Dyes in Liquid Crystals: Experimental and Computational Studies of a Guest–Host System Based on a Combined DFT and MD Approach

Practical applications of guest–host liquid crystal systems are critically dependent on the alignment of the guest species within the liquid crystal host. UV/Vis absorption spectroscopy shows that the 1,5-dihydroxy-2,6-bis-(4-propylphenyl)-9,10-anthraquinone dye aligns within the E7 nematic host, giving an experimental dichroic ratio of 9.40 and dye order parameter of 0.74. This alignment was modelled by using a combination of density functional theory (DFT) and molecular dynamics (MD) computational approaches that do not require the input of experimental data. Time-dependent DFT calculations show that the electronic transition dipole moment is highly aligned with the long molecular axis of the dye. Fully atomistic MD simulations show that the long axis of the dye is less highly aligned within the E7 host, indicating that this contribution limits the overall dye alignment and, thereby, the potential practical applications of this particular system. Importantly, this study demonstrates an experimental and combined DFT and MD computational approach that may be applied generally to guest–host systems, providing a potential route to their rational design.


Introduction
The potential for using dyes in liquid crystal devices arose from the first reported observation of dye alignment in an ematic host, [1] and numerous modes of guest-host device operation have been suggested subsequently. [2,3] These devices are based on the principle that the guest chromophorea ligns with the liquid crystal host, enabling the application of an electric field to switch the orientation of the liquid crystal matrix between that of an absorbing (coloured) state and at ransmitting (colourless) state, as shown schematically in Figure1,b ecause the absorption transition is aligned along as pecific axis within the dye. Such guest-host devices do not necessarily require polarizers or colourf ilters because the absorption properties are defined by the guest dye molecules and their alignment; hence,they mayprovide more robust devices with higher optical efficiencies and lower powerc onsumption than some more conventional liquid crystal displays (LCDs), including the poten-tial for colour displays operating in ambient light-scattering mode without the need for back-lighting. [3,4] For ag uest-host system to be suitable for ad isplay application, it mustf ulfil an umber of criteria. Of primary importance for the visual properties of ad evice are the colour and absorption coefficient of the dye, the solubility of the dye in the host, and the contrastr atio between the absorbing and transmitting states, which is determined by the alignment of the dye within the guest-host mixture. In addition, for ad evice to be useful practically,t he system must be thermally,p hotochemically and electrochemically stable to provide as uitable operational lifetime that may be several years for typical display applications. Therefore, the choice of both the dyea nd the liquid crystal host, as well as their mutualcompatibility,are crucial in designing as uccessful device.
Azo dyes werei nitially suggested for use in guest-host displays because of their elongated, rod-like molecular shape aiding alignmentw ith al iquid crystal host that typically comprises rod-like molecules. [5] Ar ange of colours is also readily achievable with the well-established synthetic chemistry of azo dyes, but their limited photochemical and electrochemical stability can give an inherent barrier to their use in practical display devices. [6] Anthraquinone dyes have been suggested as alternative guests because they are typicallym ore stable than azo dyes, but their molecular shapes are usually less rod-like and, consequently,t heir alignment within the host tends to be poorer than that of azo dyes. [7] Good alignment in liquid crystal hosts has been obtained for some anthraquinone dyes, buti t has proved challenging to obtain ar ange of colours with high absorption coefficients. [8,9] Many other classes of dyes have also been synthesised for possible use in guest-host systems including tetrazines, [10] naphthalenes, [11] perylenes [12] and acenequinones, [13] illustrating the wide range of compounds that offer potential for these applications,a nd research into new dyes for display devices is ongoing. [14] The choice of host for these applicationsi sa lso important, and many different mixtures with dyes have been tested, including nematic, [14,15] chiral nematic [16,17] and smectic [18,19] systems. Of these hosts, nematic systemsa re the simplest and the most widely studied. Chiral nematic systems potentially offer improved optical efficiency,a nd smectic Ah osts can provide the additional advantage of bistability, [20] offering the prospect of devices with lower power consumption than other guesthost devices.
Although the main focus has been on their applicationsi n display devices, dyes in liquid crystal hosts have also been proposed as the basis for materials giving diverse applications,i ncluding optical storaged evices, [21] "smart" windows, [22] switchable waveguides, [23] high-contrast polarizers [24] and polarized electroluminescent light sources. [25] Due to the number of criteria that guest-host systemsm ust fulfil for their successful use in practical display and other devices, an approach based on the rational design of both guest and host molecules is desirable. For mostg uest-host applications of liquid crystals, the effectiveness of the system is crucially dependent on the absorptiono fa ligned guest molecules within the device, such that ak nowledge and understanding of the properties that define this behaviour are key requirements to underpin an approach towards their rational design.
