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Structure and dynamics of liquid CS2: Going from ambient to elevated pressure conditions

Molecular dynamics simulation studies were performed to investigate the structural and dynamic properties of liquid carbon disulfide from ambient to elevated pressure conditions. The results obtained have revealed structural changes at high pressures, which are related to the more dense packing of the molecules inside the first solvation shell. The calculated neutron and X-Ray structure factors have been compared with available experimental diffraction data, also revealing the pressure effects on the short-range structure of the liquid. The pressure effects on the translational, reorientational and residence dynamics are very strong, revealing a significant slowing down when going from ambient pressure to 1.2 GPa. The translational dynamics of the linear CS2 molecules have been found to be more anisotropic at elevated pressures, where cage effects and librational motions are reflected on the shape of the calculated time correlation functions and their corresponding spectral densities.

The investigation of the pressure effects upon the structure and dynamics of molecular liquids has provided valuable information about various molecular mechanisms related to their macroscopic properties. When the pressure increases the dynamic properties of liquids are significantly affected [29][30][31][32][33] . The observed volume exclusion at high pressures leads to the decrease of translational diffusion and to the increase of reorientational relaxation times [34][35][36][37] . However, high pressure experimental measurements require specific experimental set up and discrete safety in general [38][39][40][41][42][43][44] .
On the other hand, these effects could be relatively easily studied by employing concerning the pressure dependence of molecular motions [35][36][37][38][39][53][54][55][56] . However, a more systematic investigation of pressure effects on the structure and dynamics of this liquid becomes indispensable in order to better understand the molecular scale phenomena at high pressure conditions. The structure of liquid CS2 at ambient conditions has been extensively studied by neutron scattering (NS) and X-ray diffraction (XRD) experiments 11,[57][58][59][60][61][62] . However, to the best of our knowledge, only one experimental study on the pressure dependence of local the structure in liquid CS2 has been quite recently reported 63 . In that study high pressure XRD measurements were performed at 293 K and up to the pressure of 1.2 GPa, just below the freezing point (1.26 GPa), using highly intense synchrotron radiation beam with a continuous energy dispersion spectrum technique. focused on very fast dynamic processes in the fluid. According to their measurements, a damped oscillatory temporal response signal is observed at high pressures during the first picoseconds following impulsive excitation. The signal obtained has been interpreted in terms of molecular reorientational motion, which is librational in character. MD simulation studies of liquid CS2 have also been reported by Fujita and Ikawa 31 at 300 K and densities corresponding to the pressure range of 1-10 kbar. The main purpose of that study was to investigate the pressure effects upon the farinfrared interaction induced absorption spectra (FIR -IIAS) of the fluid. However, the thermodynamic, structural and dynamic properties of CS2 at high pressures and the accuracy of the employed potential model of CS2 in predicting them haven't been presented in details in that study. The most recently reported MD study of liquid CS2 at high pressures is the one performed together with XRD measurements by Yamamoto et al. 63 . A rigid body potential model has been employed, using the parameters of the potential model of Zhu et al. 65 . In that study the authors mainly focused on the pressure effect on the local structure of the liquid. The comparison between the calculated and experimental structure factors has been found to be very good (see Fig. 4 in Ref. 63), despite the fact that the parameters of the model potential used were optimized to reproduce liquid properties at ambient conditions. However, 4 the reliability of this model in predicting the thermodynamic, transport and dynamic properties of liquid CS2 at high pressures was not discussed in that study.
Despite this growing interest upon liquid CS2 under pressure, no clear picture has been yet emerged concerning the dynamic behavior of the system in relation with the local structure changes at high pressures. In this context, liquid CS2 under pressure appears to be an interesting molecular liquid for further experimental and theoretical investigations.
In the present work, the investigation of the local structure and dynamics of liquid CS2 at room temperature and at pressures up to 1.2 GPa is reported for the first time by employing MD simulation techniques. The reliability of a recently proposed potential model for liquid CS2 11 in predicting the properties of the system at high pressures is also presented and discussed. The paper is organized as follows: The computational details are presented in Section II. Results and discussion are presented in Section III. The main conclusions and remarks are summarized in Section IV.

