Thesis
Reference
Experimental and theoretical studies of boron and hydrogen containing compounds in relation to potential hydrogen storage and
ionic conduction applications
SHARMA, Manish
Abstract
This thesis deals with the fundamental studies of some materials containing boron-hydrogen bonds which can potentially be used either as the hydrogen storage materials (M(BH4)2, M=Alkaline earth metal), as the solid electrolytes for batteries (Na2B12H12) or as reducing agents for CO2 (Mg(BH4)2). First part of thesis deals with borohydrides (BH4-). Synthesis and characterization of halide-free Sr(BH4)2, Ba(BH4)2 and Eu(BH4)2 is reported.
Crystallographic study of these compounds helped in identifying several new phases and a new species metal borohydride hydride (M2(BH4)H3). In depth study of B-H bond breaking is reported via isotope exchange reaction in Ca(BH4)2.A practical example of borohydride as reducing agent is reported by showing the reduction of CO2 with gamma-Mg(BH4)2. The second part of the thesis focuses on closoboranes derived from the B12H122- ion.
Compounds of this family have recently attracted great interest as solid ionic conductors for Li and Na ions.Results of DFT calculations on isolated B12H122- anions and halogen (F, Cl or Br) substituted anions were analysed in detail. Synthesis of Na2B12(SCN)H11 is [...]
SHARMA, Manish. Experimental and theoretical studies of boron and hydrogen containing compounds in relation to potential hydrogen storage and ionic conduction applications. Thèse de doctorat : Univ. Genève, 2017, no. Sc. 5101
DOI : 10.13097/archive-ouverte/unige:96376 URN : urn:nbn:ch:unige-963769
Available at:
http://archive-ouverte.unige.ch/unige:96376
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UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES
Section de Chimie et Biochimie Professeur Hans Hagemann Département de Chimie Physique
Experimental and Theoretical Studies of Boron and Hydrogen Containing Compounds In Relation to Potential Hydrogen Storage and Ionic Conduction
Applications
THÈSE
présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Chimie
par
Manish Sharma d’Inde
Thèse N° 5101 GENÈVE
Atelier d’impression ReproMail 2017
i
Acknowledgements
I would like to express my sincere gratitude towards my supervisor, Prof. Hans Hagemann, for giving me the opportunity to study at the University of Geneva and for his explanations and scientific discussions. He created a very liberal work environment and encouraged me to think independently. He gave full freedom from the choice of projects and collaborations. For me Hans is a perfect example to learn the work-life balance. He emphasized on having a good social life outside office and encouraged to play sports, visit museums, music festivals and to travel.
I would like to thank Prof. H. W. Li and Dr. A. Remhof for accepting and evaluating my thesis.
I am grateful to Dr. L. M. L. Daku for helping me to conduct computational calculations discussed in the thesis and for being the part of the thesis review committee.
Thanks to Prof. A. Hauser for his support and valuable suggestions throughout my PhD. I admire him for his art of explaining complex concepts in a lucid way.
I would like to thank all the collaborators, in particular Prof. R. Černý, E. Didelot, Dr. D.
Jeannerat, Dr. M. Pupier, Prof. T. Burgi, Dr. M. Chekini, Prof. Y. Filinchuk, F. Morelle, Prof. T.
Jensen, Dr. B. Richter, Prof. H. W. Li, Dr. L. He, Dr. A. Remhof and Dr. E. Roedern for synergic work.
I am thankful to Ma’am C. Ludy and I. Garin for helping me with bureaucratic formalities. N.
Amstutz and P. Barman for providing technical support and to Dominique Lovy for IT support.
I would like to acknowledge all the present and former members of Hauser-Hagemann group and my friends whom I met during my PhD: Teresa, Pablo, Romain, Angelina, Daniel, Andrea, Pradip, Jacob, Enza, Yolanda, Antoine, Quinchao, Jiji, Alexandra, Jan, Elia, Jakob, Igor, Ani, Rania, Mahshid, Martin and Roberto. They have been my closest friends in this period, sharing with me good and bad moments.
Finally, I would like to thank my wife and my parents for having supported me during these years.
ii
iii
Résumé
Ce travail de thèse porte sur les études fondamentales de certains matériaux contenant des liaisons bore-hydrogène qui peuvent potentiellement être utilisé comme des matériaux pour stockage de l'hydrogène, comme électrolyte solide dans les batteries, ou comme agents réducteurs pour le CO2.
La première partie de cette thèse sera consacrée aux études expérimentales des borohydrures métalliques de type M(BH4)n.
Le premier chapitre expérimental aborde la synthèse et la caractérisation des composés dépourvus d’halogénures Sr(BH4)2, Ba(BH4)2 et Eu(BH4)2. La synthèse de ces composés a été effectuée à partir de l'hydrure métallique et de Et3N-BH3. Lorsqu’ils sont chauffés à des températures élevées, ces composés sont plus stables que ceux rapportés dans la littérature obtenus par différentes voies de synthèse et impliquant des impuretés d'halogène. L'étude cristallographique de ces composés a permis d'identifier plusieurs nouvelles phases. Au cours des réactions de décomposition thermique, la formation d'un composé métal hydrure-borohydrure M2H3(BH4), avec M = Sr et Eu, a été observée pour la première fois. Le produit Eu(BH4)2 s'est révélé être un excellent luminophore émettant dans le bleu à 463 nm. De plus, plusieurs méthodes de synthèse infructueuses ou qui ont abouti à des produits impurs sont également discutées.
Dans le chapitre subséquent, la réaction d'échange hydrogène-deutérium ainsi que la réaction inverse sont étudiées pour le composé Ca(BH4)2 en fonction de la température et de la pression de deutérium (resp. d'hydrogène). La progression de cette réaction est suivie par la spectroscopie IR. Cette réaction d'échange d'isotopes fournit l'énergie d'activation minimale nécessaire à la rupture de la liaison B-H sans induire d'autres changements structurels dans le composé. On constate que l'énergie d'activation pour Ca(BH4)2 est significativement plus grande que pour le composé analogue au Mg, ce qui implique que l'ion métallique joue un rôle important dans la rupture de la liaison B-H.
Le dernier chapitre consacré aux borohydrures, étudie la réaction de Mg(BH4)2 avec le CO2. La consommation de CO2 et la formation de B2H6 sont contrôlées en utilisant la spectroscopie IR à phase gazeuse. Ces expériences montrent que le γ-Mg(BH4)2 poreux réagit facilement avec le CO2 même à température ambiante, tandis que la phase stable de α-Mg(BH4)2 réagit uniquement à température élevée. Cette réaction peut initier d'autres études concernant l’utilisation des borohydrures pour la réduction du CO2 ainsi que pour la régénération du carburant.
