Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators

Using molecular-dynamics computer simulations, we study the dynamics of a molecular liquid by means of a general class of time-dependent correlators S-ll(m),(q,t), which explicitly involve translational (TDOF) and orientational degrees of freedom (ODOF). The system is composed of rigid, linear molecules with Lennard-Jones interactions. The q dependence of the static correlators S-ll(m)(q) strongly depends on l, l', and m. The time-dependent correlators are calculated for l = l'. A test of some of the predictions of mode coupling theory (MCT) is performed for S-ll(m)(q,t) for l = 1,2 and its self-part S(ll)((s)m)(q,t), for l = 1,...,6. We find a clear signature for the existence of a single temperature T-c, at which the nature of the dynamics changes significantly. In the first scaling law regime of MCT it is found that the various correlators can be fitted with the beta correlator G(t), with the exception of those with l = 1. Since this is true for the same exponent parameter lambda as obtained for the TDOF, we thus find that MCT gives a consistent description of the dynamics of the TDOF as well as the one of the ODOF, with the exception of l = 1. This different behavior for l not equal 1 and l = 1 can also be seen from the corresponding susceptibilities (chi ")(ll)(m)(q,omega), which exhibit a minimum at about the same frequency omega(min), for all q and all l not equal 1, in contrast to (chi ")(11)(m)(q,omega) for which omega(min)' approximate to 10 omega(min). The asymptotic regime, for which the first scaling law holds, shrinks with increasing 1. The second scaling law of MCT (time-temperature superposition principle) is reasonably fulfilled for l not equal 1 but not for l = 1. Furthermore, we show that the q and (l,m) dependence of the self-part approximately factorizes, i.e., S(ll)((s)m)(q, t) congruent to C-l((s))(t)F-s(q, t) for all m.