Internal Rotation Process Research Articles

Approximate symmetry characteristics using fuzzy-subset theory study for chiral transitions of allene-1,3,-dihalides

Based on our study of the application of fuzzy-subset theory to the characterization of imperfect symmetry in some stable molecular systems and simple dynamic molecular systems, we analyze the internal rotation process of allene-1,3- dihalides. Allene-1,3-dihalides (CHX=C=CHY, where X and Y may be the same or different halogen atoms) are optically chiral nonplanar molecules. The two end-groups may internally rotate about the near straight linear C=C=C axis, and the molecule may change its chirality. The internal rotation process may pass through two different planar transition state (TS): cis-TS and trans-TS, which belong to C2v and C2h point groups (as X and Y to be same), respectively. The intrinsic reaction coordinate (IRC) corresponding to the two TS processes is denoted as cis-IRC and trans-IRC. However, for the whole IRC reaction process, only their subgroup C2 well-defined symmetry remains. Other symmetry transformations in C2v and C2h point groups can only be examined in terms of imperfect symmetry, although there appear certain reaction reversal joint point group G(RcC2v) and G(RtC2h) well-defined symmetry in the dynamics through the IRC processes. If X and Y are different, the stable molecule has no conventional nontrivial point group symmetry. The internal rotation processes may pass through two different planar TS’s (cis-and trans-TS). The TS will still be a planar molecule belonging to CS point group with the molecule plane as its symmetry plane. Other states in the IRC may belong to certain reaction reversal joint point groups, G(RM)C and G(RM)T. We have thus examined the approximate symmetry of MO’s related to C2 point group. Moreover, we have also analyzed the membership functions, representation components, and their relationships shown in the MO fuzzy main representation correlation diagrams.

Analysis of Intramolecular Dynamic Processes in Enantiomeric Diaryl Atropisomers and Related Derivatives by 2H NMR Spectroscopy in Polypeptide Liquid Crystals

We demonstrate the analytical potential of 2H-{1H} NMR spectroscopy in weakly ordering, chiral lyotropic liquid crystals made of poly(gamma-benzyl-L-glutamate) (PBLG) dissolved in chloroform or dichloromethane for investigating the intramolecular dynamic processes of four deuterated diaryls (derivatives of 1-(4'-methylphenyl)naphthalene). When the rotation of the aryl groups about the sp(2)--sp(2) bond is sufficiently slow relative to the NMR timescale, the method allows the spectral discrimination of enantiomeric atropisomers or enantiotopic directions in the prochiral derivatives. The effect of the position of substituents on the phenyl group on the conformational dynamics of these compounds has been examined as well as the nature of the organic co-solvent. When coalescence phenomena are observed, simulation of the experimental 2H-{1H} lineshapes using a formalism tailored for two deuterons undergoing mutual exchange allows the rate constants and the activation parameters for the internal rotation processes to be calculated. Experimental values of DeltaH(not equal) have been compared with data evaluated by molecular modelling calculations and the activation parameters are discussed for the various compounds. It is shown that these polypeptide mesophases have no significant impact on the interconversion dynamics of these compounds. In contrast with the nematic thermotropic phases, Haller's equation cannot be used to predict the evolution of the quadrupolar splittings (Deltanu(Q) values), and hence the order parameters, versus T in the PBLG mesophases. For these particular lyotropic systems, it is shown that an exponential function of the form Deltanu(Q)[Hz]=C x exp (-E/RT[K]) provides excellent agreement between the experimental and expected Deltanu(Q) values. Analysis of the results reported in this work suggests that orientation and chiral discrimination phenomena in these lyotropic solvents could be treated separately because they would involve different interaction mechanisms.

