Potential Energy Surfaces for Conceptual Design and Analysis of Mechanical Systems

2021 ◽  
Author(s):  
Charles A. Manion ◽  
Mark Fuge

Abstract Current computational Design Synthesis approaches have had trouble generating components with higher kinematic pairs and have instead relied on libraries of predefined components. However, higher kinematic pairs are ubiquitous in many mechanical devices such as ratchets, latches, locks, trigger mechanisms, clock escapements, and materials handling systems. In many cases there is a need to synthesize new higher kinematic pair devices. To address this problem, we develop a new representation for mechanical systems that extends the capabilities of configuration spaces to consider arbitrary energy storing mechanical devices. The key idea underlying this representation is the use of potential energy surfaces as a generalization of configuration spaces. This generalization enables modelling of mechanical systems in a physics independent manner and captures behaviors such as dynamics. By modeling a device through the lens of a potential energy surface, we demonstrate that differentiable simulation is possible. Differentiable simulation enables efficient calculation of gradients of potential energy surface parameters with respect to an objective function that depends on trajectories taken on the potential energy surface. This allows synthesis of mechanical devices with desired kinematic and dynamic behavior through gradient descent. We demonstrate this through several synthesis examples including positioning devices (e.g., a funnel) and timing devices (e.g., an oscillator).

Author(s):  
Tomas Baer ◽  
William L. Hase

Properties of potential energy surfaces are integral to understanding the dynamics of unimolecular reactions. As discussed in chapter 2, the concept of a potential energy surface arises from the Born-Oppenheimer approximation, which separates electronic motion from vibrational/rotational motion. Potential energy surfaces are calculated by solving Eq. (2.3) in chapter 2 at fixed values for the nuclear coordinates R. Solving this equation gives electronic energies Eie(R) at the configuration R for the different electronic states of the molecule. Combining Eie(R) with the nuclear repulsive potential energy VNN(R) gives the potential energy surface Vi(R) for electronic state i (Hirst, 1985). Each state is identified by its spin angular momentum and orbital symmetry. Since the electronic density between nuclei is different for each electronic state, each state has its own equilibrium geometry, sets of vibrational frequencies, and bond dissociation energies. To illustrate this effect, vibrational frequencies for the ground singlet state (S0) and first excited singlet state (S1) of H2CO are compared in table 3.1. For a diatomic molecule, potential energy surfaces only depend on the internuclear separation, so that a potential energy curve results instead of a surface. Possible potential energy curves for a diatomic molecule are depicted in figure 3.1. Of particular interest in this figure are the different equilibrium bond lengths and dissociation energies for the different electronic states. The lowest potential curve is referred to as the ground electronic state potential. The primary focus of this chapter is the ground electronic state potential energy surface. In the last section potential energy surfaces are considered for excited electronic states. A unimolecular reactant molecule consisting of N atoms has a multidimensional potential energy surface which depends on 3N-6 independent coordinates. For the smallest nondiatomic reactant, a triatomic molecule, the potential energy surface is four-dimensional (three independent coordinates plus the energy). Since it is difficult, if not impossible, to visualize surfaces with more than three dimensions, methods are used to reduce the dimensionality of the problem in portraying surfaces. In a graphical representation of a surface the potential energy is depicted as a function of two coordinates with constraints placed on the remaining 3N-8 coordinates.


1986 ◽  
Vol 41 (3) ◽  
pp. 532-534
Author(s):  
Ariel Fernández

The topology of the lower energy sheet for the Potential Energy Surface corresponding to the dynamic Jahn-Teller effect is obtained by means of homological techniques.


2015 ◽  
Vol 17 (33) ◽  
pp. 21583-21593 ◽  
Author(s):  
Sarantos Marinakis ◽  
Indigo Lily Dean ◽  
Jacek Kłos ◽  
François Lique

We present a new CH(X)–He potential energy surface which is able to reproduce all the available experimental results.


2020 ◽  
Vol 22 (33) ◽  
pp. 18488-18498 ◽  
Author(s):  
Debasish Koner ◽  
Juan Carlos San Vicente Veliz ◽  
Raymond J. Bemish ◽  
Markus Meuwly

Reproducing kernel-based potential energy surface based on MRCI+Q/aug-cc-pVTZ energies for the triplet states of N2O and quasiclassical dynamical study for the reaction, dissociation and vibrational relaxation.


