Electron Detachment and Subsequent Structural Changes of Water

Article pubs.acs.org/JPCA

Electron Detachment and Subsequent Structural Changes of Water Clusters Susanta Das,† Turbasu Sengupta,† Achintya Kumar Dutta,† and Sourav Pal*,‡ †

Physical Chemistry Division, CSIR−National Chemical Laboratory, Pune 411008, India Department of Chemistry, Indian institute of Technology Bombay, Powai, Mumbai 400 076, India

‡

S Supporting Information *

ABSTRACT: A cost-effective equation of motion coupled cluster method, EOMIP-CCSD(2), is used to investigate vertical and adiabatic ionization potential as well as ionization-induced structural changes of water clusters and compared with CCSD(T), CASPT2, and MP2 methods. The moderate N5 scaling and low storage requirement yields EOMIPCCSD(2) calculation feasible even for reasonably large molecules and clusters with accuracy comparable to CCSD(T) method at much cheaper computational cost. Our calculations shed light on the authenticity of EOMIP-CCSD(2) results and establish a reliable method to study of ionization energy of molecular clusters. We have further investigated the performance of several classes of DFT functionals for ionization energies of water clusters to benchmark the results and to get a reliable functionals for the same.

1. INTRODUCTION One of the rapidly growing fields in cluster chemistry is the study of water aggregation.1−5 Water clusters have gained exceptional attention in both experimental and theoretical areas for ubiquitous behavior. At the same time, understanding of the hydrogen bonding framework within the water clusters has attracted considerable interest because of its fundamental importance in the various fields of chemistry and biology.6−9 In particular, ionized hydrogen-bonded water clusters play an important role in the atmosphere and in biological systems. On the contrary, because of the finite pH value of bulk water, it undergoes spontaneous autoionization and the process is strongly endothermic.10 The reason behind the spontaneous ionization of water molecule is the electric-field fluctuation,11 and the kinetics and energetics of the process are guided by thermodynamic conditions, such as temperature, density, or pressure. Ionization of the water cluster results in rapid proton transfer or molecular rearrangement. The cationic water clusters in the gas phase represent a unique system that can provide structural information about aqueous proton in details.12 Mass spectrometry studies have revealed the existence of several magic number clusters, which includes (H2O)n, n = 21, 28, and 58.13 Experimentally, stability of magic numbered water clusters was first reported by Lin in 1973.14 Later, Yeh et al.15 and Jiang et al.16 explained the structure of the magic cluster in detail through IR− spectroscopic technique. They have concluded that the geometry change from 1D chain to 2D net structure occurs at around n = 10 and transition to 3D structure completed at around n = 21, which has been reported as the first magic © XXXX American Chemical Society

cluster. The same group has also explored the structural analysis of large cationic H+(H2O)n (up to n = 28) clusters. The ionization potential (IP) of the neutral species can be defined as the energy require to remove one electron from the molecule or cluster. In the case of the neutral water cluster the photo−ionization process can be summarized as eq 1 (H 2O)n + hν → [(H 2O)n ]+ + e− → (H 2O)n − 1H+ + OH + e−

(1)

Studies on the dynamics of the ionization of water cluster have shown that initially a cationic species [(H2O)n]+ is formed and then undergoes rapid intra-clusters charge redistribution, which favors proton transfer process and subsequent loss of OH. The ionization leads to the transfer of proton from one water molecule to another within the cluster, resulting in rapid rearrangement and release of a large amount of energy. Therefore, the study of IP of various size water clusters is significant because it gives an understanding of the oxidation process that takes place in aqueous medium. It is also important in understanding the chemistry of the highly ionized environment like mesosphere.17 However, the experimental study of the ionization process in water offers a significant challenge. Although it is possible to produce experimentally isolated ionized water cluster in the gas phase under extreme conditions,18 their transient lifetime Received: September 25, 2015 Revised: February 2, 2016

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DOI: 10.1021/acs.jpca.5b09389 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

