Introduction

As hydrogen (protium) consists of a single proton and a single electron, it is nature's simplest, lightest atom. The unique chemical and physical properties of the element's neutral, cationic, and anionic siblings, rely paradoxically on this ``simplicity". Since hydrogen has only one occupied electron shell it exhibits three common oxidation states: +1, 0, and $-$1 (corresponding to 1s$^0$, 1s$^1$, and 1s$^2$ electronic configurations, respectively). The relative change in the number of electrons surrounding the nucleus, associated with the transformations H^0 -> H^-I and H^0 -> H^+I (1e, 100 %), is thus the largest among the chemical elements of the periodic table; so are the relative changes of many chemical and physical key properties of these three unitary species. Therefore, hydrogen has key role in the universe and life supporting processes. In its 15-billion-year domination in the universe hydrogen is far-and-away the most abundant element in the cosmos, of which it makes 75 % of the weight composition[1]. The hydrogen fusion has crucial importance for the evolution of the stars and is the only source of remarkable amount of life-giving solar rays which provide our own planet and our plant world with energy in the form heat and light. As one of the elements present in the water molecule and the overwhelming majority of the organic compounds, hydrogen is pivotal to life. Furthermore it is one of the most important elements in the chemistry of the energy-giving materials, such as the light fractions of hydrocarbons (mineral oils and methane gas).

Hydrocarbons are technologically the most commonly used energy carriers. However, in a combustion engine only 30 % of the produced energy is due to the 2H + O -> H2O reaction^0.1. The rest is the so called ``dirty'' energy which results in CO2 production. At the same time, hydrogen's usage as fuel suggests many advantages over the hydrocarbons $-$ it is non-toxic, renewable, clean to use, and packs much more energy per bond.

The inevitable socio-economic effect of recurring fuel crises, the threat of the early end of the fossil fuels era in the coming 50 years, the increasing pollution of our environment, and the problem of an anthropogenic-induced climate change force the utilisation of clean and sustainable energy resources. Projections to the middle of the next century indicate that unabated global energy trends would lead to an annual global energy demand about four times the present level. Thus, a demand for clean and renewable energy sources has resulted in increased worldwide attention to the possibilities for a hydrogen-based economy as a long-term solution. Hydrogen is undoubtedly one of the key alternatives to replace petroleum products as a clean energy carrier for both transportation and stationary applications. Due to the unique electronic structure of its atom, hydrogen possesses the largest amount of chemical energy per bond (142 MJ$\,$mol$^{-1}$kg$^{-1}$)[2]. This is about three times higher energy than the hydrocarbons (47 MJ$\,$mol$^{-1}$kg$^{-1}$)[2]; therefore it is an excellent candidate for energy source. Furthermore, its usage promotes new technologies based on more efficient energy consumption (e.g. fuel cells based on electrochemical burning of H2 and O2)^0.2. However, technological difficulties $-$ subject to this work $-$ yet prevent the usage of H2 as widely spread energy carrier. The interest in hydrogen as energy carrier experienced a renaissance in the late 1960s and in the 1970s, and has grown even more dramatically since 1990. Partly catalysed by the deuterium cold fusion controversy;[3] many advances in hydrogen production and utilisation technologies have been made during the past decade as well. However, there remain a number of fundamental scientific and technological problems to be overcome before any large-scale utilisation of hydrogen is possible. These problems are serious holdbacks for acclaiming hydrogen as a potential energy carrier in the near future. The hydrogen storage$-$subject to this work$-$can be identified at the very forefront as one of these problems. Thus, the appearance of safety and easy to use hydrogen-storage devices is the key for the future mobile applications. Briefly, the ideal hydrogen storage material should have a low molar weight (to decrease the reservoir-to-storage mass ratio), be inexpensive, have rapid kinetics for adsorbing and desorbing H2 in the 25$-$120 temperature range, and store large quantities (6 H2 mass % of the tank and 0.045 gcm$^{-3}$ H2 density) of hydrogen reversibly, as proposed by the FreedomCAR and Vehicle Technologies (FCVT) Program. [4]

Presently, there are few ways to store hydrogen effectively. Unfortunately, they have rather limited and specialised applications. In principle, hydrogen is stored either in its elemental form, as diatomic gas, liquid, or in a chemical form as part of different chemical compounds. At normal conditions (1atm and 300 K), 1 kg H$_2$ occupies about 11 m$^3$ $-$ hardly a practical solution for wide spread applications.

A number of automobile companies have designed and manufactured prototypes of hybrid cars, where compressed or liquefied hydrogen has been used as another alternative fuel.