Theoretical study of the photoinduced intramolecular proton transfer and rotational processes in 2-(2′hydroxyphenyl)-4-methyloxazole in gas phase and embedded in β-cyclodextrin

The intramolecular proton transfer and the internal rotations of the 2-(2′hydroxyphenyl)-4-methyloxazole (HPMO) in the first electronically excited singlet state ( S 1) have been theoretically studied. Electronic calculations have been carried out within an all-single configuration interaction scheme (CIS). Time-dependent DFT (TDDFT) calculations have been performed to correct the energies of the proton transfer as CIS tends to overestimate the energy barriers. The effect of confinement of the HPMO molecule inside the cavity of β-cyclodextrin (β-CD) has also been studied. The ONIOM hybrid method is used to deal with the large host–guest system. Within the ONIOM procedure two levels of calculation are defined: CIS or TDDFT for the HPMO and the semiempirical PM3 method for the β-CD. A comparison of the electronic energies reveals that the proton-transfer process has a lower energy barrier than the subsequent internal rotation of the keto tautomer, both in the isolated system and in the host–guest complex. However, the initial energy of the wavepacket accessed upon photoexcitation (vertical transition) is high enough to surpass both barriers, so that electronic energies alone are not able to explain the different reaction times found for both processes by means of time-resolved (femtosecond) fluorescence experiments. A dynamic method based on the RRKM statistical theory has been used to account for this difference. The so calculated rate constants also reproduce the increment in the time for the internal rotation process when HPMO is confined inside the β-CD cavity. Analysis of the different factors that contribute to the rate constant disclose that this delay is due to the increment of rigidity of HPMO that takes place upon encapsulation.

Characterization of internal rotation of monorotor molecules via bifurcation analysis

The bifurcation analyses of the internal rotation processes of two different series of monorotor molecules along the reduced reaction coordinate are investigated in this Letter. Our topological analyses indicate that the internal rotation processes are characterized by the properties of critical points. Furthermore, when the energy functions are represented as the third-order generic polynomial of the reduced reaction coordinate, the processes are isomorphic to the elementary fold catastrophe.

Sphericity: a geometric approach to the internal rotation of C 2H 6, H 2O 2, and N 2H 4

From a pure geometric point of view a three-dimensional molecular configuration can be considered to be a polyhedral skeleton. Based on the convex hull of the polyhedron it is possible to define a sphericity measure for the enclosing framework. This sphericity function which may be expressed in spatial coordinates is capable to mirror information about the structural characteristics of a molecular arrangement that habitually can only be arrived at by quantum mechanical computations. This concept is applied to the well-known internal rotation process of C 2H 6, H 2O 2, and N 2H 4.

The Carbonylation Reaction of CH3Co(CO)4: A Detailed Density Functional Study

The alkyl group migration reaction CH3Co(CO)4 → CH3(CO)Co(CO)3 and the carbonyl association reaction CH3(CO)Co(CO)3 + CO → CH3(CO)Co(CO)4 have been thoroughly investigated via density functional theory techniques. In the migratory insertion reaction, two stable 16-electron acyl intermediates have been located on the B3LYP potential energy surface. Both species have the carbons of the acyl groups in the axial position. One of the intermediates is stabilized by the formation of an agostic interaction to the formally vacant site of the trigonal bipyramid, and the other is stabilized by the acyl oxygen adopting an η2 coordination geometry. The transition states between all the intermediates, as well as several internal rotation processes, have been located. An interesting feature of this reaction is that alkyl group migration is accompanied by a simultaneous twist of the alkyl group into the equatorial plane of the original trigonal bipyramid, and therefore the reaction does not take place on a Cs symmetry potential energy surface. The transition states for CO association with each intermediate have also been characterized. Our calculations indicate that the formation of the acyl intermediates proceeds via methyl migration and that thermal carbonylation of the agostically stabilized and the η2 stabilized intermediates is probably competitive.