It is well known that density functional theory calculations fail to generate correct geometries and energetics of various conformations of water clusters.47−50 Kim and coworkers have investigated the stability of different structural conformations of water clusters using diverse DFT functionals and CCSD(T)/ complete basis set (CBS) level of theory.51 They have concluded that for the water dimer cation the 2pL structure is more stable than the 2nOO structure in the CCSD(T)/CBS level. Apart from the failure of different DFT functionals to obtain such results, the MPW1K and BH&HLYP functionals using the 6-311++G** basis set give almost equivalent results in comparison with the CCSD(T)/CBS results. On the contrary, at the CCSD(T) level, the water trimer cation, the most stable structure, is the dissociated linear structure (3pL3), and there also exists a hemibonded ring structure (3nOOR) structure; however, the MPW1K and BH&HLYP functionals fail to produce the 3nOOR species. Roca-Sanjuán et al. have reported that the BH&HLYP functional underestimate IP values by 1.20 to 1.67 eV with respect to CCSD(T) level20,52,53 and only B2GP-PLYP functional properly describes the correct trend of IP; however, to the best of our knowledge, no CCSD(T) results are available for ionized water cluster beyond hexamer. Hence, it is absolutely necessary to have reliable benchmark data that can be used to investigate the relative performance of different DFT functionals. It should be noted that proper DFT functionals can perform reasonably well for the solvation of cations perform with good accuracy in comparison with correlated wave-function approaches.54 The paper is organized as follows. The next section gives computational details. Section 3 gives the numerical results of EOMIP-CCSD(2) for different water clusters as well as benchmarking of different DFT functionals. Section 4 gives the concluding remarks.

makes it difficult to study. Theoretical calculations can provide an easy and reliable way to get an insight into the chemistry of the ionized water clusters. Several theoretical calculations on IP of water clusters have been reported in the literature.19 RocaSanjuán et al. has employed MP2 and projected MP2 to determine the VIP and AIP of water clusters.20 MP2 has N5 scaling and hence it can be applied for reasonably large size water clusters; however, MP2 gives poor performance when there is a symmetry breaking21 or spin contamination in the molecule,22,23 which is very prominent in ionized water clusters.24 Another disadvantage of MP2 method is its incapability to include nondynamic correlation, which has significant contribution in determining ionization potential.25,26 The same group has further employed highly correlated CC, CCSD(T), and CASPT2 level of theory to probe electron detachment in water clusters. Although the CCSD(T) method overcomes the previously mentioned problems of MP2 method in a very elegant way, its prohibitively high N7 scaling to the basis set and huge storage requirement makes it impossible to apply beyond small molecules in a reasonable basis set.27−34 Moreover, it does not have a balanced description of the nondynamic correlation. On the contrary, CASPT2 method, although including dynamic and nondynamic correlation in a balance manner, is not size-extensive.35 Furthermore, the IP calculations in CASPT2 method requires two separate calculations and like any multireference method requires considerable experience and expertise from the part of the users. Therefore, for accurate modeling of electron-detachmentinduced phenomenon, it is necessary to use a method that treats the dynamic and nondynamic correlation in a balanced way and is black box yet is computationally not very expensive. On the contrary, the EOMIP-CCSD(2) method, which has been extremely successful in the accurate calculation of energy, structure, and properties of large open-shell molecules and molecular ionized state,36−38 represents a best alternative for the purpose. The EOMIP-CCSD(2) method is a size-extensive modification of the standard EOMIP-CCSD method, obtained by second-order truncation of the similarity transformed Hamiltonian based on perturbative orders.39−46 The method has several advantages over standard single reference MBPT and coupled-cluster methods such as (i) is capable of accurate prediction of geometrical parameters of open-shell species (ii) has comparatively lower scaling (N5) and less storage requirement consequences applicable to the larger systems. (iii) efficiently takes care of multi-reference situation and (iv) most importantly, does not incorporate any active space dependency, making it a black box. Recently, Dutta et al. has extended the idea of EOMIPCCSD(2) to formulate a new very accurate method for IP calculation within the EOMCC hierarchy. The new EOMIPCCSD(2)* method gives IP values within 0.21 eV of benchmark EOM-CCSD(2) method; however, the method is computationally more demanding due to its N6 scaling and higher storage requirement. Hence, in this paper, we used EOMIP-CCSD(2) method to study IP (VIP and AIP) of water clusters [(H2O)n; n = 1−8, 24] and ionization-induced structural changes. Our EOMIP-CCSD(2) calculations allow us to set up most accurate data at the highest theoretical level for the future references, especially for the benchmarking of DFT functionals.

