Studies on aliphatic polyesters. Part II. Ab initio, density functional and force field studies of model molecules with two carboxyl groups

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Abstract

This paper is a continuation of our study on the ester bond energetics. Here, model molecules for structural units of biodegradable polyglycolic and polylactic acids (HC(double bondO)–O–CH2–C(double bondO)–O–CH3 and HC(double bondO)–O–CH(CH3)–C(double bondO)–O–CH3), which contain two carboxyl groups in close vicinity to one another, have been considered. Rotations about the neighbouring C(sp3)–O(sp3) and C(sp3)–C(sp2) bonds adjacent to the CH2 or CH(CH3) group have been studied quantum chemically by ab initio and density functional methods (MP2, B3-LYP and B-LYP), using the standard Gaussian-type basis set 6-31G(d), as well as by the PCFF (Polymer CFF) force field. The quantum chemical results mostly are in good agreement with each other. However, for the C–O rotations, the Density Functional Theory (DFT) barriers are 0.5–3.1 kcal/mol lower than the corresponding MP2 ones. The conformational dependency of bond lengths, valence angles, and that of atomic charges also is similar in the MP2 and DFT methods. The changes in bond lengths with conformation are small, but the valence angles vary more and especially in high-energy states with low population they may open as much as 18°. The conformational dependence of the most significant atomic CHELPG charges also was found to be small, and the largest relative changes occurred in small charges that do not have a major impact on the electrostatic potential. The PCFF force field produced torsional energetics that was in serious disagreement with the quantum chemical results, especially in the case of the C–C rotations. By reoptimizing the pertinent torsion parameters of the PCFF force field, these disagreements could be removed.

Introduction

In an atomistic model of molecular systems interactions between atoms are described by potential energy functions (force fields) [1], [2], [3], [4], [5], [6], as follows:V=12i[Fii(qi−qi0)2+Fii(3)(qi−qi0)3+Fii(4)(qi−qi0)4+⋯]+i<jFij(qi−qi0)(qj−qj0)+∑Vtor+∑Vq,tor+∑Vtor,tor+∑VnbAs regards conformational analysis, the most important potential energy terms are the torsion potentials (Vtor) and the non-bonded interactions (Vnb). The torsion potential describes the potential energy associated with rotations about chemical bonds in a molecular system, and may be writtenVtor=nVn(1±cos)where Vn is a torsion parameter and n is the periodicity with respect to a torsion coordinate φ.

The non-bonded potential describes interactions between atoms that are not chemically bonded to each other or to the same atom (1,4 and higher interactions). Usually the long-range attractive dispersive and short-range repulsive interactions are accounted for by a Lennard-Jones type potential, which together with the Coulomb potential for interactions between partial charges, ei, forms the non-bonded potential. For the 9-6 potential this is:Vnb(rij)=E0,ij2R0,ijrij9−3R0,ijrij6+keiejϵ(rij)rij

In Eq. (3)Eo,ij and Ro,ij are parameters, which depend on the type of atoms i and j, rij is the distance between atoms i and j, and ϵ(rij) is the dielectric constant. The valence part, i.e. the terms that depend on the valence coordinates qi (where qi0 is the reference value of qi) indirectly affects the conformational properties through the optimized geometry of the molecular system. These terms are discussed in more details elsewhere, see for example [1], [2], [3], [4], [5], [7].

In the force field studies of molecular systems having two or more interacting polar groups, the transferability of the force field parameters has to be carefully considered. This is especially true for the partial charges (closely related to the quantum chemically calculated atomic charges) and their conformational dependence. In our recent ab initio and density functional theory (DFT) study of model molecules for aliphatic polyesters with weakly interacting carboxyl groups, it was noticed that the atomic charges of the less polar alkyl groups depended somewhat on conformation [7]. The atomic charges of the polar carboxyl groups were, instead, much less sensitive to bond rotations. Therefore, the approximation of conformationally independent partial charges in the force field was valid, as the polar groups dominate the electrostatic potential especially at shorter distances from the atoms. However, for polyglycolic (R=H) and polylactic (R=CH3) acids

that have only one carbon atom between the carboxyl groups, this approximation is not a priori evident.

