Semi-experimental Equilibrium Research Articles

High-Resolution Spectroscopy and Structure of Heavy Carbon Subchalcogenides: Tricarbon Selenide, C3Se.

Linear tricarbon selenide, C3Se, has been studied spectroscopically for the first time using a combination of high-resolution infrared and microwave techniques. Probing laser ablation products from carbon-selenium targets in a free jet expansion with He, initial spectroscopic detection was accomplished in the infrared at a wavelength of 5 μm in search of the ν1 vibrational fundamental. Along with the band of the most abundant isotopic species C380Se found centered at about 2039 cm-1, the corresponding bands of the C382Se, C378Se, C376Se, and C377Se isotopologues were also detected. Pure rotational spectra of the five C3Se isotopologues in the 8-18 GHz frequency range were observed in a supersonic jet expansion using chirped-pulse microwave spectroscopy of the discharge products of selenophene, c-C4H4Se. Spectroscopic analyses were guided by results from high-level quantum-chemical calculations carried out at the coupled-cluster level of theory using large correlation-consistent basis sets. Using the experimentally derived ground-state rotational constants of five isotopologues and calculated zero-point vibrational corrections, an accurate semiexperimental equilibrium carbon-selenium bond length is derived.

Accurate Geometries of Large Molecules at DFT Cost by Semiexperimental and Coupled Cluster Templating Fragments.

Accurate geometries of small semirigid molecules in the gas phase are available thanks to high-resolution spectroscopy and accurate quantum chemical approaches. These results can be employed for validating cheaper low-level quantum chemical models or correcting the corresponding structures of large molecules. On these grounds, in this work, a large panel of semiexperimental equilibrium structures already available in the literature is used to confirm the average error (1 mÅ for bond lengths and 2 mrad for valence angles) of a version of the Pisa composite schemes (PCS2), which is applicable to molecules containing up to about 20 atoms. Then, the geometries of 30 additional medium-sized systems were optimized at the PCS2 level to cover a more balanced chemical space containing moieties poorly represented in SE compilations. The final database is available on a public domain Web site (https://www.skies-village.it/databases/) and can be employed for correcting structures of larger molecules obtained by hybrid or double-hybrid density functionals in the framework of the templating molecule approach. Several examples show that corrections based on the structures of building blocks taken from this database reduce the error of the B3LYP geometrical parameters of large molecules by nearly an order of magnitude without increasing the computational cost. Furthermore, the results of different density functional theory (DFT) or wave function (e.g., MP2) models can be improved in the same way by simply computing both the whole molecule and suitable building blocks at the chosen level. Then, whenever reference structures of some building blocks containing up to about 20 atoms are not available, they can be purposely optimized at the PCS2 level by employing reasonable computer resources. Therefore, a new DFT-cost tool is now available for the accurate characterization of large molecules by experiment-oriented scientists.

Conformational Landscapes of 2,3-, 2,4-, 2,5-, and 2,6-Difluorobenzaldehyde Unveiled by Rotational Spectroscopy.

We report the coexistence of anti-conformers and energetically unfavorable syn-conformers of 2,3-, 2,4-, 2,5-, and 2,6-difluorobenzaldehyde in the gas phase using broadband chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy. The rotational spectra of monosubstituted 13C isotopologues of the anti-conformers have also been assigned in natural abundance, which were used to derive their vibrationally averaged geometries and semi-experimental equilibrium structures. The energy differences between anti- and syn-conformations are estimated to be 10.9, 11.3, and 12.9 kJ/mol for 2,3-, 2,4-, and 2,5-difluorobenzaldehyde, respectively, at the theoretical level of DLPNO-CCSD(T)/def2-TZVP. Despite the steric repulsion caused by the close proximity between the oxygen atom of the aldehyde group and the ortho-substituted fluorine atom, our experimental results indicate the planarity of the syn-conformations. The frequencies of the large amplitude torsion between the phenyl and aldehyde groups have been estimated by experimental inertial defects, which agree with theoretical calculation results.