2. COMPUTATIONAL DETAILS All of the EOMIP-CCSD, EOMIP-CCSD(2)*, and EOMIPCCSD(2) calculations are performed using the CFOUR software package.55 Structural optimization of all water clusters is performed in aug-cc-pVDZ56 basis, and the aug-cc-pVTZ57,58 basis set is used for single-point energy calculations. In the DFT framework, all neutral and cation water clusters, (H2O)n (n = 2−8 and 24), are optimized in the aug-cc-pVDZ basis set along with different DFT functionals, and for single-point energy calculation aug-cc-pVTZ is used. We have considered eight functionals, including the three GGA functionals (BPBE,59,60 BVWN,61 and BLYP59,62), two hybrid functionals (B3LYP63 and B3PW9162−65), one most popular meta-hybrid functional (M06-2X66,67), and two recently proposed double -hybrid (DHDFs) functionals (B2PLYP68 and mPW2PLYP69). Gaussian 09 software package70 is used for all DFT calculations. All of the optimized geometries (Cartesian coordinates) are provided in the Supporting Information (SI). 3. RESULTS AND DISCUSSION The theoretical phenomena related to the IPs are shown in Figure 1. The vertical ionization potential (VIPe) correlates the electronic transition from the ground state of a neutral system at its optimized geometry to the lowest energy state of its cation. On the contrary, the adiabatic IP (AIPe) is the energy difference between the two minima of the energy states, considering the geometry relaxation taking place in the cation and setting the lowest electronic band to the origin of the B


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contrary, produces a VIP value of 11.74 and 12.18 eV, respectively, in the same basis set. Therefore, the EOMIPCCSD(2) method seems to be accurate enough for calculations of larger water clusters. Now it is important to notice from Table 1 that all of the theoretical method significantly overestimates the IP values as compared with the experimental results. Here it should be noted that the ionization spectra of water clusters are much more complex than as suggested by Figure 1. The experimental values quoted in the Table 1 are included from the work of Ahmed and coworkers.47 In reality the experimental values are onset energies of water clusters. They represent the upper limit for the true adiabatic ionization energy of corresponding neutral water clusters and should not be compared with theoretically calculated vertical ionization energies. This is one of the central factors for discrepancy between experimental and computed results in the present as well as in the previous studies. Therefore, for one-to-one correspondence with the experimental spectra, one needs to perform a Frank−Condon overlap analysis between the neutral and cationic normal modes. Nooijen and coworkers have shown than the Frank− Condon overlap analysis within the framework of EOMIPCCSD can be used for an accurate simulation of photoelectron spectra of small molecules.71 Krylov and coworkers have performed the Frank−Condon overlap analysis of water dimer cation using EOMIP-CCSD method as well.72 They have shown that there exists a strong vibronic coupling between the normal mode corresponding the O−O bond and the Hshared− Odonor bond of the dimer cation. Their computed appearance energy of 11.10 eV also has shown very good agreement with the experimental value of 11.25 eV. The EOMIP-CCSD(2) method has all of the advantages of EOMIP-CCSD method, with additional convenience of N5 scaling and low storage requirement. Therefore, it can be used to perform the Frank− Condon overlap analysis of much larger cationic cluster; however, such a study is beyond the scope of this manuscript. Now, in the absence of any directly comparable experimental quantity, it is advisible to compare the result with that in high level theoretical method. In the present manuscript, to check

Figure 1. IP diagram. Definitions of VIPe, AIPe, and AIP0 are graphically shown through the electric and vibrational potential energy levels.

transition. The addition of the zero-point vibrational energy (ZPE) corrections to AIPe leads to AIP0. So it is obvious that only AIP0 have experimental counterparts to be compared with the 0−0 or T0 band origins, while the vertical magnitudes are typically related to the band maxima within the limit of Franck−Condon approximation. 3.1. Vertical Ionization Potential of Water Clusters. Table 1 reports the vertical ionization potential of water clusters obtained in EOMIP-CCSD(2) method along with previously reported theoretical results and experimental results. It is well known that the standard EOMIP-CCSD method gives very accurate result for IP values, but it is not computationally feasible to go beyond the water trimer owing to high scaling (iterative N6) and large storage requirement; however, the EOMIP-CCSD(2) method, because of its lower scaling and smaller storage requirement, can be used for considerably large clusters. Hence, to check the reliability of our attempt, first we benchmark our EOMIP-CCSD(2) values with full EOMIPCCSD results for water dimer and trimer, for which it is possible to use the full EOMIP-CCSD method in a reasonable basis set. The EOMIP-CCSD method gives a VIP value of 11.74 and 12.17 eV for water dimer and trimer, respectively, in aug-cc-pVTZ basis set. The EOMIP-CCSD(2) method, on the

