Energy Landscapes: An Overview

2001 ◽  
Vol 700 ◽  
Author(s):  
David J. Wales
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Dynamic Properties ◽  
Energy Landscape ◽  
Global Optimisation ◽  
Energy Landscapes ◽  
Energy Landscape Theory ◽  
Landscape Theory ◽  
Optimisation Algorithms

AbstractThe goal of energy landscape theory is to relate observable thermodynamic and dynamic properties to features of the underlying potential energy surface. Here we illustrate the approach with reference to the annealing of C60 and indicate how it may be used to design improved global optimisation algorithms.

EXPLORING THE ENERGY LANDSCAPE

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2877-2885 ◽  
Author(s):  
DAVID J. WALES
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Rate Constants ◽  
Energy Surface ◽  
Energy Landscape ◽  
High Dimensional ◽  
Global Minima ◽  
Structure Dynamics ◽  
Recent Advances ◽  
Dimensional Object

Calculations of structure, dynamics and thermodynamics in molecular science all rely on the underlying potential energy surface (PES). Recent advances allow us to visualise this high-dimensional object in a compact fashion, locate global minima efficiently, and sample multistep pathways to obtain rate constants. These methods have been applied to a wide variety of systems, including clusters, glasses and biomolecules, and enable us to treat dynamics on the experimental timescale and beyond.

scholarly journals Energy Landscapes, Self-Assembly and Viruses

2005 ◽  
Vol 6 (2) ◽  
pp. 107-110 ◽  
Author(s):  
D. J. Wales
Keyword(s):  
Protein Folding ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Self Assembly ◽  
Energy Surface ◽  
Genetic Material ◽  
Magic Number ◽  
Molecular Beams ◽  
Energy Landscapes ◽  
Guided Exploration

Phenomena such as protein folding, crystallisation, self-assembly, and the observation of magic number clusters in molecular beams are all the result of non-random searches. Analysis of the underlying potential energy surface may provide a unifying framework to explain how such events occur as the result of a guided exploration of the landscape. In particular, icosahedral shells composed of 12 pentagonal pyramids are found to be thermodynamically favourable and kinetically accessible when the pyramids are not too spiky and not too flat. Hence, viruses with icosahedral capsids not only minimise the genetic material required to encode the repeated subunits, but may also utilise the favourable properties of a potential energy surface that effectively directs self-assembly.

scholarly journals Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

2020 ◽  
Author(s):  
Elizabeth Lee ◽  
Thomas Ludwig ◽  
Boyuan Yu ◽  
Aayush Singh ◽  
François Gygi ◽  
...  
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Heterogeneous Catalysis ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Energy Landscape ◽  
Free Energy Landscape ◽  
Enhanced Sampling ◽  
Elementary Reactions

<p>Reaction rates in heterogeneous catalysis are predicted using the free energy profiles of elementary reactions. Conventionally, the energetics are computed from critical points of the potential energy surface, with harmonic free energy corrections. Here we use <i>ab initio</i> molecular dynamics and neural network-assisted enhanced sampling simulations to directly calculate the free energy landscape of a prototypical heterogeneous catalysis reaction, the dissociation of molecular nitrogen on ruthenium. We show that accelerating force- and frequency-based enhanced sampling using neural networks can characterize reactive phenomena at density functional theory-level accuracy. A previously reported molecularly adsorbed metastable state is found in the potential energy surface but is absent in the free energy surface. The potential of mean force for the dissociation reaction shows significant temperature-dependent effects beyond the standard harmonic approximation. We demonstrate that these thermodynamic effects can be important for elementary reactions on transition metal surfaces.</p>

scholarly journals The Effect of Nonnative Interactions on the Energy Landscapes of Frustrated Model Proteins

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Mark T. Oakley ◽  
David J. Wales ◽  
Roy L. Johnston
Keyword(s):  
Genetic Algorithms ◽  
Potential Energy ◽  
Global Minimum ◽  
Energy Surface ◽  
Energy Landscape ◽  
Small Degree ◽  
Energy Landscapes ◽  
Go Model ◽  
Encounter Time ◽  
Basin Hopping

The 46- and 69-residue BLN model proteins both exhibit frustrated folding to β-barrel structures. We study the effect of varying the strength of nonnative interactions on the corresponding energy landscapes by introducing a parameter λ, which scales the potential between the BLN (λ=1) and Gō-like (λ=0) limits. We study the effect of varying λ on the efficiency of global optimisation using basin-hopping and genetic algorithms. We also construct disconnectivity graphs for these proteins at selected values of λ. Both methods indicate that the potential energy surface is frustrated for the original BLN potential but rapidly becomes less frustrated as λ decreases. For values of λ≤0.9, the energy landscape is funnelled. The fastest mean first encounter time for the global minimum does not correspond to the Gō model: instead, we observe a minimum when the favourable nonnative interactions are still present to a small degree.

