Finite-size scaling for critical conditions for stable quadrupole-bound anions Available to Purchase

We present finite-size scaling calculations of the critical parameters for binding an electron to a finite linear quadrupole field. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. The model Hamiltonian consists of a charge $Q$ located at the origin of the coordinates and $k$ charges $−Q/k$ located at distances $R⃗i,$ $i=1,…,k.$ After proper scaling of distances and energies, the rescaled Hamiltonian depends only on one free parameter $q=QR.$ Two different linear charge configurations with $q>0$ and $q<0$ are studied using basis sets in both spherical and prolate spheroidal coordinates. For the case with $q>0,$ the finite size scaling calculations give an extrapolated critical value of $qc=1.469 70±0.000 05 a.u.$ by using a basis set with prolate spheroidal coordinates. For the quadrupole case with $q<0,$ we obtained an extrapolated critical value of $|qc|=3.982 51±0.000 01 a.u.$ for stable quadrupole bound anions. The corresponding critical exponent for the ground state energy $α=1.9964±0.0005,$ with $E∼(q−qc)α.$