Architectural-Physical Co-Design of 3D CPUs with Micro-Fluidic Cooling

The performance, energy efficiency and cost improvements due to traditional technology scaling have begun to slow down and present diminishing returns. Underlying reasons for this trend include fundamental physical limits of transistor scaling, the growing significance of quantum effects as transistors shrink, and a growing mismatch between transistors and interconnects regarding size, speed and power. Continued Moore's Law scaling will not come from technology scaling alone, and must involve improvements to design tools and development of new disruptive technologies such as 3D integration. 3D integration presents potential improvements to interconnect power and delay by translating the routing problem into a third dimension, and facilitates transistor density scaling independent of technology node. Furthermore, 3D IC technology opens up a new architectural design space of heterogeneously-integrated high-bandwidth CPUs. Vertical integration promises to provide the CPU architectures of the future by integrating high performance processors with on-chip high-bandwidth memory systems and highly connected network-on-chip structures. Such techniques can overcome the well-known CPU performance bottlenecks referred to as memory and communication wall. However the promising improvements to performance and energy efficiency offered by 3D CPUs does not come without cost, both in the financial investments to develop the technology, and the increased complexity of design. Two main limitations to 3D IC technology have been heat removal and TSV reliability. Transistor stacking creates increases in power density, current density and thermal resistance in air cooled packages. Furthermore the technology introduces vertical through silicon vias (TSVs) that create new points of failure in the chip and require development of new BEOL technologies. Although these issues can be controlled to some extent using thermal-reliability aware physical and architectural 3D design techniques, high performance embedded cooling schemes, such as micro-fluidic (MF) cooling, are fundamentally necessary to unlock the true potential of 3D ICs. A new paradigm is being put forth which integrates the computational, electrical, physical, thermal and reliability views of a system. The unification of these diverse aspects of integrated circuits is called Co-Design. Independent design and optimization of each aspect leads to sub-optimal designs due to a lack of understanding of cross-domain interactions and their impacts on the feasibility region of the architectural design space. Co-Design enables optimization across layers with a multi-domain view and thus unlocks new high-performance and energy efficient configurations. Although the co-design paradigm is becoming increasingly necessary in all fields of IC design, it is even more critical in 3D ICs where, as we show, the inter-layer coupling and higher degree of connectivity between components exacerbates the interdependence between architectural parameters, physical design parameters and the multitude of metrics of interest to the designer (i.e. power, performance, temperature and reliability). In this dissertation we present a framework for multi-domain co-simulation and co-optimization of 3D CPU architectures with both air and MF cooling solutions. Finally we propose an approach for design space exploration and modeling within the new Co-Design paradigm, and discuss the possible avenues for improvement of this work in the future.

Physical Design Methodologies for Low Power and Reliable 3D ICs

As the semiconductor industry struggles to maintain its momentum down the path following the Moore's Law, three dimensional integrated circuit (3D IC) technology has emerged as a promising solution to achieve higher integration density, better performance, and lower power consumption. However, despite its significant improvement in electrical performance, 3D IC presents several serious physical design challenges. In this dissertation, we investigate physical design methodologies for 3D ICs with primary focus on two areas: low power 3D clock tree design, and reliability degradation modeling and management. Clock trees are essential parts for digital system which dissipate a large amount of power due to high capacitive loads. The majority of existing 3D clock tree designs focus on minimizing the total wire length, which produces sub-optimal results for power optimization. In this dissertation, we formulate a 3D clock tree design flow which directly optimizes for clock power. Besides, we also investigate the design methodology for clock gating a 3D clock tree, which uses shutdown gates to selectively turn off unnecessary clock activities. Different from the common assumption in 2D ICs that shutdown gates are cheap thus can be applied at every clock node, shutdown gates in 3D ICs introduce additional control TSVs, which compete with clock TSVs for placement resources. We explore the design methodologies to produce the optimal allocation and placement for clock and control TSVs so that the clock power is minimized. We show that the proposed synthesis flow saves significant clock power while accounting for available TSV placement area. Vertical integration also brings new reliability challenges including TSV's electromigration (EM) and several other reliability loss mechanisms caused by TSV-induced stress. These reliability loss models involve complex inter-dependencies between electrical and thermal conditions, which have not been investigated in the past. In this dissertation we set up an electrical/thermal/reliability co-simulation framework to capture the transient of reliability loss in 3D ICs. We further derive and validate an analytical reliability objective function that can be integrated into the 3D placement design flow. The reliability aware placement scheme enables co-design and co-optimization of both the electrical and reliability property, thus improves both the circuit's performance and its lifetime. Our electrical/reliability co-design scheme avoids unnecessary design cycles or application of ad-hoc fixes that lead to sub-optimal performance. Vertical integration also enables stacking DRAM on top of CPU, providing high bandwidth and short latency. However, non-uniform voltage fluctuation and local thermal hotspot in CPU layers are coupled into DRAM layers, causing a non-uniform bit-cell leakage (thereby bit flip) distribution. We propose a performance-power-resilience simulation framework to capture DRAM soft error in 3D multi-core CPU systems. In addition, a dynamic resilience management (DRM) scheme is investigated, which adaptively tunes CPU's operating points to adjust DRAM's voltage noise and thermal condition during runtime. The DRM uses dynamic frequency scaling to achieve a resilience borrow-in strategy, which effectively enhances DRAM's resilience without sacrificing performance. The proposed physical design methodologies should act as important building blocks for 3D ICs and push 3D ICs toward mainstream acceptance in the near future.

