Equilibrium geometries of cyclic SiC3 isomers

The Semiexperimental Approach at Work: Equilibrium Structure of Radical Species

The so-called semiexperimental (SE) approach is a powerful technique for obtaining highly accurate equilibrium structures for isolated systems. This Featured Article describes its extension to open-shell species, thus providing the first systematic investigation on radical equilibrium geometries to be used for benchmarking purposes. The small yet significant database obtained demonstrates that there is no reduction in accuracy when moving from closed-shell species to radicals. We also provide an extension of the applicability of the SE approach to medium-/large-sized radicals by exploiting the so-called "Lego-brick" approach, which is based on the assumption that a molecular system can be seen as formed by smaller fragments for which the SE equilibrium structure is available. In this Featured Article we show that this model can be successfully applied also to open-shell species.

Precise Equilibrium Structure of Benzene

Recent advances in gas-phase structure determination afford outstanding agreement between the CCSD(T)/cc-pCVTZ-corrected semi-experimental (reSE) equilibrium structures and their corresponding best theoretical estimates (BTEs) of the equilibrium structures (re) based upon corrections to the CCSD(T)/cc-pCV5Z geometries for the aromatic heterocycles pyrimidine and pyridazine. Herein, that same analysis is extended to the fundamental aromatic molecule benzene, using published experimental spectroscopic data for a total of 11 available isotopologues. The incorporation of rotational constants from all of these isotopologues and CCSD(T) corrections to address the impacts of both the vibration-rotation interaction and electron-mass distribution results in a highly precise and accurate reSE structure. The CCSD(T)/cc-pCV5Z optimized geometry has been further corrected to address a finite basis set, untreated electron correlation, relativistic effects, and a breakdown of the Born-Oppenheimer approximation. This analysis achieves outstanding agreement between the re (BTE) and reSE structural parameters of benzene to a highly satisfying level (0.0001 Å), an agreement that surpasses our recently published structures of the aforementioned nitrogen-substituted benzene analogues. The D6h geometry of benzene is now known to an unprecedented precision: RC-C = 1.3913 (1) Å and RC-H = 1.0809 (1) Å. The mutual agreement between theory and experiment presented in this work validates both, substantially resolving all discrepancies between the reSE and theoretical re structures available in the literature.

Chemical Bonding Perspective on Low-Lying SiC4H2 Isomers: Conceptual Quantum Chemical Views

The nature of the chemical bonding in seven low-lying isomers of SiC₄H₂ is analyzed through quantum chemical concepts. Out of the seven, four isomers, 1-ethynyl-3-silacycloprop-1(2)-en-3-ylidene (1), diethynylsilylidene (2), 1-sila-1,2,3,4-pentatetraenylidene (4), and 1,3-butadiynylsilylidene (5), have already been identified in the laboratory. The other three isomers, 2-methylenesilabicyclo[1.1.0]but-1(3)-en-4-ylidene (3), 4-sila-2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (6), and 3-ethynyl-1-silapropadienylidene (7) remain elusive in the laboratory to date (J. Phys. Chem. A, 2020, 124, 987-1002). Deep insight into the characteristics of chemical bonding is explored with different bonding analysis tools. Quantum theory of atoms in molecules (QTAIM), interaction quantum atoms analysis, natural bond orbital analysis, adaptive natural density partitioning, electron localization function (ELF), Laplacian of electron density, energy decomposition analysis, atomic charge analysis, bond order analysis, and frontier molecular orbital analysis are employed in the present work to gain a better understanding of the chemical bonding perspective in SiC₄H₂ isomers. Different quantum chemical topology approaches (QTAIM, ELF, and Laplacian of electron density) are employed to complement each other. The obtained results dictate that the lone pair of the silicon atom participate in delocalization and influences the structural stability of isomers.

Semi-experimental equilibrium (reSE) and theoretical structures of hydrazoic acid (HN3)

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure—specifically, a semi-experimental equilibrium structure ( r eSE)—may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration–rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCV XZ ( X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent r eSE structure determination. The r eSE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained r eSE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that r eSE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational r e structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding r eSE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born–Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation.

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.

Gas phase formation of c-SiC3 molecules in the circumstellar envelope of carbon stars

