Topic

# Potential energy surface

About: Potential energy surface is a(n) research topic. Over the lifetime, 11674 publication(s) have been published within this topic receiving 307691 citation(s).

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TL;DR: In this paper, the potential energy surface is transformed into a collection of interpenetrating staircases, and the lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.

Abstract: We describe a global optimization technique using “basin-hopping” in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features that recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.

2,437 citations

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TL;DR: In this article, a method for finding saddle points without knowledge of the final state of the transition is described, which only makes use of first derivatives of the potential energy and is therefore applicable in situations where second derivatives are too costly or too tedious to evaluate, for example, in plane wave based density functional theory calculations.

Abstract: The problem of determining which activated (and slow) transitions can occur from a given initial state at a finite temperature is addressed. In the harmonic approximation to transition state theory this problem reduces to finding the set of low lying saddle points at the boundary of the potential energy basin associated with the initial state, as well as the relevant vibrational frequencies. Also, when full transition state theory calculations are carried out, it can be useful to know the location of the saddle points on the potential energy surface. A method for finding saddle points without knowledge of the final state of the transition is described. The method only makes use of first derivatives of the potential energy and is, therefore, applicable in situations where second derivatives are too costly or too tedious to evaluate, for example, in plane wave based density functional theory calculations. It is also designed to scale efficiently with the dimensionality of the system and can be applied to very large systems when empirical or semiempirical methods are used to obtain the atomic forces. The method can be started from the potential minimum representing the initial state, or from an initial guess closer to the saddle point. An application to Al adatom diffusion on an Al(100) surface described by an embedded atom method potential is presented. A large number of saddle points were found for adatom diffusion and dimer/vacancy formation. A surprisingly low energy four atom exchange process was found as well as processes indicative of local hex reconstruction of the surface layer.

2,034 citations

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TL;DR: In this article, a discrete variable representation (DVR) is introduced for use as the L2 basis of the S-matrix version of the Kohn variational method for quantum reactive scattering.

Abstract: A novel discrete variable representation (DVR) is introduced for use as the L2 basis of the S‐matrix version of the Kohn variational method [Zhang, Chu, and Miller, J. Chem. Phys. 88, 6233 (1988)] for quantum reactive scattering. (It can also be readily used for quantum eigenvalue problems.) The primary novel feature is that this DVR gives an extremely simple kinetic energy matrix (the potential energy matrix is diagonal, as in all DVRs) which is in a sense ‘‘universal,’’ i.e., independent of any explicit reference to an underlying set of basis functions; it can, in fact, be derived as an infinite limit using different basis functions. An energy truncation procedure allows the DVR grid points to be adapted naturally to the shape of any given potential energy surface. Application to the benchmark collinear H+H2→H2+H reaction shows that convergence in the reaction probabilities is achieved with only about 15% more DVR grid points than the number of conventional basis functions used in previous S‐matrix Kohn...

1,459 citations

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TL;DR: In this article, an extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions, where nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large NDE coupling is reached.

Abstract: An extension of the classical trajectory approach is proposed that may be useful in treating many types of nonadiabatic molecular collisions. Nuclei are assumed to move classically on a single potential energy surface until an avoided surface crossing or other region of large nonadiabatic coupling is reached. At such points the trajectory is split into two branches, each of which follows a different potential surface. The validity of this model as applied to the HD2+ system is assessed by numerical integration of the appropriate semiclassical equations. A 3d “trajectory surface hopping” treatment of the reaction of H+ with D2 at a collision energy of 4 eV is reported. The excellent agreement with experiment is an encouraging indication of the potential usefulness of this approach.

1,342 citations

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TL;DR: In this paper, the authors derived the classical Hamiltonian of a polyatomic system in terms of these coordinates and their conjugate momenta for the general case of an N atom system with a given nonzero value of the total angular momentum.

Abstract: The reaction path on the potential energy surface of a polyatomic molecule is the steepest descent path (if mass‐weighted Cartesian coordinates are used) connecting saddle points and minima. For an N‐atom system in 3d space it is shown how the 3N‐6 internal coordinates can be chosen to be the reaction coordinate s, the arc length along the reaction path, plus (3N‐7) normal coordinates that describe vibrations orthogonal to the reaction path. The classical (and quantum) Hamiltonian is derived in terms of these coordinates and their conjugate momenta for the general case of an N atom system with a given nonzero value of the total angular momentum. One of the important facts that makes this analysis feasible (and therefore interesting) is that all the quantities necessary to construct this Hamiltonian, and thus permit dynamical studies, are obtainable from a relatively modest number of ab initio quantum chemistry calculations of the potential energy surface. As a simple example, it is shown how the effects o...

1,251 citations