Exploring Adaptive Implementation of On-Chip Networks

As technology geometries have shrunk to the deep submicron regime, the communication delay and power consumption of global interconnections in high performance Multi- Processor Systems-on-Chip (MPSoCs) are becoming a major bottleneck. The Network-on- Chip (NoC) architecture paradigm, based on a modular packet-switched mechanism, can address many of the on-chip communication issues such as performance limitations of long interconnects and integration of large number of Processing Elements (PEs) on a chip. The choice of routing protocol and NoC structure can have a significant impact on performance and power consumption in on-chip networks. In addition, building a high performance, area and energy efficient on-chip network for multicore architectures requires a novel on-chip router allowing a larger network to be integrated on a single die with reduced power consumption. On top of that, network interfaces are employed to decouple computation resources from communication resources, to provide the synchronization between them, and to achieve backward compatibility with existing IP cores. Three adaptive routing algorithms are presented as a part of this thesis. The first presented routing protocol is a congestion-aware adaptive routing algorithm for 2D mesh NoCs which does not support multicast (one-to-many) traffic while the other two protocols are adaptive routing models supporting both unicast (one-to-one) and multicast traffic. A streamlined on-chip router architecture is also presented for avoiding congested areas in 2D mesh NoCs via employing efficient input and output selection. The output selection utilizes an adaptive routing algorithm based on the congestion condition of neighboring routers while the input selection allows packets to be serviced from each input port according to its congestion level. Moreover, in order to increase memory parallelism and bring compatibility with existing IP cores in network-based multiprocessor architectures, adaptive network interface architectures are presented to use multiple SDRAMs which can be accessed simultaneously. In addition, a smart memory controller is integrated in the adaptive network interface to improve the memory utilization and reduce both memory and network latencies. Three Dimensional Integrated Circuits (3D ICs) have been emerging as a viable candidate to achieve better performance and package density as compared to traditional 2D ICs. In addition, combining the benefits of 3D IC and NoC schemes provides a significant performance gain for 3D architectures. In recent years, inter-layer communication across multiple stacked layers (vertical channel) has attracted a lot of interest. In this thesis, a novel adaptive pipeline bus structure is proposed for inter-layer communication to improve the performance by reducing the delay and complexity of traditional bus arbitration. In addition, two mesh-based topologies for 3D architectures are also introduced to mitigate the inter-layer footprint and power dissipation on each layer with a small performance penalty.

Adaptive Routing Approaches for Networked Many-Core Systems

Through advances in technology, System-on-Chip design is moving towards integrating tens to hundreds of intellectual property blocks into a single chip. In such a many-core system, on-chip communication becomes a performance bottleneck for high performance designs. Network-on-Chip (NoC) has emerged as a viable solution for the communication challenges in highly complex chips. The NoC architecture paradigm, based on a modular packet-switched mechanism, can address many of the on-chip communication challenges such as wiring complexity, communication latency, and bandwidth. Furthermore, the combined benefits of 3D IC and NoC schemes provide the possibility of designing a high performance system in a limited chip area. The major advantages of 3D NoCs are the considerable reductions in average latency and power consumption. There are several factors degrading the performance of NoCs. In this thesis, we investigate three main performance-limiting factors: network congestion, faults, and the lack of efficient multicast support. We address these issues by the means of routing algorithms. Congestion of data packets may lead to increased network latency and power consumption. Thus, we propose three different approaches for alleviating such congestion in the network. The first approach is based on measuring the congestion information in different regions of the network, distributing the information over the network, and utilizing this information when making a routing decision. The second approach employs a learning method to dynamically find the less congested routes according to the underlying traffic. The third approach is based on a fuzzy-logic technique to perform better routing decisions when traffic information of different routes is available. Faults affect performance significantly, as then packets should take longer paths in order to be routed around the faults, which in turn increases congestion around the faulty regions. We propose four methods to tolerate faults at the link and switch level by using only the shortest paths as long as such path exists. The unique characteristic among these methods is the toleration of faults while also maintaining the performance of NoCs. To the best of our knowledge, these algorithms are the first approaches to bypassing faults prior to reaching them while avoiding unnecessary misrouting of packets. Current implementations of multicast communication result in a significant performance loss for unicast traffic. This is due to the fact that the routing rules of multicast packets limit the adaptivity of unicast packets. We present an approach in which both unicast and multicast packets can be efficiently routed within the network. While suggesting a more efficient multicast support, the proposed approach does not affect the performance of unicast routing at all. In addition, in order to reduce the overall path length of multicast packets, we present several partitioning methods along with their analytical models for latency measurement. This approach is discussed in the context of 3D mesh networks.

