Determining internal coordinate sets for optimal representation of molecular vibration.

Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced.

Vibrational Predissociation Spectra of C2 N- and C3 N- : Bending and Stretching Vibrations.

We present infrared predissociation spectra of C2 N- (H2 ) and C 3 N- (H2 ) in the 300-1850 cm-1 range. Measurements were performed using the FELion cryogenic ion trap end user station at the Free Electron Lasers for Infrared eXperiments (FELIX) laboratory. For C2 N- (H2 ), we detected the CCN bending and CC-N stretching vibrations. For the C3 N- (H2 ) system, we detected the CCN bending, the CC-CN stretching, and multiple overtones and/or combination bands. The assignment and interpretation of the presented experimental spectra is validated by calculations of anharmonic spectra within the vibrational configuration interaction (VCI) approach, based on potential energy surfaces calculated at explicitly correlated coupled cluster theory (CCSD(T)-F12/cc-pVTZ-F12). The H2 tag acts as an innocent spectator, not significantly affecting the C2,3 N- bending and stretching mode positions. The recorded infrared predissociation spectra can thus be used as a proxy for the vibrational spectra of the bare anions.

Increase of Radiative Forcing through Midinfrared Absorption by Stable CO2 Dimers?

We performed matrix-isolation infrared (MI-IR) spectroscopy of carbon dioxide monomers, CO2, and dimers, (CO2)2, trapped in neon and in air. On the basis of vibration configuration interaction (VCI) calculations accounting for mode coupling and anharmonicity, we identify additional infrared-active bands in the MI-IR spectra due to the (CO2)2 dimer. These bands are satellite bands next to the established CO2 monomer bands, which appear in the infrared window of Earth's atmosphere at around 4 and 15 µm. In a systematic carbon dioxide mixing ratio study using neon matrixes, we observe a significant fraction of the dimer at mixing ratios above 300 ppm, with a steep increase up to 1000 ppm. In neon matrix, the dimer increases the IR absorbance by about 15% at 400 ppm compared to the monomer absorbance alone. This suggests a high fraction of the (CO2)2 dimer in our matrix experiments. In atmospheric conditions, such increased absorbance would significantly amplify radiative forcings and, thus, the greenhouse warming. To enable a comparison of our laboratory experiment with various atmospheric conditions (Earth, Mars, Venus), we compute the thermodynamics of the dimerization accordingly. The dimerization is favored at low temperatures and/or high carbon dioxide partial pressures. Thus, we argue that matrix isolation does not trap the gas composition "as is". Instead, the gas is precooled to 40 K, where CO2 dimerizes before being trapped in the matrix, already at very low carbon dioxide partial pressures. In the context of planetary atmospheres, our results improve understanding of the greenhouse effect for planets of rather thick CO2 atmospheres such as Venus, where a significant fraction of the (CO2)2 dimer can be expected. There, the necessity of including the mid-IR absorption by stable (CO2)2 dimers in databases used for modeling radiative forcing, such as HITRAN, arises.

Determination of spectroscopic constants from rovibrational configuration interaction calculations.

Rotational constants and centrifugal distortion constants of a molecule are the essence of its rotational or rovibrational spectrum (e.g., from microwave, millimeter wave, and infrared experiments). These parameters condense the spectroscopic characteristics of a molecule and, thus, are a valuable resource in terms of presenting and communicating spectroscopic observations. While spectroscopic parameters are obtained from experimental spectra by fitting an effective rovibrational Hamiltonian to transition frequencies, the ab initio calculation of these parameters is usually done within vibrational perturbation theory. In the present work, we investigate an approach related to the experimental fitting procedure, but relying solely on ab initio data obtained from variational calculations, i.e., we perform a nonlinear least squares fit of Watson's A- and S-reduced rotation-vibration Hamiltonian to rovibrational state energies (resp. transition frequencies) from rotational-vibrational configuration interaction calculations. We include up to sextic centrifugal distortion constants. By relying on an educated guess of spectroscopic parameters from vibrational configuration interaction and vibrational perturbation theory, the fitting procedure is very efficient. We observe excellent agreement with experimentally derived parameters.

Alpha-Carbonic Acid Revisited: Carbonic Acid Monomethyl Ester as a Solid and its Conformational Isomerism in the Gas Phase.

