Charge regulation of monomers, polymers, and surfaces have attracted great interest in recent years because of its fundamental and practical importance to many technological applications such as bioadhesion and drug delivery. The ability to tune the properties of these ionizable species opens avenues to “smart” systems which can respond to changes in pH, salt concentration, and other environmental factors. A better understanding of when and why the electrostatic charge of these species emerges and fluctuates will allow for the more rational design to meet targeted needs. Unfortunately, the chemistry at the microscopic scale is difficult to discern and an adequate theoretical tool is needed to provide insights into the mechanisms governing the charge regulation of these species.

The purpose of this dissertation is to advance the knowledge of the charge regulation through the innovation of new theoretical methods to characterize the properties of ionizable systems. In particular, we emphasize the applications of our new theoretical methods to describe the interfacial phenomena. These new tools pave the way towards realistic models to understand bioadhesion, thermal energy storage, drug delivery, waste-water treatment and many more applications. We first developed a molecular thermodynamic model that is able to describe the charge regulation and activity coefficients of amino acids in excellent agreement with experimental data. Next, we extended the thermodynamic model using classical density functional theory to predict the interfacial behavior of amino acids at inorganic surfaces. Different from conventional methods, our model accounts for key correlation effects that dictate the charge behavior of amino acids near an interface. We also developed a coarse-grained model that can be used to predict the ionization of weak polyelectrolytes in a solution with physically realistic parameters. In order to describe weak polyelectrolytes in non-uniform fluids such as near a surface, we developed a theoretical tool known as the Ising density functional theory (iDFT), which bridges the gap between the site-binding model and polymer density functional theory. We demonstrated that iDFT is able to capture the adsorption isotherms of polypeptides near ionizable inorganic surfaces in good agreement with experimental data. The last two chapters of this dissertation are focused on theoretical developments for incorporating long-range intrachain correlations that are neglected in conventional treatments of polymers in a bulk solution or near an interface. The inclusion of long-range interactions provides an accurate description of the coupling of polymer charge and conformation in weak polyelectrolyte systems. Lastly, we combined iDFT with the single-chain-in-mean-field algorithm to capture the long-range two-body correlation effects in non-uniform fluids. The computational framework developed in this dissertation opens up new opportunities for engineering design of ionizable molecular systems.

Recent developments in physical and computer sciences enable quantitative predictions of chemical reactions and thermodynamic data from first principles by multiscale modeling. The hierarchical approach integrates different theoretical frameworks ranging from those describing phenomena at the electronic length and time scales to those pertinent to complex biomolecular systems and macroscopic phase transitions, promising broad applications to problems of practical concern. Whereas multiscale modeling has been emerging as a popular computational tool for engineering applications, the connection between calculations at different scales is far from being coherent, and the multiple choices of quantum/classical methods at each scale renders numerous combinations that have been rarely calibrated against extensive experimental data.

During my PhD studying, on one hand, we try to build a reliable multiscale procedure for predicting the solvation free energies of a large set of small molecules in liquid water at ambient conditions. Using the experimental data for the hydration free energies as the benchmark, we find that the theoretical results are sensitive to the selection of quantum-mechanical methods for determining atomic charges and solute configurations, the assignment of the force-field parameters in particular the atomic partial charges, and approximations in the statistical-mechanical calculations.

On the other hand, we have investigated four representative versions of non-local density functionals for predicting gas adsorption in both slit pore model and a large library of metal-organic frameworks (MOFs) under a broad range of temperatures and pressures, compared with Monte Carlo simulation data. Overall all four versions of DFT are reasonably accurate in comparison with the simulation results, but for each specific interested condition, there is a best candidate. Besides, DFT is able to generate density profiles revealing microscopic details such as favorable adsorption sites and self-diffusion coefficient by entropy scaling method.

From a computational perspective, the DFT calculation is at least one order of magnitude faster than conventional simulation methods, rendering it as a versatile and promising tool for large-scale screening of chemicals and nanostructured materials.

Hepatitis B virus (HBV) infects more than 2 billion people alive today and is responsible for over 1 million deaths caused by acute and chronic hepatitis and hepatocellular carcinoma every year. Although remarkable progress has been made in recent years, effective treatment and eradication of chronic HBV infection remain as a tremendous therapeutic challenge. Experimental investigations over the past few decades have resulted in vast information on the characteristic features of viral replication and molecular structures of the HBV genome as well as the viral proteins. However, it has long been recognized that the viral replication process is regulated by a balanced interaction of the geometric material and its viral proteins in a crowded cellular milieu that is hardly detectable with direct experimental means. Molecular modeling that provides a quantitative analysis of important intermolecular interactions will be invaluable for unraveling the microscopic details of physicochemical processes underlying viral formation and replication cycle and for designing new experiments to develop novel anti-viral strategies.

