Quantum Chemistry 1

Course Information

College	Anan College	Year	2023
Course Title	Quantum Chemistry 1
Course Code	1414D20	Course Category	Specialized / Compulsory
Class Format	Lecture	Credits	Academic Credit: 2
Department	Course of Chemical Engineering	Student Grade	4th
Term	Second Semester	Classes per Week	2
Textbook and/or Teaching Materials	Ryoushikagaku-kisokaranoapurochi (Kagakudouin) Fumitaka Mafune
Instructor	Ueda Kohei

Course Objectives

1. Understand the basic principles of quantum mechanics and express them mathematically.
2. Apply the Schrödinger equation to a particle in a 1-dimensional box model and derive energy levels and eigenfunctions.
3. Apply the quantum mechanics to the hydrogen atom and derive its atomic orbitals. Explain the shapes and energy levels of the atomic orbitals in terms of the principal quantum numbers.

Rubric

	Ideal Level	Standard Level	Minimum Level
Achievement 1	Understand the basic principles of quantum mechanics and express them mathematically: Schrödinger equation, wave functions, probability interpretation of wave functions, operators, eigenfunctions, eigenvalues and eigenstates, superposition principle, and expectation values.	Understand the basic principles of quantum mechanics and express them mathematically: Schrödinger equation, wave functions, probability interpretation of wave functions, eigenfunctions, eigenvalues and eigenstates, superposition principle, and expectation values.	Understand the basic principles of quantum mechanics and express them mathematically: Schrödinger equation, wave functions, probability interpretation of wave functions, superposition principle, and expectation values.
Achievement 2	Apply the Schrödinger equation to a particle in 1-dimensional box models (both of the infinite and finite potential wells) and derive energy levels and eigenfunctions.	Apply the Schrödinger equation to a particle in a 1-dimensional box model and derive energy levels and eigenfunctions.	Explain the properties of a particle in a 1-dimensional box model that obeys quantum mechanics.
Achievement 3	Apply the quantum mechanics to the hydrogen atom and derive its atomic orbitals. Explain the shapes and energy levels of the atomic orbitals in terms of the principal quantum numbers.	Apply the quantum mechanics to the hydrogen atom and explain the shapes and energy levels of the atomic orbitals in terms of the principal quantum numbers.	Apply the quantum mechanics to the hydrogen atom and explain the energy levels of the atomic orbitals in terms of the principal quantum numbers.

Teaching Method

Outline:

Quantum Chemistry is a branch of physical chemistry focused on applying quantum mechanics to chemical systems. This course introduces (1) the fundamentals of quantum chemistry using mathematics and (2) the electronic orbitals of the hydrogen atom as an important application in chemistry.

Style:

Assignments will be given for each lecture: Total time required is approximately 60 hours.
Short exercises will be given during the class. Please remember to bring your calculator.

Notice:

The course assumes that students have an understanding of the math, physics, and chemistry they have previously studied.
If you have any questions, please ask them in class.
No questions will be accepted during the exam period.

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Basic concepts of quantum chemistry 1	Derive the time-independent Schrödinger equation.
		2nd	Basic concepts of quantum chemistry 2	Apply the time-independent Schrödinger equation to free particles.
		3rd	Schrödinger's equation 1: particle in a box (one-dimensional solution)	Derive eigenfunctions and energy eigenvalues for the particle in a one-dimensional box.
		4th	Schrödinger equation 2: Applying the 1D approximation to pi-electron conjugate systems	The energy levels of the conjugated polyenes can be calculated by 1D approximation.
		5th	Schrödinger's Equation 3: Harmonic Oscillator	Calculate eigenfunctions and energy eigenvalues of harmonic oscillators.
		6th	Basic Principles of Quantum Chemistry 1	Explain wave functions and their probabilistic interpretation, orthogonality, expectation values, and operator representations of physical quantities, eigen equations, eigenfunctions, and eigenvalues.
		7th	Basic Principles of Quantum Chemistry 2	Explain the physical significance of Heisenberg's Uncertainty Principle.
		8th	midterm exam
	4th Quarter
		9th	Particle in a box in a 3-D Cartesian coordinate system (three-dimensional solution)	Derive eigenfunctions and energy eigenvalues for the particle in a three-dimensional box.
		10th	Spherically symmetric potentials and 3D polar coordinates	Explain each concept related to the Schrödinger equation in 3-dimensional polar coordinates using mathematical expressions.
		11th	Orbital angular momentum	Explain the definition of orbital angular momentum, exchange relations, polar coordinate representation, eigenequations, eigenfunctions, eigenvalues.
		12th	Hydrogen atom 1: eigenfunctions, quantum numbers, energy levels	Explain the eigenfunctions, principal quantum numbers, azimuthal quantum numbers, and magnetic quantum numbers of the hydrogen atom using mathematical expressions.
		13th	Hydrogen atom 2: ground state (1s orbital)	Illustrate the approximate shape of the wave function of the 2s orbital in the radial direction and the approximate orientation of the 2p orbitals in the ground state of the H atom.
		14th	Hydrogen atom 3: Excited states (2s, 2p orbitals)	Illustrate the approximate shape of the wave function of the 2s orbital in the radial direction and the anisotropic shape of the 2p orbitals in the excited state of the H atom.
		15th	Hydrogen atom 4: Properties of the radial direction	Calculate the maximum value of the electron probability, the expected value of the radius, etc., using the radial wavefunction in the ground and excited states.
		16th	final exam

Evaluation Method and Weight (%)

	Examination	Quiz	Portfolio	Presentation/attitude	Other	Total
Subtotal	60	0	40	0	0	100
Basic Proficiency	20	0	10	0	0	30
Specialized Proficiency	30	0	20	0	0	50
Cross Area Proficiency	10	0	10	0	0	20