Accurate ab initio quartic force fields for NH[sub 2]−] and CCH[sup −] and rovibrational spectroscopic constants for their isotopologs

Vibrational and Rovibrational Spectroscopic Data for the Ground and First-Excited States of Phosgene (COCl2), Formic Acid (HCOOH), and Chloroformic Acid (ClCOOH)

While "black box" quantum chemical computations for the determination of rovibronic spectral data are not quite at hand, the present work utilizes the titular molecules to showcase how excited-state quantum chemical methods can be conjoined to quartic force field (QFF) anharmonic rovibrational treatments to provide novel and useful predictions for such data. This work employs hybrid QFFs with explicitly correlated coupled cluster theory along with the equation-of-motion formalism to generate harmonic force constants and time-dependent density functional theory (TD-DFT) to produce anharmonic force constants for the generation of electronically excited-state rovibrational spectral data, in effect, rovibronic spectral data. Specific spectroscopic results from this work show that the fundamental C═O stretch in phosgene as well as in cis- and trans-formic acid drop from the region of around 1800 cm-1 to close to 1100 cm-1 or less in the first excited states of each molecule. While such is expected for these n → π* excitations, this work provides quantitative predictions for these fundamental vibrational frequencies. The most notable theoretical result is that the TD-DFT-based QFFs can experience unexpected failures, and their inclusion in excited-state hybrid QFFs should require at least two functionals to be employed. The computation of DFT QFFs is relatively fast, and such a "doubling up" of the QFFs will not greatly increase the computational time.

The fundamental vibrational frequencies and spectroscopic constants of the C2O2H2 isomers: molecules known in simulated interstellar ice analogues

While trans-glyoxal may not be easily observable in astronomical sources through either IR or radioastronomy due to its C2h symmetry, its cis conformer along with the cyc-H2COCO epoxide isomer should be ready targets for astrochemical detection. The present quantum chemical study shows that not only are both molecular isomers strongly polar, they also have notable IR features and low isomerisation energies of 4.1 kcal mol-1 and 10.7 kcal mol-1, respectively. These three isomers along with two other C2O2H2 isomers have had their full set of fundamental vibrational frequencies and spectroscopic constants characterised herein. These isomers have previously been shown to occur in simulated astrophysical ices making them worthy targets of astronomical search. Furthermore, the hybrid quartic force field (QFF) approach utilized herein to produce the needed spectral data has a mean absolute percent error compared to the experimentally-available, gas phase fundamental vibrational frequencies of 0.6% and rotational constants to better than 0.1%. The hybrid QFF is defined from explicitly correlated coupled cluster theory at the singles, doubles, and perturbative triples level [CCSD(T)-F12b] including core electron correlation and a canonical CCSD(T) relativity correction for the harmonic (quadratic) terms in the QFF and simple CCSD(T)-F12b/cc-pVDZ energies for the cubic and quartic terms, the so-called "F12-TcCR+DZ QFF." This method is producing spectroscopically-accurate predictions for both fundamental vibrational frequencies and principal spectroscopic constants. Hence, the values computed in this work should be notably accurate and, hence, exceptionally useful to the spectroscopy and astrochemistry communities.

Picking up Good Vibrations through Quartic Force Fields and Vibrational Perturbation Theory

Quartic force fields (QFFs) define sparse potential energy surfaces (compared to semiglobal surfaces) that are the cheapest and easiest means of computing anharmonic vibrational frequencies, especially when utilized with second-order vibrational perturbation theory (VPT2). However, flat and shallow potential surfaces are exceedingly difficult for QFFs to treat through a combination of numerical noise in the often numerically computed derivatives and in competing energy factors in the composite energies often utilized to provide high-level spectroscopic predictions. While some of these issues can be alleviated with analytic derivatives, hybrid QFFs, and intelligent choices in coordinate systems, the best practice is for predicting good molecular vibrations via QFFs is to understand what they cannot do, and this manuscript documents such cases where QFFs may fail.

Rovibrational analysis of AlCO3, OAlO2, and HOAlO2 for possible atmospheric detection

The lack of observational data for the AlO molecule in the mesosphere/lower thermosphere may be due to ablated aluminum reacting quickly to form other species. Previously proposed reaction pathways show that aluminum could be ablated in the atmosphere from meteoritic activity, but there currently exist very limited spectroscopic data on the intermediates in these reactions, limiting the possible detection of said molecules. As such, rovibrational spectroscopic data are computed herein using quartic force field methodology at four different levels of theory for the neutral intermediates AlCO3, OAlO2, and HOAlO2. Each molecule exhibits multiple vibrational modes with large vibrational transition intensities. For instance, the C-O stretch (ν1) in AlCO3 has a harmonic intensity of 536 km mol-1, the Al-O stretch (ν2) in OAlO2 has an intensity of 678 km mol-1, and the out-of-plane torsion (ν9) in HOAlO2 has an intensity of 158 km mol-1. All three molecules have exceptionally large dipole moments of 6.27, 4.21, and 5.04 D, respectively. These properties indicate that all three molecules are good candidates for potential atmospheric observation utilizing vibrational and/or rotational spectroscopic techniques.

Performance of EOM-CCSD(T)(a)*-Based Quartic Force Fields in Computing Fundamental, Anharmonic Vibrational Frequencies of Molecular Electronically Excited States with Application to the Ã1A″ State of :CCH2 (Vinylidene)

