Mathematical Tools in Theoretical Chemistry: mathematical review, many electron wave functions, Born-Oppenheimer approximation, Pauli exclusion principle, Slater determinant, operators and matrix elements, second quantization, density matrices. Hartree-Fock Theory: derivation of equations, interpretation of solutions, restricted closed-shell HF, restricted and unrestricted open-shell HF, SCF theory, Roothaan-Hall equations, further aspects. Basis Sets: Slater and Gaussian type orbitals, classification, polarization and diffuse functions, even- and well-tempered BS, contracted BS, Pople style, Dunning-Huzinaga, atomic natural orbital, correlation-consistent and polarization consistent BS, extrapolation, BS superposition error, effective core potentials. Configuration Interaction: configuration expansion, conventional CI approach, diagonalization and direct CI equations, complete and approximate CI, size consistency. Multiconfigurational Self-Consistent Theory: MCSCF wavefunction, gradient, Hessian, complete active space method, applications. Coupled Cluster Theory: coupled-cluster model, the exponential ansatz, size extensivity, CCSD model, higher excitations, open-shell CC methods, other treatments of size-extensivity. Many-Body Perturbation Theory: applications, Rayleigh-Schrödinger, Möller-Plesset, coupled cluster and MC perturbation theory. Density Functional Theory: electron density, Hohenberg-Kohn theorems, exchange-correlation functionals, local-density approximations, generalized gradient approximation, hybrid functionals, Kohn-Sham theory. Local Electron Correlation Methods: localization, localized molecular orbitals, Boys and Pipek-Mezey localization, local correlation, localized Möller-Plesset methods. Analytical Gradient Theory: properties calculated as derivatives, energy derivatives for HF wave function, molecular gradient for nonvariational wave functions. Geometry Optimization: stationary points, local models, strategies for minimization, convergence criteria, saddle point optimizations. Accurate Quantum-Chemical Calculation: errors, calibration of methods, choice of basis set, total electronic energy, chemical reactions, vibrational spectra, thermodynamic properties, solvent efects, relativistic terms in Hamiltonian.
1. Write out Schrödinger equation for molecules, u jednadžbu za molekule, explain Born-Oppenheimer approximation, Pauli exclusion principle, variational method and statement of completeness of basis.
2. Derive Hartree-Fock equations and interpret solutions for restricted closed shell HF method, and restricted and unrestricted open shell HF method.
3. Review basis sets and pseudopotentials used in quantum chemistry. Explain on examples basis set superposition error.
4. Review equations of configuration interaction and approximation methods for solutions. Explain size consistency i size extensivity.
5. Review equations of coupled cluster theory.
6. Explain application of perturbation theory in quantum chemistry.
7. Review theory of analytical gradients and explain calculation of molecular properties.
8. Define stationary and saddle points. Review algorithms for geometry optimization and convergence criteria.
9. Review principles of accurate quantum chemical calculations along with the error estimation. Explain possible improvements.
10. Present adequate skills in technical writing and oral presentations.
- 1. T. Hrenar: Teorijska kemija, rkp. u pripremi i dijelom dostupan putem Sveučilišnog centra za e učenje Merlin (http://merlin.srce.hr, za pristup je potreban AAI korisnički račun).
2. T. Helgaker, P. Jorgensen, J. Olsen: Molecular Electronic-Structure Theory, Wiley, Chichester, 2000.
3. I. N. Levine: Quantum Chemistry, 5th Ed., Prentice Hall, New Jersey, 2000.
4. A. Szabo and N. S. Ostlund: Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications, Inc., Mineola, New York 1996.
5. R. McWeeny: Methods of Molecular Quantum Mechanics, 2th Ed., Academic Press, San Diego, 2001.
6 L. Pauling and E. B. Wilson, Jr.: Introduction to Quantum Mechanics With Applications to Chemistry, Dover Publications, Inc., New York 1985.