We present fully coupled, fulldimensional quantum calculations of the inter and intramolecular vibrational states of HCl trimer, a paradigmatic hydrogenbonded molecular trimer. They are performed utilizing the recently developed methodology for the rigorous 12D quantum treatment of the vibrations of the noncovalently bound trimers of flexible diatomic molecules [Felker and Bačić, J. Chem. Phys. 158, 234109 (2023)], which was previously applied to the HF trimer by us. In this work, the manybody 12D potential energy surface (PES) of (HCl)3 [Mancini and Bowman, J. Phys. Chem. A 118, 7367 (2014)] is employed. The calculations extend to the intramolecular HClstretch excited vibrational states of the trimer with one and twoquanta, together with the lowenergy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra and intermolecular vibrational modes. The 12D calculations also show that the frequencies of the v = 1 HCl stretching states of the HCl trimer are significantly redshifted relative to those of the isolated HCl monomer. Detailed comparison is made between the results of the 12D calculations on the twobody PES, obtained by removing the threebody term from the original 2 + 3body PES, and those computed on the 2 + 3body PES. It demonstrates that the threebody interactions have a strong effect on the trimer binding energy as well as on its intra and intermolecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the threebody interactions are included. Some lowenergy vibrational states localized in a secondary minimum of the PES are characterized as well.
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Free, publiclyaccessible full text available April 28, 2025

In this work the H2O–HCN complex is quantitatively characterized in two ways. First, we report a new rigidmonomer 5D intermolecular potential energy surface (PES) for this complex, calculated using the symmetryadapted perturbation theory based on density functional theory method. The PES is based on 2833 ab initio points computed employing the augccpVQZ basis set, utilizing the autoPES code, which provides a sitesite analytical fit with the longrange region given by perturbation theory. Next, we present the results of the quantum 5D calculations of the fully coupled intermolecular rovibrational states of the H2O–HCN complex for the total angular momentum J values of 0, 1, and 2, performed on the new PES. These calculations rely on the quantum boundstate methodology developed by us recently and applied to a variety of noncovalently bound binary molecular complexes. The vibrationally averaged groundstate geometry of H2O–HCN determined from the quantum 5D calculations agrees very well with that from the microwave spectroscopic measurements. In addition, the computed groundstate rotational transition frequencies, as well as the B and C rotational constants calculated for the ground state of the complex, are in excellent agreement with the experimental values. The assignment of the calculated intermolecular vibrational states of the H2O–HCN complex is surprisingly challenging. It turns out that only the excitations of the intermolecular stretch mode can be assigned with confidence. The coupling among the angular degrees of freedom (DOFs) of the complex is unusually strong, and as a result most of the excited intermolecular states are unassigned. On the other hand, the coupling of the radial, intermolecular stretch mode and the angular DOFs is weak, allowing straightforward assignment of the excitation of the former.
Free, publiclyaccessible full text available November 7, 2024 
We present the computational methodology, which for the first time allows rigorous twelvedimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogenbonded trimers of flexible diatomic molecules. Its starting point is the approach that we introduced recently for fully coupled 9D quantum calculations of the intermolecular vibrational states of noncovalently bound trimers comprised of diatomics treated as rigid. In this paper, it is extended to include the intramolecular stretching coordinates of the three diatomic monomers. The cornerstone of our 12D methodology is the partitioning of the full vibrational Hamiltonian of the trimer into two reduceddimension Hamiltonians, one in 9D for the intermolecular degrees of freedom (DOFs) and another in 3D for the intramolecular vibrations of the trimer, and a remainder term. These two Hamiltonians are diagonalized separately, and a fraction of their respective 9D and 3D eigenstates is included in the 12D product contracted basis for both the intra and intermolecular DOFs, in which the matrix of the full 12D vibrational Hamiltonian of the trimer is diagonalized. This methodology is implemented in the 12D quantum calculations of the coupled intra and intermolecular vibrational states of the hydrogenbonded HF trimer on an ab initio calculated potential energy surface (PES). The calculations encompass the one and twoquanta intramolecular HFstretch excited vibrational states of the trimer and lowenergy intermolecular vibrational states in the intramolecular vibrational manifolds of interest. They reveal several interesting manifestations of significant coupling between the intra and intermolecular vibrational modes of (HF)3. The 12D calculations also show that the frequencies of the v = 1, 2 HF stretching states of the HF trimer are strongly redshifted in comparison to those of the isolated HF monomer. Moreover, the magnitudes of these trimer redshifts are much larger than that of the redshift for the stretching fundamental of the donorHF moiety in (HF)2, most likely due to the cooperative hydrogen bonding in (HF)3. The agreement between the 12D results and the limited spectroscopic data for the HF trimer, while satisfactory, leaves room for improvement and points to the need for a more accurate PES.

