Title: Computational study of silicon clusters doped by some main group elements
Other Titles: Computationele studie van silicium clusters gedopeerd door enkele hoofdgroep elementen
Authors: Nguyen Minh, Tam; S0222473
Issue Date: 10-Sep-2014
Abstract: <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none">This doctoral thesis reports the theoreticalinvestigations on the geometrical and electronic structures of small siliconclusters doped with some representative main group elements, including Li, Mg,B, Al and also C by using quantum chemical calculations. Deep understanding oftheir geometric and electronic structures, energetics and bonding phenomenaconstitutes a necessary step in the extensive and intensive search forpromising clusters that could be considered as building blocks for furtherassemblies. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none">Our searches for minima on thepotential energy surfaces were performed using two different approaches. In thefirst, we used a stochastic genetic algorithm to generate as many guessstructures as possible. Equilibrium structures that were initially detectedusing low-level computations, were then reoptimized using higher level methods.In the second approach, we made use of a chemical intuition, in that initialstructures of clusters SinXm were manually constructedby either substituting Si-atoms of the corresponding silicon frameworksby other element atoms, or adding dopant-atoms at various positions on surfacesof the Sin clusters. Theuse of the genetic algorithm is less effective for producing singlydoped-clusters having small sizes because most of relevant structures in Si clustersare relatively well known. On the contrary, the multi-doped and larger sizeclusters imply a huge number of initial guess structures and thus make thegenetic search necessary and more effective, even though such a search is oftentedious and computationally demanding. Nevertheless, only a combination ofdifferent search approaches allows a consistent set of lower-energy structuresto be obtained. We are confident that the isomers reported in this thesis atleast correspond to the lower-energy equilibrium structures. However, not onlya careful search is required, but the accuracy of the computational methodsused is equally crucial in the determination of global minima. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none">The low-lying isomers of the clusterswere identified on the basis of theoretical results obtained by hybrid (U)B3LYPfunctional in conjunction with the 6-311+G(d) basis set (d polarization plus spdiffuse functions), and then the ground states are assigned by high accuracy computationalmethods such as the composite G3B3 and G4 methods and when possible also the coupled-clustertheory extrapolated to the complete basis set CCSD(T)/CBS protocol. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%">Concerningthe energetics, different basic thermochemical parameters of the clustersconsidered including total atomization energies (TAE), standard enthalpies offormation (<span style="font-size:10.0pt;line-height:150%;mso-bidi-font-family:&quot;Times New Roman&quot;">&#916;Hf),ionization energies (IE), electron affinities (EA), binding energies (Eb), embedded energy (EE) anddissociation energies (De)were determined using the Gn (G3B3and G4) and CCSD(T)/CBS approaches. For bare silicon clusters, a<span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;"> uniform set of standard heats offormation for the cationic and anionic Sinclusters were determinedfor up to n = 13<span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;">. Insome cases, variations between G4 and CBS TAE values are relatively large. The differences of energeticproperties between both G4 and CBS methods can be understood from the ways ofcomputing single point electronic energies, as well as the geometries ofclusters used. Geometry is beyond any doubt an important factor in thethermochemical evaluation. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%"><span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;">For these systems, experimentalresults in the current literature were also characterized by large uncertainties,including the actual uncertainty of the standard heat of formation of the Siatom. For otherparameters such as IE<span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;">s and EAs,they were better predicted, in part due to a certain mutual cancellation oferrors in the evaluation of relative energies. The corresponding G4 results areexpected to be accurate to, or even better than, &plusmn; 0.15 eV. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%">For lithiumdoped silicon clusters, the adiabatic (AIEs) and vertical (VIEs) ionizationenergies of the SinLim clusters were evaluated. CalculatedAIE and VIE values at the B3LYP/6/311+G(d) and CCSD(T)/aug-cc-pVDZ levels forSi6Li2, Si7Li, Si10Li, Si11Licompare quite well with the corresponding experimental results obtained usingthe photo-ionization efficiency measurements.<p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%">For borondoped silicon clusters, heats of formation calculated by both G4 andCCSD(T)/CBS methods showed good agreement with available experimental data.