Article pubs.acs.org/JPCA
Motion of Br2 Molecules in Clathrate Cages. A Computational Study of the Dynamic Effects on Its Spectroscopic Behavior M. I. Bernal-Uruchurtu,*,† Kenneth C. Janda,‡ and R. Hernández-Lamoneda† †
Centro de Investigaciones Químicas, Universidad Autónoma del Estado de Morelos Av. Universidad 1001, Cuernavaca 62209, Morelos, México ‡ Department of Chemistry, University of California, Irvine, California 92697, United States S Supporting Information *
ABSTRACT: This work looks into the spectroscopic behavior of bromine molecules trapped in clathrate cages combining different methodologies. We developed a semiempirical quantum mechanical model to incorporate through molecular dynamics trajectories, the effect movement of bromine molecules in clathrate cages has on its absorption spectra. A simple electrostatic model simulating the cage environment around bromine predicts a blue shift in the spectra, in good agreement with the experimental evidence.
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years.17−23 Their development had to deal with the anisotropic distribution of the charge density on the halogen atoms or what is now commonly referred as the σ−hole. In some of these models an extra site or sites, a fictitious charge (massless point charge), allow the formation of halogen bonds with an improvement of geometries and interaction energies over the classical models. However, some shortcomings are still evident as pointed out by Kolár ̌ and Hobza.20 A force field with the correct physical behavior is still needed. In that direction, some groups have included separate, explicit terms to account for the different physical components of the interaction,23 and also a tight-binding method was recently presented.21 In this work, we use a semiempirical quantum mechanical model, PM3-PIF derived from the standard PM3 method. Some years ago we showed that it is possible to improve the quality of the results semiempirical MNDO-derived methods provide for hydrogen bonding. We did this modifying the expression used to evaluate the core−core term. The parametrized interaction function (PIF) replaced the original Gaussian form and was fitted to reproduce a high level ab initio calculated interaction potential energy surface for the water dimer.24 PM3-PIF model was first developed to treat hydrogen bonds between water molecules, it provides interaction energies and geometries of water clusters in excellent agreement with accurate experimental and theoretical results. Implemented as a force field for Born−Oppenheimer Molecular Dynamics studies, it is able to reproduce some liquid water properties, thus encouraging its use for studying chemistry in aqueous media.25 With this in mind, we decided to extend the
INTRODUCTION The solvent shifts of electronic spectra of halogens are a wellknown phenomenon that is not yet fully understood. The notions of active or inactive solvent, charge transfer complexes, the possible role of solvent−solute interactions were used to address the solution spectra of halogens.1,2 The fact that UV− vis spectra of halogen molecules are very sensitive to the local environment has lead, in the recent years, to several works aimed to the understanding of this macroscopic behavior in terms of the microscopic interactions present in these systems.3−9 A few years ago, Janda’s group showed in a series of papers10−12 that the UV−vis spectrum of halogen hydrates differs from the aqueous solution spectra. The band maximum of the valence electronic bands of Br2 in aqueous solution or in amorphous ice is blue-shifted by c.a. 1700 cm−1 whereas only 440−880 cm−1 in the hydrate.10 Raman experiments on a single Br2 hydrate crystal showed that the vibrational frequencies of Br2 inside the cages laid between the gas phase and aqueous solution values.13 Udachin diffraction experiments show that Br2 in clathrates14,15 might adopt several orientations; however, little is known about the preferred orientation of Br2 molecules inside each cage type and, in particular, how this orientation might affect the UV−vis absorption shift. We have recently reviewed interesting properties of halogens in water where we covered a large set of phenomena that still requires a model able to provide microscopic explanation of them.16 Due to the relevance of halogen bonding as a selective, directional stabilizing force in condensed phases and its potential use as a driving force in molecular recognition, several classical models have been designed in recent © XXXX American Chemical Society
Received: August 13, 2014 Revised: December 20, 2014
A
DOI: 10.1021/jp5082092 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A Table 1. Optimized PM3-PIF Parameters for Bromine in Aqueous Systemsa O−O O−H H−H Br−O Br−H a
αAB
βAB
χAB
δAB
εAB
ηAB
12.45958 49.36554 0.5197876 182.0825 318491.4
2.502734 2.276467 2.489980 1.966833 4.286785
−266.2244 −38.28750 50.10107 60.46069 −263.7062
12587.53 −145.0515 −676.3223 −6654.641 12431.67
−89486.92 651.8225 2711.768 31240.06 −138502.9
− − − 90.44330 21.69901
All parameters are in hartrees and bohrs.