Exocyclic push–pull conjugated compounds. Part 3. An experimental NMR and theoretical MO ab initio study of the structure, the electronic properties and barriers to rotation about the exocyclic partial double bond in 2- exo-methylene- and 2-cyanoimino-quinazolines and -benzodiazepines

The structure of a number of 2- exo-methylene substituted quinazolines and benzodiazepines, respectively, 1, 3a, b, 4 ( X=–CN, –COOEt ) and their 2-cyanoimino substituted analogues 2, 3c, d ( X=–CN, –SO 2C 6H 4–Me (p) was completely assigned by the whole arsenal of 1D and 2D NMR spectroscopic methods. The E/ Z isomerism at the exo-cyclic double bond was determined by both NMR spectroscopy and confirmed by ab initio quantum chemical calculations; the Z isomer is the preferred one, its amount proved dependent on steric hindrance. Due to the push–pull effect in this part of the molecules the restricted rotation about the partial C 2,C 11 and C 2,N 11 double bonds, could also be studied and the barrier to rotation measured by dynamic NMR spectroscopy. The free energies of activation of this dynamic process proved very similar along the compounds studied but being dependent on the polarity of the solvent. Quantum chemical calculations at the ab initio level were employed to prove the stereochemistry at the exo-cyclic partial double bonds of 1– 4, to calculate the barriers to rotation but also to discuss in detail both the ground and the transition state of the latter dynamic process in order to better understand electronic, inter- and intramolecular effects on the barrier to rotation which could be determined experimentally. In the cyanoimino substituted compounds 2, 3c, d, the MO ab initio calculations evidence the isomer interconversion to be better described by the internal rotation process than by the lateral shift mechanism.

Internal rotation processes inendo-cis-N-(o-tolyl)bicyclo[2.2.1]heptene-2,3-dicarboximide and its oxidation products

Atropoisomerism, a type of isomerism associated with restricted rotational properties about certain bonds, is present in endo -cis-N-(o -tolyl)bicyclo[2.2.1]heptene-2,3-dicarboximide and its oxidation products, the corresponding diol and diacid. These three compounds were studied by variable-temperature NMR and molecular modelling. Small differences in carbon and proton chemical shifts can be attributed to slight changes in geometry due to interactions of rotating groups. Copyright© 1999 John Wiley & Sons, Ltd.

A theoretical study of the effects governing the internal rotation process in allyl derivatives

Total molecular energy as a function of internal rotation around the C(sp 2 )C(sp 3 ) bond, referred to as the CC bond, in the molecules CH 2 CHCY 3 , CH 2 CHCH 2 Y, with Y = H, F, Cl, CH 3 and CH 2 CHCHY 2 , with Y = F , Cl , was calculated at the ab initio MO level, with the 6-31G ∗ basis set. The molecular geometry was fully relaxed at fixed rotational angles θ. The potential energy profiles V ( θ ) were obtained with a truncated Fourier series and the V n terms ( n = 1–3) are derived and discussed. The CC bond distances change on rotation and the highest values of the increment Δd are found in the rotational maxima. For the molecules with the CY 3 top the changes in Δd are linearly related to the changes in total molecular energy ΔE TOT , but with different slopes in the different molecules. The slopes seem to depend on the absolute length of the CC bond, and while the Δd behaviour within a molecule seems mostly dictated by hyperconjugative effects, the absolute length d is most probably determined by through-space effects. The elongation Δd is due, in the majority of the molecules examined, to a decrease in attractive interactions (barrier of attractive type) in the rotational maxima, although in 3,3,3-trichloropropene and cis -1,3,3,3-tetrachloropropene the barrier is mostly of the repulsive type (increase in repulsive interactions). This kind of correlation is less statisfactory for tops of lower symmetry: in the molecules with the CH 2 Y top it would appear that the gauche-skew barrier is of the repulsive type, and the trans-skew barrier of the attractive type. The rotational behaviour of the total energy was also analyzed according to a model of factorization in energy components ascribed to different effects, identified in the first instance as hyperconjugative and through-space effects. The hyperconjugative effect of the groups examined, ΔE π , calculated with the Natural Bond Orbital (NBO) approach, is similar to that found for the corresponding benzyl derivatives, yet slightly stronger. The rotational pattern of ΔE gp mirrors that of ΔE TOT , even though it seems necessary to take into account the presence of other effects to explain peculiar differences between these patterns. The through-space effect was further factorized in the contribution of van der Waals, ΔE vdW , and electrostatic, ΔE el . , interactions. For the calculation of ΔE el . , from atomic charges different approaches were employed (Mulliken NBO, CHELPG), yet none afforded a ΔE el . contribution quantitatively in agreement with the other factors. A qualitative description of the through-space effect of the groups considered is nevertheless attempted in order to suggest a combination of effects exerted by the susbtituents examined on the vinyl moiety, stemming from the theoretical treatment of these molecules.

