Many-body theory calculations of positron binding to halogenated hydrocarbons

Positron binding energies in halogenated hydrocarbons are calculated ab initio using many-body theory. For chlorinated molecules, including planars for which the interaction is highly anisotropic, very good to excellent agreement with experiment and recent density-functional-theory-based model-potential calculations is found. Predictions for fluorinated and brominated molecules are presented. The comparative effect of fluorination, chlorination, and bromination is elucidated by identifying trends within molecular families including dihaloethylenes and halomethanes based on global molecular properties (dipole moment, polarizability, ionization energy). It is shown that relative to brominated and chlorinated molecules, fluorinated molecules generate a less attractive positron-molecule potential due to larger ionization energies and smaller density of molecular orbitals close to the highest occupied molecular orbital, resulting in very weak, or in most cases loss of, positron binding. Overall, however, it is shown that the global molecular properties are not universal predictors of binding energies, exemplified by consideration of ${\mathrm{CH}}_3\mathrm{Cl}$ vs cis-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{F}}_2$: Despite the latter having a larger dipole moment, lower ionization energy, and similar polarizability, its binding energy is significantly smaller (25 vs 3 meV, respectively), owing to the important contribution of multiple molecular orbitals to, and the anisotropy of, the positron-molecule correlation potential.

Figure 1

Top: Calculated positron binding energies compared with experiment for chlorinated molecules. Present MBT (red circles, and striped circles for molecules difficult to converge ab initio); MBT-based model calculations using $\mathrm{\Sigma }=g{\mathrm{\Sigma }}^{\left(2\right)}+{\mathrm{\Sigma }}^{\mathrm{\Lambda }}$ with $g=1.5$ (red squares); (isotropic) polarization potential model calculation of Ref. [7] (black triangles; two for each molecule reflecting two choices of cutoff parameter); DFT-model calculation of Ref. [19] (blue squares). Vertical error bars are plus-minus the maximum difference of our calculations using screened Coulomb interactions and $GW$@RPA (random phase approximation) MO energies vs bare Coulomb interactions and HF MO energies [21]. Bottom: Positron (Dyson) wave function at 80% maximum for chlorinated and fluorinated molecules with ${\varepsilon }_b\ge 1$ meV. (a) Chloromethane; (b) dichloromethane; (c) trichloromethane; (d) tetrachloromethane (at 93%); (e) vinyl chloride; (f) vinylidene chloride; (g) cis-1,2-dichloroethylene; (h) trans-1,2-dichloroethylene (at 90%); (i) trichloroethylene; (j) cis-1,2-difluoroethylene; (k) 1-chloro-1-fluoroethylene; (l) ($Z$)-chlorofluoroethylene.

Figure 2

Dependence of positron binding energies on global molecular properties and individual MOs. (a)–(c) Calculated ${\varepsilon }_b$ vs calculated polarizabilities, dipole moments, and ionization energy for the brominated (orange), bromochlorinated (black), chlorinated (red), chlorofluorinated (green), and fluorinated (blue) molecules; symbols denote molecular families; squares are cis-dihaloethylenes ${\mathrm{C}}_2{\mathrm{H}}_{2}XY$, triangles are halomethanes ${\mathrm{CH}}_{3}X$ ($X,Y=\text{Br}$, Cl, F), and circles are isomers of ${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{Cl}}_2$. Dashed lines are guides; (d) the positron-molecule correlation strength parameters ${\mathcal{S}}_n^{\mathrm{\Gamma }}$ (circles) and ${\mathcal{S}}_n^{2+\mathrm{\Gamma }}$ (squares), and the ratio $g_n\equiv {\mathcal{S}}_n^{2+\mathrm{\Gamma }}/{\mathcal{S}}_n^2$ (crosses) for each MO $n$ against the MO HF ionization energies (vertical lines between panels) for the cis-dihaloethylenes sequence [colors as in (a)–(c)]. (e) The corresponding cumulative ${\mathcal{S}}^{2+\mathrm{\Gamma }}$ obtained by summing from the HOMO to the core orbitals. (f) The cumulative strength ${\mathcal{S}}^{2+\mathrm{\Gamma }}$ for ${\mathrm{CH}}_3\mathrm{Cl}$ (red; asterisks denote double degeneracy) and cis-${\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{F}}_2$ (blue). (g) The calculated unenhanced (${\gamma }_i=1$) and enhanced contact densities for molecules with a ${\mathrm{\Sigma }}^{GW+\mathrm{\Gamma }+\mathrm{\Lambda }}$ bound state. Colors and symbols as in (a)–(c), and diamonds are remaining molecules from Table 1.