repulsive regions, due to the anisotropy of the exchange interactions. In particular, the PES of Br2 encapsulated in the 51262 and 51263 clathrate cages was not well-reproduced. For this reason, we decided to slightly modify our fitting scheme. First, additional points were added to the fitting set; the new geometries correspond to pairs formed by a Br2 molecule and one of the water molecules that form the 51262 (T), 51263 (P), and 51264 (H) clathrate cages. To obtain a reasonable description of the short-range and repulsive regions of the PES, an additional term in the PIF function was added, thus the form used in this work is
applicability of this type of semiempirical models to the halogens in water. The explicit description of π electrons in the valence region of the halogen atom allows for a physically correct description of the σ−hole. PM3-PIF can be thought of as a flexible, polarizable force field with the advantage of providing approximate information regarding the electronic structure of the system. In this work, we apply a combination of electronic structure calculations to evaluate the electrostatic effect that the structure of water molecules forming the cages in the clathrate has on the electronic transition of Br2. First, we developed the PM3-PIF model for Br2 and water and with it we obtained several semiempirical Born−Oppenheimer molecular dynamics (SEBOMD) trajectories that allowed us to identify the preferred orientation of Br2 on the clathrate cages. Second, with a very simple electrostatic model consisting of fixed partial charges, we evaluated the effect the field created around Br2 different orientations might have on the electronic transitions, and finally, combining the information from the MD trajectories and the predicted shifts in the cages, we predict the electrostatic contribution to the average shift of Br2 inside the clathrate cages.
inter
PIF =
ABRAB)
A ,B
+
εAB R10 AB
=
cluster size Br2−H2O Br2−(H2O)2
∑ gPIF(A , B) ABRAB)
∑ αABe−(β A ,B
+
χAB R6AB
+
δAB R8AB
+
+
χAB R6AB
+
δAB R8AB
ηAB R12 AB
Table 2. Comparison of MP2/aug-cc-pVDZ (BSSE Corrected) and PM3-PIF Interaction Energies for Br2(H2O)n Clusters
inter A ,B inter
A ,B
+
With this added flexibility, the quality of the fitting improved from the previous essay. In Table 1, the parameters for the Br− O and Br−H terms of the PM3-PIF functions are shown. The overall improvement of the PM3-PIF model over the PM3 method in predicting the interaction energies of the training set is included as Supporting Information. With the best set of parameters found the optimized Br−O equilibrium distance in the H2O−Br2 complex is 3.07 Å, 0.3 Å larger than the ab initio reference, and the Br−H distance is 3.13 Å, again 0.4 Å larger than the ab initio optimized values. Although these differences are large, we found a small effect on the properties of small clusters and inside the clathrate cages. In Table 2, we compare
I. METHODOLOGY a. PM3-PIF for Br2−H2O. In this section, we briefly describe the development of the PM3-PIF model for the Br2− water interactions. This model is capable of describing the relevant interactions present in bromine in aqueous systems: hydrogen bonds, halogen bonds, and H−X interactions. PM3PIF is based on the PM3 method, and as for other systems,26,27 the basic idea is to replace the unphysical Gaussian correction functions (GCF) appearing in the core−core repulsion terms of most MNDO-based semiempirical methods by a simple function exhibiting the correct physical behavior in the whole range of intermolecular separation distances. The parametrized interaction function (PIF) is the sum of atom pair contributions, each one having five adjustable parameters: α, β, χ, δ, and ε: PIF =
inter
∑ gPIF(A , B) = ∑ αABe−(β
Br2−(H2O)3
εAB R10 AB
The parameters were optimized to reproduce a reference ab initio intermolecular energy surface for the Br2−water complex consisting of 465 geometries calculated at the MP2/aug-ccpVTZ level. All interaction energies were corrected for the BSSE error using the counterpoise method of Boys and Bernardi.28,29 In our first attempts to fit the PIF function to this PES, we found some difficulties to reproduce the short ranged and
Br2−(H2O)4
Br2−(H2O)5
a
B
geometrya
Eint (MP2) kcal/mol
Eint (PIF) kcal/mol
A B A B C D A B C D A B C A B C
−3.65 −0.58 −10.11 −6.38 −5.36 −4.67 −18.53 −12.76 −18.54 −15.69 −26.69 −28.77 −19.05 −37.56 −37.05 −36.31
−2.78 −0.80 −7.64 −6.93 −3.35 −3.14 −15.30 −9.31 −15.61 −14.82 −22.28 −27.52 −15.29 −36.60 −33.64 −33.30
Optimized geometries from ref 4. DOI: 10.1021/jp5082092 J. Phys. Chem. A XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry A
Figure 1. Potential energy surface of Br2 in the T, P, and H cages; φ and θ are arbitrarily assigned polar angles, and the PES shown consists of 145 grid points. These interaction energies, obtained using the Br−O and Br−H PM3-PIF parameters optimized in this work can be compared with Figure 6 of ref 17.
constant energy ensemble whose equilibrium condition was verified confirming that a Maxwell−Boltzmann distribution of velocities was reached and that the total energy fluctuations were
