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Ab Initio Study of Ionized Water Radical Cation (HO) in Combination with Particle Swarm Optimization Method Mei Tang, Cui-E Hu, Zhen-Long Lv, Xiang-Rong Chen, and Ling-Cang Cai J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09866 • Publication Date (Web): 09 Nov 2016 Downloaded from http://pubs.acs.org on November 17, 2016

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The Journal of Physical Chemistry

Ab Initio Study of Ionized Water Radical Cation (H2O)8+ in Combination with Particle Swarm Optimization Method Mei Tang 1, Cui-E Hu 2, Zhen-Long Lv 1, Xiang-Rong Chen 1, *, Ling-Cang Cai 3 1

Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610065, China;

2

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, China; 3

National Key Laboratory for Shock Wave and Detonation Physics Research,

Institute of Fluid Physics, Chinese Academy of Engineering Physics, Mianyang 621900, China

*

Corresponding author. E-mail: [email protected] 1

ACS Paragon Plus Environment


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Abstract: The structures of cationic water clusters (H2O)8+ have been globally explored by the particle swarm optimization method in combination with quantum chemical calculations. Geometry optimization and vibrational analysis for the fifteen most interesting clusters are computed at the MP2/aug-cc-pVDZ level and infrared spectrum calculation at MPW1K/6-311++G** level. Special attention is paid to the relationships between their configurations and energies. Both MP2 and B3LYP-D3 calculations reveal that the cage-like structure is the most stable, which is different from a five-membered-ring lowest energy structure, but agrees well with a cage-like structure in the literature. Furthermore, our obtained cage-like structure is more stable by 0.87 and 1.23 kcal/mol than previously reported structure at MP2 and B3LYP-D3 levels, respectively. Interestingly, based on their relative Gibbs free energies and the temperature dependence of populations, the cage-like structure only predominates at very low temperature and the most dominating species transforms into a new-found four-membered-ring structure from 100 to 400 K, which can contribute a lot to the experimental infrared spectrum. By topological analysis and reduced density gradient analysis we also investigate the structural characteristics and the bonding strengths of these water cluster radical cations.

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1. INTRODUCTION The ionization of water is of great importance for various biophysical and chemical processes, such as radiotherapy and photocatalytic reactions.1-8 Recently, the ionized water clusters have become a hot research topic of experimental and theoretical investigation owing that these clusters can be taken as a microscopic model of ionized water. The latest study found that the ion-radical pair separation trend is shown to continue in larger oxidized water clusters.9 Water cation clusters can be produced by ionizing their neutral counterparts through nuclear radiation,10,11 and they show their unique characteristics in comparison with their neutral counterparts.12-16 For instance, Cheng et al. found that comparing the neutral water dimer global minimum and the corresponding radical cation, there are significant geometrical changes, such as lower symmetry from Cs to C1 upon ionization and the hydrogen bond change.15 And the stationary electronic ground and excited states of the neutral and cationic water dimer are compared using a multi-configuration expansion of the many electron wave function.16 Experimentally, Haberland and Langosch successfully detected the mass spectra of (H2O)n+ (n = 3-8) and claimed that these clusters can be grown in the cold environment of a supersonic beam,17 while Shinohara et al. measured them by photoionizing the neutral Arm(H2O)n clusters (n = 2-10).18 Then, Jongma et al. obtained (H2O)n+ by directly evaporating the inert-gas-(H2O)n complexes.13 These experiments suggest that they have a configuration of H3O+(H2O)kOH and the OH radical lies beyond the first solvation shell. Dynamics of some larger size ionized

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water clusters were also experimentally and theoretically studied.19-21 In a breakthrough, Mizuse et al. measured infrared spectroscopy of water cluster radical cations (H2O)n+ (n = 3-11) and then conducted infrared photodissociation and Ar-attachment experiments for (H2O)n+ (n = 3-8).22,23 In their later work, they considered a single five-membered-ring type isomer as the ground state structure of (H2O)8+ and found that the OH radical acts as not only an H-bond donor but also an acceptor, which is a sharp contrast with smaller clusters.23 Smaller cationic water clusters, including water monomer,24-27 dimer,13,18-19,28-37 and other smaller (H2O)n+ clusters38-42 have been intensively studied for their relative simplicity. Nevertheless, the information of larger cationic water clusters is more challenging

in

theoretical

respect

not

only

because

the

conventional

exchange-correlation functionals within density functional theory often give a wrong ground state for them,43-45 but also because the local minimum on their potential energy surface increase exponentially with the cluster size.46,47 Researchers always take a great interest in structural evolution of (H2O)n+.19,22,23,36,39,42 For instance, Do and Besley predicted a range of candidate structures for (H2O)n+ (n = 3-9) with the scheme of basin hopping search algorithm in combination with quantum chemical calculations and reported that (H2O)8+ is the smallest cluster that have a cage-like lowest energy structure for (H2O)n+ clusters.42 However, Mizuse and Fujii23 and Lu et al.39 suggested that its lowest energy structure is composed of a single five-membered-ring. Thus, the lowest energy structure of (H2O)8+ is a cage-like form42 or a single five-membered-ring one23,39 is an open question. Furthermore, the

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information of (H2O)8+ and its corresponding protonated cluster H+(H2O)8 may lead to the development of model potentials that can provide a computationally efficient alternative method to explore the Eigen-type cage structure48,49 and the experimentally measured Zundel-type five-membered-ring structure50,51 for water clusters. Particle swarm optimization (PSO) algorithm is a stochastic global optimization method based on population optimization. This algorithm is different from the genetic algorithm and has obviously avoided the use of evolution operator. This algorithm has been successfully applied to the many known systems with various metallic, ionic, and covalent bonding environments, which implies the reliability of this methodology.52 In this work, we applied PSO algorithm to search the potential energy surface of ionized (H2O)8+ cluster, a similar system of H+(H2O)8, to find a diversity of its structures to recognize its ground state structure and to test the prediction ability of CALYPSO (crystal structure analysis by particle swarm optimization) code,52 study systematically on the properties of these isomers, and uncover some underlying rules from detailed analyses of this unique cluster. Our work may give deeper insights for further studying water clusters.