An understanding of the electronic absorption transitions giving rise to the colours of dyes can now be aided greatly by time-dependent density functional theory (TD-DFT) calculations, typically on molecules isolated in the gas phase or in as olvent field. These calculations can give good matches between experimental and calculated data, and they provide information on the orbitaln ature, energies and strengths of the transitions. Examples of such studies include those on azo [26,27] and anthraquinone [28,29] classes, with reports often focusingo n these systemsi nt he context of textile fibre dyeing and related industrial applications. Molecular dynamics (MD) simulations have been widely used to study liquid crystals, providing insight into their behaviour and giving successful comparisons with various experimental properties, including alignment, transitiont emperatures and rotational viscosities. MD approaches have included coarse-grain methods, in which the molecules are treated as single geometric volumes, [30] united-atoma pproaches, in which groups of atoms are combined, [31,32] and fully atomistic simulations, in whicha ll of the atoms are treated explicitly. [33] A recent report described the use of MD simulations to explore the alignment of small rigid soluteg uests in an ematic host, [34] although guest-host simulations appear to have received relatively little attention to date.
Here, we presentanew general approach to modelling the opticala nd alignment properties of dyes in liquid crystal hosts that is based on ac ombined computational method using DFT calculations and fully atomistic MD simulations, allied with experimental data on the system being modelled. We report studies on ar ecently synthesised 2,6-disubstituted anthraquinone dye (26B3OH), [35] shown in Figure 2, which is of particular interesta saliquid crystal guest dye because of its relatively rod-like molecular shape. Theh ost used in these studies, both experimental and computational, was the nematic mixture E7, as given in Figure 2, which has been the subject of many experimental and computational studies.

Results and Discussion
Experimental spectra of an aligned guest-host system The experimental UV/Vis absorption spectra of an aligned sample of 26B3OH in E7 obtained by using linearly polarized light are shown in Figure 3. The sample gave ap olarized absorptionb and at approximately 480 nm, and exhibited an orange/red colour consistentwith this band position.
The alignment of the dye molecules can be quantified by using the experimental dichroic ratio of the dye, R,d efined as the ratio of the absorbances of the dye in the aligneds ample orientated parallel (A II )a nd perpendicular (A ? )t ot he incident polarized light (Figure 3s chematic). These values may be used in Equation (1) [6,36] to obtain the experimental order parameter of the dye S exptl ,f or which av alue of 1i ndicates that the dye molecules are fully aligned, and as ample in which the dye molecules exhibit no alignment gives avalue of 0.
The aligned sample of 26B3OH in E7 gave ad ichroic ratio of R = 9.40, measured across the range of the visible absorption band, from which an experimental order parameter of S exptl = 0.74 waso btained. These values are relatively high for an anthraquinone dye, consistent with the relatively rod-like shape of the 2,6-disubstituted structure of 26B3OH.

Contributions to the experimental alignment and order parameter
In an ematic phase, the molecules align alongapreferred axis termedt he director and defined by au nit vector n.T he align-ment can be quantified by the order parameter S q ,g iven by Equation (2), in which q is the angle between the director and the long axis of an individual molecule, P 2 is the second Legendre polynomial, and the brackets < ..> denote an ensemble average over anumber of molecules and/ortime.
Guest molecules that align with al iquid crystal host adopt the same director n.I nt he case of ag uest dye, the experimental measurement of the alignment obtained from aU V/Vis dichroic ratio gives the order parameter of the associated electronic transition dipole moment( TDM) of the dye, rather than that of the long axis of the dye. As chematic representation of this TDM orientation is shown in Figure 4, in which f is the angle between the director and the electronic TDM;t his alignment results in the order parameter of the dye S f ,g iven by Equation (3), which equates here to the experimental order parameter S exptl ,given by Equation (1).