La deuxième partie de cette thèse porte sur les dérivés closoboranes de l'ion B12H122-. Les composés issus de cette famille ont récemment attiré un grand intérêt en tant que conducteurs ioniques solides pour les ions Li et Na. [1]
iv Les résultats des calculs DFT sur les anions B12H122- isolés et les anions substitués par les halogènes (F, Cl ou Br) ont été analysé en détail. Le but de cette étude est de prédire les données spectroscopiques pour les composés halogénés, puisque ces composés partiellement substitués sont difficile à préparer et à purifier. Des tendances systématiques dans diverses propriétés, comme par exemple pour l'étirement de la liaison B-H par rapport au nombre d'atomes d'hydrogène, sont observés. La stabilité thermodynamique de divers isomères est également discutée dans cette partie.
Le dernier chapitre expérimental se concentre sur la synthèse de certains substitués des closoboranes. Un mélange de Na2B12(SCN)nH(12-n) avec (n =1 et 2) a été synthétisé. La mesure de la conductivité ionique de cet échantillon montre qu’à température ambiante, la conductivité est 1000 fois meilleure par rapport au composé Na2B12H12 pur. La bromation complète et partielle de Na2B12H12 est également rapportée. Cependant, la bromation partielle donne un mélange de différents produits. Et finalement, des résultats préliminaires sur d'autres systèmes sont également inclus dans cette partie.
[1] Hansen, B. R. S.; Paskevicius, M.; Li, H.-W.; Akiba, E.; Jensen, T. R., Coord. Chem. Rev.
Metal boranes: Progress and applications, 2016, 323, 60-70.
v
Summary
This thesis deals with the fundamental studies of some materials containing boron-hydrogen bonds which can potentially be used either as the hydrogen storage materials, as the solid electrolytes for batteries or as reducing agents for CO2.
In the first part of thesis, experimental studies on metal borohydrides M(BH4)n are reported.
The first experimental chapter presents the synthesis and characterization of halide-free Sr(BH4)2, Ba(BH4)2 and Eu(BH4)2 starting from the metal hydride and Et3N-BH3. These compounds are more stable upon heating compared to other preparations reported in the literature involving halogen impurities. The crystallographic study of these compounds allowed identifying several new phases. During the thermal decomposition reactions, the formation of a metal hydride-borohydride M2H3(BH4) for M = Sr and Eu was observed for the first time.
Eu(BH4)2 has been shown to be an excellent phosphor emitting at 463 nm (blue colour). Several unsuccessful or partially successful reaction schemes which end up in impure products are also discussed.
In the next chapter, the hydrogen-deuterium exchange reaction as well as the reverse reaction is studied for Ca(BH4)2 as a function of temperature and deuterium (resp. hydrogen) pressure. The progress of this reaction is monitored using IR spectroscopy. This isotope exchange reaction provides the minimum activation energy of breaking the boron hydrogen bond without inducing further structural changes in the compound. It is observed that the activation energy for Ca(BH4)2
is significantly larger than for the analogous Mg compound, which implies that the metal ion plays an important role in the breaking of the B-H bond.
The last chapter dedicated to borohydrides explores the reaction of Mg(BH4)2 with CO2. The consumption of CO2 and formation of B2H6 is monitored using gas phase IR spectroscopy. These experiments show the porous γ-Mg(BH4)2 reacts readily with CO2 even at room temperature, while the stable α-Mg(BH4)2 phase reacts only upon heating. This reaction may initiate further studies to use borohydrides for CO2 reduction and possible fuel regeneration.
vi The second part of the thesis focuses on closoboranes derived from the B12H122- ion. Compounds of this family have recently attracted great interest as solid ionic conductors for Li and Na ions.[1]
Results of DFT calculations on isolated B12H122- anions and halogen (F, Cl or Br) substituted anions were analysed in detail. The focus of this study was the prediction of spectroscopic data for the halogenated compounds, as partially substituted compounds are not easily prepared and purified. Systematic trends in various properties, for instance, B-H stretching vs the number of hydrogen atoms are reported. The thermodynamic stability of various isomers is also discussed.
The last experimental chapter focuses on the synthesis of some substituted closoboranes. A mixture of Na2B12(SCN)nH(12-n) with (n =1 and 2) was synthesized. The measurement of the ionic conductivity of this sample shows that the conductivity at room temperature is much better (1000 fold) compared to pure Na2B12H12. Complete and partial bromination of Na2B12H12 is also reported. The partial bromination gives however mixture of different products. Further preliminary results on other systems are also included.
[1] Hansen, B. R. S.; Paskevicius, M.; Li, H.-W.; Akiba, E.; Jensen, T. R., Coord. Chem. Rev, Metal boranes: Progress and applications, 2016, 323, 60-70.
