No abstract

The fully relaxed single-bond torsional potentials in typical conjugated systems were evaluated with the aid of ab initio self-consistent-field and Møller−Plesset second-order calculations and, additionally, with several recently developed variants of the density functional theory. For this systematic investigation, 1,3-butadiene, styrene, biphenyl, 2,2‘-bithiophene, 2,2‘-bipyrrole and 2,2‘-bifuran have been selected as model molecules. As representative examples for nonconjugated systems, the molecules n-butane and 1-butene have been treated at the very same calculational levels. For all conjugated molecules, the electron correlation corrections to the self-consistent-field torsional potentials, as obtained with the density functional methods, are dramatically different from those resulting from the more conventional Møller−Plesset second-order approximation. For those cases where experimental data for torsional barriers are available, the self-consistent-field and the Møller−Plesset second-order results agree reasonably, whereas the density functional results consistently predict too large barriers. This behavior is most probably caused by an overestimation of the stability of the planar π-systems by the density functional theory variants in question.

Two electron correlation theories, second-order Møller−Plesset perturbation (MP2), and density functional (DFT) methods have been adopted to obtain fully optimized structures of styrene, trans-stilbene, and cis-stilbene. Full geometry optimizations with MP2 shows that the nonplanar conformations of styrene and trans-stilbene are preferred by 0.24 (styrene) and 0.80 kcal/mol (trans-stilbene), respectively. However, B3LYP, BLYP, and BVWN prefer a planar conformation contradicting the MP2 results. Due to the disorder of the crystal, X-ray experimental data of CC double bond length of trans-stilbene seem to be too short. Vibrational spectra of these molecules are calculated at the BLYP/6-31++G** level without any empirical scaling. The agreement with experiment is excellent, some normal modes are reassigned. The dependence of the IR spectrum as a function of conformation in the 700−800 cm-1 region allows the determination of the solution-phase conformation. Both styrene and trans-stilbene are planar in solution, implying that these molecular conformations are mainly determined by the intermolecular forces rather than intramolecular ones.

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-flip-time-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT. The spin-contamination of the response states of SF-TDDFT is nearly removed. This considerably simplifies the identification of the excited states, especially in the "black-box" type applications, such as the automatic geometry optimization, reaction path following, or molecular dynamics simulations. With the new methodology, the accuracy of the description of the excited states is improved as compared to the collinear SF-TDDFT. Several test examples, which include systems typified by strong non-dynamic correlation, orbital (near) degeneracy, and conical intersections, are given to illustrate the performance of the new method.