Theoretical Chemistry Cheat Sheet

The core ideas of Theoretical Chemistry distilled into a single, scannable reference — perfect for review or quick lookup.

PiqCue — piqcue.com/theoretical-chemistry/cheatsheet

Quick Reference

Schrodinger Equation

The fundamental equation of quantum mechanics that describes how the quantum state of a physical system changes over time. In chemistry, its time-independent form is solved to find the energy levels and wavefunctions of atoms and molecules.

Born-Oppenheimer Approximation

The assumption that nuclear and electronic motions can be treated separately because nuclei are much heavier and slower than electrons. This simplification allows the electronic Schrodinger equation to be solved for fixed nuclear positions.

Density Functional Theory (DFT)

A computational quantum mechanical method that determines electronic structure by using the electron density rather than the many-electron wavefunction, making it computationally efficient for large molecular and solid-state systems.

Molecular Orbital Theory

A method of describing chemical bonding where atomic orbitals combine to form molecular orbitals that are delocalized over the entire molecule, with electrons filling these orbitals according to energy and the Pauli exclusion principle.

Potential Energy Surface (PES)

A mathematical surface relating the energy of a molecular system to its geometric coordinates. Minima on the PES correspond to stable structures, saddle points to transition states, and pathways between them to reaction mechanisms.

Hartree-Fock Method

An approximate method for solving the electronic Schrodinger equation that treats each electron as moving in the average field of all other electrons, using a single Slater determinant of molecular orbitals.

Electron Correlation

The difference between the exact energy of a many-electron system and the Hartree-Fock energy. It arises because electrons avoid each other more effectively than the average-field approximation captures.

Transition State Theory

A theory that explains reaction rates in terms of a quasi-equilibrium between reactants and an activated complex (transition state) at the saddle point of the potential energy surface.

Basis Set

A set of mathematical functions used to represent the molecular orbitals in quantum chemical calculations. Larger, more complete basis sets yield more accurate results but require more computation.

Molecular Dynamics Simulation

A computational method that simulates the physical movements of atoms and molecules over time by numerically integrating Newton's equations of motion, using forces derived from potential energy functions.

Key Terms at a Glance

Ab Initio:Quantum chemical methods derived from first principles without empirical parameters.

Basis Set:A set of mathematical functions used to approximate molecular orbitals in quantum chemical calculations.

Bond Order:A measure of the number of chemical bonds between a pair of atoms, calculated as half the difference between bonding and antibonding electrons.

Born-Oppenheimer Approximation:The separation of nuclear and electronic motions based on the large mass difference between nuclei and electrons.

CASSCF:Complete Active Space Self-Consistent Field method for multiconfigurational systems.

Coupled Cluster:A highly accurate post-Hartree-Fock method using an exponential ansatz to include electron correlation.

Density Functional:A mathematical functional that maps the electron density to the total energy of a quantum system.

Eigenvalue:In quantum chemistry, the allowed energy values obtained by solving the Schrodinger equation.

Electron Density:The probability of finding an electron at a given point in space, used as the central variable in DFT.

Exchange Energy:The quantum mechanical energy arising from the antisymmetry requirement of the electronic wavefunction.

Force Field:A set of classical potential energy functions and parameters used in molecular mechanics and MD simulations.

Gaussian Function:A bell-shaped mathematical function widely used as basis functions in quantum chemical calculations.

Hamiltonian:The quantum mechanical operator corresponding to the total energy of a system (kinetic + potential).

Hartree-Fock:A mean-field approximation to the electronic Schrodinger equation using a single Slater determinant.

Hohenberg-Kohn Theorems:Two theorems proving that ground-state properties are uniquely determined by the electron density.

Get study tips in your inbox

We'll send you evidence-based study strategies and new cheat sheets as they're published.

We'll notify you about updates. No spam, unsubscribe anytime.