J. Phys. Chem. A 2008, 112, 3399-3408
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Microhydration of NO3-: A Theoretical Study on Structure, Stability and IR Spectra A. K. Pathak,† T. Mukherjee,† and D. K. Maity*,‡ Radiation and Photochemistry DiVision, and Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400085, India ReceiVed: NoVember 22, 2007; In Final Form: January 17, 2008
A systematic study on the structure and stability of nitrate anion hydrated clusters, NO3-‚nH2O (n ) 1-8) are carried out by applying first principle electronic structure methods. Several possible initial structures are considered for each size cluster to locate equilibrium geometry by applying a correlated hybrid density functional with 6-311++G(d,p) basis function. Three different types of arrangements, namely, symmetrical double hydrogen bonding, single hydrogen bonding and inter-water hydrogen bonding are obtained in these hydrated clusters. A structure having inter-water hydrogen bonding is more stable compared to other arrangements. Surface structures are predicted to be more stable over interior structures. Up to five solvent H2O molecules can stay around solute NO3- anion in structures having an inter-water hydrogen-bonded cyclic network. A linear correlation is obtained for weighted average solvent stabilization energy with the size (n) of the hydrated cluster. Distinctly different shifts of IR bands are observed in these hydrated clusters for different kinds of bonding environments of O-H and NdO stretching modes compared to isolated H2O and NO3- anion. Weighted average IR spectra are calculated on the basis of statistical population of individual configurations of each size cluster at 150 K.
1. Introduction Size selected gas-phase cluster spectroscopy combined with first principles based theoretical calculations has become a powerful tool to obtain molecular level information on the interaction between solute and solvent molecules. Positively charged ions have simple hydrated structures compared to a negatively charged system as cation binds strongly with solvent water molecules.1 In recent years, the study on microhydration of small anionic chemical species has been a subject of intense research from both experimental and theoretical points of view, mainly because of the strong dependency of their properties on their size and geometry. When an anionic solute is immersed into a solvent pool, the hydrogen-bonded water network gets modified to accommodate the solute species in the process of hydration. The distribution pattern of the excess electron in the negatively charged solute plays the key role to shape up the structure of the water network around the solute. Thus, a delicate balance between anion-water and water-water interactions determines the structure of hydrated clusters of the anion. Among the simplest of the systems studied by experimental and theoretical tools is the hydrated halide series, X-‚nH2O, (X ) Cl, Br, I). Several experiment, theory and simulation studies have been carried out to understand the structure and dynamic aspects of hydration at molecular level on small negatively charged ions.1-21 Beyond these simple halide anions, the next complex hydrated clusters investigated involve diatomic singly charged anions of the type Y-‚nH2O, where Y refers to OH,21,22 O2,23,24 NO,25 Cl2,26,27 Br228,29 and I230 species. Microhydration of a dianionic system, SO42- has also been studied to demonstrate the stepwise hydration pattern of these complex anion systems.31-33 At present, microhydration of another complex * Corresponding author. E-mail for correspondence:
[email protected]. † Radiation and Photochemistry Division. ‡ Theoretical Chemistry Section.
Figure 1. (A) Fully optimized structures of NO3- calculated at the B3LYP/6-311++G(d,p) level of theory showing distribution of charge over all the atoms. (B) Contour plot of the highest occupied molecular orbital (HOMO) of NO3- to show that all the three O atoms participate in the orbital. The cutoff used for the contour plot is 0.25 au.
but the most common inorganic anion, namely, nitrate anion (NO3-) is studied by theoretical means. This anion is one of the most abundant species in acidic wastes as well as in the atmosphere.34-37 It is known as the so-called terminal anion in the series of atmospheric reactions involving nitrogen and thus its study is of particular importance. The process of hydration involving nitrate anion in the atmosphere is very important, as water is present in the atmosphere in relatively large concentrations. Such a study will help to enhance our understanding of molecular level interactions between solvent water molecules and negatively charged ions in aqueous solution. These studies on size selected hydrated anion clusters also play a critical role to follow the evolution of molecular properties with the number of solvent water molecules present in the cluster and to bridge the gap between monohydrated cluster (NO3-‚H2O) to the hydrated ion in bulk aqueous solution, NO3-(aq). Theoretical studies on structural aspects of small size NO3-‚nH2O clusters are reported.38-44 However, no report on IR spectra of these clusters is available in the literature. The objective of this article is to report microscopic structure, energy parameters and IR spectra of NO3-‚nH2O clusters (n ) 1-8) based on a rigorous and systematic study. With the increase in
10.1021/jp711108q CCC: $40.75 © 2008 American Chemical Society Published on Web 03/08/2008
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Figure 2. Part 1 of 2.