Figure 1: Hybrid combustion engine. Figure adopted from presentation of John Hollis - BMW Group 07.10.2005

Thanks to the development of high specific strength composite materials, high-pressure hydrogen tanks with working pressure up to 70 MPa are now available, corresponding to a hydrogen storage capacity of about 11 wt % [5,6]. However, in terms of energy, their volumetric hydrogen storage performance is yet very poor, and the high pressure technique suffers from potential safety problems when used on board. Liquid hydrogen can provide desirable gravimetric and volumetric storage capacity, although about one third of the energy carried is consumed by the liquefaction process. Additionally, the continuous evaporation of the cryogenic liquid hydrogen during storage may lead to knotty safety and energy loss related problems occurring despite insulation and recooling systems, being well equipped. From the viewpoint of a long-term run, it is necessary to develop other forms of advanced hydrogen storage systems. A more effective usage of the energy by considering H2/O2 fuel cell systems will then require an adequate and readily accessible hydrogen-storage medium. Hence, solid hydrogen-storage materials present themselves as a first option. A common idea is that hydrogen must be diffused into a solid material which keeps it compact and slows down its gas kinetics. Generally this can be achieved by chemically binding hydrogen to other elements or compounds so that it can be easily released afterwards. Other alternatives are to make it diffuse into crystalline structures with large enough interatomic spacing, or make it absorb into porous materials. However, the choice of storage material is limited to very small part of the periodic table. On one side, hydrogen is the lightest element and on the other side, according to FCVT Program[4], the gravimetric H2/material ratio must not be smaller than 4.5 % at present. This means that the composite elements of the storage container must be with a low atomic number i.e. Li,Be,B,C,N,O,F,Na,Mg,Al, Si and P. This list of elements must be further reduced due to the toxicity and/or unfavourable chemical properties of hydrogen's compounds with Be, F, Si, and P. Thus, the effective list of chemical elements constituting the storage media now consists of only eight members. The heavier ones may enter the multiple-component system only as low-abundant additives, for instance to adjust the storage properties or as a catalyst. It can be seen that even in this form, the target material clearly does not represent an impressively large number of options for the chemist. However, there are several broad classes of solid hydrogen-storage materials that are currently investigated as good candidates for potential on-board storage medium: 1) metal materials, hydrides (e.g., MgH2),[7] imides (e.g., LiNH2),[8] and complex hydrides (e.g., NaAlH4),[2] 2) metal organic frameworks (e.g., Zn4O (1,4-benzenedicarboxylate)),[9] and 3) carbon materials (e.g., carbon nanofibers, [10] single-wall carbon nanotubes)[11].

Metal hydrides applicable for hydrogen storage are composed by a light element with metallic character and hydrogen while, complex hydrides contain additionally other metallic or nonmetallic elements. These are ionic or covalent compounds which usually can easily release hydrogen by thermolysis. Although some of them reach or even exceed the target capacities,[4] the reversible combination of hydrogen with these materials depends strongly on the range of working temperatures. Unfortunately, most hydrides are either too stable for efficient hydrogenation cycling, or too unstable. In the first case, the absorption is easy, but desorption requires excessively high temperatures. In the second case, desorption occurs readily at or below room temperature, but absorption requires extremely high pressures of hydrogen.[12] Other hydrogen-release processes like metal-hydride decomposition in water are highly effective. However, this is related to either non-reversible products, or energy expensive reactions to regenerate their parent hydrides. For example, the reaction NaBH4 + 4H2O -> NaB(OH)4 + 4H2 is exothermic by -250 kJ$\,$mol$^{-1}$[13]. Another common problem with metal-hydride materials, which appears often because of the chemically connected hydrogen, is the very slow kinetics of the up/unload process. For example, the most thoroughly studied complex hydride, NaAlH4, has been shown to release hydrogen at 110 when doped with Ti.[14] However, the kinetics is very slow and hydrogen-storage densities are too low (2.8 mass %) to meet the long-term targets[4]. Despite the present problems related to the metal$-$ and composite metal$-$hydrides so far, they can be applicable as an irreversible, relatively cheap hydrogen storage materials, similarly to many existing single-use batteries.

Chemical hydrides with empirical formula BH2NH2 and B_xN_xH_y have been probed as high capacity hydrogen storage materials for a long time (1970s and 80s). Due to their high hydrogen capacity, these hydrides have been employed, in the past, as disposable H2 sources. Mixed and ball milled together with a reactive heat-generating compound, such as LiAlH4 or a mixture, such as NaBH4 and Fe2O3 these compounds release H2 and BN when ignited. However, to meet the requirements for on-board H2 storage systems, the major issues to be addressed are the hydride regeneration/ recyclability and the control over the H2 release.

Unlike the compounds described above, metal-organic frameworks[15,16] (MOFs) hold hydrogen by physisorption. They have attracted much interest in recent years due to their porous structure (similar to that of zeolites), ability to catalyse reactions, trap and sieve molecules. MOFs are composed of inorganic clusters or complexes, including transition or lighter elements as centres linked together by organic molecules, similarly to assembling of scaffolds of rods. Frequently used organic linkers are hydrocarbons such as benzene, naphthalene, anthracene etc.