Complex organosilicon molecules are ubiquitous in the circumstellar envelope of the asymptotic giant branch (AGB) star IRC+10216, but their formation mechanisms have remained largely elusive until now. These processes are of fundamental importance in initiating a chain of chemical reactions leading eventually to the formation of organosilicon molecules-among them key precursors to silicon carbide grains-in the circumstellar shell contributing critically to the galactic carbon and silicon budgets with up to 80% of the ejected materials infused into the interstellar medium. Here we demonstrate via a combined experimental, computational, and modeling study that distinct chemistries in the inner and outer envelope of a carbon star can lead to the synthesis of circumstellar silicon tricarbide (c-SiC₃) as observed in the circumstellar envelope of IRC+10216. Bimolecular reactions of electronically excited silicon atoms (Si(¹D)) with allene (H₂CCCH₂) and methylacetylene (CH₃CCH) initiate the formation of SiC₃H₂ molecules in the inner envelope. Driven by the stellar wind to the outer envelope, subsequent photodissociation of the SiC₃H₂ parent operates the synthesis of the c-SiC₃ daughter species via dehydrogenation. The facile route to silicon tricarbide via a single neutral-neutral reaction to a hydrogenated parent molecule followed by photochemical processing of this transient to a bare silicon-carbon molecule presents evidence for a shift in currently accepted views of the circumstellar organosilicon chemistry, and provides an explanation for the previously elusive origin of circumstellar organosilicon molecules that can be synthesized in carbon-rich, circumstellar environments.

Combined Experimental and Theoretical Study on the Formation of the Elusive 2-Methyl-1-silacycloprop-2-enylidene Molecule under Single Collision Conditions via Reactions of the Silylidyne Radical (SiH; X(2)Π) with Allene (H2CCCH2; X(1)A1) and D4-Allene (D2CCCD2; X(1)A1)

The crossed molecular beam reactions of the ground-state silylidyne radical (SiH; X(2)Π) with allene (H2CCCH2; X(1)A1) and D4-allene (D2CCCD2; X(1)A1) were carried out at collision energies of 30 kJ mol(-1). Electronic structure calculations propose that the reaction of silylidyne with allene has no entrance barrier and is initiated by silylidyne addition to the π electron density of allene either to one carbon atom (C1/C2) or to both carbon atoms simultaneously via indirect (complex forming) reaction dynamics. The initially formed addition complexes isomerize via two distinct reaction pathways, both leading eventually to a cyclic SiC3H5 intermediate. The latter decomposes through a loose exit transition state via an atomic hydrogen loss perpendicularly to the plane of the decomposing complex (sideways scattering) in an overall exoergic reaction (experimentally: -19 ± 13 kJ mol(-1); computationally: -5 ± 3 kJ mol(-1)). This hydrogen loss yields the hitherto elusive 2-methyl-1-silacycloprop-2-enylidene molecule (c-SiC3H4), which can be derived from the closed-shell cyclopropenylidene molecule (c-C3H2) by replacing a hydrogen atom with a methyl group and the carbene carbon atom by the isovalent silicon atom. The synthesis of the 2-methyl-1-silacycloprop-2-enylidene molecule in the bimolecular gas-phase reaction of silylidyne with allene enriches our understanding toward the formation of organosilicon species in the gas phase of the interstellar medium in particular via exoergic reactions of no entrance barrier. This facile route to 2-methyl-1-silacycloprop-2-enylidene via a silylidyne radical reaction with allene opens up a versatile approach to form hitherto poorly characterized silicon-bearing species in extraterrestrial environments; this reaction class might represent the missing link, leading from silicon-bearing radicals via organosilicon chemistry eventually to silicon-carbon-rich interstellar grains even in cold molecular clouds where temperatures are as low as 10 K.

Rotational spectroscopy meets theory

Rotational spectroscopy is known to be a technique that is widely used to infer information on molecular structure and dynamics. In the last few decades, its role in the field of atmospheric and astrophysical investigations has rapidly grown. However, several are the challenging aspects in rotational spectroscopy, since the detection and analysis of spectra as well as interpretation of obtained results are not at all straightforward. Quantum chemistry has reached such an accuracy that can be used to disentangle these challenging situations by guiding the experimental investigation, assisting in the determination of the spectroscopic parameters, and extracting information of chemical interest. This perspective provides an overview of the theoretical background and computational requirements needed for the accurate evaluation of the spectroscopic parameters of relevance to rotational spectroscopy. The role of theory in guiding and supporting experiment is detailed through a few examples, and the interplay of experiment and theory is discussed in terms of the information of physical and chemical interest that can be derived.

Small carbides of third-row main group elements: structure and bonding in C3X compounds (X = K-Br)

The molecular structures of third-row main group tricarbides C(3)X (X = K-Br) have been studied by quantum chemical methods. It is found that less electronegative elements (K, Ca, Ga, Ge) favor either fan or rhombic structures (resulting from side interactions with either linear or triangular C(3) units), whereas the more electronegative elements (As, Se, Br) favor linear or three-membered ring structures (resulting from σ-type interactions with either linear or triangular C(3) units). The predicted global minima are of fan type for C(3)K, rhombic for C(3)Ca, C(3)Ga, and C(3)Ge, linear for C(3)As and C(3)Se, and a three-membered ring for C(3)Br. In order to aid in their possible experimental identification the molecular geometries, vibrational frequencies, IR intensities, and dipole moments have been provided. The nature of the interactions has been characterized through an analysis of the electronic charge density. In addition, the relative stability of the different isomers has been also rationalized in terms of an energy decomposition analysis.

