Stochastic Search of the Quantum Conformational Space of Small Lithium and Bimetallic Lithium−Sodium Clusters

Abstract

In this paper we report the results obtained by an implementation and application of the simulated annealing optimization procedure to the exploration of the conformational space of small neutral and charged lithium clusters (Li(n)(q), n = 5, 6, 7; q = 0, +/-1) and of the bimetallic lithium/sodium clusters (Li5Na) in their lowest spin states. Our methodology eliminates the structure guessing procedure in the process of generating cluster configurations. We evaluate the quantum energy, typically with the Hartree-Fock Hamiltonian, of randomly generated points in the conformational space and use a modified Metropolis test in the annealing algorithm to generate candidate structures for atomic clusters. The structures are further optimized by analytical methods (gradient following) at the Møller-Plesset second order perturbation theory level (MP2), in conjunction with basis sets including polarization functions with and without diffuse functions. High accuracy ab initio energies at the coupled clusters level, with single, double, and triple substitutions from the Hartree-Fock determinant (CCSD(T)), on the MP2 geometries were calculated and used to establish the relative stability of the isomers within each potential energy surface. Various cluster properties were computed and compared to existing values in order to validate our methods. Our results show excellent agreement with previous experimental and theoretical reports. Even at these small sizes, evidence for 10 new structures never reported before for the lithium clusters and four new structures for the bimetallic clusters is presented.

Structural studies of the water tetramer

“…Recently, we have proposed an application of a modified simulated annealing (SA) [13][14][15] optimization procedure with quantum evaluation of the energy (ASCEC after its Spanish acronym Annealing Simulado Con Energía Cuántica) as a tool for comprehensive generation of cluster candidate structures [16,17]. The method incorporates the comparative advantages and disadvantages of stochastic optimization over analytical methods [11], namely, initial-guess independence, exhaustive exploration of the PES and the very desirable feature of avoiding being trapped in local minima by virtue of the ability to jump over energy barriers and to sample several energy wells on the same run; however, the method is still computationally intensive because of the repetitive evaluation of the energy function.…”

Unusual solvation through both p-orbital lobes of a carbene carbon

“…Initial pseudotemperatures of 500 K and geometrical quenching routes with 5% of decrease and a total of 100 pseudo-temperatures were appropriate. 30,31 The HF/6-21G model chemistry was used to compute the energies of Markov chains of random configurations in the corresponding configurational space. Because of the computational cost due to the high frequency of energy calculations, at this stage, it is not possible to use higher levels of theory.…”

“…Among the initial guess, independent strategies for the localization of stable, chemically meaningful structures on a Potential Energy Surface (PES) stochastic sampling methods are advantageous because the ability to overcome energy barriers, which allows to visit several energy wells on the same run without getting trapped in local minima. The ASCEC algorithm [29][30][31] belongs to stochastic sampling methods and has been successfully used in the treatment of very diverse systems. [30][31][32][33][34][35][36][37][38][39][40][41][42][43] The ASCEC method consists of random walks on complex energy landscapes of atomic or molecular aggregates, producing structures that are subject to a modified Metropolis acceptance test.…”

Exploration of the (ethanol)4–water heteropentamers potential energy surface by simulated annealing and Ab initio molecular dynamics

“…These two methods were selected to compare their suitability to explore the PES of this system. SA and ADMP perform configurational searches using very different computational schemes and they have shown remarkable results in the study of neutral [18,25] and charged [26][27][28] systems. For instance, it is possible to produce initial guesses for structures of water tetramers [18] and lithium clusters [28] using an adapted version of the SA algorithm with a modified Metropolis test obtaining stationary points that are unreported previously.…”

“…SA and ADMP perform configurational searches using very different computational schemes and they have shown remarkable results in the study of neutral [18,25] and charged [26][27][28] systems. For instance, it is possible to produce initial guesses for structures of water tetramers [18] and lithium clusters [28] using an adapted version of the SA algorithm with a modified Metropolis test obtaining stationary points that are unreported previously. ADMP has also shown to be a promising alternative approach to the original Car and Parrinello method [29] to study dynamics not only for clusters [26] but also for reactions [27].…”