A theoretical study of the effects governing the internal rotation process in allyl derivatives

Total molecular energy as a function of internal rotation around the C(sp 2)C(sp 3) bond, referred to as the CC bond, in the molecules CH 2CHCY 3, CH 2CHCH 2Y, with Y = H, F, Cl, CH 3 and CH 2CHCHY 2, with Y = F, Cl, was calculated at the ab initio MO level, with the 6-31G ∗ basis set. The molecular geometry was fully relaxed at fixed rotational angles θ. The potential energy profiles V( θ) were obtained with a truncated Fourier series and the V n terms ( n = 1–3) are derived and discussed. The CC bond distances change on rotation and the highest values of the increment Δd are found in the rotational maxima. For the molecules with the CY 3 top the changes in Δd are linearly related to the changes in total molecular energy ΔE TOT , but with different slopes in the different molecules. The slopes seem to depend on the absolute length of the CC bond, and while the Δd behaviour within a molecule seems mostly dictated by hyperconjugative effects, the absolute length d is most probably determined by through-space effects. The elongation Δd is due, in the majority of the molecules examined, to a decrease in attractive interactions (barrier of attractive type) in the rotational maxima, although in 3,3,3-trichloropropene and cis-1,3,3,3-tetrachloropropene the barrier is mostly of the repulsive type (increase in repulsive interactions). This kind of correlation is less statisfactory for tops of lower symmetry: in the molecules with the CH 2Y top it would appear that the gauche-skew barrier is of the repulsive type, and the trans-skew barrier of the attractive type. The rotational behaviour of the total energy was also analyzed according to a model of factorization in energy components ascribed to different effects, identified in the first instance as hyperconjugative and through-space effects. The hyperconjugative effect of the groups examined, ΔE π , calculated with the Natural Bond Orbital (NBO) approach, is similar to that found for the corresponding benzyl derivatives, yet slightly stronger. The rotational pattern of ΔE gp mirrors that of ΔE TOT , even though it seems necessary to take into account the presence of other effects to explain peculiar differences between these patterns. The through-space effect was further factorized in the contribution of van der Waals, ΔE vdW , and electrostatic, ΔE el. , interactions. For the calculation of ΔE el. , from atomic charges different approaches were employed (Mulliken NBO, CHELPG), yet none afforded a ΔE el. contribution quantitatively in agreement with the other factors. A qualitative description of the through-space effect of the groups considered is nevertheless attempted in order to suggest a combination of effects exerted by the susbtituents examined on the vinyl moiety, stemming from the theoretical treatment of these molecules.

Ab initio MO study of the internal rotation process in α-chlorinated picolines

Conformational properties and barriers to internal rotation for the three isomeric picolines mono- bi- and trichlorosubstituted at the methyl group were studied at the theoretical level with ab initio MO calculations. Energy profiles for internal rotation of the chlorinated methyl group were obtained at the 6-31G ∗ level with full molecular geometry relaxation, and the energy of critical points was recalculated at the MP2/6-311G ∗∗ level of theory. The conformational minima and maxima of these derivatives are qualitatively similar to those found for benzene derivatives, yet differences are found in the heights of the barriers to internal rotation and in the presence of two rotational minima or maxima in the molecules with lower rotational symmetry. The origin of the barriers to rotation and of the different energy content of conformational minima is discussed in the light of the natural bond orbital (NBO) approach within the donor-acceptor viewpoint of intramolecular interactions, and electrostatic interactions between the rotating group and the ring.