As shown in Figure 4, the alignment of the TDM of au niaxial dye molecule can be considered to arise from two contributions:t he alignment of the long axis of the dye molecule with the director,d efined by angle q,a nd the alignmento ft he TDM with the long axis of the dye molecule, defined by angle b.T hese contributionsg ive rise to associated order parameters S q and S b ,r espectively,a sd efined in Equation (4), the product of which equates to S f and, hence,t ot he experimental value S exptl . [6,36]   The ability to consider the contributions to the experimental order parameter in terms of ac omponent from the molecular alignment of the guest within the host and as eparate component from the alignment of the transitiond ipole moment within the dye is very useful.F rom the perspective of materials design,itprovidesasimplification of the problem into two features, and computationally it enables the two contributionst o be calculated independently of each other.F or this model to be used, the long molecular axis of the dye must be defined quantitatively,a nd in the work reported here it is taken to be the axis of minimum momentofinertia,ashas been suggested and used in previous studies. [33,37,38] Transition dipole momentalignment within the dye The experimental UV/Vis absorption spectrum of an isotropic sample of 26B3OH in p-xylene solution is shown in Figure 5.
The absorption maximum of the visible band occurs at l max = 471 nm, resulting in the orange/red colour of the dye. The absorptionc oefficient at this wavelength wasf ound to be e max = 2.04 10 4 dm 3 mol À1 cm À1 ,a nd integration across this absorption band gives an experimental oscillator strength of f exptl = (k/n)se(ñ)dñ % 0.28, [39] by using values of the constant k = 4.32 10 À9 cm mol dm À3 and the refractive index n = 1.50.
DFT calculations were used to provide ac omputational comparisonw itht he experimental data. The DFT optimised structure of 26B3OH in the gas phase exhibits ap lanar anthraquinone core, with the hydroxyl groups lying in the same plane and the phenyl substituents rotated by 418 out of this plane, as shown in Figure 6. TD-DFT calculations on this optimised structure gave as ingle allowed electronic absorption transition in the visible region at 492 nm, with ah igh oscillator strength of 0.57 consistentw ith as trongly allowed transition, and with other allowed transitions occurring in the UV region at < 380 nm. As imulated UV/Vis absorption spectrum based on these calculated transitions is shown in Figure 5, along with the experimental data. The calculated orbital contributions indicate that the allowed visible transition is as imple HOMO-LUMO transition, and the calculated changes in electron densi-ty shown in Figure 6i ndicate that it involves charget ransfer from hydroxyl and phenyld onor substituents to acceptorq uinone carbonyl groups, which is consistent with the nature of similar transitions reported for related anthraquinones. [29] The TD-DFT calculations also provide the orientation of the TDM for each transition. Figure 7s hows the optimised structure of the dye overlaid with the orientation of the calculated TDM for the allowed visible transition (shown in red), along with the orientation of the long molecular axis (shown in blue), calculated here as the minimum moment of inertia axis. These two vectors both lie essentially in the anthraquinone plane, and they make an angle of b = 1.78,from which the definition in Equation (4) gives an order parameter of S b = 0.999 arising from their relative alignment. These values indicate that the TDM for the visible transition of this dye, which gives rise to its colour,i sh ighly aligned with the long molecular axis of the dye. Hence, it is appropriate to consider the alignmento f the TDM of the dye within the host to be uniaxial in this context.

Molecular alignment within ag uest-host system
An understanding of the alignmento fd ye molecules within ah ost requires the guest-host system to be considered as   aw hole. Here, we have used fully atomistic MD simulations to model the molecular alignment in this system.
Prior to simulating the guest-host mixture, we carried out fully atomistic MD simulations on 256 molecules of the host E7 mixture alone, in accordance with the methods used in af ully atomistic study of E7 detailed in the literature. [33] Twos eparate simulations of E7 alonew ere run, each for 200 ns:o ne simulation used an isotropic starting geometry,i nw hicht he molecules were randomly oriented;a nd the other used ap seudonematics tarting geometry,i nw hich the molecules were aligned. [33] The order parameter S q of the E7 mixture was calculated as the largeste igenvalue of the ordering tensor, Q ab ,a nd the director n as the associated eigenvector, [33,40] as given by Equation (5), in which N is the number of molecules, d is the Kronecker delta, j represents the molecule number in the simulation, a and b represent the Cartesian x, y and z axes, and a represents the component of the long molecular axis vector. The long molecular axis was defined as the axis of minimum momento fi nertia, which was calculated for each component molecule of E7. These calculations were carriedo ut for the whole ensemble of molecules at each time interval in each simulation data set.
