Chapter 10
Importance of Molecular Crystals
10.1 Motional Correlation
10.1.1 Significance and Difficulty
It is usual to consider and describe molecular dynamics in the condensed phase as
the dynamics of a single particle (molecule or moiety) except for the description
of lattice vibrations. Since the interactions among particles, including repulsion, are
the source of all properties of ensembles, the description based on the single-particle
is an imitation. For the thermodynamic equilibrium, the well established is that all
quantities can mostly be represented in terms of static correlation functions [1, 2].
Further, the fluctuation-dissipation theorem gives the representation of frequencydependent susceptibilities in terms of two-time correlation functions. The knowledge
of the correlation among them should, therefore, be indispensable for a deeper understanding of the dynamics of constituent particles of ensembles. Here, we can expect
a unique advantage of molecular systems because we can choose systems where
only a limited number of degree(s) of freedom suffice to consider. An example of an
intramolecular correlation was briefly described in Sect. 6.3.
Before proceeding into details, we notice the difficulty of studying the motional
correlation. First, it is mostly beyond the equilibrium properties, which the statistical
mechanics gives correct answers on, as in the case of the single-particle dynamics.
Second, the above point implies that the apparent effect is challenging to identify in
many experimental results. Each experiment must prepare a theoretical model(s) to
detect effects [3]. The preparation unavoidably accompanies arbitrariness. It is also
noteworthy that each experimental technique relies on theoretical models, even in
analyzing results interpretable within the single-particle description. Third, preparations of theoretical models and experimental setup are demanding. Unless a good
target is in mind, researchers will not start the preparation. In this respect, the
© 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_10
199
Importance of Molecular Crystals
10.1 Motional Correlation
10.1.1 Significance and Difficulty
It is usual to consider and describe molecular dynamics in the condensed phase as
the dynamics of a single particle (molecule or moiety) except for the description
of lattice vibrations. Since the interactions among particles, including repulsion, are
the source of all properties of ensembles, the description based on the single-particle
is an imitation. For the thermodynamic equilibrium, the well established is that all
quantities can mostly be represented in terms of static correlation functions [1, 2].
Further, the fluctuation-dissipation theorem gives the representation of frequencydependent susceptibilities in terms of two-time correlation functions. The knowledge
of the correlation among them should, therefore, be indispensable for a deeper understanding of the dynamics of constituent particles of ensembles. Here, we can expect
a unique advantage of molecular systems because we can choose systems where
only a limited number of degree(s) of freedom suffice to consider. An example of an
intramolecular correlation was briefly described in Sect. 6.3.
Before proceeding into details, we notice the difficulty of studying the motional
correlation. First, it is mostly beyond the equilibrium properties, which the statistical
mechanics gives correct answers on, as in the case of the single-particle dynamics.
Second, the above point implies that the apparent effect is challenging to identify in
many experimental results. Each experiment must prepare a theoretical model(s) to
detect effects [3]. The preparation unavoidably accompanies arbitrariness. It is also
noteworthy that each experimental technique relies on theoretical models, even in
analyzing results interpretable within the single-particle description. Third, preparations of theoretical models and experimental setup are demanding. Unless a good
target is in mind, researchers will not start the preparation. In this respect, the
© 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_10
199