Magnetic properties of cobalt clusters (20 N 200) were studied in molecular beams. The magnetization of cobalt clusters is studied at a broad range of temperatures, magnetic fields and clusters sizes. It is shown that the agnetization of ferromagnetic clusters in a cluster beam can be understood as an adiabatic process using the avoided crossing theory. Besides the ground state that bears magnetic moment of about 2 Bohr magneton per atom, an excited state that has 1 Bohr magneton per atom was discovered for every cobalt cluster observed. The energy separations between the two states was investigated by photo-ionization experiments. The ionization threshold shows that the energy gap between the two states is on the order of 0.1 eV for small clusters (N 100) and vanishes for larger clusters. Experiments also show that the polarizability of the excited state is lower than that of the ground state, which indicates a significant electronic tructure difference between the two states. Two states are also found for iron clusters (20 N 200) for which the magnetic moments per atom are about 3 Bohr magneton for the ground state and 1 Bohr magneton for the excited states. This explains the fractional magnetic moments as well as the local magnetic order observed above the Curie temperatures for iron group ferromagnets. Further experiments show two states for manganese clusters for which the ground state has magnetic moment of 1 Bohr magneton per atom in about the same size range. This suggests that the two states are a universal phenomenon of 3d transition metal clusters, which originate from the interaction between 3d and 4s electrons.

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<p>Vaggeryd is a rural municipality and wants to develop its rural areas. Therefore Vaggeryd’s municipality wants to become a cluster region within the equus industries and hence become an equine municipality where equestrians can live and run their businesses as well as providing for equine activities and competitions. The reason why it is interesting to create a cluster region is because it comes with benefits for the companies and it helps developing the regional economy (Enright, 1998; Porter, 2000). “Clusters lower barriers to new business formation that improve the environment for productivity.” (Porter, 1998a). One investment made in 2005 in the direction of becoming an equine municipality was the start up of an Advanced Vocational Education [KY] in the region, named Horse Entrepreneur.</p><p>All 23 students in this programme, year 2005 and 2006, were interviewed and it turned out that all of them wanted to start up own businesses within 10 years, but only three planned to establish their companies in Vaggeryd. Most of the students planned to move back to their home municipality. Eight students in total could, however imagine themselves establishing in Vaggeryd. The students thought that this kind of education is very important for equestrians who want to start up businesses.</p><p>The students believed that Vaggeryd’s municipality will become a good and functional equine municipality and referred to the highway E4 (which runs through the municipality), the race track and the veterinary clinic. More farms with large lands are what the students think the municipality council should invest in to attract equine companies as well as to become an equine friendly municipality.</p><p>From the cluster analysis a similar result was found. It showed that there is no agglomeration in the four investigated industries over Sweden, namely horse breeding, horse competitions, managing race tracks and gallops courses and riding educational services and horse rents. This means that the places where the entrepreneurs choose to set up their businesses are less important; hence they can likewise set up in Vaggeryd.</p><p>However a trend was expected. The districts where most of the equine businesses in Sweden take place are rural areas close to populated regions, so called semi-urban areas.</p><p>There are no cities in Vaggeryd’s municipality only two towns, Vaggeryd and Skillingaryd. The conclusion drawn is that if Vaggeryd wants to become an equine municipality it must invest (Enright, 1998; Malmberg, 2002). For example creating job opportunities, and building farms on areas with large lands. These investments are needed to attract inhabitants and business people to their municipality before the equine companies can flourish. Investments make this type of clusters attractive (Enright, 1998; Malmberg, 2002).</p><p>The cluster data revealed that there are no equine activities in Vaggeryd’s municipality today; however it has the possibility to become an equine municipality due to suitable condition, for example land plots with lakes and the closeness to highway E4.</p><p>Vaggeryd should focus on facilitating business activities and providing with updated networks in order for companies to gain from being clustered, according to the cluster theory advocated by von Hippel (1988) and Hakansson (1987). Vaggeryd suits for equine businesses which are trading goods and services with other businesses, hence which are not dependent on a location close to cities, according to Karlsson (2008) in the field of clustering in smaller regions.</p>

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaves [97]-102).

