The Case for Methyl Group Precession Accompanying Torsional Motion

2020 ◽  
Vol 73 (8) ◽  
pp. 775
Author(s):  
Jason R. Gascooke ◽  
Warren D. Lawrance
Keyword(s):  
High Precision ◽  
Rotation Axis ◽  
Molecular Structures ◽  
Rotational Line ◽  
Torsional Angle ◽  
Methyl Group ◽  
Interaction Terms ◽  
Quantum Chemistry Calculations ◽  
Torsional Angles ◽  
Vibration Coupling

For molecules containing a methyl group, high precision fits of rotational line data (microwave spectra) that encompass several torsional states require considerably more constants than are required in comparable rigid molecules. Many of these additional terms are ‘torsion-rotation interaction’ terms, but their precise physical meaning is unclear. In this paper, we explore the physical origins of many of these additional terms in the case where the methyl group is attached to a planar frame. We show that torsion-vibration coupling, which has been observed in toluene and several substituted toluenes, provides the dominant contribution to a number of the torsion-rotation constants in toluene. It is further demonstrated that this coupling is intimately related to precession of the methyl group. A number of the constants required in the high resolution fits of rotational line data are shown to arise as a natural consequence of methyl precession. By considering several molecules whose rotational line spectra have been fit to high precision, we demonstrate that the experimental evidence is consistent with the occurrence of methyl group precession. Quantum chemistry calculations of the optimised molecular structures at key torsional angles provide further evidence that methyl precession occurs. There is both a torsional angle dependent tilt of the Cmethyl-frame bond and of the methyl group principal rotation axis relative to the Cmethyl-frame bond.

scholarly journals Crystal structures of two stilbazole derivatives: bis{(E)-4-[4-(diethylamino)styryl]-1-methylpyridin-1-ium} tetraiodidocadmium(II) and (E)-4-[4-(diethylamino)styryl]-1-methylpyridin-1-ium 4-methoxybenzenesulfonate monohydrate

2018 ◽  
Vol 74 (12) ◽  
pp. 1891-1894
Author(s):  
Priya Antony ◽  
S. Antony Inglebert ◽  
Jerald V. Ramaclus ◽  
S. John Sundaram ◽  
P. Sagayaraj
Keyword(s):  
Hydrogen Bonds ◽  
Rotation Axis ◽  
Stacking Interactions ◽  
Tetrahedral Coordination ◽  
Asymmetric Unit ◽  
Methyl Group ◽  
Diethyl Amine ◽  
Molecular Salts ◽  
Benzene Rings ◽  
Distorted Tetrahedral Coordination

The title molecular salts, (C18H23N2)2[CdI4], (I), and C18H23N2 +·C7H7O4S−·H2O, (II), are stilbazole, or 4-styrylpyridine, derivatives. The cation, (E)-4-[4-(diethylamino)styryl]-1-methylpyridin-1-ium, has a methyl group attached to pyridine ring and a diethyl amine group attached to the benzene ring. The asymmetric unit of salt (I), comprises one cationic molecule and half a CdI4 dianion. The Cd atom is situated on a twofold rotation axis and has a slightly distorted tetrahedral coordination sphere. In (II), the anion consists of a 4-methoxybenzenesulfonate and it crystallizes as a monohydrate. In both salts, the cations adopt an E configuration with respect to the C=C bond and the pyridine and benzene rings are inclined to each other by 10.7 (4)° in (I) and 4.6 (2)° in (II). In the crystals of both salts, the packing is consolidated by offset π–π stacking interactions involving the pyridinium and benzene rings, with centroid–centroid distances of 3.627 (4) Å in (I) and 3.614 (3) Å in (II). In the crystal of (II), a pair of 4-methoxybenzenesulfonate anions are bridged by Owater—H...Osulfonate hydrogen bonds, forming loops with an R 2 4(8) motif. These four-membered units are then linked to the cations by a number of C—H...O hydrogen bonds, forming slabs lying parallel to the ab plane.

On Comparing Experimental and Calculated Structural Parameters

1998 ◽  
Author(s):  
Lothar Schäfer ◽  
John D. Ewbank
Keyword(s):  
Electron Diffraction ◽  
Potential Energy ◽  
Ab Initio ◽  
Structural Parameters ◽  
Molecular Structures ◽  
Gas Electron Diffraction ◽  
Torsional Angle ◽  
Internuclear Distances ◽  
Molecular Potential Energy ◽  
The One