Table 1. Low-Lying Vertical Ionization Potential (VIPe, in electronvolts) of Water Clusters Obtained by Different Theoretical Methods. Second Column Includes the Experimental Onset Energies methods

exp.a

EOMIP-CCSD(2)[A]b,c

EOMIP-CCSD(2)*[B]c,d

EOMIP-CCSD[C]c,e

CCSD(T)[D]f,g

CASPT2[E]g,h

MP2[F]g,i

dimer trimer tetramer pentamer hexamer book hexamer cage hexamer prism hexamer ring heptamer g1 heptamer g2 heptamer g3 octamer cube (d2d) octamer cube (s4) (H2O)24 (d2h)

11.25 11.15 10.94 10.94

11.74 12.18 12.19 12.07 11.60 11.45 11.61 11.94 11.67 11.67 11.56 11.89 11.90 11.72

11.64 12.06 12.04 11.91 11.55 11.40 11.56 11.90 11.44 11.44 11.36 11.65 11.64

11.74 12.17

11.79 12.27 12.27 12.10 11.69 11.99 11.65 12.14

11.72 12.26 12.19 12.19 11.53 11.81 11.67 12.09

11.79 12.37 11.93 12.17 11.69 12.00 11.75 11.58

10.93

10.91

10.92

a Ref 47 bEOMIP-CCSD(2)[A] = EOMIP-CCSD(2) \ aug-cc-pVTZ \\ EOMIP-CCSD(2) \ aug-cc-pVDZ. cThis study. dEOMIP-CCSD(2)*[B] = EOMIP-CCSD(2)* \ aug-cc-pVTZ \\ EOMIP-CCSD(2)* \ aug-cc-pVDZ. eEOMIP-CCSD[C] = EOMIP-CCSD \ aug-cc-pVTZ \\ EOMIPCCSD) \ aug-cc-pVDZ. fCCSD(T)[D] = CCSD(T) \ aug-cc-pVTZ \\ CCSD \ aug-cc-pVDZ. gRef 20 hCASPT2 [E]= CASPT2 \ ANO-L 4321 \ 321 \\ CASPT2 \ ANO−L 431 \ 21. iMP2 [F] = MP2 \ aug-cc-pVDZ.

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The VIP of water cluster decreases from tetramer to pentamer. The EOMIP-CCSD(2), among all of methods, gives the smallest deviation of 0.03 eV of pentamer as compared with CCSD(T). The values obtained in EOMIP-CCSD(2) and CCSD(T) methods are 12.07 and 12.10 eV, respectively, for water pentamer. The MP2 and CASPT2 differ by 0.07 and 0.09 eV as compared with CCSD(T) calculation. The trend of VIP values further decreases from pentamer to hexamer; however, the trend in hexamer differs from one method to another. The results for hexamer clusters in EOMIP-CCSD(2) method show good agreement in general with the CCSD(T) number, except that in cage isomer; however, in the case of cage isomer the UHF wave function shows severe spin contamination (S2 = 0.82); therefore, the reliability of the CCSD(T) results can be questioned. In particular, it is well known that spin projection considerably changes the IP values for the cages isomer in MP2 level.20 Among the three conformations of heptamer, the conformations g1 and g2 have the same VIP in the EOMIPCCSD(2) method, whereas the VIP in g3 is less by 0.11 eV. On the same track, two conformations of octamer, cube(d2d) and cube(s4), produce identical VIP and negligibly differ by 0.01 eV. We have further calculated VIP of bigger water cluster, (H2O)24, by EOMIP-CCSD(2), which is difficult to perform in CCSD(T) and may be in CCSD level also; however, we are unable to estimate the quality of EOMIP-CCSD (2) results beyond hexamer due to unavailability of CCSD(T) data as well as results of other theoretical methods. 3.2. Analysis of VIPs Obtained by Different DFT Functionals. The VIP values in EOMIP-CCSD(2) method, in general, show good agreement with the CCSD(T) result, and it can be applied to considerately large clusters as well. Now in the absence of any direct experimental observable and highlevel theoretical results beyond small cluster, the EOMIPCCSD(2) results can be used to benchmark different DFT functionals for VIP of water clusters. The deviation of DFT results with EOMIP-CCSD(2) is compiled in the Table 2 and pictorially represented in Figure 3. We have considered several classes of functionals including GGA, hybrid, meta-hybrid, and double-hybrid functionals to compute the VIP of water clusters. Overall, the results show a large scattering of VIP values among the different functionals. The GGA functional, BPBE, shows average deviation of 2.37 eV of VIP value in comparison with