Highly accurate anharmonic vibrational frequencies of electronically excited states are not as easily computed as their ground electronic state counterparts, but recently developed approximate triple excited state methods may be changing that. One emerging excited state method is equation of motion coupled cluster theory at the singles and doubles level with perturbative triples computed via the (a)* formalism, EOMEE-CCSD(T)(a)*. One of the most employed means for the ready computation of vibrational anharmonic frequencies for ground electronic states is second-order vibrational perturbation theory (VPT2), a theory based on quartic force fields (QFFs),fourth-order Taylor series expansions of the potential portion of the internuclear Watson Hamiltonian. The combination of these two is herein benchmarked for its performance for use as a means of computing rovibrational spectra of electronically excited states. Specifically, the EOMEE-CCSD(T)(a)* approach employing a complete basis set extrapolation along with core electron inclusion and relativity (the so-called "CcCR" approach) defining the QFF produces anharmonic fundamental vibrational frequencies within 2.83%, on the average, of reported gas-phase experimentally assigned values for the test set including the A ~ 1 A ″ states of HCF, HCCl, HSiF, HNO, and HPO. However, some states have exceptional accuracy in the fundamentals, most notably for ν2 of A ~ 1 A ″ HCCl in which the CcCR QFF value is within 1.8 cm-1 at 927.9 cm-1 (or 0.2%) of the experiment. Additionally, this approach produces rotational constants to, on the absolute average, within 0.41% of available experimental data, showcasing notable accuracy in the computation of rovibronic spectral data. Furthermore, utilizing a hybrid approach composed of harmonic CcCR force constants along with a set of simple EOMEE-CCSD(T)(a)*/aug-cc-pVQZ QFF cubic and quartic force constants is faster than using pure CcCR and better represents those modes that suffer from numerical instability in the anharmonic portion of the QFF, implying that this so-called "CcCR + QZ" QFF approach may be the best for future applications. Finally, complete, rovibrational spectral data are provided for A ~ 1 A 2 :CCH2, a molecule of potential astrochemical interest, in order to aid in its potential future experimental rovibronic characterization.

Quantum Chemistry and Astrochemistry: A Match Made in the Heavens

Quantum chemistry can uniquely answer astrochemical questions that no other technique can provide. Computations can be parallelized, automated, and left to run continuously providing exceptional molecular throughput that cannot be done through experimentation. Additionally, the granularity of the individual computations that are required of potential energy surfaces, reaction mechanism pathways, or other quantum chemically derived observables produces a unique mosaic that make up the larger whole. These pieces can be dissected for their individual contributions or evaluated in an ad hoc fashion for each of their roles in generating the larger whole. No other scientific approach is capable of reporting such fine-grained insights. Quantum chemistry also works from a bottom-up approach in providing properties directly from the desired molecule instead of a top-down perspective as required of experiment where molecules have to be linked to observed phenomena. Furthermore, modern quantum chemistry is well within the range of "chemical accuracy" and is approaching "spectroscopic accuracy." As such, the seemingly difficult questions asked by astrochemistry that would not be asked initially for any other application require quantum chemical reference data. While the results of quantum chemical computations are needed to interpret astrochemical observation, modeling, or laboratory experimentation, such hard questions, regardless of the original need to answer them, produce unique solutions. While questions in astrochemistry often require novel developments in and implementations of quantum chemistry as outlined herein, the applications of these solutions will stretch beyond astrochemistry and may yet impact fields much closer to Earth.

Ab Initio Potential Energy Surface and Vibration-Rotation Energy Levels of Aluminum Monohydroxide

The potential energy surface and vibration-rotation energy levels of aluminum monohydroxide in the X̃ 1A' electronic state have been determined from ab initio calculations. The equilibrium configuration of the AlOH molecule was found to be bent, although with a wide AlOH angle of 163° and a small barrier to linearity of just 4 cm-1. The AlOH molecule was definitely confirmed to be quasilinear. The predicted spectroscopic constants of the AlOH, AlOD, 26AlOH, and Al18OH isotopologues can be useful in a future analysis of high-resolution vibration-rotation spectra of these species.

Hunting for interstellar molecules: rotational spectra of reactive species

Interstellar molecules are often highly reactive species, which are unstable under terrestrial conditions, such as radicals, ions and unsaturated carbon chains. Their detection in space is usually based on the astronomical observation of their rotational fingerprints. However, laboratory investigations have to face the issue of efficiently producing these molecules and preserving them during rotational spectroscopy measurements. A general approach for producing and investigating unstable/reactive species is presented by means of selected case-study molecules. The overall strategy starts from quantum-chemical calculations that aim at obtaining accurate predictions of the missing spectroscopic information required to guide spectral analysis and assignment. Rotational spectra of these species are then recorded by exploiting the approach mentioned above, and their subsequent analysis leads to accurate spectroscopic parameters. These are then used for setting up accurate line catalogs for astronomical searches.

Spectroscopy and Photochemistry of OAlNO and Implications for New Metal Chemistry in the Atmosphere

A new aluminum-bearing species, OAlNO, which has the potential to impact the chemistry of the Earth's upper atmosphere, is characterized via high-level, ab initio, spectroscopic methods. Meteor-ablated aluminum atoms are quickly oxidized to aluminum oxide (AlO) in the mesosphere and lower thermosphere (MLT), where a steady-state layer of AlO then builds up. Concurrent formation of nitric oxide (NO) in the same region of the atmosphere will lead to the bimolecular formation of the OAlNO molecule. Molecular orbital analysis provides fundamental insights into the chemical bonding and energetic arrangement of the triplet (1 3A″) ground state and singlet (1 1A') excited-state species of OAlNO. Additionally, unpaired electrons on the terminal oxygen atom of triplet (1 3A″) OAlNO cause it to be reactive to atmospheric species, potentially impacting climate science and high-altitude chemistry. The triplet (1 3A″) ground-state species exhibits a large permanent dipole moment useful for rotational spectroscopic detection; however, similar rotational constants to the singlet (1 1A') excited-state species will hamper differentiation in a spectrum. Strong infrared intensities will assist in detection and discrimination of the different spin states and isomers. Repulsive electronic excited states of OAlNO will lead to photolysis of the Al-N bond and formation of various electronic states of AlO + NO through nonadiabatic pathways. Reaction through the OAlNO intermediate represents a means for the production of electronically excited AlO, leading to new chemistry in the atmosphere. Excitation to higher-lying electronic states will lead to fluorescence with a minor Stokes shift, useful for laboratory investigation. Such physical properties of this molecule will allow for new, unexplored chemical pathways in the MLT to be considered.

Ab Initio Rovibrational Spectroscopy of the Acetylide Anion

In this work the rovibrational spectrum of the acetylide anion HCC- is investigated using high-level electronic structure methods and variational rovibrational calculations. Using a composite approach the potential energy surface and dipole surface is constructed from explicitly correlated coupled-cluster accounting for corrections due to core-valence correlation, scalar relativistic effects and higher-order excitation effects. Previous approaches for approximating the latter are critically evaluated. Employing the composite potential, accurate spectroscopic parameters determined from variational calculations are presented. In comparison to the few available reference data the present results show excellent agreement with ground state rotational constants within 0.005% of the experimental value. Intensities determined from the variational calculations suggest the bending fundamental transition ν2 around 510 cm-1 to be the best target for detection. The rather weak CD stretching fundamental ν1 in deuterated isotopologues show a second-order resonance with the (0,20,1) state and the consequences are discussed in some detail. The spectroscopic parameters and band intensities provided for a number of vibrational bands in isotopologues of the acetylide anion should facilitate future spectroscopic investigations.

