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 MechanicsOperators in quantum mechanics Eigenfunctions and eigenvaluesCommutators Construction of operators Postulates of quantum mechanics Postulates Separation of the Schrodinger equation Hydrogen Atom Angular momentum operators DefinitionsRadial function of hydrogen atom<em>Basic Mathematical ReviewLinear 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 principleLinear variations <em>Molecular HamiltonianTime-independent non-relativistic Schrodinger equation Born-Oppenheimer Approximation Part I Part II Part IIIOrder of magnitude of effects for H<sub>2 Stationary points Internal coordinatesZ-matrix <em>Two-Electron Systems and SpinHelium atom: Ground state Basics Orbital model Formal separation Perturbation theory Variational calculationsOverview of ground state energiesElectron spin Electrons are indistinguishable Pauli principle <em>Hartree-Fock ApproximationSlater-determinantEnergy 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 TheoryLCAO-Ansatz Roothaan-Hall equations Unrestricted open-shell Hartree-Fock Spin contamination Pople{Nesbet equations <em>Correlation EnergyBasics Matrixelements Con_guration interaction method (CI) Dynamical and non-dynamical electron correlation<em>Coupled Cluster ApproachesSize Consistency Coupled Cluster Methods Approximate Coupled Cluster methods Accuracy in Coupled Cluster calculations <em>Muller-Plesset Perturbation TheoryElectron correlation with perturbation theory Convergence of MP series The dissociation problem <em>Density Functional Theory: Part IBasics Hohenberg-Kohn TheoremsKohn-Sham Theory <em>Density Functional Theory: Part IIExchange 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 IIILocal 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 setsModel calculationsCoulomb energy Resolution of identity method Local expansion of densityNumerical integration Voronoi polyhedra Radial integration Angular integration<em>Molecular PropertiesWavefunction analysis Basisfunction based population analysisElectrostatic potential derived charges Density based charges Response properties Derivative techniques <em>NMR Chemical ShieldingGeneral Chemical shifts Linear response for Hartree-Fock Calculation of response orbitals

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