Structures of molecules in ground and excited vibrational states from quasiclassical direct ab initio molecular dynamics

We demonstrate that the mean structures of molecules derived from quasiclassical direct ab initio molecular dynamics (MD) simulation, the classical simulation that takes into account quantum vibrational levels, agree well with those determined from quantum-mechanical (QM) expectation values and/or experimentally observed values. First, for a one-dimensional model potential that includes anharmonicity as the third-order potential energy term, we show that the time-averaged structure over the classical trajectory with taking account of a quantum vibrational energy level correlates with a QM structure averaged using a vibrational wave function based on the first-order perturbation theory. Next, quasiclassical direct ab initio MD and Fourier grid Hamiltonian method are applied to OH and OD radicals; the mean structures at several vibrational levels of both classical and QM methods coincide, and they are in good agreement with the structures determined experimentally. Quasiclassical direct ab initio MD is then applied to H(2)O, C(2)H(2), and C(6)H(6). For H(2)O and C(2)H(2), the classical mechanically calculated mean structural parameters agree well with the experimental values and the QM values obtained from vibrational self-consistent field. For C(2)H(2), we find that r(g)(C-H) is longer than r(e)(C-H), whereas r(mean)((0))(C-H), which is equal to r(z)(C-H), is slightly shorter than r(e)(C-H).

A theoretical study of the cyclization processes of energized CCCSi and CCCP

Calculations at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31+G(d) level of theory have shown that cyclization of both the ground state triplet and the corresponding singlet state of CCCSi may rearrange to give cyclic isomers which upon ring opening may reform linear C(3)Si isomers in which the carbon atoms are scrambled. The cyclization processes are energetically favorable with barriers to the transition states from 13 to 16 kcal mol(-1). This should be contrasted with the analogous process of triplet CCCC to triplet rhombic C(4), which requires an excess energy of 25.8 kcal mol(-1). A similar cyclization of doublet CCCP requires 50.4 kcal mol(-1) of excess energy; this should be contrasted with the same process for CCCN, which requires 54.7 kcal mol(-1) to effect cyclization.

Anharmonic vibrational levels of the two cyclic isomers of SiC3

Using coupled-cluster approach full six-dimensional analytic potential energy surfaces for two cyclic SiC(3) isomers [C-C transannular bond (I) and Si-C transannular bond (II)] have been generated and used to calculate anharmonic vibrational wave functions. Several strong low-lying anharmonic resonances have been found. In both isomers already some of the fundamental transitions cannot be described within the harmonic approximation. Adiabatic electron affinities and ionization energies have been calculated as well. The Franck-Condon factors for the photodetachment processes c-SiC(3) (-)(I)-->c-SiC(3)(I) and c-SiC(3) (-)(II)-->c-SiC(3)(II) are reported.

A systematic multireference perturbation-theory study of the low-lying states of SiC3

The three known lowest-energy isomers of SiC(3), two cyclic singlets (2s and 3s) and a linear triplet (1t), have been reinvestigated using multireference second-order perturbation theory (MRPT2). The dependence of the relative energies of the isomers upon the quality of the basis sets and the sizes of the reference active spaces is explored. When using a complete-active-space self-consistent-field reference wave function with 12 electrons in 11 orbitals [CASSCF (12, 11)] together with basis sets that increase in size up to the correlation-consistent polarized core-valence quadruple zeta basis set (cc-pCVQZ), the MRPT2 method consistently predicts the linear triplet to be the most stable isomer. A new parallel direct determinant MRPT2 code has been used to systematically explore reference spaces that vary in size from CASSCF (8,8) to full optimized reaction space [FORS or CASSCF (16,16)] with the cc-pCVQZ basis. It is found that the relative energies of the isomers change substantially as the active space is increased. At the best level of theory, MRPT2 with a full valence FORS reference, the 2s isomer is predicted to be more stable than 3s and 1t by 4.7 and 2.2 kcal/mol, respectively.

Rotational spectroscopy and equilibrium structures of S3 and S4

The sulfur molecules thiozone S3 and tetrasulfur S4 have been observed in a supersonic molecular beam in the centimeter-wave band by Fourier transform microwave spectroscopy, and in the millimeter- and submillimeter-wave bands in a low-pressure glow discharge. For S3 over 150 rotational transitions between 10 and 458 GHz were measured, and for S4 a comparable number between 6 and 271 GHz. The spectrum of S3 is reproduced to within the measurement uncertainties by an asymmetric top Hamiltonian with three rotational and 12 centrifugal distortion constants; ten distortion constants, but an additional term to account for very small level shifts caused by interchange tunneling, are required to reproduce to comparable accuracy the spectrum of S4. Empirical equilibrium (r(e)(emp)) structures of S3 and S4 were derived from experimental rotational constants of the normal and sulfur-34 species and vibrational corrections from coupled-cluster theory calculations. Quantum chemical calculations show that interchange tunneling occurs because S4 automerizes through a transition state with D2h symmetry which lies about 500 cm(-1) above the two equivalent C2upsilon minima on the potential energy surface.

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.