<p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none"><span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;">Overall, it appears that an accurateevaluation of the TAEs and thereby the standard heats of formation of silicon-basedclusters remains a great challenge for<span style="font-size:10.0pt;line-height:150%"> quantum chemical computations in order to attain thechemical accuracy of <span style="font-size:10.0pt;line-height:150%;mso-bidi-font-family:&quot;Times New Roman&quot;">&plusmn;<span style="font-size:10.0pt;line-height:150%"> 1.0 kcal/mol. Due to the non-classical bonding of clusters,the use of other thermochemical approaches (such as bond separation reactions)and more economic computational methods could not be applied. The only optionleft is to increase the quality of the wavefunctions in going beyond theCCSD(T) level. However, our preliminary computations using the full CCSDT treatmentpointed out that it is much more computer-demanding than the CCSD(T) method,which goes beyond our actual computing resources. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none">Based on the geometricalcharacteristics of the ground states, a growth mechanism for each series ofbinary silicon clusters SinXm can now beestablished. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%;mso-layout-grid-align:none;text-autospace:none">Generally, alkali (Li) orearth-alkali (Mg) dopants prefers add on an edge or a face of Sin frameworks, whereas theboron group 13 element (B, Al) favors substitution into one of the Si positionsin Sin+1counterparts. Due to the shorter B-Si bond lengths, as compared with the Al-Si counterparts,the B impurity can intrude inside the corresponding Si<i style="mso-bidi-font-style:normal">n cage (for up to n&#8805; 8). In particular, the neutral structures of doubly impurities doped siliconclusters SinX2,(X = Li, Mg, Al) have similar way of growing up: one dopant atom substitutesinto a position of Sin+1,whereas the other is usually added on an edge, or a face, of the existingcluster.<p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%">Our theoretical results also predicted that some closed-shellsystems such as Si9B-, Si10B+ , Si9Al-,and Si4C2+ are characterized by enhanced stabilities. Theirhigher thermodynamic stabilities can be understood by the Jellium shell model(JSM)<span style="font-size:10.0pt;line-height:150%;font-family:&quot;Times-Roman&quot;,&quot;serif&quot;;mso-bidi-font-family:Times-Roman">. <span style="font-size:10.0pt;line-height:150%">According to JSM, the valence electrons are supposed to befreely itinerant in a simple mean-field potential formed by the nuclei of atomsand core electrons, the valence electrons fill the hydrogen-like orbitals &#8204;&#8204;followingthe pattern of orbitals as [1S21P61D102S21F142P61G182D10…]etc… Within this model, the numbers of valence electrons of 8, 20, 34, 40, 56and 68… emerge as the magic numbersthat actually correspond to a complete filling of the successive shellelectrons. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%"><span style="font-size:10.0pt;line-height:150%;mso-bidi-font-family:&quot;Times New Roman&quot;">Concerning the bonding phenomena, electron localization <span style="font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:150%;mso-ansi-language:EN-GB;mso-fareast-language:EN-GB" lang="EN-GB">techniques (ELF and ELI-D)were used <span style="font-size:10.0pt;line-height:150%;mso-bidi-font-family:&quot;Times New Roman&quot;">to locate the whereabouts of electrons, and thereby toidentify the chemical bonds of some specific clusters such as Si­3,Si4, Si42+, Si4C2+, andSi9C. Calculations of the ring current, which is the magneticresponse of a molecule, were also carried out in order to probe <span style="font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:150%;mso-ansi-language:EN-GB;mso-fareast-language:EN-GB" lang="EN-GB">their aromaticity. This study provided a further supportfor the point of view that the existence of delocalized occupied molecularorbitals in a planar molecule is a necessary but not sufficient condition toassign a certain aromatic character (aromatic, non-aromatic or anti-aromatic)to that specific type of electrons. Different criteria (such as the magneticring current) need to be considered for a more consistent evaluation of thispopular but intriguing molecular property. <p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%">In addition, both the Si4C2+dication and the SiC9 neutral exhibit a planar tetracoordinatecarbon atom (ptC) in their lowest-lying isomer. This is caused by a drivingforce for C-planarization which includes not only the electron delocalizationon the square frame but also the bonding between C-dopant and the Si frame of thesmall dication. In the larger neutral cluster cage, the Si5 grouptends to stabilize electronically the cage by electron transfer but alsomechanically by geometrical constraints in maintaining a ptC configuration. <span style="font-size:10.0pt;mso-bidi-font-size:11.0pt;line-height:150%;mso-ansi-language:EN-GB;mso-fareast-language:EN-GB" lang="EN-GB"><p class="MsoNormal" style="margin-top:6.0pt;text-align:justify;text-indent:.5in;line-height:150%"><span style="font-size:10.0pt;line-height:150%;mso-bidi-font-family:&quot;Times New Roman&quot;">We also attempted to search for potential linkers in makingsilicon