**Classical Density Functional Theory for Fluids Adsorption in MOFs**

Yu Liu and Honglai Liu

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Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/64632

#### **Abstract**

The designing of metal organic frameworks (MOFs) requires an efficient method to predict its adsorption properties. The conventional method to do this is molecular simulation, which is time consuming. In contrast, classical density functional theory (CDFT) is a much more efficient tool. Recently, CDFT has been successfully applied to MOF adsorptions. In this chapter, we will introduce the development and the different versions of CDFT and show how to apply CDFT to predict fluid adsorption in MOFs. We have reviewed the recent applications of CDFT in MOF adsorption and mainly focused on material screening. According to the recent developments, it seems CDFT is an efficient and robust tool for material screening; how to deal with more complicated fluids is the challenge of current CDFT.

**Keywords:** classical density functional theory, fluids, material-screening, MOFs, ther‐ modynamics

## **1. Introduction**

Adsorption is one of the essential properties of MOF materials, to give an efficient prediction of which is an important issue in the designing and application of MOFs. The traditional meth‐ od to do this is molecular simulation, which is time consuming and may not be the best choice in real applications [1–3]. Take the high-throughput screenings for example, the number of MOFs in a typical screening database is more than 105 ; the typical computational time of MC simulation for each MOF is approximately 0.25 CPU hour; this means a screening time cost over 103 CPU days, which is a waste of resources. In this case, a more efficient method is needed, and the CDFT seems to be a promising alternative.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

CDFT is a thermodynamic-statistical mechanics theory for inhomogeneous fluids. The concept of CDFT originates from quantum density functional theory and was formed in the1970s [4, 5]. During the past 40 years, CDFT has been developed from simple fluids to polymers, from equilibrium to dynamic, from high symmetry modeling systems to real systems, and has revealed itself as an efficient and robust tool in various fields including adsorption, wetting, freezing, solvation, and so on [6–35].

The application of CDFT to MOF adsorption was first proposed by Siderius et al. [27] in 2009 and has been advanced by Liu et al. [26] subsequently. Siderius and Liu et al. have demon‐ strated that CDFT can be used to predict gas adsorption in MOFs. However, the numerical algorithm of these pioneered applications is too simple, which makes the computational cost of CDFT even higher than molecular simulations. Such disadvantage has been solved by Liu and Wu recently by applying the fast Fourier transform (FFT) and conjugate gradient (CG) descent method [31, 33, 35]. Now, the advanced CDFT is faster than conventional simulations by two orders of magnitude and has been successfully applied to high-throughput screening for material design [33–36].

In the rest of this chapter, we will introduce the classical density functional theory and show how to implement the theory to MOF adsorptions. The remainder of this chapter is organ‐ ized as follows: Section 2 will introduce the theoretical framework of CDFT; Section 3 will show how to apply CDFT to MOF adsorption and review recent reports in this field; and finally, Section 4 will summarize and prospect the current and future applications of CDFT on MOF adsorption.