2. COMPUTATIONAL DETAILS For (H2O)8+ clusters, their possible structures with minimum energies were searched by CALYPSO code52 in combination with quantum chemical package GAUSSIAN 09.53 CALYPSO performs structure evolution by PSO algorithm, which is excellent and efficient because each structure is guided by the best local or global

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structure in the swarm and can learn experience from its own evolution history to adjust its evolution speed and direction in the evolving process. This unbiased and intelligent means can help individuals in the swarm locate themselves to the local or global minima of the potential energy surface fast. In order to make structure prediction more efficient, point group symmetries, bond characterization matrix, and Metropolis criterion are introduced for CALYPSO to guarantee structural diversity, get rid of similar structures and enable the structural evolution towards the low-energy regions of potential energy surface,54 respectively. The number of the total generation and the population of each generation, which are two parameters in CALYPSO, both are set to 30. This ensures that most possible structures are found. In the process of searching, the first generation was randomly generated by CALYPSO, and B3LYP and HF functionals with 6-31G* and 6-31+G* basis sets are used to perform optimization in the GAUSSIAN 09 package.53 Afterwards, a certain number of lower-energy clusters evolved into the next generation together with some new randomly formed structures. This procedure continued until thirty generations are produced. Then, the most desirable structures obtained at different prediction levels were picked up and refined without any symmetry constraints at the second-order MØller-Plesset (MP2) level and density functional theory (DFT) level with the aug-cc-pVDZ and 6-311++G** basis sets. Harmonic vibrational frequencies were calculated to verify their stabilities and to obtain their zero-point vibrational energies (ZPVE). Corresponding scaling factors (0.956 at the B3LYP/6-311++G**, 0.916 at the MPW1K/6-311++G**, 0.920 at the

6


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MPW1K/aug-cc-pVDZ, 0.917 at the BH&HLYP/6-311++G**, 0.920 at the BH&HLYP/aug-cc-pVDZ, and 0.957 at the MP2/aug-cc-pVDZ level) were used to make ZPVE correction to get their total energies at DFT and MP2 levels. These scaling factors have been employed on water trimer cation successfully.38 All these methods have been tested on dimer, trimer, or larger cationic water clusters and therefore their validity are guaranteed.22,36,38-42,55-58 Among them, MP2/aug-cc-pVDZ level is concluded to be rather accurate for studying different types of cationic water clusters,38,40,41,55-58 so this computation level is adopted for related property calculation. At this level the extrapolated complete basis set (CBS) energies are calculated with the extrapolation scheme in which the electron correlation error is proportional to N-3 for the aug-cc-pVNZ basis set (N = 2:D, N = 3:T) in the following form:59 ECBS = [EN(N + 1/2)3 - EN-1(N - 1/2)3]/[(N + 1/2)3 - (N - 1/2)3] Also, the non-local electron correlation associated with the functional we used was considered by adding an empirical dispersion correction, and we use B3LYP method with empirical dispersion correction (B3LYP-D3) to compare MP2 results. Generally, the energies of the cluster structures with any dissociated molecular unit are not corrected by the basis set superposition error (BSSE),38,58,60 and previous calculations on smaller cationic water clusters indicate that the BSSEs have negligible influence on their total energies in comparison with the ZPVEs.41 Thus, ignoring BSSE correction turns out to be reasonable. Furthermore, for the proton-transferred type structure, the BSSE correction can be made. However, in the hemi-bonded type

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structure, the corresponding calculation can not be made properly because of the almost equally shared positive charge in two O-O connected water molecules.36 So it is better not to make BSSE correction for comparing the two structures at equal conditions. To check the spin contaminations, the values are verified to be near 0.75 for all the calculations of this open-shell doublet system. Topological and reduced density gradient (RDG) analyses were conducted by using the Multiwfn program.61

3. RESULTS AND DISCUSSION 3.1 Structure Analysis and Their Energy Order We adopted B3LYP and HF functionals with 6-31G* and 6-31+G* basis sets in the process of structure prediction, which suggests that the different choices of functionals and basis sets affect the obtained structures of (H2O)8+ cluster. This is different from the conclusion that basis sets have little influence on the results of (H2O)4+.41 The obtained fifteen low energy structures of (H2O)8+ are illustrated in Figure 1, including proton-transferred type isomers (denoted W1-W14, similarly hereafter) and hemi-bonded type isomer (W15). Through comparison, we structurally sort these clusters into five forms: the first form is the chain-like structure (W1) with the H3O+ moiety being threefold coordinated by the OH radical and two water molecules; the second one is branched single ring structures with the ion core occupied by three water molecules and the OH radical separated from it by one of water. This kind of structures can be further classified into three subtypes: single four-membered-ring (W2), five-membered-ring (W3-W6), and six-membered-ring 8


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structure (W7); the third is generated by a double ring with similar coordination for the H3O+ moiety and similar location for the OH radical in comparison with single ring type. In this kind of structures, W8 consists of two five-membered-rings whereas W9 is composed of a four-membered-ring and a six-membered-ring; the forth is constituted by multi-ring which can be classified into two subtypes: multi-ring with a side tail (W10 and W11) and cage-like (W12-W14) structures. The ion core still has a filled first solvation shell, however, the OH radical is separated from it by two water molecules for W12 and W14. The OH radical is a weaker hydrogen bond (HB) acceptor than a water molecule. As a result, the first solvation shell of the ion core is preferentially filled with water and the OH radical is separated from it in proton-transferred type isomers. This is consistent with the rules revealed by Mizuse et al.23 except that W1 has an ion-radial contact pair. The last form is the hemi-bonded type with a five-membered-ring structure (W15). The coordinates for the fifteen structures are included in Table S1 (see the ESI†). Figure 2 shows us their relative energy differences calculated at DFT and MP2 levels at room temperature. In our calculations, superscript a means using 6-311++G** basis set while b means using aug-cc-pVTZ basis set to obtain single point energy and using aug-cc-pVDZ for ZPVE. E0 and Ee represent relative energies with and without ZPVE correction, respectively. A four-membered-ring form has been found to exist but not prevail in (H2O)4+ or (H2O)5+ clusters40,41 and Lu et al. have predicted it as the lowest energy structure of (H2O)7+ clusters.39 However, this configuration has never been reported for (H2O)8+ cluster or its similar system