vii Table of Contents
Chapter 1 Introduction ... 1
1.1 Introduction ... 3
1.2 References ... 10
Chapter 2 Experimental & Computational Techniques ... 13
2.1 Structural characterization ... 15
2.1.1 Fourier Transform Infrared Spectroscopy ... 16
2.1.1a Attenuated Total Reflectance (ATR) ... 16
2.1.2 Raman Spectroscopy ... 17
2.1.3 Powder XRD ... 17
2.1.4 DSC ... 17
2.1.5 NMR ... 17
2.2 Computational characterization ... 18
2.2.1 Calculation on crystals ... 18
2.2.2 Orthogonalized Plane Waves (OPWs) method ... 19
2.2.3 Pseudopotential ... 20
2.2.4 Kinetic energy cutoff and Monkhorst-Pack grid ... 22
2.2.5 Details of the periodic calculations performed ... 23
2.3 References ... 24
Chapter 3 Synthesis, Structure and Decomposition of Metal Hydrides and Borohydrides ... 27
3.1 Introduction ... 29
3.2 Synthesis and Discussion ... 31
3.2.1a Synthesis of EuH2 ... 31
3.2.1b Results and Discussion... 31
3.2.2a Synthesis of M(BH4)2 (M=Sr, Ba, Eu) ... 32
3.2.2b Results and Discussions ... 32
3.2.3 Alternative Synthesis Methods ... 46
3.2.3 a, b & c Synthesis of (BaBH4)2 ... 46
Results and Observations ... 46
3.2.3 d, e & f Synthesis of Sr(BH4)2 ... 47
Results and Observations ... 47
3.3 Conclusions ... 49
3.4 Supporting Information ... 50
viii
3.5 References ... 52
Chapter 4 Isotope Exchange Reactions ... 55
4.1 Introduction ... 57
4.2 Experimental Section ... 59
4.2A. Deuterium exchange reactions in Ca(BH4)2 via solid gas reaction ... 59
4.2B. Deuterium exchange reactions in Na2B12H12 via solid gas reaction ... 60
4.2C. Deuterium exchange reactions in Na2B12H12 in DCl/D2O solution ... 60
4.3 Results and Discussion ... 62
4.3A. Solid Gas Reaction in Ca(BH4)2 ... 62
4.3 B. Deuteration by Solid Gas Reaction in Na2B12H12 ... 70
4.3 C. Deuterium exchange reactions in Na2B12H12 in DCl/D2O solution ... 74
4.4 Conclusions ... 81
4.5 References ... 82
Chapter 5 Reduction of CO2 using γ-Mg(BH4)2 ... 85
5.1 Introduction ... 87
5.2 Experimental Procedure ... 89
5.2.1 Room Temperature, in-situ IR measurement using glass cell ... 89
5.2.2 Room temperature, in-situ IR measurements using metallic cell ... 90
5.2.3 High temperature (100 °C), in-situ IR measurements using metallic cell ... 90
5.2.4 Ex-situ measurements (α- Mg(BH4)2) ... 90
5.3 Results and Observations ... 91
5.3.1 Results for experimental section 5.2.1 ... 93
5.3.2 Results for experimental section 5.2.2 and 5.2.3 ... 96
5.3.3 Results for experimental section 5.2.4 ... 99
5.4 Conclusions ... 100
5.5 References ... 102
Chapter 6 Theoretical calculations on halogenated closoboranes B12H12-nXn 2- (X=F,Cl,Br) .... 105
6.1 Introduction ... 107
6.2 Computational Details ... 108
6.3 Results and Discussions ... 109
6.3.1 Relative Stability ... 110
6.3.2 Isomerism ... 111
6.3.3 Bond Length ... 112
ix
6.3.4 Vibrational Spectra ... 113
6.3.5 NMR spectra ... 118
6.4 Conclusions ... 119
6.5 Supporting Information ... 120
6.6 References ... 122
Chapter 7 Synthesis of Various Substituted Closoboranes (B12XnH(12-n) 2-) ... 125
7.1 Introduction ... 127
7.2 Synthesis, Results and Discussions ... 128
7.2.1a Synthesis of ((C2H5)3NH)2B12H12)... 128
7.2.1b Results and Observation... 128
7.2.2a Synthesis of CaB12H12 ... 130
7.2.2b Results and Observations ... 130
7.2.3a Bromination of Na2B12H12 ... 132
7.2.3b Results and Observations ... 132
7.2.4 a Synthesis of thiocyanated closoborane ... 138
Scheme 1 ... 138
Scheme 2 ... 138
7.2.4 b Results and Observation ... 138
7.3 Conclusions ... 142
7.4 References ... 143
Chapter 8 Conclusions ... 145
8.1 Conclusions ... 147
8.2 References ... 153
x
1
Chapter 1
Introduction
2
3
1.1 Introduction
Motivation
Anthropogenic factors have caused serious climatic changes.1-4 One of the main reasons of these changes is the consumption of the fossil fuels which generates greenhouse gases.5-6 Renewable sources of energy such as solar radiation, wind, and tides provide green energy and are the key to overcome the challenge of climate change.7-9 In order to use renewable sources efficiently they need to be supported with ideal energy storage systems. Hydrogen can be used as a fuel to meet our mobile energy needs (fuel in automobiles). Hydrogen is regarded as a green fuel as it produces water upon combustion.10 Another way to store energy is the use of batteries, which can be designed for mobile or stationary applications.
The volumetric energy capacity of hydrogen is low. At the ambient conditions 1 kg of hydrogen gas occupies a volume of 11m3. In order to store hydrogen efficiently, the main methods which are available are: (i) storing hydrogen at cryogenic temperature, (ii) storing hydrogen under high pressure, (iii) physisorption of hydrogen on high surface materials, (iv) metal hydrides (incorporation of hydrogen in the host metallic structures) and (v) complex hydrides, chemisorption of hydrogen (vi) storage via chemical reactions, like metals with water.11 Each of the above listed methods has its own set of challenges to overcome before an ideal hydrogen storage system can be developed.
Batteries provide an efficient way to store electrical energy in the form of chemical energy, which can subsequently be released without any gaseous exhaust.12-13 In this context, it is essential to investigate the path to design economical, safe and rechargeable batteries.14-15 Among the available rechargeable batteries, lithium ion batteries (LIBs) present high gravimetric and volumetric energy density which is essential for portable (cell phone, laptop) and mobile (cars) applications. The available big resources of lithium are concentrated in few places, currently 75% of the world production of lithium comes from Chile, Australia and China. The potential strong increase of production of batteries for automobile applications in the near future makes it essential to look for an economical and geopolitically neutral alternative for lithium.
Sodium ion batteries (SIBs) are interesting candidates to be investigated in this context, as sodium is present in abundance all throughout the globe. However, there are currently still
4 several challenges to overcome to produce these batteries for mobile applications. One important component in a battery is the electrolyte. Currently, Natrium Superionic CONductors (NASICON) are well known electrolytes but they exhibit reasonable ionic conductivity only at high temperature. The development of solid sodium electrolytes with liquid-like ion conductivity at ambient temperature would be a big step towards developing safe all-solid state sodium-ion batteries for large scale energy storage applications.
This thesis deals with the fundamental studies of some materials containing boron-hydrogen bonds which can potentially be used as hydrogen storage materials, as solid electrolytes for sodium ion batteries or as reducing agents for CO2.
The different research projects of this thesis are part of a long term research of our group on boron hydrogen compounds. After more than a decade of investigation the synthesis, structural and vibrational properties of different compounds with BH4-
, the topic of ongoing projects has been expanded as shown in the figure 1.1.
5 Figure 1.1: Schematic representation of research projects on boron hydrogen related compounds in Prof.
Hans-Hagemann’s lab. Dark green boxes represents the work covered in this thesis.
