Quantum Mechanics Unit 13 Key Terms

Statistical thermodynamics

The link between molecular properties (like energy levels) and the bulk thermodynamic properties (average behavior of a large number of molecules)

Ensemble

The collection of macroscopic systems in thermal equilibrium with a heat reservoir

Canonical ensemble

An ensemble with common N, V, and T shared among the systems

Boltzmann distribution

The probability of a system to be in the state j with energy E_j(N,V) . It describes how probable a state is within a system among all possible energies.

Boltzmann factor

e^-E/k_bT representing the fraction of collisions with at least the minimum required energy

Partition function

contains all the thermodynamic information about a system and thus provides a bridge between spectroscopy and thermodynamics, calculated by drawing on computed or spectroscopically derived structural information about molecules.

Ensemble average of a quantity

ensemble average of any quantity, calculated using the probability distribution, is the same as the experimentally observed value

Molecular partition function

the product of the degree of freedom partition functions q = q_vibq_rotq_transq_elec. used to calculate the probability of finding a molecule with a given energy and state (i.e. vib, transl) in a system.

Translational partition function

Rotational partition function

Vibrational partition function

Electronic partition function

Characteristic vibrational temperature

Rotational temperature

Symmetry factor (or number)

Translational contributions

The contribution to the overall molecular energy due to translational energy/motion

Rotational contributions

The contribution to the overall molecular energy due to rotational energy/motion (monoatomic gases have no rotational contribution)

Vibrational contributions

The contribution to the overall molecular energy due to vibrational energy/motion (vibrational modes)

Electronic contributions

The contribution to the overall molecular energy due to electronic energy/motion (electron movement within and across energy levels)

Chemical potential

Same as Gibbs free energy, where the chemical potential is proportional to the ln of the partition function of the ground vibrational state of the molecule

Transition state theory

The theory of the rate of elementary reactions. It focuses on transient species (activated complex or transition state) located in the vicinity of the top of the barrier height (activation energy) of a reaction. The model of the elementary reaction is a two-step process.

Reactants and the activated complex are in equilibrium with each other. the rate of the reaction is given by the rate of a unimolecular process that transforms the activated complex into products

Transition state

The crucial configuration of reactant molecules at the maximum of the potential energy curve, where they have come to such a degree of closeness and distortion that a small further distortion will send them in the direction of products.

Activated complex

the cluster of atoms in the vicinity of the peak of the potential energy curve

Gibbs energy/enthalpy/entropy of activation

The Gibbs energy of activation can be divided into an entropy of activation, ∆‡S and an enthalpy of activation, ∆‡H, by writing ∆‡G = ∆‡H -T∆‡S

The rate at which the activated complex forms products depends on the rate at which it passes through a transition state. The rate constant may be parameterized in terms of the Gibbs energy, entropy, and enthalpy of activation.

Potential energy surface

The electronic energy vs. the interatomic distance, where the potential energy depends on more than one single geometric parameter, such as its various bond lengths and angles. The potential energy as a function of the relative positions of all the atoms taking part in the reaction.

the energy function is of 2 geometric parameters and keeps the other(s) at a fixed value.