Getting the Shape of Methyl Internal Rotation Potential Surfaces Right

The effect of the multidimensional character of methyl internal rotation on torsional potential functions in small conjugated methyl molecules is discussed. Partitioned energetics obtained from different ab initio calculation levels are divided into σ and π symmetry components and then further dissected by breakdown of the fully relaxed internal rotation process into separate relaxation steps and their nuclear virials. Important contributions to barrier shape, height, and origin are thus disclosed. The analysis reveals closely balanced antagonistic π and σ contributions as determinants for the barrier height and identifies the dominant contributions to the barrier origin as σ-bonding changes largely resulting from bond lengthening during methyl group rotation. Skeletal hydrogen out-of-plane motion components of the torsional coordinate (e.g. CH2 ethylenic twisting in propene) provide a general mechanism for barrier narrowing in small conjugated methyl molecules. Rydberg jet experiments are discussed as a general means for obtaining accurate torsional frequency information (including ground state) to test internal rotation potential surface models.

Internal rotation around single bonds and conformational preferences in heterocyclic analogues of benzyl methyl sulphoxide studied with NMR techniques

The conformational equilibrium related to the internal rotation processes occurring in sulphoxides of the type ArCH 2SOCH 3 (where Ar=2-thienyl, 2-furyl, 2-pyridinyl and (3-methyl)2-pyridinyl rings) were studied with 1H and 13C NMR spectroscopy. Proton chemical shifts and long-range coupling constants n J(H,H) were obtained from the iterative analysis of the multiplets and were employed, together with 13C chemical shifts, long-range n J(C,H) and relaxation parameters (NOE and non-selective T 1 values) to obtain stereochemical relationships between the protons present in these molecules. Conformational predictions at a qualitative level were also derived from total molecular energies calculated with the semi-empirical AM1/MNDO method as a function of internal coordinates. The different approaches converged to indicate that the heterocyclic rings adopt an average orientation similar to the perpendicular orientation of the phenyl ring in benzyl methyl sulphoxide and, as regards rotation around the CH 2S bond, the prevalent conformer shows that the methyl group is symmetrically oriented with respect to the methylenic protons. The barriers for internal rotation are rather low and the equilibrium between conformers is dependent on the medium properties. Attempts to obtain conformational results were performed for the molecule of omeprazole, an antiulcer drug which contains the ArCH 2SOR moiety (Ar and R are substituted 2-pyridinyl and 2-benzimidazolyl groups, respectively). With respect to the other compounds examined, the orientation of the Ar ring does not significantly differ and the benzimidazole ring seems to prefer an orientation stereochemically equivalent to that of the methyl group.

Effect of ortho substituents on the internal rotation processes and conformational preferences of 1,2-diaryl-1,1,2,2-tetrachloroethanes: a 1H and 13C NMR variable temperature and X-ray structural study

The conformational behaviour of 1,2-diaryl-1,1,2,2-tetrachloroethanes, ortho,ortho′-disubstituted with CN (1), F (2) and CO2CH3(3), and of the mesityl derivative (4), has been studied in solution by variable temperature 1H and 13C NMR spectroscopy. The internal rotation processes around the exocyclic C–C and central C–C bonds appear to have similar energy barriers and thus behave differently from the compounds without ortho substituents, studied previously, which have a higher barrier for the interconversion of anti/gauche conformers. At low temperature, compounds 1–3 exist as mixtures of gauche and anti conformers with the former prevailing; compound 4 is almost exclusively in the gauche form. The solid state crystal and molecular structure has been determined for compounds 2 and 3. The molecule of compound 2 has point symmetry , which defines perfect staggering around the central C–C bond with the aromatic rings anti. The structure is affected by statistical disorder due to two alternate orientations of the phenyl rings. The crystal structure of compound 3 indicates one asymmetrical molecule in a gauche conformation. Statistical disorder involves both the methoxycarbonyl substituents at the phenyl rings; these latter display almost the same orientation with respect to the C(sp3) carbons, in both compounds.

