HF Trimer Research Articles

HF Trimer: A New Full-Dimensional Potential Energy Surface and Rigorous 12D Quantum Calculations of Vibrational States.

HF trimer, as the smallest and the lightest cyclic hydrogen-bonded (HB) cluster, has long been a favorite prototype system for spectroscopic and theoretical investigations of the structure, energetics, spectroscopy, and dynamics of hydrogen-bond networks. Recently, rigorous quantum 12D calculations of the coupled intra- and intermolecular vibrations of this fundamental HB trimer (J. Chem. Phys. 2023, 158, 234109) were performed, employing an older ab initio-based many-body potential energy surface (PES). While the theoretical results were found to be in reasonably good agreement with the available spectroscopic data, it was also evident that it is highly desirable to develop a more accurate 12D PES of HF trimer. Motivated by this, here we report a new, and the first fully ab initio 12D PES of this paradigmatic system. Approximately 42,540 geometries were sampled and calculated at the level of CCSD(T)-F12a/AVTZ. The permutationally invariant polynomial-neural network based Δ-machine learning approach (J. Phys. Chem. Lett. 2022, 13, 4729) was employed to perform cost-efficient calculations of the basis-set-superposition error (BSSE) correction. By strategically selecting data points, this approach facilitated the construction of a high-precision PES with BSSE correction, while requiring only a minimal number of BSSE value computations. The fitting error of the final PES is only 0.035 kcal/mol. To assess its performance, the 12D fully coupled quantum calculations of excited intra- and intermolecular vibrational states of HF trimer are carried out using the rigorous methodology developed by us earlier. The results are found to be in a significantly better agreement with the available spectroscopic data than those obtained with the previously existing semiempirical 12D PES.

HCl trimer: HCl-stretch excited intramolecular and intermolecular vibrational states from 12D fully coupled quantum calculations employing contracted intra- and inter-molecular bases.

We present fully coupled, full-dimensional quantum calculations of the inter- and intra-molecular vibrational states of HCl trimer, a paradigmatic hydrogen-bonded 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 many-body 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 HCl-stretch excited vibrational states of the trimer with one- and two-quanta, together with the low-energy intermolecular vibrational states in the two excited v = 1 intramolecular vibrational manifolds. They reveal significant coupling between the intra- and inter-molecular 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 two-body PES, obtained by removing the three-body term from the original 2 + 3-body PES, and those computed on the 2 + 3-body PES. It demonstrates that the three-body interactions have a strong effect on the trimer binding energy as well as on its intra- and inter-molecular vibrational energy levels. Comparison with the available spectroscopic data shows that good agreement with the experiment is achieved only if the three-body interactions are included. Some low-energy vibrational states localized in a secondary minimum of the PES are characterized as well.

Systematic analysis of electronic barrier heights and widths for concerted proton transfer in cyclic hydrogen bonded clusters: (HF)n, (HCl)n and (H2O)n where n = 3, 4, 5.

The MP2 and CCSD(T) methods are paired with correlation consistent basis sets as large as aug-cc-pVQZ to optimize the structures of the cyclic minima for (HF)n, (HCl)n and (H2O)n where n = 3-5, as well as the corresponding transition states (TSs) for concerted proton transfer (CPT). MP2 and CCSD(T) harmonic vibrational frequencies confirm the nature of each minimum and TS. Both conventional and explicitly correlated CCSD(T) computations are employed to assess the electronic dissociation energies and barrier heights for CPT near the complete basis (CBS) limit for all 9 clusters. Results for (HF)n are consistent with prior studies identifying Cnh and Dnh point group symmetry for the minima and TSs, respectively. Our computations also confirm that CPT proceeds through Cs TS structures for the C1 minima of (H2O)3 and (H2O)5, whereas the process goes through a TS with D2d symmetry for the S4 global minimum of (H2O)4. This work corroborates earlier findings that the minima for (HCl)3, (HCl)4 and (HCl)5 have C3h, S4 and C1 point group symmetry, respectively, and that the Cnh structures are not minima for n = 4 and 5. Moreover, our computations show the TSs for CPT in (HCl)3, (HCl)4 and (HCl)5 have D3h, D2d, and C2 point group symmetry, respectively. At the CCSD(T) CBS limit, (HF)4 and (HF)5 have the smallest electronic barrier heights for CPT (≈15 kcal mol-1 for both), followed by the HF trimer (≈21 kcal mol-1). The barriers are appreciably higher for the other clusters (around 27 kcal mol-1 for (H2O)4 and (HCl)3; roughly 30 kcal mol-1 for (H2O)3, (H2O)5 and (HCl)4; up to 38 kcal mol-1 for (HCl)5). At the CBS limit, MP2 significantly underestimates the CCSD(T) barrier heights (e.g., by ca. 2, 4 and 7 kcal mol-1 for the pentamers of HF, H2O and HCl, respectively), whereas CCSD overestimates these barriers by roughly the same magnitude. Scaling the barrier heights and dissociation energies by the number of fragments in the cluster reveals strong linear relationships between the two quantities and with the magnitudes of the imaginary vibrational frequency for the TSs.

