Molecular dynamics simulation of thermomechanical coupling in cholesteric liquid crystals

The lack of a centre of inversion in a cholesteric liquid crystal allows linear cross-couplings between thermodynamic forces and fluxes that are polar vectors and pseudo vectors respectively. This makes it possible for a temperature gradient parallel to the cholesteric axis to induce a torque which rotates the director. This phenomenon is known as the Lehmann effect. The converse is also possible: one can drive a heat current by rotating the director. In this work a recently developed non-equilibrium molecular dynamics simulation algorithm is applied to calculate the cross-coupling coefficient between the temperature gradient and the torque for a molecular model system based on the Gay-Berne fluid. According to the Onsager reciprocity relations this cross-coupling coefficient is equal to the coupling between the director angular velocity and the heat current. The cross-coupling coefficients are found to be very small but non-zero and the Onsager reciprocity relations are satisfied within the statistical uncertainty.     

On the Choice of Spin Functions in the AMO Method

The alternant-molecular-orbital (AMO) method as applied to the benzene molecule is reconsidered. A variational treatment was performed to determine the singlet spin function which gives the best total energy in the five-dimensional spin space available. It is found that an AMO function containing two mixing parameters and an optimized spin function gives an energy improvement over the ordinary one-parameter AMO method, utilizing a single spin function, by 0.452 eV. Optimization of the spin function alone gives an energy lowering which is 57% of this value, while a two-parameter function with the usual spin function gives 86%. On a reconsidéré l'application de la méthode des orbitales moléculaires alternantes (AMO) à la molécule de benzène. Par un calcul variationnel on a déterminé celle des fonctions singulettes de l'espace de spin à cinq dimensions, qui donne la meilleure énergie totale. On trouve qu'une fonction AMO à deux paramètres combinée à une fonction de spin optimisée donne une amélioration de l'énergie de 0.452 eV, sur la méthode AMO ordinaire à un seul paramètre et une seule fonction de spin. Une optimisation de la fonction de spin seulement donne 57% de cette valeur-ci, tandis qu'une fonction à deux paramètres avec la fonction de spin ordinaire donne 86%. Die alternierende Molekülorbitalmethode (AMO) wurde noch einmal auf das Benzolmolekül angewendet. Mit einer Variationsberechnung wird die Singulett-Spinfunktion des fünfdimensionalen Spinraum bestimmt, die die beste Gesamtenergie liefert. Man findet das eine AMO-funktion mit zwei Parametern und einer optimisierten Spinfunktion eine Energieverbesserung über die gewöhnliche AMO-Methode mit einem Parameter und einer einzigen Spinfunktion, von 0.452 eV gibt. Optimisierung der Spinfunktion allein gibt 57% dieses Wert, während eine Zweiparameterfunktion mit der gewöhnlichen Spinfunktion 86% gibt.     

Calculation of potential energy curves for Rb2 including relativistic effects

All-electron relativistic calculations have been performed on the Rb₂ molecule. The molecular orbitals are optimized within a spin-free no-pair Hamiltonian formalism and spin-orbit coupling is treated using quasi-degenerate perturbation theory. Potential curves of the ground state and several excited states are calculated, and the spectroscopic constants T _e, D _e, R _e and ω_e are in good agreement with experimental values. The spin-orbit splittings at the 5p and 6p asymptotic limits are found to be underestimated by about 30%. Large perturbations in the spectra from the 1¹Σ⁺ _u(A) state are predicted due to an avoided crossing with a 1 ³Π_ub state caused by spin-orbit interaction. The predissociation dynamics of the 2 ¹Π_uC and 3 ¹Π_uD states is discussed. The calculations support the observation that a (1) ³ Δ_u state causes the fast predissociation of the ^{3 1}Π_uD state but rule out the (2)³Σ⁺ _u state as causing the slow predissociation at the lower part of the 3 ¹Π_uD potential energy curve.     

Transport properties of cholesteric liquid crystals studied by molecular dynamics simulation

We have studied the transport properties of a cholesteric liquid crystal by molecular dynamics simulation. The molecules consist of six soft ellipsoids of revolution, the axes of which are perpendicular to the line connecting their centres of symmetry. The angle between the symmetry axes of two adjacent ellipsoids is 7.5°, so the molecules are twisted. At high densities they form a cholesteric phase where their twist axes are oriented around the cholesteric axis and the symmetry axes of the ellipsoids are approximately parallel to the local director. We have been particularly interested in thermomechanical coupling or the Lehmann effect, which arises when a temperature gradient parallel to the cholesteric axis induces a torque that rotates the director. The converse is also possible: rotation of the director can drive a heat current. The thermal conductivity, the twist viscosity, the cross-coupling coefficient between the temperature gradient and the torque, and the cross-coupling coefficient between the director angular velocity and the heat current have been calculated by non-equilibrium molecular dynamics simulation methods (NEMD) and by evaluation of the Green-Kubo relations from equilibrium simulations. Two ensembles have been utilized: the ordinary canonical ensemble and another ensemble where the director angular velocity is constrained to be a constant of motion. All the methods give consistent results for the twist viscosity and the thermal conductivity. The NEMD estimates of the cross-coupling coefficients agree within a relative error of 20%. This is consistent with the Onsager reciprocity relations that state that the two cross-coupling coefficients should be equal. The relative error of the Green-Kubo estimates is about 100% even though the order of magnitude is the same as that of the NEMD estimates.