Figure 1

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo simulation, for prolate spheroids of elongation $e=A∕B=5$. Densities: ${\rho }^{*}=0.1$ (circles, red), 0.2 (squares, green), 0.3 (diamonds, blue), 0.4 (triangles, magenta). The solid lines are the corresponding results $b_{mn\chi }^{\mathrm{HCD}}\left(r\right)$ of solving the Ornstein-Zernike equation with the Henderson-Chan-Degrève [27, 28] modified Verlet-bridge closure.Reuse & Permissions

Figure 2

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the modified HCD Verlet-bridge closure, for oblate spheroids of elongation $e=A∕B=1∕5$. Notation as for Fig. 1.Reuse & Permissions

Figure 3

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo simulation, for prolate spheroids of elongation $e=A∕B=3$. Densities: ${\rho }^{*}=0.1$ (circles, red), 0.2 (squares, green), 0.3 (diamonds, blue), 0.4 (triangles, cyan), 0.5 (inverted triangles, magenta), 0.6 (crosses, orange). The solid lines are the corresponding results $b_{mn\chi }^{\mathrm{HCD}}\left(r\right)$ of solving the Ornstein-Zernike equation with the HCD modified Verlet-bridge closure.Reuse & Permissions

Figure 4

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the HCD modified Verlet-bridge closure, for oblate spheroids of elongation $e=A∕B=1∕3$. Notation as for Fig. 3.Reuse & Permissions

Figure 5

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the HCD modified Verlet-bridge closure, for prolate spheroids of elongation $e=A∕B=2$. Notation as for Fig. 3.Reuse & Permissions

Figure 6

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the HCD modified Verlet-bridge closure, for oblate spheroids of elongation $e=A∕B=1∕2$. Notation as for Fig. 3.Reuse & Permissions

Figure 7

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the HCD modified Verlet-bridge closure, for prolate spheroids of elongation $e=A∕B=3∕2$. Notation as for Fig. 3.Reuse & Permissions

Figure 8

(Color online) Spherical harmonic coefficients of the bridge function in the molecular frame, $b_{mn\chi }\left(r\right)$, determined by Monte Carlo and integral equation theory using the HCD modified Verlet-bridge closure, for oblate spheroids of elongation $e=A∕B=2∕3$. Notation as for Fig. 3.Reuse & Permissions

Figure 9

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.1$. The results of all elongations, eight mutual orientations, and a regular sample of all center-center separations, are superimposed. Orientations defined in Table : e, s, t, x, a, b, c, d (red, green, blue, cyan, magenta, orange, violet, yellow, respectively). Prolate elongations are shown in the upper graph, oblate elongations in the lower graph: $e=5$, $1∕5$ (triangles); 3, $1∕3$ (diamonds); 2, $1∕2$ (squares); $3∕2$, $2∕3$ (circles). Theoretical closure relations are indicated by lines: Henderson-Chan-Degrève [27, 28], solid line; modified Verlet [19, 23], dashed line; Verlet bridge [26], dot-dashed line; Percus-Yevick, double-dot-dashed line.Reuse & Permissions

Figure 10

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.2$. The results of all elongations (prolate above, oblate below), eight mutual orientations, and a regular sample of all center-center separations are superimposed. Theoretical closure relations are indicated by lines. Notation as for Fig. 9.Reuse & Permissions

Figure 11

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.3$. The results of all elongations (prolate above, oblate below), eight mutual orientations, and a regular sample of all center-center separations are superimposed. Theoretical closure relations are indicated by lines. Notation as for Fig. 9.Reuse & Permissions

Figure 12

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.4$. The results of all elongations (prolate above, oblate below), eight mutual orientations, and a regular sample of all center-center separations are superimposed. Theoretical closure relations are indicated by lines. Notation as for Fig. 9.Reuse & Permissions

Figure 13

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.5$. The results of all elongations except $e=5,1∕5$ (prolate above, oblate below), eight mutual orientations, and a regular sample of all center-center separations, are superimposed. Theoretical closure relations are indicated by lines. Notation as for Fig. 9.Reuse & Permissions

Figure 14

(Color online) Duh-Haymet plot of bridge function $b(1,2)$ versus indirect correlation function $\gamma (1,2)=h(1,2)-c(1,2)$, determined by Monte Carlo simulation, at reduced density ${\rho }^{*}=0.6$. The results of all elongations except $e=5,1∕5$ (prolate above, oblate below), eight mutual orientations, and a regular sample of all center-center separations, are superimposed. Theoretical closure relations are indicated by lines. Notation as for Fig. 9.Reuse & Permissions

Figure 15

(Color online) The equation of state (upper panel) obtained via the virial (red, light gray) and compressibility (blue, dark gray) routes and the Kerr coefficient (lower panel) for $e=3$. In both cases, theoretical predictions obtained with HNC equation (dashed lines), HCD Verlet bridge (solid lines), and MC data (circles) are shown.Reuse & Permissions