Structure determination of 2,5-difluorophenol by microwave spectroscopy

The Fourier transform microwave spectrum of 2,5-difluorophenol has been obtained in the centimeter wave range, revealing only one conformer stabilized by an intramolecular interaction where the hydrogen atom of the OH group is in a syn orientation to the fluorine atom at the 2-ring position. The heavy atom backbone structure was obtained from the rotational constants of the 13C and 18O isotopologues whose spectra were measured in natural abundance. The spectrum of the OD isotopologue obtained by deuterium enrichment was also measured, and the nuclear quadrupole hyperfine structures arising from deuterium were analyzed. The semi-experimental equilibrium structure (reSE) was determined by correcting the experimental rotational constants with the vibration-rotation interaction constants obtained via an anharmonic force field. Quantum chemical calculations at various levels of theory were used to support results from the experiments.

Tracing Prebiotic Molecules: Rotational Spectroscopy of Deuterated Glycolaldehyde and (Z)-1,2-Ethenediol.

Glycolaldehyde, an important prebiotic molecule, along with its monodeuterated species and its higher energy tautomer, (Z)-1,2-ethenediol, has been detected in the interstellar medium. Although the elemental D/H ratio in the universe is only ∼1.6 × 10-5, the deuterium relative abundance in interstellar molecules might be by far larger than this. As such, it provides a remarkable and almost unique diagnostic tool. In particular, it might help elucidate the reaction mechanisms that lead to the formation of the so-called complex organic molecules. It is therefore crucial to extend the census of the interstellar deuterated molecules. To this aim, in this work, we present for the first time a spectroscopic investigation of the rotational spectra of the CHDOD-CHO bideuterated variant of glycolaldehyde and of mono- and bideuterated species of (Z)-1,2-ethenediol (CHOD═CHOD, CHOD═CHOH, and CHOH═CHOD rotamers). For each species, more than a hundred transitions have been assigned. Their analysis led to the accurate determination of all rotational constants as well as quartic and sextic centrifugal distortion terms, thus providing spectroscopic line catalogs suitable for supporting astronomical searches. In addition, the rotational constants of the bideuterated glycolaldehyde isotopologue studied in this work allowed us to improve the semiexperimental equilibrium structure determination for this molecule.

Millimeter-wave and high-resolution infrared spectroscopy of the low-lying vibrational states of pyridazine isotopologues.

The gas-phase rotational spectrum from 8 to 750GHz and the high-resolution infrared (IR) spectrum of pyridazine (o-C4H4N2) have been analyzed for the ground and four lowest-energy vibrationally excited states. A combined global fit of the rotational and IR data has been obtained using a sextic, centrifugally distorted-rotor Hamiltonian with Coriolis coupling between appropriate states. Coriolis coupling has been addressed in the two lowest-energy coupled dyads (ν16, ν13 and ν24, ν9). Utilizing the Coriolis coupling between the vibrational states of each dyad and the analysis of the IR spectrum for ν16 and ν9, we have determined precise band origins for each of these fundamental states: ν16 (B1) = 361.213 292 7 (17) cm-1, ν13 (A2) = 361.284 082 4 (17) cm-1, ν24 (B2) = 618.969 096 (26) cm-1, and ν9 (A1) = 664.723 378 4 (27) cm-1. Notably, the energy separation in the ν16-ν13 Coriolis-coupled dyad is one of the smallest spectroscopically measured energy separations between vibrational states: 2122.222 (72) MHz or 0.070 789 7 (24) cm-1. Despite ν13 being IR inactive and ν24 having an impractically low-intensity IR intensity, the band origins of all four vibrational states were measured, showcasing the power of combining the data provided by millimeter-wave and high-resolution IR spectra. Additionally, the spectra of pyridazine-dx isotopologues generated for a previous semi-experimental equilibrium structure (reSE) determination allowed us to analyze the two lowest-energy vibrational states of pyridazine for all nine pyridazine-dx isotopologues. Coriolis-coupling terms have been measured for analogous vibrational states across seven isotopologues, both enabling their comparison and providing a new benchmark for computational chemistry.

Unlocking a new hydrogen-bonding marker: C-O bond shortening in vicinal diols revealed by rotational spectroscopy.

The conformational space of cis-1,2-cyclohexanediol, a model molecule for cyclic vicinal diols, was investigated using rotational spectroscopy and density functional theory calculations. Four low energy conformers within an energy window of 5 kJ mol-1 were identified computationally. A rotational spectrum of jet-cooled cis-1,2-cyclohexanediol was recorded with a chirped pulse Fourier transform microwave spectrometer. Two sets of rotational transitions were observed and could be assigned to conformers of cis-1,2-cyclohexanediol. The non-observation of other low energy conformers was explained by conformational conversion barrier height calculations and results from experimental spectra recorded with different carrier gases. Eight isotopologues, including those with 13C and 18O, of the lowest energy conformer were observed, allowing the determination of the semi-experimental equilibrium structure, reSE. Interestingly, the structural analysis revealed that the C-O bond length of the intramolecular hydrogen-bond donor is shorter than that of the acceptor. This appears to be a general characteristic of vicinal diols and can be used as a novel hydrogen-bond marker in such compounds.

