PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Physical Chemistry ↓


Quantum Chemistry


Introduction to quantum chemistry

Quantum chemistry is a branch of chemistry that focuses on the application of quantum mechanics to chemical systems. At its core, it provides a fundamental description of chemical reactions between molecules and atoms. By considering the dual wave-particle nature of matter, it allows us to understand and predict the behavior of atoms and molecules.

Basic principles

Quantum chemistry is based on the principles of quantum mechanics which include:

  • Wave-particle duality: matter exhibits both wave-like and particle-like properties. For example, electrons can be described as waves that occupy orbits around the nucleus.
  • Quantization: The energy levels of electrons are quantized, which means that electrons can only exist at certain energy levels. This is described by discrete quantum states.
  • Uncertainty Principle: Heisenberg's uncertainty principle states that it is impossible to know both the position and momentum of an electron with absolute certainty.
  • Pauli Exclusion Principle: No two electrons in an atom can have the same quantum numbers, thus they occupy unique states.
  • Schrödinger equation: The Schrödinger equation is the foundation of quantum chemistry. It allows us to calculate the wave function of a system, predicting the behavior of electrons.

Wave function and the Schrödinger equation

The primary goal of quantum chemistry is to solve the Schrödinger equation:

    Hψ = Eψ

Here, H is the Hamiltonian operator, which represents the total energy of the system. ψ is the wave function that describes the quantum state of the system, and E is the energy eigenvalue associated with the wave function.

Pictorial representation

Imagine the electron's wave function ψ as a cloud around the nucleus, with the cloud's density representing the probability of finding the electron at any given location. Orbitals can be viewed as three-dimensional shapes depicting where you are likely to find the electron.

    electron cloud nucleus
         ,
          ,
         ,

Solving the Schrödinger equation allows us to predict the behavior of electrons in atoms or molecules. This solution provides information about molecular shapes, bond angles, and energies.

Quantum numbers and atomic orbitals

Quantum numbers are important in defining the electron configuration and the structure of orbitals. There are four quantum numbers:

  • Principal quantum number (n): determines the energy level of the electron and is related to the shape of the orbital.
  • Angular momentum quantum number (l): Defines the shape of the orbital (s, p, d, f).
  • Magnetic quantum number (ML): Describes the orientation of the orbital in space.
  • Spin quantum number (ms): Indicates the spin direction of the electron, either +1/2 or -1/2.

Examples of atomic orbitals

Atomic orbitals such as s, p, d, and f are identified by their shape and energy. Here are some visual representations of orbitals:

    1s orbital: 2p orbital:      
     ,
    ,
    ,
    
    3d orbital: 4f orbital:
     ,
    ,
    ,

Each orbital image simplifies the complex shape predicted by solutions of the Schrödinger equation. The illustration above shows the common shapes of orbitals such as spherical for s, dumbbell-shaped for p, and so on.

Molecular orbitals and bonding

In molecules, atomic orbitals combine to form molecular orbitals. These can be bonding, anti-bonding, or non-bonding orbitals, which affect the stability of the molecule.

For example, consider the hydrogen molecule (H 2):

    H + H → H2
   ,
       
    bonding orbital

Antimolecular orbitals increase the electron density between the nuclei, causing attraction. However, antimolecular orbitals decrease the electron density, causing repulsion.

Applications of quantum chemistry

Quantum chemistry is essential in predicting molecular behavior, designing new drugs, understanding the properties of substances, and exploring chemical reactions in detail.

Design of medicines

The principles of quantum chemistry can predict how drugs interact with biological molecules at the atomic level, aiding drug discovery and design. By understanding molecular orbitals and electronic configurations, scientists can optimize the efficacy and safety of new therapies.

Physics

In materials science, quantum chemistry helps design materials with desired electronic and structural properties. For example, understanding electron behavior in semiconductors is important for the development of new electronic devices.

Chemical reactions

Quantum chemistry provides a detailed understanding of reaction mechanisms, making it possible to predict reaction outcomes. It also helps design catalysts to speed up reactions or make processes more efficient.

Advanced topics

As technology advances, calculations in quantum chemistry become more complex. Advanced methods include:

  • A priori methods: These methods, such as Hartree–Fock and post-Hartree–Fock, calculate molecular properties directly from physical constants without empirical parameters.
  • Density functional theory (DFT): A popular quantum mechanical method used to investigate electronic structure, especially for large systems.
  • Quantum Monte Carlo: a stochastic method of solving the Schrödinger equation using random sampling techniques, often used for complex systems.

Visual example of a chemical reaction

Consider the simple reaction where hydrogen and oxygen form water. In quantum perspective:

    2H2 + O2 → 2H2O
    (σ bonding)
     ,

In this reaction, molecular orbitals play an important role. Understanding how electrons fill these orbitals helps chemists understand energy changes and reaction pathways.

Conclusion

Quantum chemistry remains an important field in understanding atomic interactions and molecular structures. By applying quantum mechanics to chemical problems, it provides extensive insight into the behavior of atoms and molecules at the most fundamental level. This branch of chemistry not only helps explain the properties of known substances, but also assists scientists in discovering new chemical elements with potential applications in a variety of fields.


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Quantum Chemistry

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