Electronic

Page 1: Introduction

• Electronic Spectroscopy: Presentation by Teo Yin Yin, PhD.

• Contact Information:

  • Room: L7-25, Bangunan Makmal Kimia

  • Tel: 03-7967 7022 Ext 2546

  • Email: yinyinteo@um.edu.my

Page 2: Wave Function

• General Form of Wavefunction: A combination of radial and angular parts.

• Wavefunction Representation: Complex notations utilized, involving angular functions and radial functions:

$\Psi_{n,l,m}(R,r,\theta,\phi) = R(r)P(\theta) e^{im\phi}$

• Parameters include quantum numbers related to angular momentum.

Page 3: Quantum Numbers

• Four Quantum Numbers: Required to describe atoms:

  • n: Principal quantum number.

  • l: Azimuthal quantum number (orbital type).

  • m: Magnetic quantum number (orientation of the orbital).

  • s: Spin quantum number.

• Atomic Orbital: A one-electron wavefunction; an electron described by a specific wavefunction resides in that orbital.

  • Example: An electron in state $|\psi_{1,0,0}\rangle$ occupies orbital (n=1, l=0, m=0).

Page 4: Quantum Number Functions

• Quantum Number Explained:

  • Principal (n): Values 1, 2, 3,…; influences energy and size of the orbital.

  • Orbital (l): Values from 0 to n-1; dictates the shape of the orbital.

  • Spin (s): Values of ±1/2; describes the spin of the electron.

• Spin Orientations: Each electron's spin can only take certain values relative to the z-axis.

Page 5: Hydrogen Atom Spectrum

• Hydrogen Atom Energy Contributions:

  • Attraction between the electron and nucleus.

  • Repulsion between electrons, which is absent in hydrogen.

• Orbital Energy: In hydrogen, all orbitals with the same n value have the same energy due to the lack of inter-electronic interactions.

Page 6: Rydberg Constant and Orbital Energies

• Rydberg Constant: $R_H = 109,677 ext{ cm}^{-1}$.

• Orbital Energy Calculation:

  • Given by: $E_n = -\frac{R_H Z^2}{n^2}$ where:

  • $Z$: Atomic number, $n$: Principal quantum number.

Page 7: Energy Levels in Hydrogen Atom

• Ionization Energy (I): Represents the minimum energy needed to remove an electron from the hydrogen atom to n = ∞.

• Ionization Energy Value: For hydrogen, $I = 13.6 ext{ eV}$.

Page 8: Ground State Energy

• Ground State Energy: Lowest energy state for hydrogen is $E = -hcR_H$ corresponding to n = 1.

• Ionization Point: Occurs at $n = ∞$, when energy is supplied.

Page 9: Hydrogenic Atoms

• Definition of Hydrogenic Atom: A one-electron atom or ion with atomic number Z (examples: H, He+, Li2+, etc.).

• Emission Spectrum: Electron transitions create distinct lines in a spectrum observed when hydrogen is ionized and excited.

Page 10: Selection Rules for Transitions

• Selection Rules:

  • Allowable transitions: $ \Delta n = ext{any}, \Delta l = \pm1$

• Energy Levels Series: Transitions generate series like Lyman (n=1), Balmer (n=2), etc.

• Spectral Line Emission: Occurs when an electron transitions from higher to lower energy state.

Page 11: Atomic Hydrogen Spectrum

• Hydrogen Spectrum: Shows different regions; UV (for n=2), visible (for n=3), and IR ranges for different transitions.

Page 12: Emission Spectrum and Splitting

• Fine Structure: Energy level splitting due to spin-orbit coupling, affecting emission spectra.

Page 13: Spectroscopic Terms

• Microstates: Different configurations of electron arrangements fulfilling the electronic designation.

• Electronic Designation: Symbolized by principal quantum and sub-level information (e.g., 2p²).

Page 14: Microstates Variability

• Microstate Energy Variation: Influenced by inter-electronic repulsion; terms are groups of microstates with the same energy.