On the performance of composite schemes in determining equilibrium molecular structures.

Determination of equilibrium molecular structures is an essential ingredient in predicting spectroscopic parameters that help in identifying molecular carriers of microwave transitions. Here, the performance of two different ab initio composite approaches for obtaining equilibrium structures, "energy scheme" and "geometry scheme," is explored and compared to semi-experimental equilibrium structures. This study is performed for a set of 11 molecules which includes diatomics, linear triatomics, and a few non-linear molecules. The ab initio calculations were performed using three tiers of composite chemical recipes. The current results show that as the overall rigor of calculation is increased, the semi-experimental and the ab initio numbers agree to within 0.0003 Å for all molecules in the test set. The composite approach based on correcting the potential energy surface (energy scheme) and the one based on correcting the geometry directly (geometry scheme) show excellent agreement with each other. This work represents a step toward development of efficient and highly accurate procedures for computing ab initio equilibrium structures.

Rotational detection of the silicon-carbon chains H2C3Si and HSiCCH

The rotational spectra of two new silicon-bearing carbon chains, H2C3Si and HSiCCH have been detected by means of Fourier-transform microwave spectroscopy in a supersonic jet source equipped with an electrical discharge. On the basis of measurements between 10 and 42GHz, precise spectroscopic constants have been determined for both molecules. Along with H29SiCCH and H30SiCCH, which were detected in natural abundance, several other rare isotopic species of HSiCCH were observed using samples enriched in carbon-13 and D. From this isotopic data, a precise semi-experimental equilibrium structure was derived and compared with a re-evaluated semi-experimental equilibrium structure of the parent silylene SiH2; the deuterium isotopic measurements also provide important clues as to the formation pathway of HSiCCH in our discharge. Because other small Si-bearing chains have been detected in the circumstellar envelope of the evolved carbon star IRC+10216, both chains may be of astronomical interest.

Direct Probes of π-Delocalization in Prototypical Resonance-Stabilized Radicals: Hyperfine-Resolved Microwave Spectroscopy of Isotopic Propargyl and Cyanomethyl.

Delocalization of the unpaired electron in π-conjugated radicals has profound implications for their chemistry, but direct and quantitative characterization of this electronic structure in isolated molecules remains challenging. We apply hyperfine-resolved microwave rotational spectroscopy to rigorously probe π-delocalization in propargyl, CH2CCH, a prototypical resonance-stabilized radical and key reactive intermediate. Using the spectroscopic constants derived from the high-resolution cavity Fourier transform microwave measurements of an exhaustive set of 13C- and 2H-substituted isotopologues, together with high-level ab initio calculations of zero-point vibrational effects, we derive its precise semiexperimental equilibrium geometry and quantitatively characterize the spatial distribution of its unpaired electron. Our results highlight the importance of considering both spin-polarization and orbital-following contributions when interpreting the isotropic hyperfine coupling constants of π radicals. These physical insights are strengthened by a parallel analysis of the isoelectronic species cyanomethyl, CH2CN, using new 13C measurements also reported in this work. A detailed comparison of the structure and electronic properties of propargyl, cyanomethyl, and other closely related species allows us to correlate trends in their chemical bonding and electronic structure with critical changes in their reactivity and thermochemistry.

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.

Structural and electronic trends of optical cycling centers in polyatomic molecules revealed by microwave spectroscopy of MgCCH, CaCCH, and SrCCH

The unique optical cycling efficiency of alkaline earth metal-ligand molecules has enabled significant advances in polyatomic laser cooling and trapping. Rotational spectroscopy is an ideal tool for probing the molecular properties that underpin optical cycling, thereby elucidating the design principles for expanding the chemical diversity and scope of these platforms for quantum science. We present a comprehensive study of the structure and electronic properties in alkaline earth metal acetylides with high-resolution microwave spectra of 17 isotopologues of MgCCH, CaCCH, and SrCCH in their 2Σ+ ground electronic states. The precise semiexperimental equilibrium geometry of each species has been derived by correcting the measured rotational constants for electronic and zero-point vibrational contributions calculated with high-level quantum chemistry methods. The well-resolved hyperfine structure associated with the 1,2H, 13C, and metal nuclear spins provides further information on the distribution and hybridization of the metal-centered, optically active unpaired electron. Together, these measurements allow us to correlate trends in chemical bonding and structure with the electronic properties that promote efficient optical cycling essential to next-generation experiments in precision measurement and quantum control of complex polyatomic molecules.