It is also of interest to compare the torsional behaviour of the chain bonds with those in molecules containing only one carboxyl group, treated in our previous paper [7] in this series. Usually, the parameters of different potential energy terms (see Eq. (1)) are correlated with each other. Therefore reoptimization of some of them, to improve the accuracy of calculations of some particular molecular properties of interest, often causes some other properties to be determined incorrectly. More detailed discussion about these difficulties can be found in [7], [8], [9]. The torsion parameters are, however, less correlated with the other parameters of the force field. For this reason the torsion potential can be reoptimized by utilizing quantum chemically calculated results on the rotational behaviour of the chemical bonds in question without reoptimization of the rest of the force field. In this way it is possible to improve the ability of a force field to produce realistic rotational behaviour of, for example, flexible bonds in polymer chains.

In Ref. [7] the performance of the PCFF (Polymer CFF) force field, developed for synthetic polymers and belonging to the CFF force field family by Hagler et al. [10], [11], [12], [13], [14], [15], [16], [17], was studied utilizing a few selected model molecules containing one carboxyl group (molecules A and B in Fig. 1). It was found that the PCFF was able to reproduce correctly the C(sp2)–O(sp3) rotation but not the neighbouring C(sp3)–C(sp2) rotation, both bonds being adjacent to the carbonyl C=O group. The most recent force field for polymers, named COMPASS (Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies) [18] was found to give even worse results in this regard, especially in the case of the C–C rotations. (An exception was the conformations close to the trans conformations which the COMPASS force field reproduced better than the PCFF force field, see Ref. [7]). For this reason the COMPASS force field has not been further considered here.

In this paper, the C(sp3)–O(sp3) and C(sp3)–C(sp2) rotations, both of them adjacent to the methylene or CH(CH3) group in the model molecules IIII (see Fig. 1), are studied by ab initio and DFT methods. The ability of the PCFF force field to describe the rotational behaviour of these bonds is evaluated, and the disagreements found between the quantum chemical and PCFF results are removed by reoptimizing the corresponding torsion potentials. The effect of the second carboxyl group, present in molecules II and III, on the results is studied in more detail by comparison with the results of molecule I and those of Ref. [7] (molecules A and B). Similarities between different C(sp3)–O(sp3) and C(sp3)–C(sp2) torsions in aliphatic esters studied here and in Ref. [7] also are considered in this paper.

Section snippets

Computational details

The ab initio and DFT calculations were carried out using gaussian 94 (Revisions B.1 and E.2) [19] with the default settings of the software on a Cray C94 at the Center for Scientific Computing (Espoo, Finland). The potential energy scans were performed at the MP2 level and with the DFT [20] method utilizing two non-local gradient-corrected exchange-correlation functionals, B-LYP (non-hybrid Becke–Lee–Yang–Parr (BLYP) functional [21], [22]) and B3-LYP (hybrid three-parameter B-LYP functional [23]

Results and discussion

In the following, results concerning the rotational behaviour of the neighbouring C(sp3)–O(sp3) and C(sp3)–C(sp2) bonds around the methylene or CH(CH3) group (hereafter called the O2–C3 and C3–C4 bonds) are first presented. The conformational dependence of the geometries and electrostatic potential derived (CHELPG [25]) atomic charges are then discussed in more detail. The corresponding PCFF force field results are given in the context of the respective quantum chemical ones. Finally, the

Conclusions

The reliability of the results in atomistic simulations of large molecules and polymers, depends on the force field used. The torsion potentials and non-bonded interactions are of particular importance due to their direct effect on the population of the conformational states of molecules in molecular dynamics (MD) and Monte Carlo (MC) simulations. In the first paper of this series [7] we studied model molecules with one carboxyl group, whereas in this work the main interest was to model

Acknowledgements

The Neste Foundation (J.B. and B.M.) and TEKES, The Technology Development Center of Finland, (L.-O.P.) are gratefully acknowledged for financial support. We thank Dr Kim Palmo for valuable comments on this manuscript. We very much appreciate the referee's helpful suggestions and comments.

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