Equilibrium structures of selenium compounds: The torsionally flexible molecule of selenophenol.

The equilibrium structure of selenophenol has been investigated using rotational spectroscopy and high-level quantum mechanical calculations, offering electronic and structural insight into the scarcely studied selenium compounds. The jet-cooled broadband microwave spectrum was measured in the 2-8 GHz cm-wave region using broadband (chirped-pulse) fast-passage techniques. Additional measurements up to 18 GHz used narrow-band impulse excitation. Spectral signatures were obtained for six isotopic species of selenium (80Se, 78Se, 76Se, 82Se, 77Se, and 74Se), together with different monosubstituted 13C species. The (unsplit) rotational transitions associated with the non-inverting µa-dipole selection rules could be partially reproduced with a semirigid rotor model. However, the internal rotation barrier of the selenol group splits the vibrational ground state into two subtorsional levels, doubling the dipole-inverting µb transitions. The simulation of the double-minimum internal rotation gives a very low barrier height (B3PW91: 42 cm-1), much smaller than for thiophenol (277 cm-1). A monodimensional Hamiltonian then predicts a huge vibrational separation of 72.2 GHz, justifying the non-observation of µb transitions in our frequency range. The experimental rotational parameters were compared with different MP2 and density functional theory calculations. The equilibrium structure was determined using several high-level ab initio calculations. A final Born-Oppenheimer (reBO) structure was obtained at the coupled-cluster CCSD(T)_ae/cc-wCVTZ level of theory, including small corrections for the wCVTZ → wCVQZ basis set enlargement calculated at the MP2 level. The mass-dependent method with predicates was used to produce an alternative rm(2) structure. The comparison between the two methods confirms the high accuracy of the reBO structure and offers information on other chalcogen-containing molecules.

Determination of the semiexperimental equilibrium structure of 2-acetylthiophene in the presence of methyl internal rotation and substituent effects compared to thiophene.

The microwave spectra of thiophene and 2-acetylthiophene were recorded in the frequency range from 2 to 40 GHz using two molecular jet Fourier transform microwave spectrometers. For 2-acetylthiophene, two conformers with a syn and an anti orientation of the S1-C2 and C6O bonds (with respect to the C2-C6 bond) were identified, and the syn-conformer was more stable. The spectra of the 34S- and 13C-isotopologues of syn-2-acetylthiophene were also assigned, and the semiexperimental equilibrium structure could be determined. Compared to thiophene, at the substitution position, the S1-C2 and C2C3 bond lengths both increase by about 0.007 Å, and the bond angle S1-C2C3 decreases by 0.06°, noticeably larger than the experimental uncertainties. A-E torsional splittings were observed due to internal rotation of the methyl group hindered by a barrier height of 330.187(35) and 295.957(17) cm-1 for the syn-conformer and the anti-conformer, respectively. Geometry and internal rotation parameters are compared with those of related thiophene derivatives, as well as those of furan and 2-acetylthiophene to gain a better understanding of structure determination in the presence of methyl internal rotation.

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.

Equilibrium Structure in the Presence of Methyl Internal Rotation: Microwave Spectroscopy and Quantum Chemistry Study of the Two Conformers of 2-Acetylfuran.

For 2-acetylfuran, quantum chemistry predicted and proton magnetic resonance study reported two conformers, anti and syn, differing in the position of the carbonyl group with respect to the O1-C2 bond of the furan ring. The microwave spectrum of the title molecule was recorded in the frequency range from 2 to 26.5 GHz using a molecular jet Fourier transform microwave spectrometer, confirming the presence of both conformers. Spectroscopic parameters such as the rotational and centrifugal distortion constants could be determined with high precision. The spectra of all 13C- and 18O-isotopologues of the energetically more favorable anti-conformer could be assigned, allowing the experimental determination of bond lengths and bond angles from the heavy atom substitution rs and the semi-experimental equilibrium reSE structures. Splittings arising from the internal rotation of the acetyl methyl group could be resolved for both conformers as well as for all assigned isotopologues, from which the barrier to methyl internal rotation was determined. The torsional barrier is largely invariant at around 319 cm-1 in the parent species of anti-2-acetylfuran and its isotopologues, showing that though isotopic substitution greatly influences the rotational properties of the molecule and causes a different microwave spectrum, its effect on the methyl torsion is negligible. On the other hand, conformational effects play a decisive role, as the torsional barrier of 239.780(13) cm-1 found for syn-2-acetylfuran differs significantly from the value for anti-2-acetylfuran. The results are compared and discussed with other methyl-substituted furan derivatives and acetyl group containing ketones for a better understanding of different effects influencing molecular geometry parameters and methyl internal rotations.

