The effect of approximating some molecular integrals in coupled-cluster calculations: fundamental frequencies and rovibrational spectroscopic constants for isotopologues of cyclopropenylidene

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.

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.

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⁺.

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.

Identifying Molecular Structural Aromaticity for Hydrocarbon Classification

Determination of aromaticity in hydrocarbons may be as simple as determining the average bond length for the molecule of interest. This would greatly assist in classifying the nature of hydrocarbon chemistry, especially for large molecules such as polycyclic aromatic hydrocarbons (PAHs) where today's aromatic classification methods are prohibitively expensive. The average C-C bond lengths for a test set of known aromatic, antiaromatic, and aliphatic cyclic hydrocarbons are computed here, and they show strong delineating patterns for the structural discernment of these aromaticity classifications. Aromatic molecules have average C-C bond lengths of 1.41 Å or less with the largest molecules, PAHs, having the longest average C-C bond lengths; aliphatic species have such lengths of 1.50 Å or more; and antiaromatic species fall between the two. Consequently, a first-order guess as to the aromaticity of a system may simply arise from its geometry. Although this prediction will likely have exceptions, such simple screening can easily classify most cases, and more advanced techniques can be brought to bear on the cases that lie in the boundaries. Benchmarks for hydrocarbons are provided here, but other classes of molecular structural aromaticity likely will have to be defined on an ad hoc basis.

RI-MP3 calculations of biomolecules based on the fragment molecular orbital method

In this study, the third-order Møller-Plesset perturbation (MP3) theory using the resolution of the identity (RI) approximation was combined with the fragment molecular orbital (FMO) method to efficiently calculate a high-order electron correlation energy of biomolecular systems. We developed a new algorithm for the RI-MP3 calculation, which can be used with the FMO scheme. After test calculations using a small molecule, the FMO-RI-MP3 calculations were performed for two biomolecular systems comprising a protein and a ligand. The computational cost of these calculations was only around 5 and 4 times higher than those of the FMO-RHF calculations. The error associated with the RI approximation was around 2.0% of the third-order correlation contribution to the total energy. However, the RI approximation error in the interaction energy between the protein and ligand molecule was insignificantly small, which reflected the negligible error in the inter fragment interaction energy. © 2018 Wiley Periodicals, Inc.

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.

Photodissociation dynamics of cyclopropenylidene, c-C3 H2

In this joint experimental and theoretical study we characterize the complete dynamical "life cycle" associated with the photoexcitation of the singlet carbene cyclopropenylidene to the lowest lying optically bright excited electronic state: from the initial creation of an excited-state wavepacket to the ultimate fragmentation of the molecule on the vibrationally hot ground electronic state. Cyclopropenylidene is prepared in this work using an improved synthetic pathway for the preparation of the precursor quadricyclane, thereby greatly simplifying the assignment of the molecular origin of the measured photofragments. The excitation process and subsequent non-adiabatic dynamics have been previously investigated employing time-resolved photoelectron spectroscopy and are now complemented with high-level ab initio trajectory simulations that elucidate the specific vibronic relaxation pathways. Lastly, the fragmentation channels accessed by the molecule following internal conversion are probed using velocity map imaging (VMI) so that the identity of the fragmentation products and their corresponding energy distributions can be definitively assigned.

Structures and transition states of Ge2CH2

In this study a systematic theoretical investigation of Ge2CH2 is carried out. The singlet potential energy surface (PES) was explored using state-of-the-art theoretical methods including self-consistent field (SCF), coupled cluster theory incorporating single and double excitation (CCSD), perturbative triple [CCSD(T)] and full triples [CCSDT] with perturbative quadruple (Q), together with a variety of correlation-consistent polarized valence basis sets cc-pVXZ (where X = D, T, and Q). A total of eleven stationary points have been located on the Ge2CH2 singlet ground state PES. Among them, seven structures are minima (1S-7S), two are transition states (TS1 and TS2), and two are second-order saddle points (SSP1 and SSP2). The global minimum is predicted to be an exotic hydrogen-bridged structure 1S. The energy ordering of the seven minima (in kcal mol(-1)) obtained from focal point analysis using the extrapolation to complete basis set (CBS) limit with zero point vibrational energy (ZPVE), core correlation, diagonal Born-Oppenheimer (DBOC) and relativistic correction is 1S [0.0] < 2S [17.2] < 3S [18.3] < 4S [31.7] < 5S [39.9] < 6S [58.1] < 7S [82.1].

Anharmonic Vibrational Analysis for the Propadienylidene Molecule (H2C═C═C:)

Maier et al. found that photolysis of singlet cyclopropenylidene (1S) in a matrix yields triplet propargylene (2T), which upon further irradiation is converted to singlet propadienylidene (vinylidenecarbene, 3S). Their discovery was followed by interstellar identification of 3S by Cernicharo et al. An accurate quartic force field for propadienylidene (3S) has been determined employing the ab initio coupled-cluster (CC) with single and double excitations and perturbative triple excitations [CCSD(T)] method and the correlation-consistent core-valence quadruple-ζ (cc-pCVQZ) basis set. Utilizing vibrational second-order perturbation theory (VPT2), vibration-rotation coupling constants, rotational constants, centrifugal distortion constants, vibrational anharmonic constants, and fundamental vibrational frequencies are determined. The predicted fundamental frequencies for 3S as well as its (13)C and deuterium isotopologues are in good agreement with experimental values. The theoretical zero-point vibration corrected rotational constants B0 are consistent with experimental values within 0.3% of errors. The isotopic shifts of B0 are in close to exact agreement with experimental observations. The mean absolute deviation between theoretical anharmonic and experimental fundamental vibrational frequencies for 24 modes (excluding CH2 s-str.) is only 2.6 cm(-1). The isotopic shifts of the vibrational frequencies are also in excellent agreement with the available experimental values. However, a large discrepancy is observed for the CH2 symmetric stretch, casting doubt on the experimental assignment for this mode.