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Nuclear magnetic resonance in solid cycloheptane
Abstract
Measurements are reported of the nuclear magnetic resonance absorption lineshape and spin-lattice relaxation time of solid cycloheptane from 50K to the melting point of 265K. Considerable molecular motion is found in the various solid phases but conclusions about the types of motion involved are difficult to reach due to a lack of knowledge of the crystal structure. Although the results in phase III can be explained by molecular pseudorotation process with an activation energy of 1.7 kcal mol-1, it is quite possible that the motion of this very flexible molecule is not of a well defined nature but is a complex and irregular mixture of motions which have comparable restricting barriers. In the higher solid phases, it appears that free isotropic molecular rotation commences and that this is followed by a molecular diffusion process approximately 40K below the melting point.
Understanding the conformational behaviour of small molecules in free solution and its relationship to biological activity is of fundamental importance to drug discovery. How the free ligand's conformational envelope changes upon binding to its target to adopt the bound (bioactive) conformational envelope vitally impacts on the observed binding affinity. Minimisation of this change is crucial for optimal potency and therefore not only conformational analysis but also understanding of the molecular drivers that control conformational preferences are both required if drug ligands are to be rationally and intentionally designed. Until recently, however, comprehensive experimental measurement of the conformations that a free ligand adopts in solution conditions (its dynamic 3D structure) has not been possible. Techniques for the measurement of free ligand conformations are discussed, including a progressive and recently reported solution NMR method. The chief factors that affect ligand conformation are presented, providing a conformational design toolbox for the medicinal chemist. These two streams are combined to present a framework through which conformational design can be practised. Conformational design is a new emergent tool for the practising medicinal chemist that promises fresh insight, control and productivity in drug discovery.
In situ Raman spectra of cycloheptane have been characterized under high pressure generated by diamond anvil cell (DAC) at room temperature. The pressure is up to 17.00 GPa. With the increase of pressure, the cycloheptane experienced the liquid-solid phase transition at 0.53 GPa. During 3.45-5.58 GPa, both the curve of Raman frequence-pressure and FWHM-pressure presented inflexions, indicating a potential solid-solid phase transition of cycloheptane.
The conformational analysis for the cycloheptane molecule has been carried out at the MP2/6-311G(d,p) and MP2/cc-pVDZ levels of theory, for structural parameters and harmonic frequency calculations, and using MP4(SDTQ) and CCSD(T) highly correlated methods for energy difference evaluation, aiming the determination of the temperature-dependent thermodynamic properties. The importance of using a separate treatment of the low frequency vibrational modes for the calculation of relative Gibbs free energy values is discussed and is shown to play a key role to bring the agreement of the theoretical conformational population predictions with the experimental gas phase reported value at 310K.
Ring-inversion barriers for the 3- and 4-cyclohexenyl radicals were investigated by an electron paramagnetic resonance (EPR) method and were found to be 7.0 ± 0.9 and 2.4 ± 0.5 kcal mol-1 in fluid solution. The inversion motions and the magnitudes of the barriers were closely related to those of the corresponding cyclohexenones and methylenecyclohexanes.
Am Beispiel der drei stereoisomeren Reihen der trisubstituierten Dioxepane (I)-(III) wird gezeigt, daß durch dreifache Substitution die Konformationsbestimmung von 7-gliedrigen Ringen erheblich vereinfacht wird (13C-NMR, Bß-Etherat-katalysierte Equilibrierung).
The phase transition behavior in solid cycloheptane has been investigated by differential scanning calorimetry and vibrational spectroscopy (infrared and Raman). The spectra of four stable phases and of two glassy crystalline phases have been obtained. The spectrum of the stable, low-temperature phase, phase IV, is very different from the spectra of the other phases, indicating that this is the only ordered phase. The observed low-frequency Raman spectra are consistent with isotropic reorientation and anisotropic reorientation, related to a molecular pseudorotation process, occurring in phases I and II and phase III, respectively. The spectra of the glassy crystalline phases indicate that these phases possess static disorder, which is related to that of the corresponding high-temperature phases.