Laboratory Observation of, Astrochemical Search for, and Structure of Elusive Erythrulose in the Interstellar Medium.

Rotational spectroscopy provides the most powerful means of identifying molecules of biological interest in the interstellar medium (ISM), but despite their importance, the detection of carbohydrates has remained rather elusive. Here, we present a comprehensive Fourier transform rotational spectroscopic study of elusive erythrulose, a sugar building block likely to be present in the ISM, employing a novel method of transferring the hygroscopic oily carbohydrate into the gas phase. The high sensitivity of the experiment allowed the rotational spectra of all monosubstituted isotopologue species of 13C-12C3H8O4 to be recorded, which, together with quantum chemical calculations, enabled us to determine their equilibrium geometries (reSE) with great precision. Searches employing the new experimental data for erythrulose have been undertaken in different ISM regions, so far including the cold areas Barnard 1, the pre-stellar core TMC-1, Sagittarius B2. Although no lines of erythrulose were found, this data will serve to enable future searches and possible detections in other ISM regions.

The puzzling hyper-fine structure and an accurate equilibrium geometry of succinic anhydride.

An accurate semiexperimental equilibrium structure of succinic anhydride has been determined from a combination of experiment and theory. The cm-wave and mm-wave rotational spectra of succinic anhydride, 3,4-dihydrofuran-2,5-dione, were recorded in a pulsed supersonic jet using Fourier-transform microwave spectroscopy and in a free-jet using mm-wave absorption spectroscopy. Many lines in the cm-wave spectrum show fine structure and after eliminating all other possibilities the origin of this fine structure is determined to be from spin-spin interaction. Accurate rotational and quartic centrifugal distortion constants are determined. Assignments of 13C and 18O singly substituted isotopologues in natural abundance were used to obtain a substitution geometry for the heavy atoms of succinic anhydride. Theoretical approaches permitted the calculation of a Born-Oppenheimer ab initio structure and the determination of a semiexperimental equilibrium structure in which computed rovibrational corrections were utilized to convert vibrational ground state rotational constants into equilibrium constants. The agreement between the semiexperimental structure and the Born-Oppenheimer ab initio structure is excellent. Succinic anhydride has been shown to have a planar heavy atom equilibrium structure with the effects of a large amplitude vibration apparent in the resultant rotational constants.

How flexible is the disulfide linker? A combined rotational-computational investigation of diallyl disulfide.

The symmetrically substituted diallyl disulfide adopts a non-symmetric conformation in the gas-phase, as observed with supersonic-jet rotational spectroscopy. The determination of the equilibrium structure with a predicate mixed regression illustrates both the benefits of the mass-dependent method for moderately large molecules and the structural peculiarities of the disulfide bridge.

The S-S Bridge: A Mixed Experimental-Computational Estimation of the Equilibrium Structure of Diphenyl Disulfide.

The disulfide bridge (-S-S-) is an important structural motif in organic and protein chemistry, but only a few accurate equilibrium structures are documented. We report the results of supersonic-jet microwave spectroscopy experiments on the rotational spectra of diphenyl disulfide, C6 H5 -S-S-C6 H5 (including all 13 C and 34 S monosubstituted isotopologues), and the determination of the equilibrium structure by the mixed estimation (ME) method. A single conformation of C2 symmetry was observed in the gas phase. This disulfide is a challenging target since its structure is determined by 34 independent parameters. Additionally, ab initio calculations revealed the presence of three low-frequency vibrations (<50 cm-1 ) associated to phenyl torsions which would prevent the calculation of an accurate force field. For this reason, instead of the semiexperimental method, we used the mass-dependent (rm ) method to fit the structural parameters concurrently to moments of inertia and predicate parameters, affected with appropriate uncertainties. The predicates were obtained by high-level quantum-chemical computations. A careful analysis of the results of different fits and a comparison with the ab initio optimizations confirms the validity of the used methods, providing detailed structural information on the title compound and the disulfide bridge.