Approche efficace pour la conception des architectures multiprocesseurs sur puce électronique

Les systèmes multiprocesseurs sur puce électronique (On-Chip Multiprocessor [OCM]) sont considérés comme les meilleures structures pour occuper l'espace disponible sur les circuits intégrés actuels. Dans nos travaux, nous nous intéressons à un modèle architectural, appelé architecture isométrique de systèmes multiprocesseurs sur puce, qui permet d'évaluer, de prédire et d'optimiser les systèmes OCM en misant sur une organisation efficace des nœuds (processeurs et mémoires), et à des méthodologies qui permettent d'utiliser efficacement ces architectures. Dans la première partie de la thèse, nous nous intéressons à la topologie du modèle et nous proposons une architecture qui permet d'utiliser efficacement et massivement les mémoires sur la puce. Les processeurs et les mémoires sont organisés selon une approche isométrique qui consiste à rapprocher les données des processus plutôt que d'optimiser les transferts entre les processeurs et les mémoires disposés de manière conventionnelle. L'architecture est un modèle maillé en trois dimensions. La disposition des unités sur ce modèle est inspirée de la structure cristalline du chlorure de sodium (NaCl), où chaque processeur peut accéder à six mémoires à la fois et où chaque mémoire peut communiquer avec autant de processeurs à la fois. Dans la deuxième partie de notre travail, nous nous intéressons à une méthodologie de décomposition où le nombre de nœuds du modèle est idéal et peut être déterminé à partir d'une spécification matricielle de l'application qui est traitée par le modèle proposé. Sachant que la performance d'un modèle dépend de la quantité de flot de données échangées entre ses unités, en l'occurrence leur nombre, et notre but étant de garantir une bonne performance de calcul en fonction de l'application traitée, nous proposons de trouver le nombre idéal de processeurs et de mémoires du système à construire. Aussi, considérons-nous la décomposition de la spécification du modèle à construire ou de l'application à traiter en fonction de l'équilibre de charge des unités. Nous proposons ainsi une approche de décomposition sur trois points : la transformation de la spécification ou de l'application en une matrice d'incidence dont les éléments sont les flots de données entre les processus et les données, une nouvelle méthodologie basée sur le problème de la formation des cellules (Cell Formation Problem [CFP]), et un équilibre de charge de processus dans les processeurs et de données dans les mémoires. Dans la troisième partie, toujours dans le souci de concevoir un système efficace et performant, nous nous intéressons à l'affectation des processeurs et des mémoires par une méthodologie en deux étapes. Dans un premier temps, nous affectons des unités aux nœuds du système, considéré ici comme un graphe non orienté, et dans un deuxième temps, nous affectons des valeurs aux arcs de ce graphe. Pour l'affectation, nous proposons une modélisation des applications décomposées en utilisant une approche matricielle et l'utilisation du problème d'affectation quadratique (Quadratic Assignment Problem [QAP]). Pour l'affectation de valeurs aux arcs, nous proposons une approche de perturbation graduelle, afin de chercher la meilleure combinaison du coût de l'affectation, ceci en respectant certains paramètres comme la température, la dissipation de chaleur, la consommation d'énergie et la surface occupée par la puce. Le but ultime de ce travail est de proposer aux architectes de systèmes multiprocesseurs sur puce une méthodologie non traditionnelle et un outil systématique et efficace d'aide à la conception dès la phase de la spécification fonctionnelle du système.