Our simulations of E7 alone essentially replicate those in the report [33] that first demonstrated the approach we have adopted here;t he Supporting Information gives plots of the order parameters ( Figure S1) and densities ( Figure S2) versus time, and the dihedrala ngle distribution functions ( Figure S3) obtained. The simulation from an isotropic startingg eometry evolvedt oan ematic phase by approximately 75 ns, and averaging over 75-200 ns (the end of the run) gave an order parameter of S q = 0.885;t he pseudo-nematic starting geometry enableda veraging over al ongerr ange of 30-200 ns and gave as imilar value of S q = 0.877. These values are comparable to those of 0.81 and 0.83, respectively,r eported from the final stages of slightly shorter runs carried out by using the same two approaches with ad ifferent MD package. [33] Although the order parameter of E7 simulated here is significantly highert han the experimental values of S = 0.64 estimated here and S = 0.65 reported in the literature [33] (see the Supporting Information), the overestimation is consistent with other fully atomistic MD studies of cyanobiphenyl mixtures. [33,41] Ak ey reasonf or the overestimation is probablyt he use of af orce field in which the non-bondedi nteractions, andp articularly the van der Waals interactions modelled by Lennard-Jones potentials, are not optimised for this type of system,a sd iscussed in the literature; [32,33,41] the development of force fieldst hat are tuned specifically for liquid crystal systemsi s av ery important area of research, [32,34] but we have used the default Lennard-Jones parameters of the OPLS force field here because our aim was to carry out ac omputational study that did not requirep arameterisation based on experimental data from the systemu nder study.A nother contribution to the overestimationm ay arise from using the minimum moment of inertia axes to calculate the order parameter;a nd redefining the internal director n of the ensemble at every time interval rather than using an externalr eference frame inherently maximises the order parameter calculated for the system. An additional simulation carried out with 3872 rather than 256 molecules of E7 showed that increasing the size of the system did not significantly affect the calculated order parameter,a sd escribed in the Supporting Information ( Figure S4).
Ag uest-host simulation was run by using the same general conditions as those used for the E7 mixture alone, and from an isotropic starting point. The simulation consisted of 400 molecules of E7 with five dye molecules randomly distributed amongst them;t his composition was chosen as ab alance between generating sufficient data form eaningful analysis, providing ad ye concentration of 2.06 wt %, which is comparable to that of 1.5 wt %f or the aligned experimental sample, and giving ar easonable computational time. The simulation was run for 500 ns, which we found was necessary to ensure that each of the five dye molecules exhibited comparable angle distributionsa gainst the hostd irector and explored af ull range of orientations aroundt he director,a sd escribed in the Supporting Information (Figure S5 and S6). This simulation time is significantly longert han those reported for many liquid crystal MD studies, and it was required because of the small number of dye molecules in the simulation. During the simulations, small-scale motiona bout the equilibrium geometries was observed for both host and guest molecules, and no aggregation of the dye molecules was apparent. Figure 8s hows as napshot of the final geometry of the simulation, at 500 ns.
An analysis of the alignment of the molecules during the guest-host simulation is shown by the order parameter plots in Figure 9. The guest-host system evolvedt oanematic phase in approximately 120 ns, which is longer than the time of ap- www.chemeurj.org proximately 75 ns for the E7 host alone (described above). Averaging over 120-500 ns (the end of the run) gave an order parameter of S q = 0.881 for the E7 molecules in the guest-host system,m atching that of S q = 0.885 obtained for the host alone ( Figure S1 in the Supporting Information), and an order parameter of S q = 0.921 for the dye molecules versus the host director.
An additional guest-host simulation was run from ap seudonematics tarting geometry,s imilar to that for the E7 host alone (described above). This simulation enabled averaging from an earlier time of 30 ns, and it gave order parameters for the E7 molecules (S q = 0.879) and dye molecules (S q = 0.896) that were comparable to those from the isotropic starting point ( Figure S7 in the Supporting Information).
The order parameters from the simulations indicate that the dye molecules are more alignedt han the hostm olecules in the guest-host system. They are also consistentw ith the higher experimental order parameter we observe for the dye in the guest-host system than that reported experimentally for the E7 host alone, both herea nd in the literature. [33] The effect of ag uest dye having ah igher order parameter than its host has been observed experimentally for ar ange of systems, and it generally arises for dyes that have slightly longer molecular structures than those of their hosts, as discussed in the literature. [6] Hence, the higher simulated and experimental order parameters obtained here for the 26B3OH dye than the E7 host may be attributable to its relatively long and rigid rod-like structure in comparison with the slightly shorter and more flexible host molecules (Figure 2).
