Semi-experimental Equilibrium Structure Research Articles

Semi-Experimental Equilibrium (reSE) and Theoretical Structures of Pyridazine (o-C4H4N2).

A semi-experimental equilibrium structure (reSE) of pyridazine (o-C4H4N2) has been determined using the rotational spectra of 18 isotopologues. Spectroscopic constants of four isotopologues are reported for the first time (measured from 235 to 360 GHz), while spectroscopic constants for previously reported isotopologues are improved by extending the frequency coverage (measured from 130 to 375 GHz). The experimental values of the ground-state rotational constants (A0, B0, and C0) from each isotopologue were converted to determinable constants (A0″, B0″, and C0″), which were then corrected for the effects of vibration-rotation interactions and electron-mass distributions using CCSD(T)/cc-pCVTZ calculations. The resultant reSE for pyridazine determines bond distances to within 0.001 Å and bond angles within 0.04°, a reduction in the statistical uncertainties by at least a factor of two relative to the previously reported reSE. The improvement in precision appears to be largely due to the use of higher-level theoretical calculations of the vibration-rotation and electron-mass effects, though the incorporation of the newly measured isotopologues ([4-2H, 4-13C]-, [4-2H, 5-13C]-, [4-2H, 6-13C]-, and [4,5-2H, 4-13C]-pyridazine) is partially responsible for the improved determination of the hydrogen-containing bond angles. The computed equilibrium structure (re) (CCSD(T)/cc-pCV5Z) and a "best theoretical estimate" of the equilibrium structure (re) both agree with the updated reSE structure within the statistical experimental uncertainty (2σ) of each structural parameter.

Precise equilibrium structure of thiazole (c-C3H3NS) from twenty-four isotopologues.

The pure rotational spectrum of thiazole (c-C3H3NS, Cs) has been studied in the millimeter-wave region from 130 to 375GHz. Nearly 4800 newly measured rotational transitions for the ground vibrational state of the main isotopologue were combined with previously reported measurements and least-squares fit to a complete sextic Hamiltonian. Transitions for six singly substituted heavy-atom isotopologues (13C, 15N, 33S, 34S) were observed at natural abundance and likewise fit. Several deuterium-enriched samples were prepared, which gave access to the rotational spectra of 16 additional isotopologues, 14 of which had not been previously studied. The rotational spectra of each isotopologue were fit to A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The experimental values of the ground-state rotational constants (A0, B0, and C0) from each isotopologue were converted to determinable constants (A0″, B0″, and C0″), which were corrected for effects of vibration-rotation interactions and electron-mass distributions using coupled-cluster singles, doubles, and perturbative triples calculations [CCSD(T)/cc-pCVTZ]. The moments of inertia from the resulting constants (Ae, Be, and Ce) of 24 isotopologues were used to determine the precise semi-experimental equilibrium structure (re SE) of thiazole. As a basis for comparison, a purely theoretical equilibrium structure was estimated by an electronic structure calculation [CCSD(T)/cc-pCV5Z] that was subsequently corrected for extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born-Oppenheimer correction. The precise re SE structure is compared to the resulting "best theoretical estimate" structure. Some, but not all, of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the re SE results. The possible origin of the discrepancies between the best theoretical estimate re and semi-empirical re SE structures is discussed.

Determination of the "Privileged Structure" of 8-Hydroxyquinoline.

An accurate semi-experimental equilibrium structure of 8-hydroxyquinoline (8-HQ) has been determined combining experiment and theory. The cm-wave rotational spectrum of 8-HQ was recorded in a pulsed supersonic jet using broadband dual-path reflection and narrowband Fabry-Perot-type resonator Fourier-transform microwave spectrometers. Accurate rotational and quartic centrifugal distortion constants and 14 N quadrupole coupling constants are determined. Rotational constants of all 13 C, 18 O and 15 N singly substituted isotopologues in natural abundance and those of a chemically synthesized OD isotopologue were used to obtain geometric parameters for all the heavy atoms and the hydroxyl hydrogen from a number of structure determination models. Theoretical approaches allowed for the determination of a semi-experimental equilibrium structure, in which computed rovibrational and electronic corrections were utilized to convert vibrational ground state constants into equilibrium constants. Despite the molecule having only a horizontal plane of symmetry and possessing 11 individual heavy atoms, microwave spectroscopy has allowed for a reliable and accurate structure determination. A mass dependent, structure was determined and proved to be equally reliable by comparison with the B3LYP-D3(BJ)/aVTZ equilibrium structure.