HF trimer: 12D fully coupled quantum calculations of HF-stretch excited intramolecular and intermolecular vibrational states using contracted bases of intramolecular and intermolecular eigenstates.

We present the computational methodology, which for the first time allows rigorous twelve-dimensional (12D) quantum calculations of the coupled intramolecular and intermolecular vibrational states of hydrogen-bonded 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 reduced-dimension 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 hydrogen-bonded HF trimer on an abinitio calculated potential energy surface (PES). The calculations encompass the one- and two-quanta intramolecular HF-stretch excited vibrational states of the trimer and low-energy 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 donor-HF 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.

Изотопные эффекты в спектрах комплексов с водородными связями. Расчет колебательных спектров поглощения димеров (D-=SUB=-2-=/SUB=-CO)-=SUB=-2-=/SUB=- и D-=SUB=-2-=/SUB=-CO·sDF и тримеров D-=SUB=-2-=/SUB=-CO·s(DF)-=SUB=-2-=/SUB=- и (D-=SUB=-2-=/SUB=-CO)_2·sDF

The frequencies and intensities for the vibrational bands of absorption spectra of hydrogen-bonded (D2CO)2 and D2CO∙∙∙DF dimers, two D2CO∙∙∙(DF)2 trimers and four (D2CO)2∙∙∙DF trimers are calculated in the MP2/aug-cc-pVTZ approximation with the basis set superposition error taken into account. Anharmonic values of spectral parameters were obtained using the vibrational second-order perturbation theory. The influence of hydrogen bonds on the spectral parameters was determined from comparison of the values calculated for monomers, dimers, and trimers in the same approximation. The data obtained were compared with the results of previous calculations of (H2CO)2 and H2CO∙∙∙HF dimers and H2CO∙∙∙(HF)2 and (H2CO)2∙∙∙HF trimers. It was shown that one D2CO∙∙∙(DF)2 trimer and two (D2CO)2∙∙∙DF trimers have significant binding energies and strong absorption bands, which makes them promising candidates for detection by spectroscopic methods.

Erratum: "Intermolecular vibrational states of HF trimer from rigorous nine-dimensional quantum calculations: Strong coupling between intermolecular bending and stretching vibrations and the importance of the three-body interactions" [J. Chem. Phys. 157, 194103 (2022)

Erratum: "Intermolecular vibrational states of HF trimer from rigorous nine-dimensional quantum calculations: Strong coupling between intermolecular bending and stretching vibrations and the importance of the three-body interactions" [J. Chem. Phys. 157, 194103 (2022)

Intermolecular vibrational states of HF trimer from rigorous nine-dimensional quantum calculations: Strong coupling between intermolecular bending and stretching vibrations and the importance of the three-body interactions.

We present the computational methodology that allows rigorous and efficient nine-dimensional (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 lowest-energy 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 hydrogen-bonded trimer, on the rigid-monomer version of an ab initio calculated potential energy surface (PES). They are the first to include fully the stretch-bend 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 stretch-bend 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 full-dimensional 12D quantum calculations will be required to obtain definitive vibrational excitation energies for a given PES. Our study also demonstrates that the nonadditive three-body interactions are very significant in (HF)3 and have to be included in order to obtain accurate intermolecular vibrational energy levels of the trimer.

