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 → Theoretical and Computational Chemistry ↓


Quantum chemistry methods


Quantum chemistry is a fundamental discipline in theoretical and computational chemistry that uses the principles of quantum mechanics to solve chemical problems. By understanding how atoms and molecules behave at the quantum level, chemists can predict chemical properties and reactions with great accuracy. In this comprehensive overview, we will explore the various methods used in quantum chemistry and their applications.

Introduction to quantum chemistry

At its core, quantum chemistry seeks to understand the behavior of electrons in atoms and molecules. The foundation of quantum chemistry lies in the Schrödinger equation, which describes how the quantum state of a physical system changes over time. This equation is central to many computational techniques used to predict the properties of molecules.

Schrödinger Equation: ĤΨ = EΨ

In this equation, Ĥ is the Hamiltonian operator, Ψ is the wave function of the system, and E is the energy of the system. The wave function contains all the information about the system, which can be used to calculate observable properties.

Methods in quantum chemistry

There are several major methods used in quantum chemistry. Each method provides different levels of approximation and computational efficiency, making them suitable for different types of problems.

Hartree–Fock method

The Hartree-Fock (HF) method is one of the simplest quantum chemistry methods. It is an ab initio method, meaning that it attempts to solve the Schrödinger equation from first principles without empirical parameters.

The HF method approximates the many-electron wave function as a single Slater determinant, which is an antisymmetrical product of one-electron wave functions called orbitals. This method involves solving a set of equations known as the Hartree-Fock equations to obtain the best possible orbitals.

NucleusElectron Orbitals

The Hartree-Fock method is used to calculate ground state energies and electronic distributions for small molecules. However, it does not take into account electron correlation, which can lead to errors in predicting chemical properties.

Density functional theory (DFT)

Density functional theory (DFT) is a widely used method in quantum chemistry, as it strikes a balance between computational cost and accuracy. DFT focuses on the electron density rather than the wave function as its primary variable.

In DFT, the energy of a system is expressed as a functional of the electron density. The main advantage of DFT is its ability to incorporate electron correlation through various approximations known as exchange-correlation functionals.

E[ρ] = T[ρ] + V[ρ] + J[ρ] + E_xc[ρ]

Here, T[ρ] is the kinetic energy, V[ρ] is the potential energy due to attractive forces, J[ρ] is the classical repulsion energy, and E_xc[ρ] is the exchange-correlation energy.

electron density

Practical applications of DFT include the study of large molecular systems, solid state systems, and reaction pathways in chemistry.

Configuration interaction (CI)

Configuration interaction (CI) is an approach that improves the Hartree–Fock method by considering electron correlation more explicitly. It involves constructing a wave function from a linear combination of Slater determinants, each of which represents a different electronic configuration.

Ψ_CI = Σ c_i Φ_i

The coefficients c_i are varied to minimize the energy of the system. While CI provides accurate results, it is computationally demanding and is usually used for small systems.

Advanced methods

Coupled cluster methods (CC)

Coupled cluster methods are considered the most accurate for quantum chemistry because of their treatment of electron correlation. They express the wave function as an exponential ansatz of excitation operators acting on the Hartree–Fock wave function.

Ψ_CC = exp(T) Ψ_HF

In this formula, T is the cluster operator that accounts for the electron excitations. CC methods can accurately predict molecular properties and reaction energies for small to medium-sized systems.

Quantum Monte Carlo (QMC)

Quantum Monte Carlo (QMC) methods use statistical sampling to solve the Schrödinger equation. They are probabilistic methods that can approximate electron correlation with great accuracy. Despite being highly accurate, QMC is computationally intensive and is generally reserved for systems where other methods struggle.

Applications of quantum chemistry methods

Methods of quantum chemistry are invaluable tools for many areas of science and technology. Here are some examples of their applications:

  • Predicting reaction mechanisms and rates.
  • Designing new materials and drugs.
  • Understanding and engineering catalytic processes.
  • To investigate the electronic properties of solids.

Through computational chemistry scientists can model complex systems with a high level of accuracy and understanding, paving the way for innovative solutions across a variety of industries.

Challenges and growth

Despite the advances in quantum chemistry methods, challenges remain. Accurately modeling large and complex systems can be computationally prohibitive. Advances in algorithms and computational power continue to push the field forward, improving the efficiency and scalability of these methods.

The integration of machine learning with quantum chemistry is a promising development, offering possibilities to increase prediction accuracy and reduce computational demands.

Conclusion

The methods of quantum chemistry provide a deeper understanding of chemical phenomena through the lens of quantum mechanics. From the Hartree-Fock method to DFT, CI and beyond, these techniques enable chemists to predict and explain the properties of molecules and reactions. As computational power and methods develop, quantum chemistry will continue to play a key role in scientific progress, bringing theoretical chemistry closer to experimental observation.

Mastering these methods is essential for ambitious chemists who want to contribute to this exciting and influential field.


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Quantum chemistry methods

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