Theoretical Rovibronic Treatment of the X̃ 2Σ+ and à 2Π States of C2H and the X̃ 1Σ+ State of C2H– from Quartic Force Fields

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.

DFT + F12 QFFs for Cost-Effective Rovibrational Spectral Data Predictions of Ground and Excited Electronic States

The quest for faster computation of anharmonic vibrational frequencies of both ground and excited electronic states has led to combining coupled cluster theory harmonic force constants with density functional theory cubic and quartic force constants for defining a quartic force field (QFF) utilized in conjunction with vibrational perturbation theory at second order (VPT2). This work shows that explicitly correlated coupled cluster theory at the singles, doubles, and perturbative triples levels [CCSD(T)-F12] provides accurate anharmonic vibrational frequencies and rotational constants when conjoined with any of B3LYP, CAM-B3LYP, BHandHLYP, PBE0, and ωB97XD for roughly one-quarter of the computational time of the CCSD(T)-F12 QFF alone for our test set. As the number of atoms in the molecule increases, however, the anharmonic terms become a greater portion of the QFF, and the cost comparison improves with HOCO+ and formic acid, requiring less than 15 and 10% of the time, respectively. In electronically excited states, PBE0 produces more consistently accurate results. Additionally, as the size of the molecule and, in turn, QFF increase, the cost savings for utilizing such a hybrid approach for both ground- and excited-state computations grows. As such, these methods are promising for predicting accurate rovibrational spectral properties for electronically excited states. In cases where well-behaved potentials for a small selection of targeted excited states are needed, such an approach should reduce the computational cost compared to that of methods requiring semiglobal potential surfaces or variational treatments of the rovibronic Hamiltonian. Such applications include spectral characterization of comets, exoplanets, or any situation in which gas phase molecules are being excited by UV-vis radiation.

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.

F12+EOM Quartic Force Fields for Rovibrational Predictions of Electronically Excited States

Quartic force fields (QFFs) constructed using a sum of ground-state CCSD(T)-F12b energies with EOM-CCSD excitation energies are proposed for computation of spectroscopic properties of electronically excited states. This is dubbed the F12+EOM approach and is shown to provide similar accuracy to previous methodologies at lower computational cost. Using explicitly correlated F12 approaches instead of canonical CCSD(T), as in the corresponding (T)+EOM approach, allows for 70-fold improvement in computational time. The mean percent difference between the two methods for anharmonic vibrational frequencies is only 0.10%. A similar approach is also developed herein which accounts for core correlation and scalar relativistic effects, named F12cCR+EOM. The F12+EOM and F12cCR+EOM approaches both match to within 2.5% mean absolute error of experimental fundamental frequencies. These new methods should help in clarifying astronomical spectra by assigning features to vibronic and vibrational transitions of small astromolecules when such data are not available experimentally.

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.

Confirmation of gaseous methanediol from state-of-the-art theoretical rovibrational characterization

High-level rovibrational characterization of methanediol, the simplest geminal diol, using state-of-the-art, purely ab initio techniques unequivocally confirms previously reported gas phase preparation of this simplest geminal diol in its C₂ conformation. The F12-TZ-cCR and F12-DZ-cCR quartic force fields (QFFs) utilized in this work are among the largest coupled cluster-based anharmonic frequencies computed to date, and they match the experimental band origins of the spectral features in the 980-1100 cm^-1 range to within 3 cm^-1, representing a significant improvement over previous studies. The simulated spectrum also matches the experimental spectrum in the strong Q branch feature and qualitative shape of the 980-1100 cm^-1 region. Additionally, the full set of rotational constants, anharmonic vibrational frequencies, and quartic and sextic distortion constants are provided for both the lowest energy C₂ conformer as well as the slightly higher C_s conformer. Several vibrational modes have intensities of 60 km mol^-1 or higher, facilitating potential astronomical or atmospheric detection of methanediol or further identification in laboratory work especially now that gas phase synthesis of this molecule has been established.

