III. The range of relatively large R, where the Coulomb and exchange interactions can be neglected, and the intermolecular forces have the character of
attraction. For a very large R, the interaction delay must be taken into
account.
When species approach each other at a distance of R . 2 Å (range I), the system
should be considered as a single quasi-molecule. In the range II, both repulsive and
attractive forces exist, and there is a minimum of intermolecular potential energy
due to their competition. For distances R . 8 Å (ranges II and I), the exchange
interaction must be taken into account. In the range II, it can be considered as low,
and perturbation theory (PT) (see Sect. 3.6) can be utilized. In the first-order PT,
the exchange energy can be separated from the electrostatic energy; in the
higher-order, this cannot be done. The terms in the expression for the interaction
energy are called, in this case, the exchange-polarization energy. In addition to the
exchange in this range, there are interactions due to charge transfer from one
species to another.
In the range III, the exchange forces can be neglected. The intermolecular
interactions are negligible, and one can use standard PT to describe them. In the
first-order PT, it gives the energy of direct electrostatic interaction of species; in
higher orders, the polarization energy is obtained, resulting from the mutual
polarization of the electronic clouds of species. In the second-order PT, the
polarization energy can be divided into induction and dispersion energy; in higher
orders, such a division is impossible. (They will be discussed in more detail below).
The magnetic interactions (associated with a non-zero total electron spin) are much
weaker; they can manifest themselves only at relatively large distances since
electrostatic interactions fall off with a distance R quickly (see below).
Consider the nature of the intermolecular interaction forces in somewhat more
detail.
3.3.1 Exchange Interaction
At distances less than 8 Å, it is necessary to take into account the electron exchange
between particles, which is a consequence of the Pauli principle, according to which
the wave function of the system has to be antisymmetric to electron permutations.
The energy of the exchange interaction depends exponentially on 1/R; however,
even in the region of the vdW minimum, it must be taken into account (see
Fig. 3.4). At short distances, the interacting species must be considered as a single
quasi-molecule.
50
3 Theory of Elementary Processes
attraction. For a very large R, the interaction delay must be taken into
account.
When species approach each other at a distance of R . 2 Å (range I), the system
should be considered as a single quasi-molecule. In the range II, both repulsive and
attractive forces exist, and there is a minimum of intermolecular potential energy
due to their competition. For distances R . 8 Å (ranges II and I), the exchange
interaction must be taken into account. In the range II, it can be considered as low,
and perturbation theory (PT) (see Sect. 3.6) can be utilized. In the first-order PT,
the exchange energy can be separated from the electrostatic energy; in the
higher-order, this cannot be done. The terms in the expression for the interaction
energy are called, in this case, the exchange-polarization energy. In addition to the
exchange in this range, there are interactions due to charge transfer from one
species to another.
In the range III, the exchange forces can be neglected. The intermolecular
interactions are negligible, and one can use standard PT to describe them. In the
first-order PT, it gives the energy of direct electrostatic interaction of species; in
higher orders, the polarization energy is obtained, resulting from the mutual
polarization of the electronic clouds of species. In the second-order PT, the
polarization energy can be divided into induction and dispersion energy; in higher
orders, such a division is impossible. (They will be discussed in more detail below).
The magnetic interactions (associated with a non-zero total electron spin) are much
weaker; they can manifest themselves only at relatively large distances since
electrostatic interactions fall off with a distance R quickly (see below).
Consider the nature of the intermolecular interaction forces in somewhat more
detail.
3.3.1 Exchange Interaction
At distances less than 8 Å, it is necessary to take into account the electron exchange
between particles, which is a consequence of the Pauli principle, according to which
the wave function of the system has to be antisymmetric to electron permutations.
The energy of the exchange interaction depends exponentially on 1/R; however,
even in the region of the vdW minimum, it must be taken into account (see
Fig. 3.4). At short distances, the interacting species must be considered as a single
quasi-molecule.
50
3 Theory of Elementary Processes