Lecture Notes In Computational Chemistry. Electronic Structure Theory

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Zurich: Physical Chemistry Institute University of Zurich, 2005. - 146 p.<strong>Contents<em>Basic Quantum Mechanics Operators in quantum mechanics Eigenfunctions and eigenvalues Commutators Construction of operators Postulates of quantum mechanics Postulates Separation of the Schrodinger equation Hydrogen Atom Angular momentum operators Definitions Radial function of hydrogen atom <em>Basic Mathematical Review Linear algebra Vector spaces Operators Matrices Determinants Dirac notation Change of basis Eigenvalue problem Functions of matrices Perturbation theory Derivation Energy corrections Corrections ψ<sub>n<sup>(1) and E<sub>n<sup>(2) Summary The variation method The variation principle Linear variations <em>Molecular Hamiltonian Time-independent non-relativistic Schrodinger equation Born-Oppenheimer Approximation Part I Part II Part III Order of magnitude of effects for H<sub>2 Stationary points Internal coordinates Z-matrix <em>Two-Electron Systems and Spin Helium atom: Ground state Basics Orbital model Formal separation Perturbation theory Variational calculations Overview of ground state energies Electron spin Electrons are indistinguishable Pauli principle <em>Hartree-Fock Approximation Slater-determinant Energy expectation value for Slater determinants Unitary transformation of spin orbitals Hartree-Fock method Solution of the Hartree-Fock equations Orbital energies and Koopmans' theorem Brillouin's theorem <em>Molecular Orbital Theory LCAO-Ansatz Roothaan-Hall equations Unrestricted open-shell Hartree-Fock Spin contamination Pople{Nesbet equations <em>Correlation Energy Basics Matrixelements Con_guration interaction method (CI) Dynamical and non-dynamical electron correlation <em>Coupled Cluster Approaches Size Consistency Coupled Cluster Methods Approximate Coupled Cluster methods Accuracy in Coupled Cluster calculations <em>Muller-Plesset Perturbation Theory Electron correlation with perturbation theory Convergence of MP series The dissociation problem <em>Density Functional Theory: Part I Basics Hohenberg-Kohn Theorems Kohn-Sham Theory <em>Density Functional Theory: Part II Exchange and correlation energy Density operators Electron-electron interaction One-determinant wave functions Exchange and correlation energy in the Kohn-Sham method <em>Density Functional Theory: Part III Local density approximation Gradient corrections Exchange functional of Becke (1988) Correlation functionals of Perdew et al. Lee-Yang-Parr (LYP) correlation functional (1988) Hybrid functionals Basis sets Model calculations Coulomb energy Resolution of identity method Local expansion of density Numerical integration Voronoi polyhedra Radial integration Angular integration <em>Molecular Properties Wavefunction analysis Basisfunction based population analysis Electrostatic potential derived charges Density based charges Response properties Derivative techniques <em>NMR Chemical Shielding General Chemical shifts Linear response for Hartree-Fock Calculation of response orbitals

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