Bridging Static and Dynamical Descriptions of Chemical Reactions: An ab Initio Study of CO 2 Interacting with Water Molecules Gre ́ goire A. Gallet, † Fabio Pietrucci, † and Wanda Andreoni* ,†,‡ † Centre Europe ́ en de Calcul Atomique et Mole ́ culaire (CECAM), Ecole Polytechnique Fé de ́ rale de Lausanne, Switzerland ‡ Institut de The ́ orie des Phé nome ̀ nes Physiques, Ecole Polytechnique Fe ́ de ́ rale de Lausanne, Switzerland * S Supporting Information ABSTRACT: Extracting reliable thermochemical parameters from molecular dynamics simulations of chemical reactions, although based on ab initio methods, is generally hampered by difficulties in reproducing the results and controlling the statistical errors. This is a serious drawback with respect to the quantum-chemical description based on potential energy surfaces. This work is an attempt to fill this gap. We apply molecular dynamics, based on density functional theory (DFT) and empowered by path metadynamics (MTD), to simulate the reaction of CO 2 with (one, two, and three) water molecules in the gas phase. This study relies on a strategy that ensures a precise control of the accuracy of the reaction coordinates and of the reconstructed free- energy surface on this space, namely, on (i) fully reversible MTD simulations, (ii) a committor probability analysis for the diagnosis of the collective variables, and (iii) a cluster analysis for the characterization of the reconstructed free-energy surfaces. This robust procedure permits a meaningful comparison with more traditional calculations of the potential energy surfaces that we also perform within the same DFT computational scheme. This comparison shows in particular that the reactants and products of systems with only three water molecules can no longer be understood in terms of one structure but must be described as statistical configuration ensembles. Calculations carried out with different prescriptions for the exchange-correlation functionals also allow us to establish their quantitative effect on the activation barriers for the formation and the dissociation of carbonic acid. Their decrease induced by the addition of one water molecule (catalytic effect) is found to be largely independent of the specific functional. 1. INTRODUCTION The reaction of carbon dioxide (CO 2 ) with water in various phases is of fundamental importance in diverse fields of chemis- try, ranging from biochemistry to environmental chemistry. In particular, its role is crucial in many of the routes in use or being explored for the capture and sequestration of CO 2 . 1-3 This explains the renewed and ever growing interest in char- acterizing the interaction of CO 2 with water at the microscopic level. 4,5 Theory and computations could be highly relevant in these studies, because of the difficulty in experiments to observe the various steps of these reactions. The path toward this target is by far not straightforward. On one hand, characterization and understanding of molecular reac- tions is rooted in well-established theories (see, e.g., ref 6-8) also dealing with nuclear quantum effects; 9-12 on the other, the complexity of the real systems calls for efficient approaches, thus implying other approximations. The study of chemical reactions in condensed phases, especially in solution, has long been pursued within hybrid schemes with the “solvent” modeled as a continuum. 13 The inclusion of density functional theory (DFT) in molecular dynamics (MD) 14 has marked an important step forward for the investigation of physical and chemical processes in condensed matter systems. Nowadays, the typical approach to the study of chemical reactions in condensed phases uses DFT-MD, which has recently been empowered by accelerated sampling methods like metadynamics. 15-17 Although partial studies of CO 2 in solution have already been made using metadynamics simulations, 18-20 a number of issues remain open which must be solved before applying these techniques with confidence to predict the physi- cal behavior of CO 2 -water systems. In particular, we should be able to answer the following questions: (i) to what extent do the available implementations of DFT “correctly” describe these systems, and (ii) to what extent can we rely on the characterization of the free-energy surface (FES) from a DFT metadynamics-based simulation at finite temperature? In other words, is the robustness of this method comparable to that of the computations of the potential energy surface (PES) for the same reactions? In this paper, we investigate both i and ii questions by studying the association and dissociation reactions + → + − n n CO HO H CO ( 1)H O 2 2 2 3 2 (1) (n = 1,2,3) in the gas phase in a systematic way: We use several exchange-correlation (xc) functionals and, within the same computational schemes, determine local minima and transition states of the potential energy surface (PES) and of the room- temperature (RT) free-energy surface (FES). Investigating the reactions in eq 1 in the gas phase gives us the opportunity to make a one-to-one comparison of our DFT results for the PES features with those of high-level post- Hartree-Fock approaches, 21-26 like Møller-Plesset second- order perturbation theory (MP2), quadratic configuration-intera- ction, and coupled-cluster theory. On the other hand, the characterization of the FES we present here is unprecedented: it Received: July 7, 2012 Article pubs.acs.org/JCTC © XXXX American Chemical Society A dx.doi.org/10.1021/ct300581n | J. Chem. Theory Comput. XXXX, XXX, XXX-XXX