Stakeholders play an important role for firm’s performance and survival. Being able to balance multiple stakeholder’s needs an interest simultaneously and at the same time achieve best value for provided services/products is often referred to "acting as an informed client". Real estate firms should be more involved with core stakeholders (their tenants) in order to improve their corporate social performance and productivity. Cluster theory distinguish how certain industries and firms can be interconnected, developing collaborations through geographical proximity. The effects are asymmetrical, dependent on the type cluster, the type of product/services and the firm’s included in the cluster. By combining stakeholder management and cluster theory, real estate firms are able to improve their knowledge regarding tenant’s interconnection and contribute to the development of already identified clusters within the Stockholm County. The aim of this thesis is to contribute to the ongoing research regarding stakeholder management, with the usage of cluster theory. A quantitative- and qualitative analysis is conducted, using a self-administered questionnaire. A total amount of 64 retail tenants (around 80% response rate) and 28 office tenants (around 12% response rate) participated in the study. Results from the quantitative- and qualitative analysis is triangulated with secondary data, aimed to improve the reliability of the results. Both retail- and office tenants were invited to the study and the correlation between the two targets groups was determined, aimed to measure office tenant’s perception regarding cluster externalities. Results from the analysis shows that industries like information and communication, business services and credit and insurance are considered to be clustered. The highest level of science base diversity is achieved by those industries, implying a strong presence of activities sharing a common knowledge base. Retail tenant’s value suitable products (question 3) and proximity to their costumer (question 6), while office tenants value personal contacts (question 24) and proximity to major transportation routes (question 10). In addition, retail tenants have a positive attitude towards cluster externalities, while office tenants have dived perceptions or simply ignores cluster externalities, explained by the insignificant correlation between their answers. The conclusion of the study is that further research is needed, using a more extensive qualitative analysis. A larger share of participants active within industries that are considered to be clustered will provide real estate firms with the knowledge of how to proceed with their stakeholder management. It is therefore considered that certain office tenants are dependent on cluster externalities and that real estate firms should actively engage in their business, acting as a "business in society". / Intressenter har en stor påverkan på ett företags utveckling och överlevnad. Att hitta en balans mellan att tillgodose olika intressenters intressen och behov, samtidigt som man utvinner högsta avkastning för genomförda produkter/tjänster, kallas "acting as an informed client". Fastighetsföretag bör vara mer involverade med sina nyckelintressenter, allt för att kunna förbättra sin produktivitet och sitt samhällsansvar. Klusterteori identifierar hur olika sektorer kan vara sammankopplade i form av samarbeten, något som uppkommit genom en geografisk koncentrering av olika företag. Effekterna från klustring är åtskilda och beror oftast på karaktären av klustret, vilken typ av produkter/tjänster som klustret erbjuder, samt vilka typer av företag som är inkluderade i klustret. Genom att kombinera klusterteori med intressenthantering, ges fastighetsföretag möjlighet att utveckla sin kunskap gällande intressenters sammankopplingar, något som kan komma att stärka den pågående utvecklingen av Stockholms olika kluster. Syftet med examensarbetet är att bidra till pågående forskning inom området för intressenthantering, med hjälp av klusterteori. En kvantitativ och kvalitativ studie har genomförts, den kvalitativa studien baseras på en enkät. Totalt deltog 64 butikshyresgäster (80% svarsfrekvens) och 28 kontorshyresgäster (12% svarsfrekvens) i studien. Resultatet från den kvantitativa och kvalitativa studien har triangulerats, med avsikt att öka reliabiliteten av studien. Både butiks-och kontorshyresgäster var inbjudna till att delta i studien och korrelationen mellan