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]

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.

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.

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.

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.

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.

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.

Accuracy Meets Interpretability for Computational Spectroscopy by Means of Hybrid and Double-Hybrid Functionals

Accuracy and interpretability are often seen as the devil and holy grail in computational spectroscopy and their reconciliation remains a primary research goal. In the last few decades, density functional theory has revolutionized the situation, paving the way to reliable yet effective models for medium size molecules, which could also be profitably used by non-specialists. In this contribution we will compare the results of some widely used hybrid and double hybrid functionals with the aim of defining the most suitable recipe for all the spectroscopic parameters of interest in rotational and vibrational spectroscopy, going beyond the rigid rotor/harmonic oscillator model. We will show that last-generation hybrid and double hybrid functionals in conjunction with partially augmented double- and triple-zeta basis sets can offer, in the framework of second order vibrational perturbation theory, a general, robust, and user-friendly tool with unprecedented accuracy for medium-size semi-rigid molecules.