Growing String Method Research Articles

Finding the transition state without initial guess: The growing string method for Newton trajectory to isomerization and enantiomerization reaction of alanine dipeptide and poly(15)alanine

We report a new, high-dimensional application of a method for finding a transition state (TS) between a reactant and a product on the potential energy surface: the search of a growing string along a reaction path defined by any Newton trajectory in combination with the Berny method (Quapp, J Chem Phys (2005), 122, 174106; we have provided this algorithm on a web page). Two given minima are connected by a one-dimensional, but usually curvilinear reaction coordinate. It leads to the TS region. The application of the method to alanine dipeptide finds the TS of the isomerisation C(7 ax) --> C(5), some TSs of the enantiomerisation of C(7 ax) from L-form to quasi-D-form, and it finds the TS region of a transition of a partly unfolded, bent structure which turns back into a mainly alpha-helix in the Ac(Ala)(15)NHMe polyalanine (all at the quantum mechanical level B3LYP/6-31G: the growing string calculation is interfaced with the Gaussian03 package). The formation or dissolvation of some alpha- or 3(10)-hydrogen bonds of the helix are discussed along the TS pathway, as well as the case of an enantiomer at the central residue of the helix.

Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jonnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.

A growing string method for the reaction pathway defined by a Newton trajectory

The reaction path is an important concept of theoretical chemistry. We use a projection operator for the following of the Newton trajectory (NT) along the reaction valley of the potential energy surface. We describe the numerical scheme for the string method, adapting the proposal of a growing string (GS) by [Peters et al.,J. Chem. Phys. 120, 7877 (2004)]. The combination of the Newton projector and the growing string idea is an improvement of both methods, and a great saving of the number of iterations needed to find the pathway over the saddle point. This combination GS-NT is at the best of our knowledge new. We employ two different corrector methods: first, the use of projected gradient steps, and second a conjugated gradient method, the CG+ method of Liu, Nocedal, and Waltz, generalized by projectors. The executed examples are Lennard-Jones clusters, LJ(7) and LJ(22), and an N-methyl-alanyl-acetamide (alanine dipeptide) rearrangement between the minima C7(ax) and C5. For the latter, the growing string calculation is interfaced with the GASSIAN03 quantum chemical software package.

Comprehensive DFT Study of Nitrous Oxide Decomposition over Fe-ZSM-5

The reaction mechanism for nitrous oxide decomposition has been studied on hydrated and dehydrated mononuclear iron sites in Fe-ZSM-5 using density functional theory. In total, 46 different surface species with different spin states (spin multiplicity M(S) = 4 or 6) and 63 elementary reactions were considered. Heats of adsorption, activation barriers, reaction rates, and minimum energy pathways were determined. The approximate minimum energy pathways and transition states were calculated using the "growing string method" and a modified "dimer method". Spin surface crossing (e.g., O(2) desorption) was considered. The minimum potential energy structure on the seam of two potential energy surfaces was determined with a multiplier penalty function algorithm by Powell and approximate rates of spin surface crossings were calculated. It was found that nitrous oxide decomposition is first order with respect to nitrous oxide concentration and zero order with respect to oxygen concentration. Water impurities in the gas stream have a strong inhibiting effect. In the concentration range of 1-100 ppb, the presence of water vapor influences the surface composition and the apparent rate coefficient. This is especially relevant in the temperature range of 600-700 K where most experimental kinetic studies are performed. Apparent activation barriers determined over this temperature range vary from 28.4 (1 ppb H(2)O) to 54.8 kcal/mol (100 ppb H(2)O). These results give an explanation why different research groups and different catalyst pretreatments often result in very different activation barriers and preexponential factors. Altogether perfect agreement with experimental results could be achieved.

A growing string method for determining transition states: comparison to the nudged elastic band and string methods.

Interpolation methods such as the nudged elastic band and string methods are widely used for calculating minimum energy pathways and transition states for chemical reactions. Both methods require an initial guess for the reaction pathway. A poorly chosen initial guess can cause slow convergence, convergence to an incorrect pathway, or even failed electronic structure force calculations along the guessed pathway. This paper presents a growing string method that can find minimum energy pathways and transition states without the requirement of an initial guess for the pathway. The growing string begins as two string fragments, one associated with the reactants and the other with the products. Each string fragment is grown separately until the fragments converge. Once the two fragments join, the full string moves toward the minimum energy pathway according to the algorithm for the string method. This paper compares the growing string method to the string method and to the nudged elastic band method using the alanine dipeptide rearrangement as an example. In this example, for which the linearly interpolated guess is far from the minimum energy pathway, the growing string method finds the saddle point with significantly fewer electronic structure force calculations than the string method or the nudged elastic band method.