Quantum chemical methods were used for the theoretical determination of the conformational population for the relevant conformers of cyclononane, i.e., TBC, TCB, TCC, and M4 (or C1), which have been previously investigated experimentally through detailed examination of the nuclear magnetic resonance (NMR) spectrum. Our best Gibbs free energy result, evaluated with MP4(SDTQ)/6-31G(d,p)//MP2/6-31G(d,p) energy differences and MP2/6-31G(d,p) thermal corrections, lead to a temperature-dependent population in excellent agreement with the experimental results based on the analysis of the low temperature 13C NMR spectrum. The nice agreement with experiment is achieved using MP2 harmonic frequencies for the evaluation of vibration partition functions within the standard statistic thermodynamics formalism. Theoretical temperature-dependent infrared (IR) and 13C NMR spectra were simulated and compared with experimental data, which confirmed the ab initio conformational population reported here. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
This paper begins an exploration of the use of the combination of DFT computations with experimental inelastic neutron scattering (INS) spectra as a method for establishing what conformation is present in a molecular crystal at low temperature. Presented here are INS spectra of a series of medium-sized cycloalkanes: C6H12, C7H14, C8H16, C10H20, C12H24, and C14H28. Optimized geometries and normal mode calculations were performed at B3LYP/6-311G(d,p) on the lowest energy conformations (i.e., those thermally accessible at the experimental temperature of 30 K). The calculated and observed spectra were analyzed for the best fit from each set of conformers, allowing a prediction of the dominant conformation in a conformationally rich system. For each cycloalkane, the calculated spectrum for the lowest energy conformer shows good agreement with experiment while the higher energy conformations have a much poorer fit. With little ambiguity, the lowest energy conformer is therefore predicted to be the dominant conformation, consistent with the diffraction data available for C6H12, C10H20, C12H24, and C14H28. These results indicate that INS spectroscopy may be a useful tool in determining the dominant conformation in a crystal lattice in cases such as this in which the intermolecular interactions are weak and the different conformers are calculated to have distinguishable spectra. Such an analysis is applied to the cases of C7H14 and C8H16 for which no low-temperature X-ray analysis is available. Clear structure predictions result, and the conformer observed is that computed to be of lowest energy for the molecule in isolation.
The theory of Provotorov is made use of for studying the shape of the nuclear magnetic resonance signals recorded after lock-in detection and the saturation effect of the field modulation. The analysis is developed under restrictive conditions which simplify the calculations, but correspond nevertheless to practical experimental procedures. It permits the choice of suitable conditions for obtaining accurate results on the shape of the absorption line and the spinlattice relaxation times. Dans cet article, la théorie de Provotorov est mise à profit pour étudier la forme des signaux de résonance magnétique nucléaire enregistrés après détection au lock-in, et les effets de saturation provoqués par la modulation de champ. L'analyse est développée dans des conditions restrictives qui simplifient notablement les calculs, mais qui correspondent cependant à des situations expérimentales pratiques. Elle permet de préciser les conditions à choisir pour obtenir des renseignements assurés quant à la forme de la courbe d'absorption et des temps de relaxation spin-réseau.
The use of non-quadratically convergent minimisation procedures for empirical force-field calculations can give rise to misleading descriptions of the geometry and symmetry of molecules as well as overestimating the steric energy to some extent.
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An electron diffraction investigation has been carried out for the molecules n-butane, n-pentane, n-hexane, and n-heptane in the gaseous phase. Mean bond lengths and bond angles were reported in earlier papers. The present paper is concerned with information derivable from the observed spectrum of nonbonded distances. A scheme is presented for determining both trans and gauche bond angles despite the fact that the 2.5-Å nonbonded C···C trans and gauche radial distribution peaks are too badly overlapped to be resolved. Formulas are given for calculating torsional ``shrinkage effect'' corrections for nonbonded distances.
