Chapter 5
Lattice Dynamics of Molecular Crystals
5.1 Scope of This Chapter
Lattice vibration is the description of atomic and molecular dynamics within the
lowest-order approximation, i.e., harmonic approximation. Despite its limitation
originating from the approximated nature, it is fundamental for understanding the
properties of crystalline materials at temperatures lower than characteristic temperatures (to be introduced later). Its study has a long history accordingly. The monograph by Born and Huang [1] describes the results in the early stage. Although some
methods were proposed and even utilized in specific problems for incorporating the
anharmonic effects neglected in the treatments [2–5], they are not described in this
book because, nowadays, molecular simulations become handy (but can be blind with
physical mechanisms behind phenomena). On the other hand, it may be noteworthy that a kind of elementary excitations, solitons, is known to exist in intrinsically
anharmonic systems [6, 7] and was also suggested for molecular systems [8, 9].
These are, however, beyond the scope of this chapter.
5.2 Atomic Case
We start with a simple case that treats atomic arrays (in one-dimension) and crystals
(in three-dimension) to let this chapter be self-contained. The extension to molecular
crystal is given in the next section. Readers familiar to the atomic case (described in
any textbooks of solid-state physics) may skip this section.
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_5
85
Lattice Dynamics of Molecular Crystals
5.1 Scope of This Chapter
Lattice vibration is the description of atomic and molecular dynamics within the
lowest-order approximation, i.e., harmonic approximation. Despite its limitation
originating from the approximated nature, it is fundamental for understanding the
properties of crystalline materials at temperatures lower than characteristic temperatures (to be introduced later). Its study has a long history accordingly. The monograph by Born and Huang [1] describes the results in the early stage. Although some
methods were proposed and even utilized in specific problems for incorporating the
anharmonic effects neglected in the treatments [2–5], they are not described in this
book because, nowadays, molecular simulations become handy (but can be blind with
physical mechanisms behind phenomena). On the other hand, it may be noteworthy that a kind of elementary excitations, solitons, is known to exist in intrinsically
anharmonic systems [6, 7] and was also suggested for molecular systems [8, 9].
These are, however, beyond the scope of this chapter.
5.2 Atomic Case
We start with a simple case that treats atomic arrays (in one-dimension) and crystals
(in three-dimension) to let this chapter be self-contained. The extension to molecular
crystal is given in the next section. Readers familiar to the atomic case (described in
any textbooks of solid-state physics) may skip this section.
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_5
85