Chapter 2
Computational Methods
Abstract This chapter describes the different methods used in computational chemistry to determine the structure of a molecule. It starts with the presentation of the
molecular Hamiltonian. Then, the different ab initio methods are reviewed in detail.
The approximations are discussed, and a particular emphasis is put on their effect on
the accuracy. The molecular mechanics methods and the combined quantum/classical
methods are also briefly reviewed.
2.1 Introduction
This chapter is not intended to be a thorough review of computational chemistry. It
is an introduction to the methods that are used to compute a molecular structure. The
number of books and reviews on this subject is considerable. A few of them are cited
in the text. Some modern sources are: Allen and Császár (2011) and Helgaker et al.
(2000). A more general presentation of the computational chemistry is in Schleyer
(1998) and Cramer (2004).
Although the first quantum mechanical determination of a molecular geometry
was made as early as 1927 (see introduction), ab initio methods only became competitive with experimental techniques in the nineties thanks to new developments in
computational methods and as a result of spectacular advances in computer technology. At present, their accuracy rivals and even surpasses that of experimental
measurements. Furthermore, they are now an indispensable tool for experimentalists as they allow to considerably increase the accuracy of their results and to study
much more complicated molecules. It will be the main subject of this book. However,
ab initio methods are still time consuming and, moreover, limited to small molecules
(perhaps one hundred atoms for the simplest ab initio methods). It would be extremely
desirable to have a method that is at the same time fast and applicable to very large
molecules such as drugs and proteins.
For this reason, the molecular mechanics methods are also described. They use
classical (Newtonian) mechanics to predict the energy of a molecule as a function
of its conformation allowing among others the prediction of the structure. These
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_2
7
Computational Methods
Abstract This chapter describes the different methods used in computational chemistry to determine the structure of a molecule. It starts with the presentation of the
molecular Hamiltonian. Then, the different ab initio methods are reviewed in detail.
The approximations are discussed, and a particular emphasis is put on their effect on
the accuracy. The molecular mechanics methods and the combined quantum/classical
methods are also briefly reviewed.
2.1 Introduction
This chapter is not intended to be a thorough review of computational chemistry. It
is an introduction to the methods that are used to compute a molecular structure. The
number of books and reviews on this subject is considerable. A few of them are cited
in the text. Some modern sources are: Allen and Császár (2011) and Helgaker et al.
(2000). A more general presentation of the computational chemistry is in Schleyer
(1998) and Cramer (2004).
Although the first quantum mechanical determination of a molecular geometry
was made as early as 1927 (see introduction), ab initio methods only became competitive with experimental techniques in the nineties thanks to new developments in
computational methods and as a result of spectacular advances in computer technology. At present, their accuracy rivals and even surpasses that of experimental
measurements. Furthermore, they are now an indispensable tool for experimentalists as they allow to considerably increase the accuracy of their results and to study
much more complicated molecules. It will be the main subject of this book. However,
ab initio methods are still time consuming and, moreover, limited to small molecules
(perhaps one hundred atoms for the simplest ab initio methods). It would be extremely
desirable to have a method that is at the same time fast and applicable to very large
molecules such as drugs and proteins.
For this reason, the molecular mechanics methods are also described. They use
classical (Newtonian) mechanics to predict the energy of a molecule as a function
of its conformation allowing among others the prediction of the structure. These
© Springer Nature Switzerland AG 2020
J. Demaison and N. Vogt, Accurate Structure Determination of Free
Molecules, Lecture Notes in Chemistry 105,
https://doi.org/10.1007/978-3-030-60492-9_2
7