Scaling Theory for Electronic Structure

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Sabre Kais of Purdue University is supported by the Theoretical and Computational Chemistry Program to develop and apply the finite scaling method in several related projects. First, the finite size scaling method will be adapted for studying the critical behavior of a quantum Hamiltonian as a function of a set of parameters. This method will be generalized using Gaussian basis sets to search for new stable multiply-charged anions in the gas phase. As well, methods will be developed to predict and calculate the formation of resonances for atomic and molecular anions. Next, the Feynmann path integral approach will be used to advance the finite size scaling method for mapping quantum problems to effective classical lattice systems. The method will be combined with other simulation techniques to obtain critical parameters for molecular systems. Finally, finite size scaling will be explored to enable correlation of structural and thermodynamic properties of small clusters with their corresponding bulk matter. A long-term goal of this research is the creation of a single approach that will enable accurate computational chemistry calculations for atomic, molecular, and cluster properties at the lowest effective cost. Success in this area could obviate the need to carry out mundane or even hazardous experiments to determine necessary chemical information. This work could also permit the exploration of transient chemical species that could otherwise be difficult or impossible to study experimentally.