Trimers formed by formaldehyde with hydrogen fluoride: Structures, energetics, and infrared absorption spectra

Equilibrium nuclear configurations of two stable H2CO∙∙∙(HF)2 trimers and four stable (H2CO)2∙∙∙HF trimers are calculated in the MP2/aug-cc-pVTZ approximation with the basis set superposition error taken into account. Anharmonic values of frequencies and intensities for infrared absorption bands are computed. For comparison, the analogous calculations were carried out in the same approximation for the monomers and homo- and heterodimers. The changes in the spectral parameters of absorption bands upon formation of trimers are examined. The main emphasis was on revealing the cooperativity of H-bonding effects in trimers of different composition and the correlations between the intramonomer and intermonomer charge transfer, the structural and spectral changes upon formation of trimers. It was found that three predicted trimers have sufficiently large binding energies and their HF stretching bands are significantly shifted from strong bands of monomers and dimers, which can facilitate their experimental observation.

The structure and vibrational spectral parameters of a complex of HF with the planar (H2CO)2 dimer

Equilibrium nuclear configurations of the planar formaldehyde homodimer (H2CO)2 and the (H2CO)2···HF complex are determined in the MP2/6-311++G(3df, 3pd) approximation taking into account the superposition error of basis sets of monomers. Harmonic values of the frequencies and intensities of fundamental transitions between vibrational states of these hydrogen-bonded complexes were calculated using the Gaussian 09 package of programs. Anharmonic values of the frequencies and intensities of the ν(H–F) stretching vibration and several intermolecular vibrations in the (H2CO)2···HF trimer were obtained from variational solutions of one-, two-, and three-dimensional vibrational Schrodinger equations. The anharmonic influence of the C=O and hydrogen bond O···H–F stretching vibrations, as well as of librational vibrations of monomers, on the spectral parameters of the strongest ν(H–F) absorption band of trimer was studied.

The cyclic ground state structure of the HF trimer revealed by far infrared jet-cooled Fourier transform spectroscopy

The rovibrationally resolved Fourier transform (FT) far infrared (FIR) spectra of two intermolecular librations of (HF)3, namely the in-plane ν6 and out-of-plane ν4 bending fundamentals centered, respectively, at about 494 cm(-1) and 602 cm(-1), have been recorded for the first time under jet-cooled conditions using the supersonic jet of the Jet-AILES apparatus. The simultaneous rotational analysis of 245 infrared transitions belonging to both bands enabled us to determine the ground state (GS), ν6 and ν4 rotational and centrifugal distortion constants. These results provided definite experimental answers to the structure of such a weakly bound trimer: firstly the vibrationally averaged planarity of cyclic (HF)3, also supported by the very small value of the inertia defect obtained in the GS, secondly the slight weakening of the hydrogen bond in the intermolecular excited states evidenced from the center of mass separations of the HF constituents determined in the ground, ν6 = 1 and ν4 = 1 states of (HF)3 as well as the decrease of the fitted rotational constants upon excitation. Finally, lower bounds of about 2 ns on ν6 and ν4 state lifetimes could be derived from the deconvolution of experimental linewidths. Such long lifetimes highlight the interest in probing low frequency intermolecular motions of molecular complexes to get rid of constraints related to the vibrational dynamics of coupled anharmonic vibrations at higher energy, resulting in loss of rotational information.

Fluorohydrogenate Cluster Ions in the Gas Phase: Electrospray Ionization Mass Spectrometry of the [1-Ethyl-3-methylimidazolium+][F(HF)2.3–] Ionic Liquid

Electrospray ionization of the fluorohydrogenate ionic liquid [1-ethyl-3-methylimidazolium][F(HF)2.3] ionic liquid was conducted to understand the nature of the anionic species as they exist in the gas phase. Abundant fluorohydrogenate clusters were produced; however, the dominant anion in the clusters was [FHF(-)], and not the fluoride-bound HF dimers or trimers that are seen in solution. Density functional theory (DFT) calculations suggest that HF molecules are bound to the clusters by about 30 kcal/mol. The DFT-calculated structures of the [FHF(-)]-bearing clusters show that the favored interactions of the anions are with the methynic and acetylenic hydrogen atoms on the imidazolium cation, forming planar structures similar to those observed in the solid state. A second series of abundant negative ions was also formed that contained [SiF5(-)] together with the imidazolium cation and the fluorohydrogenate anions that originate from reaction of the spray solution with silicate surfaces.

