Lesson 2

Molecular Properties

In this lesson, we will study the case study of some interesting calculation by investigating molecular properties and effect of size of basis set and its correction so-called Basis Set Superposition Effect (BBSE). Generally the chemist defines the multipole as an expansion of mathematical infinite series in many forms. The case study and most popular well-know is written Multipole in spherical coordinate. However, the solution of multipole expansion is the dimension of molecular properties of molecule. The first (the zeroth-order) term in the multipole expansion is called the monopole moment, the second (the first-order) term is called the dipole moment, the third (the second-order) is called the quadrupole moment, the fourth (third-order) term is called the octupole moment, and so forth.

where δ_(αβ) is the Kronecker delta and r^2 ≡ |r|^2. Removing the trace is common, because it takes the rotationally invariant r^2 out of the second rank tensor.