Accuracy of the equilibrium structure of sulphur dioxide

The ground state rotational spectra of 12 different isotopologues of sulphur dioxide have been refitted in a consistent way and an accurate experimental cubic force field has been determined. The experimental, semi-experimental and ab initio equilibrium structures have been calculated and found in good agreement across themselves. Different approximations limiting the accuracy are discussed. In particular, the influence of centrifugal distortion is analysed. A method is proposed to estimate the higher-order rovibrational corrections (γ-constants). Although an accurate semi-experimental structure was obtained for 19 isotopologues, it was not possible to determine and account for the breakdown of the Born–Oppenheimer approximation. Finally, it was shown that the ab initio CCSDTQ level of theory was required to obtain a good agreement with the experimental structure.

Precise equilibrium structure determination of thiophene (c-C4H4S) by rotational spectroscopy-Structure of a five-membered heterocycle containing a third-row atom.

The rotational spectrum of thiophene (c-C4H4S) has been collected between 8 and 360GHz. Samples of varying deuterium-enrichment were synthesized to yield all possible deuterium-substituted isotopologues of thiophene. A total of 26 isotopologues have been measured and least-squares fit using A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The resultant rotational constants (A0, B0, and C0) from each reduction were converted to determinable constants (A″, B″, and C″) to remove the impact of centrifugal distortion. The computed vibrational and electron mass corrections [CCSD(T)/cc-pCVTZ] were applied to the determinable constants to obtain semi-experimental equilibrium rotational constants (Ae, Be, and Ce) for 24 isotopologues. A precise semi-experimental equilibrium (re SE) structure has been achieved from a least-squares fit of the equilibrium moments of inertia. The combination of the expanded isotopologue rotational data with high-level computational work establishes a precise re SE structure for this sulfur-containing heterocycle. The CCSD(T)/cc-pCV5Z structure has been obtained and corrected for the extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born-Oppenheimer correction. The precise re SE structure is compared to the resulting "best theoretical estimate" structure. Several of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the re SE results. The possible origin of the discrepancies for the computed parameters that fall outside the statistical uncertainties is discussed.

How accurate is the determination of equilibrium structures for van der Waals complexes? The dimer N2O⋯CO as an example.

Plausible methods for accurate determination of equilibrium structures of intermolecular clusters have been assessed for the van der Waals dimer N2O⋯CO. In order to assure a large initial dataset of rotational parameters, we first measured the microwave spectra of the 15N2O⋯12CO and 15N2O⋯13CO isotopologs, expanding previous measurements. Then, an anharmonic force field was calculated ab initio and a semi-experimental equilibrium structure was determined. The dimer structure was also calculated at the coupled-cluster level of theory using very large basis sets with diffuse functions and counterpoise correction. It was found that the contributions of the diffuse functions and the counterpoise correction are not additive and do not compensate each other although they have almost the same value but opposite signs. The semi-experimental and ab initio structures were found to be in fair agreement, with the equilibrium distance between the centers of mass of both monomers being 3.825(13) Å and the intermolecular bond length r(C⋯O) = 3.300(9) Å. In this case, the mass-dependent method did not permit us to determine reliable intermolecular parameters. The combination of experimental rotational constants and results of ab initio calculations thus proves to be very sensitive to examine the accuracy of structural determinations in intermolecular clusters, offering insight into other aggregates.

Molecular structure determination: Equilibrium structure of pyrimidine (m-C4H4N2) from rotational spectroscopy (re SE) and high-level ab initio calculation (re) agree within the uncertainty of experimental measurement.

The pure rotational spectrum of pyrimidine (m-C4H4N2), the meta-substituted dinitrogen analog of benzene, has been studied in the millimeter-wave region from 235 GHz to 360 GHz. The rotational spectrum of the ground vibrational state has been assigned and fit to yield accurate rotational and distortion constants. Over 1700 distinct transitions were identified for the normal isotopologue in its ground vibrational state and least-squares fit to a partial sextic S-reduced Hamiltonian. Transitions for all four singly substituted 13C and 15N isotopologues were observed at natural abundance and were likewise fit. Deuterium-enriched samples of pyrimidine were synthesized, giving access to all eleven possible deuterium-substituted isotopologues, ten of which were previously unreported. Experimental values of rotational constants and computed values of vibration-rotation interaction constants and electron-mass corrections were used to determine semi-experimental equilibrium structures (re SE) of pyrimidine. The re SE structure obtained using coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] corrections shows exceptional agreement with the re structure computed at the CCSD(T)/cc-pCV5Z level (≤0.0002 Å in bond distance and ≤0.03° in bond angle). Of the various computational methods examined, CCSD(T)/cc-pCV5Z is the only method for which the computed value of each geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The exceptionally high accuracy and precision of the structure determination is a consequence of the large number of isotopologues measured, the precision and extent of the experimental frequency measurements, and the sophisticated theoretical treatment of the effects of vibration-rotation coupling and electron mass. Taken together, these demanding experimental and computational studies establish the capabilities of modern structural analysis for a prototypical monocyclic aromatic compound.

