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

ALEJANDRO FERRÓN, PABLO SERRA Y SABRE KAIS

JOURNAL OF CHEMICAL PHYSICS

AMER INST PHYSICS

Año: 2004 vol. 120 p. 8412 - 8419

0021-9606

We present  finite-size scaling  calculationsof 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 originof the coordinates and$k$ charges $-Q/k$ located at distances $ec{R_{i}};;i=1,ldots,k$.After  proper scaling of distances and energies, the rescaled Hamiltoniandepends only on one free parameter  $q=Q,R$.Two different linear charge configurations with $q> 0$ and $q< 0$ are studied using basis sets in bothspherical and  prolate spheroidal coordinates. For the case with $q> 0$,the finite size scaling calculations give an extrapolated critical valueof $q_{c}=1.46970 pm 0.00005; a.u.$ by using basis set with prolatespheroidal coordinates.For the quadrupole case with$q< 0$, we obtained an extrapolated critical valueof $|q_{c}|=3.98251 pm 0.00001; a.u.$ for stable quadrupole bound anions.The corresponding critical exponent for the ground state energy$alpha=1.9964pm0.0005$, with $E sim (q-q_c)^{alpha}$.