the reliability of our results, we compare the numbers obtained in EOMIP-CCSD(2) method with CCSD(T) and other theoretical results, as shown in Figure 2. We specially focus

Figure 2. Average deviation of vertical ionization potential obtained as compared with the CCSD(T) method. Our result shows that the EOMIP-CCSD(2) is the best alternative method with respect to the CCSD(T) to study the VIP accurately of large-size water clusters.

on the comparison with CCSD(T), which presumably gives the most reliable results among the available one. The EOMIPCCSD(2) gives a VIP value of 11.74 eV for the dimer in aug-ccpVTZ basis, whereas CCSD(T) produces 11.79 eV of VIP for the same. CASPT2 gives a deviation of 0.07 eV for water dimer and MP2 yields identical result as compared with CCSD(T). On the contrary, the EOMIP-CCSD(2)* method produces an average deviation of 0.15 eV with CCSD(T). The VIP values gradually increase from dimer to trimer. In the case of water trimer, EOMIP-CCSD(2) gives a deviation of 0.09 eV with respect to CCSD(T). The CASPT2 results marginally differ by 0.01 eV from the CCSD(T) method, whereas MP2 and EOMIP-CCSD(2)* deviate from CCSD(T) by 0.10 and 0.21 eV, respectively. The CCSD(T) value of VIP for tetramer is 12.27 eV, whereas EOMIP-CCSD(2) yields 12.19 eV for the same. The VIPs of tetramer obtained through the other methods, that is, CASPT2, MP2, and EOMIP-CCSD(2)*, differ from CCSD(T) by 0.08, 0.34, and 0.23 eV, respectively.

Table 2. Deviation in VIPe Obtained through Different DFT Functionals as Compared with EOMIP-CCSD(2) Method and Experimental Onset Energiesa

a

clusters size

BPBE

BVWN

BLYP

B3LYP

B3PW91

M06-2X

B2PLYP

mPW2PLYP

dimer trimer tetramer pentamer hexamer book hexamer cage hexamer prism hexamer ring heptamer g1 heptamer g2 heptamer g3 octamer cube (d2d) octamer cube (s4) (H2O)24 (d2h)

0.67(0.18) 1.52(0.49) 1.96(0.71) 2.25(1.12) 2.14 1.79(1.27) 2.00 2.45 2.10(1.34) 2.10 2.15 2.08(1.11) 2.27 7.74

0.25(0.74) 0.69(0.34) 1.10(0.15) 1.39(0.26) 1.21 0.89(0.37) 1.10 1.58 1.24(0.48) 1.25 1.22 1.28(0.31) 1.25 2.26

0.71(0.22) 1.61(0.58) 2.02(0.77) 2.32(1.19) 2.11 1.88(1.36) 1.95 2.52 2.15(1.39) 2.15 2.11 2.14(1.17) 2.23 3.22

0.14(0.35) 0.85(0.18) 1.12(0.13) 1.40(0.27) 1.21 0.93(0.41) 0.91 1.50 1.06(0.30) 1.06 1.27 1.15(0.18) 1.19 1.95

0.18(0.31) 0.83(0.20) 1.15(0.10) 1.38(0.25) 1.24 0.93(0.41) 1.01 1.51 1.11(0.35) 1.11 1.19 1.18(0.21) 1.22 1.95

0.19(0.68) 0.00(1.03) 0.14(1.11) 0.24(0.89) 0.01 0.04(0.56) 0.00 0.28 0.04(0.80) 0.04 0.02 0.05(1.02) 0.04 0.39

0.50(0.01) 0.35(0.68) 0.34(0.91) 0.46(0.67) 0.02 0.10(0.62) 0.04 0.25 0.11(0.87) 0.07 0.06 0(0.97) 0 0.60

