Semi-quartic force fields retrieved from multi-mode expansions: Accuracy, scaling behavior, and approximations

Zero-Point-Energy Driven Isotopic Exchange of the [H3O]- anion Probed by Mid-Infrared Action Spectroscopy

We present the first observation of vibrational transitions in the [H3O]- anion, an intermediate in the anion-molecule reaction of water, H2O, and hydride, H-, using a laser-induced isotopic H/D exchange reaction action spectroscopy scheme applied to anions. The observed bands are assigned as the fundamental and first overtone of the H2O-H- vibrational stretching mode, based on anharmonic calculations within the vibrational perturbation theory and vibrational configuration interaction. Although the D2O·D- species has the lowest energy, our experiments confirm the D2O·H- isotope to be a sink of the H/D exchange reaction. Ab initio calculations corroborate that the formation of D2O·H- is favored, as the zero-point-energy difference is larger between D2 and H2 than between D2O·H- and D2O·D-.

Anharmonic Vibrational Spectroscopy of Germanium-Containing Clusters, GexC4-x and GexSi4-x (x = 0-4), for Interstellar Detection

An extensive, high-level theoretical study on tetra-atomic germanium carbide/silicide clusters is presented. Accurate harmonic and anharmonic vibrational frequencies and rotational constants are calculated at the CCSD(T)-F12a(b)/cc-pVT(Q)Z-F12 levels of theory. With growing capabilities to discern more of the chemical composition of the interstellar medium (ISM), an accurate database of reference material is required. The presence of carbon is ubiquitous in the ISM, and silicon is known to be present in interstellar dust grains; however, germanium-containing molecules remain elusive. To begin understanding the presence and role of germanium in the ISM, we present this study of the vibrational and rotational spectroscopic properties of various germanium-containing molecules to aid in their potential identification in the ISM with modern observational tools such as the James Webb Space Telescope. Structures studied herein include rhomboidal (r-), diamond (d-), and trapezoidal (t-) tetra-atomic molecules of the form GexC4-x and GexSi4-x, where x = 0-4. The most promising structure for detection is r-Ge2C2 via the ν4 mode with a frequency of 802.7 cm-1 (12.5 μm) and an intensity of 307.2 km mol-1. Other molecules that are potentially detectable, i.e., through vibrational modes or rotational transitions, include r-Ge3C, r-GeSi3, d-GeC3, r-GeC3, and t-Ge2C2.

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.

Comprehensive quantum chemical analysis of the (ro)vibrational spectrum of thiirane and its deuterated isotopologue

The (ro)vibrational spectra of thiirane, c-C2H4S, and its fully deuterated isotopologue, c-C2D4S, have been studied by means of vibrational configuration interaction theory, VCI, its incremental variant, iVCI, and subsequent variational rovibrational calculations, RVCI, which rely on multidimensional potential energy surfaces of coupled-cluster quality including up to four-mode coupling terms. Accurate geometrical parameters, fundamental vibrational transitions and first overtones, rovibrational spectra and rotational spectroscopic constants have been determined from these calculations and were compared with experimental results whenever available. A number of tentative misassignments in the vibrational spectra could be resolved and most results for the deuterated thiirane are high-level predictions, which may guide experiments to come. Besides this, a new implementation of infrared intensities within the iVCI framework has been tested for the transitions of the title compounds and are compared with results obtained from standard VCI calculations.

Pitfalls in the n-mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Deposition products predicted from conceptual DFT: The hydrolysis reactions of MoF6, WF6, and UF6

Metal hexafluorides hydrolyze at ambient temperature to deposit compounds having fluorine-to-oxygen ratios that depend upon the identity of the metal. Uranium-hexafluoride hydrolysis, for example, deposits uranyl fluoride (UO2F2), whereas molybdenum hexafluoride (MoF6) and tungsten hexafluoride deposit trioxides. Here, we pursue general strategies enabling the prediction of depositing compounds resulting from multi-step gas-phase reactions. To compare among the three metal-hexafluoride hydrolyses, we first investigate the mechanism of MoF6 hydrolysis using hybrid density functional theory (DFT). Intermediates are then validated by performing anharmonic vibrational simulations and comparing with infrared spectra [McNamara et al., Phys. Chem. Chem. Phys. 25, 2990 (2023)]. Conceptual DFT, which is leveraged here to quantitatively evaluate site-specific electrophilicity and nucleophilicity metrics, is found to reliably predict qualitative deposition propensities for each intermediate. In addition to the nucleophilic potential of the oxygen ligands, several other contributing characteristics are discussed, including amphoterism, polyvalency, fluxionality, steric hindrance, dipolar strength, and solubility. To investigate the structure and composition of pre-nucleation clusters, an automated workflow is presented for the simulation of particle growth. The workflow entails a conformer search at the density functional tight-binding level, structural refinement at the hybrid DFT level, and computation of a composite free-energy profile. Such profiles can be used to estimate particle nucleation kinetics. Droplet formation is also considered, which helps to rationalize the different UO2F2 particle morphologies observed under varying levels of humidity. Development of predictive methods for simulating physical and chemical deposition processes is important for the advancement of material manufacturing involving coatings and thin films.