It was found that a given gauche conformation has a higher free energy than its corresponding trans counterpart by about 610 cal/mole. If the source of this free-energy difference is steric, arising from repulsions between hydrogens on gauche carbons, there should be structural as well as thermodynamic manifestations. The positions of a total of 21 independent nonbonded C···C radial distribution peaks were interpreted in terms of a model of steric deformations in gauche structures. The results, including estimates of standard errors, were φ(gauche)=61.0±3° dihedral angle, α(trans)=112.65±0.3° C–C–C angle, α(gauche)—α(trans)=0.1°±1°, and the distortion from planarity of trans conformations adjacent to gauche was η=7±4°. The C–C bond length and C–C–C bond angle, averaged over all conformations, were 1.5328±0.002 Å and 112.71±0.15°, respectively.
The nuclear magnetic resonance absorption spectrum and the spin-lattice relaxation time have been measured for the protons in polycrystalline cyclohexane between 100 degrees K and its freezing-point (279\cdot 6 degrees K). It has been found that the second moment (mean square width) of the measured spectrum for temperatures at which the lattice is effectively rigid, namely, below 150 degrees K, is consistent with a molecular structure having D3d symmetry, tetrahedral bond angles, C\chembond{1,0} C bond lengths of 1\cdot 54 angstrom and C\chembond{1,0} H bond lengths of 1\cdot 10 angstrom. If the HCH angle is treated as a parameter to be determined, it is found to be 1071/2± 3 degrees. On warming from 155 to 180 degrees K the second moment decreases to a value which indicates the reorientation of the molecules about their triad axes. Analysis of the spin-lattice relaxation time, which falls rapidly in this temperature range, shows that the height of the barrier hindering this reorientation is 11 ± 1 kcal/mole. Just below 186 degrees K, the temperature at which there is a polymorphic change, the reorientation frequency is of the order 106 c/s. The polymorphic transformation is accompanied by discontinuous changes in the second moment and the relaxation time. It is concluded that in the higher temperature modification the molecules have a considerable freedom of reorientation, such that the intramolecular contribution to the second moment becomes negligibly small. Just above 186 degrees K the mean reorientation frequency exceeds 3 × 107 c/s. A final narrowing of the line between 220 and 240 degrees K is thought to be due to vacancy diffusion of the molecules within the lattice, causing the intermolecular contribution to the second moment to vanish also. Details are given of the gas-flow cryostat used in this work. The theoretical formulation of the second moment has been extended to include the modification of the intermolecular contribution during reorientation.
A simple fast method is described for producing three dimensional `ball-and-stick' representations of molecules, using a digital plotter; any viewpoint at a reasonable distance away is suitable.
From determinations of the low temperature thermal properties and vapor pressure of cycloheptane, cyclooctane and 1,3,5-cycloheptatriene, values of the entropy in the liquid and vapor states and the heat of vaporization, all at 298.16°K, were obtained. These results and values of the heats of formation derivable from literature data were used to compute values of ..delta..Hf°, ..delta..Ff°, ..delta..Sf° and logââ Kf for all three compounds in the liquid and vapor states at 298.16°K. In the solid state the thermal behavior of each substance is complex; there are transitions between four different crystalline forms of cycloheptane, three of cyclooctane and two of 1,3,5-cycloheptatriene.
An algorithm is described for rapid calculation of cartesian coordinates of atoms from internal molecular coordinates. Two procedures are given for efficient calculation of first derivatives of the Cartesian coordinates with respect to internal coordinates, and the manner in which higher derivatives may be obtained is indicated.
Energy functions of bending of the C—C—C angle and of twisting of the CH2—CH2 torsional angle have been examined through their effect on calculations of stable conformations and excess enthalpies of all the cycloalkane molecules from C6H12 to C12H24.The total strain energy was expressed as a function of the internal coordinates—bond lengths, bond angles and torsional angles. H—H distances were derived by matrix algebra, and the method of steepest descent was applied. Energy parameters like the bending force constant, the zero-strain value of bond angles, torsional potential barrier, were varied one at a time, and their effect on conformation and strain energy examined. Results have been compared with calorimetric measurements and with Xray and electron diffractions. Enthalpy of translation-rotation-vibration was also considered and found to be significant. Best agreement between calculations and experiment was obtained when the energy parameters were derived from n-alkanes. Thus, the n-alkane bond angle value of 112·7° is preferable to the tetrahedral angle as the zero-strain value; the torsional potential barrier of propane, 3·4 kcal/mole, is preferable to the corresponding value for ethane, 2·8 kcal/mole.