6 Diversity in structures and applications of boron-hydrides
Boron hydrogen compounds BxHy were first studied by Alfred Stock.16 He decomposed magnesium boride with acid, to obtain the first boron hydride B4H10 (liquid) whose physical and chemical properties were thoroughly investigated. Heating of B4H10 yielded diborane B2H6 (gas) and the thermal decomposition of diborane resulted in the formation of B10H14 (crystal).17 Apart from regular 2-center-2- electron covalent bonds, boron can also form 3-center-2-electron (3c- 2e) covalent bonds (with hydrogen and boron itself).18-20 The structure of B2H6 contains two 3c- 2e bonds, this structure of diborane was initially proposed by Christopher Longuet-Higgins.21 These fascinating bonding properties led to many experimental and theoretical studies on boron- hydrogen compounds, with many experiments being performed more than 50 years ago. For instance, the volatile compound U(BH4)4 was considered for the separation and purification of uranium in the Manhattan project.22-23 Some compounds like liquid B5H9 or solid B10H14 have been considered as potential rocket fuel about 50 years ago because of their high energy content;
however their toxicity is a serious impediment for this application.24 Today, over 25 neutral boron-hydrogen compounds and an even larger number of borane anions BxHyn-
are known.25 The structures of some of these compounds can be classified according to the Wade rule as arachno- (BnHn+6), nido- (BnHn+4) and closo- (BnHn2-
) boranes.26-28
This thesis focuses mainly on two types of compounds, namely tetrahydroborates (BH4-) and dodecahydro-closo-dodecaborates (B12H122-). Tetrahydroborates are referred as borohydrides and dodecahydro-closo-dodecaborates have been referred as closoboranes throughout in the thesis.
Metal borohydrides have various properties. They find well established applications in organic chemistry as reducing agents.29-30 The reducing nature of borohydrides was first investigated by Schlesinger and H.C Brown.30 Since then borohydrides are used as reducing agents in organic chemistry (H. C. Brown was awarded with Nobel Prize due to his work in the field of borane- organoborane in 1979). Since about 15-20 years, they are studied for their potential as light hydrogen storage material (for mobile applications) and more recently as fast ion conductors for new types of batteries.31-35
Hydrogen desorption properties of borohydrides were already investigated in the middle of last century.36-37 A revived interest in metal hydrides and borohydrides came after Bogdanovic
7 demonstrated a reversible hydrogen release and uptake in titanium doped aluminium hydride. 38 Since then many new metal borohydrides have been synthesized and characterized. However, with some transition metals (eg Zn), instead of hydrogen the release of diborane has been observed. A brief summary of the research done on metal borohydrides in the last decade is presented in a recent review.39
The thermal decomposition of metal borohydrides goes through a series of intermediate steps and can result in the formation of higher boranes like Mn+ (B12H122-)n/2 (where M is the metal).40 Closoboranes have recently gained an increased interest as potential electrolyte for all solid state batteries. Na2B12H12 shows a dramatic high superionic conductivity (~0.1 S/cm) after an order- disorder phase transition at high temperature (~540 K).41-42 Tang et al have studied the structural changes and phase transitions by anion and cation modifications of closoboranes M2B12X12 (M = alkali metal, X=H, Cl, Br).43-44
Outline of the thesis
This thesis is divided into two sections. The first section deals with borohydrides (BH4-
) and the second section deals with closoboranes (B12H122-
). In the beginning of the first section, different synthesis schemes to synthesize metal borohydrides are discussed. The following chapters in this section show the results and observations for the different projects done on the materials synthesised in the synthesis part. These projects show the versatile nature of applications of borohydrides in different fields like hydrogen storage and reduction of CO2 gas.
The figure above shows the different aspects considered in this thesis. In the first part, high temperature decomposition reactions, the activation energy for the breaking of the boron- hydrogen bond monitored by isotopic substitution reactions, and finally the use of (γ-Mg(BH4)2) as reducing agent for carbon dioxide are studied. In the second part, closoboranes and substituted closoboranes as potential solid state electrolytes are studied both experimentally and theoretically. These different projects are described in more detail in the following paragraphs.
Chapter 3 of this thesis is dedicated to the “Synthesis, Structure and decomposition of Halide Free Metal Borohydride” in this regard. A detailed study of the synthesis of several borohydrides is reported while for europium, the synthesis of europium hydride starting from pure europium metal is also discussed. The compounds discussed in this section cannot be used as hydrogen
8 storage materials as the mass of the cation (metal) is large, but these materials can also be used to synthesize mixed cationic compounds. Studying these compounds also imparts us a better understanding of the dehydrogenation process in borohydrides.
In order to investigate the hydrogen release process from borohydrides, it is essential to understand boron-hydrogen bond breaking. Chapter 4 of this thesis, “Isotope exchange reaction in Ca(BH4)2” is an attempt to study the kinetics and thermodynamics of boron hydrogen breaking without causing any major structural degradation due to the thermal decomposition in Ca(BH4)2. Deeper understanding of this step would help us to better understand and control the dehydrogenation step. We have used infrared spectroscopy as a tool to monitor the isotope exchange reaction. The distinct bands for B-H and B-D stretching, facilitates the calculation of amount of H or D in the reaction sample and thus kinetic parameters for the reaction can also be calculated.
In a collaborative work with Prof. Y. Fillinchuk (Université Catholique de Louvain) and Prof.
H. W. Li (International Research Center for Hydrogen Energy, Kyushu University, Japan), we have investigated reducing nature of a porous phase of magnesium borohydride γ-Mg(BH4)2. The kinetics of the reduction reaction is studied using gas phase infrared spectroscopy. These results are so far unpublished and summarized in chapter 5 of this thesis.
Furthermore, in a research project of our laboratory in collaboration with Prof. T. Jensen (Aaarhus University), we have studied the destabilization of alkali borohydrides by the addition of BF4-
which led to a dramatic lowering of the decomposition temperature and the formation of B12H122-.45 This led us to investigate theoretically the structure and spectroscopic properties of various B12HnX(12-n)2- (X = F, Cl or Br and n = 1-3, 9-12) anions. The results of this computational study are presented in chapter 6 of the thesis. The results for fluoride mixed closoboranes have been published in the reference [33], while the results on bromide and chloride mixed closoboranes are still unpublished.46
Chapter seven of this thesis deals with developing a system based on closoboranes which can exhibit ionic conductivity in the range of few mS/cm at room temperature. Due to the high interest in the area of potential efficient solid ionic conductors, we have started a series of
9 experiments to synthesize and purify halide-hydride mixed closoboranes. Preliminary experimental results on the synthesis of substituted closoboranes are presented in chapter 7.
In order to avoid numerous repetitions, we have summarized in chapter 2 entitled “Experimental Techniques” the spectroscopic techniques and computational details which have been used throughout the entire thesis, while more specific details are given in each chapter separately.
10
1.2 References
[1] Vitousek, P. M.; Mooney, H. A.; Lubchenco, J.; Melillo, J. M., Science Human Domination of Earth's Ecosystems, 1997, 277, 494-499.
