*CHEM2013 *Atomic and Molecular Interactions

## Module Overview

### Aims and Objectives

#### Module Aims

The aim of this course is to provide a core for future studies in chemistry and allied subjects, in the following areas: the quantum mechanical approach to describing the interactions between electrons and nuclei within an atom or molecule; qualitative and quantitative descriptions of the interactions between molecules. Core mathematical concepts and methods are also taught. Lecture component: The aims of the module are to provide: • an introduction to the quantum mechanical description of atoms and molecules; • the form and solutions to the Schrödinger equation; • a working understanding of operators and wavefunctions. • a qualitative understanding of the physical origin of intermolecular interactions and their influence on the structure of molecular assemblies; • quantitative descriptions of the physical contributions to interactions between molecules; • an introduction to common model potentials for describing intermolecular interactions. • an understanding of: operators; eigensystems; matrix functions and determinants; complex numbers and functions; Practical component: The laboratory component is designed to offer both consolidation and development of practical expertise and knowledge. In addition to coverage of more advanced techniques and strategy the course will develop expertise in areas essential to all practical work: safe working practices (risk, hazard and control measures); keeping a laboratory record, laboratory report writing (written and verbal communication of results); error estimation and treatment. Students will undertake a series of three experiments, of which the titles below are examples: • Intermolecular Forces in Biological Molecules • Fluorescence Spectroscopy • Electrochemistry • Infrared Spectroscopy Where the theory underlying the experiments has not previously been covered in lectures it will be detailed in the script, as well as being covered by (in person or videoed) introductory theory lectures. A number of additional e-resources are also available to aid understanding of the background theory, equipment and procedures, and analysis. Each experiment is preceded by a prelaboratory exercise that that will help prepare you for the experimental work. There are separate learning outcomes for each experiment and these are further specified in the practical scripts.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

- apply the basic principles of quantum mechanics that underpin the interactions between electrons and nuclei to obtain the energy levels and electronic structure of atoms and molecules;
- Present the results of a practical investigation in a concise and clear manner.
- form molecular wavefunctions as a linear combination of atomic orbital, including the application of Huckel theory to conjugated molecules;
- calculate atomic and molecular properties using quantum mechanical techniques.
- recognise the types of forces acting within individual molecules and in molecular assemblies and classify these in terms of their relative strength and origin;
- provide and apply mathematical descriptions of electrostatic, polarisation, dispersion and repulsion contributions to intermolecular interactions;
- calculate intermolecular interactions using model potentials.
- Evaluate the risks associated with an experiment and understand how to mitigate against those risks;
- Use a variety of advanced equipment (e.g. spectrometers; potentiostats) to conduct experiments in Physical Chemistry;
- Interpret data from an experiment, including applying the results to relevant theoretical models and thoroughly evaluating the associated errors;

