Section Multipole matrix elements

Information in a response calculation

dipole elements

The matrix elements of the 3 dipole operator components between occupied and virtual orbitals: outer loop over the operators (in order: y, z, x), loop over virtual MOs, inner loop over occupied MOs

quadrupole elements

Similar as for dipole. Order of operators:
√(3)*xy
√(3)*yz
z2-(x2+y2)/2
√(3)*xz
√(3)*(x2-y2)/2

octupole elements

Similar as for dipole and quadrupole. Order of operators:
√(10)*y*(3*x2-y2)/4
√(15)*xyz
√(6)*y*(4*z2-x2-y2)/4
z*(z2-3(x2-y2)/2)
√(6)*x*(4*z2-x2-y2)/4
√(15)*z*(x2-y2)/2
√(10)*x*(x2-3y2)/4

hexadecapole elements

Similar as for dipole and quadrupole. Order of operators:
√(35)*xy*(x2-y2)/2
√(70)*z*(3x2y-y3)/4
√(5)*xy*(6z2-x2-y2)/2
√(10)*(4yz3-3yz*(x2+y2))/4
(8z4-24*z2*(x2+y2)+3(x4+2x2y2+y4))/8
√(10)*(4xz3-3xz*(x2+y2))/4
√(5)*(x2-y2)*(6z2-x2-y2)/4
√(70)*z*(x3-3xy2)/4
√(35)(x4-6x2y2+y4)/8