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

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.

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.

pbqff: Push-Button Quartic Force Fields

pbqff is an open-source program for fully automating the production of quartic force fields (QFFs) and their corresponding anharmonic spectroscopic data. Rather than being a monolithic piece of code, it consists of several key modules including a generic interface to quantum chemistry codes and, notably, queuing systems; a molecular point group symmetry library; an internal-to-Cartesian coordinate conversion module; a module for the ordinary least-squares fitting of potential energy surfaces; and an improved second-order rotational and vibrational perturbation theory package for asymmetric and symmetric tops that handles type-1 and -2 Fermi resonances, Fermi resonance polyads, and Coriolis resonances. All of these pieces are written in Rust, a modern, safe, and performant programming language that has much to offer for scientific programming. This work introduces pbqff and its surrounding ecosystem, in addition to reporting new anharmonic vibrational data for c-(C)C₃H₂ and describing how the components of pbqff can be leveraged in other projects.

Cyclopropenylidene: Clustering and Interaction with Water Molecules

Cyclopropenylidene (c-C₃H₂, abbreviated CPD) is a highly reactive, planar, partially aromatic carbene discovered in the interstellar medium, and, also recently, in the outer solar system. It is demonstrated herein on cogent quantum chemical grounds that CPD which possesses an electric dipole moment of 3.4 D is capable of forming stable dimer and trimer clusters through hydrogen-bonding. These attributes of CPD are conducive to the formation of stable hydrogen-bonded conformations with one- and two-water molecules. Having determined its consistency with the second-order Møller-Plesset perturbation theory MP2, we employ the ωB97xD hybrid density functional theory in conjunction with a 6-311++G(2d,2p) basis set for a credible description of noncovalent interactions involved in clustering. Molecular electrostatic potential (MESP) and characteristic vibrational frequency shifts upon clustering are presented.

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.

From six to eight Π-electron bare rings of group-XIV elements and beyond: can planarity be deciphered from the "quasi-molecules" they embed?

Ab initio molecular orbital theory is used to study the structures of six and eight π-electron bare rings of group-XIV elements, and even larger [n]annulenes up to C₁₈H₁₈, including some of their mono-, di-, tri-, and tetra-anions. While some of the above rings are planar, others are nonplanar. A much spotlighted case is cyclo-octatetraene (C₈H₈), which is predicted to be nonplanar together with its heavier group-XIV analogues Si₈H₈ and Ge₈H₈, with the solely planar members of its family having the stoichiometric formulas C₄Si₄H₈ and C₄Ge₄H₈. A similar situation arises with the six π-electron bare rings, where benzene and substituted ones up to C₃Si₃H₆ or so are planar, while others are not. However, the explanations encountered in the literature find support in ab initio calculations for such species, often rationalized from distinct calculated features. Using second-order Møller-Plesset perturbation theory and, when affordable (particularly tetratomics, which may allow even higher levels), the coupled-cluster method including single, double, and perturbative triple excitations, a common rationale is suggested based on a novel concept of quasi-molecules or the (3+4)-atom partition scheme. Any criticism of tautology is therefore avoided. The same analysis has also been successfully applied to even larger [n]annulenes, to their mixed family members involving silicon and germanium atoms, and to the C₁₈ carbon ring. Furthermore, it has been extended to annulene anions to check the criteria of the popular Hückel rule for planarity and aromaticity. Exploratory work on cycloarenes is also reported. Besides a partial study of the involved potential energy surfaces, equilibrium geometries and harmonic vibrational frequencies have been calculated anew, for both the parent and the actual prototypes of the quasi-molecules.

Investigation of the Failure of the MP2 Method to Describe the Out-of-Plane Bending Motions of Carbon-Carbon Double-Bonded Molecules: The Role of Atomic Orbitals

We present a detailed study on the role of atomic orbitals in the unphysical description of the out-of-plane bending (OOPB) vibrations with the MP2 method. The anharmonicities of the OOPB vibrations are found to be unphysically large for several basis sets with the MP2 method. We find that the inclusion of additional valence s and p orbitals to the basis set leads to the lowering of π* orbitals' energies along with the generation of several spurious low-energy virtual molecular orbitals (VMOs). Such erroneous VMOs create a disbalance between the σ and π correlations for the planar structure of the molecules. Since the OOPB vibrations distort the π* orbitals, the disbalance in the σ and π correlations leads to errors in the derivatives of the correlation energy with respect to the displacement along with OOPB modes. The diffuse functions in the basis set enhance the unphysical anharmonicities of the OOPB modes since these functions are of s- and p-type atomic orbitals. The polarization atomic orbitals of higher angular momentum improve the description of the π* orbitals and thereby reduce the disbalance between the σ and π correlations in the MP2 calculations. We find that the unphysical frequencies for the OOPB modes are significantly eliminated with the d and f orbitals on the C atoms in the basis set.