Page 15: Term Symbols

• Term Symbol Representation:

• Mentioned representations include S, P, D, F letters denoting total angular momentum.

Page 16: Relation Between Spin and Angular Momentum

• Spin and Magnetic Moments: Each electron contributes a magnetic moment from its angular momentum; interaction leads to total angular momentum.

Page 17: Spin-Orbit Coupling Interaction

• Spin-Orbit Coupling: Dependency on nuclear charge; strong for high-Z atoms affecting energy levels.

Page 18: Angular Momentum Variations

• Angular Momentum Interaction: Interaction effects based on parallel or opposed orientation of magnetic moments, impacting energy level splitting.

Page 19: Total Electronic Angular Momentum

• Total Angular Momentum (J): Combined from spin (s) and orbital (l) angular momentum.

Page 20: Example of Electron Configuration Calculation

• Multiplicity from Electron Configuration: Example to determine values of l and s.

Page 21: Combining Angular Momentum Contributions

• Method of Combining l and s: Demonstrates calculations for jz using allowed summation of components.

Page 22: Resulting j Values

• Permitted j Values: Explained regarding their combinations and the impact of their orientations.

Page 23: Quantum State Description

• Quantum States: Representation through microstates associated with configurations like 2P.

• Microstates Count: Deduced using formulae, influencing electronic levels.

Page 24: Angular Momentum Summation

• Angular Momentum Types: Explanation of configurations when combining l and s values, affecting energy states.

Page 25: Reinforcement or Opposition in Angular Momentum

• Combination Methods: Outlined processes for angular momentum contributions (adding or opposing).

Page 26: Energy Term Labels

• Energy Term Representations: Detailed how terms appear in configurations, explaining stability and configurations.

Page 27: Energy Levels as per Configurations

• Configurations Example: Various electronic configurations and their corresponding energy levels described.

Page 28: Fine Structure Influence

• Fine Structure Dependence: On energy levels and transition selection rules concerning allowed or forbidden transitions.

Page 29: Inclusion of Splitting Effects

• Energy Splitting: Explicit connection of energy levels through visual diagrams, illustration of electronic states.

Page 30: Formation of Sodium D lines

• Sodium Spectral Lines: Origin of observed spectral lines related to electron transitions in electronic configurations.

Page 31: Many Electron Atoms Characteristics

• Overview of Electron Occupation: Similarity in orbital types but differing energies; highlights on Pauli’s and Hund’s principles.

Page 32: Closed Shell Definition

• Closed Shell Concept: Electron configurations and their contributions to total angular momentum.

Page 33: Defining Orbital Angular Momentum

• L Value Representation: Overall angular momentum states defined using term symbols and state representations.

Page 34: Orbital Contributions Calculation for Non-Equivalent Electrons

• Energy Terms Calculation: By adding total angular momentum contributions, determining maximum and minimum values.

Page 35: Coupling Processes of Electrons

• Coupling Methods for Electrons: Demonstration of orbital angular momentum based on unique electron configurations.

Page 36: Example for Non-Equivalent Electron Terms

• Terms Determination: Explained through configurations identifying single and multiple electrons in orbitals.

Page 37: Summation Spins for Three Electrons

• Spin Contributions: Calculating resulting energies and terms when more than two electrons involved.

Page 38: Spin Contributions Explained

• Comprehensive Spin Contribution Methodologies: Summing methods based on odd and even electron configurations.

Page 39: Term Multiplicity

• Multiplicity Calculation: How multiplicities relate to electronic configurations and identifications of states.

Page 40: Total Spin States of Electrons

• Electrons with Half Spin: Resulting allowed configurations for cases with multiple electrons in unfilled shells.

Page 41: Spin Configurations for Two Electrons

• State Representation: Overview of resultant configurations with pairs of electrons and their allowed spin values.

