Quantum Chemistry Methods

The ever-increasing development of computer technology has led to a boom in numerical simulation and modeling methods in all fields, from economics to meteorology, biochemistry and nuclear physics. In this context, and as far as the physico-chemical properties of matter are concerned, quantum chemical methods can be used to study a large number of molecular properties, and in particular to simulate chemical reactions and even biochemical processes. For any molecular system, for example, we can now compute :

• energy quantities: total energy, ionization energy, electron affinity;

• geometric quantities: bond lengths and angles, conformations ;

• spectroscopic properties: ultraviolet-visible, infrared and microwave spectra, luminescence spectra ;

• electrical properties: dipole and multipole moments, polarizabilities and hyperpolarizabilities;

• magnetic properties: NMR chemical shifts and coupling constants, magnetic susceptibilities and couplings, electron paramagnetic resonance (EPR) g and A tensors.

In this article, we present various methods for solving Schrödinger's equation, including those based on Hartree-Fock (HF) theory and post-HF correlated techniques, which enable precise solutions of the equation to be achieved, as well as those based on density functional theory (DFT) and time-dependent DFT (TD-DFT), which are among the main tools of current computational chemistry. Technical aspects are also covered, such as the atomic orbital bases to be used, solvation, mixed quantum mechanical/molecular mechanical (QM/MM) methods and molecular dynamics. A detailed example of molecular orbital calculation is also presented.