Kernel energy method: Basis functions and quantum methods

Abstract

AbstractThe kernel energy method (KEM) has been illustrated with peptides and has been shown to reduce the computational difficulty associated with obtaining ab initio quality quantum chemistry results for large biological compounds. In a recent paper, the method was illustrated by application to 15 different peptides, ranging in size from 4 to 19 amino acid residues, and was found to deliver accurate Hartree–Fock (HF) molecular energies within the model, using Slater‐type orbital (STO)‐3G basis functions. A question arises concerning whether the results obtained from the use of KEM are wholly dependent on the STO‐3G basis functions that were employed, because of their relative simplicity, in the first applications. In the present work, it is shown that the accuracy of KEM does not depend on a particular choice of basis functions. This is done by calculating the ground‐state energy of a representative peptide, ADPGV7B, containing seven amino acid residues, using seven different commonly employed basis function sets, ranging in size from small to medium to large. It is shown that the accuracy of the KEM does not vary in any systematic way with the size or mathematical completeness of the basis set used, and good accuracy is maintained over the entire variety of basis sets that have been tested. Both approximate HF and density functional theory (DFT) calculations are made. We conclude that the accuracy inherent in the KEM is not dependent on a particular choice of basis functions. The first application, to 15 different peptides mentioned above, employed only HF calculations. A second question that arises is whether the results obtained with the use of KEM will be accurate only within the HF approximation. Therefore, in the present work we also study whether KEM is applicable across a variety of quantum computational methods, characterized by differing levels of accuracy. The peptide, Zaib4, containing 74 atoms, was used to calculate its energy at seven different levels of accuracy. These include the semi‐empirical methods, AM1 and PM5, a DFT B3LYP model, and ab initio HF, MP2, CID, and CCSD calculations. KEM was found to be widely applicable across the spectrum of quantum methods tested. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006