The challenging equilibrium structure of HSSH: Another success of the rotational spectroscopy / quantum chemistry synergism

The simplest molecule with a disulfide bond, hydrogen disulfide (HSSH), represents an ideal test model for the determination of accurate gas-phase equilibrium structures for molecules containing third-row elements. First, pure theoretical composite schemes based on the coupled-cluster (CC) theory, which take into account the extrapolation to the complete basis set limit, core-valence correlation contributions, higher excitations in the CC expansion, and relativistic effects, allow for calculating accurate reference geometrical parameters. Second, using experimental vibrational ground-state rotational constants for a set of isotopologues, in conjunction with vibrational corrections based on second-order vibrational perturbation theory formulation and the recently developed Molecular Structure Refinement (MSR) software, we have determined the semi-experimental (SE) equilibrium structure of HSSH. The comparison of SE parameters with the computational best estimates shows an agreement within 0.001 Å for distances and 0.1° for angles, thus further validating the SE approach as cost-effective, provided that the required experimental data are available. Together with the intrinsic interest of HSSH, also in connection with astrochemistry, highly accurate structural properties of a prototypical disulfide bond can serve as references for future studies of larger molecules of biological interest containing this challenging moiety.

The heavy atom substitution and semi-experimental equilibrium structures of 2-ethylfuran obtained by microwave spectroscopy

The substitution rs and semi-experimental equilibrium reSE structures of the two conformers of 2-ethylfuran were obtained using a combination of microwave spectroscopy and quantum chemistry. The microwave spectrum was recorded using a molecular jet Fourier-transform spectrometer operating in the frequency range of 2.0 GHz–26.5 GHz. The spectra of all 13C and 18O isotopologues of both conformers could be measured in their natural abundances and the experimental gas-phase heavy atom structures were determined. All spectra were fitted using a semi-rigid rotor model including centrifugal distortion correction. The molecular geometries were compared with those of related molecules within the frame of the current literature. This work indicated that in some cases, the time required for recording survey scans of a Fourier-transform resonator setup can be reduced significantly with supports from adequate quantum chemical methods and spectral analysis skill.

Accuracy of semiexperimental equilibrium structures: Sulfine as an example

The Born-Oppenheimer ab initio equilibrium structure of sulfine, CH2SO, was computed at the CCSD(T) level of theory using basis sets up to quintuple zeta quality. The semiexperimental equilibrium structure was also determined from the ground state rotational constants and different anharmonic force fields. The factors affecting the accuracy and the precision of this semiexperimental structure were investigated. It was found that the accuracy of the structure, contrary to its precision (i.e. the standard deviations of the structural parameters), is not sensitive to the quality of the force field (B3LYP, B2PLYPD3 and MP2) and to neglecting of the centrifugal or electronic corrections.

Determination of a semi-experimental equilibrium structure of 1-phosphapropyne from millimeter-wave spectroscopy of [formula omitted] and [formula omitted

Trideuterated 1-phosphapropyne (CD3CP) has been produced by co-pyrolysis of phosphorus trichloride and esadeuterated ethane. The rotational spectra of CD3CP in the ground and the low-lying vibrational states v8 (CCP bending mode) and 2 v8 have been investigated in the millimeter-wave region. Very accurate values of the quartic centrifugal distortion constants DJ and DJK and of the sextic distortion constants HJK and HKJ have been obtained for the ground state. l-type resonance effects have been taken into account in the analysis of the spectra of the degenerate bending states, so that the energy difference between the v8|l| = 20, and v8|l| = 22 states could be determined, together with a number of spectroscopic constants involved in the l-type resonance. Moreover, for the parent isotopologue CH3CP a new set of excited-state lines (v8 = 1, 2 and v4 = 1) were recorded up to 330 GHz, and a global analysis including all available rotational and rovibrational transitions related to the ground and v8 = 1, 2 states has been performed. A satisfactory fit could only be obtained by making a reassignment of the few transition wavenumbers previously measured for the 2ν80←ν8±1 hot band [M.K. Bane et al., J. Mol. Spectrosc.275 (2012) 9–14].The experimental work has been combined with quantum-chemical computations. Quadratic and cubic force constants of 1-phosphapropyne have been calculated at MP2 level of theory with a basis set of triple-ζ quality. A semi-experimental equilibrium structure has been derived by correcting experimental ground-state rotational constants by means of theoretical vibration-rotation interaction constants.