The effecto fa dding the 26B3OH dye to the E7 host was also studied experimentally by measuring the nematic-isotropic transition temperature (T NI ), which gave values of 59.4 8Cf or the host and 61.7 8Cf or the guest-host system. This observed increasei nT NI is attributable to the effect of adding ad ye that exhibits liquid crystalline behaviour in its pure form and has a T NI value of > 390 8C, [35] which is much highert han that of E7. In general,t he order parameter of an ematic system increases as the temperature is decreased at < T NI ,w hich is often expressed in terms of the reduced temperature, T/T NI ,a tw hich an observation is made. In the systems tudied here, the increase of 2.3 8Ci nT NI on adding the dye effectively lowers the reduced temperature of an observation made at 300 Kf rom 0.902 to 0.896, whichi savery small change that is unlikely to have asignificant effect on the order parameter.

Combining DFT and MD results
The separate calculations of the componentso ft he order parameter of the dye, S b = 0.999 from the TD-DFT calculation and S q = 0.921 from the MD simulation, combine using Equation (4) to give an overall value of S f = 0.920 for the dye in this guesthost system. The fact that this calculated value is higher than the experimental value of S exptl = 0.74 is probablya ttributable, principally,t ot he MD simulations giving ah ost environment that is too highly ordered, as indicated by the high S q order parameters calculated for E7, as discussed above.T he value of S b obtained here from calculations on as tatic isolated molecule may also contribute to ah igh calculated value of S f because conformational changes may modify this value on going to ad ynamic sample in the condensed phase. However,t he calculated transition is mainly localised on the relatively rigid anthraquinone core of this symmetric dye, and such an effect is probablys mall for this particular system.
The calculated contributions of the components to the alignment of the 26B3OH dye within the E7 host are shown schematically in Figure10. The calculated values indicate that the experimental dichroicr atio and associated order parameter of this particular dye in the E7 host are limited not by the alignment of the transition dipole with the long molecular axis of the dye (S b )b ut principally by the alignment of the dye within the host (S q ). This interpretation illustrates the value of expressing the overall order parameter of the dyea st wo sepa- Figure 9. Order parametersoft he E7 host molecules calculated by using Equation(5) (top), and of the 26B3OH dye molecules calculated by using Equation (2) versus the host director (bottom), averaged over all respective molecules for each time interval.T he insets give order parameter valuesobtained by averaging over 120-500ns, as shown by the ranges plotted in black. Figure 10. Schematic representation of the host E7 director and the calculated order parameters for the alignment of the 26B3OH dye and the TDM of its visible absorption transition. (In thispictorial representation:t he cone is drawn at an angleofq=13.38,corresponding to that which wouldderive from applying Equation (2) to ahypothetical d-distribution, [42] whereas the value of S q actually arises from arange of q angles in the simulation, as shown in FigureS5int he Supporting Information;t he TDM is drawn at an angle of b = 1.78 to the long axis of the dye.) rate components, and it provides ab etter understanding of the alignment of the guest-host system than given by the dichroic ratio measurement alone.
In ab roader context,t his study illustrates ag eneral approach that uses ac ombination of DFT calculations, giving spectroscopic information, and MD simulations, providing dynamic information on molecular geometries, to develop an understanding of these contributions to the overall performance of ag uest-host liquid crystal system,a longside experimental data. The computational approach described here was used withoutt he input of experimental data, apart from defaulto r literaturev alues for the MD parameters, and, hence, it may offer the potential to assist in the rational design of new dyes and guest-host systems. Moreover,t he MD simulations provide much more information than the second-ranko rder parameter < P 2 > ,o nw hichw eh ave focused here, including full orientational distribution functions for the dye molecules and correlation functions for dye andE 7m olecules, which may assist in the fundamental understanding of such guest-host systems.

Conclusion
Ag uest anthraquinone dye has been shown experimentally to align within an ematic liquid crystal host. DFT calculations have given the alignmento ft he transition dipole moment within the dye, and fully atomistic MD simulations have modelled the alignment of the dyew ithin the host. Importantly,t he combination of DFT calculations and MD simulations presented here, along with experimental data on the same sample system, demonstrate ag eneral approacht os tudying and understanding the alignmento fg uest molecules in liquid crystal hosts. This approach enables data from UV/Vis spectroscopic measurements on aligneds amples to be compared directly with order parameters obtained from computational studies, and the DFT calculations also provide information on the nature of the transitions giving rise to the colour of the dye. This general approachm ay be appliedr eadily to ar ange of different guest molecules and hosts.
