Theoretical study of spin-orbit coupling in molecules

Theoretical models to study spin-obit coupling with multi-configurational wavefunctions have been developed both methodologically and implemented into the widely distributed quantum chemistry package GAMESS. Various aspects of making the spin-orbit coupling studies more efficient and thus more available, such as extensive usage of symmetry and parallelisation have been studied. A theoretical development of one, two and partial two electron approaches to spin-orbit coupling is given and tested on a representative set of molecules. A new accurate method to study the vibrational structure of molecules, limited in the current formulation to diatomics, has been proposed. Two chemically interesting systems have been studied, the reaction path of titanium cation and ethane, and the vibrational structure of CO+ and O 2+

Mapping Enzymatic Catalysis using the Effective Fragment Molecular Orbital Method: Towards all ab initio Biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be $18.3\pm 3.5$ kcal mol$^{-1}$ for MP2/cc-pVDZ and $19.3\pm 3.6$ for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.Comment: SI not attache

Differential noncircular pulleys for cable robots and static balancing

In this paper, we introduce a mechanism consisting of a pair of noncircular pulleys with a constant-length cable. While a single noncircular pulley is generally limited to continuously winding or unwinding, the differential cable routing proposed here allows to generate non-monotonic motions at the output of the arrangement, i.e. the location of the idler pulley redirecting the cable. The equations relating its motion to rotation angles of the noncircular pulleys and to the cable length are presented in the first part of this paper. Next, we introduce a graphical method allowing us to obtain the required pulley profiles for a given output function. Our approach is finally demonstrated with two application examples: the guiding of a cable-suspended robot along a complex trajectory using a single actuator, and the static balancing of a pendulum with a 360 degree rotational range of motion

Empirical corrections and pair interaction energies in the fragment molecular orbital method

The energy and analytic gradient are developed for FMO combined with the Hartree-Fock method augmented with three empirical corrections (HF-3c). The auxiliary basis set approach to FMO is extended to perform pair interaction energy decomposition analysis. The FMO accuracy is evaluated for several typical systems including 3 proteins. Pair interaction energies computed with different approaches in FMO are compared for a water cluster and protein-ligand complexes.Comment: Revised version accepted in Chemical Physics Letter

Hybrid RHF/MP2 geometry optimizations with the Effective Fragment Molecular Orbital Method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by chorismate mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.Comment: 11 pages, 3 figure