This Ph.D. research focuses on molecular modeling of capsid formation, genome packaging and maturation of HBV particles under various mutagenesis and physiological conditions. A suite of theoretical models has been developed to facilitate better understanding of the fundamentals of viral replication cycles and enabling new therapeutic breakthrough for future treatment of HBV infection. Specifically, I applied an effective coarse-grained model for the key viral components and quantified the stability of nucleocapsids based on statistical mechanics. The theoretical model yields faithful results for describing the effects of temperature and ion concentration on viral particle formation, supporting an experimentally derived hypothesis that suggests the balanced electrostatic interaction for the capsid stability and genome encapsidation. In addition, I analyzed the thermodynamic basis for the viral genome packaging, the dynamic structures of nucleocapsids at different stages of the replication cycle, and the correlation between the viral structure to the maturing signals of HBV nucleocapsids by using the classical density functional theory (DFT). The DFT analysis provides a quantitative description of the microscopic structure of the protein-RNA/DNA complex underlying nucleocapsid formation and the related thermodynamic properties. The theoretical predictions on the optimal genome length and nucleocapsid structure are in good agreement with available experiments for the wild type HBV and mutants with truncated C-terminal domain of the capsid proteins. To establish concrete connection between the capsid structure and HBV maturing signals, I further investigated molecular recognition between viral envelope and capsid proteins. Specific protein-protein interactions were identified through molecular docking and molecular dynamic (MD) simulations. It is expected accomplishments from this work will contribute to broadening a fundamental understanding of the HBV replication cycle.

Solvation and solvent effects play an important role in diverse chemical processes ranging from reaction kinetics to molecular recognition, solubility, solvato-chromism and phase separations. Despite enormous activities in this field, quantitative solvation calculations remain an enormous intellectual challenge.

My thesis is focused on development and application of molecular density functional theory (MDFT) and molecular dynamics (MD) simulation to predicting solvation properties. Accomplishments include 1) improved the average unsigned error of MDFT predictions for the room-temperature solvation free energies (SFE) of 504 pharmaceutical molecules in water from 1.04 kcal/mol to 0.66 kcal/mol; 2) established a more reliable numerical procedure to calculate the direct correlation functions (DCF) of solvent from MD simulations; 3) extended MDFT prediction of SFE to different temperatures and calibrated the theoretical results with experimental data for the hydration free energies of 5 nitrotolunenes and a library of 197 solutes at 277 K, 298 K and 313 K. In addition, I investigated the 3-dimensional (3D) solvation structure of amine-grafted silica gel in liquid water by applying a spherical harmonics expansion method to the MD trajectories. The simulation results provide evidence on the strong influence of the silica surface on hydration structure, which is often ignored in the theoretical analysis of surface reactions. Furthermore, I developed a hybrid method for predicting the SFE of spherical ions by combining MDFT with MD simulations. The numerical analysis justifies the universality of the bridge functional that can be reasonably approximated by the modified fundamental measure theory (MFMT) for hard-sphere systems.

Results from this thesis demonstrate that the DCFs are important in application of MDFT to SFE predictions. Based DCF from on integral-equation methods, MDFT can also capture the temperature effect on SFE in good agreement with experiment. In addition, the hybrid MDFT-MD method provides accurate predictions of hydration free energies for charged solutes and the numerical analysis sheds light on future theoretical development. The efficient sampling method for generating 3D density profiles from MD may open up opportunities for application of MDFT to more complex systems, for example, protein solvation and enzyme kinetics. By studying the solvation structure of amine-grafted silica shell, I found that the silica surface affects not only the distribution of surrounding water but also the hydrogen-bonding network. This surface effect is long-ranged and can be reduced with longer grafted amine chains.

With ever-increasing computer power and rapid developments in molecular theories, high-throughput computation will be instrumental to future materials design and discovery. This Ph.D. thesis explores the potential applications of the classical density functional theory (DFT) for fast screening of nanostructured porous materials for gas storage and separation. In addition to developing the computational methods, major efforts have been devoted to clarifying two fundamental yet long debated issues in the adsorption field, i.e., accurate prediction of the heat effect from adsorption isotherm and the connection between the BET and geometric surface areas of porous materials.

First we have investigated methane adsorption in a large library of metal-organic frameworks (MOFs) using four versions of classical DFT. The molecular thermodynamic model has been used to identify promising MOF materials and possible variations of operation parameters to meet the ARPA-E target set by the U.S. Department of Energy for natural gas storage.

The BET surface area is highly sensitive to the selected pressure region to perform the liner fitting and also the definition of the probe molecule used to determine the surface area. In this thesis, we provide a comprehensive analysis of the BET method. Based on extensive simulation data for over 1000 materials with complex structures and heterogeneous interactions, we find that the surface area obtained by standard BET method is not necessarily correlated with its geometrical accessible surface area.

Heat of adsorption is of both fundamental and practical importance. Here we present a rigorous theoretical procedure to predict isosteric heat. Quantitative relations between the differential heat and various isosteres have been established with the GCMC simulation for gas adsorption in amorphous and crystalline porous materials. The inconsistencies with conventional methods for the analysis of heat effect have been clarified in the context of the exact results for model systems.

By developing new computational methods for rapid prediction of gas adsorption and diffusivity and by resolving a number of controversial issues related to materials characterization and heat analysis, we hope that the theoretical work will have broad impacts on both materials design and industrial applications of gas adsorption and separation processes.