Figure 1

(Color online) Schematics of the PE crystal structure in its base-centered orthorhombic unit cell. Lattice parameters $a$ and $b$ are indicated, while the parameter $c$, which is the polymer repetition length, is perpendicular to the plane shown. Solid (broken) circles represent ${\mathrm{CH}}_2$ units in the plane (a distance $c∕2$ out of the plane). The angular orientation of the polymers is determined by the setting angle $\theta$, defined as the angle between the a axis $(a>b)$ and the intrapolymer carbon plane.Reuse & Permissions

Figure 2

The nonlocal correlation energy $E_c^{\mathrm{nl}}$ for pairs of PE. For the practical evaluation of $E_c^{\mathrm{nl}}$ in the crystal the range of integration in Eq. (1) is important. Simple pair interaction calculations give a fast estimate of the range needed, although the full calculation includes all density within the integration range. Shown here are the relative sizes (meV per polymer segment) of the polymers’ contributions to $E_c^{\mathrm{nl}}$ (as pairs with the polymer at the circle centers), evaluated at the separations (Å) and relative angles shown. The contours show length-averaged electron densities. Polymers that are closer than $9\mathrm{\AA }$ (thick dashed circle) to the center polymer contribute with an energy of $321\mathrm{meV}$. This is 99.4% of the total nonlocal correlation energy $E_c^{\mathrm{nl}}$ of all the polymers shown $\left(323\mathrm{meV}\right)$.Reuse & Permissions

Figure 3

(Color online) The cohesive-energy contour map calculated with vdW-DF, expressed as energy per ${\mathrm{CH}}_2$ group as a function of the lattice parameters $a$ and $b$. The plot (but not the calculation) is restricted to show the energetics at setting angle $\theta =44°$, the optimal angle found with vdW-DF (Table ). The full (dashed) contour curves are separated by 1 $\left(10\right)\mathrm{meV}∕{\mathrm{CH}}_2$, with values given in $\mathrm{meV}∕{\mathrm{CH}}_2$. The equilibrium parameters (summarized in Table ) obtained from experiments and from a LDA-DFT study are shown for comparison.Reuse & Permissions