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H+(H2O)8. In our results, branched single four-membered-ring structure (W2) is the most energy-desirable with ZPVE correction using MPW1K, BH&HLYP, and B3LYP functionals in the DFT calculations (denoted MPW1Kb E0, BH&HLYPb E0 and B3LYPa E0 in Figure 2, respectively). Another new-found isomer W7 has been found for H+(H2O)8 but not for (H2O)8+ cluster. Interestingly, according to MP2 energy, the ground state structure is predicted to be the cage-like structure W12 with and without ZPVE correction (denoted MP2b E0, MP2/CBS E0, and MP2/CBS Ee in Figure 2, respectively). The discrepancy of MP2/CBS energies with and without ZPVE correction (MP2/CBS E0 and MP2/CBS Ee) indicates that this correction has an important effect on determining the energy orderings of (H2O)8+ clusters, as reported in studying smaller cationic water clusters.40,41 The ZPVE corrected MP2 energies obtained using aug-cc-pVTZ basis set and CBS (MP2b E0 and MP2/CBS E0) show consistent energy arrangement, which validates the correlation-consistent basis set extrapolation scheme.59 At MP2/CBS level without ZPVE correction (MP2/CBS Ee) W12 and W14 are found to be the two lowest energy structures. To explain the discrepancy about its ground state structure between DFT and MP2 calculations, the isomer W12 is also predicted as the lowest energy structure by B3LYP-D3 energies, which agrees well with our high level ab initio results. At this level W12 is more stable by 1.43 kcal/mol than W2. This cage-like lowest energy structure is different from the most stable five-membered-ring structure proposed by Mizuse and Fujii23 and Lu et al.39 (very similar to W3). However, it gives validity to

10


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the structure obtained by Do and Besley (very similar to W12),42 and it is more stable by 0.87 and 1.23 kcal/mol than the cage-like structure42 at MP2 and B3LYP-D3 levels, respectively. Table

1

lists

B3LYP/6-311++G**,

the

MPW1K/6-311++G**,

MPW1K/aug-cc-pVTZ,

BH&HLYP/6-311++G**, BH&HLYP/aug-cc-pVTZ,

B3LYP-D3/aug-cc-pVTZ, and MP2/CBS interaction energies of water octamer cation clusters. These interaction energies mean the interaction energies between the neutral water molecules and the water monomer cation (H2O+): △E(cation cluster) = E(cation cluster) – (n-1)E(water monomer) – E(water monomer cation).19 From Table 1, we find that the choices of functionals and basis sets have an effect on their energy differences. For example, the four most stable structures are W2, W4, W3, and W7 at MPW1K/6-311++G** level whereas the energy order turns to W2, W3, W13, and W4 at BH&HLYP/6-311++G** level. In addition, the turn changes to W2, W4, W6, and W7 at MPW1K/aug-cc-pVTZ level. Furthermore, the energy arrangement is W12, W14, W13, and W3 for the ZPVE uncorrected case and it changes to W12, W3, W13, and W4 when the ZPVE is included at MP2/CBS level. Despite their different energy orderings, W2 is predicted to be the most stable at traditional DFT calculations. However, W12 turns out to be the most stable in MP2 and B3LYP-D3 calculations, which is in good agreement with results obtained from the viewpoint of their relative energies. The discrepancy of the lowest energy structure is due to the neglect of non-local electron correlation associated with the functionals we used as explained before.

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The stability of charged compounds can be identified by adiabatic ionization potential (AIP), which is the energy difference between the relaxed positively charged compound and its neutral counterpart. For these (H2O)8+ clusters, the AIPs can be calculated by the formula: Iad = E[(H2O)8+] – E[(H2O)8], where E[(H2O)8+] and E[(H2O)8] denote the energies of the cationic water cluster (H2O)8+ and the neutral cluster (H2O)8 at their optimized states. The obtained AIPs of these (H2O)8+ clusters lie in 8.99 – 9.90 eV and it seems that the smaller an AIP it has, the more stable it is. In comparison with cases of smaller cationic water clusters,40,41 their AIPs begin to decrease with size. Together with the interaction energies of (H2O)2-6+ clusters reported by Lee and Kim19 and those of (H2O)8+ in this work, it is clear that these cationic water clusters show their increasing stability as their size increases. Formation energy (EF) is considered to be a reasonable quality to measure interaction strength within a supermolecule. Generally, it was calculated with respect to the complete dissociation of the cation into the isolated OH, H3O+, and H2O, which uses the expression: △E = E[(H2O)8+] – E(OH) – E(H3O+) – 6E(H2O),62 where E[(H2O)8+], E(OH), E(H3O+), and E(H2O) are their respective energies calculated at their ground states. These obtained formation energies have an analogous changing trend as relative energies do (see EF in Table 1 and relative energies in Figure 2) because EF is also associated with the stability of a structure. The proton-transferred type isomers W3 and W12 have the maximum value of -117.2 kcal/mol, and the hemi-bonded type isomer W15 has the minimum value of -96.1 kcal/mol. The strength of hydrogen bonds can be expressed by the average formation energy with

12


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the scheme: EHB = EF/N, where N is the number of hydrogen bonds.40 We also listed these values for the studied clusters in Table 1, which are in the range of 11.6-16.1 kcal/mol. Obviously, a smaller number of hydrogen bonds are often associated with a larger bonding energy in (H2O)8+, which can also be found in (H2O)5+.40 And the number of hydrogen bonds may not be a decisive factor for the stability of these clusters. The natural bond orbital (NBO) charge of the molecular fragments is obtained by natural population analysis. For the proton-transferred structures W1-W14, the NBO charge of the positively charged ion is 0.37 - 0.40. For the OH radical it is 0.50 - 0.52 and for water molecules only 0.01 - 0.05, which is in general agreement with the charge distribution in the ion-radical clusters. However, this is different from the case of cationic water dimer clusters where most of the excess charge is distributed on the ion.36 For W15, the positive charge is almost equally shared over the two hemi-bonded water molecules, constituting 92% of the excess charge (q = +1), as in the case of the hemi-bonded structure of cationic water trimer clusters.19 3.2 Temperature Effect on the Energy Order Temperature can affect the energy of a molecule by stimulating its vibration, rotation and transformation. However, the above analyses are based on the energies calculated at room temperature. So in this part we consider the temperature effect. Figure 3 depicts its dependence on the relative Gibbs free energies of (H2O)8+ clusters with respect to W2, whose free energy is the lowest from 100 to 400 K. Compared with the behavior in smaller cationic water clusters (H2O)4+ and (H2O)5+,40,41 the

