1) Introduction: Rydberg-constant, separating the center of mass motion in the
two-body problem,
atomic
units, virial theorem, the role of Ekin
and Epot in the formation of a chemical
bond on the example of the H2+ molecular ion
2) Principles 1: the necessity of approximations, perturbational vs. variational
methods, the
variation principle
,
Eckart’s inequality
,
nonlinear variation (two examples:
H-exp, H-gauss),
3) Principles 2: linear variation, Löwdin’s
orthogonalization,
Born--Oppenheimer approximation,
Hellmann--Feynman theorem
,
4) He atom 1: ground state, shielding (screening), Cb-integral,
comparison of various approximations:
perturbation,
variation (what is the erratum in it?);
Hartree-Fock
method for the ground state of He, Hylleraas-solution, Pekeris-solution,
(
Pekeris-paper
),
various types of
correlation
5) He atom 2:
excited states,
exchange integral
(a paper for K>0
),
ortho-He,
para-He, two-electron
Slater determinants,
Slater determinants, Fermi-hole vs Coulomb-hole, Hartree-Fock method in general (briefly)
6) Dirac-equation: Application of the Dirac-equation for H atom,
the spin in electric and/or magnetic field, the spin-orbit coupling
7) Hund’s rules: atomic term symbols, LS-coupling, jj-coupling, the role of configurational interaction on the
example of Mg atom, periodic system, Grotrian diagram
8) H2+ molecular ion: description with
various approximate
(and
exact
)
methods, molecular orbitals, LCAO method
9) H2 molecule:
description with various approximate methods, comparison of the MO and
VB methods
10) Diatomic molecules: correlation diagram, avoided crossing, N2
and O2 molecule, paramagnetism of the latter
11) Polyatomic molecules 1:
energy levels
and
vibrational modes
of H2O molecule,
hybridisation
12) Polyatomic molecules 2: the role of symmetries, the use of character tables
(NH3, CH4, C60)
Budapest,
2023-09-13
Kürti Jenő
Recommended literature:
- P.
Atkins, R. Friedman: Molecular Quantum Mechanics, Oxford University Press 2010
- I. Mayer:
Simple Theorems, Proofs, and Derivations in Quantum Chemistry, Springer Science+Business Media New York 2003
- H. Haken,
H.C. Wolf: Molecular Physics and Elements of Quantum Chemistry, Springer-Verlag Berlin Heidelberg 1987
- H. Haken,
H.C. Wolf: Molekülphysik und Quantenchemie,
Springer-Verlag Berlin Heidelberg 1995
- The
Feynman Lectures in Physics: http://www.feynmanlectures.info/
- Kapuy Ede, Török Ferenc, Az atomok
és molekulák kvantumelmélete
- Marx György: Kvantummechanika
- Erostyák János -- Kürti Jenő -- Raics Péter -- Sükösd Csaba: Fizika
III. egyetemi tankönyv megfelelő fejezetei
