Analysis of the Errors in the Electrostatically Embedded Many-Body Expansion of the Energy and the Correlation Energy for Zn and Cd Coordination Complexes with Five and Six Ligands and Use of the Analysis to Develop a Generally Successful Fragmentation Strategy

Abstract

In the present paper, we apply the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE) to the calculation of zinc-ligand and cadmium-ligand bond dissociation energies, and we analyze the errors due to various fragmentation schemes in a variety of neutral, positively charged, and negatively charged Zn2+ and Cd2+ coordination complexes. As a result of the analysis, we are able to present a new, simple, and unambiguous fragmentation strategy. Following this strategy, we show that both methods perform well for zinc-ligand and cadmium-ligand bond dissociation energies for all systems studied in the paper, including a model of the catalytic site of the zinc-bearing anthrax toxin lethal factor (LF), which has garnered substantial attention as a target for drug development. To draw general conclusions we consider ten pentacoordinate and hexacoordinate zinc and cadmium containing coordination complexes, each with 10 or 15 different fragmentation schemes. By analyzing errors, we developed a prescription for the optimal fragmentation strategy. With this scheme, and using MP2 correlation energies as a test, we find that the electrostatically embedded three-body expansion of the correlation energy (EE-3B-CE) method is able to reproduce all 53 conventionally calculated bond energies with an average absolute error of only 0.59 kcal/mol. The paper also presents EE-MB-CE calculations using the CCSD(T) level of theory on an LF model system. With CCSD(T), EE-3B-CE has an average error of 0.30 kcal/mol.

Trouble with the Many-Body Expansion

“…So far we have only presented data for noncovalent water clusters, but MBE convergence problems also arise in valence-bonded systems. This has great implications for fragmentation methods, which in most cases use a truncated MBE, or something analogous to it, to approximate the total energies of large chemical systems. ,− …”

Accurate Composite and Fragment-Based Quantum Chemical Models for Large Molecules

“…Further extensions of the EE-MB method (EE-MB-CE and EE-MB-NE) were proposed to accurately reproduce the MP2 energies of large water clusters. The applicability of EE-MB method has been illustrated through several other challenging systems. − …”

Fragment Quantum Mechanical Method for Large-Sized Ion–Water Clusters

“…The crucial role played by the ion–water complex in biology underlines the importance of an accurate and detailed knowledge of the structure and dynamics of these species in solution . Because of the long-range electrostatic polarization effect arising from charged ions and charge transfer between ions and water molecules, the many-body QM effect in the ion–water cluster is more significant than that of the pure water cluster, which presents a grand challenge for fragmentation methods. , Therefore, the development of a robust and broadly applicable method, that can accurately calculate the energy of large-sized ion–water clusters with a reduced cost, is of great importance for high-level ab initio studies on aqueous solutions.…”