An Electronic Structure Perspective of the Promoter Modes in Proton Transfer Reactions

The changes in the electronic structure are analyzed along the IRC of proton transfer reactions in two model systems, formic acid dimer and cyclic HF trimer. The IRC consists of three regions. In the first region, the two units between which a proton is exchanged approach each other. The vibrational mode associated with this movement is called the promoter mode. Computational evidence is provided to suggest that during this period the electrons in the lone pair of the acceptor atom delocalize significantly into the antibonding orbital of the covalent bond between the donor and hydrogen atoms. This reduces the barrier to the proton transfer. The force constants associated with the migrating protons also decrease as a result of the delocalization of lone pair electrons into the σ* orbital, and the associated stretching vibrational frequencies decrease along the IRC up to the transition state. In the second part of the IRC, the proton migration occurs. Finally, the two monomers retreat to the new equilibrium positions. On the basis of this, it is suggested that the role of the promoter mode is to enhance the flow of the lone pair electrons into the σ* orbital such that the barrier to the actual proton migration comes down. This can be used to identify them.

Ab initio study of the structure, cooperativity, and vibrational properties of HNC ternary complexes with two HF molecules

MP2/aug-cc-pVDZ calculations have been used to provide information on the three ternary systems comprising one HNC and two HF molecules. The binding distances, frequency shifts, and interaction energies in these systems have been analysed to study the cooperativity of hydrogen bond in these systems. The cooperativity of hydrogen bond in HNC–HF–HF trimer is larger than that in HF–HF–HNC trimer. The result indicates that the proton acceptor HNC plays a more important role in enhancing the cooperativity of hydrogen bond. Many-body interaction analyses have also been performed for these ternary systems.

Symmetry-Adapted Perturbation Theory Analysis of the N···HX Hydrogen Bonds

The main aim of the study was the detailed investigation of the interaction energy decomposition in dimers and trimers containing N...HX bonds of different types. The study of angular dependence of interaction energy terms partitioned according to the symmetry-adapted perturbation theory (SAPT) was performed for the dimers containing N...HX bonds as mentioned above: ammonia-HX (X = F, Cl, Br) and pyridine-HF complexes. It was found that the electrostatic and induction terms exhibit strong angular dependence, while the exchange contributions are less affected. The dispersion terms are virtually nondirectional. In addition, the three-body SAPT interaction energy analysis for the mixed acid-base NH3...(HF)2 and (NH3)2...HF trimers revealed strong differences between interactions of similar strength but different types (i.e., hydrogen bond and general electrostatic interaction). The importance of the induction terms for the nonadditivity of the interaction energy in strongly polar systems was confirmed.

USING LEBEDEV GRIDS, SINE SPHERICAL HARMONICS, AND MONOMER CONTRACTED BASIS FUNCTIONS TO CALCULATE BENDING ENERGY LEVELS OF HF TRIMER

We calculate energy levels of a six-dimensional bending Hamiltonian for HF trimer using a finite basis representation (FBR) in conjunction with the Lanczos eigensolver. We improve on our previous method [J. Chem. Phys.115, 9781 (2001)] using three techniques: (1) Lebedev's quadrature scheme is used to reduce the size of quadrature grid by a factor of 3.4. (2) Since the barrier separating the two equivalent versions of HF trimer is high and wide, it is a good approximation to confine the bending motion to one well by using sine spherical harmonics basis functions (this reduces the size of the basis by a factor of 8). (3) The sine spherical harmonic basis is contracted for each monomer to generate a very efficient basis. It is shown that the best approach is to combine all the three techniques.

Six-dimensional variational calculation of the bending energy levels of HF trimer and DF trimer

The bending energy levels of HF and DF trimer were calculated variationally using a six-dimensional kinetic-energy operator derived by constraining the stretch degrees of freedom to their equilibrium values. A basis of direct products of spherical harmonics is used to represent the wave function. The symmetry adapted Lanczos method is used to calculate levels of all symmetries from one sequence of matrix-vector products. Two efficient ways of implementing the symmetry-adapted Lanczos method are presented. To determine the concerted hydrogen bond breaking tunneling splitting in HF and DF trimer one needs to use the D3h point group. By doing D3h calculations, we find that the splitting is negligible for the low-lying levels. If the tunneling is unfeasible, the appropriate group is C3h. Our calculation using the most accurate SO-3+HF3BG potential developed by Quack, Stohner, and Suhm indicates that two gas-phase overtone bending bands of HF trimer should be reassigned, and that the noble gas matrix spectra of the bending fundamental bands are significantly shifted from their gas-phase counterparts.