An E ⇌ Z isomerization of an electrophilic vinyl azide by 15N. A probe for internal rotation processes in the carbanionic intermediate of nucleophilic vinylic substitution

AbstractThe label incorporation and Z → E isomerization in the reaction of 3‐azidomethylenedihydro‐(3H)‐furan‐2‐one with Na15NN2 in 1:1 water–acetone were measured as a probe for internal clockwise vs anticlockwise rotation in the intermediate carbanion.

Internal rotation and conformational preferences in 1,2-diaryl derivatives of 1,1,2,2-tetrachloroethane: a 1H DNMR and X-ray structural study

The title compounds show in their 1H NMR spectra recorded at room temperature signals of different line-width characteristic of molecules with slow internal rotation around sterically crowded single bonds. From the DNMR study in [2H6]acetone solution of the 4,4′-(compound 1) and 3,3′-bis(benzoic acid) dimethyl ester (compound 2) and of the 3,3′-bispyridine (compound 3) derivative the dynamic parameters of two internal rotation processes, with different energies of activation, were extracted. The internal rotation process with higher energy barrier (ΔG*= 13–14 kcal mol–1) was assigned to the anti⇌gauche conformer interconversion, and that with lower energy barrier (ΔG*= 8–9 kcal mol–1) to the rotation of aromatic rings around the C(sp3)–C(sp2) bond in the gauche conformer. The conformer populations measured at low temperature showed that the gauche conformer is the more abundant. The structural features of the conformers of compounds 1–3 were also investigated theoretically at a semi-empirical level with the AM1/MNDO method. The results of these calculations show that the anti conformer is the most stable one, yet the gauche form has higher polarity and this result could explain the increase of the gauche population in polar solvents. For compound 3 calculations were extended to the whole energy hypersurface having as coordinates the angles of rotation around the central C(sp3)–C(sp3) and C(sp3)–C(sp2) bonds. The theoretical free-energies of activation, even if largely underestimated, show that the barriers for the different internal processes follow the order: barrier for rotation around the C(sp3)–C(sp3) bond > barrier for rotation around the C(sp3)–C(sp2) bond in the gauche conformer > barrier for rotation around the C(sp3)–C(sp2) bond in the anti conformer. This order fits the trend of the first two barriers, experimentally determined. For compound 3 and for the 4,4′-bisbenzonitrile (compound 4) derivative, the crystal and molecular structure was obtained from X-ray analysis: the molecules have crystallographically dictated symmetry with perfectly staggered anti conformation. Longer C–Cl bond lengths and smaller Cl–C–Cl bond angles than those present in structurally similar compounds indicate steric crowding around the C(sp3)–C(sp3) bond. Solid state conformations are in excellent agreement with the calculated ground-state rotational structure of these molecules.

Influence of sulphur oxidation on the conformational and molecular stability of dimethyl disulphide: a theoretical ab initio MO approach

The conformational behaviour in the internal rotation process around the S-S bond was investigated in dimethyl disulphide, dimethyl thiosulphinate and a-dimethyl disulphoxide with the ab initio molecular orbital method at the 6–31 G ∗ atomic orbital basis set level. For each molecule the conformational minima and transition states relative to the internal rotation process were characterized with full geometry relaxation as minima and saddle points. Vibrational analysis of these conformations was carried out and thermodynamic parameters relative to the ground state conformational equilibria and transition states for conformer interconversion were derived. The conformational behaviour of the two diastereoisomers of a-dimethyl disulphoxide was found to be markedly different. An interpretation of the relative stability of ground and transition states was given within two different models of vicinal interactions. A number of calculated structural parameters of these molecules agree with an empirical description of their relative stability, although the seemingly remarkable instability of the a-disulphoxide with respect to the other molecules cannot be predicted with certainty. A multiconfigurational self-consistent field approach applied to the ground state of the corresponding molecules in which the methyl group is substituted with a hydrogen atom shows that in the case of the a-disulphoxide the S-S bond length is much greater than in the other compounds and one excited electronic structure contributes strongly to its ground state electronic structure.