de två fokusgrupperna fastställdes, allt för att kunna mäta kontorshyresgästers förhållningssätt gentemot klustringseffekter. Resultatet från studien visar att sektorer så som information- och kommunikation, företagstjänster, kredit- och försäkringar anses vara klustrade. Det högsta värdet gällande grunden för kunskapsdiversifiering uppmättes av dessa sektorer, vilket i sin tur symboliserar att företag inom klusterna delar gemensamma kunskapsområden. Butikshyresgäster värderar faktorer så som, anpassade produkter (fråga 3) och närheten till sina kunder (fråga 6), medan kontorshyresgästerna värderar personliga kontakter (fråga 24) och närheten till snabba transportmöjligheter (fråga 10). Ytterligare så uppvisar butikshyresgäster ett intresse för klustringseffekter, medan kontorshyresgäster uppvisar ringa intresse eller olika intresse gällande klustringseffekter, vilket kan förklaras med den insignifikanta korrelationen mellan de två grupperna. Slutsatsen från examensarbetet är att mer kvalitativ forsning inom området är nödvändigt, för att kunna säkerställa huruvida kontorshyresgäster värderar klustringseffekter. Vidare ska ytterligare forskning fokusera på sektorer som anses vara klustrade inom Stockholmsområdet, allt för att kunna urskilja hur fastighetsföretagen ska kunna utveckla sin intressenthantering. Studien påvisar att det finns företag på Stockholmsmarknaden som använder sig av klustringseffekter och att fastighetsföretagen bör aktivt föra en dialog med dessa företag, för att kunna agera som ett "företag i samhället".

Despite the fact that higher-order tensors (HOTs) plague electronic structure methods and severely limits the modeling of interesting chemistry problems, introduction and application of higher-order tensor (HOT) decompositions, specifically the canonical polyadic (CP) decomposition, is fairly limited. The CP decomposition is an incredibly useful sparse tensor factorization that has the ability to disentangle all correlated modes of a tensor. However the complexities associated with CP decomposition have made its application in electronic structure methods difficult. Some of the major issues related to CP decomposition are a product of the mathematics of computing the decomposition: determining the exact CP rank is a non-polynomially hard problem, finding stationary points for rank-R approximations require non-linear optimization techniques, and inexact CP approximations can introduce a large degree of error into tensor networks. While other issues are a result of the construction of computer architectures. For example, computer processing units (CPUs) are organized in a way to maximize the efficiency of dense linear algebra and, thus, the performance of routine tensor algebra kernels, like the Khatri-Rao product, is limited. In this work, we seek to reduce the complexities associated with the CP decomposition and create a route for others to develop reduced-scaling electronic structure theory methods using the CP decomposition. In Chapter 2, we introduce the robust tensor network approximation. This approximation is a way to, in general, eliminate the leading-order error associated with approximated tensors in a network. We utilize the robust network approximation to significantly increase the accuracy of approximating density fitting (DF) integral tensors using rank-deficient CP decompositions in the particle-particle ladder (PPL) diagram of the coupled cluster method with single and double substitutions (CCSD). We show that one can produce results with negligible error in chemically relevant energy differences using a CP rank roughly the same size as the DF fitting basis; which is a significantly smaller rank requirement than found using either a nonrobust approximation or similar grid initialized CP approximations (the pseudospectral (PS) and tensor hypercontraction (THC) approximations). Introduction of the CP approximation, formally, reduces the complexity of the PPL diagram from 𝓞(N⁶) to 𝓞(N⁵) and, using the robust approximation, we are able to observe a cost reduction in CCSD calculations for systems as small as a single water molecule. In Chapter 3, we further demonstrate the utility of the robust network approximation and, in addition, we construct a scheme to optimize a grid-free CP decomposition of the order-four Coulomb integral tensor in 𝓞(N⁴) time. Using these ideas, we reduce the complexity of ten bottleneck contractions from 𝓞(N⁶) to 𝓞(N⁵) in the Laplace transform (LT) formulation