2009 ◽  
Vol 18 (04) ◽  
pp. 907-913 ◽  
Author(s):  
V. PASHKEVICH ◽  
Y. PYATKOV ◽  
A. UNZHAKOVA

Various fission processes are described in terms of high-dimensional potential energy surface in the frame of the Strutinsky shell correction method for actinide region. The complete deformation space is necessary to study the potential energy minima responsible for the cluster radioactivity, cold fission and cold multi-fragmentation valleys. The nuclear shape families for the different fission configurations are obtained without any specific change of the parameters. The coordinate system based on the Cassini ovaloids makes it possible to increase the number of independent deformation parameters without divergence. The higher orders of the deformation are shown to play an important role in the description of the potential energy surface structure.


1988 ◽  
Vol 121 ◽  
Author(s):  
G. V. Gibbs ◽  
M. B. Boisen ◽  
R. T. Downs ◽  
A. C. Lasaga

ABSTRACTModels of the oxide and sulfide structure-types of quartz and cristobalite have been made using potential energy surfaces derived from MO calculations on small molecules. The bond length and angle and the volume compressibility data calculated for quartz match those observed for pressures up to 40 kbars. An analysis of the force constants that define the potential energy surface indicates that the bulk modulus of the mineral is governed primarily by the bending force constant of the bridging angle. Similar calculations were completed for the GeO2 form of quartz, but the agreement with the observed data is somewhat poorer. A modeling of the CO2 form of quartz predicts that it would be significantly harder, more incompressible and show less expansibility than the SiO2 form.


2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Simon Schreck ◽  
Annette Pietzsch ◽  
Brian Kennedy ◽  
Conny Såthe ◽  
Piter S. Miedema ◽  
...  

Abstract Thermally driven chemistry as well as materials’ functionality are determined by the potential energy surface of a systems electronic ground state. This makes the potential energy surface a central and powerful concept in physics, chemistry and materials science. However, direct experimental access to the potential energy surface locally around atomic centers and to its long-range structure are lacking. Here we demonstrate how sub-natural linewidth resonant inelastic soft x-ray scattering at vibrational resolution is utilized to determine ground state potential energy surfaces locally and detect long-range changes of the potentials that are driven by local modifications. We show how the general concept is applicable not only to small isolated molecules such as O2 but also to strongly interacting systems such as the hydrogen bond network in liquid water. The weak perturbation to the potential energy surface through hydrogen bonding is observed as a trend towards softening of the ground state potential around the coordinating atom. The instrumental developments in high resolution resonant inelastic soft x-ray scattering are currently accelerating and will enable broad application of the presented approach. With this multidimensional potential energy surfaces that characterize collective phenomena such as (bio)molecular function or high-temperature superconductivity will become accessible in near future.


2014 ◽  
Vol 68 (1) ◽  
Author(s):  
Li-Li Zhang ◽  
Hui-Ling Liu ◽  
Hao Tang ◽  
Xu-Ri Huang

AbstractThe singlet and triplet potential energy surfaces for the reaction of HS+ with the simplest primary amine, CH3NH2, were determined at the CCSD(T)/6-311+G(d,p) level using the B3LYP/6-311G(d,p) and QCISD/6-311G(d,p) geometries. All possible reaction channels were explored. The results show that three paths on the singlet potential energy surface and one path on the triplet potential energy surface are competitive. These four feasible paths provide products which are presented in the paper and they are consistent with previous experimental results. On the other hand, the stationary points involved in the most favourable path all lie below those of the reactant and thus the title reaction is expected to be rapid, which is also consistent with the experiment.


2018 ◽  
Vol 20 (8) ◽  
pp. 5407-5414 ◽  
Author(s):  
François Lique ◽  
Izaskun Jiménez-Serra ◽  
Serena Viti ◽  
Sarantos Marinakis

The inelastic scattering of PO (X, v = 0) has been investigated by quantum scattering calculations using a new potential energy surface.


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