The tacit assumption underlying all science is that, of two competing theories, the one in closer agreement with experiment is the better one. In structural chemistry the same principle applies but, when calculated and experimental structures are compared, closer is not necessarily better. Structures from ab initio calculations, specifically, must not be the same as the experimental counterparts the way they are observed. This is so because ab initio geometries refer to nonexistent, vibrationless states at the minimum of potential energy, whereas structural observables represent specifically defined averages over distributions of vibrational states. In general, if one wants to make meaningful comparisons between calculated and experimental molecular structures, one must take recourse of statistical formalisms to describe the effects of vibration on the observed parameters. Among the parameters of interest to structural chemists, internuclear distances are especially important because other variables, such as bond angles, dihedral angles, and even crystal spacings, can be readily derived from them. However, how a rigid torsional angle derived from an ab initio calculation compares with the corresponding experimental value in a molecule subject to vibrational anharmonicity, is not so easy to determine. The same holds for the lattice parameters of a molecule in a dynamical crystal, and their temperature dependence as a function of the molecular potential energy surface. In contrast, vibrational effects are readily defined and best described for internuclear distances, bonded and non-bonded ones. In general, all observed internuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. To illustrate how the operations of an experimental technique affect the nature of its observables, gas electron diffraction shall be used as an example.

Optical Property and Photoisomerization of Some Functional Azobenzene Derivatives with Aromatic Substituted Groups

2011 ◽  
Vol 121-126 ◽  
pp. 1009-1013
Author(s):  
Ti Feng Jiao ◽  
Xu Hui Li ◽  
Qiu Rong Li ◽  
Jing Xin Zhou
Keyword(s):  
Molecular Structure ◽  
Optical Property ◽  
Potential Application ◽  
Uv Light ◽  
Molecular Structures ◽  
Functional Material ◽  
Methyl Group ◽  
Uv Light Irradiation ◽  
The Difference ◽  
Azobenzene Derivatives

Some functional azobenzene derivatives with aromatic substituted groups have been synthesized and their photoisomerization have also been investigated. It has been found that depending on different substituted groups, such as phenyl or naphthyl segments, the formed azobenzene derivatives showed different properties, indicating distinct regulation of molecular skeletons. Spectral data confirmed commonly the characteristic absorption of substituted groups and aromatic segments in molecular structures. In addition, the photoisomerization of all compounds in solution can show trans-to-cis photoisomerization by UV light irradiation, and demonstrate distinct isomerization ratio depending on effect of different substituted headgroups. The difference is mainly attributed to the aromatic substituted headgroups and methyl group in molecular structure. The present results have showed that the special properties of azobenzene derivatives could be effectively turned by modifying molecular structures of objective compounds with proper substituted groups, which show potential application in sensor and functional material field.

Molecular structures of dichloro(dimethyl)germane and trichloro(methyl)germane determined by vapour phase electron diffraction

1977 ◽  
Vol 55 (6) ◽  
pp. 1104-1110 ◽  
Author(s):  
John E. Drake ◽  
J. Lawrence Hencher ◽  
Quang Shen
Keyword(s):  
Electron Diffraction ◽  
Diffraction Data ◽  
Confidence Level ◽  
Systematic Errors ◽  
Vapour Phase ◽  
Molecular Structures ◽  
Electron Diffraction Data ◽  
Geometrical Parameters ◽  
Methyl Group ◽  
Uncertainty Estimates

The molecular structures of dichloro(dimethyl)germane and trichloro(methyl)germane have been determined in the vapour phase by electron diffraction. The principal geometrical parameters for (CH3)2GeCl2 are rg(Ge—Cl) = 2.143 ± 0.004 Å, rg(Ge—C) = 1.928 ± 0.006 Å, [Formula: see text].and [Formula: see text] In the analysis of CH3GeGl3 recently reported values of the rotational constants were combined with the electron diffraction data to give rg(Ge—Cl) = 2.132 ± 0.003 Å, rg(Ge—C) = 1.893 ± 0.010 Å, [Formula: see text] and [Formula: see text]In both cases the methylgermane geometry was assumed for the methyl group [Formula: see text] which was fixed in the staggered configuration with respect to the C2GeCl2 and CGeCl3 frames respectively. Both random and systematic errors were included in the uncertainty estimates, which are believed to be approximately at the 95% confidence level. In the case of (CH3)2GeCl2 the uncertainties in [Formula: see text] were enlarged to four times the least-squares values in order to reflect the difficulty of resolving the Cl … Cl, C … Cl, and C … C distances in the analysis.