of the perturbative triple, (T), correction to CCSD. We show that introducing CP into the LT (T) method with a CP rank roughly the size of the DF fitting basis reduces the cost of computing medium size molecules by a factor of about 2.5 and introduces negligible error into chemically relevant energy differences. Furthermore, we implement these low-cost algorithms using newly developed, optimized tensor algebra kernels in the massively-parallel, block-sparse TiledArray [Calvin, et. al Chemical Reviews 2021 121 (3), 1203-1231] tensor framework. / Doctor of Philosophy / Electronic structure methods and accurate modeling of quantum chemistry have developed alongside the advancements in computer infrastructures. Increasingly large and efficient computers have allowed researchers to model remarkably large chemical systems. Sadly, for as fast as computer infrastructures grow (Moores law predicts that the number of transistors in a computer will double every 18 months) the cost of electronic structure methods grows more quickly. One of the least expensive electronic structure methods, Hartree Fock (HF), grows quartically with molecular size; this means that doubling the size of a molecule increase the number of computer operations by a factor of 16. However, it is known that when chemical systems become sufficiently large, the amount of physical information added to the system grows linearly with system size.[Goedecker, et. al. Comput. Sci. Eng., 2003, 5, (4), 14-21] Unfortunately, standard implementations of electronic structure methods will never achieve linear scaling; the disparity between actual cost and physical scaling of molecules is a result of storing and manipulating data using dense tensors and is known as the curse of dimensionality.[Bellman, Adaptive Control Processes, 1961, 2045, 276] Electronic structure theorists, in their desire to apply accurate methods to increasingly large systems, have known for some time that the cost of conventional algorithms is unreasonably high. These theorists have found that one can reveal sparsity and develop reduced-complexity algorithms using matrix decomposition techniques. However, higher-order tensors (HOTs), tensors with more than two modes, are routinely necessary in algorithm formulations. Matrix decompositions applied to HOTs are not necessarily straight-forward and can have no effect on the limiting behavior of an algorithm. For example, because of the positive definiteness of the Coulomb integral tensor, it is possible to perform a Cholesky decomposition (CD) to reduce the complexity of tensor from an order-4 tensor to a product of order-3 tensors.[Beebe, et. al. Int. J. Quantum Chem., 1977, 12, 683-705] However, using the CD approximated Coulomb integral tensors it is not possible to reduce the complexity of popular methods such as Hartree-Fock or coupled cluster theory. We believe that the next step to reducing the complexity of electronic structure methods is through the accurate application of HOT decompositions. In this work, we only consider a single HOT decomposition: the canonical polyadic (CP) decomposition which represents a tensor as a polyadic sum of products. The CP decomposition disentangles all modes of a tensor by representing an order-N tensor as N order-2 tensors. In this work, we construct the CP decomposition of tensors using algebraic optimization. Our goal, here, is to tackle one of the biggest issues associated with the CP decomposition: accurately approximating tensors and tensor networks. In Chapter 2, we develop a robust formulation to approximate tensor networks, a formulation which removes the leading-order error associated with tensor approximations in a network.[Pierce, et. al. J. Chem. Theory Comput., 2021 17 (4), 2217- 2230] We apply a robust CP approximation to the coupled cluster method with single and double substitutions (CCSD) to reduce the overall cost of the approach. Using this robust CP approximation we can compute CCSD, on average, 2.5-3 times faster and introduce negligibly small error in chemically relevant energy values. Furthermore in Chapter 3, we again use the robust CP network approximation in conjunction with a novel, low cost approach to compute order-four CP decompositions, to reduce the cost of 10 high cost computations in the the perturbative triple, (T), correction to CCSD. By removing these computations, we are able to reduce the cost of (T) by a factor of about 2.5 while introducing significantly small error.

