Computational investigations of the electronic structure of molecular actinide compounds

233 Pages·2009·4.5 MB·English

by  L. Jonasson

Computational Investigations of the
Electronic Structure of Molecular
Actinide Compounds

Submitted by:
L. Jonasson

For the degree of:
Doctor of Philosophy

Supervisor:
Professor N. Kaltsoyannis

University College London, 2009
Abstract
In this PhD thesis the electronic structure of a range of actinide compounds has been
investigated using density functional theory. The reason for using DFT instead of other
methods is mainly due to the size of the compounds which makes multireference
calculations prohibitively expensive, but also to make comparisons with previously
calculated DFT results.
The first chapter presents the basic concepts of electronic structure theory and the
chemical properties of the actinides and lanthanides. The theoretical foundation of DFT
and the consequences of relativity are also introduced.
In the second chapter the bonding in mixed MUCl , MUCl 2-, NpReCl 2- and
6 8 8
PuOsCl 2- (M = Mo, W) systems is investigated and compared with previous work on the
8
M Cl , M Cl 2-, U Cl and U Cl 2- systems. The study shows that the total bonding
2 6 2 8 2 6 2 8
energy in the mixed compounds is the average of the two “pure” compounds.
The third chapter deals with systems of plenary or lacunary Keggin
phosphomolybdate coordination to actinide (Th), lanthanide (Ce, La, Lu) and transition
metal (Hf, Zr) cations: [PMo O ]3-, [PMo O ] 14-, [PMo O ] 6- and
12 40 11 39 2 12 40 2
[PMo O ][PMo O ]10-. These large, highly anionic systems proved to be very
11 39 12 40
challenging computationally. The main result of the study confirms that the bonding is
ionic and that there are few differences in the behaviour of the transition metals.
In the fourth chapter the electronic spectrum of NpO 2+, NpO Cl 2- and
2 2 4
NpO (OH) 2- is calculated using time dependent DFT. TDDFT has proved adequate for
2 4
the uranium analogues of these systems and this extends previous work on f0 systems to
f1 systems. The results show that TDDFT is in poor agreement with both experimental
results and multireference calculations for these compounds.
In chapter five, group 15 and 16 uranyl analogues have been investigated. For the
UE (E = O, S, Se, Te) analogues the geometry bends for all chalcogens heavier than O.
2
The UE 2+ analogues remain linear all the way down group 16. In U(NCH ) 2+ the
2 3 2
formation of a π “back bone” along the axis of the molecule was noted. The σ-bonding
valence MOs stabilize while the π MOs are destabilized down group 15 and 16.
Chapter six is a summary of the results in this thesis and an outlook on potential
future work.
Acknowledgements

I would first like to thank my supervisor Nik Kaltsoyannis for his patience and support in
helping me finish this PhD project. There were times when results were not forthcoming
or needed explanations but he provided stability, calm and guidance at those times.

I would like to thank Jonas Häller for letting me know about UCL and this PhD project as
well as the continuous support in my research and being a fellow Swede abroad. Still
need to work a bit on the nationalism but overall a very good friend. I would also like to
thank Rosie, Luke, Kieran, Amy, Andrea, German, Andy, Ross, Zoso, Matt, Laura and
everyone, past and present, who has been working in G19 for their support and
interesting discussions about a lot of different topics, be they scientific or otherwise. We
are all proof that natural light is vastly overrated!

I have met a lot of people in London who have made the last three years enjoyable. It
would be impossible to name them all here. You know who you are. I would like to
mention a few people I have spent a lot of time with during my time here, Mike, Sophie,
Marta, Zbig and Kasia, who have been flatmates with me. Having to hunt new
accommodation every autumn definitely brings you closer and we have had some great
times together.