Page 42: Electrons Occupy Orientations

• States Consideration: Neglecting completely filled shells when calculating term symbols for minimal energy.

Page 43: Closed Shells Contribution

• Closed Shell Effects: Their lack of contribution to angular momentum impacting spectral properties of elements.

Page 44: Coupling Processes Explained

• Hamiltonian Operators: Representation of electron interactions through different coupling terms.

Page 45: Total Angular Momentum Understanding

• Single Electron Angular Momentum: Explained theory for total angular momentum in heavier elements with multiple electrons.

Page 46: Methods to Analyze Electron Contributions

• Two Electrons Contributions Analyzing: How both methods work for analyzing angular momentum states.

Page 47: Permitted Values of Angular Momentum Quantum Numbers

• j Values from Configuration: Explanation on permitted values derived from configurations.

Page 48: Relation Between j and L Values

• Multiplicity versus States: How multiplicities relate to observable levels in configurations.

Page 49: Configuration Details for Specific Electron Cases

• Examples of Specific Configurations: Analyzed within binding states, revealing significance of j values.

Page 50: Angular Momentum Contribution Collection

• Methods Apply for Large Atoms: Russell-Saunders versus j-j coupling, understanding contributions.

Page 51: Establishing Term Symbols

• Labeling States: Described through term symbols, emphasizing multiplicities and angular momentum.

Page 52: Electron Arrangement Stability

• Lowest Energy State Arrangements: Guidance on stability and electronic configurations.

Page 53: Parameters for Molecular Term Symbols

• Labeling Molecular States: Differences emphasized between atomic and molecular systems in labeling.

Page 54: Molecular Symmetry Considerations

• Cylindrical Symmetry: Implications on angular momentum quantization.

Page 55: Molecular Orbital States Designation

• Molecular Orbitals and Angular Momentum: Clarification on using Greek letters for state identification.

Page 56: Molecular Orbital Functionality

• Interactions Between Atomic Orbitals: Displayed properties of bonding versus anti-bonding interactions.

Page 57: Total Orbital Angular Momentum

• Total Orbital Angular Momentum: Represented through Λ combined from multiple electrons’ contributions.

Page 58: Spin Quantum Number Considerations

• Total Spin Quantum Number Explained: Relevance across configurations.

Page 59: Spin-Orbit Coupling in Molecular Interactions

• Effect of Spin on Angular Momentum: Interaction implications based on axial orientation.

Page 60: Total Angular Momentum and States

• Z-Component of Angular Momentum: Definitions of z-component contributions compared against terms of energy states.

Page 61: Molecular Inversion Process

• Wave Function Considerations: Explanation of g/u symmetry and their relevance to molecular states.

Page 62: Molecular Orbital Classifications

• Class System of Molecular Orbitals: Discussion on bonding and anti-bonding types and their classifications.

Page 63: Overall Parity Determination

• Parity Rules: Generating conditions based on occupied orbitals of states.

Page 64: Symmetric and Antisymmetric States

• Labeling for Reflection Symmetries: Assigning states based on their behavior under reflection.

Page 65: Spin Multiplicity in Linear Molecules

• Defining Quantities for Molecule's Characteristics: Different angular momentum designations including renaming multipliers.

Page 66: Molecular Configurations Explained through Examples

• Example configurations Analyzed: Showcasing electronic status, multiplicities, and states.

Page 67: Illustrating B2+ Ion States

• Description of Molecular Terms: Reflect on σ states, their assignments, and resulting terms.

Page 68: Sample Configurations Analysis

• Observations of Molecular Orbital Contributions: Initial and excited state comparisons made clear.

Page 69: Understanding Configurations for Non-equivalent Electrons

• Determinant States Analysis: Terms analyzed through multiple electron interactions displaying variations.

Page 70: Total Contributions for λ in Systems

• Total Molecular Orbital Angular Momentum Quantification: Through specific electron configurations, showcasing total λ contributions.

