Introduction to Quantum Chemistry for Materials Science
📚 5 Chapters | 💻 40 Code Examples | ⏱️ 100-120 min | 🎯 Intermediate to Advanced
Quantum chemistry is the field that seeks to understand the electronic states of atoms and molecules based on quantum mechanics. In materials science, it is essential knowledge for understanding chemical bonding, reactivity, and physical properties from first principles. Starting from the Schrödinger equation, this series systematically covers the fundamentals of quantum chemistry required for materials science, including the molecular orbital method (Hartree-Fock method) and density functional theory (DFT).
Beyond theory, through practical calculations with PySCF, you will implement actual electronic-state calculations, from the hydrogen molecule to organic molecules and solid-state materials. You will master the theory that underpins first-principles calculations, bridging into the computational materials science of Materials Informatics.
Wave functions and their probabilistic interpretation, the Schrödinger equation, operators and expectation values of physical quantities, Hermitian operators, a particle in a one-dimensional box, the exact solution of the harmonic oscillator, the tunneling effect, the uncertainty principle, commutation relations, angular-momentum operators, and spherical harmonics
Start Learning →The Schrödinger equation for the hydrogen atom, solutions of the radial equation, atomic orbitals (s, p, d, f orbitals), electron spin and the Pauli exclusion principle, many-electron atoms and the Hartree approximation, the Slater determinant, the electronic states of molecules and the Born-Oppenheimer approximation, the hydrogen molecular ion (H₂⁺) and covalent bonding, and the fundamentals of the variational method
Start Learning →Derivation of the Hartree-Fock equations, the Fock operator, the self-consistent field (SCF) method, the Roothaan equations, basis functions (Slater-type and Gaussian-type orbitals), LCAO-MO (linear combination of atomic orbitals), the Hückel molecular orbital method, the extended Hückel method, electron correlation and configuration interaction (CI), and post-Hartree-Fock methods
Start Learning →The Hohenberg-Kohn theorems, electron density and total energy, the Kohn-Sham equations, exchange-correlation functionals, the local density approximation (LDA), the generalized gradient approximation (GGA), hybrid functionals (B3LYP, PBE0), plane-wave basis sets and pseudopotentials, band-structure calculations, the density of states (DOS), and the electronic states of solids
Start Learning →Molecular calculations with PySCF (HF, DFT), structure optimization and vibrational analysis with ASE, reaction-path searches and transition-state calculations, excited-state calculations (TD-DFT), solid-state band calculations (integration with Quantum ESPRESSO and VASP), integration with the Materials Project API, connection to machine-learning potentials, and materials-science applications (catalysts, battery materials, semiconductors)
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