Fully Quantum Mechanical Description of Proteins in Solution. Combining Linear Scaling Quantum Mechanical Methodologies with the Poisson−Boltzmann Equation

In this paper we report a method for solving the Schrödinger equation for large molecules in solution which involved merging a linear scaling divide and conquer (D&C) semiempirical algorithm with the Poisson−Boltzmann (PB) equation. We then assess the performance of our self-consistent reaction field (SCRF) approach by comparing our D&C-PB calculations for a set of 29 neutral and 36 charged molecules with those obtained by ab initio GVB and DFT (B3LYP) methods, Cramer and Truhlar's semiempirical generalized-Born SM5 model, and with the experimental solvation free energies. Furthermore, we show that our SCRF method can be used to perform fully quantum mechanical calculations of proteins in solution in a reasonable amount of time on a modern workstation. We believe that all electrostatic interactions in biological systems require a quantum mechanical description in order to obtain an accurate representation. Thus, our new SCRF method should have an impact on the computational study of physical and chemical phenomena occurring in proteins and nucleic acids, which are, in general, strongly influenced by electrostatic interactions. Moreover, this may lead to novel insights into classic problems like protein folding or drug design.