Fração de ejeção e volumes do ventrículo esquerdo medidos com eco 3D e com tomografia ultra-rápida

FUNDAMENTO: O ecocardiograma tridimensional em tempo real (ECO 3D) e a tomografia computadorizada ultra-rápida (CT) são dois novos métodos de análise da fração de ejeção e dos volumes do VE. OBJETIVO: Comparar as medidas da FEVE e dos volumes do VE aferidos pelo ECO 3D e pela CT ultra-rápida. MÉTODOS: Foram estudados pelo ECO 3D e pela CT ultra-rápida de 64 cortes, 39 pacientes consecutivos (27 homens, média etária de 57±12 anos). Foram analisados: FEVE e volumes do VE. Análise estatística: coeficiente de correlação (r: Pearson), teste de Bland & Altman, teste de regressão linear, 95 % IC, p<0,05. RESULTADOS: Medidas do ECO 3D: a FEVE variou de 56,1 a 78,6 (65,5±5,58)%; volume diastólico final variou de 49,6 a 178,2 (87±27,8)ml; volume sistólico final variou de 11,4 a 78 (33,1±13,6)ml. Medidas da CT: a FEVE variou de 53 a 86 (67,8±7,78)%; volume diastólico final variou de 51 a 186 (106,5±30,3) ml; volume sistólico final variou de 7 a 72 (35,5±13,4)ml. As correlações entre ECO 3D e CT foram: FEVE (r: 0,7888, p<0,0001, 95% IC 0,6301 a 0,8843); volume diastólico final (r: 0,7695, p<0,0001, 95% IC 0,5995 a 0,8730); volume sistólico final (r: 0,8119, p<0,0001, 95% IC 0,6673 a 0,8975). CONCLUSÃO: Nesta série, foi observada boa correlação entre as medidas da FEVE e entre os volumes ventriculares aferidos pelo ECO3D e pela CT ultra-rápida de 64 cortes.

Comparação entre a ecocardiografia 2D e 3D na avaliação do remodelamento reverso após a TRC

FUNDAMENTO: A ecocardiografia consiste em método muito útil para seleção e avaliação de resposta à terapia de ressincronização cardíaca (TRC). O eco 3D já tem seu papel estabelecido na avaliação dos volumes ventriculares e fração de ejeção ventricular esquerda (FEVE) com excelente correlação de resultados quando comparado à RNM. OBJETIVO: Comparar a avaliação dos volumes ventriculares (VDVE, VSVE), FEVE e massa do VE antes e após a TRC pela ecocardiografia bi (Eco 2D) e tridimensional (Eco 3D). MÉTODOS: Foram avaliados 24 pacientes com IC CFIII ou IV (NYHA), ritmo sinusal QRS > 150 ms, em vigência de terapêutica otimizada para IC submetidos a TRC. Foram realizados eletrocardiograma (ECG), avaliação clínica, Eco 2D e 3D antes, três e seis meses após a TRC. A comparação entre as técnicas foi realizada utilizando-se a correlação de Pearson (r). RESULTADOS: No momento basal, a correlação entre os métodos foi de 0,96 para avaliação do VDVE, 0,95 para avaliação do VSVE, 0,87 para FEVE, e 0,72 para massa do VE. Após três meses da TRC, a correlação entre os métodos para análise do VDVE foi de 0,96, 0,95 para VSVE, 0,95 para FEVE, e 0,77 para massa do VE. Após seis meses da TRC, a correlação entre o Eco 2D e 3D para análise do VDVE foi de 0,98, 0,91 para VSVE, 0,96 para FEVE, e 0,85 para massa do VE. CONCLUSÃO: Neste estudo foi observada redução dos VDVE,VSVE, além de melhora da FEVE após a TRC. Houve excelente correlação entre o Eco 2D e o 3D para avaliação dos volumes ventriculares e FEVE, e boa correlação entre os métodos para avaliação da massa ventricular esquerda antes e após a TRC.

Tradução para o português brasileiro, adaptação transcultural e validação do 3D Assessment of Hand Function

Pós-graduação em Bases Gerais da Cirurgia - FMB

Nanowires for 3d silicon interconnection – low temperature compliant nanowire-polymer film for z-axis interconnect

Semiconductor chip packaging has evolved from single chip packaging to 3D heterogeneous system integration using multichip stacking in a single module. One of the key challenges in 3D integration is the high density interconnects that need to be formed between the chips with through-silicon-vias (TSVs) and inter-chip interconnects. Anisotropic Conductive Film (ACF) technology is one of the low-temperature, fine-pitch interconnect method, which has been considered as a potential replacement for solder interconnects in line with continuous scaling of the interconnects in the IC industry. However, the conventional ACF materials are facing challenges to accommodate the reduced pad and pitch size due to the micro-size particles and the particle agglomeration issue. A new interconnect material - Nanowire Anisotropic Conductive Film (NW-ACF), composed of high density copper nanowires of ~ 200 nm diameter and 10-30 µm length that are vertically distributed in a polymeric template, is developed in this work to tackle the constrains of the conventional ACFs and serves as an inter-chip interconnect solution for potential three-dimensional (3D) applications.