Fundamental Vibrational Frequencies and Spectroscopic Constants of Substituted Cyclopropenylidene (c-C3HX, X = F, Cl, CN)

The recent detection of ethynyl-functionalized cyclopropenylidene (c-C₃HC₂H) has initiated the search for other functional forms of cyclopropenylidene (c-C₃H₂) in space. There is existing gas-phase rotational spectroscopic data for cyano-cyclopropenylidene (c-C₃HCN), but the present work provides the first anharmonic vibrational spectral data for that molecule, as well as the first full set of both rotational and vibrational spectroscopic data for fluoro- and chloro-cyclopropenylidenes (c-C₃HF and c-C₃HCl). All three molecules have fundamental vibrational frequencies with substantial infrared intensities. Namely, c-C₃HCN has a moderately intense fundamental frequency at 1244.4 cm^-1, while c-C₃HF has two large intensity modes at 1765.4 and 1125.3 cm^-1 and c-C₃HCl again has two large intensity modes at 1692.0 and 1062.5 cm^-1. All of these frequencies are well within the spectral range covered by the high-resolution EXES instrument on NASA's Stratospheric Observatory for Infrared Astronomy (SOFIA). Further, all three molecules have dipole moments of around 3.0 D in line with c-C₃H₂, enabling them to be observed by pure rotational spectroscopy, as well. Thus, the rovibrational spectral data presented herein should assist with future laboratory studies of functionalized cyclopropenylidenes and may lead to their interstellar or circumstellar detection.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

Metal cyclopropenylidene sandwich cluster and nanowire: structural, electronic, and magnetic properties

Organometallic sandwich clusters and nanowires can offer prototypes for molecular ferromagnet and nanoscale spintronic devices due to the strong coupling of local magnetic moments in the nanowires direction and experimental feasibility. Here, on the basis of first-principles calculations, we reportTM_n(c-C₃H₂)_n+1(TM= Ti, Mn;n= 1-4) sandwich clusters and 1D [TM(c-C₃H₂)]_∞sandwich nanowires building from transitional metal and the smallest aromatic carbene of cyclopropenylidene (c-C₃H₂). Based on the results of lattice dynamic and thermodynamic studies, we show that the magnetic moment of Mn_n(c-C₃H₂)_n+1clusters increases linearly with the number ofn, and 1D [Mn(c-C₃H₂)]_∞nanowire is a stable ferromagnetic semiconductor, which can be converted into half metal with carrier doping. In contrary, both Ti_n(c-C₃H₂)_n+1and 1D [Ti(c-C₃H₂)]_∞nanowire are nonmagnetic materials. This study reveals the potential application of the [TM(c-C₃H₂)]_∞nanowire in spintronics.

Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding

Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.

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.

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).

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⁺.

How do the Hückel and Baird Rules Fade away in Annulenes?

Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.

Bootstrap Embedding for Molecules

Fragment embedding is one way to circumvent the high computational scaling of accurate electron correlation methods. The challenge of applying fragment embedding to molecular systems primarily lies in the strong entanglement and correlation that prevent accurate fragmentation across chemical bonds. Recently, Schmidt decomposition has been shown effective for embedding fragments that are strongly coupled to a bath in several model systems. In this work, we extend a recently developed quantum embedding scheme, bootstrap embedding (BE), to molecular systems. The resulting method utilizes the matching conditions naturally arising from using overlapping fragments to optimize the embedding. Numerical simulation suggests that the accuracy of the embedding improves rapidly with fragment size for small molecules, whereas larger fragments that include orbitals from different atoms may be needed for larger molecules. BE scales linearly with system size (apart from an integral transform) and hence can potentially be useful for large-scale calculations.

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.

Anomalous description of the anharmonicity of bending motions of carbon–carbon double bonded molecules with the MP2 method: ethylene as a case study

In this work, we report anomalous descriptions of bending modes of the smallest carbon–carbon double bonded molecule ethylene with the MP2 method.