In the search for molecular species in the interstellar medium and extraterrestrial planetary atmospheres, theoretical methods continue to be an invaluable tool to astronomically minded chemists. Using state-of-the art methods, this doctoral work characterizes the electronically excited states of interstellar radicals, cations, and even rare anions and also predicts the gas phase fundamental vibrational frequencies of the cis and trans-HOCO radicals, as well as the cis-HOCO anion. First, open-shell coupled cluster methods of singles and doubles (CCSD) and singles and doubles with triples-inclusion (CC3) are tested on the C₂H and C₄H radicals. The significant double-excitation character, as well as the quartet multiplicity of some states yields inaccurate excitation energies and large spin contamination with CCSD. CC3 somewhat improves this for select states, but discrepancies between CC and multireference results for certain states exist and likely arise from the lack of spin adaptation in conventional spin-orbital CC. Next, coupled-cluster methods predict the presence of an excited state of the closed-shell allyl cation and its related H₂CCCHCH₂⁺ cousin at 443 nm near an unidentified laboratory peak at 442.9 nm which is also close to one of the largest unattributed interstellar absorption features. Additionally, the dipole moments, electron binding energies, and excited states of neutral radicals and corresponding closed-shell anions of interstellar interest are also computed. These are calibrated against experimental data for CH₂CN⁻ and CH₂CHO⁻. Since coupled cluster theory closely reproduces the known experimental data, dipole-bound excited states for eight previously unknown anions are predicted: CH2SiN⁻ , SiH₂CN⁻, CH₂SiHO⁻, SiN⁻, CCOH⁻, HCCO⁻, SiCCN⁻, and SiNC⁻. In addition, we predict the existence of one rare valence-bound excited state of CH₂SiN⁻ and also SiCCN⁻ as well as even rarer two valence-bound states of CCSiN⁻. Lastly, the reaction of CO + OH and its transient potential intermediate, the HOCO radical, may be responsible for the regeneration of CO₂ in the Martian atmosphere, but past spectroscopic observations have not produced a full gas-phase set of the fundamental vibrational frequencies of the HOCO radical. Using established, highly-accurate quantum chemical coupled cluster tech- niques and quartic force fields, all six fundamental vibrational frequencies for 1 ²A′ cis and trans-HOCO and 1 ¹A′ cis-HOCO⁻ are computed in the gas phase. / Ph. D.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: The binary cluster model is used to investigate the properties of exotic structures and decays in various nuclei. A simple method is described to choose the possible clusters forming within the nucleus, by assuming the nucleus consists of a mixture of up to four different core-cluster pairs. A phenomenological potential is then used, with optimized parameters, to describe the even-even 222-232Th nuclei within the binary cluster model, by calculating exotic decay half-lives, reduced electromagnetic transition probabilities, and energy spectra. After finding that all experimentally observed heavy ion emissions are predicted with the model and calculated structure observables are reproduced within good agreement of the experimentally measured values, the model was extended to include the even-even 230-234U, 236-240Pu and 222-224Ra nuclei. We found that almost all experimentally observed heavy ion emissions are predicted within the model with reasonable accuracy in the calculated halflives, and found good agreement in the other calculated structure observables. / AFRIKAANSE OPSOMMING: Die binêre bondel model is gebruik om die eienskappe van eksotiese strukture en verval in verskeie nukliedes te ondersoek. ’n Eenvoudige metode is gebruik om die moontlike bondels wat binne die nuklied vorm te kies, deur die aanname te maak dat die nuklied uit ’n mengsel van tot vier verskillende kern-bondel pare bestaan. ’n Fenomenologiese potensiaal is dan gebruik, met optimale parameters, om die ewe-ewe 222-232Th nukliedes met die binêre bondel model te beskryf, deur eksotiese verval halfleeftye, verminderde elektromagnetiese oorgangswaarskynlikhede, en energie spektra te bereken. Nadat daar gevind is dat alle vrygestelde swaar ione wat eksperimenteel waargeneem is deur die model voorspel word, en berekende struktuur waarneembares tot goeie ooreenstemming met die eksperimentele waardes produseer is, is die model uitgebrei om die ewe-ewe 230-234U, 236-240Pu en 222-224Ra nukliedes in te sluit. Daar is gevind dat byna alle vrygestelde swaar ione wat eksperimenteel waargeneem is deur die model voorspel word met redelike akkuraathied in die berekening van hul halfleeftye, asook dat daar goeie ooreenstemming tussen die berekende en eksperimentele waardes van ander struktuur waarneembares was.