The Unexplored World of Cycloalkene-Water Complexes: Primary and Assisting Interactions Unraveled by Experimental and Computational Spectroscopy.

The intermolecular interactions in cycloalkene-water adducts were computationally characterized, thus demonstrating that the primary O-H⋅⋅⋅πC=C hydrogen bond is dominated by the electrostatic interaction. A deeper investigation by means of a joint rotational spectroscopy/state-of-the-art quantum chemistry approach also led to the determination of an accurate semi-experimental equilibrium structure for the cyclopentene adduct.

Bond Length Alternation Observed Experimentally: The Case of 1H-Indazole.

Bond length alternation is a chemical phenomenon in benzene rings fused to other rings, which has been mainly predicted theoretically. Its physical origin is still not clear and has generated discussion. Here, by using a strategy that combines microwave spectroscopy, custom-made synthesis and high-level ab initio calculations, we demonstrate that this phenomenon is clearly observed in the prototype indazole molecule isolated in the gas phase. The 1H-indazole conformer was detected by rotational spectroscopy, and its 17 isotopologues resulting from single and double heavy atom substitution (13 C and 15 N) were also unambiguously observed. Several experimental structures were determined and, in particular, the most useful semi-experimental equilibrium structure (re SE ), allowed determination of the heavy atom bond lengths to milli-Ångstrom precision. The experimentally determined bond length alternation is estimated to correspond to 60:40 contributions from the two resonant forms of 1H-indazole.

Accurate equilibrium structures of methyl methacrylate and methacrylic acid by microwave spectroscopy and dispersion corrected calculations.

The rotational constants of s-trans and s-cis methyl methacrylate and methacrylic acid are determined from microwave spectra. All singly substituted heavy-atom isotopologs of the four species are measured in natural abundance. The experimental rotational constants are combined with anharmonic vibrational corrections using the Coulomb-attenuating method, Becke, three-parameter, Lee-Yang-Parr density functional with Grimme's D3 dispersion corrections and the Becke-Johnson damping function, yielding precise semi-experimental equilibrium rotational constants. These constants are used to determine semi-experimental equilibrium structures with sub-picometer accuracy, suitable for benchmarking purposes.

Semiexperimental equilibrium structure of 1-methylisatin from gas-phase electron diffraction data and structural changes in isatin due to 1-methyl and 5-fluoro substituents as predicted by coupled cluster computations

ABSTRACTThe molecular structure of 1-methylisatin (1) has been studied by gas-phase electron diffraction (GED) and quantum chemical computation up to the coupled cluster (CCSD(T)) level of theory. The semiexperimental equilibrium structure (Cs point group symmetry) has been determined from the GED data taking into account anharmonic vibrational corrections calculated in curvilinear coordinates with the B2PLYP force field. To observe fine structural effects due to the presence of different kinds of substituents, the accurate molecular structures of isatin (2) and 5-fluoroisatin (3) were also computed at the CCSD(T) level. The (O=)C–C(=O) carbon–carbon bonds of the pyrroline moiety in 1–3 are found to be remarkably longer than the typical single C–C bond. The electron donating methyl group causes a decrease of the C−N−C angle and an elongation of the N−C bond lengths in the pyrroline ring by 0.7° and up to 0.008 Å, respectively, whereas the electron withdrawing fluorine atom increases the ipso CCC angle by 2.5° in comparison to that in unsubstituted isatin.

Unveiling the Sulfur-Sulfur Bridge: Accurate Structural and Energetic Characterization of a Homochalcogen Intermolecular Bond.