In this work, earlier studies reporting α-H2 CO3 are revised. The cryo-technique pioneered by Hage, Hallbrucker, and Mayer (HHM) is adapted to supposedly prepare carbonic acid from KHCO3 . In methanolic solution, methylation of the salt is found, which upon acidification transforms to the monomethyl ester of carbonic acid (CAME, HO-CO-OCH3 ). Infrared spectroscopy data both of the solid at 210 K and of the evaporated molecules trapped and isolated in argon matrix at 10 K are presented. The interpretation of the observed bands on the basis of carbonic acid [as suggested originally by HHM in their publications from 1993-1997 and taken over by Winkel et al., J. Am. Chem. Soc. 2007 and Bernard et al., Angew. Chem. Int. Ed. 2011] is inferior compared with the interpretation on the basis of CAME. The assignment relies on isotope substitution experiments, including deuteration of the OH- and CH3 - groups as well as 12 C and 13 C isotope exchange and on variation of the solvents in both preparation steps. The interpretation of the single molecule spectroscopy experiments is aided by a comprehensive calculation of high-level ab initio frequencies for gas-phase molecules and clusters in the harmonic approximation. This analysis provides evidence for the existence of not only single CAME molecules but also CAME dimers and water complexes in the argon matrix. Furthermore, different conformational CAME isomers are identified, where conformational isomerism is triggered in experiments through UV irradiation. In contrast to earlier studies, this analysis allows explanation of almost every single band of the complex spectra in the range between 4000 and 600 cm-1 .

Decomposing anharmonicity and mode-coupling from matrix effects in the IR spectra of matrix-isolated carbon dioxide and methane.

Gas-phase IR spectra of carbon dioxide and methane are nowadays well understood, as a consequence of their pivotal roles in atmospheric- and astrochemistry. However, once those molecules are trapped in noble gas matrices, their spectroscopic properties become difficult to conceptualize. Still, such spectra provide valuable insights into the vibrational structure. In this study, we combine new matrix-isolation infrared (MI-IR) spectra at 6 K in argon and neon with in vacuo anharmonic spectra computed by vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI). The aim is to separate anharmonicity from matrix effects in the mid-infrared spectra of 12C16O2, 12CH4, and 12CD4. The accurate description of anharmonic potential energy surfaces including mode-coupling allows to reproduce gas-phase data with deviations of below 3 cm-1. Consequently, the remaining difference between MI-IR and VSCF/VCI can be attributed to matrix effects. Frequency shifts and splitting patterns turn out to be unsystematic and dependent on the particular combination of analyte and noble gas. While in the case of neon matrices these effects are small, they are pronounced in xenon, krypton, and argon matrices. Our strategy allows us to suggest that methane rotates in neon matrices - in contrast to previous reports.

On the synergy of matrix-isolation infrared spectroscopy and vibrational configuration interaction computations.

The key feature of matrix-isolation infrared (MI-IR) spectroscopy is the isolation of single guest molecules in a host system at cryogenic conditions. The matrix mostly hinders rotation of the guest molecule, providing access to pure vibrational features. Vibrational self-consistent field (VSCF) and configuration interaction computations (VCI) on ab initio multimode potential energy surfaces (PES) give rise to anharmonic vibrational spectra. In a single-sourced combination of these experimental and computational approaches, we have established an iterative spectroscopic characterization procedure. The present article reviews the scope of this procedure by highlighting the strengths and limitations based on the examples of water, carbon dioxide, methane, methanol, and fluoroethane. An assessment of setups for the construction of the multimode PES on the example of methanol demonstrates that CCSD(T)-F12 level of theory is preferable to compute (a) accurate vibrational frequencies and (b) equilibrium or vibrationally averaged structural parameters. Our procedure has allowed us to uniquely assign unknown or disputed bands and enabled us to clarify problematic spectral regions that are crowded with combination bands and overtones. Besides spectroscopic assignment, the excellent agreement between theory and experiment paves the way to tackle questions of rather fundamental nature as to whether or not matrix effects are systematic, and it shows the limits of conventional notations used by spectroscopists.

Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational-Vibrational Spectrum of Water in Solid Noble Gas Matrices.