0.48(0.01) 0.27(0.76) 0.22(1.03) 0.35(0.78) 0.09 0.17(0.69) 0.11 0.22 0.17(0.93) 0.13 0.09 0.04(0.93) 0.02 0.47

Available experimental values are given in the parentheses. D


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B3PW91, produce results similar to each other with an improved accuracy as compared with the GGA functionals. The lowest fluctuations of 0.71 and 0.14 eV are observed for water dimer calculated by using B3LYP and B3PW91 functionals, whereas (H2O)24 yields the largest fluctuation, which is identical at 1.95 eV for both the functionals. On the contrary, the widely used meta-hybrid, M06-2X functional, gives remarkably good agreement with EOMIP-CCSD(2) method. The M06-2X gives the smallest average absolute deviation of 0.08 eV as compared with EOMIP-CCSD(2) result. The M06-2X functional gives identical value of VIP as that of EOMIP-CCSD(2) method for water trimer and hexamer prism. The rest of the water clusters also show marginal deviation from EOMIP-CCSD(2) results. The double-hybrid functionals, B2PLYP and mPW2PLYP, give better performance as compared with GGAs and hybrid functionals; however, the average absolute deviation in double-hybrid functionals is slightly on the higher side (0.33 eV) as compared with meta hybrid, M06-2X functional. Therefore, from the comparison with EOMIP-CCSD(2) results, the M06-2X functional seems to be the most suitable one for calculation of ionization energies of larger water clusters. 3.3. Ionization-Induced Structural Changes. Cationic water clusters are optimized in the EOMIP-CCSD(2) method using aug-cc-pVDZ basis set, and the Cartesian coordinate of optimized geometries are reported in the Supporting

Figure 3. Average deviation of vertical ionization potential obtained through different DFT functionals with EOMIP-CCSD(T) results. Among the different classes of functionals, the meta-hybrid functional, M06-2X, shows the best performance to calculate the VIP of water clusters of various size.

EOMIP-CCSD(2) results. It shows the smallest deviation of 0.67 eV for dimer and the largest of 7.74 for (H2O)24. Similarly, in the case of BVWN, the smallest and largest deviations are observed for water dimer (0.25 eV) and (H2O)24 (2.26 eV), respectively. Another GGA functional, BLYP, also shows a similar trend. Two popular hybrid functionals, B3LYP and

Figure 4. EOMIP-CCSD(2)\aug-cc-pVDZ optimized structure for the ground state of the cationic water clusters. E


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an average R(O−O) distance of 2.52 Å for the water dimer, whereas the reported values of CCSD, CASPT2, and MP2 methods are 2.54, 2.49, and 2.56 Å, respectively. In the case of trimer, the average R(O−O) distance in EOMIP-CCSD(2) method increases by 0.56 Å with respect to the dimer. The CCSD, CASPT2, and MP2 methods also give a similar qualitative trend, that is, increment of the average R(O−O) distance on going from dimer to trimer; however, the average R(O−O) distance decreases in the case of tetramer. The EOMIP-CCSD(2) method gives a value of 2.57 Å, and CCSD, CASPT2, and MP2 methods result in values of 2.74, 2.71, and 2.72 Å, respectively, for the tetramer. The EOMIP-CCSD(2) method predicts an average R(O−O) distance of 2.67 Å for water pentamer. Within the hexamer analogues, the prism shows the highest average R(O−O) distance in all of the methods; however, they differ for the lowest average R(O−O) distance. The EOMIP-CCSD(2) method predicts the lowest average R(O−O) distance for the hexamerbook, whereas the other three methods yield the lowest value for its cage analogue. For the heptamer, the g1 isomer shows an average bond length of 2.81 Å in EOMIP-CCSD(2) method. On the contrary, g2 and g3 show nearly identical average bond lengths of 2.93 and 2.94 Å, respectively. The octamer, cube-d2d, and cube-s4 have identical average bond lengths of 2.86 and 2.87 Å, respectively, in EOMIP-CCSD(2) method. No other high-level theoretical results are available for heptamer and octamer cationic clusters. For the smaller cluster, the bond lengths in CCSD, MP2, and CASPT2 methods are in qualitative agreement with that in EOMIP-CCSD(2). The only exception is noticed in the case of tetramer, where CCSD, MP2, and CASPT2 methods overestimates the average R(O−O) distance by a large extent, as compared with the EOMIP-CCSD(2) method. 3.4. Adiabatic Ionization Potential of Water Clusters. The computed adiabatic ionization potentials for different water clusters are compiled in Table 4. In the literature, several theoretical treatments are reported from perturbation methods to coupled cluster with various basis sets. We have compared the performance of our EOMIP-CCSD(2) approach with available MP2, CASPT2, and CCSD(T) values. Careful analysis of available theoretical results shows less scattering of AIP as