Improved semi-experimental equilibrium structure and high-level theoretical structures of ketene.

The millimeter-wave rotational spectrum of ketene (H2C=C=O) has been collected and analyzed from 130 to 750GHz, providing highly precise spectroscopic constants from a sextic, S-reduced Hamiltonian in the Ir representation. The chemical synthesis of deuteriated samples allowed spectroscopic measurements of five previously unstudied ketene isotopologues. Combined with previous work, these data provide a new, highly precise, and accurate semi-experimental (reSE) structure for ketene from 32 independent moments of inertia. This reSE structure was determined with the experimental rotational constants of each available isotopologue, together with computed vibration-rotation interaction and electron-mass distribution corrections from coupled-cluster calculations with single, double, and perturbative triple excitations [CCSD(T)/cc-pCVTZ]. The 2σ uncertainties of the reSE parameters are ≤0.0007 Å and 0.014° for the bond distances and angle, respectively. Only S-reduced spectroscopic constants were used in the structure determination due to a breakdown in the A-reduction of the Hamiltonian for the highly prolate ketene species. All four reSE structural parameters agree with the "best theoretical estimate" (BTE) values, which are derived from a high-level computed re structure [CCSD(T)/cc-pCV6Z] with corrections for the use of a finite basis set, the incomplete treatment of electron correlation, relativistic effects, and the diagonal Born-Oppenheimer breakdown. In each case, the computed value of the geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The discrepancies between the BTE structure and the reSE structure are 0.0003, 0.0000, and 0.0004 Å for rC-C, rC-H, and rC-O, respectively, and 0.009° for θC-C-H.

Barrier to Methyl Internal Rotation and Equilibrium Structure of 2-Methylthiophene Determined by Microwave Spectroscopy

The microwave spectrum of 2-methylthiophene was recorded in a frequency range from 2 to 26.5 GHz using a molecular-jet Fourier transform microwave spectrometer with a Fabry–Pérot type resonator chamber and coaxial arrangement of the resonator and the molecular beam. Measuring and assigning spectra of the 34S and 13C isotopologues allowed the determination of the semiexperimental equilibrium structure (reSE). Comparing the structure to that of thiophene revealed a decrease in the ∠(S−C2−C3) angle from 111.595(6)° to 111.37(1)° by addition of the methyl group to the C(2) position, as well as an increase in the S−C2 bond length from 1.7102(1) Å to 1.7219(2) Å. A–E splittings from internal rotation of the methyl group were observed, and the V3 potential in the vibrational ground state was determined to be 197.7324(18) cm−1. The V3 value and the rotational constants A, B, C were calculated with a large number of different methods and basis sets for benchmarking purposes by comparing them to the fitted parameters. The V3 value was also compared to those of other thiophene and furan derivatives to gain a better understanding of the steric and electrostatic effects in these classes of compounds.

Accurate equilibrium structures of some challenging molecules: FNO, ClNO, HONO, FNO2, and N2O

It is sometimes difficult to determine the structure of some molecules because the optimization using standard ab initio methods (coupled-cluster with single, double, and perturbative triples [CCSD(T)] level) does not give the correct result and the experimental and semiexperimental methods are not accurate because the system of normal equations of the least-squares method is ill-conditioned. In such a case, it may be still possible to derive an accurate equilibrium structure in the following way: the experimental rotational constants are compared to those obtained at the CCSD(T) level, the latter being corrected to take into account the rovibrational correction (and, if necessary, the electronic correction). Extrapolating (or interpolating) the rotational constants calculated with different basis sets (e.g. cc-pwCVTZ and cc-pwCVQZ) towards the experimental values as a function of the bond lengths and angles permits to obtain an accurate equilibrium structure. This method is first tested on two molecules for which the multireference effects are important: O3 and HOON. It is then, applied to molecules with a weak N–X bond (HONO, FNO, ClNO, FNO2, and N2O) for which the single reference CCSD(T) method gives bonds that are too short. The results are compared to the experimental and semiexperimental equilibrium structures. As a further check, the structure of ClNO is calculated at the CCSDTQ level and the structures of FNO and ClNO are calculated at the MRCI-F12 level. From a comparison of the different results, it appears that the accuracy of the proposed method is better than 0.002 Å for the bond lengths and 0.3° for the angles.

