Generalized Electronic Diabatic Approach to Structural Similarity in Two-Dimensional Potential Energy Surfaces of Various Topologies GUSTAVO A. ARTECA, 1,2 JEAN PIERRE RANK, 1 O. TAPIA 2 1 De ´partement de Chimie et Biochimie & Biomolecular Sciences Programme, Laurentian University, Ramsey Lake Road, Sudbury, ON, Canada P3E 2C6 2 Department of Physical Chemistry, Uppsala University, Box 579, S-751 23 Uppsala, Sweden Received 30 January 2007; accepted 5 June 2007 Published online 10 October 2007 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.21475 ABSTRACT: Active site properties in some proteins can be affected by conformational fluctuations of neighbor residues, even when the latter are not involved directly in the binding process. A local environment thus appears to alter the relevant potential energy surface and its reaction paths. Here, some aspects of this phenomenon are simulated within a generalized electronic diabatic (GED) scheme to study the geometry and structural similarity for a class of two-dimensional (2D) energy surfaces. The electronic quantum state is a linear superposition of diabatic basis functions, each of which is taken to represent a single (pure) electronic state for the isolated material system. Here, we describe a model reaction of isomerization by shifts in amplitudes for three diabatic species (reactant, product, and an open-shell transition state) coupled in an external field. The “effective” 2D energy surface in the field is characterized in terms of critical points, and the amplitudes along the main reaction paths. A new feature is the introduction of a phase diagram where all possible potential-energy-surface topologies (consistent with three-state systems in two linear coordinates) are matched with actual model parameters. By varying the coupling strengths between diabatic states, we classify regions of this phase diagram in terms of electronic and structural similarities; some regions comprise models whose reaction paths have geometries that belong to the catchment region of the reactant, yet are electronically akin to the diabatic transition state or product. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem 108: 651– 666, 2008 Key words: diabatic states; potential energy surfaces; topology; structural similarity Introduction A n enzyme’s catalytic power arises mainly from the fact that the immediate biomolecular environment of the active site provides an electro- static organization that can modify the electronic properties of a bound substrate [1, 2]. In this con- text, this immediate environment (which can in- clude solvation) is not incidental but rather an in- tegral part of the reaction. In some special cases, however, there is evidence of subtler (entatic) ef- fects [3– 6], whereby the non-immediate environment is also able to affect biomolecular function. This is particularly evident in proteins whose functions are electron and proton transfer (“tunneling”), as well Correspondence to: O. Tapia; e-mail: orlando.tapia@fki.uu.se International Journal of Quantum Chemistry, Vol 108, 651– 666 (2008) © 2007 Wiley Periodicals, Inc.