Bond angles around a tetravalent atom.

Relationships among the six bond angles about a central tetravalent atom depend on symmetry, ranging from the most symmetrical Td point group to the least symmetrical C1 point group having only the identity element. Exact relationships are derived here in two ways: (1) a purely algebraic treatment of the general mathematical conditions among the bond angles, followed by factorizations that arise from various symmetry constraints and (2) a reverse approach based on geometric analysis, starting with the most symmetrical Td case and relaxing constraints stepwise to lower point groups. The mathematical formulas show systematically how the degrees of freedom among the bond angles increase from zero to a maximum of five as the symmetry is relaxed from the Td symmetry.

Rotational spectrum, tunneling motions, and potential barriers of benzyl alcohol.

The rotational spectra of benzyl alcohol and of its OD isotopologue have been assigned and measured in a supersonic expansion, either with pulsed-jet Fourier transform microwave or free jet absorption millimeter wave spectroscopy. The spectrum is consistent with a gauche conformation of the oxygen atom, characterized by a theta (OC(7)-C(1)C(2)) dihedral angle of approximately 55 degrees. Such a configuration is 4-fold degenerate, corresponding to minima with theta approximately +/-60 degrees, +/-120 degrees. The four equivalent minima are separated by two kinds of barrier, corresponding to theta = +/-90 degrees, and 0 or 180 degrees. Only the theta = +/-90 degrees barriers are low enough to generate a tunneling splitting, which has been measured in a spectrum strongly perturbed by tunneling interactions. The observed splittings diminish considerably upon deuterium substitution. The tunneling splittings are consistent with a barrier about 280 cm(-1) and high level ab initio calculations predicting a 320 cm(-1) barrier.

Microwave spectroscopy and structures of two conformers of 1H-heptafluoropropane.

Two conformations of 1,1,2,2,3,3,3-heptafluoropropane (1H-heptafluoropropane, HFP) have been observed and characterized by its microwave rotational spectrum. The HC(1)C(2)C(3) dihedral angle is analogous to the CCCC dihedral angle in butane and exhibits both trans and gauche orientations. Rotational transitions of all three selection rules are observed for the gauche conformer, consistent with C(1) symmetry. Only a- and b-type transitions are observed for the trans form, consistent with a 180 degrees dihedral angle and overall C(s) symmetry. Computed models at the PBE0/VTZ level are in excellent agreement with experimental results. The structures were characterized by scaling the principal coordinates of the computed models to exactly reproduce the observed second moments.

Two conformers observed and characterized in isobutylbenzene.

The microwave spectrum of isobutylbenzene (2-methyl-1-phenylpropane) reveals the presence of two conformers that are characterized by their microwave spectra and by quantum chemical calculations. The more stable conformer has a gauche configuration of the C(phenyl)-C(1)-C(2)-H chain coupled with a approximately 80 degrees dihedral angle between the phenyl group and the C(phenyl)-C(1)-C(2) plane with C(1) symmetry. The less stable conformer has a plane of symmetry, C(s), with an anti configuration of the C(phenyl)-C(1)-C(2)-H chain coupled with a 90 degrees dihedral angle between the phenyl group and the C(phenyl)-C(1)-C(2) plane. The rotational constant values are 3070.9273(4) MHz, 736.01980(6) MHz, and 680.92889(6) MHz for the C(1) species and 2500.780(8) MHz, 885.72743(10) MHz, and 770.42036(10) MHz for the C(s) species. Quantum chemical calculations are in agreement with these structures and predict a relative energy between those two conformers of 0.4 kcal/mol.

Helical C(2) structure of perfluoropentane and the C(2v) structure of perfluoropropane.

Saturated hydrocarbons have structures with completely staggered bonds and dihedral angles of 180 degrees . Substituting hydrogen by fluorine results in a slight shift from 180 degrees , giving rise to a helical structure. X-ray diffraction studies on fibers and computational studies on perfluoroalkanes estimate a dihedral angle of about 17 degrees from the trans position. The rotational spectra of perfluoropentane and its three (13)C isotopomers have been observed and assigned using a pulsed-jet Fourier transform microwave spectrometer. The rotational constants for the parent species are A 990.6394(3) MHz, B 314.0002(1) MHz, and C 304.3703(1) MHz, respectively. The determination of an exact dihedral angle has been challenging, as the helical twist has proven to be quite sensitive to the structural inputs and constraints. A series of r(0) structures incorporating various model constraints and a Kraitchman analysis gives a range of 13-19 degrees for the torsional angle. An objective approach, which only assumes overall C(2) symmetry, is to scale the principal coordinates from ab initio models by the square root of the ratio of the observed second moments to the computed second moments. The scaled structures of computed models at various levels of theory reproduce the parent second moments exactly and the (13)C second moments very well, giving a dihedral angle of 17 +/- 1 degrees from trans. The microwave spectrum of perfluoropropane has also been observed and assigned. The rotational constants are A 1678.5982(9) MHz, B 900.1968(10) MHz, and C 955.3216(11) MHz, respectively. Unlike longer perfluoroalkanes, perfluoropropane has a nonhelical, C(2v) structure. Computations are in excellent agreement with experimental results.