nanowires. We found that the Mg dopant, due to its large electrontransfer capacity, behaves as a cation Mgdelta+ and thereby induces anionic entity with the Sindelta-anionic partner. The resulting Mg cation can be served as a linker between Sin blocks leading tostabilized linear [(Sik)Mg]lstructures in part due to electrostatic attraction forces. <span style="font-size:10.0pt;line-height:150%;mso-fareast-font-family:Calibri;mso-bidi-font-family:&quot;Times New Roman&quot;;mso-ansi-language:EN-GB;mso-fareast-language:EN-GB" lang="EN-GB">This allowed us to identify some suitable membersthat can further be used as superatoms for assemblies. We thus probed thefive-, seven-, eight- and ten-atom Si building blocks, and the role of the Mgelement as the linkers connecting them. <span style="font-size:10.0pt;line-height:200%;font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">Calculated results ofthe average assembling energy which gave us an idea about the tendency ofassembling the cluster of (SikMg)l with <i style="mso-bidi-font-style:normal">k = 5, 7, 8, 10, show that silicon clusters Si<i style="mso-bidi-font-style:normal">k tend to assemble in ring forms (<b style="mso-bidi-font-weight:normal">Rl) over the linear forms(Ll)as the assembling energy of the Rl are larger than those of the Ll.However, a more important fact is that the average assembling energy of thelinear form tends to increase with the increasing size (<b style="mso-bidi-font-weight:normal">l), implying that a(longer) nanowire can be considered as a plausible possibility.<span style="font-size:10.0pt;line-height:200%;font-family:&quot;Times New Roman&quot;,&quot;serif&quot;;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA">
Table of Contents: Table of Contents

Chapter 1. Introduction 1
Chapter 2. Determination of Atomization Energies and Heats of Formation 13
2.1. Heats of formation and total atomization energies 14
2.2. Choice of quantum chemical methods 18
2.2.1. The Coupled-cluster theory 18
2.2.2. The Composite G4 method 20
2.2.3. The Complete basis set approach (CCSD(T)/CBS) 22
2.2.4. Total Atomization Energies (TAE) 23
2.3. Total atomization energies, heats of formation and thermochemical parameters of small silicon clusters and their ions using G4 and CBS method 24
2.3.1. Shape of the lowest-lying isomers of Sin clusters and their ion 25
2.3.2. Total atomization energies (TAE) 27
2.3.3. Heats of formation (∆fHo) 31
2.3.4. Electron affinities (EA) and ionization energies (IE) 32
2.3.5. Relative stability of clusters and dissociation energies 35
2.4. Concluding remarks 38
Chapter 3. Singly and doubly lithium doped silicon clusters: Geometrical and electronic structures and ionization energies 45
3.1. Introduction 46
3.2. Experimental results 47
3.3. Computations 48
3.4. Results and discussion 49
3.4.1. Structures of SinLim0/+ with n = 2-11 and m = 1,2 49
3.4.2. Growth Mechanisms of SinLim0/+ 62
3.4.3. Dissociation Energies 66
3.5. Concluding remarks 68
Chapter 4. Thermochemical Parameters and Growth Mechanism of the Boron Doped Silicon Clusters 71
4.1. Introduction 72
4.2. Computational methods 73
4.3. Results and discussion 74
4.3.1. Thermochemical properties of clusters 74
4.3.2. Lower-lying isomers of SinB clusters and their growth mechanism 78
4.3.3. Relative stability of clusters considered 87
4.3.4. Dissociation energies 90
4.3.5. Enhanced stability and Jellium electron shell model (JSM) 91
4.4. Concluding remarks 94
Chapter 5. Structure, Thermochemical Properties and Growth Sequence of Aluminum Doped Silicon Clusters and Their Anions 97
5.1. Introduction 98
5.2. Computational methods 98
5.3. Results and discussion 99
5.3.1. Lower-lying isomers of SinAlm clusters in both neutral and anionic states 99
5.3.2. Equilibrium growth sequence of the SinAlm clusters 112
5.3.3. Thermochemical properties 114
5.3.4. Thermodynamic stability of clusters 117
5.3.5. Dissociation energies 119
5.3.6. Jelium electron shell model (JSM) 121
5.4. Concluding remarks 124
Chapter 6. SinMgm: Toward Silicon Nanowires with Magnesium Linkers 127
6.1. Introduction 128
6.2. Lower-lying isomers of SinMgm clusters in both neutral and cationic states 129
6.2.1. The singly magnesium doped SinMg0/+ 130
6.2.2. The doubly magnesium doped SinMgm0/+ with n = 1-10 and m = 2 133
6.3. Growth pattern of the equilibrium SinMgm clusters 139
6.4. Thermochemical properties 140
6.5. Thermodynamic stability 142
6.6. In search of silicon nanowires with magnesium linkers 143
6.7. Concluding remarks 148
Chapter 7. Chemical Bonding in Si3, Si4, Si42+, Si4C2+ and Si9C 151
7.1. Introduction 152
7.2 The silicon trimer 154
7.2.1. A qualitative analysis of the electronic states: the Walsh diagrams of Si3 155
7.2.2. An analysis of the chemical bonding of Si3 158
7.2.3. Ring current and aromaticity 159
7.3. The silicon tetramer: Si4, Si42+ and Si4C2+ 162
7.3.1. Structure of the tetramer Si4 and its dication Si42+ 162
7.3.2. Structure of the doped dication Si4C 2+ 167
7.4 Si9C: A stable C-doped silicon cluster 171
7.5 Concluding remarks 173
Chapter 8. General Conclusions and Perspectives 177
ISBN: 978-90-8649-744-7
Publication status: published
KU Leuven publication type: TH
Appears in Collections:Quantum Chemistry and Physical Chemistry Section

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