[2] Nature Clim. Change The human factor, 2012, 2, 555-555, doi:10.1038/nclimate1657.
[3] Min, S.-K.; Zhang, X.; Zwiers, F. W.; Hegerl, G. C., Nature Human contribution to more-intense precipitation extremes, 2011, 470, 378-381.
[4] Syvitski, J. P. M.; Kettner, A. J.; Overeem, I.; Hutton, E. W. H.; Hannon, M. T.; Brakenridge, G. R.;
Day, J.; Vorosmarty, C.; Saito, Y.; Giosan, L.; Nicholls, R. J., Nature Geosci Sinking deltas due to human activities, 2009, 2, 681-686.
[5] Canadell, J. G.; Le Quéré, C.; Raupach, M. R.; Field, C. B.; Buitenhuis, E. T.; Ciais, P.; Conway, T.
J.; Gillett, N. P.; Houghton, R. A.; Marland, G., Proceedings of the National Academy of Sciences Contributions to accelerating atmospheric CO2 growth from economic activity, carbon intensity, and efficiency of natural sinks, 2007, 104, 18866-18870.
[6] Lehmann, J., Nature A handful of carbon, 2007, 447, 143-144.
[7] Chu, S.; Cui, Y.; Liu, N., Nat Mater The path towards sustainable energy, 2017, 16, 16-22.
[8] Gielen, D.; Boshell, F.; Saygin, D., Nat Mater Climate and energy challenges for materials science, 2016, 15, 117-120.
[9] Streimikiene, D.; Sivickas, G., Environ Int The EU sustainable energy policy indicators framework, 2008, 34, 1227-40.
[10] Nat. Energy Hydrogen on the rise, 2016, 1, 16127.
[11] Züttel, A., Mater. Today Materials for hydrogen storage, 2003, 6, 24-33.
[12] Palomares, V.; Serras, P.; Villaluenga, I.; Hueso, K. B.; Carretero-Gonzalez, J.; Rojo, T., Energy Environ. Sci. Na-ion batteries, recent advances and present challenges to become low cost energy storage systems, 2012, 5, 5884-5901.
[13] Dietrich, P.; Wokaun, A.; Bauer, C., Aqua Gas Chemical energy storage. A contribution to the energy strategy 2050, 2012, 92, 22-27.
[14] Armand, M.; Tarascon, J. M., Nature Building better batteries, 2008, 451, 652-657.
[15] Tarascon, J. M.; Armand, M., Nature Issues and challenges facing rechargeable lithium batteries, 2001, 414, 359-367.
[16] Johnson, W. C., J. Chem. Educ. Hydrides of Boron and Silicon (Stock, Alfred), 1934, 11, 256.
[17] Wiberg, E., Pure Appl. Chem. Alfred Stock and the renaissance of inorganic chemistry, 1977, 49, 691-700.
11 [18] Eberhardt, W. H.; Crawford, B., Jr.; Lipscomb, W. N., J. Chem. Phys. The valence structure of the boron hydrides, 1954, 22, 989-1001.
[19] Price, W. C., J. Chem. Phys. The Structure of Diborane, 1947, 15, 614-614.
[20] Price, W. C., J. Chem. Phys. The Absorption Spectrum of Diborane, 1948, 16, 894-902.
[21] Longuet-Higgins, H. C.; Bell, R. P., J. Chem. Soc. 64. The structure of the boron hydrides, 1943, 250-255.
[22] Ghiassee, N.; Clay, P. G.; Walton, G. N., Journal of Inorganic and Nuclear Chemistry Thermal decomposition of U(BH4)4, 1981, 43, 2909-2913.
[23] Paine, R. T.; Schonberg, P. R.; Light, R. W.; Danen, W. C.; Freund, S. M., Journal of Inorganic and Nuclear Chemistry Photochemistry of U(BH4)4 and U(BD4)4, 1979, 41, 1577-1578.
[24] Agarwal, J. P., Wiley-VCH, Weinheim, Germany High Energy Materials: Propellants, Explosives and Pyrotechnics, 2010.
[25] Greenwood, N. N.; Earnshaw, A., Chemistry of Elements. VCH Verlagsgesellschaft: 1988; p 1700 pp.
[26] Wade, K., Nat Chem Bonding with boron, 2009, 1, 92-92.
[27] Mingos, D. M. P., Accounts of Chemical Research Polyhedral skeletal electron pair approach, 1984, 17, 311-319.
[28] Jemmis, E. D.; Balakrishnarajan, M. M., Journal of the American Chemical Society Polyhedral Boranes and Elemental Boron: Direct Structural Relations and Diverse Electronic Requirements, 2001, 123, 4324-4330.
[29] Zhu, Y.; Hosmane, N. S., Coord. Chem. Rev. Nanocatalysis: Recent advances and applications in boron chemistry, 2015, 293–294, 357-367.
[30] Schlesinger, H. I.; Brown, H. C.; Finholt, A. E.; Gilbreath, J. R.; Hoekstra, H. R.; Hyde, E. K., J.
Am. Chem. Soc. Sodium Borohydride, Its Hydrolysis and its Use as a Reducing Agent and in the Generation of Hydrogen1, 1953, 75, 215-219.
[31] Schlapbach, L.; Zuettel, A., Nature Hydrogen-storage materials for mobile applications, 2001, 414, 353-358.
[32] Matsuo, M.; Orimo, S.-i., Adv. Energy Mater. Lithium Fast-Ionic Conduction in Complex Hydrides: Review and Prospects, 2011, 1, 161-172.
[33] Li, C.; Peng, P.; Zhou, D. W.; Wan, L., Int. J. Hydrogen Energy Research progress in LiBH4 for hydrogen storage: A review, 2011, 36, 14512-14526.
[34] He, T.; Pachfule, P.; Wu, H.; Xu, Q.; Chen, P., Nat. Rev. Mater. Hydrogen carriers, 2016, 1, 16059.
[35] Ley, M. B.; Jepsen, L. H.; Lee, Y.-S.; Cho, Y. W.; Bellosta von Colbe, J. M.; Dornheim, M.; Rokni, M.; Jensen, J. O.; Sloth, M.; Filinchuk, Y.; Joergensen, J. E.; Besenbacher, F.; Jensen, T. R., Mater.
Today (Oxford, U. K.) Complex hydrides for hydrogen storage - new perspectives, 2014, 17, 122-128.
12 [36] Fedneva, E. M.; Alpatova, V. I.; Zh, V. I. M., Neorgan. Khim. Thermal stability of lithium borohydride, 1964, 9, 1519-20.
