# The role of pair correlation function in the dynamical transition predicted by the mode coupling theory

## TL;DR

This paper explores how the structure of liquids encodes the mode coupling transition temperature, showing that a mean field dynamical theory based on pair correlations can predict the transition similarly to microscopic MCT.

## Contribution

The paper introduces a mean field dynamical density functional theory that links liquid structure directly to the mode coupling transition temperature, differing from microscopic MCT predictions.

## Key findings

- Pair configuration entropy vanishes at the transition temperature.
- The developed theory predicts a transition temperature close to the mode coupling temperature.
- Dynamics depend solely on the liquid's structure, not on other factors.

## Abstract

In a recent study we have found that for a large number of systems the configuration entropy at pair level, $S_{c2}$, which is primarily determined by the structural information, vanishes at the mode coupling transition temperature $T_{c}$. Thus it appears that the information of the transition temperature is embedded in the structure of the liquid. In order to investigate this we describe the dynamics of the system at the mean field level and using the concepts of the dynamical density function theory show that the dynamics depends only on the structure of the liquid. Thus this theory is similar in spirit to the microscopic MCT. However unlike microscopic MCT, which predicts a very high transition temperature, the present theory predicts a transition temperature which is similar to $T_{c}$. Thus our study reveals that the information of the mode coupling transition temperature is embedded in the structure of the liquid.