Pathak et al.
Microhydration of NO3-
J. Phys. Chem. A, Vol. 112, No. 15, 2008 3401
Figure 2. Part 2 of 2. Fully optimized structures calculated at B3LYP/6-311++G(d,p) level of theory for (I) NO3-‚H2O, (II) NO3-‚2H2O, (III) NO3-‚3H2O, (IV) NO3-‚4H2O, (V) NO3-‚5H2O, (VI) NO3-‚6H2O, (VII) NO3-‚7H2O, and (VIII) NO3-‚8H2O clusters. Uppercase letters are used to refer different minimum energy conformers for each hydrated cluster size arranged in order of stability showing “A” as the most stable one. N atoms are shown by marking “N” on the spheres; the smallest spheres refer to H atoms, and the rest correspond to O atoms in each structure. In each case, the distance between the N and O atoms is ∼1.25 Å, the distance between O of NO3- and H-bonded H atoms is 1.8-2.3 Å, and the distance between O and H atoms in inter-water hydrogen-bonded network is 1.8-2.0 Å.
number of solvent water molecules in hydrated clusters, the number of minimum energy configurations that are close in energy for each size hydrated clusters is expected to increase. Thus, weighted average properties of clusters become more meaningful. Weighted average molecular properties are also calculated at present on the basis of the statistical population of different minimum energy configurations of a particular size of hydrated cluster at 150 K. 2. Theoretical Methods Geometry optimizations are carried out following a popular hybrid density functional, namely, Becke’s three-parameter nonlocal exchange (B3) and Lee-Yang-Parr (LYP) nonlocal correlation functionals (B3LYP) with the Gaussian triple split valence, 6-311++G(d,p) basis function.45 Single-point energy calculations of each optimized structure are carried out by applying second-order Møller-Plesset perturbation theory (MP2) adopting the same set of basis function. A search for minimum energy structures is performed by applying an algorithm based on the Newton-Raphson procedure for each of these molecular clusters with several initial structures designed on the basis of chemical intuition. The most important concern in this search procedure is to guess a good initial geometry of the cluster based on chemical intuition, which might converge during the optimization to a structure having a local or the global energy minima. At present, several possible starting geometries are designed systematically on the basis of different possible three-dimensional structures. In the first case, initial structures are considered where each solvent water molecule was kept at a distance of ionic hydrogen bonding with one of the three oxygen atoms of NO3- anion and far from another solvent water molecule to have any inter-water hydrogen bonding. In the second case, guess structures were considered where each water molecule was kept at a distance of ionic hydrogen bonding with one of the three oxygen atoms of NO3anion and also at a distance to have an inter-water hydrogen bonding with another solvent H2O molecule. In the third case, a few solvent water molecules were initially kept at a distance
of ionic hydrogen bonding with one of the three oxygen atoms of NO3- anion and far from another solvent water molecule to have any inter-water hydrogen bonding. Remaining solvent water molecules were kept at a distance of ionic hydrogen bonding with one of the three oxygen atoms of NO3- and also at a distance where inter-water hydrogen-bonding interaction can exists. These structures were then allowed to relax, producing equilibrium minimum energy structures. It is to be noted that the adopted optimization procedure does not guarantee locating the global minimum energy structure. However, rigorous searches have been undertaken to find all possible equilibrium structures that may exist for NO3-‚nH2O systems. Hessian calculations are carried out for all the optimized minimum energy structures to check the nature of the equilibrium geometry as well as to generate IR spectra. The