# Microscopic Pair Potentials and the Physical Properties of the Condensed Phases of Parahydrogen
## 1 Introduction
These potentials yield an EOS in reasonable agreement with experiment at moderate pressure (25 kPa); it is possible to \"tweak\" the SG potential, so that the theoretically predicted EOS will be in satisfactory agreement with experiment up to pressures of the order of \(10^{8}\) kPa range [32; 39]; these modifications are essentially _ad hoc_, however, and tailored to reproduce experimental values of only one or few physical quantities (usually the pressure). A different approach consists of determining the (time-independent) interaction between two \(p\)-H\({}_{2}\) molecules on the basis of first principle electronic structure calculations. The resulting potential energy surface reflects the lack of spherical symmetry of the molecule, so that the pairwise interaction depends not just on the distance between the molecules, but also on their relative orientation. An effective central potential is obtained by angular averaging. The most recently proposed _ab initio_ intermolecular potential for general use in the study of the condensed phases of \(p\)-H\({}_{2}\) is that of [PERSON] et al. [40], henceforth also referred to as P.  
A theoretical study has established the accuracy of this potential in the determination of the viscosity and thermal conductivity of hydrogen in the gas phase [41], but no systematic comparison has yet been carried out of thermodynamic properties of the condensed phases of \(p\)-H\({}_{2}\), computed from first principles using the SG and P potentials (shown for comparison in Figure 1). This is the goal of this work. Figure 1: Comparison of [PERSON] [40] and [PERSON] [27] (dashed line) intermolecular pair potential for \(p\)-H\({}_{2}\). Specifically, we report results of large-scale computer simulations of the equilibrium solid and liquid phases of of \(p\)-H\({}_{2}\), based on QMC, making use of both the SG and Patkowski pair potentials. For completeness, we also report results of some calculations in which the Buck and the _ab initio_ potential by [PERSON] and [PERSON] [PERSON] and [PERSON] (2016) were utilized. The purpose of this project is to determine whether recent _ab initio_ potentials (and specifically the P) may represent a better choice than the SG, as a general-purpose potential to study condensed phases of \(p\)-H\({}_{2}\) in different settings, including droplets [42; 43; 44], as well as in confinement [45; 46]. The results of this investigation paint a rather complex picture, in part due to inconsistencies between existing experimental data by different groups. In general we find that the _ab initio_ potential, which have a stiffer repulsive core at short intermolecular distance, yield structural correlations, such as the static structure factor, with higher peaks, compared to those computed with the SG and Buck potential; for the liquid phase, this means better agreement with experiment, in fact close agreement with at least some of the reported experimental results. The pressure computed with the P potential is positive for both equilibrium phases (while the SG potential yields negative pressures), with values that suggest that the incorporation of three-body terms into the P potential could bring the estimates yielded by it in agreement with experiment; this is because three-body terms, at the thermodynamic conditions of interest here, have been shown to result in a softening of the interaction, and therefore an overall reduction of the pressure [47]. Finally, the P potential yields an approximately 10% higher value of the kinetic energy per molecule than the SG; whether that means better or worse agreement with experiment really depends on what experiment one considers, i.e., there presently exist different, incompatible estimates. Therefore, it is necessary to resolve this outstanding experimental disagreement in order to make quantitative progress on the theoretical (computational) front.