Barriers to internal rotation in biphenyl radical ions

Molecular orbital theory shows that the conformation of, and barriers to rotation in, radical ions of biphenyl derivatives are greatly different from those of the neutral compounds. The results are consistent with the ESR results on the cation radicals of some substituted biphenyls.     

Potential function of internal rotation for isoprene from ab initio calculations and experimental data

Ab initio computations of the potential energy curve of internal rotation around the central single C---C bond of isoprene have been performed at the Hartree—Fock level with a 3·21G basis set. The similarity of the slope of the curve obtained and the potential energy curve calculated for a more complete basis set (7s3p/4s2p) [Kavana-S2ebø, J. Mol. Struct. 106 (1984) 259] is discussed. The values of the Pitzer function F(φ), its Fourier expansion coefficients, and coefficients of the potential energy expansion were calculated from data given in the above reference. The correction of the potential energy expansion coefficients was carried out from frequencies of torsional “hot” bands of isoprene and torsional overtone of its second rotational isometric form. It was shown that the isoprene second isomer is realized as a gauche-form. The potential energy expansion coefficients were obtained as follows: V₁ = 399.9, V₂ = 1330.22, V₃ = 781.8 and V₄ = −175.8 cm⁻¹.     

Potential barriers of internal rotation in halogen-substituted ethanes

A simple model is proposed for calculating torsional vibrational frequencies and torsion potentials in ethane-type molecules. The model is based on internuclear coulomb electrostatic interactions of the end atoms in molecular groups undergoing rotations. The effective charges on the nuclei are considered to be the model parameters. The results of calculations show that the model can reliably reproduce the frequencies of torsional vibrations for rotational conformers and that the effective charges are transferable among halogen-substituted ethanes, both symmetrical and asymmetrical.Orenburg Pedagogical Institute. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 39–43, January–February, 1993.     

Potential functions of internal rotation in gauche-isomers of n-mononitroalkanes

Internal rotation in gauche-mononitroalkanes CH₃(CH₂) _n NO₂, n ≤ 7 is studied by means B3LYP/6-311++g(3df,3pd) and MP2/6-311++g(3df,3pd). Thirty six potential functions (V(φ)) are found for all rotations. It is shown that starting from a particular n value, the potential functions associated with certain molecular fragments change slightly during the lengthening of a hydrocarbon chain. Similar dependences V(φ) are presented in the form of generalized functions with averaged coefficients (V _av(φ)) that are transferable and recommended for use in molecular simulations. The rotation of tops without symmetry elements is considered.     

Potential functions of internal rotation in symmetrical ortho-unsubstituted biphenyls

K. A. Timiryazev Moscow Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 28, No. 4, pp. 56–61, July–August, 1987.     

Potential energy calculations for the double internal rotation in acetone and dimethylamine

In the present work, the problem of the determination of the potential energy surface of double rotor molecules is examined in the case of acetone and dimethylamine. From the symmetry adapted functional form for the potential of acetone that of dimethylamine is deduced and the minimum number of conformations to be calculated is derived in order to have a reliable surface (minimal expansion). The potential energy functions for acetone and dimethylamine are then determined using different standard procedures. Special emphasis is put on the electronic correlation effects in the calculation. It is found that these effects significantly improve the potential energy function.     

分子阻障内旋转的配分函数

本文用WIGNER-KIRKWOOD微扰展开法来推导分子阻障内旋转配分函数的近似表示式,准确到h[2]项,所得公式只包含两个参量(即分子自由旋转配分函数Qf和势垒高度UO与kT之比值)并可用BESSEL函数来表示,数值计算结果表明,在内旋转转动惯量较大,温度较高这一实用上最为重要的范围内,根据本文中所得公式,对任意的Qf值和U0/kT值,可直接算得阻障势能所产生的熵的修正值(Sir-Srir)/k,比用数值求解法较为简单而准确,如计及微扰展开的高次项,还可以在整个温度范围内取得良好的数值结果。不仅如此,本文所得出的解析公式容易推广到多维运动的情况中去,因此较PITZER的数值求解法具有更普遍的意义。     

A simple approximation for the vibrational partition function of a hindered internal rotation

A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.     

Hindered rotation in an "exploded" biphenyl

The first cases of hindered rotation around the triple bond in simple diphenylacetylenes were observed, including that in chiral 2,2'-bis(trimethylsilyl)-6,6'-bis(dimethylthexylsilyl)diphenylacetylene.     

Potential function of internal rotation of (CH3)2CClNO,CH3CCl2NO,and their deuterium analogs

The potential function has been constructed for internal rotation of the NO-group in (CH₃)₂CClNO, CH₃CCl₂NO, and their deuterium analogs. It has been established that the N=O bond in the cis_Cl conformer of CH₃CCl₂NO does not eclipse the C-Cl bond, rather forming an angle of approximately 30. It has been shown that a change in substitutent on the -carbon atom may produce a substantial change in the form of the potential function of internal rotation (PFIR) of the NO group.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 550–555, March, 1990.     

