Quantum Harmonic Oscillator Model for Vibrations in Polyatomic Molecules

These flashcards cover key vocabulary related to the quantum harmonic oscillator model and its application in polyatomic molecular vibrations.

Quantum Harmonic Oscillator (QHO)

A model that describes the vibrational modes of molecules, based on quantum mechanics.

Boltzmann Distribution

A probability distribution that predicts the distribution of particles among the available energy states.

Potential Energy Surface (PES)

A theoretical representation of the energy of a system as a function of the nuclear coordinates.

Normal Mode Coordinate (x)

Defined as the difference in bond length (r) from the equilibrium bond length (r0), represented as x = r - r0.

Hessian Matrix

A square matrix of second-order partial derivatives of a scalar-valued function.

Transition-State Theory

A theory that describes the rate of chemical reactions in terms of a transition state and its energy.

Dynamical Matrix (Dij)

A matrix that, when diagonalized, yields eigenvalues related to the vibrational frequencies and mass-weighted coordinates of the normal modes.

Eigenvalue Equation

An equation that describes the eigenvalues and eigenvectors of a matrix, crucial for solving systems in quantum mechanics.

Vibrational Energy Levels

Quantized energy levels associated with the vibrational states of a molecule.

Imaginary Harmonic Modes

Vibrational modes that correspond to negative eigenvalues in the Hessian matrix, indicating instability.