Integrating firefly algorithm with density functional theory for global optimization of Al42− clusters

  • Arka Mitra
  • Gourhari Jana
  • Prachi Agrawal
  • Shamik SuralEmail author
  • Pratim K. ChattarajEmail author
Regular Article


The crux of quantum chemistry lies in the minimization of energy functional to obtain the optimized geometry of a molecule. This involves formulating the energy minimization task as a global optimization (GO) problem and using an appropriate algorithm for determining the best solution out of a number of feasible solutions. Several new and unconventional algorithms are proposed that augment the efforts toward GO of clusters of atoms using rigorous quantum chemical methods. Among these, swarm intelligence-based nature-inspired metaheuristic algorithms have particularly drawn considerable attention. However, it still has certain drawbacks. In this work, we propose the use of firefly algorithm (FA) in conjunction with density functional theory (DFT)-based calculations for solving the GO problem and establish its superioriority in performance over particle swarm optimization (PSO) through extensive computational studies. Specifically, we show how such a “FA + DFT” approach can be used for GO of Al42− clusters. Each possible structure in the three-dimensional search space is treated as a firefly particle. Starting with an initial pool of particles, newer sets of particles are generated using an evolutionary mechanism, thereby moving toward solutions with particles having “better” structures. This novel approach also enables the possibility of incorporating molecule specific domain knowledge. For example, knowing that Al42− clusters are planar, we can restrict the search space so that only planar structures are explored, thereby achieving faster convergence of the algorithm. As an extension of the current technique, an important correlation between energy stabilization and aromaticity is established.


Aluminum cluster Energy minimization Firefly algorithm Particle swarm optimization Aromaticity 



PKC would like to thank DST, New Delhi, for the J. C. Bose National Fellowship. SS, AM, and PA thank CSE for the computational facilities. GJ thanks IIT, Kharagpur, for his fellowship.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest regarding the publication of this article, financial, and/or otherwise.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Electronics and Electrical Communication EngineeringIndian Institute of Technology KharagpurKharagpurIndia
  2. 2.Department of Chemistry and Centre for Theoretical StudiesIndian Institute of Technology KharagpurKharagpurIndia
  3. 3.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia
  4. 4.Department of Computer Science and EngineeringIndian Institute of Technology KharagpurKharagpurIndia
  5. 5.Department of ChemistryIndian Institute of Technology BombayPowai, MumbaiIndia

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