We present the computational methodology that allows rigorous and efficient ninedimensional (9D) quantum calculations of the intermolecular vibrational states of noncovalently bound trimers of diatomic molecules, with the monomers treated as rigid. The full 9D vibrational Hamiltonian of the trimer is partitioned into a 3D “frame” (or stretching) Hamiltonian and a 6D “bend” Hamiltonian. These two Hamiltonians are diagonalized separately, and a certain number of their lowestenergy eigenstates is included in the final 9D product contracted basis in which the full 9D intermolecular vibrational Hamiltonian is diagonalized. This methodology is applied to the 9D calculations of the intermolecular vibrational levels of (HF)3, a prototypical hydrogenbonded trimer, on the rigidmonomer version of an ab initio calculated potential energy surface (PES). They are the first to include fully the stretchbend coupling present in the trimer. The frequencies of all bending fundamentals considered from the present 9D calculations are about 10% lower than those from the earlier quantum 6D calculations that considered only the bending modes of the HF trimer. This means that the stretchbend coupling is strong, and it is imperative to include it in any accurate treatment of the (HF)3 vibrations aiming to assess the accuracy of the PES employed. Moreover, the 9D results are in better agreement with the limited available spectroscopic data that those from the 6D calculations. In addition, the 9D results show sensitivity to the value of the HF bond length, equilibrium or vibrationally averaged, used in the calculations. The implication is that fulldimensional 12D quantum calculations will be required to obtain definitive vibrational excitation energies for a given PES. Our study also demonstrates that the nonadditive threebody interactions are very significant in (HF)3 and have to be included in order to obtain accurate intermolecular vibrational energy levels of the trimer.

The methodological advances made in recent years have significantly extended the range and dimensionality of noncovalently bound, hydrogenbonded and van der Waals, molecular complexes for which fulldimensional and fully coupled quantum calculations of their rovibrational states are feasible. They exploit the unexpected implication that the weak coupling between the inter and intramolecular rovibrational degrees of freedom (DOFs) of the complexes has for the ease of computing the highenergy eigenstates of the latter. This is done very effectively by using contracted eigenstate bases to cover both intra and intermolecular DOFs. As a result, it is now possible to calculate rigorously all intramolecular rovibrational fundamentals, together with the lowlying intermolecular rovibrational states, of complexes involving two small molecules beyond diatomics, binary polyatomic moleculelarge (rigid) molecule complexes, and endohedral complexes of light polyatomic molecules confined inside (rigid) fullerene cages. In this Perspective these advances are reviewed in considerable depth. The progress made thanks to them is illustrated by a number of representative applications. Whenever possible, direct comparison is made with the available infrared, farinfrared, and microwave spectroscopic data.more » « less

We present a methodology that, for the first time, allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a triatomic molecule in a nanoscale cavity, in this case, H_{2}O inside the fullerene C_{60}. Both moieties are taken to be rigid. Our treatment incorporates the quantum sixdimensional translation–rotation (TR) wave functions of the encapsulated H_{2}O, which serve as the spatial parts of the initial and final states of the INS transitions. As a result, the simulated INS spectra reflect the coupled TR dynamics of the nanoconfined guest molecule. They also exhibit the features arising from symmetry breaking observed for solid H_{2}O@C_{60}at low temperatures. Utilizing this methodology, we compute the INS spectra of H_{2}O@C_{60}for two incident neutron wavelengths and compare them with the corresponding experimental spectra. Good overall agreement is found, and the calculated spectra provide valuable additional insights.