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods

Ab initio computer simulations of anharmonic vibrational spectra provide nuanced insight into the vibrational behavior of molecules and complexes. The computational bottleneck in such simulations, particularly for ab initio potentials, is often the generation of mode-coupling potentials. Focusing specifically on two-mode couplings in this analysis, the combination of a local-mode representation and multilevel methods is demonstrated to be particularly symbiotic. In this approach, a low-level quantum chemistry method is employed to predict the pairwise couplings that should be included at the target level of theory in vibrational self-consistent field (and similar) calculations. Pairs that are excluded by this approach are "recycled" at the low level of theory. Furthermore, because this low-level pre-screening will eventually become the computational bottleneck for sufficiently large chemical systems, distance-based truncation is applied to these low-level predictions without substantive loss of accuracy. This combination is demonstrated to yield sub-wavenumber fidelity with reference vibrational transitions when including only a small fraction of target-level couplings; the overhead of predicting these couplings, particularly when employing distance-based, local-mode cutoffs, is a trivial added cost. This combined approach is assessed on a series of test cases, including ethylene, hexatriene, and the alanine dipeptide. Vibrational self-consistent field (VSCF) spectra were obtained with an RI-MP2/cc-pVTZ potential for the dipeptide, at approximately a 5-fold reduction in computational cost. Considerable optimism for increased accelerations for larger systems and higher-order couplings is also justified, based on this investigation.

Spectroscopic characterization of [H, Cl, S, O] molecular system: Potential candidate for detection in Venus atmosphere

Accurate spectroscopic parameters have been obtained for the identification of the [H, Cl, S, O] molecular system in the Venus atmosphere using computational methods. These calculations employed both standard and explicitly correlated coupled cluster techniques. All isomers possess C1 symmetry, with HOSCl being the most stable isomer. Only HOSCl and trigonal-HSOCl isomers are thermodynamically stable relative to the first dissociation limit HCl + SO. Fundamental modes of the lowest three isomers exhibit many anharmonic resonances, resulting in complex spectra. All isomers are found to be stable in the visible region as the calculation of vertical energy transition indicates. No electronic states were found to strongly absorb in the near UV-vis region.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues

Aminoborane, H₂ NBH₂ and its isotopologues, H₂ N¹⁰ BH₂ , D₂ NBD₂ , and D₂ N¹⁰ BD₂ , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν₇ band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Spectroscopy and photochemistry of ClSSO

Sulfur-chlorine cycles play a role in the atmosphere of Venus. It is thought that many sulfur-chlorine bearing molecules could be present in Venus's atmosphere and play an important role in its chemical processes. The goal of this work is to provide new insight into the electronic structure and spectroscopy of the [Cl, S, S, O] molecular system. Eight isomers could be formed, but only three were found to be thermodynamically stable relative to the first dissociation limit. We spectroscopically characterized the two lowest energy stable isomers, C1-ClSSO and trans-ClSSO, using the accurate CCSD(T)-F12/aug-cc-pVTZ method. The dipole moments of the two lowest energy stable isomers are predicted to be 1.90 and 1.60 debye, respectively. The C1-ClSSO isomer is suitable for laser induced fluorescence detection since the lowest excited electronic states absorb in the visible, ∼610 nm, and near UV region, 330 nm. We mapped the evolution of the low-lying excited electronic states along the ClS, SS, and SO bond lengths to find that the production of ClS, SO, or S₂O is plausible, whereas the production of ClS₂ is not allowed.

High-dimensional neural network potentials for accurate vibrational frequencies: the formic acid dimer benchmark

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

The linear molecular ions H₂He⁺, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H₂He+n, HHe+n, and He+n families, respectively. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Comparison of body definitions for incremental vibrational configuration interaction theory (iVCI)

Within incremental vibrational configuration interaction theory (iVCI), the vibrational state energy is determined by means of a many-body expansion, i.e., it is a sum of terms of increasing order, which allow for an embarrassingly parallel evaluation. The convergence of this expansion depends strongly on the definition of the underlying bodies, which essentially decompose the correlation space into fragments. The different definitions considered here comprise mode-based bodies, excitation level-based bodies, and energy-based bodies. An analysis of the convergence behavior revealed that accounting for resonances within these definitions is mandatory and leads to a substantial improvement of the convergence, that is, the expansions can be truncated at lower orders. Benchmark calculations and systematic comparisons of the different body definitions for a small set of molecules, i.e., ketene, ethene, and diborane, have been conducted to study the overall performance of these iVCI implementations with respect to accuracy and central processing unit time.

Adaptive Fitting of Potential Energy Surfaces of Small to Medium-Sized Molecules in Sum-of-Product Form: Application to Vibrational Spectroscopy

A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.