Structural and electronic trends of optical cycling centers in polyatomic molecules revealed by microwave spectroscopy of MgCCH, CaCCH, and SrCCH

The unique optical cycling efficiency of alkaline earth metal-ligand molecules has enabled significant advances in polyatomic laser cooling and trapping. Rotational spectroscopy is an ideal tool for probing the molecular properties that underpin optical cycling, thereby elucidating the design principles for expanding the chemical diversity and scope of these platforms for quantum science. We present a comprehensive study of the structure and electronic properties in alkaline earth metal acetylides with high-resolution microwave spectra of 17 isotopologues of MgCCH, CaCCH, and SrCCH in their 2Σ+ ground electronic states. The precise semiexperimental equilibrium geometry of each species has been derived by correcting the measured rotational constants for electronic and zero-point vibrational contributions calculated with high-level quantum chemistry methods. The well-resolved hyperfine structure associated with the 1,2H, 13C, and metal nuclear spins provides further information on the distribution and hybridization of the metal-centered, optically active unpaired electron. Together, these measurements allow us to correlate trends in chemical bonding and structure with the electronic properties that promote efficient optical cycling essential to next-generation experiments in precision measurement and quantum control of complex polyatomic molecules.

Complete, Theoretical Rovibronic Spectral Characterization of the Carbon Monoxide, Water, and Formaldehyde Cations

New high-level ab initio quartic force field (QFF) methods are explored which provide spectroscopic data for the electronically excited states of the carbon monoxide, water, and formaldehyde cations, sentinel species for expanded, recent cometary spectral analysis. QFFs based on equation-of-motion ionization potential (EOM-IP) with a complete basis set extrapolation and core correlation corrections provide assignment for the fundamental vibrational frequencies of the A˜2B1 and B˜2A1 states of the formaldehyde cation; only three of these frequencies have experimental assignment available. Rotational constants corresponding to these vibrational excitations are also provided for the first time for all electronically excited states of both of these molecules. EOM-IP-CCSDT/CcC computations support tentative re-assignment of the ν1 and ν3 frequencies of the B˜2B2 state of the water cation to approximately 2409.3 cm-1 and 1785.7 cm-1, respectively, due to significant disagreement between experimental assignment and all levels of theory computed herein, as well as work by previous authors. The EOM-IP-CCSDT/CcC QFF achieves agreement to within 12 cm-1 for the fundamental vibrational frequencies of the electronic ground state of the water cation compared to experimental values and to the high-level theoretical benchmarks for variationally-accessible states. Less costly EOM-IP based approaches are also explored using approximate triples coupled cluster methods, as well as electronically excited state QFFs based on EOM-CC3 and the previous (T)+EOM approach. The novel data, including vibrationally corrected rotational constants for all states studied herein, provided by these computations should be useful in clarifying comet evolution or other remote sensing applications in addition to fundamental spectroscopy.

Connections between the accuracy of rotational constants and equilibrium molecular structures

Rotational spectroscopy is the technique of choice for investigating molecular structures in the gas phase. Indeed, rotational constants are strongly connected to the geometry of the molecular system under consideration. Therefore, they are powerful tools for assessing the accuracy that quantum chemical approaches can reach in structural determinations. In this review article, it is shown how it is possible to measure the accuracy of a computed equilibrium geometry based on the comparison of rotational constants. But, it is also addressed what accuracy is required by computations for providing molecular structures and thus rotational constants that are useful to experiment. Quantum chemical methodologies for obtaining the "0.1% accuracy" for rotational constants are reviewed for systems ranging in size from small molecules to small polycyclic aromatic hydrocarbons. This accuracy for systems containing two dozen or so atoms opens the way towards future applications such as the accurate characterization of non-covalent interactions, which play a key role in several biological and technological processes.

Energy Landscape and Structural and Spectroscopic Characterization of Diazirine and Its Cyclic Isomers

Identifying new nitrogenated hydrocarbon molecules in the interstellar medium (ISM) is challenging because of the lack of comprehensive spectroscopic data from experiments. In this computational work, we focus on investigating the structures, relative energies, spectroscopic constants, and energy landscape of the cyclic isomers of diazirine (c-CH2N2) using ab initio quantum chemical methods. Density functional theory (DFT) methods and coupled cluster theory with singles and doubles including perturbative triples [CCSD(T)] and CCSD(T) with the explicitly correlated F12b correction [CCSD(T)-F12b] were employed for this purpose along with large correlation consistent cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. Harmonic vibrational frequencies, infrared vibrational intensities, rotational constants, and dipole moments are reported. Anharmonic vibrational fundamentals along with centrifugal distortion constants, and vibration-rotation interaction constants are also reported for all the cyclic isomers. The energies computed with the CCSD(T) and CCSD(T)-F12b methods were extrapolated to the one-particle complete basis set (CBS) limit following a three-point formula. At the CCSD(T)-F12b/CBS level of theory, the 3,3H-diazirine (c-CH2N2) is the lowest energy cyclic isomer followed by 1,3H-diazirine, (E)-1,2H-diazirine, and (Z)-1,2H-diazirine, which are 20.1, 47.8, and 51.3 kcal mol-1 above the 3,3H-diazirine, respectively. Accurate structures and spectroscopic constants that are reported here could be useful for future identification of these cyclic nitrogenated organic molecules in the interstellar medium or circumstellar disks.

