Exploring Complex Energy Surfaces

Wang and D. D. Johnson, Density Functional Study of Structural Trends for Late Transition Metal 13 Atom Clusters, Rhys. Rev. B 75 (2007), 235405. 

De Vita, and R. Car, Structure and Electronic Properties of Amorphous Indium Phosphide from First Principles, Phys. Rev. B 57 (1998), 1594. 

Two excellent sources for learning about MD algorithms in classical simulations are M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon, Oxford, UK, 1987, and D. Frenkel and B. Smit, Understanding Molecular Simulations From Algorithms to Applications, 2nd ed., Academic, San Diego, 2002. 

For further details on the algorithms underlying ab initio MD, see M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64 (1992), 1045, and R. M. Martin, Electronic Structure Basic Theory and Practical Methods, Cambridge University Press, Cambridge, 2004. 

The development of improved ab initio MD algorithms using DFT remains an active area. For one example of work in this area, see T. D. Kiihne, M. Krack, F. R. Mohamed, and M. Parrinello, Phys. Rev. Lett. 98 (2007), 066401. Similar work exists for performing MD using high-level quantum chemistry techniques, as described, for example, in J. M. Herbert and M. Head-Gordon, Phys. Chem. Chem. Phys. 7 (2005), 3629. 

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We have wandered over a rather complex energy surface (Fig. 10.13), exploring every possible side reaction until there was nothing more that was reasonable to do. Lx)oking at the stability of all the possibilities on the surface, we arrived at the correct, most favored product. The reaction path is shown vertically on the left and the side routes are shown to the right side. The path name for the forward reaction only is shown. 

HyperChem combines molecular computation and visualization tools with a flexible and intuitive graphical user interface. Its computational algorithms enable users to calculate and explore potential energy surfaces for molecular systems, both simple and complex. Energy minimization and transition state search, molecular dynamics, Langevin dynamics, and Monte Carlo calculations are supported, with extensive user control and customization capabilities. This article summarizes methods used to compute potential energy surfaces in HyperChem, and provides references to the literature that describe the theoretical and computational approaches upon which HyperChem s implementation is based. More complete and current information may be obtained from Hypercube s website. 

The second problem also reflects the exceptional difficulty of exploring complex conformational energy surfaces. Quite simply, only the lowest-cost methods are applicable to anything but molecules with only a few degrees of conformational freedom. In practice and at the present time, this translates to molecular mechanics models. (Semi-empirical quantum chemical models might also represent practical alternatives, except for the fact that they perform poorly in this role.) Whereas molecular mechanics models such as MMFF seem to perform quite well, the fact of the matter is, outside the range of their explicit parameterization, their performance is uncertain at best. 

In this section we will present results of ab initio molecular dynamics simulations performed for more complex chemical reactions. Catalytic copolymerization of a-olefins with polar group containing monomers, chosen here as an example, is a complex process involving many elementary reactions. While for many aspects of such a process the standard approach by static quantum chemical calculations performed for the crucial reaction intermediates provides often sufficient information, for some aspects it is necessary to go beyond static computations. In the case of the process presented here, MD was priceless in exploring the potential energy surfaces for a few elementary reactions that were especially difficult for a static approach, due to a large number of alternative transition states and thus, alternative reaction pathways.77... 

After performing ab initio and solvation calculations to examine the decarboxylation reaction in water, the free energy surface of the enzyme-catalyzed reaction was explored. An initial ODCase-OMP complex was constructed from the structure of the ODCase-6-azaUMP complex reported by Pai and coworkers,22... 

Ab initio molecular orbital theory is utilized to study the hydrogen abstraction reaction of n-bromopropane with hydroxyl radical and chlorine atom. The stability of the trans and gauche isomers of n-bromopropane is explored. The potential energy surface of both reactions is characterized by pre- and post-reactive complexes, as well as transition state structures in both trans and gauche isomeric forms. The importance of these two reactions relies on the ultimate product distribution from both reactions. Differences in the reactivity of 1-bromopropane toward OH and Cl are observed. The reaction of n-bromopropane with OH radical favors the abstraction of hydrogen atoms while the reaction with Cl atoms favors the abstraction of hydrogen atoms at the a and p carbon sites. 

The complexity of the PES for the pair of H CO with H2O offers a rich field of candidates for minima and stationary points. Kumpf and Damewood explored an extensive region of the potential energy surface of the HjCO- HOH complex using a polarized basis set of the 6-3IG variety. Correlation was added, as well as zero-point vibrations, once stationary points were identified. Thirteen different configurations were considered. 

The HjO HP-HF complex was reexamined more recently in conjunction with a comparison with H O H O -HF. The focus of this work was an exploration of the potential energy surface to identify all the local minima. In addition to the cyclic structure of Fig. 5.27, a bifurcated geometry, in which the water serves as double proton acceptor, was also located as a minimum of the PES of H O -HF—HF. In the complex containing a pair of water molecules and one HF, the only minimum located was of cyclic type. Both of these structures are illustrated in Fig. 5.28. 

Van der Waals Complexes a Tool to Explore the Potential Energy Surface in the Electron-transfer Region... 

In reaction kinetics two of the most often used of Eyring s many contributions are the concept of activated complex and the use of potential energy surface to follow the course of an elementary reaction. These are employed in the present paper to explore the mechanism of some photosensitized reactions. 

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