Multidimensional conformational analysis of allyl methyl disulfide: a key component of garlic

2000 ◽  
Vol 78 (3) ◽  
pp. 362-382 ◽  
Author(s):  
Alvin C Lin ◽  
Salvatore J Salpietro ◽  
Eugen Deretey ◽  
Imre G Csizmadia
Keyword(s):  
Potential Energy ◽  
Conformational Analysis ◽  
Ab Initio ◽  
Lipid Lowering ◽  
Torsional Angle ◽  
Organosulfur Compounds ◽  
Cholesterol Lowering ◽  
Torsional Angles ◽  
Activity Mechanism ◽  
Molecular Computations

Organosulfur compounds in garlic, like allyl methyl disulfide, have been found to be involved in antimutagenic, anticarcinogenic, antithrombotic, and lipid-lowering activities, and it has also been found to act as an antioxidant. Ab initio molecular computations were performed on dihydrogen disulfide (1) with respect to torsional angle τ1 = τ(H·S-S·H), hydrogen methyl disulfide (2) with respect to torsional angle τ1 = τ(H·S-S·CH3), and allyl methyl disulfide (3) with respect to torsional angles τ1 = τ(H3C2·CH2·S-S·CH3), τ2 = τ(H3C2·CH2-S·S·CH3), and τ3 = τ(H3C2-CH2·S·S·CH3). Potential energy curves (PEC) were obtained from 1 and 2, i.e., E = E(τ1), from which optimized structures were obtained at the HF/6-31G* level of theory. These optimized structures were used to investigate the potential energy hypersurface surface (PEHS) of 3, i.e., E = E(τ1,τ2,τ3). One-dimensional scans along τ2 and τ3 (where τ1 = ±90°; τ1 = 180°) were performed at the HF/3-21G* level of theory. From these scans, six lower energy pairs of enantiomeric minima (i.e., [g+g+g+| g-g-g-], [g+ag- | g-ag+], [g+g-g+ | g-g+g-], [g+g+g-| g-g-g+], [g+ag- | g-ag+], and [g+g-g-| g-g+g+]) as well as 3 higher energy minima (i.e., [g+g+s | g-g-s], [g+as | g-as], and [g+g-s | g-g+s]) were optimized at τ1 = ±90° at the HF/6-31G* and B3LYP/6-31G* levels of theory. The global minimum was determined to be the [g+g-g+ | g-g+g-] enantiomeric pair of conformers, and the fully symmetrical anti-anti-anti [a a a] structure was determined to be a second-order saddle point on the PEHS of 3. Although there are no stereocentres in 3, there is chirality in the conformational twist with respect to the [a a a] conformation through τ1 = τ2 = τ3 = 180°. Based on the energies and MO diagrams of the HUMO and LUMO +1 of 3, the anticarcinogenic and cholesterol lowering activity mechanism of 3 is presented.Key words: ab initio MO computations, allyl methyl disulfide, multidimensional conformational analysis (MDCA), anticarcinogenic, cholesterol lowering.

Sense of sequential 1,5-sigmatropic rearrangements of dimethyl-3,3-dialkyl-3H-pyrazole-4,5-dicarboxylates. Crystal and molecular structures of two dimethyl-4,5-dialkyl-1H-pyrazole-1,3-dicarboxylates

1991 ◽  
Vol 69 (3) ◽  
pp. 373-378 ◽  
Author(s):  
Christopher S. Frampton ◽  
Michael W. Majchrzak ◽  
John Warkentin
Keyword(s):  
Dicarboxylic Acid ◽  
Key Words ◽  
Dimethyl Ester ◽  
Molecular Structures ◽  
X Ray Diffraction ◽  
Methyl Group ◽  
X Ray ◽  
Crystal And Molecular Structures ◽  
Sigmatropic Rearrangements ◽  
Methoxycarbonyl Group

3,3-Dialkyl-3H-pyrazole-4,5-dicarboxylic acid dimethyl esters (4), obtained by cycloaddition of R1R2C=N+=N− (R1 = R2 = CH3; R1 = CH3, R2 = CH2CH3) to CH3O2CC≡CCO2CH3, rearrange thermally by 1,5-sigmatropic alkyl shifts to both N and C. The latter rearrangement is followed by two successive 1,5-sigmatropic shifts of a methoxycarbonyl group. Final products of the threefold rearrangement were shown to be 4,5-dialkyl-1H-pyrazole-1,3-dicarboxylic acid dimethyl esters (6), rather than the isomeric 3,4-dialkyl-1H-pyrazole-1,5-dicarboxylic acid dimethyl esters (7), by means of single crystal X-ray diffraction. Those products therefore result from alkyl migration to C-4 of 4, followed by sequential migration of the methoxycarbonyl group, initially at C-4, to C-3 and then to N-2 of 4. In the initial alkyl migration step, ethyl migrates in preference to methyl, and in subsequent migration steps the methoxycarbonyl group migrates faster than the ethyl or methyl group. Crystals of 4-ethyl-5-methyl-1H-pyrazole-1,3-dicarboxylic acid dimethyl ester (6b) are monoclinic, of space group P21/n, with a = 7.907(1) Å, b = 11.087(2) Å, c = 13.199(3) Å, V = 1124.9(4) Å 3, Dc = 1.34 g cm−3, Dm = 1.33 g cm−3 for Z = 4, and R1 = 0.0772 (R2 = 0.0626) for 1474 reflections (R1 = 0.0428, R2 = 0.0422 for 903 reflections with I > 3σ(I)). The structure of 6a is similar. Key words: 3,3-dialkyl-3H-pyrazoles, 1,5-sigmatropic rearrangements of; 4,5-dialkyl-1H-pyrazoles, crystal and molecular structures; 1,5-sigmatropic rearrangements of pyrazoles, sense of.

