(a brief reminder of electromagnetism) Maxwell Equations (a brief reminder of electromagnetism)

Maxwell’s equations of electromagnetism All relationships between electric and magnetic fields and their sources summarized by four equations. James Clerk Maxwell 1831-1879

Faraday’s Coil

Basic Facts – Maxwell Equations obtained by generalizing of observations intrinsically relativistic can be made compatible with QM- quantum electrodynamics this lecture: “classical” electric and magnetic field

Maxwell Equations electric charge “source” magnetic charge (monopole) “vector”

Maxwell Equations 12 variables .... 8 equations

Maxwell Equations 12 variables .... 8 equations “material relations”

Potentials scalar potential vector potential satisfied automatically:

Look at the cross section Called: “Electromagnetic Waves” Accelerating electric charges give rise to electromagnetic waves E and B are perpendicular (transverse) We say that the waves are “polarized.” E and B are in phase (peaks and zeros align)

General solutions (retarded) potentials, j(r’) field sources (e.g. molecules) observer (r) A(r) (retarded) potentials, in chemistry we do not care about relativity at this point

Multipole Expansions molecules dimension ~ r’ << observation distance r

Multipole expansion of electrostatic field elektric monopole elektric dipole quadrupole octupole etc.

Magnetic field - similarly magnetic dipole , Discrete charges: .

Electrodynamics @ Schrödinger equation: p  p + qA V  V + q.

Molecule @ Electric Field  = -r.E E = E - p0.E - E..E + ... molecular electric dipole molecular polarizability

Molecule @ Magnetic Field (static field) E = E - m0.B - B..B + ... .

Molecule @ Magnetic Field (static field) E = E - m0.B - B..B + ... molecular magnetic dipole . molecular magnetic susceptibility

Dependence of magnetic properties on coordinate origin - observable variables (should not) depend on the origin

Dependence of magnetic properties on coordinate origin - observable variables (should not) depend on the origin Solution: - infinite basis of AOs computation in molecular origin GIAO gauge invariant atomic orbitals (London or Field-Dependent AOs) special methods Important : NMR, VCD!!

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