The substituted alkyne 3-heptyne is eclipsed.

Although butane exists in staggered anti and gauche conformations, when the ethyl groups are separated by a C[triple bond]C triple bond (3-hexyne), the stable conformation changes to eclipsed, (1)C(2v). Using rotational microwave spectroscopy, we have studied another example, 3-heptyne, the C[triple bond]C elongated analogue of pentane. The most stable conformer of pentane has anti-anti (AA) conformations about the central C-C bonds (C(2v)) and the next most stable has a gauche dihedral angle (GA, C1). This microwave study determines that the extended analogue of the AA form is not staggered about the C[triple bond]C axis but eclipsed (Cs). Also, the elongated analogue of the GA conformer is also not staggered but nearly eclipsed. The conformations of low-polarity substituted acetylenes is determined by dispersion attractions between the end groups. A microwave study of the AA and GA conformers of pentane is also reported.

Molecular structures and compositions of trans-1,2-dichlorocyclohexane and trans-1,2-difluorocyclohexane in the gas phase: an electron-diffraction investigation.

The structures and compositions of gaseous trans-1,2-dichloro- (DCCH) and trans-1,2-difluorocyclohexane (DFCH), each of which may exist with the halogen atoms in a diaxial (aa) or diequatorial (ee) conformation, have been investigated by electron diffraction. The analysis was aided by rotational constants from microwave spectroscopy for the ee form of DFCH and by ab initio and density functional theory molecular orbital calculations for all species. The skeletons of the molecules have similar parameter values, but for the Cl-C-C-Cl and F-C-C-F fragments there are significant differences between the corresponding C-C-X bond angles and the X-C-C-X torsion angles in the two systems. There are also significant differences between the values of these parameters in the aa and ee forms of the same system. The composition of DCCH at 100 degrees C was measured to be 60(4)% aa, and that of DFCH at 70 degrees C was 42(7)% aa; the uncertainties are estimated 2sigma. From the preferred B3LYP/aug-cc-pVTZ calculations, the predicted theoretical composition is 51.2% aa for DCCH and 40.8% aa for DFCH. (Calculations at the levels B3LYP/6-31G(d) and MP2/6-31G(d) give similar results for DCCH, but both predict more aa than ee for DFCH.) Values (r(g)/A and angle(alpha)/degree) for some of the more important parameters of the aa/ee forms of DCCH are = 1.525(4)/1.525(6), C-Cl = 1.806(2)/1.787(2), angleC2-C1-Cl = 107.3(3)/111.5(3), angleC1-C2-C3 = 113.9(5)/111.6(5), angleC2-C3-C4 = 111.3(12)/109.9(12), and Cl-C2-C3-Cl = 165.3(9)/-59.4(9); and for DFCH C-C = 1.525(6)/1.520(9), C-F = 1.398(2)/1.390(2), angleC2-C1-F = 106.5(6)/109.2(6), angleC1-C2-C3 = 111.4(9)/110.9(9), angleC2-C3-C4 = 113.1(10)/113.1(10), and F-C2-C3-F = 171.1(37)/-67.2(37). The structures and compositions are discussed.

Four conformers characterized in allyl nitrite.

Allyl nitrite, O=NOCH(2)CH=CH(2), can exist in conformations which include syn (S) and anti (A) configurations of O=N-O-C, anti or gauche (G) configurations of N-O-C-C, and syn or skew (Sk) configurations of O-C-C=C. Four of them have been observed and characterized by their microwave spectra and quantum chemical calculations to have AGSk' (0.0 kcal/mol), AGSk (0.2(2) kcal/mol), SASk (0.2(2) kcal/mol), and SAS (0.9(2) kcal/mol) configurations about the three successive dihedral angles. All four are observed in microwave studies of the vapor at 300 and 200 K and the first three are seen in pulsed-jet beams. The SAS form apparently relaxes to the SASk conformer during expansion in the pulsed-jet. Quantum chemical calculations reveal that the two possible conformers with anti-anti configurations of the O=N-O-C-C fragment, AAS and AASk, are transition states, unstable configurations, or of marginal stability, consistent with structures observed in this and other previously studied alkyl nitrites. The remaining four possible conformers are predicted to have relative energies within 1 kcal/mol of the observed conformers but were not observed experimentally.