The self-association of 2-pyrrolidinone in cyclohexane and in carbon tetrachloride has been investigated using infrared and Raman spectroscopy and dielectric polarization measurements. In CC14 solutions up to 0.3 M the results have been interpreted as being indicative of the presence of monomers, dimers, and trimers. A computer fit of the data gives a dimerization constant, K1, of 118 ± 30 M_1 and a trimerization constant, K2, of 15 ± 10 M-1. The dipole moments of the species in CC14 are 3.74, 1.64, and 3.8 D for the monomer, dimer, and trimer, respectively. The Raman and infrared spectra show that the dimer probably has a cyclic, essentially planar structure and, along with the magnitude of the dipole moment, suggest that the trimer is also a cyclic species. The presence of some acyclic dimer and trimer as well as small amounts of higher oligomers cannot be excluded. In cyclohexane the predominant species appear to be the monomer and dimer although no model system was found which would best fit the experimental electric moment data. The dipole moment of the monomeric species in cyclohexane has been found to be 3.3 D by a graphical procedure. Selfassociation of 2-pyrrolidinone does not occur in 1,4-dioxane and the dipole moment in this solvent is 3.80 trans conformation, when < 9 it adopts the cis conformation and when = 9 both cis and trans isomers coexist.1-3 Dielectric polarization measurements indicate that the trans lactams undergo self-association in non-polar solvents forming chain oligomers while cis lactams form predominantly cyclic dimers.3 Numerous infrared spectroscopic investigations of dilute solutions of 2-pyrrolidinone and other cis lactams in carbon tetrachloride have been reported. In all cases the data and the thermodynamic parameters derived from it were interpreted on the basis of a two species system: monomer and cyclic dimer.4-9 However, in their study of e-caprolactam in CC14, Lord and Porro noted that they did not obtain a constant value for the dimerization constant for solutions with a concentration greater than about 0,2 M.9 Vapor phase osmometry was used to investigate the function of ring size on the selfassociation of a series of lactams in benzene10 and equilibrium constants and thermodynamic parameters were determined assuming a monomer-dimer system. Ebullioscopic mea-D.
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.
Free vapor-phase molecules of iodine heptafiuoride are pentagonal bipyramids with axial bonds (1.786± 0.007 A esd) shorter than equatorial bonds (1.858±0.004 Al. They are deformed from Doh symmetry on the average by 7.5 0 ring puckering displacements (e2" symmetry) and 4.5 0 axial bend displacements (e,' symmetry). The distortion from Doh, interpreted in terms of the points-on-a-sphere variant of the valence-shell electron-pair theory, is compatible with an effective force law between electron pairs of Vij""' r;r" with n in the broad vicinity of 3.5. Expressing forces harder than simple Coulomb repulsions and much softer than conventional atom-atom nonbonded repulsions, the potential-energy law is in a range consistent with Gillespie's bond-bond repulsion theory. The simplest interpretation of the diffraction intensities is that the molecules undergo essentially free pseudorotation along a pathway (predominantly e2" displacement coordinates) connecting 10 equivalent C2 structures via C. intermediates. The observed pseudoradial displacement suggests a value of about 5 cml for the pseudoangular rotation constant h/8tr 2 cI.fI • The appreciable axial bend induced by the ring pucker is correlated in phase with the pucker displacement. This correlation is responsible for introducing a pronounced skewing of the Fax ••• FeQ radial distribution peak (i.e., an "anharmonic shrinkage") and also presumably imparts significant infrared activity to the e2" modes in overtones and combination bands. Furthermore, the axial bend gives the molecule a dipole moment which may explain recent molecular-beam experiments by Klemperer et al.
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