scholarly journals Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

2020 ◽  
Author(s):  
Elizabeth Lee ◽  
Thomas Ludwig ◽  
Boyuan Yu ◽  
Aayush Singh ◽  
François Gygi ◽  
...  
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Heterogeneous Catalysis ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Energy Landscape ◽  
Free Energy Landscape ◽  
Enhanced Sampling ◽  
Elementary Reactions

<p>Reaction rates in heterogeneous catalysis are predicted using the free energy profiles of elementary reactions. Conventionally, the energetics are computed from critical points of the potential energy surface, with harmonic free energy corrections. Here we use <i>ab initio</i> molecular dynamics and neural network-assisted enhanced sampling simulations to directly calculate the free energy landscape of a prototypical heterogeneous catalysis reaction, the dissociation of molecular nitrogen on ruthenium. We show that accelerating force- and frequency-based enhanced sampling using neural networks can characterize reactive phenomena at density functional theory-level accuracy. A previously reported molecularly adsorbed metastable state is found in the potential energy surface but is absent in the free energy surface. The potential of mean force for the dissociation reaction shows significant temperature-dependent effects beyond the standard harmonic approximation. We demonstrate that these thermodynamic effects can be important for elementary reactions on transition metal surfaces.</p>

scholarly journals Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

2020 ◽  
Author(s):  
Elizabeth Lee ◽  
Thomas Ludwig ◽  
Boyuan Yu ◽  
Aayush Singh ◽  
François Gygi ◽  
...  
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Heterogeneous Catalysis ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Energy Landscape ◽  
Free Energy Landscape ◽  
Enhanced Sampling ◽  
Elementary Reactions

<p>Reaction rates in heterogeneous catalysis are predicted using the free energy profiles of elementary reactions. Conventionally, the energetics are computed from critical points of the potential energy surface, with harmonic free energy corrections. Here we use <i>ab initio</i> molecular dynamics and neural network-assisted enhanced sampling simulations to directly calculate the free energy landscape of a prototypical heterogeneous catalysis reaction, the dissociation of molecular nitrogen on ruthenium. We show that accelerating force- and frequency-based enhanced sampling using neural networks can characterize reactive phenomena at density functional theory-level accuracy. A previously reported molecularly adsorbed metastable state is found in the potential energy surface but is absent in the free energy surface. The potential of mean force for the dissociation reaction shows significant temperature-dependent effects beyond the standard harmonic approximation. We demonstrate that these thermodynamic effects can be important for elementary reactions on transition metal surfaces.</p>

scholarly journals Impact of Conformational Substates and Energy Landscapes on Understanding Hemoglobin Kinetics and Function

2021 ◽  
Author(s):  
William A. Eaton
Keyword(s):  
Protein Folding ◽  
Protein Function ◽  
Energy Landscape ◽  
Rate Theory ◽  
Energy Landscapes ◽  
New Era ◽  
Energy Landscape Theory ◽  
Conformational Substates ◽  
Landscape Theory ◽  
And Function

AbstractHans Frauenfelder’s discovery of conformational substates in studies of myoglobin carbon monoxide geminate rebinding kinetics at cryogenic temperatures (Austin RH, Beeson KW, Eisenstein L, Frauenfelder H, & Gunsalus IC (1975) Dynamics of Ligand Binding to Myoglobin. Biochemistry 14(24):5355–5373) followed by his introduction of energy landscape theory with Peter Wolynes (Frauenfelder H, Sligar SG, & Wolynes PG (1991) The Energy Landscapes and Motions of Proteins. Science 254(5038):1598–1603) marked the beginning of a new era in the physics and physical chemistry of proteins. Their work played a major role in demonstrating the power and importance of dynamics and of Kramers reaction rate theory for understanding protein function. The biggest impact of energy landscape theory has been in the protein folding field, which is well-known and has been documented in numerous articles and reviews, including a recent one of my own (Eaton WA (2021) Modern Kinetics and Mechanism of Protein Folding: a Retrospective. J. Phys. Chem. B. 125(14):3452–3467). Here I will describe the much less well-known impact of their modern view of proteins on both experimental and theoretical studies of hemoglobin kinetics and function. I will first describe how Frauenfelder’s experiments motivated and influenced my own research on myoglobin, which were key ingredients to my work on understanding hemoglobin.

An accurate, global, ab initio potential energy surface for the H + 3 molecule

2000 ◽  
Vol 98 (5) ◽  
pp. 261-273 ◽  
Author(s):  
Oleg L. Polyansky, Rita Prosmiti, Wim Kl
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface
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