By combining rotational spectroscopy in supersonic expansion with the capability of state-of-the-art quantum-chemical computations in accurately determining structural and energetic properties, the genuine nature of a sulfur-sulfur chalcogen bond between dimethyl sulfide and sulfur dioxide has been unveiled in a gas-jet environment free from collision, solvent and matrix perturbations. A SAPT analysis pointed out that electrostatic S⋅⋅⋅S interactions play the dominant role in determining the stability of the complex, largely overcoming dispersion and C-H⋅⋅⋅O hydrogen-bond contributions. Indeed, in agreement with the analysis of the quadrupole-coupling constants and of the methyl internal rotation barrier, the NBO and NOCV/CD approaches show a marked charge transfer between the sulfur atoms. Based on the assignment of the rotational spectra for 7 isotopologues, an accurate semi-experimental equilibrium structure for the heavy-atom backbone of the molecular complex has been determined, which is characterized by a S⋅⋅⋅S distance (2.947(3) Å) well below the sum of van der Waals radii.

Blurring out hydrogen: The dynamical structure of teflic acid.

The microwave spectra of 10 teflic acid isotopologues were recorded in the frequency range of 3-25 GHz using supersonic jet-expansion Fourier transform microwave spectroscopy. Despite being asymmetric in its equilibrium structure, the delocalization of the hydrogen atom leads to a symmetric top vibrational ground state structure. In this work, we present the zero point structure obtained from the experimental rotational constants and an approach to determine the semi-experimental equilibrium structure aided by ab initio data. The Te-O bond length determined in the equilibrium structure is accurate to the picometer and can be used as a benchmark for computational methods treating relativistic effects.

Equilibrium molecular structures of vinyl carbon chains: Vinyl acetylene, vinyl diacetylene, and vinyl cyanide

Semi-experimental equilibrium and high-level quantum-chemical structures are reported for three hydrocarbons containing the vinyl (H2C = CH–) group: vinyl acetylene, vinyl diacetylene and vinyl cyanide. Semi-experimental equilibrium structures have been obtained through a combination of new experimental results from Fourier transform microwave spectroscopy combined with force field calculations performed at the coupled-cluster singles and doubles model augmented by a perturbative correction for triple excitations, CCSD(T), level of theory. Comparison against equilibrium structures obtained by high-level CCSD(T) computations employing large correlation-consistent basis sets with up to 1090 basis functions yields excellent agreement. From this combined study, we find the carbon atom backbone in the vinyl group is largely unaffected when bound to different substituents, such as –H, –CCH, –C4H, –CN.

Fourier Transform Microwave Spectrum of Propene-3-d1 (CH2═CHCH2D), Quadrupole Coupling Constants of Deuterium, and a Semiexperimental Equilibrium Structure of Propene.

The ground-state rotational spectrum of propene-3-d1, CH2═CHCH2D, was measured by Fourier transform microwave spectroscopy. Transitions were assigned for the two conformers, one with the D atom in the symmetry plane (S) and the other with the D atom out of the plane (A). The energy difference between the two conformers was calculated to be 6.5 cm-1, the S conformer having lower energy. The quadrupole hyperfine structure due to deuterium was resolved and analyzed for both conformers. The experimental quadrupole coupling and the centrifugal distortion constants compared favorably to their ab initio counterparts. Ground-state rotational constants for the S conformer are 40582.157(9), 9067.024(1), and 7766.0165(12) MHz. Ground-state rotational constants for the A conformer are 43403.75(3), 8658.961(2), and 7718.247(2) MHz. For the A conformer, a small tunneling splitting (19 MHz) due to internal rotation was observed and analyzed. Using the new rotational constants of this work as well as those previously determined for the 13C species and for some deuterium-substituted species from the literature, a new semiexperimental equilibrium structure was determined and its high accuracy was confirmed. The difficulty in obtaining accurate coordinates for the out-of-plane hydrogen atom is discussed.

Determination of accurate semiexperimental equilibrium structure of proline using efficient transformations of anharmonic force fields among the series of isotopologues

ABSTRACTThe complete semiexperimental (SE) equilibrium structure of proline (45 degrees of freedom) is determined using the mixed estimation method. The cubic force fields for the parent and eight isotopologues of proline molecule are evaluated at the MP2-FC/cc-pVTZ level in Cartesian coordinates. The accuracy of the SE structure is verified by optimising the structure with the CCSD(T) model and a basis set of quadruple-ζ quality. A significantly more accurate equilibrium structure of proline is obtained when compared to the previous one. It is shown that the employed technique is efficient for the determination of SE equilibrium structures of rather large molecules. A simple transformation of anharmonic force fields between normal coordinate and Cartesian coordinate representations is proposed. The suggested technique allows efficient evaluation of the rotation–vibration interaction constants for a number of isotopologues, once the cubic force field of any species is found either in normal or Cartesian coordinates.