AB initio calculations on the equilibruim geometry and rotation barriers in biphenyl

The geometry of the biphenyl molecule has been studied with the MO LCAO method using a gausian basis set of “double zeta” quality. For various values of the twist angle between the phenyl ring planes the positions of the hydrogen atoms in the 2-position and the distance between the two rings have been simultaneously optimized. The lowest energy has been obtained for a non-planar conformation having a twist angle of 32°. The rotation barriers are 1.2 and 4.5 kcal/mol for the planar perpendicular cases, respectively.     

Adiabatic approximations to internal rotation

A number of subtle and confusing issues are addressed concerning large amplitude motion (LAM) coordinates (chi) for internal molecular motions, using the methyl rotation in acetaldehyde (CH(3)CHO) as a model problem. If the LAM coordinate is chosen to be one of the H-C-C-O dihedral angles rho(1), rho(2), or rho(3), it lacks the required 2pi3 periodicity, and its use is thus undesirable. An excellent local internal coordinate for this model problem is tau(3)=13(rho(1)+rho(2)+rho(3)-2pi). A similarly good but nonlocal coordinate for the adiabatic approximation of internal rotation is provided by the intrinsic reaction coordinate s. Comparison of the mass-independent V(0)(tau(3)) and the mass-dependent V(0)(s) internal rotation curves shows that the two are virtually identical for the parent isotopolog of acetaldehyde. A unified internal coordinate projection scheme for determining complementary vibrational frequencies and subsequently V(ZPVE)(chi) along a path for LAM has been formulated, where V(ZPVE)(chi) is the zero-point vibrational energy correction to the internal rotation curve. In addition to its simplicity, the projection scheme developed for a distinguished reaction path generated by constrained optimizations is appealing because the vibrational frequencies along the LAM path are invariant to chemically meaningful choices of the internal coordinates for the complementary modes.     

A study of the ethane internal rotation barrier

In an effort to deduce the source of the ethane internal rotation barrier, we have investigated the contributions of exchange energy and orthogonality: two effects that are required by the Pauli principle. Fully antisymmetrized, partially antisymmetrized and non-antisymmetrized optimized orbital product wavefunctions were determined. Results show that the exchange energy contribution to the barrier is negligible only when it is evaluated from energy-localized orbitals; even in this case the small total results from cancellation of large contributions. The barrier is apparently caused by the orthogonality that is required between CH orbitals on opposite ends of the molecule. The CC bond has insignificant participation in this effect.     

Molecular design of correlated internal rotation

Disrotatory coupling of the internal rotational degrees of freedom in double rotor molecules has been studied for bis(9-triptycyl)methanes (Tp₂CH₂) and bis-(9-triptycyl) ethers (Tp₂O). These molecules undergo rapid internal rotation in a strictly gear-meshed fashion, giving rise to new stereoisomerism in the 2, 2′- and 3,3′-dichloro derivatives. The racemic and meso isomers which arise due to different phase relationship between the substituted benzene rings were separated by HPLC. The high energy barrier to the gear-slipping process was obtained as 32 - 33 and 42 - 43 kcal mol^?1 for Tp₂CH₂ and Tp₂O, respectively, by the isomerization study. The low energy barrier to the gear-meshing process was determined to be ca. 4.5 kcal mol^?1 by analyzing the exciplex fluorescence dynamics for a Tp₂O carrying the naphthalene chromophore on one Tp unit and the tert-amino group on the other. The molecular structure of Tp₂O has been determined by an X-ray analysis; the molecule adopts a bevel gear-shaped structure with the C_s point group in which the CO bond lengths average 1.412 Å and the ∠COC angle is widened to 135.8°. An attempt at reproducing the observed structural features by means of an empirical force-field calculation is described. A possible extension of the concept and further results on correlated internal rotation and phase isomers are discussed.     

Phenyl group rotation in polystyrene and the nature of twofold anisotropic internal rotation

A review of the experimental evidence for phenyl group rotation in various polystyrenes and improvements in the interpretation of spin relaxation data for dilute solutions of randomly coiled polymers led to a new calculation of the correlation time for phenyl group rotation from nuclear magnetic resonance (NMR) data. Both ¹³C and ¹⁹F NMR data were reconsidered by using a model which includes motional modulation of the dipole–dipole interaction by overall rotatory diffusion, backbone rearrangements, and internal anisotropic rotation. The choice of a twofold potential to characterize local resistance to internal phenyl group rotation strongly influences the estimate of the rate of phenyl group rotation. The magnetic resonance data are found to be consistent with a correlation time for phenyl group rotation which is one to six times longer than the average correlation time for backbone rearrangement.