Theoretical Rovibrational Spectroscopy of Magnesium Tricarbide-Multireference Character Thwarts a Full Analysis of All Isomers

Magnesium tricarbide isomers are studied herein with coupled cluster theory and multireference configuration interaction to support their possible detection in astrochemical environments such as the circumstellar envelope surrounding the star IRC +10216 or in terrestrial laboratories. Magnesium-bearing species may abound in the interstellar medium (ISM), but only eight (MgNC, MgCN, HMgNC, MgC₂H, MgC₃N, MgC₄H, MgC₅N, and MgC₆H) have been directly identified thus far. Several possible isomers for the related MgC₃ system are explored in their singlet and triplet spin multiplicities. Overall, this work offers quantum chemical insight of rovibrational spectroscopic data for MgC₃ using quartic force fields (QFFs) based on the CCSD(T) and CCSD(T)-F12 levels of theory at the complete basis set (CBS) limit. Additional corrections with small basis set CCSDT(Q) and scalar relativistic effects are also included in the analysis. Salient multireference character is found in the singlet diamond electronic state, which makes a definitive assignment of the ground state challenging. Nevertheless, coupled cluster-based composite energies and multireference configuration interaction both predict that the ¹A₁ diamond isomer is 1.6-2.2 kcal mol^-1 lower in energy than the ³A₁ diamond isomer. Furthermore, highly accurate binding energies of various isomers MgC₃ are provided for comparison to photodetachment experiments. Dipole moments along with harmonic infrared intensities will guide efforts for astronomical and spectroscopic characterization.

Spectral Signatures of Hydrogen Thioperoxide (HOSH) and Hydrogen Persulfide (HSSH): Possible Molecular Sulfur Sinks in the Dense ISM

For decades, sulfur has remained underdetected in molecular form within the dense interstellar medium (ISM), and somewhere a molecular sulfur sink exists where it may be hiding. With the discovery of hydrogen peroxide (HOOH) in the ISM in 2011, a natural starting point may be found in sulfur-bearing analogs that are chemically similar to HOOH: hydrogen thioperoxide (HOSH) and hydrogen persulfide (HSSH). The present theoretical study couples the accuracy in the anharmonic fundamental vibrational frequencies from the explicitly correlated coupled cluster theory with the accurate rotational constants provided by canonical high-level coupled cluster theory to produce rovibrational spectra for use in the potential observation of HOSH and HSSH. The ν6 mode for HSSH at 886.1 cm-1 is within 0.2 cm-1 of the gas-phase experiment, and the B0 rotational constant for HSSH of 6979.5 MHz is within 9.0 MHz of the experimental benchmarks, implying that the unknown spectral features (such as the first overtones and combination bands) provided herein are similarly accurate. Notably, a previous experimentally-attributed 2ν1 mode, at 7041.8 cm-1, has been reassigned to the ν1+ν5 combination band based on the present work's ν1+ν5 value at 7034.3 cm-1. The most intense vibrational transitions for each molecule are the torsions, with HOSH having a more intense transition of 72 km/mol compared to HSSH's intensity of 14 km/mol. Furthermore, HOSH has a larger net dipole moment of 1.60 D compared to HSSH's 1.15 D. While HOSH may be the more likely candidate of the two for possible astronomical observation via vibrational spectroscopy due to the notable difference in their intensities, both HSSH and HOSH have large enough net dipole moments to be detectable by rotational spectroscopy to discover the role these molecules may have as possible molecular sulfur sinks in the dense ISM.

F12-TZ-cCR: A Methodology for Faster and Still Highly Accurate Quartic Force Fields

The F12-TZ-cCR quartic force field (QFF) methodology, defined here as CCSD(T)-F12b/cc-pCVTZ-F12 with further corrections for relativity, is introduced as a cheaper and even more accurate alternative to more costly composite QFF methods like those containing complete basis set extrapolations within canonical coupled cluster theory. F12-TZ-cCR QFFs produce B₀ and C₀ vibrationally averaged principal rotational constants within 7.5 MHz of gas-phase experimental values for tetraatomic and larger molecules, offering higher accuracy in these constants than the previous composite methods. In addition, F12-TZ-cCR offers an order of magnitude decrease in the computational cost of highly accurate QFF methodologies accompanying this increase in accuracy. An additional order of magnitude in cost reduction is achieved in the F12-DZ-cCR method, while also matching the accuracy of the traditional composite method's B₀ and C₀ constants. Finally, F12-DZ and F12-TZ are benchmarked on the same test set, revealing that both methods can provide anharmonic vibrational frequencies that are comparable in accuracy to all three of the more expensive methodologies, although their rotational constants lag behind. Hence, the present work demonstrates that highly accurate theoretical rovibrational spectral data can be obtained for a fraction of the cost of conventional QFF methodologies, extending the applicability of QFFs to larger molecules.

High-level ab initio quartic force fields and spectroscopic characterization of C2N. Phys Chem Chem Phys 2021;23:26227-26240. [PMID: 34787132 DOI: 10.1039/d1cp03505c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

While it is now well established that large carbon chain species and radiative electron attachment (REA) are key ingredients triggering interstellar anion chemistry, the role played by smaller molecular anions, for which REA appears to be an unlikely formation pathway, is as yet elusive. Advancing this research undoubtedly requires the knowledge (and modeling) of their astronomical abundances which, for the case of C₂N^-, is largely hindered by a lack of accurate spectroscopic signatures. In this work, we provide such data for both ground -CCN^-(³Σ^-) and low-lying c-CNC^-(¹A₁) isomers and their singly-substituted isotopologues by means of state-of-the-art rovibrational quantum chemical techniques. Their quartic force fields are herein calibrated using a high-level composite energy scheme that accounts for extrapolations to both one-particle and (approximate) -particle basis set limits, in addition to relativistic effects, with the final forms being subsequently subject to nuclear motion calculations. Besides standard spectroscopic attributes, the full set of computed properties includes fine and hyperfine interaction constants and can be readily introduced as guesses in conventional experimental data reduction analyses through effective Hamiltonians. On the basis of benchmark calculations performed anew for a minimal test set of prototypical triatomics and limited (low-resolution) experimental data for -CCN^-(³Σ^-), the target accuracies are determined to be better than 0.1% of experiment for rotational constants and 0.3% for vibrational fundamentals. Apart from laboratory investigations, the results here presented are expected to also prompt future astronomical surveys on C₂N^-. To this end and using the theoretically-predicted spectroscopic constants, the rotational spectra of both -CCN^-(³Σ^-) and c-CNC^-(¹A₁) are derived and their likely detectability in the interstellar medium is further explored in connection with working frequency ranges of powerful astronomical facilities. Our best theoretical estimate places c-CNC^-(¹A₁) at about 15.3 kcal mol^-1 above the ground-state -CCN^-(³Σ^-) species.

