Finite-size scaling for critical conditions for stable quadrupole-bound anions

ALEJANDRO FERRÓN; PABLO SERRA; SABRE KAIS

JOURNAL OF CHEMICAL PHYSICS

AMER INST PHYSICS

Año: 2004 vol. 120 p. 8412 - 8419

0021-9606

We present  finite-size scaling  calculations of the critical parametersfor binding an electron to  a  finite linear quadrupole field. This approach gives very accurate results for the critical parametersby 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 $vec{R_{i}}; i=1,...,k$. 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 $q_{c}=1.46970 pm 0.00005 a.u.$ by using basis set with prolate spheroidal coordinates. For the quadrupole case with q< 0, we obtained an extrapolated critical value of $|q_{c}|=3.98251 pm 0.00001 a.u.$ for stable quadrupole bound anions. The corresponding critical exponent for the ground state energy $alpha=1.9964 pm 0.0005$, with $E sim (q-q_c)^{alpha}$.