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relative Gibbs free energies of (H2O)8+ change more remarkably, which reveals that temperature has a greater effect on the stability of larger cationic water clusters compared with smaller ones. This may be due to that in (H2O)8+ clusters ring and cage-like structures dominate and therefore steric effect or strain should exist, leading to their significant energy changes with the rising temperature. On the other hand, for (H2O)8+ themselves the discrepancy of their relative Gibbs free energies becomes more observable when temperature rises. Associated with their structures, at rising temperature the six more stable structures are chain-like and branched sing-ring isomers, all of which have a small number of hydrogen bonds, whereas the stability of the multi-ring structures decreases, all of which have one or two more hydrogen bonds. Together with results reported in (H2O)5+ clusters,40 we speculate that at elevated temperature the number of hydrogen bonds may affect the relative stabilities of cationic water clusters and these clusters with a larger number of hydrogen bonds are easier to lose their stabilities. From Figure 3, the lowest-free-energy isomer is a cage-like structure at 0 K. At the temperature of 170 K, three branched single ring structures dominate, including W2, W4 and W5, which is in line with the results reported in H+(H2O)8 clusters at both temperatures.63 At 273 K, there exist some differences: the lowest-free-energy isomer keeps unchanged for (H2O)8+ clusters whereas it turns into a branched chain structure for H+(H2O)8 clusters.63 However, the chain-like structure (W1) of (H2O)8+ clusters is expected to become most stable at the temperature higher than 400 K. This is due to that its relative Gibbs free energies decrease notably with temperature

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elevated whereas others (W3-W14) increase visibly. Note that almost all the reported configurations of its similar system H+(H2O)850 have been found for (H2O)8+ in our work,

including

a

single

five-membered-ring,

six-membered-ring,

double

five-membered-ring, and cage-like structures. So based on the above analysis of (H2O)8+ and its similar system H+(H2O)8, together with previous work,22,50,51,63-65 it may be plausible to construct the structures of cationic water clusters from the known structures of their protonated counterparts. Since the structures of (H2O)8+ clusters are similar to those of H+(H2O)8, whose structures are dependent on the temperature,50,51,63,66 a thermal population of four most dominating species and four different kinds of structures has been studied to explore the temperature dependency on their configurations in Figure 4. Here their relative populations at different temperatures are obtained through Boltzmann population − ∆G / RT / formula: pi = e i

∑

j

e

− ∆G j / RT

, where pi is the relative population of the ith

cluster, and ∆Gi is the Gibbs free energy of the ith cluster relative to the most stable one. R is the ideal gas constant, and T is the thermal temperature. This kind of cationic water cluster favors the multi-ring structures that mainly are cage-like form at low temperature but a less compacted form with a single ring at a little higher temperature, which has been reported for its protonated counterpart H+(H2O)8.63 It is expected that the transformation of the lowest-free-energy structure of (H2O)8+ cluster from cage-like to single-ring type occurs at temperature lower than 50 K. This may lead that single-ring structure are constructed at around 200 K based on experiment23 while cage-like structure are predicted theoretically42 about its most stable structure. The

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relative populations of double ring structures are calculated to be very small from 0 to 400 K. As mentioned in its similar system H+(H2O)8,49,50,63 its neutral counterpart (H2O)8,67 and smaller cationic water clusters,40,41 the entropy effect may influence the relative stability of (H2O)8+ clusters remarkably as the temperature increases from their Gibbs free energies and thermal populations. To better explore why cage-like isomers with a larger number of hydrogen bonds become more unstable with rising temperature, we have visualized vibrational modes of W2 and W12 in the high frequency range. The results can be found Figure S1 ( see in the ESI†). 3.3 Infrared Spectra of the Five Lowest Energy Clusters IR spectrum is often used as a powerful tool to identify or to discriminate the structures of certain water clusters.68 For (H2O)8+ cluster, Mizuse et al. have measured its IR spectrum recently and reported that the MPW1K/6-311++G(3df,2p) level can give fairly desirable results in reproducing the experimental IR spectrum.22 Additionally, we find that the MPW1K/6-311++G** level gives better results than MP2/aug-cc-pVDZ level at high energy end. Therefore, their IR spectra are simulated at MPW1K/6-311++G** level,38 which are shown in Figure 5. It is found that the consistency between simulated and experimental spectra can be obtained by one or two isomers of (H2O)8+ cluster23,39,42 and H+(H2O)8.50 In our work, W2 and W4 have the relative populations of 62% and 22% at 180 K, respectively. As a result, their simulated IR spectra can match the experimental spectrum. However, to explain the experimental spectrum more sufficiently, we also include the computed IR spectra of three more isomers W3, W11, and W12. The calculated frequencies of representative

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single ring and cage-like structures are listed in Table 2. Mizuse and Fujii used a five-membered-ring type isomer23,39 to explain experimental IR spectrum and found that the band at ~ 3680 cm-1 loses its intensity in the observed spectrum of (H2O)8+ compared with that of H+(H2O)8.23 They suggested the low intensity of this band indicates that the OH radical takes place of the three-coordinated site, which is occupied by a water molecule in H+(H2O)8. In our results, the OH radical of W2 and W3 is threefold coordinated with water molecules. The weak band at 3694 cm-1 is evidenced for W3 whereas this band disappears for W2. For W4, the broad absorption below 3000 cm-1 suggests the protonated water monomer structural motifs and the intense peak at about 3200 cm-1 can be attributed to the stretch of that O-H bond of H3O+ moiety towards its neighbor water molecule. The new-found isomer W6 contributes to the characteristic ~ 3350 cm-1 band, which mainly comes from stretch of the first solvation shell to the second shell. In the 3500 – 3600 cm-1 region, the triplet feature is measured experimentally and reasonable frequencies are produced in Table 2. For instance, Frequencies (3501 and 3572 cm-1) of W2 are in good agreement with experiment (3543 and 3576 cm-1). These bands originate from the hydrogen-bonded OH stretch of water towards an OH radical. For W2, W6, W7 and W11, only two bands are reproduced in this region, whereas the observed spectrum show one more band. This fact means the coexistence of single ring and cage-like structures. It is reported that vibrational bands above 3600 cm-1 have been used extensively to identify the morphological development in water clusters.22 Bands in this region are