Anharmonic fundamental vibrational frequencies and spectroscopic constants of the potential HSO2 radical astromolecule

The recent report that HSO₂ is likely kinetically favored over the HOSO thermodynamic product in hydrogen addition to sulfur dioxide in simulated Venusian atmospheric conditions has led to the need for reference rotational, vibrational, and rovibrational spectral data for this molecule. While matrix-isolation spectroscopy has been able to produce vibrational frequencies for some of the vibrational modes, the full infrared to microwave spectrum of 1 ²A' HSO₂ is yet to be generated. High-level quantum chemical computations show in this work that the >2.5 D dipole moment of this radical makes it a notable target for possible radioastronomical observation. Additionally, the high intensity antisymmetric S-O stretch is computed here to be 1298.3 cm^-1, a 13.9 cm^-1 blueshift up from H₂ matrix analysis. In any case, the full set of rotational and spectroscopic constants and anharmonic fundamental vibrational frequencies is provided in this work in order to help characterize HSO₂ and probe its kinetic favorability.

What It Takes to Compute Highly Accurate Rovibrational Line Lists for Use in Astrochemistry

ConspectusWe review the Best Theory + Reliable High-Resolution Experiment (BTRHE) strategy for obtaining highly accurate molecular rovibrational line lists with InfraRed (IR) intensities. The need for highly accurate molecular rovibrational line lists is twofold: (a) assignment of the many rovibrational lines for common stable molecules especially those that exhibit a large amplitude motion, such as NH₃, or have a high density of states such as SO₂; and (b) characterization of the atmospheres of exoplanets, which will be one of the main areas of research in astronomy in the coming decades. The first motivation arises due to the need to eliminate lines due to common molecules in an astronomical observation in order to identify lines from new molecules, while the second motivation arises due to the need to obtain accurate molecular opacities in order to characterize the atmosphere of an exoplanet. The BTRHE strategy first consists of using high-quality ab initio quantum-chemical methods to obtain a global potential energy surface (PES) and dipole moment surface (DMS) that contains the proper physics. The global PES is then refined using a subset of the reliable high-resolution experimental data. The refined PES then gives energy-level predictions to an accuracy similar to the reproduction accuracy of the experimental data used in the refinement step in the interpolation region (i.e., within the range of the experimental data used in the refinement step). The accuracy of the energy levels will slowly degrade as they are extrapolated to spectral regions beyond the high-resolution experimental data used in the refinement step. However, because the degradation is slow, the predicted energy levels can be used to assign new high-resolution experiments, and the data from these can then be used in a subsequent refinement step. In this way, the global PES eventually can yield highly accurate energy levels for all desired spectral regions including to very high energies and high J values. We show that IR intensities computed with the BTRHE rovibrational wave functions and the DMS can be very accurate provided one has minimized the fitting error of the DMS and tested the completeness of the DMS. Some examples of our work on NH₃, CO₂, and SO₂ are given to highlight the usefulness of the BTRHE strategy and to provide ideas on how to further improve its predictive power in the future. In particular, it is shown how successive refinement steps, once new high-resolution data are available, can lead to PESs that yield highly accurate transition energies to larger spectral regions. The importance of including nonadiabatic corrections to reduce the J-dependence of errors for H-containing molecules is shown with work on NH₃. Another very important aspect of the BTRHE approach is the consistency across isotopologues, which allows for highly accurate line lists for any isotopologue once one is obtained for the main isotopologue (which has more high-resolution data available for refinement).

The unsolved issue with out-of-plane bending frequencies for CC multiply bonded systems

More than 30 years ago two groups independently identified a problem in the calculation of the out-of-plane bending (OPB) vibrational frequencies for the ethylene molecule using correlated electronic structure methods. Several studies have been done in the meantime to try and understand and resolve this issue. In so doing this problem has been found to be far more insidious than previously realized for acetylene-like and benzene-like molecules, which can become non-linear and non-planar, respectively. The one common feature that all molecules with this problem have is that they contain CC multiple bonds, and so this has been called the "CC multiple bond OPB frequency issue" or "the CC OPB problem." Various explanations for this problem have been advanced such as basis set superposition error, basis set incompleteness error, linear dependences in the basis set, proper balancing of the basis set between saturation and inclusion of higher angular momentum functions, etc. and possible solutions have arisen from these suggestions. All of these proposed solutions, however, amount to one main point connecting them all: modifying the one-particle basis set in some way. None of the explanations that have been advanced, however, really fit all of the data for all of the molecules where this problem has been identified, and importantly, none of these diagnostic tests have been applied to similar molecules where this issue does not appear. In this review, the studies over the last 30 plus years are discussed and relevant data from each of these is compared and contrasted. It is hoped that by collecting and analyzing the data from these studies a path forward to understanding and resolving this issue will become evident.

Highly-accurate quartic force fields for the prediction of anharmonic rotational constants and fundamental vibrational frequencies

The CcCR quartic force field (QFF) methodology is capable of computing B₀ and C₀ rotational constants to within 35 MHz (0.14%) of experiment for triatomic and larger molecules with at least two heavy atoms. Additionally, the same constants for molecules with four or more atoms agree to within 20 MHz (0.12%) of experiment for the current test set. This work also supports previous claims that the same QFF methodology can produce fundamental vibrational frequencies with a deviation less than 5.7 cm^-1 from experiment. Consequently, this approach of augmenting complete basis set extrapolated energies with treatments of core electron correlation and scalar relativity produces some of the most accurate rovibrational spectroscopic data available.

Rovibrational Quantum Chemical Treatment of Inorganic and Organometallic Astrochemicals

ConspectusOur two groups have both independently and collaboratively been pushing quantum-chemical techniques to produce highly accurate predictions of anharmonic vibrational frequencies and spectroscopic constants for molecules containing atoms outside of the typical upper p block. Methodologies employ composite approaches, relying on various levels of coupled cluster theory-most often at the singles, doubles, and perturbative triples level-and quartic force field constructions of the potential portion of the intramolecular Watson Hamiltonian. Such methods are known to perform well for organic species, and we have extended this to molecules containing atoms outside of this realm.One notable atom that has received much attention in this application is magnesium. Mg is the second-most-abundant element in the Earth's mantle, and while molecules containing this element are among the confirmed astrochemicals, its further atomic abundance in the galaxy implies that many more molecules (both purely inorganic and organometallic) containing element 12 exist in astrophysical regions in chemical sizes between those of atoms and dust-sized nanocrystals. Our approach discussed herein is producing quality benchmarks and predicting novel data for magnesium-bearing molecules.The story is similar for Al and Si, which are also notably abundant in both rocky bodies and the universe at large. While Na, Sc, and Cu may not be as abundant as Mg, Al, and Si, molecules containing Na and transition metals have also previously been reported to be detected beyond the Earth. Consequently, the need to produce spectral reference data for molecules containing such atoms is growing. While several experimental groups (including, notably, the groups in Arizona, Boston, and France/Spain) have clearly led the way in detection of inorganic/organometallic molecules in space, computational support and even rational design can provide novel avenues for the detection of molecules containing atoms not typically studied in most laboratories. The application of quantum chemistry to other elements beyond carbon and its cronies at the top right of the periodic table promises a better understanding of the observable universe. It will also provide novel and fundamental chemical insights pushing the "central science" into new molecular territory.

