On-the-fly ab intito calculations of anharmonic vibrational frequencies: Local-monomer theory and application to HCl clusters

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

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.

Probing vibrational coupling via a grid-based quantum approach-an efficient strategy for accurate calculations of localized normal modes in solid-state systems

In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid-state surfaces is presented. The associated normal mode vectors are approximated solely on the basis of structural information and obtained via diagonalization of a reduced Hessian. The grid-based Numerov procedure in one and two dimensions is then applied to an adequate scan of the respective potential surface yielding the associated vibrational wave functions and energy eigenvalues. This not only provides a detailed description of anharmonic effects but also an accurate inclusion of the coupling between the investigated vibrational states on a quantum mechanical level. All results obtained for the constructed normal modes are benchmarked against their analytical counterparts obtained from the diagonalization of the total Hessian of the entire system. Three increasingly complex systems treated at quantum chemical level of theory have been considered, namely the symmetric and asymmetric stretch vibrations of an isolated water molecule, hydroxyl groups bound to the surface of GeO2 (001), α-quartz(001) and Rutil (001) as well as crystalline Li2 NH serving as an example for a bulk material. While the data obtained for the individual systems verify the applicability of the proposed methodology, comparison to experimental data demonstrates the accuracy of this methodology despite the restriction to limit this methodology to a few selected vibrational modes. The possibility to investigate vibrational phenomena of localized normal modes without the requirement of executing costly harmonic frequency calculations of the entire system enables the application of this method to cases in which the determination of normal modes is prohibitively expensive or not available for a particular level of theory. © 2018 Wiley Periodicals, Inc.

Vibrational Study of Iodide-Based Room-Temperature Ionic-Liquid Effects on Candidate N719-Chromophore/Titania Interfaces for Dye-Sensitised Solar-Cell Applications from Ab-Initio Based Molecular-Dynamics Simulation

The accurate ab-initio modelling of prototypical and well-representative photo-active interfaces for candidate dye-sensitised solar cells is a challenging problem. To this end, using ab-initio molecular-dynamics (AIMD) simulation based on Density Functional Theory (DFT), the effects of explicit solvation by iodide-based, I−[bmim]+ room-temperature ionic liquids (RTILs) have been assessed on modelling a N719-chromophore sensitising dye adsorbed onto an anatase-titania (101) surface. In particular, the vibrational spectra for this model photo-active interface were calculated by means of Fourier transformed mass-weighted velocity autocorrelation functions. These were compared with experiment and against each other to gain an understanding of how using iodine-based RTILs as the electrolytic hole acceptor alters the dynamical properties of the widely-used N719 dye. The effect of Perdew-Burke-Ernzerhof (PBE) and Becke-Lee-Yang-Parr (BLYP) functionals on the vibrational spectra were assessed. PBE generally performed best in producing spectra which matched the typically expected experimental frequency modes.

Acid Dissociation in HCl-Water Clusters is Temperature Dependent and Cannot be Detected Based on Dipole Moments

The dissociation of acids in aqueous environments at low temperatures in the presence of a limited amount of water is underlying a wealth of processes from atmospheric to interstellar science. For the paradigmatic case of HCl(H_{2}O)_{n} clusters, our extensive ab initio path integral simulations quantify in terms of free energy differences and barriers that n=4 water molecules are indeed required to dissociate HCl at low temperatures. Increasing the temperature, however, reverses the process and thus counteracts dissociation by fluctuation-driven recombination. The size of the electric dipole moment is shown to not correlate with the acid being in its dissociated or molecular state, thus rendering its measurement as a function of n unable to detect the dissociation transition.

Static vs dynamic DFT prediction of IR spectra of flexible molecules in the condensed phase: The (ClCF2CF(CF3)OCF2CH3) liquid as a test case

First-principles molecular dynamics (FPMD) simulations in the framework of Density Functional Theory (DFT) are carried out for the prediction of the infrared spectrum of the fluorinated molecule ClCF₂CF(CF₃)OCF₂CH₃ in liquid and gas phase. This molecule is characterized by a flexible structure, allowing the co-existence of several stable conformers, that differ by values of the torsional angles. FPMD computed spectra are compared to the experimental ones, and to Boltzmann weighted IR spectra based on gas phase calculations.

Anharmonic effects in the quantum cluster equilibrium method

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

On the benefits of localized modes in anharmonic vibrational calculations for small molecules

Anharmonic vibrational calculations can already be computationally demanding for relatively small molecules. The main bottlenecks lie in the construction of the potential energy surface and in the size of the excitation space in the vibrational configuration interaction (VCI) calculations. To address these challenges, we use localized-mode coordinates to construct potential energy surfaces and perform vibrational self-consistent field and L-VCI calculations [P. T. Panek and C. R. Jacob, ChemPhysChem 15, 3365 (2014)] for all vibrational modes of two prototypical test cases, the ethene and furan molecules. We find that the mutual coupling between modes is reduced when switching from normal-mode coordinates to localized-mode coordinates. When using such localized-mode coordinates, we observe a faster convergence of the n-mode expansion of the potential energy surface. This makes it possible to neglect higher-order contributions in the n-mode expansion of the potential energy surface or to approximate higher-order contributions in hybrid potential energy surfaces, which reduced the computational effort for the construction of the anharmonic potential energy surface significantly. Moreover, we find that when using localized-mode coordinates, the convergence with respect to the VCI excitation space proceeds more smoothly and that the error at low orders is reduced significantly. This makes it possible to devise low-cost models for obtaining a first approximation of anharmonic corrections. This demonstrates that the use of localized-mode coordinates can be beneficial already in anharmonic vibrational calculations of small molecules and provides a possible avenue for enabling such accurate calculations also for larger molecules.