scholarly journals Modeling and Analysis of System Error for Highly Curved Freeform Surface Measurement by Noncontact Dual-Axis Rotary Scanning

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 554
Author(s):  
Li Miao ◽  
Linlin Zhu ◽  
Changshuai Fang ◽  
Ning Yan ◽  
Xudong Yang ◽  
...  
Keyword(s):  
High Precision ◽  
Measurement Accuracy ◽  
Rotation Axis ◽  
Optical Probe ◽  
Measuring System ◽  
Freeform Surface ◽  
Normal Vector ◽  
Profile Measurement ◽  
Freeform Surfaces ◽  
System Error

Profile measurement is a key technical enabler in the manufacturing of highly curved freeform surfaces due to their complex geometrical shape. A current optical probe was used to measure nearly rotary freeform surfaces with the help of one rotation axis, because the probe needs to measure along the normal vector of the surface under the limitation of the numerical aperture (NA). This kind of measuring system generally has a high cost due to the high-precision, multi-axis platform. In this paper, we propose a low-cost, dual-axis rotation scanning method for a highly curved freeform surface with an arbitrary shape. The optical probe can scan the surface profile while always keeping consistent with the normal vector of the measuring points with the help of the double rotation axis. This method can adapt to the changes in curvature in any direction for a highly curved freeform surface. In addition, the proposed method provides a system error calibration technique for the rotation axis errors. This technique can be used to avoid the dependence of the measuring system on the high-precision platform. The three key system errors that affect the measurement accuracy such as installation error of the B-axis, A-axis, and XZ perpendicularity error are first analyzed through establishing an error model. Then, the real error values are obtained by the optimal calculation in the calibration process. Finally, the feasibility of the measurement method is verified by measuring one cone mirror and an F-theta mirror and comparing the results to those obtained using commercial equipment. The maximum measurable angle of the system is ±90°, the maximum measurable diameter is 100 mm, and the measurement accuracy of the system reaches the micron level in this paper.

scholarly journals Crystal structures of trans-acetyldicarbonyl(η5-cyclopentadienyl)(1,3,5-triaza-7-phosphaadamantane)molybdenum(II) and trans-acetyldicarbonyl(η5-cyclopentadienyl)(3,7-diacetyl-1,3,7-triaza-5-phosphabicyclo[3.3.1]nonane)molybdenum(II)

2020 ◽  
Vol 76 (4) ◽  
pp. 547-551 ◽  
Author(s):  
Mitchell R. Anstey ◽  
John L. Bost ◽  
Anna S. Grumman ◽  
Nicholas D. Kennedy ◽  
Matthew T. Whited
Keyword(s):  
Oxygen Atom ◽  
Dominant Role ◽  
Molecular Structures ◽  
Carbonyl Groups ◽  
Methyl Group ◽  
Extended Structure ◽  
Carbonyl Ligands ◽  
Cyclopentadienyl Ligand ◽  
Migratory Insertion ◽  
Neighboring Molecule

The title compounds, [Mo(C5H5)(COCH3)(C6H12N3P)(CO)2], (1), and [Mo(C5H5)(COCH3)(C9H16N3O2P)(C6H5)2))(CO)2], (2), have been prepared by phosphine-induced migratory insertion from [Mo(C5H5)(CO)3(CH3)]. The molecular structures of these complexes are quite similar, exhibiting a four-legged piano-stool geometry with trans-disposed carbonyl ligands. The extended structures of complexes (1) and (2) differ substantially. For complex (1), the molybdenum acetyl unit plays a dominant role in the organization of the extended structure, joining the molecules into centrosymmetrical dimers through C—H...O interactions with a cyclopentadienyl ligand of a neighboring molecule, and these dimers are linked into layers parallel to (100) by C—H...O interactions between the molybdenum acetyl and the cyclopentadienyl ligand of another neighbor. The extended structure of (2) is dominated by C—H...O interactions involving the carbonyl groups of the acetamide groups of the DAPTA ligand, which join the molecules into centrosymmetrical dimers and link them into chains along [010]. Additional C—H...O interactions between the molybdenum acetyl oxygen atom and an acetamide methyl group join the chains into layers parallel to (101).

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