Anharmonic Frequencies and Spectroscopic Constants of OAlOH and AlOH: Strong Bonding but Unhindered Motion

The astrophysical buildup of premineral nanocrystals from atoms to the smallest network-covalent solids will require observations of various small molecules containing the most common elements in minerals including aluminum and oxygen. The present work utilizes high-level quantum chemical quartic force field (QFF) approaches to produce anharmonic vibrational frequencies and spectroscopic constants for such species. The computed B_eff for the astrochemically known AlOH molecule at 15780.5 MHz is a mere 40 MHz above the experimental value implying that the B_eff for OAlOH at 5580.9 MHz is similarly accurate. The additional 7.31 D dipole moment in OAlOH implies that this molecule is a viable target for interstellar observation. Unlike the other anharmonic vibrational frequencies reported in this work, the Al-O-H bending frequencies in both AlOH and OAlOH are poorly described in the present QFF results. However, this failing actually highlights the fact that these bends are exceptionally floppy yet with counterintuitive exceedingly strong bonding. The Al-O bond energies are 128.2 and 107.2 kcal/mol, respective of AlOH and OAlOH, while the barriers to linearity are meager 16.6 and 380.7 cm^-1 (0.1 and 1.1 kcal/mol).

The structure of ScC2 (X̃2A1): A combined Fourier transform microwave/millimeter-wave spectroscopic and computational study

Pure rotational spectra of Sc¹³C₂ (X̃²A₁) and Sc¹²C¹³C (X̃²A') have been measured using Fourier transform microwave/millimeter-wave methods. These molecules were synthesized in a DC discharge from the reaction of scandium vapor, produced via laser ablation, with ¹³CH₄ or ¹³CH₄/¹²CH₄, diluted in argon. The N_Ka,Kc = 1_0,1 → 0_0,0, 2_0,2 → 1_0,1, 3_0,3 → 2_0,2, and 4_0,4 → 3_0,3 transitions in the frequency range of 14 GHz-61 GHz were observed for both species, each exhibiting hyperfine splittings due to the nuclear spins of ¹³C (I = 1/2) and/or Sc (I = 7/2). These data have been analyzed with an asymmetric top Hamiltonian, and rotational, spin-rotation, and hyperfine parameters have been determined for Sc¹³C₂ and Sc¹²C¹³C. In addition, a quartic force field was calculated for ScC₂ and its isotopologues using a highly accurate coupled cluster-based composite method, incorporating complete basis set extrapolation, scalar relativistic corrections, outer core and inner core electron correlation, and higher-order valence correlation effects. The agreement between experimental and computed rotational constants, including the effective constant (B + C), is ∼0.5% for all three isotopologues. This remarkable agreement suggests promise in predicting rotational spectra of new transition metal-carbon bearing molecules. In combination with previous work on Sc¹²C₂, an accurate structure for ScC₂ has been established using combined experimental (B, C) and theoretical (A) rotational constants. The radical is cyclic (or T-shaped) with r_(Sc-C) = 2.048(2) Å, r_(C-C) = 1.272(2) Å, and ∠_(C-Sc-C) = 36.2(1)°. The experimental and theoretical results also suggest that ScC₂ contains a C₂ ^- moiety and is largely ionic.

Rotational state-changing collisions of C2H- and C2N- anions with He under interstellar and cold ion trap conditions: A computational comparison

We present an extensive range of quantum calculations for the state-changing rotational dynamics involving two simple molecular anions that are expected to play some role in the evolutionary analysis of chemical networks in the interstellar environments, C₂H^- (X¹Σ⁺) and C₂N^- (X³Σ^-), but for which inelastic rates are only known for C₂H^-. The same systems are also of direct interest in modeling selective photo-detachment experiments in cold ion traps where the He atoms function as the chief buffer gas at the low trap temperatures. This study employs accurate, ab initio calculations of the interaction potential energy surfaces for these anions, treated as rigid rotors, and the He atom to obtain a wide range of state-changing quantum cross sections and rates at temperatures up to about 100 K. The results are analyzed and compared for the two systems to show differences and similarities between their rates of state-changing dynamics.

Overcoming the out-of-plane bending issue in an aromatic hydrocarbon: the anharmonic vibrational frequencies of c-(CH)C3H2. Phys Chem Chem Phys 2020;22:12951-12958. [PMID: 32478782 DOI: 10.1039/d0cp01889a]

The challenges associated with the out-of-plane bending problem in multiply-bonded hydrocarbon molecules can be mitigated in quartic force field analyses by varying the step size in the out-of-plane coordinates. Carbon is a highly prevalent element in astronomical and terrestrial environments, but this major piece of its spectra has eluded theoretical examinations for decades. Earlier explanations for this problem focused on method and basis set issues, while this work seeks to corroborate the recent diagnosis as a numerical instability problem related to the generation of the potential energy surface. Explicit anharmonic frequencies for c-(CH)C₃H₂⁺ are computed using a quartic force field and the CCSD(T)-F12b method with cc-pVDZ-F12, cc-pVTZ-F12, and aug-cc-pVTZ basis sets. The first of these is shown to offer accuracy comparable to that of the latter two with a substantial reduction in computational time. Additionally, c-(CH)C₃H₂⁺ is shown to have two fundamental frequencies at the onset of the interstellar unidentified infrared bands, at 5.134 and 6.088 μm or 1947.9 and 1642.6 cm^-1, respectively. This suggests that the results in the present study should assist in the attribution of parts of these aromatic bands, as well as provide data in support of the laboratory or astronomical detection of c-(CH)C₃H₂⁺.