[37] Stasinevich, D. S.; Egorenko, G. A., Zh. Neorg. Khim. Thermographic study of borohydrides of alkali metals and magnesium at pressures up to 10 atm, 1968, 13, 654-8.
[38] Bogdanović, B.; Schwickardi, M., J. Alloys Compd. Ti-doped alkali metal aluminium hydrides as potential novel reversible hydrogen storage materials1, 1997, 253–254, 1-9.
[39] Paskevicius, M.; Jepsen, L. H.; Schouwink, P.; Cerny, R.; Ravnsbaek, D. B.; Filinchuk, Y.;
Dornheim, M.; Besenbacher, F.; Jensen, T. R., Chem. Soc. Rev. Metal borohydrides and derivatives - synthesis, structure and properties, 2017, 46, 1565-1634.
[40] Welchman, E.; Thonhauser, T., Journal of Materials Chemistry A Decomposition mechanisms in metal borohydrides and their ammoniates, 2017, 5, 4084-4092.
[41] Udovic, T. J.; Matsuo, M.; Unemoto, A.; Verdal, N.; Stavila, V.; Skripov, A. V.; Rush, J. J.;
Takamura, H.; Orimo, S.-i., Chem. Commun. Sodium superionic conduction in Na2B12H12, 2014, 50, 3750-3752.
[42] Verdal, N.; Her, J.-H.; Stavila, V.; Soloninin, A. V.; Babanova, O. A.; Skripov, A. V.; Udovic, T. J.;
Rush, J. J., J. Solid State Chem. Complex high-temperature phase transitions in Li2B12H12 and Na2B12H12, 2014, 212, 81-91.
[43] Udovic, T. J.; Matsuo, M.; Tang, W. S.; Wu, H.; Stavila, V.; Soloninin, A. V.; Skoryunov, R. V.;
Babanova, O. A.; Skripov, A. V.; Rush, J. J.; Unemoto, A.; Takamura, H.; Orimo, S.-i., Advanced Materials Exceptional Superionic Conductivity in Disordered Sodium Decahydro-closo-decaborate, 2014, 26, 7622-7626.
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13
Chapter 2 Experimental &
Computational Techniques
14
15
2.1 Structural characterization
The structural characterizations discussed in the thesis were performed using FTIR, Raman, XRD, DSC, NMR and mass spectrometry.
FTIR spectroscopy has been systematically used to check not only the purity of the samples (residual solvent removal etc), but also to study to local structure of BH4- based on the expertise acquired in our laboratory in the last 15 years. Raman spectra complement these analysis. Also, during isotope exchange, the frequency of vibrations for different isotopes changes, as the frequency is inversely proportional to square root of mass. Thus IR/Raman spectra were also used to monitor the progress of isotope exchange reactions in various projects by monitoring the area under B-H and B-D stretching peaks.
Differential Scanning Calorimetry coupled to thermogravimetry (DSC/TG) was used to check the thermal stability of synthesised products. The temperature at which products thermally decomposes or show any phase transformation were obtained using DSC.
Temperature dependent synchrotron X-ray powder diffraction (SR-XPD) analysis was used to analyse the crystal structure and their decomposition products. SR-XPD data used for the crystal structure solutions and refinements were collected between RT and 773 K at the Swiss- Norwegian Beamlines of ESRF (European Synchrotron Radiation Facility, Grenoble, France) and analysed by Radovan Cerny and Emilie Didelot (Department of Quantum Matter Physics of the University of Geneva). Periodic density functional theory (DFT) calculations were applied to identify the exact position of hydrogen for Ba(BH4)2.
DFT calculations on isolated species in the gas phase also helped to characterize halogen substituted closoboranes. All the possible positional isomers for each compound were also characterized with the help of DFT calculations. Experimentally synthesizing halogen substituted closoboranes B12H(12-n)Xn2-
in pure phase for X = F, Cl and Br and n =0-3 and 9-12 is challenging. The halogen gases X2 (X=F, Cl, and Br) are highly reactive and may rapidly form a multitude of compounds (mono, di or tri halo substituted) compared to pseudo halogen substituted (–SCN) closoboranes. Thus pseudo-halogen substituted closoboranes were synthesized to form mono-thiocyanate substituted compounds. NMR and MS spectra were used to characterize the substitution. 11B {1H} NMR also helped to find out the progress of deuteration in Na2B12H12 during reaction with concentrated DCl.
Mass spectrometry is helpful to analyse the different compounds formed during bromination of sodium closoboranes.
16 2.1.1 Fourier Transform Infrared Spectroscopy
Attenuated Total Reflection Fourier Transform Infrared Spectroscopy (ATR-FTIR) was performed on solid samples. Biorad Excalibur instrument equipped with a Specac Golden Gate heat-able ATR set-up was used for FTIR. The spectral resolution was set to 1 cm-1. Samples were loaded on ATR setup in an inert atmosphere of Nitrogen. Powdered sample was pressed between diamond crystal and bridge clamped sapphire anvil to ensure optimum optical contact of the powder.
2.1.1a Attenuated Total Reflectance (ATR)
ATR-FTIR is based on attenuation effect of light when infrared light is internally reflected at the interface of diamond and sample (from high refractive index medium to low refractive index medium). Light penetrates into the rarer medium as an evanescent wave. The penetration depth of evanescent wave is in the order of microns (0.2 – 5 µm).
An infrared beam is directed to a diamond crystal (optical dense medium, refractive index 2.417 for yellow light) at the specific angle to create the total internal reflection. As a result of the internal reflection, an evanescent wave is created beyond the surface of the diamond. This evanescent wave interacts with the sample which is in close contact with diamond crystal (due to pressure by a spring loaded sapphire anvil), thus sample absorbs parts of the light wave (bands of the infrared spectrum). Reflected wave reaching the detector Evanescent wave is passed back to IR beam and finally to a detector.1
Figure 2.1: Schematic representation of a single reflection ATR system, similar to the one used for FTIR mentioned in the thesis.
17 2.1.2 Raman Spectroscopy
Raman spectra were recorded with a homemade setup. The laboratory assembled Raman Instrument consists of a solid state 50mW 488nm laser, a Kaiser Optical Holospec f/1.8 monochromator equipped with the Princeton Instruments liquid nitrogen cooled CCD camera.
The instrument is controlled by a program developed by D. Lovy at the department of Chime Physique at the University of Geneva. All measurements were performed in the backscattering configuration. The samples were contained in standard melting point capillaries which were filled in the glove box and then sealed using vacuum grease.