Conception de systèmes mécaniques auto-adaptatifs pour la locomotion

RÉSUMÉ Les mécanismes auto-adaptatifs (ou sous-actionnés) permettent d’accomplir des tâches complexes en utilisant un nombre minimal d’actionneurs. Leur caractéristique principale est la division de l’actionnement, à l’aide de mécanismes souvent différentiels, entre plusieurs mouvements de sortie dont la séquence de déclenchement peut être contrôlée à l’aide d’éléments passifs. Actuellement, ils sont majoritairement employés pour fabriquer des doigts ou de mains robotiques capables de s’adapter mécaniquement à la forme de l’objet à saisir, sans utiliser de contrôle en boucle fermée. Il est ainsi possible d’effectuer des économies substantielles en générant de manière purement mécanique un comportement qui nécessiterait autrement un grand nombre de moteurs et de capteurs. Dans ce projet, deux thèmes distincts, liés à l’application de cette philosophie de conception au domaine de la locomotion, sont explorés avec comme but principal de transférer l’expertise développée avec les doigts auto-adaptatifs vers de nouveaux cas d’utilisation. En premier lieu, un mécanisme de patte mécanique à deux degrés de liberté, actionné par un seul moteur, a été développé. En cas de collision avec un obstacle durant la phase de vol, le ratio de transmission de l’actionnement est altéré, combinant ainsi les deux degrés de liberté pour permettre à la patte de glisser le long de l’obstacle à la recherche d’un nouveau point d’appui. Ce mécanisme a été analysé en profondeur, notamment par le biais de la théorie des visseurs, afin de quantifier sa capacité d’adaptation. Il a ensuite été possible de procéder à une optimisation multi-objectifs visant à mettre en évidence le compromis entre les capacités d’adaptation de la patte et la qualité de la trajectoire générée. La validation expérimentale de ce mécanisme est également présentée. Le second thème relève du domaine de la réadaptation. Le mécanisme développé correspond à celui d’une orthèse entièrement passive, capable de générer des couples correcteurs sur les articulations de la hanche et du genou. Pour ce faire, un système de poulies non-circulaires et de câbles relie les rotations de ces deux articulations à l’allongement de deux ressorts. La synthèse des profils des poulies, par le biais d’une méthode graphique innovante, est décrite, de même que les résultats expérimentaux obtenus à l’aide du prototype réalisé. Les travaux réalisés dans le cadre du présent projet ont par ailleurs mené à d’autres contributions dans le domaine des poulies non-circulaires, soit un mécanisme d’équilibrage statique et un autre permettant de guider une plateforme suspendue le long d’une trajectoire de type « pick-and-place ».----------ABSTRACT Self-adaptive mechanisms (also referred to as underactuated) allow to perform complex tasks using only a minimal number of actuators. Their main characteristic is their ability to distribute actuation, often using differential mechanisms, between several output motions which can be triggered sequentially through the use of passive elements. As of now, they are mostly used in fingers and hands able to mechanically adapt to the shape of the grasped object, without relying on closed-loop control. Indeed, they allow for significant cost savings by generating purely mechanically a behavior which would otherwise require several motors and sensors. In this project, two separate themes, both linked to the application of this design philosophy to the field of locomotion, are explored. The main goal is to transfer existent expertise developed for self-adaptive fingers to new use cases. First, a two degree of freedom mechanical leg, driven by a single motor, has been developed. In case of an unexpected collision with an obstacle during the swing phase, the actuation transmission ratios are altered, thus combining both degrees of freedom to generate a sliding motion along the obstacle in search of the next foothold. This mechanism is here analyzed in depth through the application of screw theory, in order to quantify this adaptation capability. A multi-objective optimization was subsequently performed to highlight the trade-off between the mechanism’s adaptation to obstacles and the quality of the generated leg endpoint trajectory. Experimental results validating the increased reachable ground clearance for the proposed linkage are provided. The second theme belongs to the field of rehabilitation. The developed mechanism is a fully passive orthosis able to generate correcting torques to the hip and knee joints of the leg. This behavior is obtained by relating the elongations of two springs to these articular rotations by the means of cables and non-circular pulleys. The synthesis of the pulley profiles, through an innovative graphical method, as well as initial experimental results are presented. This project has also yielded relevant contributions to the field of non-circular pulleys, with one mechanism developed to achieve static balancing of a pendulum, and another guiding a suspended platform through a pick-and-place trajectory

A Study of the Relative Importance of One and Two-Electron Contributions to Spin–Orbit Coupling

The existing methods to estimate the magnitude of spin–orbit coupling for arbitrary molecules and multiconfigurational wave functions are reviewed. The form-factor method is extended from the original singlet–triplet formulation into arbitrary multiplicities. A simplified version of the mean-field method (the partial two-electron method, P2E) is formulated and tested versus the full two-electron operator on a set of representative molecules. The change of the one and two-electron spin–orbit coupling down the Periodic Table is investigated, and it is shown that the computationally much less demanding P2E method has an accuracy comparable to that of the full two-electron method

Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension

The paper examines a trapped one-dimensional system of multicomponent spinless fermions that interact with a zero-range two-body potential. We show that when the repulsion between particles is very large the system can be approached analytically. To illustrate this analytical approach we consider a simple system of three distinguishable particles, which can be addressed experimentally. For this system we show that for infinite repulsion the energy spectrum is sixfold degenerate. We also show that this degeneracy is partially lifted for finitely large repulsion for which we find and describe corresponding wave functions.Comment: Paper in connection with the 22nd European Conference on Few-Body Problems in Physics, Krakow, Poland, 9-13 September 201