population of the minimum energy configurations of each size clusters has been calculated on the basis of free energy change (∆G) at 150 K following Boltzmann distribution. The statistical population of different equilibrium structures is calculated at various temperatures ranging from 75 to 298 K. The weighted average properties are reported only at 150 K as the size selected clusters spectroscopy experiments on such systems are mostly carried out at around this temperature. All electronic structure calculations have been carried out applying GAMESS program system on a LINUX cluster platform.46 The MOLDEN program system has been adopted for visualization of molecular geometry, molecular orbital, and normal modes and to generate IR spectra.47 3. Results and Discussion Geometry optimization of isolated nitrate anion in the gas phase, NO3- produces a structure of D3h symmetry as the most stable structure by applying the B3LYP density functional with a Gaussian split valence 6-311++G(d,p) basis set. The calculated N-O bond distance is 1.261 Å and the optimized structure with atomic charges (in au) over the atoms is displayed in Figure 1A to illustrate that all the three oxygen atoms are equally negative. The highest occupied molecular orbital (HOMO) of
3402 J. Phys. Chem. A, Vol. 112, No. 15, 2008 NO3- system is displayed in Figure 1B, again to demonstrate that all the three O atoms participate equally in this molecular orbital. The effect of hydration is introduced by successive addition of discrete solvent H2O molecules surrounding NO3species. When a solvent H2O molecule approaches the solute NO3- moiety, an ionic interaction between the negatively charged oxygen atom of NO3- and the H atom of solvent H2O takes place. Discrete water molecules are added successively to the solute by various possible ways based on chemical intuition as discussed in the previous section, and full geometry optimization is carried out to locate equilibrium structures at the B3LYP/6-311++G(d,p) level of theory. This leads to several minimum energy structures for each of the discrete hydrated clusters. The calculated energy parameters are improved by single-point energy calculations at MP2 level of theory. Minimum energy configurations, various energy parameters and IR spectra of each size hydrated cluster, NO3-‚nH2O (n ) 1-8) are discussed in the following subsections. 3.1. Structure. Different minimum energy structures obtained on full geometry optimization of each size hydrated cluster of nitrate anion, NO3-‚nH2O (n ) 1-8) are displayed in Figure 2. The calculated energy parameters are listed in Table 1 for each minimum energy structure of the hydrated clusters. Two stable minimum energy structures are obtained on full geometry optimization of the monohydrate cluster, NO3-‚H2O as shown in Figure 2-I(A,B). In contrast to the earlier reported structure,39 the most stable structure has a symmetric double-hydrogenbonding (DHB) arrangement where two O atoms from NO3group and two H-atoms of the solvent H2O molecule are connected by H-bonding of 2.06 Å. Calculated NO bond distances are 1.25 and 1.27 Å, respectively, for the spectator and H-bonded bonds. Structure I-B having one single hydrogen bond (SHB) between one oxygen atom of the nitrate anion and the H atom of the solvent H2O molecule is less stable than structure I-A by 2.78 kcal/mol. The calculated H-bond distance is 1.83 Å, and so this SHB should be stronger than each DHB of structure I-A. Again, NO bond distances are 1.25 and 1.27 Å, respectively, for the spectator and H-bonded bonds. Hessian calculations have predicted all the normal-mode frequencies to be real. The calculated binding enthalpy (∆H) of the more stable structure I-A is 14.68 kcal/mol at 298.15 K. The reported experimental ∆H for the monohydrated cluster is 14.60 kcal/ mol measured by gas-phase clustering equilibrium experiment at room temperature.48 Binding