calculations are performed for (D2O)3, which directly reveal the significant effects of the three-body interactions on the vibrational energy levels and the low-frequency spectrum of the trimer.

In a recent work, we reported on the computation of intermolecular bending states in water trimer, a 9D problem when the monomers are treated as rigid and the intermonomer distances are fixed. In this paper, we present the results of an effort to ascertain the vibrational character of those states. The large-amplitude, highly coupled nature of these vibrations presents significant challenges with respect to their assignment. We introduce a new methodology, based on the use of symmetry coordinates for all nine of the torsional and librational degrees of freedom that constitute the intermolecular bending modes in the trimer, which addresses those challenges. The approach ultimately yields expressions for the bend eigenstates as expansions over small numbers of physically meaningful terms, from which the contributions of the torsional and librational excitations to a bending state can be identified and quantified. Results for approximately one hundred bending states with excitation energies below ∼560 cm−1 are presented.

In a recent work we reported on the computation of intermolecular bending states in water trimer, a 9D problem when the monomers are treated as rigid and the intermonomer distances are fixed. In this paper we present the results of an effort to ascertain the vibrational character of those states. The large-amplitude, highly-coupled nature of these vibrations presents significant challenges in respect to their assignment. We introduce a new methodology, based on the use of symmetry coordinates for all nine of the torsional and librational degrees of freedom that constitute the intermolecular bending modes in the trimer, which addresses those challenges. The approach ultimately yields expressions for the bend eigenstates as expansions over small numbers of physically meaningful terms, from which the contributions of the torsional and librational excitations to a bending state can be identified and quantified. Results for approximately one hundred bending states with excitation energies below ∼ 560 cm−1 are presented.

The water trimer, as the smallest water cluster in which the three-body interactions can manifest, is arguably the most important hydrogen-bonded trimer. Accurate, fully coupled quantum treatment of its excited intermolecular vibrations has long been an elusive goal. Here, we present the methodology that for the first time allows rigorous twelve-dimensional (12D) quantum calculation of the intermolecular vibration-tunneling eigenstates of the water trimer, with the monomers treated as rigid. These 12D eigenstates are used to simulate the low-frequency absorption spectrum of the trimer for direct comparison with the measured far-infrared (FIR) spectrum of the water trimer in helium nanodroplets. The 12D calculations reveal weak coupling between the large-amplitude torsional and intermolecular stretching vibrations. The calculated torsional tunneling splittings are in excellent agreement with spectroscopic results. There are visible differences between the spectrum simulated using the 12D eigenstates and that based on our earlier 9D calculations where the stretching vibrations are not included. The peaks in the 12D spectrum are generally shifted to slightly lower energies relative to those in the 9D spectrum, as well as the measured FIR spectrum, and are often split by intermolecular stretch–bend Fermi resonances that the 9D treatment cannot capture.

Water trimer, as the smallest water cluster in which the three-body interactions can manifest, is arguably the most important hydrogen-bonded trimer. We present the methodology that for the first time allows rigorous twelve-dimensional (12D) quantum calculation of its intermolecular vibration-tunneling eigenstates, with the monomers treated as rigid. These 12D eigenstates are used to simulate the low-frequency absorption spectrum of the trimer, for direct comparison with the measured far-infrared (FIR) spectrum of water trimer in helium nanodroplets. The 12D calculations reveal weak coupling between the large-amplitude torsional and intermolecular stretching vibrations. The calculated torsional tunneling splittings are in excellent agreement with spectroscopic results. There are visible differences between the spectrum simulated using the 12D eigenstates and that based on our earlier 9D calculations where the stretching vibrations are not included. The peaks in the 12D spectrum are generally shifted to slightly lower energies relative to those in the 9D spectrum, as well as the measured FIR spectrum, and are often split by intermolecular stretch-bend Fermi resonances.

We present the computational methodology that enables the first rigorous nine-dimensional (9D) quantum calculations of the intermolecular bending states of the water trimer, as well as its low-frequency spectrum for direct comparison with experiment. The water monomers, treated as rigid, have their centers of mass (cm's) at the corners of an equilateral triangle, and the intermonomer cm-to-cm distance is set to a value slightly larger than that in the equilibrium geometry of the trimer. The remaining nine strongly coupled large-amplitude bending (angular) degrees of freedom (DOFs) enter the 9D bend Hamiltonian of the three coupled 3D rigid-water hindered rotors. Its 9D eigenstates encompass excited librational vibrations of the trimer, as well as their torsional and bifurcation tunneling splittings, which have been the subject of much interest. The calculations of these eigenstates are extremely demanding, and a sophisticated computational scheme is developed that exploits the molecular symmetry group of the water trimer, G₄₈, in order to make them feasible in a reasonable amount of time. The spectrum of the low-frequency vibrations of the water trimer simulated using the eigenstates of the 9D bend Hamiltonian agrees remarkably well with the experimentally observed far-infrared (FIR) spectrum of the trimer in helium nanodroplets over the entire frequency range of the measurements from 70 to 620 cm^-1. This shows that most peaks in the experimental FIR spectrum are associated with the intermolecular bending vibrations of the trimer. Moreover, the ground-state torsional tunneling splittings from the present 9D calculations are in excellent agreement with the spectroscopic data. These results demonstrate the high quality of the ab initio 2 + 3-body PES employed for the DOFs included in the bound-state calculations.

We present the computational methodology that enables the first rigorous nine-dimensional (9D) quantum calculations of the intermolecular bending states of the water trimer, as well as its low-frequency spectrum for direct comparison with experiment. The water monomers, treated as rigid, have their centers of mass (cm's) at the corners of an equilateral triangle, and the intermonomer cm-to-cm distance is set to a value slightly larger than that in the equilibrium geometry of the trimer. The remaining nine strongly coupled large-amplitude bending (angular) degrees of freedom (DOFs) enter the 9D bend Hamiltonian of the three coupled 3D rigid-water hindered rotors. Its 9D eigenstates encompass excited librational vibrations of the trimer, as well as their torsional and bifurcation tunneling splittings which have been the subject of much interest. For this reason, the calculation of these eigenstates by diagonalizing the 9D bend Hamiltonian represents the most rigorous high-dimensional quantum treatment to date of the intermolecular vibrational states of the water trimer and its excited-state tunneling splittings. Such calculations are extremely demanding, and a sophisticated computational scheme is developed that exploits the molecular symmetry group of the water trimer, G48, in order to make them feasible in a reasonable amount of time. The spectrum of the low-frequency vibrations of the water trimer simulated using the eigenstates of the 9D bend Hamiltonian agrees remarkably well with the experimentally observed far-infrared (FIR) spectrum of the trimer in helium nanodroplets over the entire frequency range of the measurements from 70 to 620 cm−1. This shows that most peaks in the experimental FIR spectrum are associated with the intermolecular bending vibrations of the trimer. Moreover, the ground-state torsional tunneling splittings from the present 9D calculations are in excellent agreement with the spectroscopic data. These results demonstrate the high quality of the ab initio 2+3-body PES employed for the DOFs included in the bound-state calculations.