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 → Theoretical and Computational Chemistry ↓


Quantum chemical methods


Quantum chemical methods are an important part of theoretical and computational chemistry. These methods use the principles of quantum mechanics to solve chemical questions. They help simulate and understand molecular properties and reactions at the atomic scale. It involves the mathematical description of electrons in atoms and molecules. Quantum mechanics is important because it provides the most accurate description of molecular systems.

The journey of quantum chemistry began with the development of quantum mechanics in the early 20th century. Scientists such as Erwin Schrödinger, Werner Heisenberg and Paul Dirac laid down the basic principles. Today, these principles form the basis of quantum chemical methods.

Basic concepts

At the core of quantum chemistry is the Schrödinger equation. This equation is important in predicting the behavior of quantum systems. It describes how the quantum state of a physical system changes over time. The equation is:

hΨ = eΨ

Where:

  • H is the Hamiltonian operator (which represents the total energy of the system).
  • Ψ is the wave function that contains all the information about the system.
  • E is the energy of the system.

Solving the Schrödinger equation gives us information about the wave function and energy associated with the molecular system.

Major quantum chemical methods

Quantum chemical methods are mainly divided into two categories: ab initio methods and semi-empirical methods.

Early methods

The term "ab initio" means "from first principles". These methods do not rely on experimental data, but are based entirely on the laws of quantum mechanics. The most common ab initio methods include:

Hartree-Fock (HF) method

The Hartree-Fock method is a fundamental ab initio approach. This method assumes that electrons do not correlate with each other and move independently in the net field of all other electrons. The HF approximation ignores electron-electron correlation. Despite its simplicity, Hartree-Fock provides a baseline for more advanced methods.

The HF function is a single Slater determinant, which can be visualized as:

These circles represent electron orbitals, and the intersecting lines represent the interaction between them according to the HF method.

Density Functional Theory (DFT)

Density functional theory has become extremely popular due to its balance of accuracy and computation cost. Unlike HF, DFT takes electron correlation into account by focusing on the electron density. The electron density, ρ(r), simplifies the complex electron wave function, which can sometimes make DFT easier and faster.

This curve shows a typical electron density distribution over distance, which plays an important role in DFT.

Post-Hartree–Fock methods

These methods include high accuracy techniques that correct for the limitations of the HF method. Some common post-Hartree–Fock methods are:

  • Møller–Plesset turbulence theory (MPN): uses turbulence theory to incorporate electron correlation in HF.
  • Configuration interaction (CI): considers multiple electronic configurations to assess correlation.
  • Coupled cluster (CC) theory: known for its accuracy, considers all-electron correlations.

Semi-empirical methods

Semi-empirical methods combine quantum mechanical theories with experimental data. These methods reduce computational costs. They are based on the Hartree-Fock formalism but use parameterizations derived from experimental data. Popular semi-empirical methods include:

  • PM3 (Parametric Method 3)
  • AM1 (Austin Model 1)
  • MNDO (Modified Neglect of Diatomic Overlap)

Semi-empirical methods are useful for larger molecules, where computational resources and time are a concern.

Applications of quantum chemical methods

Quantum chemical methods have diverse applications in chemistry and beyond. They are essential for the following:

  • Calculations of molecular properties: These include bond lengths, angles, dipole moments, etc.
  • Prediction of spectra: Quantum methods predict and interpret NMR, IR, UV/Vis spectra.
  • Reaction Mechanism: Information about reaction pathway, transition state etc.
  • Materials Science: Design and Evaluation of New Materials.

For example, predicting the dipole moment of a molecule is important in the study of molecular polarity:

, ,

This diagram shows the dipole moment as a vector from the positive charge to the negative charge.

Challenges and limitations

Quantum chemical methods provide invaluable information, but they are not without limitations. The computational cost for high-accuracy methods grows exponentially with the size of the system. Striking a balance between computational cost and accuracy is an ongoing challenge.

There are always challenges in choosing the appropriate method for a particular system or reaction. A simple method such as HF may be suitable for initial investigations, while more complex methods such as DFT or post-Hartree-Fock may be necessary for detailed information.

As computer power and algorithms advance, these limitations are rapidly being overcome, raising hopes for future developments in quantum chemistry.

Conclusion

Quantum chemical methods have opened new horizons in the understanding of molecular systems and chemical reactions. From providing theoretical frameworks to assisting in experimental predictions, these methods continue to evolve and influence various scientific fields.

Quantum chemical methods remain an indispensable tool in modern chemistry, offering deep insights into molecular properties and reactions. As computational advances continue, these methods promise even more detailed and accurate molecular descriptions.


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Quantum chemical methods

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