The Rotational Barrier in Ethane: A Molecular Orbital Study (original) (raw)
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Theoretical Analysis of the Rotational Barrier of Ethane
Accounts of Chemical Research, 2007
The understanding of the ethane rotation barrier is fundamental for structural theory and the conformational analysis of organic molecules and requires a consistent theoretical model to differentiate the steric and hyperconjugation effects. Due to recently renewed controversies over the barrier's origin, we developed a computational approach to probe the rotation barriers of ethane and its congeners in terms of steric repulsion, hyperconjugative interaction, and electronic and geometric relaxations. Our study reinstated that the conventional steric repulsion overwhelmingly dominates the barriers.
Journal of Molecular Structure: THEOCHEM, 2001
Internal rotational barriers around the exocyclic partial CvC double bond were calculated for a wide group of heterocyclic derivatives as a function of the different structure of the heterocyclic ring and of the nature of heteroatoms, by means of MO abinitio theory. The rotational barriers refer to the two-fold potential energy, V 2 , obtained from single-determinant Hartree± Fock (HF) wave functions and at MP2/6-31G p //HF/6-31G p level of theory. The V 2 values seem to represent homogeneously the rotational barrier in substituted ethylenes with varying polar character of the CvC bond, ranging from unpolarized ethylene to molecules having a marked push±pull character, and thus allow the effect of substituents on the height of the barrier to be compared. Sets of parameters quantifying the heteroatom effect of constantly modulating the barrier in the different heterocyclic rings were extracted, and two heteroatoms were found to have an additive effect when acting in the same ring. The difference between the V 2 values and the rotational barriers calculated from the HF energy of the perpendicular conformation is discussed in the light of a qualitative approach based on calculated contributions of singlet excited states to the electronic con®guration of the perpendicular conformation. q
Rotational barriers. 2. Energies of alkane rotamers. An examination of gauche interactions
Journal of The American Chemical Society, 1988
The barrier to rotation about the C2-C3 bond in n-butane has been calculated using several basis sets, complete geometry optimization, and correction for electron correlation. Neither the basis set size nor inclusion of electron correlation has a large effect on the magnitude of the rotational barrier or the trans/gauche energy difference. After correction for zero-point energy differences, the former is found to be 6.34 kcal/mol, while the latter is 0.86, in very good agreement with the experimental value. The trans/gauche energy difference in n-pentane is the same as that for butane, and similar values are found for the two gauche forms of n-hexane and the symmetrical gauche form of octane. The structures and energies of several conformers of pentane and hexane with two and three gauche fragments also have been obtained. It is found that the pentane rotamer with two consecutive gauche kinks has roughly twice the gauche energy, but the hexane conformer with three consecutive gauche kinks has considerably less than 3 times that value. The energy differences for the rotamers of 2-methylbutane and 2,3-dimethylbutane are well reproduced by the calculations. Vibrational frequencies are estimated at the 3-21G level for all species, and the zero-point energies and enthalpy changes (H298 -Ho) are calculated. The difference in enthalpy between an axial and equatorial methyl substituent on cyclohexane is calculated to be 2.17 kcal/mol after correcting for vibrational energy differences. The relationship between the energy of a methylene group in cyclohexane and in trans-n-alkanes is examined.
Abstract: The energetics of rotation about the N-C' (Phi) and C-C' (Psi) bonds of methyl groups in simple amide and peptide systems have been studied by experimental and theoretical methods. X-Ray crystal structure analyses of 12 molecular confor- mations indicated that the position of the minimum in phi (C'-N-C-H) was equal to 180 deg (ie., C-H anti to the C'-N bond). In Psi (H-C-C'-N) the minimum was found to be 0 deg, ie., methyl C-H syn to the C'-N bond, based on analysis of ten molecular structures. Variations from these rotational minima appeared to be induced by crystal forces. In order to better understand these phenomena, ab initio molecular orbital, and empirical force field calculations of the rotational potential surface, and lattice energy calculations of the effect of crystal forces on the conformation were carried out. Minimal basis set molecular orbital calculations as carried out here and by others seem to yield results in disagreement with the experimental observations. When extended basis set calculations were carried out it was found that the calculated rotational potential surface in Phi is compatible with the experimental results. The location of the minimum in Psi is still not correct, however, although the barrier was found to be almost negligible (0.1-0.2 kcal/mol vs. -1 kcal/mol in the minimal basis sets). Lattice energy calculations on N- methylacetamide indicated that the crystal forces were of the same magnitude as those due to the rotational potential, in agreement with the experimental observation from various crystals that these forces seem to affect the intramolecular conformations. The minimized lattice energies at different Phi's and Psi's were combined with the rotational potential energies as obtained from the various quantum mechanical methods in order to compare the predicted conformation with that observed. The empirical force field calculations using four previously derived different sets of potential functions (three of which having been obtained from fitting crystal data) all yielded the correct minimum in Phi. However, in Psi all potentials predicted a minimum in dis- agreement with the experimental results as in the case of the quantum mechanical calculations. Thus in Psi, all theoretical methods yield the same result, which seems to be at odds with the experimental observations. The results also indicated that a 12th pqwer repulsion may be too "stiff' when applied to the short intramolecular interactions important in determining rotational potentials, Thus in Psi all theoretical methods yield the same result, which seems to be at odds with the experimental observations. The results also indicated that a 12th power repulsion may be too "stiff' when applied to the short intramolecular interactions important in determining rotational potentials.