Symmetry-adapted perturbation theory of nonadditive three-body interactions in van der Waals molecules. II. Application to the Ar2–HF interaction

Symmetry-adapted perturbation theory (SAPT) of three-body forces is applied to characterize the nonadditive interactions in the Ar2–HF trimer. The origins of the anisotropy of the nonadditive Ar2–HF potential are discussed, and the results are compared with the existing ab initio data. The multipole-expanded expressions for the induction, induction–dispersion, and dispersion nonadditivities in terms of the multipole moments and (hyper)polarizabilities are derived for the special case of atom–atom–diatom complexes, and the validity of the multipole approximation is investigated by comparison of the expanded and nonexpanded energies computed at the same level of the theory and in the same basis sets. Finally, recent (semi)empirical models of nonadditive interactions in Ar2–HF based on the exchange quadrupole electrostatic interaction are analyzed in terms of contributions as defined by SAPT. It is shown that the present level of the SAPT theory correctly accounts for the terms included in the exchange quadrupole electrostatic model.

Vibrational frequency shifts and thermodynamic stabilities of (HF) n isomers ( n=4–8)

Based on the spectroscopic data available for the HF dimer and trimer and taking into account the cooperativity effect, the force fields of larger (HF) n clusters ( n=4–8) have beeen determined for various isomeric structures and used to calculate the frequency shifts for the stretching vibrations. The comparison with recent experimental results, obtained with size selection, suggests that tailed ring structures (i.e. symmetric rings with additional HF units attached to them) might play an important role in the cluster distribution in expansion-cooled molecular beams. Thermodynamic calculations show that tailed ring structures have comparably high stabilities.

Nonadditivity effects in the molecular interactions of H2O and HF trimers by the symmetry-adapted perturbation theory

Nonadditivity contribution to the three-body interaction energy is studied in terms of the symmetry-adapted perturbation theory for many-electron systems. Each component of energy, particularly the second-order exchange dispersion and exchange induction contributions, is given by a combination of electrostatic interaction energies in Longuet–Higgins representation of the intermolecular charge distribution. The formulas of these energies are derived with the Hartree–Fock approximation and by taking triple-electronic exchanges among three monomers into account. Numerical calculation has been performed for the cyclic planar H2O and HF trimers, considering only single-electronic exchanges between molecules. The three-body effect of the second-order exchange energy has been found to be repulsive, while the main part of attractive contribution is due to the induction. The ratio of three-body energy to two-body one for the dispersion is much smaller than that for the induction, though the latter decreases more rapidly than the former as the angle between monomers increases. As a result, the three-body contribution lowers the total interaction energy slightly near the van der Waals minimum in both trimers. The contribution of two-body energies is also shown.

Ab initio models for multiple‐hydrogen exchange: Comparison of cyclic four‐ and six‐center systems

AbstractHigh‐level ab initio calculations {QCISD(T)/6‐311 +G**//MP2(fu)/6‐31 +G**, with corrections for higher polarization [evaluated at MP2/6‐311 +G(3df,2p)] and ΔZPE//MP2(fu)/6‐31 +G**, i.e., comparable to Gaussian‐2 theory} indicate concerted mechanisms for double‐ and triple‐hydrogen exchange reactions in HF and HCl dimers and trimers, in mixed dimers and trimers containing one NH3, and in mixed dimers of HF, HCl, and NH3 with formic acid. All these reactions proceed via cyclic four‐ or six‐center transition structures, the latter being generally more favorable. Calculated activation barriers (ΔHd̊ at 0 K, kcal/mol) are 42.3 for (HF)2, 20.3 for (HF)3, 41.2 for (HCl)2, 25.6 for (HCl)3, 36.0 for NH3‐HF, 10.6 for NH3(HF)2, 19.9 for NH3‐HCl, 2.3 for NH3(HCl)2, 9.7 for HCO2H‐HF, 7.0 for HCO2H‐HCl, and 11.3, for HCO2H‐NH3. The barriers are lower for the more ionic systems and when more ion pair character is present. © John Wiley & Sons, Inc.