Structural and chemical basis for anticancer activity of a series of 'beta'-tubulin ligands: molecular modeling and 3D QSAR studies

An important approach to cancer therapy is the design of small molecule modulators that interfere with microtubule dynamics through their specific binding to the ²-subunit of tubulin. In the present work, comparative molecular field analysis (CoMFA) studies were conducted on a series of discodermolide analogs with antimitotic properties. Significant correlation coefficients were obtained (CoMFA(i), q² =0.68, r²=0.94; CoMFA(ii), q² = 0.63, r²= 0.91), indicating the good internal and external consistency of the models generated using two independent structural alignment strategies. The models were externally validated employing a test set, and the predicted values were in good agreement with the experimental results. The final QSAR models and the 3D contour maps provided important insights into the chemical and structural basis involved in the molecular recognition process of this family of discodermolide analogs, and should be useful for the design of new specific ²-tubulin modulators with potent anticancer activity.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.

The chemical evolution of IC 10

Context. Dwarf irregular galaxies are relatively simple unevolved objects where it is easy to test models of galactic chemical evolution. Aims. We attempt to determine the star formation and gas accretion history of IC 10, a local dwarf irregular for which abundance, gas, and mass determinations are available. Methods. We apply detailed chemical evolution models to predict the evolution of several chemical elements (He, O, N, S) and compared our predictions with the observational data. We consider additional constraints such as the present-time gas fraction, the star formation rate (SFR), and the total estimated mass of IC 10. We assume a dark matter halo for this galaxy and study the development of a galactic wind. We consider different star formation regimes: bursting and continuous. We explore different wind situations: i) normal wind, where all the gas is lost at the same rate and ii) metal-enhanced wind, where metals produced by supernovae are preferentially lost. We study a case without wind. We vary the star formation efficiency (SFE), the wind efficiency, and the time scale of the gas infall, which are the most important parameters in our models. Results. We find that only models with metal-enhanced galactic winds can reproduce the properties of IC 10. The star formation must have proceeded in bursts rather than continuously and the bursts must have been less numerous than similar to 10 over the whole galactic lifetime. Finally, IC 10 must have formed by a slow process of gas accretion with a timescale of the order of 8 Gyr.

Beryllium abundances along the evolutionary sequence of the open cluster IC 4651-A new test for hydrodynamical stellar models

Context. Previous analyses of lithium abundances in main sequence and red giant stars have revealed the action of mixing mechanisms other than convection in stellar interiors. Beryllium abundances in stars with Li abundance determinations can offer valuable complementary information on the nature of these mechanisms. Aims. Our aim is to derive Be abundances along the whole evolutionary sequence of an open cluster. We focus on the well-studied open cluster IC 4651. These Be abundances are used with previously determined Li abundances, in the same sample stars, to investigate the mixing mechanisms in a range of stellar masses and evolutionary stages. Methods. Atmospheric parameters were adopted from a previous abundance analysis by the same authors. New Be abundances have been determined from high-resolution, high signal-to-noise UVES spectra using spectrum synthesis and model atmospheres. The careful synthetic modeling of the Be lines region is used to calculate reliable abundances in rapidly rotating stars. The observed behavior of Be and Li is compared to theoretical predictions from stellar models including rotation-induced mixing, internal gravity waves, atomic diffusion, and thermohaline mixing. Results. Beryllium is detected in all the main sequence and turn-off sample stars, both slow- and fast-rotating stars, including the Li-dip stars, but is not detected in the red giants. Confirming previous results, we find that the Li dip is also a Be dip, although the depletion of Be is more modest than for Li in the corresponding effective temperature range. For post-main-sequence stars, the Be dilution starts earlier within the Hertzsprung gap than expected from classical predictions, as does the Li dilution. A clear dispersion in the Be abundances is also observed. Theoretical stellar models including the hydrodynamical transport processes mentioned above are able to reproduce all the observed features well. These results show a good theoretical understanding of the Li and Be behavior along the color-magnitude diagram of this intermediate-age cluster for stars more massive than 1.2 M(circle dot).

Dynamical Lorentz symmetry breaking in 3D and charge fractionalization

We analyze the breaking of Lorentz invariance in a 3D model of fermion fields self-coupled through four-fermion interactions. The low-energy limit of the theory contains various submodels which are similar to those used in the study of graphene or in the description of irrational charge fractionalization.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.