Quadrupole,octopole,and hexadecapole electric moments of SIGMA,II,DELTA,and PHI electronic states:Cylindrically asymmetric charge density distributions in linear molecules with nonzero electronic angular momentum

摘要

The number of independent components,n,of traceless electric 2~l-multipole moments is determined for C_(infinity upsilon)molecules in SIGMA~(+-),II,DELTA,and PHI electronic states(LAMBDA=0,1,2,3).Each 2~l pole is defined by a rank-l irreducible tensor with(2l+1)components P_m~(l)proportional to the solid spherical harmonic r~lY_m~l(theta,phi).Here we focus our attention on 2~l poles with l=2,3,4(quadrupole THETA,octopole OMEGA,and hexadecapole PHI).An important conclusion of this study is that n can be 1 or 2 depending on both the multipole rank l and state quantum number LAMBDA.For SIGMA~(+-)(LAMBDA=0)states,all 2~l poles have one independent parameter(n=l).For spatially degenerate states-II,DELTA,and PHI(LAMBDA=1,2,3)-the general rule reads n=1 for l<2|LAMBDA|(when the 2~l-pole rank lies below 2|LAMBDA|)but n=2 for higher 2~l poles with l>=2|LAMBDA|.The second nonzero term is the off-diagonal matrix element.Thus,a II(LAMBA=1)state has one dipole(mu_z)but two independent 2~l poles for l>=2-starting with the quadrupole[THETA_(zz),(THETA_(xx)-THETA_(yy))].A DELTA(LAMBDA=2)state has n=1 for 2~(1,2,3)poles(mu_z,THETA_(ZZ),OMEGA_(zzz))but n=2 for higher 2~((l>=4))poles-from the hexadecapole PHI up.For PHI(LAMBDA=3)states,it holds that n=1 for 2~1 to 2~5 poles but n=2 for all 2~((l>=6))poles.In short,what is usually stated in the literature-that n=1 for all possible 2~l poles of linear molecules-only applies to SIGMA~(+-)states.For degenerate states with n=2,all Cartesian 2'-pole components(l>=2|LAMBDA|)can be expressed as linear combinations of two irreducible multipoles,P_(m=0)~(l)and P_(|m|=2 LAMBDA)~(l)[parallel(z axis)and anisotropy(xy plane)].Our predictions are exemplified by the THETA,OMEGA,and PHI moments calculated for LAMBDA=0-3 states of selected diatomics(in parentheses):CHI ~2SIGMA~+(CN),CHI ~2II(NO),a ~3II_u(C2),CHI ~2 DELTA(NiH),CHI ~3DELTA(TiO),CHI ~3PHI(CoF),and CHI ~4PHI(TiF).States of II symmetry are most affected by the deviation from axial symmetry.