Chapter 15 : MPC – Molecular degrees of freedom: vibration and rotation

In the Born-Oppenheimer approximation, we froze the position of the nuclei to find the electronic energy. The position of the nuclei was considered as a parameter that can be modified and we were able to construct the Lenard-Jones potential for the liaisons or the surface (or hypersurface) of potential energy for molecules with more than […]

Chapter 14 : MPC – The LCAO theory

This theory says that each molecular orbital Φa is described by a linear combination of atomic orbitals {χ} centred on the M nuclei of the molecule. The molecular orbitals have the symmetry of one of the irreducible representations of the group G. This symmetry is taken into account in the LCAO coefficients. Some are null […]

Chapter 13 : MPC – The methods of approximation and the quantic chemistry

We have seen quite a lot of new stuff up to now. We described monoelectronic and polyelectronic atoms and developed the description to molecules through the approximation of Born-Oppenheimer, the theory of groups and the CSOC. All of this teaches us how orbitals are and how they change during a reaction. Yet, we did not […]

Chapter 12 : MPC – Orbital angular moment L

The electrons revolving on an orbital generate an angular moment. ML is the quantic number associated to the projection of L on the internuclear axis. The projection is degenerated because it can either be in the positive values of the z axis or in the negative ones. The projection of L can thus give ML […]

Chapter 11 : MPC – Group’s theory

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. […]

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 […]