Conformational characteristics of poly(ethylene imine) (PEI) have been investigated by a rotational isomeric state (RIS) analysis of ab initio molecular orbital (MO) calculations and 1H and 13C NMR experiments for a monomeric model compound, N,N ‘-dimethylethylenediamine (di-MEDA). From the MO and NMR data, it was shown that the C−C and C−N bonds of di-MEDA have high gauche (71−93%) and trans (64−86%) preferences, respectively. Conformational energies of PEI were determined from the MO calculations for di-MEDA at the MP2/6-311++G(3df, 3pd)//HF/6-31G(d) level. The high gauche stability in the C−C bond was indicated to stem from a moderate and a weak intramolecular N−H···N hydrogen bonds; the interaction energies were evaluated as −1.54 and −0.58 kcal mol-1, respectively. The RIS scheme including rotational and inversional isomerizations was developed and applied to PEI to evaluate the chain dimension and diad probabilities. With the conformational energies determined as above, the characteristic ratio and meso-diad probability of PEI at 25 °C were calculated to be 2.9 and 0.63, respectively. In polar and protic solvents, the intramolecular hydrogen bonds are weakened, and consequently the PEI chain extends. Branching effects on the conformation were investigated from MO and NMR analysis for monomeric model compounds of branched PEI, N, N,N ‘-trimethylethylenediamine and N, N,N ‘ ,N ‘-tetramethylethylenediamine; the gauche preference in the C−C bonds, due to the hydrogen bonds, is reduced with increasing number of methyl groups. Ab initio MO calculations were carried out for the double-stranded helix found in anhydrous PEI crystal. The PEI chain was indicated to adopt the isotactic form exclusively. The natural bond orbital analysis showed that intermolecular N−H···N hydrogen bonds are formed between paired chains of the double helix. The enthalpy of association per repeating unit was estimated to be −3.6 kcal mol-1 at the MP2/6-311+G(2d,p)//HF/6-31G(d) level.

Conformational characteristics of poly(propylene sulfide) (PPS, [CH2C*H(CH3)S] x ) have been investigated. Proton and carbon-13 NMR vicinal coupling constants observed from its monomeric model compound, 1,2-bis(methylthio)propane (BMTP, CH3S−CH2−C*H(CH3)−SCH3), were analyzed to yield bond conformations of the S−C, C−C*, and C*−S bonds. Ab initio molecular orbital (MO) calculations at the MP2/6-311+G(3df,2p)//HF/6-31G(d) and B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) levels were carried out for BMTP to evaluate free energies and dipole moments of all the possible conformers. Conformational energies and bond dipole moments of BMTP were estimated therefrom. Conformational energies of BMTP and PPS were also determined by simulations based on the rotational isomeric state scheme for experimental observations of bond conformations of BMTP, characteristic ratio of atactic PPS, and dipole moment ratios of isotactic and atactic PPS. The first-order interaction energies for the S−C (E σ) and the C−C* (E α and E β) bonds were obtained as follows:  E σ = −1.0 to −0.60 kcal mol-1, E α = 0.5−0.6 kcal mol-1, and E β = 1.1−1.2 kcal mol-1. The second-order ω1 and ω2 interactions, representing intramolecular C−H···S interactions, are repulsive:  E ω 1 = 0.6−0.9 kcal mol-1 and E ω 2 = 1.0−1.2 kcal mol-1. The S−C, C−C*, and C*−S bonds were found to prefer the gauche, trans, and trans states, respectively. The conformational characteristics of unperturbed PPS are similar to those of poly(ethylene sulfide) but significantly different from those of its corresponding polyether, poly(propylene oxide) (PPO), although isotactic PPS and PPO are isomorphous. The conformational characteristics of PPS are discussed in terms of solvent effect, crystal structure, and thermal properties.

Conformational characteristics of poly(methylene sulfide) (PMS) and its oligomeric model compounds have been investigated. Carbon-13 NMR measurements for a dimeric model compound, bis(methylthio)methane, in the gas phase as well as in solutions were carried out, and the first-order interaction energy E σ representing the gauche stabilization of the C−S bond was determined from observed vicinal C−H coupling constants. For example, the E σ value for the gaseous dimer was evaluated as −1.43 ± 0.01 kcal mol-1, being in good agreement with the ab initio molecular orbital calculation (−1.38 kcal mol-1) at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d) level. The conformational energy E σ showed solvent dependence; polar solvents stabilize the trans conformation, in which dipole moments are parallel to each other and hence the molecule becomes polar. The characteristic ratio, dipole moment ratio, and configurational entropy of unperturbed PMS were estimated by the rotational isomeric state scheme and compared with those of poly(methylene oxide) (PMO). The PMS chain was indicated to be more flexible than PMO. The difference in melting point between PMS (245 °C) and PMO (180 °C) was suggested to come mainly from that in enthalpy (ΔH u) of fusion:  ΔH u(PMS) > ΔH u(PMO). The geometrical parameters, electron densities, and atomic charges of trimers of PMS and PMO, obtained from the MO calculations, showed that the gauche stability in the C−S bond of the PMS homologues comes partly from antiparallel dipole−dipole interaction and nS → hyperconjugation formed in the gauche state, partly from steric S···S repulsion occurring in the trans form. It was also shown that sulfur electrons have such flexibility as to reduce the S···S repulsion and unfavorable (parallel) dipole−dipole interaction.