Forty‐megacycle‐per‐second proton magnetic resonance studies of solid Si(CH3)4, Ge(CH3)4, Sn(CH3)4, and Pb(CH3)4 have shown that methyl group reorientation occurs in all four compounds at temperatures as low as 77°K. T1 measurements show that the energy barrier to methyl reorientation in the X(CH3)4 family goes roughly as the inverse sixth power of the methyl separation. From linewidth measurements we find general molecular reorientation only in solid Si(CH3)4 and Ge(CH3)4 and only at temperatures just below the melting point. The activation energies are 7 and 10 kcal/mole, respectively. Self‐diffusion was found only in the metastable α phase of Si(CH3)4—an interesting result since the entropy of melting of α‐phase Si(CH3)4 is 8.34 eu, somewhat high for a plastic crystal. The experimental energy barrier to self‐diffusion in α‐phase Si(CH3)4 is about 6.2 kcal/mole. Proton magnetic resonance and thermal studies indicate that the X(CH3)4 family obeys the qualitative features of the Pople—Karasz theory of melting. A number of methods for calculating rigid‐lattice and methyl‐reorientation second moments are considered. A means is given for estimating the intermolecular contribution to the rigid‐lattice second moment when the crystal structure is unknown but the density of the solid is known. The method agrees well with other calculations.
A protocol for examining symmetrical ring conformations of six- to ten-membered cycloalkanes without recourse to models is developed and used to order their modes of interconversion and calculate the energy barriers involved, both for symmetrical modes of transition and for pseudo-rotation. The principles of conformational analysis for substituted rings are also set forth.
Constants in the functions used for the calculation of minimum-energy conformations for n-butane and cycloalkanes were varied so as to find the set which best reproduced a dozen items of experimental data (geometry and energies). The resultant best functions were then applied to obtain the geometry and energies of the symmetrical cycloalkane rings.
A relatively complete calculation of the low-energy conformations of cycloheptane is presented. The various paths for pseudorotation and the various transition states are rigorously characterized. It is shown that the pseudorotation paths of cycloheptane can be visualized as occurring on a helical track wound around a torus. Our results for the equilibrium conformations of cycloheptane are compared to the results of other calculations and found to agree qualitatively. Our calculated results give the best agreement with the available rotational constants, but final determination of the details of the potential functions and of the detailed properties of the conformations of cycloheptane will have to await the results of future experiments.
Circuit modifications are described which enable a Varian A‐60 spectrometer to be used for relaxation studies of chemically‐shifted protons. T 1 and T 2 values greater than 0.1 sec can be measured on the modified instrument at ambient temperature. Owing to severe convection effects in the probe assembly, relaxation measurements are made with difficulty at other temperatures. Methods of time‐averaging relaxation data are also discussed.
The velocity of longitudinal and transverse ultrasonic waves has been measured in polycrystalline samples of dl-camphene, cyclohexane and cyclohexanol over extended temperature ranges that encompass both the rotational and the nonrotational forms of these solids. In the case of cyclohexane and cyclohexanol the velocity of longitudinal waves near the melting point is practically the same for the liquid and for the rotational solid; it is therefore striking that the longitudinal velocity jumps by 30–50 percent in going from the rotational to the nonrotational form at the transition point. Values of the elastic constants for the rotational forms of camphene and cyclohexane are deduced from the velocities and the mean adiabatic compressibilites are calculated. The results for camphene are in agreement with the independently measured isothermal compressibility. Debye temperatures are calculated from the velocities at different temperatures for rotational and non-rotational forms of all three substances. The Debye temperatures for the rotational forms of camphene and cyclohexane are low and lie in the neighborhood of 50°K; those for the rotational and non-rotational forms of cyclohexanol are in agreement with previously published values obtained from the specific heats. Incidental to this work, the densities of the three substances in both rotational and nonrotational forms were measured over large temperature ranges.