Page 71: Current Molecule Examples with Their Limits

• Respective Terms Comparison: Determining typical parity characters through comparisons of systems.

Page 72: Energy Ordering Observations

• Hund’s Rule Application: Explains energy arrangement in electronic states for atomic configurations viably.

Page 73: Basics of Molecular Electronic States

• Electronic States Completion: Various properties across diatomic molecules and their transitions.

Page 74: Selection Rules Summary

• Transition Process Guidelines: Emphasizing essential conservation laws during transitions.

Page 75: Electronic Transition Overview

• Molecular Reactions Upon Photon Absorption: How specific energy frequencies influence changes in states.

Page 76: Energy Order for Electronic Transitions

• Photonic Influence on Electronic States: Expected ranges and transitions noted under conditions.

Page 77: General Observations on Potential Energy Curves

• Potential Curves Representation: Different curves represent excited states and dynamics.

Page 78: Vibrational Analysis Associated with Energy States

• Curves Comparison: Characterizing vibrational representations against equilibria under energetic states.

Page 79: Solving the Nuclear Schrödinger Equation

• Finding Vibrational Level Associated: Each rotational level represented with vibrational levels discussed.

Page 80: Spectral Observations in Polyatomic Molecules

• Labeling of States Variation: Depends majorly on symmetry and quantum angular momentum specifics.

Page 81: Transition Metals and Their Complexes

• Introduction to Transition Metal Chemistry: Behavior and characteristics noted in molecular interactions and ligand attachment.

Page 82: d Orbital Conservation under Crystal Field

• Orbital Splitting upon Arrangements: Describing energy arrangement concerning electron configurations.

Page 83: Octahedral Complexes Analysis

• Coordination Influence and Orbital Interaction: Dispersion of electron states grounded within electron valency potentials.

Page 84: Absorption Energy Characteristics

• Influence of Δo: Dependency on symmetry resulting in absorption changes spotted in visible regions.

Page 85: Tetrahedral vs Octahedral Configurations

• Comparison of Setups: Noting orbital orders and energies transitioned concerning tetrahedral arrangements.

Page 86: d1 Configuration Considerations

• Single Electron Impacts on term states during interactions with ligands.

Page 87: Octahedral Coordination and Configuration Changes

• Describing Vertex Concentrations: Observing changes from state transitions and coordination types.

Page 88: Term State Analysis in Ligand Configurations

• Electron Promotion Changes: Yielding a progressive understanding of term shifts through energetic levels.

Page 89: Free Ion Electromagnetic Responses

• Spectroscopic Changes Analysis: Through configuration transitions and energy class differences.

Page 90: Spectroscopic States in d Configuration

• Transition Analysis Across Levels: Coherent diagnostic for terms positioned on different configurations.

Page 91: Terms Splitting Discussion

• Detailed Orbital Examination: Focused on symmetry and resulting term variation.

Page 92: Orbital Analysis on Transition Mechanisms

• Charge Distribution Behavior: State-to-state transitions and their excitation frames analyzed.

Page 93: State Transition Explained

• Comparative Analysis Across Complexes: Understanding energy orderings affected by electronic states.

Page 94: Transition Electron Assumptions

• Terms Comparison through energy positionings governed by charge configurations elucidated.

Page 95: Absorptions Detailing in Specific Configurations

• Identifying Spectroscopic Peaks Analysis: Noting transitions and detailing resonances observed.

Page 96: Electron Configurations in Octahedral Fields

• Comparative d-d Transitions: Detailing similarities across configurations in questions to understand transitions involving d electrons.

Page 97: Example State Transition in Weak Fields

• Characterization of Ground State Terms: Notable transitions through spectroscopic data.

Page 98: Weak and Strong Field Configurations

• Differentiated Absorptions in Complexes: Imbued within spectroscopic bands and their resonances.

Page 99: Absorption Observations Across Similar Configurations

• States Outcomes Acknowledged: Showcasing weak transitions via defined terms.