enthalpies of the monohydrated cluster calculated by applying BHHLYP hybrid density functional and MP2 methods are 14.49 and 14.76 kcal/mol, respectively. The calculated values suggest that the present adopted hybrid density functional, namely, B3LYP, should be adequate for the present systems. To further validate the suitability of this particular functional, vertical detachment energy (VDE) of the monohydrate cluster, NO3-‚H2O is also calculated following these two popular hybrid density functionals as well as MP2 methods with 6-311++G(d,p) basis functions. The calculated VDE values are 4.93, 5.33 and 4.08 eV, respectively at B3LYP, BHHLYP and MP2 levels compared to the measured value of 4.6 eV following photodetachment photoelectron spectroscopy.38 Again, it is observed that B3LYP functional performs well on these hydrated clusters. Thus geometry optimizations and Hessian calculations of all these hydrated clusters have been carried out by applying the costeffective correlated B3LYP hybrid density functional. Three minimum energy structures are predicted for the dihydrate cluster, NO3-‚2H2O and displayed in Figure 2-II(AC). The structures are very close in energy with a difference in
Pathak et al. TABLE 1: Calculated Energy Parameters and Molecular Properties of NO3-‚nH2O Clusters (n ) 1-8)a energy (kcal/mol)
system
population at 150 K
relative energy,b ∆E
solvent stabilizationc energy, Esolv
interaction energy,c,d, Eint
I-A I-B
0.59 0.41
NO3-‚H2O 0 16.31, 16.44 2.78 13.53, 13.60
17.05, 17.18 (15.40) 14.07, 14.11 (12.70)
II-A II-B II-C
0.50 0.23 0.27
NO3-‚2H2O 0 30.82, 31.10 1.31 29.51, 29.71 1.95 28.87, 29.20
32.47, 32.71 (30.67) 27.77, 27.84 (26.29) 31.12, 31.32 (29.00)
III-A III-B III-C III-D III-E
0.41 0.29 0.11 0.14 0.05
NO3-‚3H2O 0 44.02 0.26 43.76 0.39 43.63 0.66 43.36 1.04 42.98
37.50 (35.52) 33.00 (30.76) 46.67 (44.09) 39.62 (37.19) 42.57 (40.05)
IV-A IV-B IV-C IV-D IV-E IV-F
0.68 0.10 0.11 0.04 0 0.07
NO3-‚4H2O 0 59.90 3.35 56.55 3.58 56.32 3.98 55.92 4.86 55.04 5.16 54.74
42.44 (39.66) 50.71 (47.91) 47.30 (44.09) 53.43 (50.06) 55.23 (52.16) 50.90 (47.90)
V-As V-B V-C V-D V-E V-F V-G V-H V-I
0.51 0.30 0.03 0.07 0.02 0.05 0 0.01 0.01
NO3-‚5H2O 0 74.29 2.29 72.00 5.88 68.41 6.53 67.76 6.77 67.52 6.82 67.47 7.67 66.62 7.69 66.60 8.30 65.99
51.30 (48.09) 45.81 (42.90) 59.98 (56.15) 59.71 (56.54) 60.37 (56.24) 62.91 (59.36) 64.83 (60.93) 58.38 (54.84) 63.78 (60.08)
VI-A VI-B VI-C VI-D VI-E VI-F VI-G VI-H VI-I
0.73 0.05 0.07 0.10 0.03 0.01 0 0.01 0
NO3-‚6H2O 0 87.09 1.90 85.19 5.61 81.48 5.94 81.15 7.53 79.56 8.93 78.16 9.80 77.28 9.89 77.20 11.03 76.06
59.11 (55.49) 63.51 (59.41) 59.87 (56.79) 60.17 (55.85) 65.88 (65.28) 70.95 (67.00) 68.48 (64.33) 71.59 (67.26) 70.90 (67.01)
VII-A VII-B VII-C VII-D VII-E VII-F VII-G VII-H VII-I VII-J
0.25 0.31 0.20 0.08 0 0.05 0.11 0 0 0
NO3-‚7H2O 0 100.69 1.01 99.68 2.31 98.38 3.38 97.31 8.78 91.91 10.43 90.26 11.36 89.33 13.31 87.38 14.00 86.69 14.20 86.49
67.32 (63.24) 66.91 (62.95) 65.80 (61.86) 70.60 (66.09) 71.02 (66.44) 72.26 (67.08) 76.43 (72.07) 76.95 (72.84) 75.15 (71.26) 74.70 (70.45)
VIII-A VIII-B VIII-C VIII-D VIII-E VIII-F VIII-G VIII-H VIII-I VIII-J VIII-K VIII-L
0.11 0.34 0.09 0.07 0.07 0.13 0.08 0.04 0.02 0.01 0 0.04
NO3-‚8H2O 0 112.10 1.22 110.88 1.68 110.42 3.13 108.97 4.11 107.99 5.04 107.06 5.44 106.66 7.33 104.77 9.67 102.43 10.07 102.03 13.16 98.94 13.58 98.52
73.50 (69.15) 72.53 (68.30) 73.91 (69.44) 77.39 (72.68) 77.08 (72.20) 72.36 (68.29) 76.80 (72.11) 76.12 (71.00) 77.43 (73.19) 77.27 (72.43) 81.03 (75.42) 81.57 (77.09)
a Energy values are calculated at the MP2/6-311++G(d,p) level of theory. b ∆E ) relative energy (energy of any structure - energy of structure A in NO3-‚nH2O system). c Data in italics refer to values calculated at CCSD(T)/6-311++G(d,p) level. d Values in parentheses refer to basis set superposition error (BSSE)-corrected data.
Microhydration of NO3relative stability of
