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Suggested Curriculum for Computational Chemistry

Copyright (c) RDMCHEM LLC 2020

 

Computational chemistry is a powerful tool for introducing, exploring, and applying concepts encountered throughout the chemistry curriculum. The aim of these lessons is to provide students and/or instructors ways to interact with selected topics using the QuantumChemistry package exclusively within Maple with no need to collate multiple software packages!   Lessons are written to emphasize learning objectives rather than Maple coding.   However, in order to show students and instructors how the calculations are set up,  each lesson contains the Maple syntax and coding required to interact with the selected topic.  In some cases, questions are asked of the student with the answer provided as a subsection.   As such, each lesson can be used 'as-is' or modified as desired to be used by students in a classroom setting, laboratory setting, or as an out of class guided inquiry assignment.

 

These lessons are designed for a graduate-level course in Computational Chemistry.   Lesson 1 (Hartree-Fock Method) presents the Hartree-Fock method for computing the energies and properties of atoms and molecules.  Lesson 2 (Electronic Transitions of 1,3-Butadiene) studies the electronic transitions in the conjugated molecule 1,3-butadiene using the Hartree-Fock method with connections to the particle in a box.  Lesson 3 (Correlation Energy) introduces the idea of correlation energy and looks at several applications that exemplify the need to go beyond the Hartree-Fock approximation.  Lesson 4 (Many-body Perturbation Theory) shows how Rayleigh-Schrödinger perturbation theory can be applied to computing the correlation energy of atoms and molecules.  Lesson 5 (Density Functional Theory) introduces the widely used density functional theory for computing the energy of molecules through a one-electron Schrödinger equation that includes electron correlation.  Lesson 6 (Variational 2-RDM Method) presents the variational 2-RDM method in which the energy of molecules is computed as a functional of the 2-electron reduced density matrix (2-RDM).  Lesson 7 (Geometry Optimization and Normal Mode Analysis) involves calculating the optimum geometry for a triatomic and corresponding normal modes.  Advanced students can focus on different electronic structure methods and basis sets.  Lesson 8 (Vibrational Spectroscopy and PES) allows students to construct potential energy surfaces for a diatomic using various levels of electronic structure theory and to calculate the associated rovibrational spectrum.   

 

1. Hartree-Fock Method

This lesson presents the Hartree-Fock method for computing the energies and properties of atoms and molecules

 

2. Electronic Transitions of 1,3-Butadiene

This lesson studies the electronic transitions in the conjugated molecule 1,3-butadiene using the Hartree-Fock method with connections to the particle in a box.

 

3. Correlation Energy

This lesson introduces the concept of correlation energy and provides pedagogical examples of the qualitative failures of Hartree-Fock.

 

4. Many-body Perturbation Theory

This lesson shows how Rayleigh-Schrödinger perturbation theory can be applied to computing the correlation energy of atoms and molecules.

 

5. Density Functional Theory

This lesson introduces the widely used density functional theory for computing the energy of molecules through a one-electron Schrödinger equation that includes electron correlation.

 

6. Variational 2-RDM Method

This lesson presents the variational 2-RDM method in which the energy of molecules is computed as a functional of the 2-electron reduced density matrix (2-RDM).

 

7. Geometry Optimization and Normal Mode Analysis

This lesson involves finding the optimum geometry for a triatomic and the associated vibrational normal modes.

 

8. Vibrational Spectroscopy and Potential Energy Surfaces

This lesson allows students to go beyond a normal mode analysis to calculate ab initio potential energy surfaces and associated rovibrational energies of a diatomic using a variational matrix method.