Quantum Monte Carlo calculations of van der Waals interactions between aromatic benzene rings

The magnitude of finite-size effects and Coulomb interactions in quantum Monte Carlo simulations of van der Waals interactions between weakly bonded benzene molecules are investigated. To that extent, two trial wave functions of the Slater-Jastrow and Backflow-Slater-Jastrow types are employed to calculate the energy-volume equation of state. We assess the impact of the backflow coordinate transformation on the nonlocal correlation energy. We found that the effect of finite-size errors in quantum Monte Carlo calculations on energy differences is particularly large and may even be more important than the employed trial wave function. In addition to the cohesive energy, the singlet excitonic energy gap and the energy gap renormalization of crystalline benzene at different densities are computed.

Figure 1

Top: The smallest and largest simulation cells with volumes $V_s=336.4334{\text{Å}}^3$ and $V_l=3691.9989{\text{Å}}^3$, respectively, which are used to calculate the vdW interactions between the benzene molecules. Bottom: Wigner-Seitz radius $r_S$ and cutoff length $r_{ij}^C$ as linear functions of $R$.

Figure 2

Relative DMC energy as calculated using the Ewald and MPC potentials and SJ and BSJ wave functions. The data points are fitted to $\frac{C_6}{R^6}+\frac{C_8}{R^8}+\frac{C_{10}}{R^{10}}$, where $C_n$, with $n=6,8,10,\cdots$, are fitting parameters and $R$ is the smallest distance between the center of mass of the benzene molecules. The reference line is the DMC energy at the largest separation.

Figure 3

Singlet DMC excitonic gap, which is determined using the SJ and BSJ wave functions in conjunction with the bare Ewald potential as a function of $R$.