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generated by free OH stretching modes of water molecules with different coordination numbers and our calculation gives reasonable frequencies in this ranges as shown in Table 2. For example, frequencies (3640, 3705, and 3733 cm-1) of W2 are in excellent agreement with the corresponding experiment values (3652, 3715, and 3739 cm-1), implying that this new-found four-membered-ring structure is correct. The simulated IR spectra of W11 and W12 reproduce the experimental spectrum well in the 3500 – 3800 cm-1 region, which is consistent with the conclusion that the computed IR spectrum of a cage-like structure matches experiment well.42 However, below 3500 cm-1 the computed bands of this kind of structure can not match experimental IR spectrum well, which suggests that the IR spectrum of (H2O)8+ is also attributable to single ring structures. According to the structures of the seven isomers, which give satisfactory agreement between simulated and observed spectra, we confirmed that OH radicals are more likely to be embedded in this kind of cluster to form H-bond with water molecules than stay on the terminal site. This conclusion is in line with the statement proposed by Lu et al.39 3.4 Topological Analysis on the Four Lowest Energy Clusters Reduced density gradient (RDG) is defined as RDG(r) = 1/2(3π2)1/3|▽ρ(r)| ρ(r)4/3 and it is a dimensionless quantity used to describe the difference between the actual electron density and a homogeneous electron distribution.69 Johnson et al. reported that the sign of the second Hessian eigenvalue of electron density can be utilized to identify the type of interaction and the strength of the interaction can be obtained from the density on the non-covalent interaction surface.70 As a result, we

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can discriminate van der Waals interaction, hydrogen bond, and steric effect by this means. The calculated RDGs at the bond critical points (BCPs) of four representative clusters are illustrated in Figure 6, where the blue, green, and red stand for the strong attraction, van der Waals interaction, and strong repulsion, respectively. Figure 6a-d reveals that the H3O+ motifs in these water clusters are inclined to have a strong attraction with its neighbor water molecules, which can also be found in smaller cationic water clusters.40 Further inspection on W2 and W3 indicates that if the OH radical acts as two-proton acceptor and one-proton donor, it will have a stronger interaction with water molecule acting as proton acceptor than that acting as proton donor. W2, W3, W4, and W12 are ring or cage-like structures, so the RDG suggests that a weak repulsion (steric) effect may exist at their (3,-1) CPs. BCPs are also denoted (3,-1) CPs, where the first number in parentheses equals the number of nonzero eigenvalues, or principal curvatures, of the Hessian of ρ(r) at the critical points, while the second is equal to the sum of the signs of the three eigenvalues. RDG can visually distinguish the interaction in a complex, but it is difficult to give a quantitive comparison, especially if the interactions are of the same magnitude. It is proposed that weak interactions, such as hydrogen bonds, can be sorted and quantitively described by the electron density ρ(r) and its second derivatives▽2ρ(r) at the (3,-1) CPs where the gradients of ρ(r) equal to zero. For instance, covalent interaction typically has a large ρ(r) and a negative▽2ρ(r) whereas non-covalent interactions such as hydrogen bonding have a low ρ(r) and a positive▽2ρ(r).71 In order to give a deeper insight on the interaction within these clusters, we obtained the

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electron densities and their second derivatives at their (3,-1) CPs for the four (H2O)8+ clusters. The results, as well as the bond length of these hydrogen bonds are listed in Table 3. Koch and Popelier found a set of criteria to judge the C-H…O hydrogen bonding interaction within a complex.72 They proposed that ρ(r) at the (3,-1) CPs should lie in the range of 0.002-0.035 a.u. and ▽2ρ(r) should lie in 0.014-0.139 a.u. But from Table 3, we find that many values of ρ(r) for these four clusters are larger than the corresponding criterion, although the values of ▽2ρ(r) are located in their criteria. These criteria seem not plausible in identifying the hydrogen bonding interactions in (H2O)8+ clusters as reported previously in smaller cationic water clusters.40 Parthasarathi et al. sorted the interaction within a complex into five categories: the value of ρ(r) lies in 0-0.022 a.u. for van der Waals and weak interaction; it lies in 0.022-0.052 a.u. for moderate HBs; it lies in 0.052-0.091 a.u. for strong HBs; it lies in 0.091-0.120 a.u. for very strong HB; and above 0.120 a.u., it is for covalent bond.73 Based on this sorting method, most interactions in these water clusters can be regarded as moderate HBs. The computed values indicate that the strongest HBs in the W2, W3, W4, and W12 are located at the third, the fourth, the eighth, and the second BCPs, respectively. From Figure 6, all these strongest HBs play a role in bridging the second solvation shell, which ensures that the corresponding branches are tightly bonded by the central H3O+ motifs. Owing that these clusters favor a separated ion-radical structure, the conclusion deduced from smaller water clusters40 that the interaction between the H3O+ and OH radical may be stronger than that between H3O+ and water molecules in

20


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the first shell can not be found in (H2O)8+ clusters. The weakest interactions in W2 and W3 lie in the fifth and the second BCPs; for W4 it lies in the third one and for W12 in the ninth one. As reported in smaller water clusters,40 the strength of the interactions within (H2O)8+ clusters relies on both the exact location (in the first or second shell) of the interaction and the concrete environment of the constituent elements (a water molecule or an OH radical). The weak interaction between the OH radical and water molecule is found to exist in the first shell in (H2O)5+,40 however, it tends to lie in beyond the first shell in the (H2O)8+ clusters. We also presented the corresponding average values of the most stable neutral (H2O)8 cluster in Table 3. Through comparison we find that all the average electron densities [at the (3,-1) CPs, similarly hereafter] of (H2O)8+ clusters are greater than those of their neutral counterpart, whereas all the average lengths of the HBs are shorter. This reveals that removing an electron from neutral (H2O)8 cluster can generally strengthen the hydrogen bonding interactions, which is similar to the case of smaller water clusters.40 Studies found that a exponential relationship existing between the electron densities and the corresponding lengths of HBs,74,75 which has been applied to (H2O)5+.40 For the four low energy (H2O)8+ clusters, the changing tendency of their electron densities with the bond lengths is depicted in Figure 7a and the dependence of the second derivatives of the electron densities on ρ(r) is shown in Figure 7b. We obtained an expression ρ(dHB) = 17812.04exp(-dHB/0.20) + 0.02 with a correlation coefficient of 0.994 for the former, and another expression ▽2ρ(r) = -31.95ρ2(r) + 3.63ρ(r) + 0.01 together with a correlation coefficient of 0.976 for the

