Apparent contradiction between calculated kinetic and potential energy fractions of phonons in molecular solids with implications on condensed-phase chemistry

MRS Advances ◽  
2017 ◽  
Vol 2 (9) ◽  
pp. 513-518
Author(s):  
Brent Kraczek

ABSTRACTMany computational and experimental analyses of molecular excitation rely on relative atomic velocities to identify the excitation of chemical bonds. These are often interpreted through the aid of normal mode calculations. We address two potential gaps in this approach: 1. Relative velocities may not reflect the total potential energy absorbed by the bond. 2. Normal mode calculations omit interactions between neighboring molecules, effectively assuming a similarity between condensed- and gas-phase chemistry. Phonon calculations implicitly include interactions between neighboring molecules and allow analyses of both relative velocities and potential energies in solids.In the present work, we compare kinetic and potential energy fractions of the phonon modes of the molecular solids nitromethane and β-HMX. We show that velocity-based methods are likely sufficient to analyze nitromethane. However, they cannot detect the majority of excitation ofthe N-N bonds in β-HMX, the scission of which appears to begin major decomposition pathways in the molecules.In the broader context of condensed-phase chemistry, this implies that important interactions may not all be identifiable through analyses that rely solely on relative atomic velocities.

Author(s):  
Carmel Majidi ◽  
George G. Adams

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.


2009 ◽  
Vol 9 (2) ◽  
pp. 5289-5320 ◽  
Author(s):  
D. Lowe ◽  
D. Topping ◽  
G. McFiggans

Abstract. A coupled box model of photochemistry and aerosol microphysics which explicitly accounts for size-dependent chemical properties of the condensed-phase has been developed to simulate the multi-phase chemistry of chlorine, bromine and iodine in the marine boundary layer (MBL). The model contains separate seasalt and non-seasalt modes, each of which may be composed of 1–16 size-sections. By comparison of gaseous and aerosol compositions predicted using different size-resolutions with both fixed and size-dependent aerosol turnover rates, it was found that, for halogen-activation processes, the physical property initialisation of the aerosol-mode has a significant influence on gas-phase chemistry. Failure to adequately represent the appropriate physical properties can lead to substantial errors in gas-phase chemistry. The size-resolution of condensed-phase composition has a less significant influence on gas-phase chemistry.


2009 ◽  
Vol 23 (31) ◽  
pp. 5819-5834 ◽  
Author(s):  
OLCAY ÜZENGI AKTÜRK ◽  
OĞUZ GÜLSEREN ◽  
MEHMET TOMAK

Although the stable structures and other physical properties of small Ag n and Au n, were investigated in the literature, phonon calculations are not done yet. In this work, we present plane-wave pseudopotential calculations based on density-functional formalism. The effect of using the generalized gradient approximation (GGA) and local density approximation (LDA) to determine the geometric and electronic structure and normal mode calculations of Ag n and Au n, is studied up to eight atoms. Pure Au n and Ag n clusters favor planar configurations. We calculated binding energy per atom. We have also calculated the normal mode calculations and also scanning tunneling microscope (STM) images for small clusters for the first time.


Author(s):  
Jieyu Wang ◽  
Xianwen Kong

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.


Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania

This paper deals with an adaptive refinement technique of a B-spline degenerate shell finite element model, for the free vibration analysis of curved thin and moderately thick-walled structures. The automatic refinement of the solution is based on an error functional related to the density of the total potential energy. The model refinement is generated by locally increasing, in a sub-domain R of a local patch domain, the number of shape functions while maintaining constant the functions polynomial order. The local refinement strategy is described in a companion paper, written by the same authors of this paper and presented in this Conference. A two-step iterative procedure is proposed. In the first step, one or more sub domains to be refined are identified by means of a point-wise error functional based on the system total potential energy local density. In the second step, the number of shape functions to be added is iteratively increased until the difference of the total potential energy, calculated on the sub domain between two iteration, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed.


2019 ◽  
Vol 807 ◽  
pp. 135-140
Author(s):  
Xi Jin Fu

Based on the first-principles, using CCSD(T) ab initio calculation method, many-body potential energy of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at T=300K, and firstly establish and discuss the face-centered cubic (fcc) atomic crystal configurations of two-, three-, and four-body terms by geometry optimization. The results shows that the total number of (Ar)2 clusters is 903, which belongs to 12 different geometric configurations, the total number of (Ar)3 clusters is 861, which belongs to 25 different geometric configurations, and the total number of (Ar)4 clusters of is 816 which belongs to 27 different geometric configurations. We find that the CCSD(T) with the aug-cc-pVQZ basis set is most accurate and practical by comprehensive consideration. The total potential energy Un reachs saturation at R>2.0Å when the only two-and three-body interaction energy are considered. When R≤2.0Å, the total potential energy Un must consider four-and higher-body interaction energy to achieve saturation. Many-body expansion potential of fcc solid argon is an exchange convergent series.


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