Basic Principles of Spectroscopy + MOT Notes (Teachers)

H3 Chemistry 9813 Molecular Orbital Theory and Basic Principles of Spectroscopy © 2026/JC2/Term 2/Chemistry Department 1 Anglo-Chinese Junior College Department of Chemistry Molecular Orbital Theory and Basic Principles of Spectroscopy Prepared by: ACJC Chemistry Department in collaboration with H3 Chemistry NLC Contents Page Molecular Orbital Theory Quantum Mechanical Model of the Atom 3 The Wave Nature of Electrons The Uncertainty Principle The Quantum Mechanical Model Revisiting the Atomic Orbitals 4 The Molecular Orbital (MO) Theory Model of Chemical Bonding 6 Linear Combination of Atomic Orbitals (LCAO) Homonuclear Diatomic Molecules 7 Example 1: Molecular Orbital Diagram of Hydrogen 8 - Why hydrogen is diatomic but helium is not? Example 2: Molecular Orbital Diagram of Oxygen 9 - Two special properties of molecular oxygen 12 Question 3: Molecular Orbital Diagram of Fluorine 13 Question 4: Molecular Orbitals within F2+ Molecular Orbital Diagram of Nitrogen – Extra reading 14 Molecular Orbital Diagram of Hydrogen Fluoride – Extra reading Conjugated and Aromatic Molecules 15 Polyalkene – 1,3-butadiene 1,3,5-hexatriene 16 1,3,5,7-octatetraene Benzene 17 Basic Principles of Spectroscopy A Brief History of Spectroscopy 18 Principles of Spectroscopy 19 Types of Energy in Spectroscopy 20 Quantisation of Energy Levels 21 Types of Spectroscopy 22 Spectroscopic Measurements 23

H3 Chemistry 9813 Molecular Orbital Theory and Basic Principles of Spectroscopy © 2026/JC2/Term 2/Chemistry Department 2 Learning Outcomes Candidates should be able to: (a) understand basic molecular orbital (MO) theory, involving (i) atomic and molecular orbitals (ii) bonding, anti-bonding and non-bonding orbitals (iii) molecular orbitals with σ and π symmetry (b) understand that molecular orbitals represent discrete electronic energy levels in molecules [see also e(ii)] (c) apply linear combination of atomic orbitals (LCAO) principles to obtain the shape and relative energies of molecular orbitals in the following: (i) simple homonuclear diatomic molecules such as H2, O2, and F2 (ii) benzene and linear polyenes (molecular orbitals of π symmetry only) [quantitative treatment of LCAO is not required] (d) construct and interpret molecular orbital diagrams, and identify the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for the following: (i) simple homonuclear diatomic molecules such as H2, O2, and F2 (ii) benzene and linear polyenes (molecular orbitals of π symmetry only) [knowledge of orbital mixing between orbitals of the same symmetry is not required] (e) understand the following in relation to the fundamental principles of spectroscopy: (i) properties of electromagnetic radiation ‒ the electromagnetic spectrum (with range of wavelengths for different types of radiation used in spectroscopy) ‒ the photon as a discrete packet (quantum) of electromagnetic energy ‒ the relationship between wavelength, frequency and speed of light, including the use of the equation, E = hf (ii) the quantisation of energy in relation to ‒ electronic, vibrational and rotational energy levels ‒ nuclear energy levels in applied magnetic field (iii) energy level transitions associated with the absorption and emission of photons with energy matching the energy gap Recommended readings and resources 1 Inorganic Chemistry third edition, Catherine Housecroft and Alan Sharpe 2 Organic Chemistry second edition, Jonathan Clayden, Nick Greeves and Stuart Warren 3 The Molecular Nature of Matter and Change with Advanced Topics eighth edition, Martin Silberberg and Patricia Amateis 4 http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/mo.html 5 https://www.masterorganicchemistry.com/2017/05/05/the-pi-molecular-orbitals-of-benzene/ 6 http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/ 7 http://www.chem.kyushu- .ac.jp/~robertson/General_Chemistry/Files/Molecular_orbital_theory.pdf 8 https://chem.libretexts.org/Textbook_Maps/Physical_and_Theoretical_Chemistry_Textbook_Ma ps/Map%3A_Physical_Chemistry_(McQuarrie_and_Simon)/09%3A_The_Chemical_Bond%3A_ Diatomic_Molecules/9.10%3A_Molecular_Orbital_Theory_Predicts_that_Molecular_Oxygen_is_ Paramagnetic

H3 Chemistry 9813 Molecular Orbital Theory and Basic Principles of Spectroscopy © 2026/JC2/Term 2/Chemistry Department 3 Quantum Mechanical Model of the Atom The Wave Nature of Electrons Light particles have been known to possess wave -like properties, from the way they interact with each other (interference) and the slight bending that occurs when light encounters the edge of an object (diffraction). In 1924, Louis de Broglie argued that electrons and other particles should also possess wave- like properties. This phenomenon is referred to as wave-particle duality, and was proven by electron diffraction experiments, and put to use in the electron microscope. Thus, a particle with a certain mass m and moving at velocity v (i.e., with a certain momentum mv) possesses an associated wave of wavelength .  = ℎ 𝑚𝑣 , where h is the Planck’s constant (found in the first page of your Data Booklet) The Uncertainty Principle The consequence of electrons having wave -like properties is that it becomes impossible to know exactly both the momentum (i.e., mass x velocity) and position of the electron at the same instant in time. This is a statement of Heisenberg’s Uncertainty Principle. The Quantum Mechanical Model Instead of trying to define the exact position and momentum of an electron, we focus on the probability of finding the electron in a given volume of space . The proba bility of finding an electron at a given point in space is determined from the square of a function called ψ (“psi”), i.e., ψ 2. ψ is a mathematical function which describes the behaviour of an electron particle-wave, and is called the wavefunction. These wavefunctions are equations obtained from calculations based on the quantum mechanical model of the atom, proposed in 1926 by Erwin Schrödinger. Schrödinger’s equation can only be solved for one electron system; for multi-electrons systems, appropriate approximations are required to solve it. Solving the equation gives rise to 3 quantum numbers describing a three dimensional space called an atomic orbital. • Principal quantum number, n, defines the orbital size • Angular momentum quantum number, l, defines the shape • Magnetic quantum number, ml, defines the orientation of the orbital. As wavefunctions are mathematically obtained, each orbital has a specific energy associated with it. Therefore, electrons in atoms can exist only at certain “allowed” energy levels determined by the orbitals they are associated with.

H3 Chemistry 9813 Molecular Orbital Theory and Basic Principles of Spectroscopy © 2026/JC2/Term 2/Chemistry Department 4 Revisiting the Atomic Orbitals In a hydrogen atom, the only orbital of concern is the 1s orbital, which is spherical. The probability of finding an electron decreases rapidly as the distance from the nucleus increases, although it never goes all the way to zero, even at large distances. As a result, there is no definite boundary to the atom, and the atom has no definite size. For practical purposes, we represent the 1s orbital as a sphere within which there is 95% probability of finding the electron. The figure below shows the electron probability, contour probability and radial probability of 1s, 2s and 3s orbitals respectively. The shape of the graph of electron probability vs. distance from nucleus (r) can be understood from the fact that as r incre ases, surface area (4 r2) increases more rapidly than the decrease in electron probability. Other orbitals such as p orbitals and d orbitals are also desc