Can anyone explain how I can calculate the quadrupole

Solved: (a) Show that the quadrupole term in the multipole The monopole moment (Q) is a scalar, the dipole moment (p) is a vector, the quadrupole moment (Q i j ) is a second-rank tensor, and so on. (b) Find all nine components of Q i j for the configuration in Fig. 3.30 (assume the square has side a and lies in the xy plane, centered at the origin). Quadrupolar coupling - NMR Wiki Jul 20, 2011 Directional Dependence of Hydrogen Bonds: a Density-based Dec 13, 2011

## Quadrupole Interactions.

The quadrupole tensor Q ij (8) is symmetric, real-valued and traceless. It has three real eigenvalues. The total charge is independent of our choice of origin. In general, the lowest non-zero multipole is independent of origin, but higher order multipoles do depend on the origin. (See Jackson Problem 4.4.) 3 The quadrupole moment Cartesian tensor is given by1 Qe ij = X k qk h 3x (k) i xj −(r (k))2δ ij i, (3) where k labels each charge and i and j label the components of the position vector x. Note that the charges all lie in the x–y plane (corresponding to z = 0). Moreover, r(k) is the distance of the kth charge from the origin, located at the

### Quadrupole and Higher Moments There are two common definitions for the quadrupole moment of a charge distribution. The first and least common in Chemistry equates the quadrupole moment tensor with the second moment tensor A αβ defined above. The second definition and the one we will use almost exclusively defines it as 22 11 13 (3 ) 222 NN

Quadrupole and Higher Moments There are two common definitions for the quadrupole moment of a charge distribution. The first and least common in Chemistry equates the quadrupole moment tensor with the second moment tensor A αβ defined above. The second definition and the one we will use almost exclusively defines it as 22 11 13 (3 ) 222 NN The monopole moment (Q) is a scalar, the dipole moment (p) is a vector, the quadrupole moment (Q i j ) is a second-rank tensor, and so on. (b) Find all nine components of Q i j for the configuration in Fig. 3.30 (assume the square has side a and lies in the xy plane, centered at the origin). We consider whether use of traceless multipole moment densities in macroscopic electromagnetism can yield physically acceptable results. For harmonic plane wave fields it is shown that a traceless electric quadrupole density yields linear constitutive relations for which the dynamical material constants (permittivity and magnetoelectric coefficients) and response fields are unphysical. The traceless quadrupole moment of carbon dioxide, £ ) Qjj - Q⊥,is-4.3 DÅ. In stark contrast, all of the £ii values of carbodiimide are close to zero and only the off-diagonal quadrupole moment element£xy is quite large with £xy)-6.2 DÅ. 1. Introduction The most important reactions of carbodiimides all involve Traceless synonyms, Traceless pronunciation, Traceless translation, English dictionary definition of Traceless. as the traceless part of the second-moment tensor dipole moment is about 3.336 × 10 −12 C m, and a debye (D) is 10 −18 cgs esu. An atomic unit of electric dipole moment is a0e, where a0 is the radius of the first Bohr orbit for hydrogen and e is the magnitude of the electronic charge. An atomic unit of dipole moment is about 8.478 × 10 −29 C m.