My parents, sister, niece and grandparents in Sweden have not seen me that often during
my time in the UK but, thanks to modern technology, I have been able to keep in touch
with them all regularly. I have been home enough each year to rest, relax and enjoy the
incredible nature we take for granted. Their encouragement and backing have helped me
greatly.
Contents
Chapter 1 - Introduction...............................................................................................9
Introduction.............................................................................................................9
General features of the actinides and lanthanides...................................................10
Electronic structure theory.........................................................................................14
Introduction...........................................................................................................14
The Schrödinger equation......................................................................................14
The variational principle........................................................................................16
Linear combination of atomic orbitals....................................................................17
Basis sets...............................................................................................................18
Pauli principle .......................................................................................................21
Slater determinants................................................................................................21
The Hartree-Fock method......................................................................................21
Electron exchange and correlation.........................................................................24
Post-Hartree-Fock methods....................................................................................24
Relativistic effects.....................................................................................................27
Density Functional Theory........................................................................................32
Kohn-Sham density functional theory....................................................................32
The Kohn-Hohenberg theorems.............................................................................32
Calculating the electronic energy...........................................................................33
Exchange-correlation functionals...........................................................................36
Local density approximation..................................................................................37
Generalized gradient approximation......................................................................38
Hybrid functionals.................................................................................................39
Time dependent density functional theory..............................................................40
Atomic charge analysis schemes................................................................................42
Mulliken charge analysis scheme...........................................................................42
Voronoi charge analysis scheme............................................................................43
Hirshfeld charge analysis scheme ..........................................................................43
Mayer bond order analysis.........................................................................................44
Codes........................................................................................................................44
Gaussian03............................................................................................................45
ADF......................................................................................................................46
Frozen core approximation....................................................................................46
Energy decomposition............................................................................................47
Research Projects..........................................................................................................48

Chapter 2 - Analysis of metal-metal bonding in MUCl , MUCl 2-, NpReCl 2- and
6 8 8
PuOsCl 2- (M = Mo, W)...............................................................................................51
8
Introduction...................................................................................................................51
Aim...........................................................................................................................54
Computational details................................................................................................54
Results..........................................................................................................................55
MUCl (M = Mo, W).................................................................................................55
6
Geometry...............................................................................................................55
Electronic structure................................................................................................56
Energy decomposition analysis..............................................................................58
Mayer bond orders.................................................................................................63
MUCl 2- (M = Mo, W)...............................................................................................64
8
Geometry...............................................................................................................64
Electronic structure................................................................................................65
Energy decomposition analysis..............................................................................68
Mayer bond orders.................................................................................................72
NpReCl 2-..................................................................................................................73
8
Geometry...............................................................................................................73
Electronic structure................................................................................................74
Energy decomposition analysis..............................................................................75
Mayer bond orders.................................................................................................76
PuOsCl 2-..................................................................................................................77
8
Geometry...............................................................................................................77
Electronic structure................................................................................................77
Mayer bond order..................................................................................................79
Periodic trends.......................................................................................................79
Conclusions...................................................................................................................82

Chapter 3 - The coordination properties of plenary and lacunary Keggin
phosphomolybdates to tri- and tetravalent cations....................................................84
Polyoxometallates.....................................................................................................84
Aim...........................................................................................................................89
Computational details................................................................................................90
Results..........................................................................................................................92
X[PMo O ] 10- (X = Ce, Th).......................................................................................92
11 39 2
Geometry..................................................................................................................92
Atomic charge analysis..............................................................................................94
Mulliken population analysis.....................................................................................95
Energy decomposition...............................................................................................96
Mayer bond order analysis.........................................................................................97
X[PMo O ]3- and X[PMo O ] 6- (X = Zr4+, Hf4+, La3+, Lu3+)....................................98
12 40 12 40 2
Geometry..................................................................................................................98
Atomic charge analysis............................................................................................101
Hirshfeld charge analysis.....................................................................................101
Voronoi charge analysis.......................................................................................103
Energy decomposition analysis................................................................................105
X[PMo O ]3- (X = Zr4+, Hf4+, La3+, Lu3+)..........................................................105
12 40
X([PMo O ]3-) (X = Zr4+, Hf4+, La3+, Lu3+)......................................................106
12 40 2
Mulliken population analysis...................................................................................108
X[PMo O ][PMo O ]6- (X = Zr4+, Hf4+).................................................................110
11 39 12 40
Energy decomposition.............................................................................................112
Atomic charge analysis............................................................................................112
Mulliken population analysis...................................................................................115
Mayer bond order analysis.......................................................................................116
Conclusions.................................................................................................................118
Chapter 4 - The electronic spectrum of NpO 2+, NpO Cl 2- and NpO (OH) 2- using
2 2 4 2 4
time-dependent density functional theory................................................................120
Introduction.................................................................................................................120
The electronic structure of actinyls..........................................................................120
Uranyl.................................................................................................................120
Neptunyl..............................................................................................................123
Aim.........................................................................................................................125
Computational details..............................................................................................126
Results........................................................................................................................129
Geometry................................................................................................................129
Electronic structure..................................................................................................130
UO 2+ and NpO 2+...............................................................................................130
2 2
UO Cl 2- and NpO Cl 2-.......................................................................................137
2 4 2 4
NpO (OH) 2-........................................................................................................144
2 4
NpO (H O) 2+......................................................................................................149
2 2 5
Na (GeW O ) (NpO ) 14-....................................................................................150
2 9 34 2 2 2
Electronic transitions...............................................................................................152
UO 2+ and NpO 2+...............................................................................................152
2 2
UO Cl 2- and NpO Cl 2-.......................................................................................155
2 4 2 4
NpO (OH) 2-........................................................................................................159
2 4
Na (GeW O ) (NpO ) 14-....................................................................................163
2 9 34 2 2 2
Conclusions.................................................................................................................167