Figure 2: Single-crystal structures of different MOFs (MOF-5 (1), IRMOF-6 (2), and IRMOF-8 (3)) illustrated for a single cube fragment of their respective cubic three-dimensional extended structure. On each of the corners there is a cluster [OZn4(CO2)6] of an xygen-centered Zn4 tetrahedron that is bridged by six carboxylates of an organic linker (Zn, blue polyhedron; O, red spheres; C, black spheres). The large yellow spheres represent the largest sphere that would fit in the cavities without touching the van der Waals atoms of the frameworks. Hydrogen atoms have been omitted. Addopted from ref. Rosi

Thus, an unlimited number of MOFs can be created consisting of different pore sizes and shapes. It is suggested that based on their large surface area ($\ge$ 3,000 m$^2$/g) they are suitable for storage of hydrogen and other gases[9]. However, since these materials are fairly new, the research is still in early phase.

Carbon materials like activated carbon (ACs) and ball-milled graphite are already known with their abilities to adsorb different gaseous compounds. The interest in carbon materials as hydrogen-storage media has been additionally increased during the last decade by the discovery of the fullerenes and nanotubes.[11] The hydrogen-storage behaviour of carbonaceous materials with high specific surface area, such as AC and AC fibres, has been investigated since the 1980s. A capacity of 3$-$6 wt % was reproducibly obtained at cryo-temperatures, although at room temperature the capacity is well below 1 wt % [17,18]. Ball-milled (under hydrogen-gas atmosphere) graphite powder shows considerable hydrogen storage capacity partialy due to chemisorption; however, the desorption temperature is too high for it to be used in practice[19,20]. Hydrogen storage in mesoporous carbons was also reported recently [21]. Although hydrogen uptake investigations based on various carboneous materials have been performed, there is no doubt that carbon nanotubes (CNTs)/nanofibers (CNFs) have been most intensively studied for hydrogen storage in recent years. However, the interaction of H$_2$ with graphite surfaces, slit pores, [22,23] carbon nanotubes, [11,24,25,26,27] and nanofibers [28] have been reported in the literature, not without controversy[29,30,31,32], applying arguments based on both, experimental and theoretical results. Despite the numerous articles and discussions whether carbon materials are suitable for hydrogen storage, the research on that topic is still on the agenda of many theoretical and experimental scientists. So far, no general conclusion can be drawn from the above cited reviews on whether carbon is suitable for hydrogen storage. In fact, structural characteristics, synthesis techniques and post-treatment methods may evidently influence the hydrogen-storage behaviour of any kind. However, experimental and theoretical investigations suggest a close relation between the nano-scale structure of the materials and their abilities to absorb hydrogen gas. Two main reasons can be referred as a source of the above mentioned problems. On one hand, besides diamond, graphite and C60$-$solid, no other carbon allotrope has well defined periodic structure. Moreover, it is difficult to manipulate them in the nano scale range. Although theoretically possible, the simulations of such many-body systems as gases, are not computationally affordable for the appropriate level of theory.

The dispersion or van der Waals interactions are the main obstacle for these simulations. Dispersion interaction appears between molecules, fragments of molecules, solutes, and solids, and it is named after F. London, who gave the first physical description of this phenomenon[33]. In his famous formula (Eq.1), the dispersion interaction is defined between two neutral, separated particles with a nonoverlapping charge densities and without a permanent dipole moment. The dispersion energy depends on the distance between the particles $r$, the polarisabilities ${\alpha}^{'}_1$ and ${\alpha}^{'}_2$, and the ionisation energies of the interacting particles $I_1$ and $I_2$:

$$\jot9pt U_{London}{\approx}-\frac{3}{2}\, \frac{I_1I_2}{I_1+I_2}\,{\alpha}^{'}_1 {\alpha}^{'}_2\, \frac{1}{r^6}$$ (0.1)

Hence, the dispersion interaction between nonpolar molecules is always attractive and slowly decrease as $r^{-6}$. It is several orders of magnitude weaker than the typical covalent or ionic interactions and is a factor of 10 smaller than the hydrogen bridge bond. Therefore, proper assessment of these interactions requires appropriate high accuracy calculations. Despite this simple physical picture, because of the many-body problem, a straightforward first principle quantum-mechanical description of the interaction is not trivial.

This present work is devided into two parts. Part I is concerned with the principles used to evaluate the H2 storage capacities of the carbon media. The problems discussed in this part include the methodology of calculating the real H2 gas properties (Chapter 1) and the evaluation of the interaction potential between a hydrogen molecule and carbon media (Chapter 2). The applicability range of the method together with the aproximations are discussed as well. In Part II a number of potential H2$-$host structures is proposed. In order to demonstrate the aplicability of the methodology described in Part I, Chapter 3 presents the more detailed data set of calculations. Although demonstrating the same methodology as in the 3$^{rd}$ chapter, the last three chapters discuss only the relation between the storage capacities and the structural properties of the carbon media.