2.1.3 Powder XRD
Powder X-ray diffraction patterns were obtained on a STOE STADI P diffractometer in Debye- Scherrer geometry with monochromated Cu-Kα1 radiation. The phase composition was determined by the Rietveld method using the software FullProf2.
2.1.4 DSC
Differential scanning calorimetry data were measured using a NETZSCH STA449 F3 instrument. The measurements were performed under an inert atmosphere of nitrogen with a purge rate of 20ml/min. The samples were contained in Al2O3 (or Aluminium, maximum temperature = 600 °C) crucibles with a lid to prevent exposure to atmosphere while mounting.
Samples were loaded in crucibles in an inert atmosphere of nitrogen. The heating rate was set at 10 °C/min.
2.1.5 NMR
11B NMR experiments were recorded at 298 K on a Bruker AVANCE III HD-NanoBay 300 MHz (and 400 MHz) spectrometer, equipped with a 5 mm BB(F)-H-D probe, at a frequency of 300.13 MHz (400.13 MHz).
18
2.2 Computational characterization
2.2.1 Calculation on crystals
The theoretical description of the electronic structure of a crystalline system relies on the use of the Bloch’s theorem, which states that the eigenfunctions of the Hamiltonian of the system can be written as the product of a plane wave and a function with the periodicity of the Bravais lattice of the system. A wavefunction describing an electronic state of the system thus reads:
𝜓𝑛𝒌(𝒓) = 𝒆𝒊𝒌.𝒓𝑢𝑛𝒌(𝒓) (2.1) where 𝑢𝑛𝒌(𝒓) is a periodic function with the periodicity of the Bravais lattice and thus verifies for any lattice vector R,
𝑢𝑛𝒌(𝒓 + 𝑹) = 𝑢𝑛𝒌(𝒓), (2.2)
k is a vector of the reciprocal space and the quantum number n is the so-called band index used to distinguish the many solutions to the Schrödinger equation at a given k. The name of this quantum number is due to the fact that to each solution is associated an eigenvalue n which is a continuous function of k, termed “band” with band index n. The set of functions 𝑛𝒌 =𝑛(𝒌) defines the band structure of the system.
Practically, given that for any reciprocal lattice vector K: 𝜓𝑛,𝒌+𝑲(𝒓) = 𝜓𝑛,𝒌(𝒓), one lets k take values in the first Brillouin zone only so as to achieve a unique description of the electronic structure. Furthermore, the functions 𝒖𝒏𝒌(𝒓) being periodic, it can be expanded in a basis set of plane waves, which allows the use of efficient Fourier transform methods.
However, the use of a plane-wave basis set poses a challenge because an enormous number of plane waves are necessary to represent the strongly localized core orbitals and the inner nodal structures of the valence wavefunctions, thus possibly making the use of plane waves computationally prohibitive. In order to overcome this challenge, the ‘frozen core approximation’ can be used. According to this approximation, the contribution of the core states to the chemical bonding and to the properties of the system is negligibly small and thus one can ignore their variation; that is, keep them frozen to their values in a reference system.
19 Based on this approximation, several methods have been developed to efficiently treat the electronic structures of crystalline systems using plane waves. This includes the plane-wave pseudopotential methods, which have been used in this work, or the Projector Augmented Waves (PAWs) method, which all have been preceded by the Orthogonalized Plane Wave (OPWs) method.3-4
2.2.2 Orthogonalized Plane Waves (OPWs) method
The OPWs method was developed in 1940 by Herring.5 In this method, the valence states are built by using plane waves which have been made orthogonal to the core states, the so-called OPWs. An OPW 𝜙𝑘 thus reads:
𝛟𝒌 = 𝒆𝒊𝒌.𝒓+ ∑ 𝒃𝒋 𝒌𝒋𝒖𝒋(𝒓) (2.3)
where 𝑢𝑗 is the wavefunction of the j-th core level, (2.4)
and 𝑏𝑘𝑗 is a constant which is defined such that 𝜙𝑘 is orthogonal to all the core levels, thus:
𝒃𝒌𝒋 = − ∫ 𝒅𝒓 𝒖𝒋∗(𝒓)𝒆𝒊𝒌.𝒓 (2.5)
𝑢𝑗 is an eigenfunction of the Schrodinger equation for the core states
𝟏
𝟐𝜵𝟐𝒖𝒋+ (𝑬𝒋− 𝑽𝒋)𝒖𝒋 = 𝟎 (2.6) 𝐸𝑗 is the total energy associated to 𝑢𝑗 and 𝑉𝑗 denotes the potential of the system.
Using the OPW method, the wavefunction of a valence state (𝜓𝑣) of a periodic crystal is described by a linear combination of OPWs. It is the sum of a smooth wavefunction (𝜓̌𝒗) and a sum over the localized wavefunctions of the core states (∑ 𝐵𝑗 𝑗𝑢𝑗(𝑟)):
𝜓𝑣(𝒓) = 𝜓̌𝑣(𝒓) + ∑𝑗𝐵𝑗𝑢𝑗(𝒓) (2.7)
All the quantities of the relation (2.7) can be expressed in terms of the original OPWs rewritten 𝑥𝑞𝑂𝑃𝑊(𝒓) = {𝑒𝛺1 𝑖𝒒.𝒓− ∑ ⟨𝑢𝑗 𝑗|𝒒⟩𝑢𝑗(𝒓)}, where ⟨𝑢𝑗|𝒒⟩ = ∫ 𝑑𝒓 𝑢𝑗(𝒓)𝑒𝑖𝒒.𝒓 (2.8, 2.9)
by the Fourier transforms:
20 𝜓𝑣(𝒓) = ∫ 𝑑𝒒 𝑐(𝒒)𝜒𝒒𝑂𝑃𝑊(𝒓) (2.10)
𝜓̌𝒗(𝒓) = ∫ 𝑑𝒒 𝑐(𝒒)𝑒𝑖𝒒.𝒓 (2.11) 𝐵𝑗 = ∫ 𝑑𝒒 𝑐(𝒒)⟨𝑢𝑗|𝒒⟩ (2.12)
The simplest approach is to assume that the core states in the molecules or solids are the same as in the atoms. That is, to choose them to be atomic core orbitals.6
2.2.3 Pseudopotential
The basic idea in pseudopotential methods is to replace the strong Coulomb potential of the nucleus of an atom by a much softer potential which reproduces the complicated effect of both the nucleus and the core electrons. The wavefunctions of the resulting pseudo-atom also referred to as pseudo-wavefunctions are nodeless.