Information(SI). Geometrical parameters obtained through EOMIP-CCSD(2) method are compared with available CCSD, CASPT2, and MP2 results. To the best of our knowledge, experimental values are so far unavailable. The observed structural distortions due to electron detachment are demonstrated in Figure 4. The optimized geometries are found to be cationic (H2O)n−1H+1, as predicted by eq 1. We have also observed a cationic dimer-like structure similar to hydrazine in the stable ground state. On the contrary, trimer and tetramer prefer chain geometry, and pentamer, hexamerbook, and hexamer-ring form cyclic structure on electron detachment. It is interesting to note that other conformers of hexamer and conformers of heptamer transform to cage structures, whereas cationic octamer isomers have a cubeshaped ground state as a result of electron detachment. The number of O−O bonds differs from one structure to another, and analysis of their individual bond length may not be very instructive; however, the average R(O−O) distance of cationic species can be a suitable parameter to study the ionization-induced structural changes of different clusters and is reported in Table 3. The EOMIP-CCSD(2) method predicts Table 3. Average R(O−O) Distance (in Å) of the Cationic Water Clusters Obtained by Different Theoretical Methods

a

methods

EOMIP-CCSD(2)a

CCSDb

CASPT2b

MP2b

dimer trimer tetramer pentamer hexamer book hexamer cage hexamer prism hexamer ring heptamer g1 heptamer g2 heptamer g3 octamer cube (d2d) octamer cube (s4)

2.52 3.06 2.57 2.67 2.69 2.71 2.85 2.69 2.81 2.93 2.94 2.86 2.87

2.55 3.12 2.74 2.73 2.71 2.70 2.91 2.73

2.50 3.08 2.71 2.69 2.67 2.66 2.85 2.70

2.53 3.11 2.72 2.71 2.69 2.68 2.90 2.71

This study. bRef 19.

Table 4. Low-Lying Adiabatic Ionization Potentials (AIP0, in eV) of Water Clusters Obtained by Experimental and Different Theoretical Methods methods

expa

EOMIP-CCSD(2)[A]b,c

EOMIP-CCSD[B]c,d

CCSD(T)[C]e,f

CASPT2[D]f,g

MP2[E]h,i

dimer trimer tetramer pentamer hexamer book hexamer cage hexamer prism hexamer ring heptamer g1 heptamer g2 heptamer g3 octamer cube (d2d) octamer cube (s4)

10.80

10.65 9.95 9.70 9.31 9.24 9.20 9.34 9.23 9.27 9.00 8.95 9.21 9.21

10.41 10.14

10.75 10.00 9.71 9.39 9.27 9.38 9.41 9.22

10.77 10.08 9.71 9.42 9.19 9.46 9.57 9.24

10.82 10.07 9.79 9.48 9.35 9.46 9.49 9.31

a

Ref 48. bEOMIP-CCSD(2)[A] = EOMIP-CCSD(2) \ aug-cc-pVTZ \\ EOMIP-CCSD(2) \ aug-cc-pVDZ. cThis study. dEOMIP-CCSD[B] = EOMIP-CCSD \ aug-cc-pVTZ \\ EOMIP-CCSD) \ aug-cc-pVDZ. eCCSD(T)[C] = CCSD(T) \ aug-cc-pVTZ \\ CCSD \ aug-cc-pVDZ. fRef 20. g CASPT2[D]= CASPT2 \ ANO-L 4321 \ 321 \\ CASPT2 \ ANO-L 431 \ 21. hMP2[E] = MP2 \ aug-cc-pVDZ. iRef 19. F


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potential to be the best alternative method to calculate the ionization energies of medium- and large-size water clusters.

