Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Quantum Chemistry ↓


Atomic orbitals


In exploring atomic structure within quantum chemistry, one cannot ignore the important concept of atomic orbitals. These are regions in an atom where there is a high probability of finding an electron. Atomic orbitals play an important role in defining the electronic configuration of an atom and subsequently the chemical behaviour of the elements.

Understanding the concept of orbitals

Orbitals are obtained from the wave functions described in quantum mechanics. A fundamental equation in quantum mechanics, the Schrödinger equation, helps find these wave functions. It is represented as:

Hψ = Eψ

Here, H is the Hamiltonian operator, ψ is the wave function, and E is the energy eigenvalue. These wave functions are solutions that describe the probability of finding the electron in a particular region around the nucleus.

These regions are called atomic orbitals and can be visualized as three-dimensional shapes where there is a 95% probability of finding an electron at any given time.

Types of atomic orbitals

Atomic orbitals are classified into different types depending on their shape. These include:

  • s-orbitals: These are spherical. They can be seen as a sphere where the electron density is evenly distributed around the nucleus. The size of the s-orbital increases as the principal quantum number increases.
  • p-orbitals: These are shaped like dumbbells and are oriented along the x, y and z axes. For example, in a p-orbital:
  • d-orbitals: These are more complex with a four-lobed shape and are important to the chemistry of transition metals. For example, the lobes of the dx^2-y^2 orbital are oriented along the x and y axes.
  • f-orbitals: Even more complex than d-orbitals, f-orbitals are important in describing the behavior of the inner transition metals such as the lanthanides and actinides.

Quantum numbers and orbital sizes

Quantum numbers are necessary to describe the properties of atomic orbitals, just as an address is needed to identify the location of a house. These numbers include:

  • Principal quantum number (n): Indicates the energy level of an orbital, commonly known as the shell number.
  • Angular momentum quantum number (l): Determines the shape of the orbital. Its value depends on n and ranges from 0 to n-1. For example, l = 0 represents an s-orbital, l = 1 represents a p-orbital, and so on.
  • Magnetic quantum number (ml): Describes the orientation of the orbital in space. Its value can range from -l to +l.
  • Spin quantum number (ms): This indicates the spin of the electron within the orbital, which takes the value of +1/2 or -1/2.

Importance of orbitals in chemical bonding

Atomic orbitals play an important role in the formation of chemical bonds.

When two atoms approach, their atomic orbitals overlap. This overlap leads to the formation of molecular orbitals, which is described by the constructive or destructive interference of atomic wave functions.

  • Bonding orbital: Formed due to constructive interference, resulting in lower energy between the nuclei and increased electron density, which stabilizes the bond.
  • Antibonding orbital: Formed due to destructive interference, characterized by a node between the nuclei, which points to instability.

For example, in the hydrogen molecule (H2), the two H 1s orbitals overlap to form σ (sigma) molecular orbitals.

Visualizing classes with probability density

An effective way to look at orbitals is through a probability density plot, which shows where the electron is most likely to be found. For example, as expressed graphically with a radial distribution function:

0RPossibility

The red curve shows the probability density of an electron within the s-orbital.

Electronic configuration and Aufbau principle

The concept of orbitals is important in explaining the electronic configuration of atoms, which predicts the distribution of electrons among orbitals. According to the Aufbau principle, electrons fill low-energy orbitals before filling high-energy orbitals. Thus, the general order of filling orbitals is:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p...

This order is affected by both electron shielding and sub-shell energy levels.

Explaining atomic orbitals is fundamental to understanding advanced topics in chemistry, playing a vital role in determining molecular shape, chemical reactivity, and bonding properties. Becoming familiar with this concept helps in exploring more complex molecular phenomena and the behavior of matter under different conditions.


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Atomic orbitals

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