### Syllabus

• The Schrödinger eigenvalue equation is introduced as the central principle which governs the behaviour of electrons, atoms and molecules. The solution of the equation produces the wavefunction from which all experimentally observable properties of matter can be computed. The conditions that must be satisfied by chemically acceptable wavefunctions are discussed. • Differentiation of functions is revisited and operator notation is introduced. Quantum mechanical operators are defined. The Hamiltonian operator is built from the kinetic energy and potential energy operators. • Integration of functions is revisited and the calculation of experimentally observable properties (e.g. energy, dipole moment, etc.) from the wavefunction is presented. Normalisation and orthogonality of wavefunctions are discussed. • Vectors are reviewed. The Coulomb potential for interaction between point charges is introduced and with the help of vectors it is defined in 1, 2, and 3 dimensions. The importance of this potential in all sorts of chemical situations is discussed and demonstration of how the same potential describes interactions between electrons, nuclei and either is shown. • The problem of the particle in a 1-dimensional box is solved and its solutions are used to construct a simple model for the energy levels of conjugated polyenes. The particle in a 2-dimensional box is solved as a model quantum system where there is degeneracy between its energy levels. • The Hamiltonian operator is constructed, first for the hydrogen atom and then for any atom. • The wavefunctions of the Hydrogen atom which are built from Spherical Harmonics and radial functions are introduced and various properties such as their energy levels are examined. • The Pauli exclusion principle is introduced and it is shown how the Hydrogen wavefunctions can be extended to describe polyelectronic atoms and hence the periodic table. • The Born-Oppenheimer approximation to separate electronic from nuclear motion is described and the Hamiltonian operator (and Schrödinger equation) for molecules is constructed. • Molecular wavefunctions are approximated as products of molecular orbitals. The molecular orbitals are constructed from atomic orbitals via the Linear Combination of Atomic Orbitals (LCAO) approach. • Matrices, determinants and operations such as matrix multiplication are reviewed. The variational principle that allows LCAO calculations to be performed is described. Examples of LCAO calculations are presented and discussed in terms of the Huckel theory of conjugated molecules and other approaches of more general applicability. • The role intermolecular forces play in chemistry is described. • The Coulomb potential is revisited as the principle for describing permanent inter-molecular electrostatic interactions, using a partial charge approach. • The concept of multipole moments is described, and how the lowest multipole moment of a molecule may be determined. The role of electrostatic potential in understanding permanent electrostatic interaction is discussed, along with how a combination of multipole moments may be used to reproduce molecular electrostatic potentials. • The direct calculation of dipole-dipole interaction energies is given, and the distance dependence of all other multipole-multipole interactions is outlined. The link between the partial charge model and multipole descriptions is presented. • Induced interactions are described, together with how they are related to the electric field. The energy expression for the induction energy arising from a dipole is given. The distance dependency and non-pairwise additivity of induction is emphasised. • Dispersion interactions are introduced as a quantum mechanical effect due to electronic correlation and an approximate classical model for describing them is presented. • The relative strengths of the long-range intermolecular forces are discussed for a range of atomic and molecular systems. • The physical basis of hydrogen bonds and their role in affecting the properties of matter is given. • Repulsive forces are described in terms of a simple physical picture. An exponential dependence on distance is outlined. • Model potentials are introduced as an approximate method for computing molecular structure and interactions, starting from the Lennard-Jones potential as an example. The concepts of effective pair potentials and combining rules are outlined. • The advantages and disadvantages of model potentials as compared to the quantum mechanical calculations for molecules are discussed and demonstrated by examples. • The role of intermolecular forces in the chemistry part of the module. At the end of the module the students will be comfortable with the mathematical foundations of quantum theory and well prepared for future work in the area of quantum chemistry.

### Learning and Teaching

#### Teaching and learning methods

Lectures, problem-solving Seminars with group working and tutor support Practical chemistry: Prelaboratory e-learning; pre-lab skills lectures/ Seminars; practical sessions, supporting demonstrations, group and one-to-one tuition Practical hours includes pre-laboratory e-learning Workshop hours includes 12 hours for math workshops Preparation for scheduled sessions hours includes other independent study Feedback is provided • In Seminars through assistance with the set work. • In the practicals through assistance from demonstrators and members of staff on duty. • On the reports submitted for the practical excercises. • In-class feedback through use of interactive clicker-based questions. • Through generic feedback following the examinations. • Upon request by viewing of marked examination scripts.

Type | Hours |
---|---|

Workshops | 12 |

Lecture | 30 |

Completion of assessment task | 24 |

Practical classes and workshops | 38 |

Preparation for scheduled sessions | 26 |

Revision | 10 |

Workshops | 10 |

Total study time | 150 |

#### Resources & Reading list

Atkins & de Paula (2014). Physical Chemistry: Thermodynamics, Structure, and Change.

Steiner (2008). The Chemistry Maths Book.

Monk and Munro (2010). Maths for Chemistry.

D. O. Hayward (2002). Quantum Mechanics for Chemists.

### Assessment

#### Assessment Strategy

The practical and examination components must be passed separately at the module pass mark for the student’s programme, i.e. 40% if core, 25% if compulsory or optional if compensation is allowed.

#### Summative

Method | Percentage contribution |
---|---|

Examination (2 hours) | 75% |

Practical write-ups | 25% |

#### Referral

Method | Percentage contribution |
---|---|

Examination (2 hours) | 75% |

Practical write-ups | 25% |

### Linked modules

Pre-requisites: CHEM1033 and CHEM1034 OR CHEM1022 and CHEM1030