Chapter 5 - Investigations of the bonding and bending in group 15 and group 16
uranyl analogues........................................................................................................169
Introduction.................................................................................................................169
Uranyl analogues.....................................................................................................169
Group 16 uranyl analogues..................................................................................169
Group 15 uranyl analogues..................................................................................171
Aim.........................................................................................................................173
Computational details..............................................................................................174
Results........................................................................................................................175
Geometry of UE 2+ (E = O, S, Se, Te)......................................................................175
2
Electronic structure - UE 2+ (E = O, S, Se, Te).........................................................178
2
SOF electronic structure......................................................................................178
SOC electronic structure......................................................................................181
SOF molecular orbital Mulliken decomposition...................................................183
Mulliken atomic orbital population analysis.............................................................186
Atomic charge analysis............................................................................................188
Energy decomposition - UE 2+ (E = O, S, Se, Te)....................................................190
2
Geometry of UE (E = O, S, Se Te).........................................................................193
2
Electronic structure..................................................................................................196
E-U-E = 180°.......................................................................................................196
E-U-E = 120°.......................................................................................................199
Why is UE 2+ linear and UE (E = O, S, Se, Te) bent?.............................................202
2 2
Geometry of U(XR) 2+ (X = N, P, As; R = H, CH ).................................................204
2 3
Electronic structure - U(XR) 2+ (X = N, P, As; R = H, CH )....................................207
2 3
U(XR) 2+ (X = N, P, As; R = H)..........................................................................207
2
U(XR) 2+ (X = N, P, As; R = CH ).......................................................................209
2 3
Mulliken population analysis...................................................................................214
Mayer bond order analysis.......................................................................................214
Atomic charge analysis............................................................................................215
Conclusions.................................................................................................................217

Chapter 6 - Summary................................................................................................219

Appendix 1 - Electronic structure of Na (Ge W O ) (NpO ) 14- and electronic
2 2 9 34 2 2 2
transitions in NpO Cl 2- and NpO (OH) 2-...............................................................222
2 4 2 4

References..................................................................................................................226
Chapter 1
Introduction

Actinides
Introduction
All of the projects in this thesis are connected to the actinides, a group of elements
usually confined to the outskirts of chemistry. Many of the actinides are radioactive and,
when moving across the series, increasingly short-lived, making experimental
investigations of them difficult and expensive. However, the field of actinide chemistry
does exist and the following section will give a brief overview of the chemical properties
of the actinides and the f-block elements in general. A more in depth introduction into the
electronic structure of uranium and neptunium containing systems will follow in Chapter
4, relating to the investigation of the electronic structure of species containing these
atoms.

Figure 1.1. The general set of 5f orbitals as calculated in ADF
9
Chapter 1 - Introduction

General features of the actinides and lanthanides
The elements in the periodic table with atomic number 57-71 are known as the
lanthanides after the first element of the series, lanthanum. Similarly, elements 89-103 are
referred to as the actinides, named for actinium. Moving across both series the primary
shell being filled is the f shell, 4f for the lanthanides and 5f for the actinides, with the 5f
orbitals displayed in Figure 1.1.

5
e
at 4
st
n
o
dati 3
xi
o
al
m
r 2
o
F
1
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Figure 1.2. The formal oxidation states of the lanthanides. Filled circles represent the
most common oxidation states, open circle indicate other possible oxidation states

In neutral lanthanides the valence electrons are distributed in the 4f, 5d and 6s orbitals.
As the lanthanides are ionized, these orbitals are stabilized due to experiencing an
increased effective nuclear charge, with the 4f orbitals being the most stabilized orbital.
After three ionizations the 5d and 6s orbitals are emptied and the 4f orbitals so stabilized
that the energy of removing additional electrons exceeds the energetic gain of forming a
bond in the +4 oxidation state; thus the 4f is rendered inaccessible for chemical reactions.
This is one of the main characteristics of lanthanide chemistry; almost all the lanthanides
prefer the +3 oxidation state, with a few exceptions such as when the f shell can become
empty (f0), half-filled (f7) or full (f14). One example of this is Ce which has been found at
+4.1

10