Electronic Properties of Water in Liquid Environment. A Sequential QM/MM Study Using the Free Energy Gradient Method Herbert C. Georg* Instituto de Física, Universidade Federal de Goia ́ s, CP 131, 74001-970, Goiâ nia, GO, Brazil Sylvio Canuto Instituto de Física, Universidade de Sã o Paulo, CP 66318, 05314-970, Sã o Paulo, SP, Brazil ABSTRACT: There is a continuous search for theoretical methods that are able to describe the effects of the liquid environment on molecular systems. Different methods emphasize different aspects, and the treatment of both the local and bulk properties is still a great challenge. In this work, the electronic properties of a water molecule in liquid environment is studied by performing a relaxation of the geometry and electronic distribution using the free energy gradient method. This is made using a series of steps in each of which we run a purely molecular mechanical (MM) Monte Carlo Metropolis simulation of liquid water and subsequently perform a quantum mechanical/molecular mechanical (QM/MM) calculation of the ensemble averages of the charge distribution, atomic forces, and second derivatives. The MP2/aug-cc-pV5Z level is used to describe the electronic properties of the QM water. B3LYP with specially designed basis functions are used for the magnetic properties. Very good agreement is found for the local properties of water, such as geometry, vibrational frequencies, dipole moment, dipole polarizability, chemical shift, and spin-spin coupling constants. The very good performance of the free energy method combined with a QM/MM approach along with the possible limitations are briefly discussed. 1. INTRODUCTION Water is both one of the most important and one of the most common substances in earth. It has a very simple molecular structure. Nevertheless, a number of interesting properties arise when many water molecules come together. 1 It is by far the champion substance in the number of anomalies, many of them with important implications to life. It is perhaps the most studied substance, but still there is not a completely satisfactory theoretical model to treat bulk water. Common approaches for simulating water in condensed phase using molecular dynamics (MD) or Monte Carlo (MC) may be classified in three types: fully quantum (QM), fully classical (MM) and mixed quantum-classical (QM/MM). The QM approach is satisfactory because of its generality (as no empirically fitted parameter is needed) as well as the possibility to cover a wide range of phenomena (as the electronic motion is also taken into account). However, the price for such high level approach is a very high computational demand that imposes some severe limitations on the size of the system. Ab initio simulations of liquid water are typically limited to a relatively small number of molecules even for large computer resources. Also, generally, only a small total time span is realistic at present times. There is a continuous increase in the developments and applications of QM/MM methods. 2,3 Indeed, the use of a QM/MM approach in different problems in molecular and biomolecular systems has shown its feasibility and accuracy. 2,3 It is indispensable for several problems in molecular and biomolecular systems. In this sense, much attention has been devoted to the theoretical study of the properties of a reference molecule in the presence of other molecules treated as a solvent. In particular, water has deserved special attention. 4-8 For instance, Moriarty and Karlströ m 4 have performed a geometry optimization of a reference water molecule in liquid environment using a conventional QM/MM approach in which the reference water was treated at the Hartree-Fock (HF) level. It is known experimentally that both the O-H bond and the H-O-H angle increase from gas to liquid phase. Their results show the same trend, but their O-H bonds are a little underestimated, and the H-O-H angle is a little over- estimated. Certainly, those results are affected by the lack of accuracy of the HF method for calculating the molecular geometry and charge distribution. Nymand and Åstrand 5 have also optimized the geometry of water in liquid environment. They used the CASSCF method to treat the central water embedded in the electric field (ensemble averaged) of the surrounding water molecules represented by point charges. The ensemble of solvent water was obtained with a single MD simulation using the polarizable NEMO potential 9 and keeping all the water molecules in rigid gas-phase geometry. They have found an equilibrium in-liquid geometry that is in good accord with the experimental Received: May 1, 2012 Revised: August 10, 2012 Published: August 15, 2012 Article pubs.acs.org/JPCB © 2012 American Chemical Society 11247 dx.doi.org/10.1021/jp304201b | J. Phys. Chem. B 2012, 116, 11247-11254