Semiexperimental and mass-dependent structures by the mixed regression method: Accurate equilibrium structure and failure of the Kraitchman method for ethynylcyclohexane.

The mixed regression method for determination of molecular structures is reviewed and applied to the investigation of ethynylcyclohexane, using both semiexperimental and mass-dependent methods. This methodology provides an efficient and computationally affordable route to obtain accurate molecular reference data, preventing ill-conditioning in the structural least-squares determinations from experimental rotational constants. New supersonic-jet microwave measurements are reported to obtain inertial data for the axial and equatorial species of ethynylcyclohexane, together with all 13C isotopologues of the equatorial form. The semiexperimental equilibrium (reSE) and mass-dependent (rm(2)) structures of the molecule are compared with high-level ab initio optimizations, showing that both methods deliver compatible structures with accuracies of about 0.002 Å for bond lengths and 0.2° for bond angles. We confirm that dependable predicates can be obtained for a large variety of bonds. Finally, we verify that the substitution method completely fails to determine a reliable structure for the title compound.

Axial-equatorial isomerism and semiexperimental equilibrium structures of fluorocyclohexane.

An experimental-computational methodology combining rotational data, high-level ab initio calculations and predicate least-squares fitting is applied to the axial-equatorial isomerism and semiexperimental equilibrium structure determination of fluorocyclohexane. New supersonic-jet microwave measurements of the rotational spectra of the two molecular conformations, together with all 13C isotopologues of both isomeric forms are reported. Equilibrium rotational constants are obtained from the ground-state rotational constants corrected for vibration-rotation interactions and electronic contributions. Equilibrium structures were determined by the mixed estimation (ME) method. Different computational methods were tested for the evaluation of predicate values of the structural parameters, and a computationally effective procedure for estimating reliable dihedral angles is proposed. Structural parameters were fitted concurrently to predicate parameters and moments of inertia, affected with appropriate uncertainties. The new structures of the title compound are regarded as accurate to 0.001 Å and 0.2°, illustrating the advantages of this methodology. Structural comparisons are offered with the cyclohexane prototype, revealing subtle substituent effects. For comparison purposes the equilibrium structures for the two fluorocyclohexane isomers and cyclohexanone are computed from high-level ab initio theory with inclusion of adjustments for basis set dependence and correlation of the core electrons.

N-Methyl Inversion and Accurate Equilibrium Structures in Alkaloids: Pseudopelletierine.

A rotational spectroscopy investigation has resolved the conformational equilibrium and structural properties of the alkaloid pseudopelletierine. Two different conformers, which originate from inversion of the N-methyl group from an axial to an equatorial position, have been unambiguously identified in the gas phase, and nine independent isotopologues have been recorded by Fourier-transform microwave spectroscopy in a jet expansion. Both conformers share a chair-chair configuration of the two bridged six-membered rings. The conformational equilibrium is displaced towards the axial form, with a relative population in the supersonic jet of Naxial /Nequatorial ≈2/1. An accurate equilibrium structure has been determined by using the semiexperimental mixed-estimation method and alternatively computed by quantum-chemical methods up to the coupled-cluster level of theory. A comparison with the N-methyl inversion equilibria in related tropanes is also presented.

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.

The equilibrium molecular structures of 2-deoxyribose and fructose by the semiexperimental mixed estimation method and coupled-cluster computations.

Fructose and deoxyribose (24 and 19 atoms, respectively) are too large for determining accurate equilibrium structures, either by high-level ab initio methods or by experiments alone. We show in this work that the semiexperimental (SE) mixed estimation (ME) method offers a valuable alternative for equilibrium structure determinations in moderate-sized molecules such as these monosaccharides or other biochemical building blocks. The SE/ME method proceeds by fitting experimental rotational data for a number of isotopologues, which have been corrected with theoretical vibration-rotation interaction parameters (αi), and predicate observations for the structure. The derived SE constants are later supplemented by carefully chosen structural parameters from medium level ab initio calculations, including those for hydrogen atoms. The combined data are then used in a weighted least-squares fit to determine an equilibrium structure (r). We applied the ME method here to fructose and 2-deoxyribose and checked the accuracy of the calculations for 2-deoxyribose against the high level ab initio r structure fully optimized at the CCSD(T) level. We show that the ME method allows determining a complete and reliable equilibrium structure for relatively large molecules, even when experimental rotational information includes a limited number of isotopologues. With a moderate computational cost the ME method could be applied to larger molecules, thereby improving the structural evidence for subtle orbital interactions such as the anomeric effect.