A. Potential Model
Carbon disulfide is one of the simplest triatomic molecules belonging to the D∞h point symmetry group. The molecules in the ground state are linear centro-symmetric with a positive quadrupole moment Q and zero permanent dipole moment μ 10 .
Theoretical and simulation studies have been presented in the literature devoted to the development of effective potential models, in order to model the intermolecular interactions between the CS2 molecules. By surveying the literature, a few models of interest were found and will be briefly outlined. The same potential model has also been used to study several relaxation processes in liquid CS2 38,[70][71][72][73] .
The CS2 molecule carries a quadrupole moment and exhibits polarizability anisotropy. In addition, CS2 is a rather flexible molecule and this fact causes to some extent deviations from its rigidity. In view of these facts, Zhu et al. 65 reported a new potential model for liquid CS2 composed of intermolecular LJ atom-atom and Coulombic electrostatic terms plus a third term describing the intramolecular harmonic vibrations. This model has been further used in a number of forthcoming simulation studies mainly at ambient conditions 31,[75][76][77] .
The intermolecular potential energy surface of CS2 obtained by ab initio quantum mechanical calculations (at the MP2 level of theory) of the interaction energies for a range of dimer configurations and center-of-mass (COM) separation distances has also recently reported 78 . However due to the angular dependency of the potential model parameters, one has to express them as series of bipolar spherical harmonic functions. Thus, due to the fact that each parameter in the model contains a significantly large number (182) of parameters, it is obvious that this CS2-CS2 proposed potential model is not simple and computationally convenient to be used in simulation studies of the liquid. In the same study, a simple analytical spherical onesite intermolecular potential of CS2 has also been developed. However, a spherical potential for a linear and strong anisotropic molecular liquid such as CS2 may be considered as an insufficient one and obviously may not be used in the framework of a simulation study tried to study in details the structure and dynamics of the liquid and especially to interpret available scattering data.
The potential model employed in the present study is the one proposed by Neufeind et al. 11 . Prior to describing the details of this particular potential model, it would be reasonable to summarize the method employed by them to obtain the parameters of their proposed potential model. In their study Neufeind et al. mainly focused on the determination of the local structure in terms of the partial structure factors of liquid CO2 and CS2 at the same density by a combination of a 12 C/ 13 C isotope substitution ND experiment with an XRD one. The main aim of that study was to understand the physical origin of the differences in their properties and to explore fundamental questions related to their different behavior in general, like e.g.

why CS2 is a liquid at ambient conditions and CO2 is not. Neufeind et al. pointed out
that their different behavior could be attributed to their interaction potentials rather than to their different size or mass. In that study ND and XRD experiments were performed in order to determine the partial structure factors of both liquids. It was 6 found, however, that the scattering contrast between the 12 C/ 13 C isotopes was very small, a fact that introduced serious problems regarding the mathematical procedure employed to determine the partial structure factors and the site-site partial distribution functions. Nevertheless, it is known that recently alternative methods, based on modern computational tools, have been developed in order to extract in details the 3dimensional (3D) microstructure of the molecules in the liquid using the available scattering data. Such techniques, like Reverse Monte Carlo (RMC) 79 [94] and empirical potential structure refinement (EPSR) 80,81 , have been used in previous studies of several liquid systems to depict the 3D local structure around the molecules.

A. Thermodynamics
The comparison of the calculated pressure with the experimental one at each simulated thermodynamic state point constitutes one of the most fundamental criteria to validate the potential model used. The calculated pressure at the three simulated state points (Table 2) has been found to be in very good agreement with experiment.
The deviations |Pexp-Psim|/ Pexp from the experimental values are very small, especially at high pressures, and sufficiently smaller compared with corresponding pressure predictions in previous MD studies of this liquid based on other side-side LJ (12 -6 -1) potentials (see for instance Table III in Ref. 38).
The calculated intermolecular potential energy of the Upot,sim (kJ/mol) and the contributions of the electrostatic terms to its overall value, are also presented in Table   II. The enthalpy of vaporization for each simulated state point has been calculated using the relation: It may be observed that although the overall potential energy and the vaporization enthalpy change by about 4.3 kJ/mol when going from ambient pressure to 12 kbar, the change in the contribution of electrostatic interactions to the total potential energy is small (0.25 kJ/mol) and LJ interactions are the dominating ones even at very high pressures. In general the simulated potential energy Upot,sim is in quite reasonable agreement with experimental values reported for liquid CS2 67-69 .

