THE DEVELOPMENT OF DENSITY FUNCTIONAL THEORY VIA JACOB’S LADDER FOR GENETIC MOLECULES

Abstract

This article provides a comprehensive review of the historical, technical, and methodological development of density function theory, based on the five-stage Jacobian ladder proposed by Purdue. It begins with the fundamentals of density function theory, progressing from the simplest approaches that treat electrons as a homogeneous gas and employ sample approximations, to highly accurate methods that begin by simulating the physical and chemical properties of the electron. The article analyzes how each rung of the ladder contributes to improving the accuracy of calculations relative to the computational cost. First-order modifications begin with the local density approximation (LDA) and progress to more complex degrees (B3LYP), which predict reaction energies and band gaps. Third-order approximations (GGA) currently represent the optimal balance between accuracy and efficiency for most complex chemical processes. This article discusses how each rung of the ladder improves the accuracy of predicting the properties of complex systems and aids in understanding the binding of molecules to nucleic acids and proteins—a crucial aspect of genetics. It highlights current challenges in addressing weak-strength and interconnected systems, while also pointing to the future of integrating artificial intelligence to develop higher degrees of the Jacobs ladder.