Interplay of experiment and theory: high resolution infrared spectrum and accurate equilibrium structure of BF2OH.

The high-resolution Fourier transform infrared (FTIR) spectrum of (11)BF2OH (difluoroboric acid) is analyzed taking into account numerous interactions. The ν1, ν2 and ν3 infrared bands are analyzed for the first time, whereas the parameters of the 6(1), 7(1), 8(1) and 9(1) states and for the 4(1) and 9(2) interacting states are redetermined. These results are used to check the quality of the ab initio force field. It is found that the ab initio rovibrational corrections are more accurate than the experimental ones. An earlier attempt to determine a semiexperimental structure did not allow us to obtain an accurate equilibrium structure. The reasons of this failure are investigated. This failure was mainly due to the lack of useful experimental information. Indeed, there is no isotopic substitution available for the fluorine atoms, and the boron atom is extremely close to the center of mass. Furthermore, the available isotopic substitutions (H → D and (16)O → (18)O) induce a large rotation of the principal axis system which amplifies the errors. However, the mixed estimation method has allowed us to determine a complete and reliable equilibrium structure. Thanks to this method, it is possible to determine an accurate structure, even in extremely difficult cases. An extensive analysis of the quality of structure calculations at the CCSD(T) level is also performed using basis sets up to five ζ quality. It was found that, at the convergence limit, the effects of the diffuse functions are practically disappearing, whereas the core-core and core-valence electron correlation effects are quite important for the bond lengths.

Electron delocalization in polyenes: a semiexperimental equilibrium structure for (3E)-1,3,5-hexatriene and theoretical structures for (3Z,5Z)-, (3E,5E)-, and (3E,5Z)-1,3,5,7-octatetraene.

Electronic structure theory reveals that π-electron delocalization increases with the chain length in polyenes. To analyze quantitatively this effect a semiexperimental equilibrium structure has been determined for trans-hexatriene by the mixed estimation method. For this fit rotational constants for a number of carbon and hydrogen isotopologues as well as a high-level ab initio structure have been used. The accuracy is 0.001 Å for bond lengths and 0.1° for bond angles. For the three isomers of octatetraene, high-level ab initio calculations have given a comparably accurate structure. These structures have been used in comparison with the structure of s-trans-butadiene to show that "C═C" bonds increase in length and "C-C" bonds decrease in length as the polyene chain lengthens. These structural effects of π-electron delocalization increase toward the center of polyenes. Most likely, π-π conjugation in the molecules studied plays a large part in their planarity that, in turn, forces the hydrogen atoms of cis fragments in bay regions to be in a close contact. Their distance is indeed shorter than the sum of their van der Waals radii, and they seem to participate in a six-membered ring.

Equilibrium structures of three-, four-, five-, six-, and seven-membered unsaturated N-containing heterocycles.

Up to six different techniques are utilized to estimate the equilibrium structures (r(e)) of a series of mostly unsaturated, N-containing heterocycles. Accurate Born-Oppenheimer (r(e)(BO)) and, if allowed, semiexperimental (r(e)(SE)), as well as empirical (r(m)-type) estimates of the equilibrium structures of three-membered (1H- and 2H-azirine, aziridine), four-membered (azete), five-membered (pyrrole, pyrazole, imidazole), six-membered (pyridine, pyrimidine, uracil), and seven-membered (1H-azepine) rings, containing usually one but in some cases two N atoms, are determined. The agreement among the structural results of the different techniques is very satisfactory. It is shown that it is possible to use the CCSD(T) electronic structure method with the relatively small wCVTZ basis set, with all electrons correlated, and the effect of further basis set enlargement, wCVTZ → wCVQZ, computed at the MP2 level, to obtain reliable equilibrium structures for the semirigid molecules investigated. Extension to larger basis sets does not significantly improve the accuracy of the computed results. Although all molecules investigated are oblate, and their principal axis system is subject to large rotations upon isotopic substitution, the semiexperimental method, when applicable, provides accurate results, though in the difficult cases it must be augmented with the mixed regression method. Finally, it is noteworthy that the empirical mass-dependent (r(m)) method also delivers surprisingly accurate structures for this class of compounds.