B. Intermolecular Structure
The intermolecular structure has been investigated in terms of partial atom-atom pair radial distribution functions (prdf), ga-b(r), presented in Figure 1. The center of mass (comcom) C-C prdf at normal pressure (state point A) exhibits a main first peak located at 4.9 Å followed by a well-defined minimum at 6.9 Å, which characterizes the size of the first solvation shell. Focusing on the left side of the first peak, a weak shoulder is located at 4.0 Å, which could be an indication of some kind of local structure formation among the first neighboring molecules. Though the C-C prdf at 1 bar generally exhibits a similar behavior with the prdfs obtained by previously reported potential models, however, its local extrema are slightly different. A similar trend may be observed for the C-S and S-S prdfs at 1 bar. The C-S prdfs exhibits a double maximum with peaks of similar amplitude, located at about 4.0 and 5.0 Å respectively, followed by a minimum at 6.1 Å. On the other hand, the resulting shape of the S-S prdf exhibits the typical behavior of monoatomic or spherically symmetric molecular liquids with a sharp first maximum at 3.9-4.0 Å and a well-formed minimum at 5.2Å.
The behavior of these three prdfs at elevated pressures is also presented in the same figure. The maxima and minima of the com-com (gcc(r) prdfs of CS2 are shifted towards shorter distances exhibiting an increase of the peak amplitudes and a more oscillating behavior with pressure. The greatest changes in the shape of the gcc(r) function are obtained at the highest pressure studied (state point C). The first peak of the function becomes higher than that at normal pressure, the position of its first minimum decreases from 6.9 to 6.2 Å and the above mentioned shoulder at short distance grows up to a local narrow peak of low amplitude located at 3.7 Å followed The greatest change on the shape of the C-C prdf has been observed at the highest pressure studied (state point C). Up to the location of the formed sub-shell (as it may be easily seen from the local narrow maximum in the range 3.7 to 4 Å) the local coordination number is about 2 molecules and up to the first main peak ( r ~ 4.75 Å) it becomes n(r)=5 molecules. A similar behavior has been observed for the other two atom-atom prdfs, namely gcs(r) and gss(r), when increasing the pressure. By inspecting the pressure effect on these prds, a systematic change of the double maximum located at distances of 4.0 and 5.0Å respectively might be observed. As the pressure increases the first peak at 4.0 Å becomes prominent, exhibiting also a higher amplitude, and the prdf is shifted at shorter distances as in the case of the gcc(r) prdfs.
It is well known that up to the distance range where the C-C prdfs exhibit their first maximum, repulsive interactions are the predominant ones and the shape of these functions is mainly determined by the pair intermolecular potential; g(r) ~ exp[-U(r)].
In order to further analyze the pressure effects on this very-short intermolecular structure, the contribution of the nearest neighbors in the overall shape of the prdfs , which means that it is formed due to the nearest located first neighbor molecule, while in the latter case due to the first and second nearest molecules. Such an observation indicates the dense packing of two neighbor molecules around a central CS2 at very short distances at high pressures conditions, creating in this way an inner sub-shell inside the first solvation shell of CS2, as it is also reflected by the presence of the peak at very short distances at 1.2 GPa.
Apart from the calculated prdfs, the neutron and X-Ray structure factors were calculated at each simulated thermodynamic condition. The neutron scattering structure factor can be expressed as 87 : where  b is the coherent neutron scattering length for species α. The average is a spherical one over wave vectors of modulus q. The partial static structure factors involving species α and β are defined as: and l r  is the instantaneous vector position of atom l . In the case of X-Ray scattering the structure factor can be expressed as: where: In the last equation   is the fraction of α and  International Tables for Crystallography. Using the above mentioned formalisms, the neutron and X-Ray structure factors were calculated for each of the three simulated thermodynamic conditions and are presented in Figures 3 a,b. This is the first time that both the neutron and X-Ray structure factors are being simultaneously calculated at these specific thermodynamic conditions, using the direct method instead of the Fourier transform method of the radial distribution function. The direct method poses in general a better choice, especially in the low-q regime. The Fourier transform method also suffers from the cut-off ripple artifact of g(r) and finite size effects 88 .
The pressure effects on the intermolecular structure in liquid CS2 are also reflected on the shape of the calculated neutron and X-Ray structure factors. The shift on the first peak position at a higher wave vector value (from 1.95 Å -1 at ambient conditions to 2.12 Å -1 at 1. Apart from the calculated atom-atom radial distribution functions, the pressure effects on the local orientational order in the liquid were investigated by calculating the angle distributions for pairs of CS2 molecules, having a C-C distance less or equal than 4 Å. As it has been mentioned above, this distance corresponds to the small peak observed in the C-C prdf, which our analysis has revealed that arises mainly due to the contribution of the two nearest neighbors around a central CS2 molecule. The calculated normalized angle distributions for all the simulated thermodynamic state points are presented in Figure 5. It can be clearly seen for Figure 5, that at high pressures (state point C) the shape of the angle distribution is significantly different, signifying that the existence of near-parallel configurations between a central CS2 molecules and its two nearest neighbors is more promoted at high pressures. This 12 observation is also in agreement with the findings of previous molecular simulation studies of Fujita and Ikawa 31 .