In the specific example presented here, the modelled order parameters were higher than the experimental values, which may be attributable principally to limitations of the force field used in the MD simulations of the host. However,t he ability to provide aq uantitative predictionofg uest alignment in al iquid crystal host without the input of experimental data offers the potentialt oc ompared ifferent systems computationally,a nd, thereby,t op rovide as tep towards an efficient method of rational design that may be relevant in developingn ew guesthost systems for display devices and other applications.

Experimental Section Synthesis and experimental methods
The synthesis, purification and characterisation of 1,5-dihydroxy-2,6-bis-(4-propylphenyl)-9,10-anthraquinone (26B3OH) has been reported previously; [35] E7 (Merck) and p-xylene (> 99 %; Sigma-Al-drich) were used as received. UV/Vis absorption spectra were recorded using aH itachi U-3010 spectrophotometer.S olution samples were prepared by dissolving 26B3OH in p-xylene;s pectra versus solvent were recorded at room temperature (ca. 298 K) using matched quartz cuvettes with ap ath length of 1mm. Guesthost samples were prepared by heating am ixture of E7 and 26B3OH (ca. 1.5 wt %) above the clearing point to ensure full dissolution of the dye, and sonicating the mixture for about 2min after cooling to room temperature;v isual and microscope inspections of the mixture showed no evidence of precipitation. Cells for aligned samples were constructed by spin-coating glass microscope slides with as aturated solution of nylon-6,6 in formic acid, drying them in an oven at 100 8C, and then rubbing the nylon in ad efined direction to provide alignment surfaces;t wo slides were used to make ac ell with ap ath length of approximately 20 mm, and observation with am icroscope and crossed polarizers confirmed the alignment of the guest-host samples. Polarized UV/Vis absorption spectra of aligned samples were recorded at 300 K versus air,u sing aG lan-laser polarizer (Newport 10GL08) between the lamp and the sample to polarize the beam. Initially,t he sample cell was rotated to maximise the absorbance at the peak wavelength of the visible band and the parallel measurement was recorded;t he cell was then rotated by 908 and the perpendicular measurement was recorded. The spectrum of an aligned sample of E7 alone was also recorded versus air at each of these orientations, and subtractions of these reference spectra were used to obtain the data presented. The N-I transition temperatures of E7 alone and of the guest-host system were obtained by microscopy,b y using aZ eiss Axioskop 40 polarizing transmitted light microscope with aMettler FP82HT microfurnace and FP90 central processor.

Computational methods
DFT calculations were performed by using the Gaussian 09 software package. [43] The structural optimisation was carried out on an isolated 26B3OH molecule in an all-trans configuration by using the B3LYP functional [44,45] with the 6-31G(d) basis set. This optimised geometry was then used for the subsequent time-dependent DFT (TD-DFT) calculation, which was carried out at the same level of theory.Asimulated UV/Vis absorption spectrum was generated by summing Gaussian bands (50 nm FWHM) with the peaks at the calculated transition wavelengths and with the respective oscillator strengths. Fully atomistic MD simulations were carried out using the GRO-MACS 4.5.5 package. [46][47][48][49] The simulations used the OPLS AA force field [50,51] apart from the inter-ring torsions in 26B3OH and in molecules of the E7 mixture, for which reported biphenyl and cyanobiphenyl torsional force constants were used, [52] and the atomic charges within 26B3OH, for which HLYc harges [53] calculated from the optimised DFT structure were used. Simulations were run by using 2f st ime-steps, periodic boundary conditions, and at 300 K and 1bar maintained by using av elocity-rescale thermostat [54] and Parrinello-Rahman pressure coupling. [55] Av an der Waals cut-off radius of 9was used, and electrostatic interactions were calculated by using the Particle Mesh Ewald method with ac ut-off of 9. [56,57] All bond lengths were constrained throughout the simulation by using the P-LINCS algorithm. [58] Simulations of the E7 mixture were carried out with the component molecules in the relative wt %r atios given in Figure 2( and with the numbers given in Ta ble S1 in the Supporting Information);t he sizes of the simulations are described in the main text, and further details of the MD simulation methods are given in the Supporting Information.
Minimum moment of inertia axes were defined as the eigenvectors associated with the minimum eigenvalues of the diagonalised moment of inertia tensors [59] calculated for structures obtained from both DFT and MD methods.