Rotational-vibrational spectroscopy of water in solid noble gas matrices has been studied for many decades. Despite that, discrepancies persist in the literature about the assignment of specific bands. We tackle the involved rotational-vibrational spectrum of the water isotopologues H216O, HD16O, and D216O with an unprecedented combination of experimental high-resolution matrix isolation infrared (MI-IR) spectroscopy and computational anharmonic vibrational spectroscopy by vibrational configuration interaction (VCI) on high-level ab initio potential energy surfaces. With VCI, the average deviation to gas-phase experiments is reduced from >100 to ≈1 cm-1 when compared to harmonic vibrational spectra. Discrepancies between MI-IR and VCI spectra are identified as matrix effects rather than missing anharmonicity in the theoretical approach. Matrix effects are small in Ne (≈1.5 cm-1) and a bit larger in Ar (≈10 cm-1). Controversial assignments in Ne MI-IR spectra are resolved, for example, concerning the ν3 triad in HDO. We identify new transitions, for example, the ν2 101 ← 110 transition in D2O and H2O or the ν3 000 ← 101 transition in D2O, and reassign bands, for example, the band at 3718.9 cm-1 that is newly assigned as the 110 ← 111 transition. The identification and solution of discrepancies for a well-studied benchmark system such as water prove the importance of an iterative and one-hand combination of theory and experiment in the field of high-resolution infrared spectroscopy of single molecules. As the computational costs involved in the VCI approach are reasonably low, such combined experimental/theoretical studies can be extended to molecules larger than triatomics.

Low frequency vibrational anharmonicity and nuclear spin effects of Cl-(H2) and Cl-(D2).

Low frequency combination bands of 35Cl-(H2) and 35Cl-(D2) have been measured in the region between 600 and 1100 cm-1 by infrared predissociation spectroscopy in a cryogenic 22-pole ion trap using a free electron laser at the FELIX Laboratory as a tunable light source. The 35Cl-(H2) (35Cl-(D2)) spectrum contains three bands at 773 cm-1 (620 cm-1), 889 cm-1 (692 cm-1), and 978 cm-1 (750 cm-1) with decreasing intensity toward higher photon energies. Comparison of the experimentally determined transition frequencies with anharmonic vibrational self-consistent field and vibrational configuration interaction calculations suggests the assignment of the combination bands v1 + v2, 2v1 + v2, and 3v1 + v2 for 35Cl-(H2) and 2v1 + v2, 3v1 + v2, and 4v1 + v2 for 35Cl-(D2), where v1 is the 35Cl-⋯H2 stretching fundamental and v2 is the Cl-(H2) bend. The observed asymmetric temperature dependent line shape of the v1 + v2 transition can be modeled by a series of ∑+-∏ ro-vibrational transitions, when substantially decreasing the rotational constant in the vibrationally excited state by 35%. The spectrum of 35Cl-(D2) shows a splitting of 7 cm-1 for the strongest band which can be attributed to the tunneling of the ortho/para states of D2.

Borylated Cymantrenes and Tromancenium Salts with Unusual Reactivity.

In continuation of our study of the chemistry of cationic (cycloheptatrienyl)(cyclopentadienyl)manganese(I) sandwich complexes, so-called "tromancenium" salts, we report here on their boron-substituted derivatives focusing on useful boron-mediated synthetic applications. Transmetalation of lithiated tricarbonyl(cyclopentadienyl)manganese ("cymantrene") with boric or diboronic esters affords monoborylated cymantrenes that are converted by advanced high-power LED photosynthesis followed by oxidation with tritylium to their 8-boron-substituted tromancenium complexes. These new functionalized tromancenium salts are fully characterized by 1H/11B/13C/19F/55Mn NMR, IR, UV-vis, HRMS spectroscopy, single-crystal structure analysis (XRD) and cyclic voltammetry (CV). IR spectra were thoroughly analyzed by density functional theory (DFT) on the harmonic approximation in qualitative agreement of calculated vibrations with experimental values. Uncommon chemical reactivity of these borylated tromancenium salts is observed, due to the strongly electron-withdrawing cationic tromancenium moiety. No Suzuki-type cross-coupling reactions proved so far achievable, but unusual copper-promoted amination with sodium azide under microwave irradiation is possible. Diazoniation of aminotromancenium affords an extremely reactive dicationic tromanceniumdiazonium salt, which is too labile for standard Sandmeyer reactions, in contrast to analogous chemistry of cobaltocenium salts. Overall, borylated tromancenium salts display unexpected and intriguing chemical properties with the potential for novel synthetic applications in future work.