C. Dynamic Properties
Apart from the intermolecular structure of the liquid at the investigated range of thermodynamic conditions, several dynamic properties were also investigated in the present study by calculating the corresponding time correlation functions (tcf). In order to extract more information about the dynamic processes taking place inside the first solvation shell of CS2, the residence dynamics inside this shell were investigated.
According to the literature 89 , the residence tcf inside a solvation shell around a central molecule i could be defined as: The corresponding residence time is defined as: The variable ij h has been defined in the following way: This slowing down has also been observed in the calculated self-diffusion coefficients of CS2. The self-diffusion coefficients were estimated from the calculated mean square displacements of the molecules using the well-known Einstein relation: The calculated mean square displacements as a function of time are depicted in Figure   7 and the calculated self-diffusion coefficients are presented in Table III,  ) it can be also observed that even at high pressures our MD simulation results are in very good agreement with the experiment.
A similar change in the dynamics of CS2 molecules at elevated pressure conditions has also been observed for reorientational dynamics. In this case, reorientational 14 motions of the CS2 molecules can be investigated in terms of the Legendre reorientational tcfs: In this equation u  is a unit vector along a specified direction inside a molecule and  P is a Legendre polynomial (   The calculated first and second order Legendre reorientational tcfs for the bond axis vector of CS2 are presented for Figures 8a,b. The corresponding reorientational times are also presented in Table 3. From this table it can be observed that the first-order 15 The parallel and perpendicular components at each time t are expressed as: of the com velocity tcfs have also been calculated by performing a Fourier transform of the tcfs: have been calculated by numerical integration using a Bode rule, after applying a Hanning window to the calculated velocity tcfs. The calculated normalized spectral densities are depicted in Figure 10a. From this figure the absence of a peak at ambient conditions can be observed. However, as the pressure increases a peak located at the low-frequency region starts to appear, located at 24 cm -1 at 0.  Figure 10b, where it may be seen that this peak is even more pronounced. Such a finding indicates that the appearance of this shoulder at 125 cm -1 could be attributed to the reflection of correlated dimer motions on single molecule dynamics.

IV. Conclusions
In the framework of the present study classical molecular dynamics simulations have been performed to study the pressure effects on the structural and dynamic properties of liquid carbon disulfide in a wide range of thermodynamic conditions, from ambient pressures up to 1.2 GPa. The results obtained have revealed structural changes at high pressures, which are related to the more dense packing of the molecules inside the first solvation shell. The dense packing of two neighbor molecules around a central CS2 at very short distances at high pressures has been observed, creating in this way an inner sub-shell inside the first solvation shell of CS2. The calculated neutron and X-Ray structure factors have been compared with available experimental diffraction data, also revealing the pressure effects on the short-range structure of the liquid.
Apart from the intermolecular structure of the liquid at the investigated range of thermodynamic conditions, several dynamic properties were also investigated. A significant slowing down of the dynamics at high pressures has been observed, reflected on the increase of the calculated relaxation times and the decrease of the self-diffusion coefficients by an order of magnitude. The calculated spectral densities of the velocity tcfs have also revealed the importance of cage effects and intermolecular interactions at very short distances in the high-pressure regime.  The numbers in brackets (parentheses) are standard deviations of the calculated properties.