Anharmonic Frequencies of (MO)2 and Related Hydrides for M = Mg, Al, Si, P, S, Ca, and Ti and Heuristics for Predicting Anharmonic Corrections of Inorganic Oxides

The low-frequency vibrational fundamentals of D_2h inorganic oxides are readily modeled by heuristic scaling factors at fractions of the computational cost compared to explicit anharmonic frequency computations. Oxygen and the other elements in the present study are abundant in geochemical environments and have the potential to aggregate into minerals in planet-forming regions or in the remnants of supernovae. Explicit quartic force field computations at the CCSD(T)-F12b/cc-pVTZ-F12 level of theory generate scaling factors that accurately predict the anharmonic frequencies with an average error of less than 1.0 cm^-1 for both the metal-oxygen stretching frequencies and the torsion and antisymmetric stretching frequencies. Inclusion of hydrogen motions is less absolutely accurate but is similarly relatively predictive. The fundamental vibrational frequencies for the seven tetra-atomic inorganic oxides examined presently fall below 876 cm^-1 and most of the hydrogenated species do as well. Additionally, ν₆ for the SiO dimer is shown to have an intensity of 562 km mol^-1, with each of the other molecules having one or more frequencies with intensities greater than 80 km mol^-1, again with most in the low-frequency infrared range. These intensities and the frequencies computed in the present study should assist in laboratory characterization and potential interstellar or circumstellar observation.

Highly Accurate Quartic Force Field and Rovibrational Spectroscopic Constants for the Azirinyl Cation (c-C2NH2+) and Its Isomers

The azirinyl cation is an aromatic cyclic molecule that is isoelectronic with cyclopropenylidene, c-C₃H₂, and c-C₃H₃⁺. Cyclopropenylidene has been shown to be ubiquitous, existing in many different astrophysical environments. Given the similar chemistry between C and N, and the relative abundances between C and N in astrophysical environments, it is expected that there should be aromatic ringed molecules that incorporate N in the ring, but as yet, no such molecule has been identified. To address this issue, the present study uses high levels of electronic structure theory to compute a highly accurate quartic force field (QFF) for the azirinyl cation and its two lowest lying isomers, the cyanomethyl and isocyanomethyl cations. The theoretical approach uses the singles and doubles coupled-cluster method that includes a perturbative correction for connected triple excitations, CCSD(T), together with extrapolation to the one-particle basis set limit and corrections for scalar relativity and core-correlation. The QFF is then used in a second-order vibrational perturbation theory analysis (VPT2) to compute the fundamental vibrational frequencies and rovibrational spectroscopic constants for all three C₂NH₂⁺ isomers. The reliability of the VPT2 vibrational frequencies is tested by comparison to vibrational configuration interaction (VCI) calculations, and excellent agreement is found between the two approaches. Fundamental vibrational frequencies and rovibrational spectroscopic constants for all singly substituted ¹³C, ¹⁵N, and D isotopologues are also reported. It is expected that the highly accurate spectroscopic data reported herein will be useful in the identification of these cations in high-resolution experimental or astronomical observations.

ArCH2 + : A Detectable Noble Gas Molecule

The noble gas molecular cation, ArCH₂ ⁺ , has been observed in mass spectrometry experiments, and the present work is providing high-level quantum chemical predictions for the vibrational and rotational spectroscopic data necessary to observe this molecule in situ in other laboratory conditions. The Ar-C stretch in this cation is a bright fundamental vibrational frequency that should be observable in the early regions of the far-infrared at 421.2 cm^-1 for the universally most common ³⁶ Ar isotope. The near-prolate nature of this molecule and its 2.91 D dipole moment should also make it distinguishable for submillimeter detection, as well. Furthermore, the Ar-C bond strength in ArCH₂ ⁺ is greater than the global minimum for the dissociation of the experimentally known ArOH⁺ cation. As a result, the infrared spectrum of this simple organo-noble gas molecule is likely waiting to be observed and may already exist in the spectra of hydrocarbon cations in argon-matrix condensed phase experiments.

Characterization of Azirine and Its Structural Isomers

The structures and spectroscopic properties of azirine (C₂H₃N), a nitrogen-containing three-membered cyclic molecule, and its isomers were studied with state-of-the-art ab initio quantum chemical methods. Azirine is isomeric with methyl cyanide (CH₃CN) and methyl isocyanide (CH₃NC)-both observed in the star-forming regions of Sgr B2. In this study, we characterize the stationary points on the potential energy surface, relative energies, dipole moments, rotational constants, and harmonic vibrational frequencies of the 2 H-azirine ( a), 1 H-2,2 H-azirine ( b, carbene isomer), and 1 H-azirine ( c) cyclic isomers. The CCSD(T) method and density functional theory (DFT), using the ωB97-X functional, along with Dunning's cc-pVXZ (X = T and Q) basis sets were used to optimize molecular geometries and calculate vibrational frequencies. The 2 H-azirine, an imine isomer ( a), was found to be the lowest in energy among the cyclic isomers, followed by the carbene isomer ( b), and last the 1 H-azirine, an enamine isomer ( c). All three cyclic isomers have a C _s symmetry equilibrium structure. Azirines, if identified (three linear C₂H₃N isomers are already identified in the same source toward the galactic center, Sgr B2), would be the first nitrogen-containing cyclic molecules identified in an astronomical observation.

Rovibrational analysis of c-SiC2H2: Further evidence for out-of-plane bending issues in correlated methods

While the issue of properly describing the out-of-plane bends (OPBs) in sp² hybridized carbon atoms has reappeared for c-SiC₂H₂, the present quantum chemical study provides a new characterization of this molecule in order to aid in its potential detection in astrophysically relevant studies. Combining the previous, high-level approach with MP2-F12/aug-cc-pVDZ gives exceptionally accurate results for the comparison of experimental rotational constants and seemingly reliable vibrational frequencies. Most notably, the brightest fundamental vibrational frequency in c-SiC₂H₂, the b₁ OPB, is predicted to lie at 673.4 cm^-1, within 4.0 cm^-1 of the previous matrix isolation experiment. As with c-C₃H₂, CCSD(T)-F12/aug-cc-pVTZ appears to be quite susceptible to over estimating the OPB anharmonic correction in c-SiC₂H₂ and may also do such for in-plane bends, as well. MP2-F12/aug-cc-pVDZ is less susceptible to these errors, and increasing the step size reduces this positive anharmonicity issue in both the cases. The OPB underestimation, however, likely still remains. Finally, estimates for some anharmonic vibrational frequencies are provided for the methylated form, c-SiC₂HCH₃, which is likely also a product of gas phase reactions of ·SiH with various alkynes.