The pseudopotential approximation was introduced by Hans Hellmann in 1934.7 Further development in this field was done by Antonick,8-9 and Philips and Kleinmann10 (PKA).
Assuming that the true valence wavefunction 𝜓𝑣(𝑟) solution of 𝐻𝜓𝑖𝑣(𝑟) = [−𝟏
𝟐𝜵𝟐+ 𝑽] 𝜓𝑖𝑣(𝑟) = 𝜀𝑖𝑣𝜓𝑖𝑣(𝑟) (2.13)
reads:
𝜓𝑖𝑣(𝒓) = 𝜓̌𝑖𝑣(𝒓) − ∑ ⟨𝑗 𝜓𝑗𝑐|𝜓̌𝑖𝑣⟩𝜓𝑗𝑐(𝒓) (2.14)
where 𝜓̌𝑖𝑣 is a smooth wavefunction and where the sum ensures the orthogonality to the core functions 𝜓𝑗𝑐, they showed that the wavefunctions 𝜓̌𝑖𝑣 are solutions of
𝐻
𝑃𝐾𝐴𝜓̌
𝑖𝑣(𝑟) = [−
𝟏𝟐
𝜵
𝟐+ 𝑽
𝑷𝑲𝑨]
𝜓̌
𝑖𝑣(𝑟) = 𝜀
𝑖𝑣𝜓̌
𝑖𝑣(𝑟)
(2.15)21 where 𝑉𝑃𝐾𝐴 is the sought pseudopotential given by 𝑉𝑃𝐾𝐴 = 𝑉 + 𝑉𝑅 . 𝑉𝑅 is a repulsive non-local operator that results from the condition of orthogonality; it acts on the pseudo-wavefunction 𝜓𝑖𝑣(𝑟) with the effect shown below:
𝑉𝑅𝜓𝑖𝑣(𝑟) = ∑ (𝜀𝑗 𝑖𝑣 − 𝜀𝑗𝑐) ⟨𝜓𝑗𝑐|𝜓𝑖𝑣⟩ 𝜓𝑗𝑐(𝑟) (2.16) The above two equations show that the pseudopotential acting on the valence electrons is the sum of a long-range local attractive potential and a short-range repulsive non-local potential and that it is thus softer than the original potential V.
There is no uniqueness in the definition of pseudopotentials. They are derived either empirically or by ab-initio methods. Emprical pseudopotentials were proposed by Cohen and Bergstresser.11 For deriving empirical pseudopotentials, their parameters are varied to obtain a good agreement with the properties of a series of systems. Cohen and Bergstresser used spectroscopic data to construct the pseudopotentials. The ab-initio pseudopotentials are constructed using atomic all- electron calculations. There should be a good agreement between the valence properties calculated using pseudopotentials and all electron methods. In the calculation related with Ba(BH4)2, described in the thesis ab initio norm-conserving and ultra-soft pseudopotentials were used.
A norm-conserving pseudopotential (NCPP) should be same as the atomic potential outside the
“core region” of radius Rc (Rc = chosen core radius).12 For the pseudopotential to be transferable and reproduce the scattering properties of the real potentials, the logarithmic derivative of the all- electron 𝜓𝑙(𝑟) and nodeless pseudo- 𝜓𝑙𝑃𝑆(𝑟) wavefunctions should agree at Rc. Inside the sphere of radius Rc, the pseudopotential and radial pseudo-orbital 𝜓𝑙𝑃𝑆 differ from their all-electron counterparts but the integrated charge (Ql) should be the same for 𝜓𝑙𝑃𝑆 and for the all-electron radial orbital 𝜓𝑙 for a valence state. The conservation of Ql insures that the total charge in the core region is correct and the normalized pseudo-orbital is equal to the true orbital outside of Rc. Ultrasoft pseudopotentials (USPP) allow to perform calculations with the smallest possible cut- off energy for the plane-wave basis set.4 This requirement becomes important if the study involves the second row and 3d elements because a large number of plane waves are required to describe the localized 2p and 3d valence states.13 This approach was developed independently by
22 Vanderbilt14 and Bloch15. An USPP differs from NCPP mainly due to (a) USPP allow us to choose more than one reference energy per quantum state (l). It guarantees a good transferability over a wide energy range for larger cut off radii rc. (b) USPP allow to choose much larger value for rc as the only restriction is the matching of pseudo and the all-electron function for r > rc. The ultra-soft and norm-conserving radial pseudo wavefunctions for the 2p state of oxygen are shown in Figure 2.2. An all-electron wavefunction is also shown for the comparison.14
Figure 2.2: 2p radial wavefunction for oxygen (solid line), and corresponding norm-conserving and ultrasoft pseudo wave functions (dotted and dashed line respectively).14
2.2.4 Kinetic energy cutoff and Monkhorst-Pack grid
An infinite plane-wave basis set cannot be used and it must be truncated. The expansion of the wavefunction is limited to plane waves characterized by the reciprocal lattice vectors contained within a sphere of the radius defined by the kinetic energy cutoff, Ecut. A larger value of Ecut corresponds to more flexible basis set and thus to more accurate results but at the expense of a higher computational cost. The choice of Ecut is made carefully in order to ensure that the results obtained for the quantities of interest are close to those that may be obtained in the complete basis limit.
23 Many calculations in crystals involve integrating periodic functions of a wave vector over either the entire Brillouin zone (BZ) or over specified portions. For this purpose, methods have been developed to give special points of the BZ that allow for efficient integrations. Chadi and Cohen gave a method to compute functions at carefully selected points in the Brillouin zone.16 The most widely used method was proposed by Monkhorst and Pack.17 It gives a uniform set of points determined by eq (2.17).
𝑘𝑛1,𝑛2,𝑛3 = ∑ 2𝑛𝑖−𝑁𝑖−1
2𝑁𝑖
3𝑖 𝐺𝑖 (2.17) where the Gi are the primitive vectors of the reciprocal lattice.
2.2.5 Details of the periodic calculations performed
Density functional theory18-19 was applied to the characterisation of the structural and vibrational properties of three candidate structures of Ba(BH4)2. Periodic DFT calculations were thus performed with the PBE functional20 using the Quantum Espresso program package, which is based on pseudopotentials and planewaves21. The calculations consisted in geometry optimisations followed by the determination of the phonons at Γ within density functional perturbation theory22. We employed ultrasoft pseudopotentials23 and a 5×4×4 Monkhorst-Pack grid17, and expanded the wavefunctions and the charge density in plane waves up to a kinetic- energy cutoff of 80 Ry and 800 Ry, respectively.
