equations, are analyzed in this chapter by associating a set of trajectories starting
from different initial conditions to the fate of the collision process (like the angle of
deflection) and working out the value of quantities of experimental relevance (like
cross sections and rate coefficients).
The observed failure of the classical mechanics treatment to reproduce some key
features of measured data (like the elastic differential cross section in two body
collisions) is traced back to the quantum nature of molecular processes and to the
related uncertainty principle. This drives the reader in chapter two to the use of
quantum techniques for evaluating the properties of both bound and elastically
scattered atom–atom systems. Related quantum treatments are then discussed and
analytical solutions are first worked out for some prototype cases to the end of
guiding the reader to use of special functions. Then, some basic numerical techniques and related pseudocodes useful for integrating the corresponding
Schrödinger equation for generic atom–atom interactions, are illustrated and applied
in order to compare related results with corresponding classical ones.
At this point, the reader is ready to abandon the constraint that atoms are
structureless bodies and deal in chapter three with the electronic structure of atoms
and molecules. To move in this direction, we discuss some techniques used for
carrying out ab initio calculations of electronic energies and discuss the adoption of
both one electron functions and variational principle. Along this line, the electronic
structure of polyatomic molecules, molecular orbitals, Hartree–Fock, and
self-consistent field (SCF) molecular orbital (MO) models are discussed in some
detail. Then, we end up by illustrating post Hartree–Fock configuration interaction,
multiconfiguration self-consistent fields, and perturbation methods for the calculation of electronic energies and other molecular properties. To better deal with
larger systems, mention is made also to some empirical corrections simplifying the
electronic structure calculations for large sets of atoms as well as for a large number
of molecular geometries of the same molecule and a large number of molecules.
Finally, the techniques used to shape potential energy global and local functional
formulations to fit the distinctive features of computed ab initio values are discussed with the specific intention of attributing to related parameters a physical
correspondence.
Next, in chapter four, concepts and techniques to be used for carrying out
dynamical calculations of reactive systems starting from atom–diatom elementary
processes are considered. To this end, the motion of nuclei is disentangled from that
of the electrons by introducing the Born–Oppenheimer approximation. Then, for
atom–diatom systems, different sets of coordinates are discussed for singling out
those better suited for representing the interaction and for integrating dynamics
equations. For the latter, different choices are discussed for classical and quantum
treatments as well as for time-dependent and time-independent techniques. The
integration of dynamics equations allows to figure out the typical features of the
atomistic phenomenology of atom–diatom systems such as the effect of a different
allocation of energy to the various degrees of freedom in promoting reactivity, the
importance of providing an accurate representation of the potential energy surface,
the merits and demerits of adopting reduced dimensionality approaches, or dealing
viii
Preface
from different initial conditions to the fate of the collision process (like the angle of
deflection) and working out the value of quantities of experimental relevance (like
cross sections and rate coefficients).
The observed failure of the classical mechanics treatment to reproduce some key
features of measured data (like the elastic differential cross section in two body
collisions) is traced back to the quantum nature of molecular processes and to the
related uncertainty principle. This drives the reader in chapter two to the use of
quantum techniques for evaluating the properties of both bound and elastically
scattered atom–atom systems. Related quantum treatments are then discussed and
analytical solutions are first worked out for some prototype cases to the end of
guiding the reader to use of special functions. Then, some basic numerical techniques and related pseudocodes useful for integrating the corresponding
Schrödinger equation for generic atom–atom interactions, are illustrated and applied
in order to compare related results with corresponding classical ones.
At this point, the reader is ready to abandon the constraint that atoms are
structureless bodies and deal in chapter three with the electronic structure of atoms
and molecules. To move in this direction, we discuss some techniques used for
carrying out ab initio calculations of electronic energies and discuss the adoption of
both one electron functions and variational principle. Along this line, the electronic
structure of polyatomic molecules, molecular orbitals, Hartree–Fock, and
self-consistent field (SCF) molecular orbital (MO) models are discussed in some
detail. Then, we end up by illustrating post Hartree–Fock configuration interaction,
multiconfiguration self-consistent fields, and perturbation methods for the calculation of electronic energies and other molecular properties. To better deal with
larger systems, mention is made also to some empirical corrections simplifying the
electronic structure calculations for large sets of atoms as well as for a large number
of molecular geometries of the same molecule and a large number of molecules.
Finally, the techniques used to shape potential energy global and local functional
formulations to fit the distinctive features of computed ab initio values are discussed with the specific intention of attributing to related parameters a physical
correspondence.
Next, in chapter four, concepts and techniques to be used for carrying out
dynamical calculations of reactive systems starting from atom–diatom elementary
processes are considered. To this end, the motion of nuclei is disentangled from that
of the electrons by introducing the Born–Oppenheimer approximation. Then, for
atom–diatom systems, different sets of coordinates are discussed for singling out
those better suited for representing the interaction and for integrating dynamics
equations. For the latter, different choices are discussed for classical and quantum
treatments as well as for time-dependent and time-independent techniques. The
integration of dynamics equations allows to figure out the typical features of the
atomistic phenomenology of atom–diatom systems such as the effect of a different
allocation of energy to the various degrees of freedom in promoting reactivity, the
importance of providing an accurate representation of the potential energy surface,
the merits and demerits of adopting reduced dimensionality approaches, or dealing
viii
Preface