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latter. In Figure 7b, the quadratic behavior of (H2O)8+ clusters implies that with the enhancement of the hydrogen bonding interaction, some covalent feature may begin to appear, which has been found in smaller water clusters.40 3.5 Molecular Orbitals of the Six Lowest Energy Clusters The frontier molecular orbitals often have a close link with the chemical reactivity of a molecule and molecular orbitals can show its bonding properties. For these (H2O)8+ clusters, singly occupied molecular orbital (SOMO) are formed because one electron has been removed from their neutral counterparts. In Figure 8, their SOMOs and SOMO-1 orbitals are shown to explore how they are constituted. Considering the similarity among certain types of isomers, we focus on the molecular orbitals of six representative isomers, including W2, W3, W4, W6, W7, and W12. Their SOMOs are composed of the π orbital of the OH radical completely and not shared by H3O+ ion or any water molecule, which is similar to the case of (H2O)2+ cluster that the SOMO of its ion-radical isomer can be identified as a lone pair orbital on OH radical.36 The difference between the SOMOs of these six isomers is subtle, which depends on the locations of the OH radical. The SOMO-1 orbital of new-found W2 is mainly formed by the π orbital of H3O+ ion and its two adjacent water molecules, while the SOMO-1 orbital of W7 mainly consists of the π orbitals of one water molecule. For W3, its SOMO-1 orbital is mainly formed by the π orbital of the water molecule located at the second solvation shell together with some contribution from the H3O+ ion. The SOMO-1 orbitals of single ring and cage-like structures, including W4, W6, and W12, are both shared by the OH radical and its neighbor

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water molecules. Together with SOMOs and SOMO-1 orbitals of smaller cationic water clusters,41 π orbitals are considered as the dominating component in the singly occupied orbitals and the highest doubly occupied orbitals of these water clusters, which conforms to textbook chemistry and confirms the reliability of our structures in turn.

4. CONCLUSION Previous work on the lowest energy structure of (H2O)8+ cluster argued about a cage-like configuration (very similar to W12) found by using basin hoping algorithm and a five-membered-ring configuration (very similar to W3) obtained by constructing structures from the known structures of H+(H2O)8. Our work can provide a diversity of these structures, which indicates the excellent performance of PSO search algorithm and CALYPSO on water clusters. Both MP2 and B3LYP-D3 calculations predict W12 as the most stable structure, which is different from a five-membered-ring lowest energy structure, but gives validity to a cage-like structure in the literature. Our studies confirm that the structures and thermal behavior of (H2O)8+ are

similar to

H+(H2O)8.

According to

MP2

free energy,

the

four-membered-ring isomer W2 is the most dominating species from 100 K to 400 K. However, this configuration has not been reported previously in (H2O)8+ or H+(H2O)8, and the experimental infrared spectrum can be better reproduced with this cluster. Compared with smaller cationic water clusters, temperature influences more remarkably on their relative stabilities. Although the number of hydrogen bonds is not a decisive factor for the stability of these clusters, we speculate that the number of 23



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hydrogen bonds may affect their relative stabilities at elevated temperature and these clusters with a large number of hydrogen bonds are easier to lose their stabilities. Topological analysis and reduced density gradient analysis reveal that if the OH radical takes the place of the three-coordinated site, it will have a stronger interaction with water molecule acting as proton acceptor than that acting as proton donor.

Supporting Information Cartesian coordinates of the fifteen optimized structures (Table S1) and vibrational modes of four-membered-ring and cage-like structures in the high frequency range (Figure S1). Complete author lists of refs 7 and 52. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS The authors would like to thank the support by the NSAF Joint Fund Jointly set up by the National Natural Science Foundation of China and the Chinese Academy of Engineering Physics (Grant Nos. U1430117, U1230201). Some calculations are performed on the ScGrid of Supercomputing Center, Computer Network Information Center of Chinese Academy of Sciences. We also acknowledge the support for the computational resources by the State Key Laboratory of Polymer Materials Engineering of China in Sichuan University.

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(57) Park, M.; Shin, I.; Singh, N. J.; Kim, K. S. Eigen and Zundel Forms of Small Protonated Water Clusters: Structures and Infrared Spectra. J. Phys. Chem. A 2007, 111, 10692-10702. (58) Lee, H.M.; Kim, K.S. Water Dimer Cation: Density Functional Theory vs Ab Initio Theory. J. Chem. Theory. Comput. 2009, 5, 976-981. (59) Min, S. K.; Lee, E. C.; Lee, H. M.; Kim, D. Y.; Kim, D.; Kim, K. S. Complete Basis Set Limit of Ab Initio Binding Energies and Geometrical Parameters for Various Typical Types of Complexes. J. Comput. Chem. 2008, 29, 1208-1221. (60) Kim, H.; Lee, H. M. Ammonia-Water Cation and Ammonia Dimer Cation. J. Phys. Chem. A 2009, 113, 6859-6864. (61) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580-592. (62) Novakovskaya, Y. V.; Stepanov, N. F. Structure and Energy of Water Clusters. Int. J. Quantum Chem. 1997, 61, 981-990. (63) Luo, Y.; Maeda, S.; Ohno, K. Quantum Chemistry Study of H+(H2O)8: A Global Search for Its Isomers by the Scaled Hypersphere Search Method, and Its Thermal Behavior. J. Phys. Chem. A 2007, 111, 10732-10737. (64) Nguyen, Q. C.; Ong, Y. S.; Kuo, J. L. A Hierarchical Approach to Study the Thermal Behavior of Protonated Water Clusters H+(H2O)n. J. Chem. Theory Comput. 2009, 5, 2629–2639. (65) Luo, Y.; Maeda, S.; Ohno, K. Automated Exploration of Stable Isomers of H+(H2O)n (n = 5-7) via Ab Initio Calculations: An Application of the Anharmonic