Quantum calculations of the IR spectrum of liquid water using ab initio and model potential and dipole moment surfaces and comparison with experiment

The calculation and characterization of the IR spectrum of liquid water have remained a challenge for theory. In this paper, we address this challenge using a combination of ab initio approaches, namely, a quantum treatment of IR spectrum using the ab initio WHBB water potential energy surface and a refined ab initio dipole moment surface. The quantum treatment is based on the embedded local monomer method, in which the three intramolecular modes of each embedded H2O monomer are fully coupled and also coupled singly to each of six intermolecular modes. The new dipole moment surface consists of a previous spectroscopically accurate 1-body dipole moment surface and a newly fitted ab initio intrinsic 2-body dipole moment. A detailed analysis of the new dipole moment surface in terms of the coordinate dependence of the effective atomic charges is done along with tests of it for the water dimer and prism hexamer double-harmonic spectra against direct ab initio calculations. The liquid configurations are taken from previous molecular dynamics calculations of Skinner and co-workers, using the TIP4P plus E3B rigid monomer water potential. The IR spectrum of water at 300 K in the range of 0-4000 cm(-1) is calculated and compared with experiment, using the ab initio WHBB potential and new ab initio dipole moment, the q-TIP4P/F potential, which has a fixed-charged description of the dipole moment, and the TTM3-F potential and dipole moment surfaces. The newly calculated ab initio spectrum is in very good agreement with experiment throughout the above spectral range, both in band positions and intensities. This contrasts to results with the other potentials and dipole moments, especially the fixed-charge q-TIP4P/F model, which gives unrealistic intensities. The calculated ab initio spectrum is analyzed by examining the contribution of various transitions to each band.

Efficient anharmonic vibrational spectroscopy for large molecules using local-mode coordinates

This article presents a general computational approach for efficient simulations of anharmonic vibrational spectra in chemical systems. An automated local-mode vibrational approach is presented, which borrows techniques from localized molecular orbitals in electronic structure theory. This approach generates spatially localized vibrational modes, in contrast to the delocalization exhibited by canonical normal modes. The method is rigorously tested across a series of chemical systems, ranging from small molecules to large water clusters and a protonated dipeptide. It is interfaced with exact, grid-based approaches, as well as vibrational self-consistent field methods. Most significantly, this new set of reference coordinates exhibits a well-behaved spatial decay of mode couplings, which allows for a systematic, a priori truncation of mode couplings and increased computational efficiency. Convergence can typically be reached by including modes within only about 4 Å. The local nature of this truncation suggests particular promise for the ab initio simulation of anharmonic vibrational motion in large systems, where connection to experimental spectra is currently most challenging.

Isolating the spectral signature of H3O+ in the smallest droplet of dissociated HCl acid

The smallest droplet of HCl acid, H₃O⁺(H₂O)₃Cl⁻, and its isolated H₃O⁺ infrared signature.

“Plug and play” full-dimensional ab initio potential energy and dipole moment surfaces and anharmonic vibrational analysis for CH4–H2O

The first full-dimensional potential energy surface of CH₄–H₂O dimer is presented, and vibrational analysis of this dimer is performed.

Efficient calculation of anharmonic vibrational spectra of large molecules with localized modes

The analysis and interpretation of the vibrational spectra of complex (bio)molecular systems, such as polypeptides and proteins, requires support from quantum-chemical calculations. Such calculations are currently restricted to the harmonic approximation. Here, we show how one of the main bottlenecks in such calculations, the evaluation of the potential energy surface, can be overcome by using localized modes instead of the commonly employed normal modes. We apply such local vibrational self-consistent field (L-VSCF) and vibrational configuration interaction (L-VCI) calculations to a cyclic water tetramer and a helical hexa-alanine peptide. The results show that the use of localized modes is equivalent to the commonly used normal modes, but offers several advantages. First, a faster convergence with respect to the excitation level is observed in L-VCI calculations. Second, the localized modes provide a reduced representation of the couplings between modes that show a regular coupling pattern. This can be used to disregard a significant number of small two-mode potentials a priori. Several such reduced coupling approximations are explored, and we show that the number of single-point calculations required to evaluate the potential energy surface can be significantly reduced without introducing noticeable errors in the resulting vibrational spectra.

Effects of Zero-Point Delocalization on the Vibrational Frequencies of Mixed HCl and Water Clusters

We demonstrate the significant effect that large-amplitude zero-point vibrational motion can have on the high-frequency fundamental vibrations of molecular clusters, specifically small (HCl)n-(H2O)m clusters. Calculations were conducted on a many-body potential, constructed from a mix of new and previously reported semiempirical and high-level ab initio potentials. Diffusion Monte Carlo simulations were performed to determine ground-state wave functions. Visualization of these wave functions indicates that the clusters exhibit delocalized ground states spanning multiple stationary point geometries. The ground states are best characterized by planar ring configurations, despite the clusters taking nonplanar configurations at their global minima. Vibrational calculations were performed at the global minima and the Diffusion Monte Carlo predicted configurations and also using an approach that spans multiple stationary points along a rectilinear normal-mode reaction path. Significantly better agreement was observed between the calculated vibrational frequencies and experimental peak positions when the delocalized ground state was accounted for.