Non long-range corrected density functionals incorrectly describe the intensity of the CH stretching band in polycyclic aromatic hydrocarbons

We present a comprehensive study of the most relevant numerical aspects influencing frequencies and intensities in the infrared spectrum of isolated polycyclic aromatic hydrocarbons (PAHs) regarding the overestimate of the IR CH-stretching bands. We use naphthalene as benchmark and show the validity of our results to different members of the PAH family. Our analysis relies on widely employed density functional theory methods and second-order vibrational perturbational theory for the computation of vibrational eigenstates. We have focused on the elucidation of the origin of the systematic overestimate of the intensities in the CH-stretching region. To rule out nonfundamental numerical errors, we have initially considered the influence of the electronic basis set and various other parameters on the different stages of the vibrational analysis. In a second stage, we have benchmarked the results of different density functional theory functionals with respect to the aforementioned overestimate taken as the ratio between the most prominent features of the spectrum, the CH-bending and the CH-stretching bands. Our results unambiguously indicate that the long-range correction plays a major role in this spurious numerical issue. More specifically, this phenomenon is due to an incorrect description of the charge distribution (and hence dipole) within the symmetrically relevant CH bonds. Long-range correction specifically remedies this issue. It improves the description of the intensities in the stretching region while at the same time it does not perturb significantly the rest of the spectrum. With respect to the frequencies, we have observed an overall improvement when compared to noncorrected functionals.

Critical benchmarking of popular composite thermochemistry models and density functional approximations on a probabilistically pruned benchmark dataset of formation enthalpies

First-principles calculation of the standard formation enthalpy, ΔH_f° (298 K), in such a large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and certain composite wave function theories (cWFTs). Unfortunately, the accuracies of popular range-separated hybrid, "rung-4" DFAs, and cWFTs that offer the best accuracy-vs-cost trade-off have until now been established only for datasets predominantly comprising small molecules; their transferability to larger systems remains vague. In this study, we present an extended benchmark dataset of ΔH_f° for structurally and electronically diverse molecules. We apply quartile-ranking based on boundary-corrected kernel density estimation to filter outliers and arrive at probabilistically pruned enthalpies of 1694 compounds (PPE1694). For this dataset, we rank the prediction accuracies of G4, G4(MP2), ccCA, CBS-QB3, and 23 popular DFAs using conventional and probabilistic error metrics. We discuss systematic prediction errors and highlight the role an empirical higher-level correction plays in the G4(MP2) model. Furthermore, we comment on uncertainties associated with the reference empirical data for atoms and the systematic errors stemming from these that grow with the molecular size. We believe that these findings will aid in identifying meaningful application domains for quantum thermochemical methods.

Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces

The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz. The novelty of our algorithm lies in the fact that the fit is performed in terms of a direct product of a Schmidt basis, also known as natural potentials. These encode in a non-trivial way all the physics of the problem and, hence, circumvent the usual extra ad hoc and a posteriori adjustments (e.g., damping functions) of the fitted PES. Moreover, we avoid the intermediate refitting stage common to other tensor-decomposition methods, typically used in the context of nuclear quantum dynamics. The resulting SOP-FBR PES is analytical and differentiable ad infinitum. Our ansatz is fully general and can be used in combination with most (molecular) dynamics codes. In particular, it has been interfaced and extensively tested with the Heidelberg implementation of the multiconfiguration time-dependent Hartree quantum dynamical software package.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Machine learning modeling of Wigner intracule functionals for two electrons in one-dimension

In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function (W), thanks to a universal functional transformation (F), whose formal existence is akin to that of the exchange-correlation functional in density functional theory. While the exact dependence of F on W is unknown, a few approximate parametric models have been proposed in the past. Here, for a dataset of 923 one-dimensional external potentials with two interacting electrons, we apply machine learning to model F within the kernel Ansatz. We deal with over-fitting of the kernel to a specific region of phase-space by a one-step regularization not depending on any hyperparameters. Reference correlation energies have been computed by performing exact and Hartree-Fock calculations using discrete variable representation. The resulting models require W calculated at the Hartree-Fock level as input while yielding monotonous decay in the predicted correlation energies of new molecules reaching sub-chemical accuracy with training.

Refined analysis of the X̃ 2A2←X̃ 1A1 photoelectron spectrum of furan

The X̃ ²A₂←X̃ ¹A₁ photoelectron spectrum of furan has been studied by a time-independent eigenstate-free Raman wave function approach based on multi-dimensional potential energy surfaces obtained from explicitly correlated distinguishable clusters calculations. Individual vibronic transitions with the most significant Franck-Condon factors were determined by our recently developed residual-based algorithm for the calculation of eigenpairs in conjunction with the formalism of contracted invariant Krylov subspaces. The account of anharmonic and temperature effects allowed us to explain most bands in an experimental high-resolution zero kinetic energy photoelectron spectrum. This led to the reassignment of many spectral features, as well as a refined interpretation of the intensity mechanism for the corresponding transitions.