Microwave spectrum, structure, and dipole moment of 2-fluorophenylacetylene

The rotational spectra of the parent and eight 13C isotopomers of 2-fluorophenylacetylene were measured using chirped-pulsed Fourier-transform microwave spectroscopy in the frequency range 6–18 GHz. The rotational constants for the parent isotopomer were determined to be A0 = 2949.41825(17) MHz, B0 = 1495.78081(13) MHz, and C0 = 992.23008(9) MHz. The total dipole moment was determined to be 1.720(2) Debye from Stark measurements. The molecular geometry parameters were obtained experimentally using Kraitchman substitution and semi-experimental equilibrium structure. These structural parameters and dipole moments were compared with the data calculated at the B3LYP/6-311+G(2d,p) level and analyzed using the natural bond orbital method.

Rotational spectra of singly substituted rare isotopologues of two conformers of 3,3,3-trifluoropropanol

The conformational distribution and the associated conformational conversion paths of 3,3,3-trifluoropropanol (TFP) were explored experimentally and theoretically using jet-cooled chirped pulse and cavity Fourier transform microwave spectroscopy in tandem with quantum chemical calculations. Rotational spectra of two TFP conformers, as well as their singly substituted 13C, 18O, and OD isotopologues, were measured and analyzed. The semi-experimental equilibrium rotational constants of the two conformers were also extracted for all isotopologues using the anharmonic calculations and used to obtain the semi-experimental equilibrium geometries.

Precise equilibrium structures of 1H- and 2H-1,2,3-triazoles (C2H3N3) by millimeter-wave spectroscopy.

The 1H- and 2H-1,2,3-triazoles are isomeric five-membered ring, aromatic heterocycles that may undergo chemical equilibration by virtue of intramolecular hydrogen migration (tautomerization). Using millimeter-wave spectroscopy in the 130-375GHz frequency range, we measured the spectroscopic constants for thirteen 1H-1,2,3-triazole and sixteen 2H-1,2,3-triazole isotopologues. Herein, we provide highly accurate and highly precise semi-experimental equilibrium (re SE) structures for the two tautomers based on the spectroscopic constants of each set of isotopologues, together with vibration-rotation interaction and electron-mass distribution corrections calculated using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The resultant structures are compared with a "best theoretical estimate" (BTE), which has recently been shown to be in exceptional agreement with the semi-experimental equilibrium structures of other aromatic molecules. Bond distances of the 1H tautomer are determined to <0.0008 Å and bond angles to <0.2°. For the 2H tautomer, bond angles are also determined to <0.2°, but bond distances are less precise (2σ ≤ 0.0015). Agreement between BTE and re SE values is discussed.

Semi-experimental equilibrium (re SE) 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 (re SE)-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-pCVXZ (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 re SE structure determination. The re SE 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 re SE 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 re SE 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 re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding re SE 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.

Effective and equilibrium structures of XYn-type molecules: SCl2, PF2, PO2, ZrO2, and CF2S as additional example and nonbonded distances F…F, Cl…Cl and O…O

When the effective structure (r0) of a molecule can be determined without isotopic substitution, as for the XYn molecules, it is possible to correct this structure using an offset in order to obtain a good approximation of the equilibrium structure (re). The r0 – re offsets are (in Å) 0.0025(12) for a bond between two heavy atoms, 0.0084(9) for a bond between a heavy atom and hydrogen, and 0.0058(7) for a bond between a heavy atom and deuterium. For the bond angles, the offset is: ∠0 – ∠e = 0.22(4) degree. This empirical method is used to estimate the equilibrium structures of SCl2, PF2, PO2 and ZrO2. The obtained structures are found in good agreement with newly determined semiexperimental equilibrium structures. Finally, this empirical method is applied to a larger set of molecules to determine equilibrium nonbonded distances F…F, Cl…Cl, and O…O. An accurate equilibrium structure is determined for CF2S.