(T)+EOM Quartic Force Fields for Theoretical Vibrational Spectroscopy of Electronically Excited States

(T)+EOM quartic force fields (QFFs) are proposed for ab initio rovibrational properties of electronically excited states of small molecules. The (T)+EOM method is a simple treatment of the potential surface of the excited state using a composite energy from the CCSD(T) energy for the ground-state configuration and the EOM-CCSD excitation energy for the target state. The method is benchmarked with two open-shell species, HOO and HNF, and two closed-shell species, HNO and HCF. A (T)+EOM QFF with a complete basis set extrapolation (C) and corrections for core correlation (cC) and scalar relativity (R), dubbed (T)+EOM/CcCR, achieves a mean absolute error (MAE) as low as 1.6 cm^-1 for the à ²A' state of HOO versus an established benchmark QFF with CCSD(T)-F12b/cc-pVTZ-F12 (F12-TZ) for this variationally accessible electronically excited state. The MAE for anharmonic frequencies for (T)+EOM/CcCR versus F12-TZ for HNF is 7.5 cm^-1. The closed-shell species are compared directly with the experiment, where a simpler (T)+EOM QFF using the aug-cc-pVTZ basis set compares more favorably than the more costly (T)+EOM/CcCR, suggesting a possible influence of decreasing accuracy with basis set size. Scans along internal coordinates are also provided which show reasonable modeling of the potential surface by (T)+EOM compared to benchmark QFFs computed for variationally accessible electronic states. The agreement between (T)+EOM/CcCR with F12-TZ and CcCR benchmarks is also shown to be quite accurate for rotational constants and geometries, with an MAE of 0.008 MHz for the rotational constants of (T)+EOM/CcCR versus CcCR for à ²A' HOO and agreement within 0.003 Å for bond lengths.

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.

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).

Highly-excited state properties of cumulenone chlorides in the vacuum-ultraviolet

Recent observations of chloromethane in interstellar environments suggest that other organohalogens, which are known to be critically important in Earth's atmosphere, may also be of significance beyond our own terrestrial veil. This raises the question of how such molecules behave under extreme conditions such as when exposed to vacuum ultraviolet (VUV) radiation. VUV photons promote molecules to highly excited states that fragment in non-statistical patterns controlled by the initial femtosecond dynamics. A detailed understanding of VUV-driven photochemistry in complex organic molecules that consist of more than one functional group is a particularly challenging task. This quantum chemical analysis reports the electronic states and ionization potentials up to the VUV range (6-11 eV) of the chlorine-substituted cumulenone series molecules. The valence and Rydberg properties of lone-pair terminated, π-conjugated systems are explored for their potential resonance with lone pairs from elsewhere in the system. The carbon chain elongation within the family ClHCnO, where n = 1-4, influences the electronic excitations, associated wavefunctions, and ionization potentials of the molecules. The predicted geometries and ionization potentials are in good agreement with the available experimental photoelectron spectra for formyl chloride and chloroketene, n = 1-2. Furthermore, comparison between the regular cumulenone species and the corresponding chlorinated derivatives exhibit similar behaviors especially for n = 3, where the allene backbone in propadienone chloride is severely bent. Most notably for the excited states is that the Rydberg character becomes more dominant as the energy increases, with some retaining valence characters.

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⁺.

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.

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 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.

Symmetry breaking and spectral considerations of the surprisingly floppy c-C3H radical and the related dipole-bound excited state of c-C3H. J Chem Phys 2017;146:224303. [PMID: 29166048 DOI: 10.1063/1.4985095]

The C₃H radical is believed to be prevalent throughout the interstellar medium and may be involved in the formation of polycyclic aromatic hydrocarbons. C₃H exists as both a linear and a cyclic isomer. The C_2v cyclopropenylidenyl radical isomer was detected in the dark molecular cloud TMC-1, and the linear propenylidenyl radical isomer has been observed in various dark molecular clouds. Even though the c-C₃H radical has been classified rotationally, the vibrational frequencies of this seemingly important interstellar molecule have never been directly observed. Established, highly accurate quartic force field methodologies are employed here to compute useful geometrical data, spectroscopic constants, and vibrational frequencies. The computed rotational constants are consistent with the experimental results. Consequently, the three a₁ (ν₁, ν₂, and ν₃) and one b₁ (ν₆) anharmonic vibrational frequencies at 3117.7 cm^-1, 1564.3 cm^-1, 1198.5 cm^-1, and 826.7 cm^-1, respectively, are reliable predictions for these, as of yet unseen, observables. Unfortunately, the two b₂ fundamentals (ν₄ and ν₅) cannot be treated adequately in the current approach due to a flat and possible double-well potential described in detail herein. The dipole-bound excited state of the anion suffers from the same issues and may not even be bound. However, the trusted fundamental vibrational frequencies described for the neutral radical should not be affected by this deformity and are the first robustly produced for c-C₃H. The insights gained here will also be applicable to other structures containing three-membered bare and exposed carbon rings that are surprisingly floppy in nature.

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.

Vibrational frequencies and spectroscopic constants of three, stable noble gas molecules: NeCCH+, ArCCH+, and ArCN+

The search for possible, natural, noble gas molecules has led to quantum chemical, spectroscopic analysis of NeCCH⁺, ArCCH⁺, and ArCN⁺.