Coupled cluster theory for positron binding in anions and polyatomic molecules

Abstract

We present the positron coupled cluster singles and doubles (POS-CCSD) method to calculate positron binding energies in molecules. This framework treats electrons and positrons on an equal footing and includes up to simultaneous double-electron-single-positron excitations. We benchmark the approach by computing binding energies for atomic anions and several polar and non-polar polyatomic systems, comparing the results with independent theoretical studies and, where available, experimental data. The fully converged results for H$^{-}$ are in excellent agreement with quantum Monte Carlo and multi-reference configuration interaction results. Quantitative agreement with experiments is not reached in the present study due to the slow convergence of the binding energy with respect to the size of the orbital bases for the electrons and the positron. However, the POS-CCSD results underscore the critical role of electron correlation in the description of electron-positron systems required for a balanced description of these complex systems. In addition, we examine nuclear relaxation effects following positron attachment in LiH.

Figures (12)

• Figure 1: Pictorial representation of the electron-positron capture process. Because of the electron polarization, a bonded meta-stable state (energy minimum) is observed. The dissociation energy is referred to as $\varepsilon_{b}$. Vibrational-Feshbach resonant attachment occurs when the kinetic energy of the incoming positron, $\textrm{E}_{\textrm{kin}}$, plus the binding energy matches a vibrational excitation of the molecule, $\omega_{\nu}$.
• Figure 2: Pictorial representation of the positron Hartree-Fock wave function and the effect of the excitation operators in the cluster on the positron HF wave function. The electronic part $\ket{\textrm{POS-HF}}$ is a Slater determinant where $\alpha$ and $\beta$ electrons occupy the first $N_{e}/2$ orbitals, with $N_{e}$ the number of electrons in the system. The single positron occupies the lowest energy orbital I. The effect of the excitation operators T$_{1}$ and T$_{2}$ is to move one or two electrons from the occupied orbitals to the virtual orbitals, $\Gamma$ excites the single positron, while $S_1$ and $S_2$ generate simultaneous electron-positron excitations corresponding to single-electron-single-positron and double-electron-single-positron excitations, respectively. An active space restriction in the cluster operator can be obtained by selecting a restricted set of orbitals to which the particles can be excited. For example, in this figure only the orbitals in the light blue panels would be included in the cluster indices used in the POS-CC calculation
• Figure 3: POS-CCSD calculated positron binding energies for LiH, formaldehyde and acetonitrile vs. number of orbitals included in the active space. Converged calculations require larger active spaces than are currently feasible with our current implementation and computational resources. Orbital energies of up to $\sim 150$ eV are included in the 500 orbital active space for all molecules.
• Figure 4: Difference in convergence to the full space result for the positron and electron active space selection for a LiH molecule at the aug-cc-pVQZ level. In Fig.\ref{['fig:Active_space_in_QZ']}a the full electronic active space is used in the calculation while in Fig.\ref{['fig:Active_space_in_QZ']}b the full positron active space is included.
• Figure 5: PES for LiH with and without positron attachment. We notice that the presence of the positron moves the equilibrium minimum to larger distances for every basis set. Each surface is shifted by the energy of the minimum of the POS-CCSD calculation for a given basis.