Thesis (PhD (Physics))-University of Stellenbosch, 2009. / ENGLISH ABSTRACT: A binary cluster model is used to investigate the properties of the ground state band of 212Po, modelled as a 208Pb-alpha core-cluster system. The results obtained using a microscopic corecluster potential are compared to those obtained with a purely phenomenological potential. The two potentials were found to exhibit similar surface behaviour and thus give similar predictions for the ground state alpha decay half-life. They however generate very different energy spectra, with the results from the phenomenological potential clearly superior. We optimize the phenomenological potential parameters, and propose an additional short range interaction to improve the underbinding generally found for the J¼ = 0+ ground state. We then investigate two possible scenarios for generating the negative parity states in 212Po. We find that both are necessary in order to produce low-lying negative parity states which are able to decay via electric dipole transitions to the positive parity states of the ground state band. Finally we present a novel calculation of the properties of the low-lying positive and negative parity states of 218Rn described as a doubly closed 208Pb core plus a 10Be cluster. / AFRIKAANSE OPSOMMING: ’n Binêre bondel model word gebruik om die eienskappe van die grondtoestands energie band van 212Po, te modeleer as ’n 208Pb-alpha kern-bondel sisteem te ondersoek. Die resultate verkry vanaf ’n mikroskopiese kern-bondel potentiaal word vergelyk met die wat verkry is met ’n suiwer fenomenologiese potentiaal. Die twee potentiale is verkry om dieselfde oppervlakte toestande voor te stel en gee sodoende dieselfde voorspellings vir die grondtoestand alpha verval halfleeftyd. Alhoewel dit baie verskillende energie spektra genereer, toon die resultate van die fenomenologiese potentiaal dat dit duidelik beter is. Ons optimiseer hierdie fenomenologiese parameters en stel ’n addisionele kort ry-afstands interaksie voor om die algemene ondergebondenheid wat oor die algemeen by die J¼ = 0+ grondtoestand voorkom, te verbeter. Ons ondersoek ook hierdie twee moontlike scenarios om die negatiewe pariteitstoestande in 212Po te genereer. Ons vind dat beide scenarios noodsaaklik is om laagliggende pariteitstoestande te produseer, sodat verval deur elektriese dipool oorgange na die positiewe pariteitstoestande van die grondtoestandsband moontlik is. Laagliggende positiewe en negatiewe pariteitstoestande, van die 218Rn wat beskryf word as ’n dubbelgeslote 208Pb kern en ’n 10Be bondel.

Many-body perturbation theory and coupled-cluster theory, combined with carefully constructed basis sets, can be used to accurately compute the properties of small molecules. We applied a series of methods and basis sets aimed at reaching the ab initio limit to determine the barrier to planarity for ethylene cation. For potential energy surfaces corresponding to bond dissociation, a single Slater determinant is no longer an appropriate reference, and the single-reference hierarchy breaks down. We computed full configuration interaction benchmark data for calibrating new and existing quantum chemical methods for the accurate description of potential energy surfaces. We used the data to calibrate single-reference configuration interaction, perturbation theory, and coupled-cluster theory and multi-reference configuration interaction and perturbation theory, using various types of molecular orbitals, for breaking single and multiple bonds on ground-state and excited-state surfaces. We developed a determinant-based method which generalizes the formulation of many-body wave functions and energy expectation values. We used the method to calibrate single-reference and multi-reference configuration interaction and coupled-cluster theories, using different types of molecular orbitals, for the symmetric dissociation of water. We extended the determinant-based method to work with general configuration lists, enabling us to study, for the first time, arbitrarily truncated coupled-cluster wave functions. We used this new capability to study the importance of configurations in configuration interaction and coupled-cluster wave functions at different regions of a potential energy surface.