Accurate equilibrium structures for piperidine and cyclohexane.

Extended and improved microwave (MW) measurements are reported for the isotopologues of piperidine. New ground state (GS) rotational constants are fitted to MW transitions with quartic centrifugal distortion constants taken from ab initio calculations. Predicate values for the geometric parameters of piperidine and cyclohexane are found from a high level of ab initio theory including adjustments for basis set dependence and for correlation of the core electrons. Equilibrium rotational constants are obtained from GS rotational constants corrected for vibration-rotation interactions and electronic contributions. Equilibrium structures for piperidine and cyclohexane are fitted by the mixed estimation method. In this method, structural parameters are fitted concurrently to predicate parameters (with appropriate uncertainties) and moments of inertia (with uncertainties). The new structures are regarded as being accurate to 0.001 Å and 0.2°. Comparisons are made between bond parameters in equatorial piperidine and cyclohexane. Another interesting result of this study is that a structure determination is an effective way to check the accuracy of the ground state experimental rotational constants.

Why it is sometimes difficult to determine the accurate position of a hydrogen atom by the semiexperimental method: structure of molecules containing the OH or the CH3 group.

The semiexperimental (SE) technique, whereby equilibrium rotational constants are derived from experimental ground-state rotational constants and corrections based on an ab initio cubic force field, has the reputation to be one of the most accurate methods to determine an equilibrium structure ( reSE). However, in some cases, it cannot determine accurately the position of the hydrogen. To investigate the origins of this difficulty, the SE structures of several molecules containing either the OH or the CH3 group are determined and compared to their best ab initio counterparts. It appears that an important factor is the accuracy of the geometry used to calculate the force field, in particular when the least-squares system is not well conditioned. In this case, the mixed regression method is often an easy way to circumvent this difficulty.

Semiexperimental equilibrium structures for cis,cis- and trans,trans-1,4-difluorobutadiene by the mixed estimation method and definitive relative energies of the isomers.

Equilibrium molecular structures accurate to 0.001 Å and 0.2° have been determined for cis,cis- and trans,trans-1,4-difluorobutadiene by the semiexperimental mixed estimation method. In this method, structures are fitted concurrently to equilibrium rotational constants and bond parameters obtained from an intermediate level of electronic structure theory. The effect of fluorine substitution on the carbon backbone of butadiene is surprisingly small. Definitive energy differences for the ground states were computed, employing the focal-point analysis (FPA) technique, between the trans,trans and cis,cis isomers (ΔH°0 = 5.6(3) kJ mol(-1)) and the cis,trans and cis,cis isomers (ΔH°0 = 3.2(2) kJ mol(-1)) of 1,4-difluorobutadiene. These differences confirm the exceptional relationship that the trans,trans isomer has the highest energy and the cis,cis isomer the lowest energy, endorsing what was reported earlier on the basis of experimental observations in benzene solution.

Accurate determination of the deformation of the benzene ring upon substitution: equilibrium structures of benzonitrile and phenylacetylene.

Accurate equilibrium, re, structures of the monosubstituted benzene molecules benzonitrile, C6H5CN, and phenylacetylene, C6H5CCH, have been determined using two different, to some extent complementary techniques. The semiexperimental, r(e)(SE), structural parameters are the result of a least-squares fit to equilibrium rotational constants derived from experimental effective ground-state rotational constants and rovibrational corrections based principally on an ab initio cubic force field. The composite ab initio Born-Oppenheimer, r(e)(BO), structural parameters are obtained from frozen-core and all-electron MP2 and the CCSD(T) geometry optimizations using Gaussian basis sets up to quintuple-zeta quality. The DFT(B3LYP) method, with two different Gaussian basis sets, 6-31G* and 6-311+G(3df,2pd), was used to calculate the cubic force field employed during the r(e)(SE) structure determination. With the 6-31G* basis set, the error of the rovibrational correction is to a large extent random, whereas with the 6-311+G(3df,2pd) basis set it is mainly systematic. As shown here, systematic errors do not have a significant effect on the accuracy of the derived structure; the quality of the structural fit, however, is sensitive to the true accuracy of the ground-state rotational constants. An even more important general conclusion of this study is that the addition of extra rotational constants from multisubstituted species does not seem to improve the accuracy of the r(e)(SE) structures, quite in contrast to the highly desirable availability of data corresponding to all singly substituted species.