32


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Downward Following Algorithm. J. Comput. Chem. 2009, 30, 952–961. (66) Miyazaki, M.; Fujii, A.; Ebata, T.; Mikami, N. Infrared Spectroscopic Evidence for Protonated Water Clusters Forming Nanoscale Cages. Science 2004, 304, 1134-1137. (67) Kim, J.; Mhin, B. J.; Lee, S. J.; Kim, K. S. Entropy-Driven Structures of the Water Octamer. Chem. Phys. Lett. 1994, 219, 243-246. (68) Singh, N. J.; Park, M.; Min, S. K.; Suh, S. B.; Kim, K. S. Magic and Antimagic Protonated Water Clusters: Exotic Structures with Unusual Dynamic Effects. Angew. Chem., Int. Ed. 2006, 45, 3795-3800. (69) Andersson, M. P.; Uvdal, P. New Scale Factors for Harmonic Vibrational Frequencies using the B3LYP Density Functional Method with the Triple-ζ Basis Set 6-311+G(d,p). J. Phys. Chem. A 2005, 109, 2937-2941. (70) Johnson, E. R.; Keinan, S.; Mori-Sánchez, P.; Contreras-García, J.; Cohen, A. J.; Yang, W. Revealing Noncovalent Interactions. J. Am. Chem. Soc. 2010, 132, 6498-6506. (71) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon Press: Oxford, 1990. (72) Koch, U.; Popelier, P. L. A. Characterization of CHO Hydrogen Bonds on the Basis of the Charge Density. J. Phys. Chem. 1995, 99, 9747-9754. (73) Parthasarathi, R.; Subramanian, V.; Sathyamurthy, N. Hydrogen Bonding without Borders: An Atoms-in-Molecules Perspective. J. Phys. Chem. A 2006, 110, 3349-3351.

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(74) Mata, I.; Alkorta, I.; Molins, E.; Espinosa, E. Universal Features of the Electron Density Distribution in Hydrogen-Bonding Regions: A Comprehensive Study Involving H…X (X = H, C, O, F, S, Cl, π) Interactions. Chem. Eur. J. 2010, 16, 2442-2452. (75) Ramírez, F.; Hadad, C. Z.; Guerra, D.; David, J.; Restrepo, A. Structural Studies of the Water Pentamer. Chem. Phys. Lett. 2011, 507, 229-233.

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Page 35 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Interaction energies (kcal/mol) of (H2O)8+ cluster obtained without (△Ee) and with (△E0) zero point vibrational energy (ZPVE) correction at the MP2 and DFT levels and other quantities obtained at the MP2 level. N: the number of hydrogen bond; EHB: average hydrogen bond energy; Ef: formation energy; Iad: ZPVE corrected adiabatic ionization potential (eV). -△E0a MPW1K/BH&HLYP/B3LYP

-△E0b MPW1K/BH&HLYP

-△Eec

-△E0c

-△E0d

n

N

EHB

Iad

-EF

1

7

16.1

9.20

112.4

140.6/140.7/138.6

131.4/131.8

144.2

134.6

134.2

2

8

14.6

9.00

116.8

145.0/145.7/143.0

135.3/136.4

149.6

139.0

139.3

3

9

13.0

8.99

117.2

144.7/145.6/142.6

134.4/135.8

151.6

139.4

140.1

4

8

14.6

9.00

117.0

144.9/145.1/142.8

135.2/135.9

150.0

139.2

139.6

5

8

14.6

9.02

116.5

143.9/144.4/141.8

134.2/135.1

149.6

138.7

138.6

6

8

14.6

9.02

116.4

144.5/145.0/142.4

134.8/135.7

150.2

138.6

139.0

7

8

14.5

9.03

116.3

144.6/145.0/142.4

134.8/135.6

149.8

138.5

138.9

8

9

12.9

9.03

116.2

143.2/143.5/141.1

133.4/134.1

149.2

138.4

138.6

9

9

12.7

9.13

113.9

141.1/141.8/139.1

131.4/132.5

148.2

136.1

136.7

10

10

11.6

9.04

115.9

141.9/142.9/140.0

131.5/132.8

151.2

138.1

139.3

11

9

12.9

9.05

115.9

142.8/143.7/140.8

132.7/133.9

151.0

138.1

138.8

12

10

11.7

8.99

117.2

143.6/140.7/141.6

133.1/134.6

153.5

139.4

140.7

13

10

11.7

8.99

117.1

144.0/145.2/141.3

133.4/135.0

152.7

139.3

140.5

14

10

11.7

9.00

116.8

143.4/144.3/141.3

132.7/134.2

152.8

139.0

140.4

15

8

12.0

9.90

96.1

133.9/132.8/140.1

123.4/122.9

143.1

118.3

137.9

a

The 6-311++G** basis set was used

b

The aug-cc-pVDZ basis set was used for ZPVE and the aug-cc-pVTZ basis set was

used for single point energy c

MP2 method with complete basis set (CBS) scheme was used

d

B3LYP/aug-cc-pVTZ level with empirical dispersion correction was used

35



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Page 36 of 47

Table 2. Selected vibrational frequencies of seven important structures of (H2O)8+ cluster at MPW1K/6-311++G** level and the corresponding experimental values. Structures

Frequencies (3500-3600 cm-1)

Frequencies (3600-3800 cm-1)

W2

3501,3572

3640,3705,3733

W3

3457,3510,3634

3674,3694,3705,3724

W4

3407,3554,3598

3609,3703,3727

W6

3546,3589

3622,3687,3692

W7

3476,3524

3602,3678,3752

W11

3539,3576

3650,3713,3739,3779

W12

3573,3650,3658

3704,3735,3757,3771

Exp.22

3497,3543,3576

3652,3684,3715,3739

36


Page 37 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Electron densities ρ(r) (a.u.) and its second derivatives ▽2ρ(r) (a.u.) at the bond critical points (BCPs) of (H2O)8+ cluster and its neutral counterpart, together with their hydrogen bond lengths dHB (Å), where Avg. represents the average value.

W2

W12

BCP

ρ(r)

▽2ρ(r) dHB

BCP

ρ(r)

▽2ρ(r) dHB

1

0.039

0.104

2.721

1

0.039

0.104

2.718

2

0.069

0.113

2.540

2

0.034

0.092

2.796

3

0.080

0.098

2.509

3

0.032

0.089

2.829

4

0.038

0.103

2.734

4

0.039

0.104

2.722

5

0.020

0.074

2.912

5

0.035

0.093

2.779

6

0.042

0.106

2.709

6

0.061

0.113

2.579

7

0.025

0.084

2.850

7

0.051

0.112

2.633

8

0.058

0.110

2.594

8

0.102

0.045

2.456

Avg.