Page 100: Coloration from d Orbital Splitting

• Connected Absorption Mechanisms: Understanding the impacts causing coloration in complex species.

Page 101: Titanium Spectral Analysis

• Examining Specific Absorption Claims: Color properties linked with electronic transitions analytically.

Page 102: Absorption and Complementary Color Relations

• Interactive Color Resulting Properties: Detailed implications on observed colors influenced by electron excitations.

Page 103: Molecular Orbital Energy Levels

• Relative Placement Examination: Outlining bonding behavior and relative energy linked through shared orbitals.

Page 104: Absorption Spectrometer Functions

• Functional Ranges and Electron Transitions: Spectroscopic barriers and elevation towards particular bonding levels noted.

Page 105: Important Electron Transitions

• Critical Transitions for Absorption: Recognizing needed energy levels embedded within pi-bond structures.

Page 106: Radical Electron Transition Analysis

• Comparative Studies for Energy Absorption: Noting molecular structures affecting their respective transitions and encompassing energy placements.

Page 107: Absorption Spectrum Examination

• Absorption Rates in Absence of Bonds: Detailing transformations evidenced in colorless species and their corresponding transitions.

Page 108: Chromophore Absorption Traits

• Energy Properties of Chromophores: Addressing energy transitions and tying them to specific characteristics.

Page 109: Delocalization Factors in Absorption Properties

• Conjugation Influence: How it lowers energy gaps, directly associating increased absorption into higher wavelengths.

Page 110: Wavelength Shifts Observed with Conjugation

• Diminishing Energy Gaps through Conjugation: Leading into the shifts across peak absorptions.

Page 111: Phenolphthalein Spectroscopic Analysis

• Visible Absorption Characteristics: Discussing distinct behavior of phenolphthalein across different states.

Page 112: Summary of Excited Phenomena

• Excited States Fluorescence and Phosphorescence: Detailed influencing internal and external transitions identified clearly.

Page 113: State Labeling for Polyatomic Molecules

• Ground State Clarity Across Molecules: Identification and characteristics explained through changes in the molecular orbitals.

Page 114: Radiative vs Non-Radiative Processes

• State Transition Dynamics: Exploring transitional behaviors between excited and ground states.

Page 115: Jablonski Diagram Functionality

• Electronic and Radiative Transition Illustrations: Outlining important transitions seen through diagrams and flow motions.

Page 116: Processing Radiative Transitions

• Vibration and Radiation Interaction: Detailing the process of excited states and their fading due to radiation._

Page 117: Internal Conversion Dynamics

• Transformation Possibilities: Explanatory highlights around internal processes described functionally.

Page 118: Jablonski Diagram Inclusion

• Energy State Representation: Fluorescent behavior due to internal transitions illustrated visually.

Page 119: Distinguishing Between Fluorescence and Phosphorescence

• Differences noted in Emissions: Explaining the difference between transient stages versus prolonged emissions seen in phosphorescence.

Page 120: Fluorescence Mechanism Overview

• Radiative Emissions Post Absorption: Detailed relationships in transition states experienced.

Page 121: Molecule Behavior Post-Excitation

• Retention of Energy Post Absorption: Internal interactions leading to electron retention and emission behaviors.

Page 122: Frequency Shifts and External Influences

• Color Shift Dynamics: Impacts based on surrounding environmental shifts.

Page 123: Principles of Phosphorescence Extraction

• Transition through Triplet States Importance: Analysis on transition impacts and energy movement noted.

Page 124: Effect of Intersystem Crossing on Transitions

• Role of Spin Dynamics: Discussing crossing dynamics among states impacting observable emissions.

Page 125: Endurance of Phosphorescence Confirmed

• Slow Energy Release Dynamics: Expounding on retention and delayed emission due to surrounding interactions.

Page 126: Solid Sample Focus on Phosphorescence

• Intensity Derivations Highlighted: Enhanced focus on solid-state capabilities leading to distinct emissions.