compared with the VIP of water clusters. This is presumably due to the cancellation of error introduced during the geometry optimization in both ground state and ionized state for all methods. We have calculated AIP of water clusters up to octamer including four hexamer, three heptamer, and two octamer analogues in the framework of EOMIP-CCSD(2). Among the available theoretical methods, CCSD(T) gives the most accurate results until date. Hence, we compare the authenticity of our results with CCSD(T), as shown in Figure 5. The EOMIP-CCSD(2) contributes the average deviation of

4. CONCLUSIONS The EOMIP-CCSD(2) method is used to investigate vertical and adiabatic ionization potential of water clusters. The obtained results are compared with standard ab initio EOMIP-CCSD, EOMIP-CCSD(2)*, CCSD(T), CASPT2, and MP2 levels of theory. The optimized geometrical parameters [average R(O−O)] are also compared with the various high-level ab initio methods. Our results based on EOMIP-CCSD(2) method shows nice agreement with the most trusted but highly expensive CCSD(T) method for both ionization energies and structural changes that takes place upon ionization. Therefore, the EOMIP-CCSD(2) method can be a reliable choice to calculate IP of medium- and large-size water clusters for which coupled-cluster calculations are not feasible due to their high computational scaling and large storage requirement. It can also be used for calibration of other approximate wave-function- and DFT-based methods; however, to get reliable agreement with experiments, one needs to perform a Frank−Condon overlap analysis between the neutral and cationic normal modes. Such a study within the framework of EOMIP-CCSD(2) method is in progress and will be reported in future manuscript.

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Figure 5. Average deviation of adiabatic ionization potential as compared with CCSD(T) method. The performance of EOMIPCCSD(2) to calculate AIP of water is reasonably good in comparison with CCSD(T) method.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b09389. Cartesian coordinates of neutral and cationic water clusters in different size. (PDF)

0.07 eV, whereas CASPT2 and MP2 give 0.06 and 0.08 eV, respectively, as compared with CCSD(T) method. The AIP of water dimer obtained through the EOMIP-CCSD(2) method is 10.65 eV, which deviates by 0.1 eV with respect to CCSD(T), whereas CASPT2 and MP2 methods show deviation of 0.02 and 0.07 eV, respectively. On the contrary, the EOMIPCCSD(2) method gives nice agreement with CCSD(T) method for the water trimer. The CASPT2 and MP2 method shows deviation of 0.08 and 0.07 eV with respect to CCSD(T). In the case of the tetramer, CASPT2 shows an identical result with CCSD(T), and EOMIP-CCSD(2) differs marginally by 0.01 eV; however, for the same cluster, MP2 overestimates the AIP by an amount of 0.08 eV. In the case of pentamer, CASPT2 performs well as compared with MP2 and EOMIPCCSD(2). The AIP values obtained for the same cluster by CCSD(T), MP2, CASPT2, and EOMIP-CCSD(2) are 9.39, 9.48, 9.42, and 9.31 eV, respectively. Among the four hexamer analogues, the water cluster with prism shape has the largest value of AIP (9.34 eV in EOMIP-CCSD(2) method), and ring structure become the lowest one with AIP value 9.20 eV in EOMIP-CCSD(2). The EOMIP-CCSD(2) gives the lowest deviation of 0.01 eV for ring conformation as compared with CCSD(T), whereas MP2 yields highest deviation of 0.09 eV for the same conformation. The deviations of other conformations of hexamer are in between of 0.01 and 0.09 eV for all of the methods. We have further calculated AIP of heptamer and octamer using EOMIP-CCSD(2) method but are unable to compare the reliability of the calculated numbers owing to the unavailability of AIP data of other methods in the literature. The relative performance of EOMIP-CCSD(2), CASPT2, and MP2 with respect to CCSD(T) is pictorially demonstrated in Figure 5, which implies that the EOMIP-CCSD(2) has

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], [email protected]. Phone: +91 022-25767195. Fax: +91 022-25767152. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.D. and A.K.D. acknowledge CSIR (Council of Scientific and Industrial Research) for funding of the Research Fellowship. T.S. acknowledges UGC (University Grant Commission) for Research Fellowship. We acknowledge Center of Excellence in Scientific Computing at CSIR-NCL, CSIR-C-MMACS, and the CSIR 12th Five year plan for MSM project (csc 0129) grant. S.P. acknowledges a grant from the SSB project of CSIR and the J. C. Bose Fellowship grant of DST towards partial fulfillment of this work.

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Electron Detachment and Subsequent Structural Changes of Water

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