A study of the rotational barriers for some organic compounds using the G3 and G3CEP theories
Journal of Molecular Modeling, 2014
The G3, G3CEP, MP4, MP4CEP, QCISD(T), and QCISD(T)CEP methods were applied to study 43 internal rotational barriers of different molecules. The calculated G3 and G3CEP barriers were accurate with respect to those obtained experimentally, typically showing deviations of <0.50 kcal mol −1 . The results for the MP4CEP, MP4, QCISD(T), and QCISD(T)CEP calculations were less accurate, and larger deviations of approximately ±1 kcal mol −1 were observed. The accuracy of G3CEP was comparable to that of G3, but a reduction in CPU time of between 5 and 35 % was observed when the dependence of the pseudopotentials on the size of the molecule and atom type was taken into account. The behaviors of the energy components show that these corrections depend on the molecular environment and whether the calculations are performed with all electrons or pseudopotentials. Usually, the predominance of a specific effect follows a distinct pattern when the G3 and G3CEP results are compared. For the G3 calculations, the most important component of the corrected MP4/6-31G(d) rotational energy is ΔE 2df,p . Among the 43 molecules, 29 were dependent on polarization effects, ΔE 2df,p ; 19 were dependent on diffuse functions, ΔE + ; and 13 depended on the effects of more elaborate basis functions (ΔE G3large ). Similar behavior was observed for the G3CEP calculations: polarization effects were more important for 25 molecules, followed closely by the effect of diffuse functions for 23 molecules, and finally the effect of large basis sets (19 molecules). ΔE QCI correction seldom resulted in significant effects on the G3 and G3CEP calculations.
Molecular orbital study of internal rotation
Journal of the American Chemical Society, 1969
The CND0/2 molecular orbital method is used to predict and explain the barriers to internal rotation in a number of molecules. The observed 3: 2: 1 ratio of the barriers in ethane, methylamine, and methyl alcohol is approximately reproduced as are most trends in the barriers of fluoro-substituted propenes; however, the calculated trends for fluoro-substituted ethanes are incorrect. The barriers in H202, F202, N2H4, N 2 F 4 , and NH20H and the effect of geometry optimization on these barriers are also discussed. The major source of the barriers in the first group of molecules is predicted to be due primarily to nonbonded interactions across the axial bonds, while interactions between the lone pairs on the axial bonds are found to be important in the latter group. It is concluded that CNDO will be applicable to further barrier studies only if nonbonded interactions involving highly electronegative atoms (e.g., F) are unimportant.
The Journal of Chemical Physics, 2008
Continuing our recent endeavor, we systematically investigate in this work the origin of internal rotational barriers for small molecules using the new energy partition scheme proposed recently by one of the authors ͓S. B. Liu, J. Chem. Phys. 126, 244103 ͑2007͔͒, where the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. Specifically, we focus in this work on six carbon, nitrogen, and oxygen containing hydrides, CH 3 CH 3 , CH 3 NH 2 , CH 3 OH, NH 2 NH 2 , NH 2 OH, and H 2 O 2 , with only one rotatable dihedral angle ЄH-X-Y-H ͑X , Y =C,N,O͒. The relative contributions of the different energy components to the total energy difference as a function of the internal dihedral rotation will be considered. Both optimized-geometry ͑adiabatic͒ and fixed-geometry ͑vertical͒ differences are examined, as are the results from the conventional energy partition and natural bond orbital analysis. A wealth of strong linear relationships among the total energy difference and energy component differences for different systems have been observed but no universal relationship applicable to all systems for both cases has been discovered, indicating that even for simple systems such as these, there exists no omnipresent, unique interpretation on the nature and origin of the internal rotation barrier. Different energy components can be employed for different systems in the rationalization of the barrier height. Confirming that the two differences, adiabatic and vertical, are disparate in nature, we find that for the vertical case there is a unique linear relationship applicable to all the six molecules between the total energy difference and the sum of the kinetic and electrostatic energy differences. For the adiabatic case, it is the total potential energy difference that has been found to correlate well with the total energy difference except for ethane whose rotation barrier is dominated by the quantum effect.