0.046

0.099

2.696

Avg.

0.049

0.094

2.689

1

0.067

0.110

2.555

1

0.043

0.108

2.697

2

0.068

0.111

2.546

2

0.024

0.080

2.883

3

0.066

0.110

2.554

3

0.062

0.112

2.578

4

0.033

0.092

2.781

4

0.080

0.097

2.508

5

0.032

0.090

2.794

5

0.042

0.106

2.689

6

0.037

0.093

2.763

6

0.026

0.083

2.872

7

0.030

0.091

2.793

7

0.030

0.090

2.796

8

0.029

0.086

2.828

8

0.026

0.082

2.877

9

0.028

0.087

2.850

9

0.063

0.112

2.569

10

0.032

0.094

2.776

Avg.

0.044

0.097

2.719

Avg.

0.042

0.096

2.724

Avg.

0.032

0.085

2.836

W4

W3

(H2O)8

37



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Page 38 of 47

Figure Captions

Figure 1. Structures of (H2O)8+ cluster predicted by the particle swarm optimization method. Figure 2. Energy (kcal/mol) of the fourteen (H2O)8+ isomers without (Ee) and with (E0) zero point vibrational energy (ZPVE) correction with respect to W12 at MP2 and DFT levels. Figure 3. Relative Gibbs free energies of the fourteen proton-transferred structures of (H2O)8+ cluster below 400 K with respect to W2 Figure 4. (a) Temperature-dependent population of four dominanting isomers, viz. W2, W3, W4, and W12. (b) Temperature-dependent population of chain, single-ring, double-ring, and multi-ring structures for (H2O)8+ cluster. Figure 5. Simulated IR spectra for the five lowest energy structures compared with the experimental result. Figure 6. (a)-(d) Reduced density gradient (RDG) figures of the four lowest energy clusters. Figure 7. (a) Relationships between the electron densities and hydrogen bond lengths; (b) Relationships between the electron densities and its second derivatives for the four lowest energy structures of (H2O)8+ cluster. Figure 8. (a)-(f) The singly occupied orbitals (SOMO) and the highest doubly occupied orbitals (SOMO-1) of W2, W3, W4, W6, W7 and W12, respectively.

38


Page 39 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Structures of (H2O)8+ cluster predicted by the particle swarm optimization method.

39


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Relative energy (kcal/mol)


Page 40 of 47

b

MP2 E0 MP2/CBS Ee MP2/CBS E0 b B3LYP-D3 E0 a B3LYP E0 b MPW1K E0 b BH&HLYP E0 b wB97XD E0

10 8 6 4 2 0 -2 1

2

3

4

5

6

7

8

9 10 11 12 13 14

Cationic water cluster Wn (n=1-14)

Figure 2. Energy (kcal/mol) of the fourteen (H2O)8+ isomers without (Ee) and with (E0) zero point vibrational energy (ZPVE) correction with respect to W12 at MP2 and DFT (MPW1K, BH&HLYP, and B3LYP) levels, respectively. The MP2/CBS energies were extrapolated by using MP2/aug-cc-pVDZ and MP2/ aug-cc-pVTZ energies. B3LYP-D3 method means using B3LYP functional with empirical dispersion correction. a

The 6-311++G** basis set was used

b

The aug-cc-pVDZ basis set was used for ZPVE and the aug-cc-pVTZ basis set was

used for single point energy.

40


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Relative Gibbs energy (kcal/mol)

Page 41 of 47

10 W2 W1 W3 W4 W5 W6 W7 W8 W9 W10 W11 W12 W13 W14

8 6 4 2 0 0

100

200

300

400

Temperature (K)

Figure 3. Relative Gibbs free energies of the fourteen proton-transferred structures of (H2O)8+ cluster below 400 K with respect to W2, in the calculation single point energies are obtained at MP2/CBS level and ZPVEs at the MP2/aug-cc-pVDZ level.

41



(a)

0.8

W2 W3 W4 W12

0.4

Population

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 47

0.0 (b)

0.8 Ch SR DR MR

0.4 0.0 0

100

200

300

400

Temperature (K)

Figure 4. (a) Temperature-dependent population of four dominanting isomers, viz. W2, W3, W4, and W12. (b) Temperature-dependent population of chain structures (Ch), branched single-ring structures (SR), double-ring structures (DR), and multi-ring structures that mainly are cage-like ones (MR) for (H2O)8+ cluster.

42


Page 43 of 47

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


W4

W3

W2

W12

W11

2200 2400 2600 2800 3000 3200 3400 3600 3800 4000

Wavenumber (1/cm)

Figure 5. Simulated IR spectra for the five lowest energy structures compared with the experimental result. The top panel is reprinted with permission from Mizuse et al., J. Phys. Chem. A 2013, 117, 929-938. Copyright 2013 Royal Society of Chemistry.23

43



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Page 44 of 47

Figure 6. (a)-(d) Reduced density gradient (RDG) figures of the four lowest energy clusters, where Arabic numbers denote the bond critical points in the corresponding clusters. The blue, green, and red represent the strong attraction, van der Waals interaction

and

strong

repulsion,

respectively.

44


Page 45 of 47

(a)

0.10 0.09

ρ (a.u.)

0.08 0.07 0.06 0.05 0.04 0.03 0.02 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90

Å

dHB ( )

0.11

(b)

0.10

(a.u.)

0.09 0.08

2 ∇ ρ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.07 0.06 0.05 0.04 0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

ρ (a.u.)

Figure 7. (a) Relationships between the electron densities and hydrogen bond lengths; (b) Relationships between the electron densities and its second derivatives for the four lowest energy structures of (H2O)8+ cluster. 45



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Page 46 of 47

Figure 8. (a)-(f) The singly occupied orbitals (SOMO) and the highest doubly occupied orbitals (SOMO-1) of W2, W3, W4, W6, W7 and W12, respectively. The value of the surface is 0.03 a.u.

46


Page 47 of 47

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Table of Contents Image

47


Ab Initio Study of Ionized Water Radical Cation - ACS Publications

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