Because of the particular geometries of some molecules, the CSCO may be different. Instead of the CSCO that we had with the atom, we want to determine the CSCOH: the complete set of operators commuting with Ĥ. It is thus a set larger than the CSCO because the operator don’t have to commute between them. […]
Author: Dr GERARD Thomas
Chapter 10 : MPC – Molecules and Born-Oppenheimer
The Hamiltonian quickly becomes monstrously difficult when several atoms and electrons are considered. To illustrate this point, the equations of the Hamiltonians for H, H2+ and H2 are showed below: For a molecule with M nuclei of atomic number Z1, Z2, Z3, …, ZM and n electrons, the global expression is The Hamiltonian can be […]
Chapter 9 : MPC – polyelectronic atoms
The presence of a second electron induces a term of repulsion between electrons. This term is positive so it increases the energy of the orbitals. The rest of the equation is similar to the Hamiltonian of the hydrogen. We can compare the energy of the orbitals with those two models. The repulsion is large in […]
Chapter 8 : molecular physical chemistry – operators
Operators can be applied to the wave functions and respect the equation of Schrödinger. The operator inversion Î is an operator such as, if a central symmetry can be found, For instance, the orbital s have a centre of symmetry. We say that this state is even. If we apply the inversion operator to this […]
Chapter 7 : Molecular physical chemistry – the hydrogen
To begin smoothly, we will describe the simplest uncharged molecule: the hydrogen. It is composed of one proton with a positive charge e and one electron of opposite charge –e that revolves around the proton at a distance r. In quantum mechanics, the system is described by the equation of Schrödinger Ψ is a wave […]
Chapter 6 : mass spectra – exercises
The solutions immediately follow the problems. You can use this website to find fragments corresponding to a given m/z ratio: MS fragments. The methodology to obtain the answer is given. Problem 1 The two following spectra come from two isomers with the formula C10H14. Determine the structure of each of them. Answer The isomer A […]
Chapter 5 : NMR proton: principles
A full section can be (and will be) dedicated to the detailed setup of the nucleus magnetic resonance (NMR) and to the analyses we can perform with this tool. In this section, we don’t need a lot of explanations on the NMR theory as it is a technique oriented section. We will however give an […]
Chapter 4 : Mass spectra
The result of the mass spectrometry is given on the form of a histogram giving the abundance of species as a function of their m/z ratio (we write it M as well, as the ions are usually monocharged). It is called a spectrum of mass. The abundance is given in % of the largest peak. […]
Chapter 3 : Mass spectrometry
Mass spectrometry is one of the most used technique in laboratories because it allows to determine the structure of one molecule. For this technique, the sample should be a pure solution, containing only one molecule that will be analysed within a very short time period. It is why mass spectrometers are often queuing a chromatographic […]
Chapter 2 : Organic chemistry – Exercises
This section is a full part of the course and contains some reactions that were not addressed in the main course. It is challenging to understand by yourselves some mechanisms with the hints that are in the exercises. If you don’t succeed, don’t worry. The solutions and the description of the reactions are directly following […]