Rotational Spectroscopy of a Triatomic Molecular Anion

Rotational transitions of the nonlinear triatomic molecular anion NH_{2}^{-} have been observed by terahertz spectroscopy in a cryogenic radio frequency ion trap. Absorption of terahertz photons has been probed by rotational state-dependent photodetachment of the trapped negative ions near the detachment threshold. Using this two-photon scheme, the two lowest rotational transitions for the asymmetric top rotor NH_{2}^{-} have been found. For the para nuclear spin configuration, the 1_{0}←0_{0} transition frequency was determined to be 933 954(2) MHz, and for the ortho configuration the 1_{+1}←1_{-1} transition frequency was determined to be 447 375(3) MHz. This result appears to preclude the recent tentative assignment of an interstellar absorption feature to NH_{2}^{-}.

Overcoming the Failure of Correlation for Out-of-Plane Motions in a Simple Aromatic: Rovibrational Quantum Chemical Analysis of c-C3H2

Truncated, correlated, wave function methods either produce imaginary frequencies (in the extreme case) or nonphysically low frequencies in out-of-plane motions for carbon and adjacent atoms when the carbon atoms engage in π bonding. Cyclopropenylidene is viewed as the simplest aromatic hydrocarbon, and the present as well as previous theoretical studies have shown that this simple molecule exhibits this behavior in the two out-of-plane bends (OPBs). This nonphysical behavior has been treated by removing nearly linear dependent basis functions according to eigenvalues of the overlap matrix, by employing basis sets where the spd space saturatation is balanced with higher angular momentum functions, by including basis set superposition/incompleteness error (BSSE/BSIE) corrections, or by combining standard correlation methods with explicitly correlated methods to produce hybrid potential surfaces. However, this work supports the recently described hypothesis that the OPB problem is both a method and a basis set effect. The correlated wave function's largest higher-order substitution term comes from a π → π* excitation where constructive interference of both orbitals artificially stabilizes the OPB. By employing schema to overcome this issue, the symmetric OPB ν₉ is the predicted to be the second-brightest transition, and it will be observed very close to 775 cm^-1. However, more work from the community is required to formulate better how carbon atoms interact with their adjacent atoms in π-bonded systems. Such bonds are ubiquitous in all of chemistry and beyond.

Towards a quantum chemical protocol for the prediction of rovibrational spectroscopic data for transition metal molecules: Exploration of CuCN, CuOH, and CuCCH

High accuracy electronic structure computations for small transition metal-containing molecules have been a long term challenge. Due to coupling between electronic and nuclear wave functions, even experimental/theoretical identification of the ground electronic state requires tremendous efforts. Quartic force fields (QFFs) are effective ab initio tools for obtaining reliable anharmonic spectroscopic properties. However, the method that employs complete basis set limit extrapolation ("C"), consideration of core electron correlation ("cC"), and inclusion of scalar relativity ("R") to produce the energy points on the QFF, the composite CcCR methodology, has not yet been utilized to study inorganic spectroscopy. This work takes the CcCR methodology and adapts it to test whether such an approach is conducive for the closed-shell, copper-containing molecules CuCN, CuOH, and CuCCH. Gas phase rovibrational data are provided for all three species in their ground electronic states. Equilibrium geometries and many higher-order rovibrational properties show good agreement with earlier studies. However, there are notable differences, especially in computation of fundamental vibrational frequencies. Even with further additive corrections for the inner core electron correlation and coupled cluster with full single, double, and triple substitutions (CCSDT), the differences are still larger than expected indicating that more work should follow for predicting rovibrational properties of transition metal molecules.

Towards completing the cyclopropenylidene cycle: rovibrational analysis of cyclic N3+, CNN, HCNN+, and CNC. Phys Chem Chem Phys 2017;19:22860-22869. [PMID: 28812071 DOI: 10.1039/c7cp04257d]

The simple aromatic hydrocarbon, cyclopropenylidene (c-C₃H₂), is a known, naturally-occurring molecule. The question remains as to whether its isoelectronic, cyclic, fellow aromatics of c-N₃⁺, c-CNN, HCNN⁺, and c-CNC^- are as well. Each of these are exciting objects for observation of Titan, and the rotational constants and vibrational frequencies produced here will allow for remote sensing of Titan's atmosphere or other astrophysical or terrestrial sources. None of these four aromatic species are vibrationally strong absorbers/emitters, but the two ions, HCNN⁺ and c-CNC^-, have dipole moments of greater than 3 D and 1 D, respectively, making them good targets for rotational spectroscopic observation. Each of these molecules is shown here to exhibit its own, unique vibrational properties, but the general trends put the vibrational behavior for corresponding fundamental modes within close ranges of one another, even producing nearly the same heavy atom, symmetric stretching frequencies for HCNN⁺ and c-C₃H₂ at 1600 cm^-1. The c-N₃⁺ cation is confirmed to be fairly unstable and has almost no intensity in its ν₂ fundamental. Hence, it will likely remain difficult to characterize experimentally.

The rovibrational nature of cis- and trans-HNNS: A possible nitrogen molecule progenitor

The HNNS radical has been promoted recently as a viable intermediate in the interstellar creation of the spectroscopically elusive nitrogen molecule. Any confirmation of this pathway or utilizing HNNS as a tracer of N₂ depends upon the ability to observe the radical intermediate whether in the laboratory or in the interstellar medium. Established and accurate quantum chemical procedures are employed here to produce spectroscopic constants, fundamental vibrational frequencies, and intensities that can be utilized for any possible detection of HNNS. While trans-HNNS is confirmed here to be 3.0 kcal/mol lower in energy than cis-HNNS, the latter will be more readily observed rotationally due to its significantly larger dipole moment. The N-N bond in cis-HNNS is stronger than in trans-HNNS, and earlier work has suggested that cis-HNNS is more useful in the creation of N₂ from NH and NS. Hence, the detection of cis-HNNS may be of greater value anyway. Furthermore, the N-N stretch in either conformer is also exceptionally bright and will occur in the mid-infrared with nearly 30 cm^-1 separating the fundamentals of the two conformers. Finally, the low isomerization barrier can be affected significantly upon deuteration also making ND an interesting consideration as a starting material in the interstellar formation of N₂.