*Unraveling Hydrogen Bonded Clustering with Water: Density Functional Theory Perspective DOI: http://dx.doi.org/10.5772/intechopen.99958*

**Table 1.**

*ΔE8: ΔE at*  *ΔE9: ΔE at*  *ΔE10: ΔE at MP2/CBS level (Ref. [16]).*

*ΔE11: ΔE at* 

*nH: Number of hydrogen bonds.*

*CCSD(T)/CBS*

 *level (Ref. [16]).*

*M06-2X/aug-cc-pVTZ*

*M06/aug-cc-pVTZ*

 *level (Ref. [16]).*

 *level (Ref. [16]).*

*Comparison of interaction energies (in kcal.mol1) for (H2O)n,n=2–6, with various model chemistries. (Refer text for details.)*




*Unraveling Hydrogen Bonded Clustering with Water: Density Functional Theory Perspective DOI: http://dx.doi.org/10.5772/intechopen.99958*

#### **Table 3.**

*Mean unsigned errors (MUE) for bond lengths (in) computed for (H2O)2 and (H2O)3 using various model chemistries. The reference structural parameters were taken from the experimental data (ref. [76]).*


#### **Table 4.**

*Mean unsigned errors (MUE) for bond angles (in degrees) computed for (H2O)2 and (H2O)3 using various model chemistries. The reference structural parameters were taken from the experimental data (ref. [76]).*

functionals recommended to study water clusters are: MN15 [16, 54, 77], ωB97X-D, M06, M06-L, M06-2X and the broad applicability density functional, viz. PBE0. The recommended basis set should be triple zeta-quality viz. aug-cc-pVTZ,

aug1-ccp-VTZ and def2-TZVP. A comparison of the interaction energy of (H2O)2 computed with various model chemistries is given in **Table 5**.

It is clear from the **Table 5** that the truncated basis set, viz. aug1-cc-pVTZ yield interaction energies that are at par with its parent basis set viz. aug-cc-pVTZ. However, the reduction in number of basis functions results in boosting the speed of computation by a factor of 2.0 or more for the geometry optimization as well as vibrational frequency computations of water trimer (H2O)3. This is expected to boost-up further for larger clusters. Thus, aug1-cc-pVTZ basis set is recommended for DFT-study on water clusters.

The vibrational frequency analysis of smaller clusters viz. (H2O)n, where n = 1–4 show shift as well as splitting of vibrational infra-red)IR) frequencies with successive addition of water molecules. The H-O-H bending frequency shows blue-shifts whereas stretching frequencies (symmetric and asymmetric stretching) show red-shift with successive addition of water molecules. This feature is akin to the earlier studies [4, 51, 78]. The vibrational frequency analysis for smaller clusters upto tetramer performed with PBE0/aug1-cc-pVTZ model chemistry is given in **Table 6**. Also, the successive addition is associated with increase in the spectral intensity. The increase in spectral intensity is an indication of charge separation which may be seen in terms of increase in number of hydrogen (denoted by nH in **Table 1**) with addition of water molecule to the given cluster.

The review of the present literature also reveals that the energetic stability of smaller clusters (H2O)*<sup>n</sup>* with *n* ≤ 10 are predominantly dependent on the total number of hydrogen bonds (HBs) in the given cluster. These hydrogen bonds are the manifestation of donor-acceptor (da) arrangement of water molecules. In case of two dimensional structures the (H2O)n clusters with maximum number of donor-acceptor type of hydrogen bonds are energetically more favorable. Hence,


#### **Table 5.**

*Interaction energy (in kcal.Mol<sup>1</sup> ) of water dimer, (H2O)2 computed with various model chemistries.*

*Unraveling Hydrogen Bonded Clustering with Water: Density Functional Theory Perspective DOI: http://dx.doi.org/10.5772/intechopen.99958*


#### **Table 6.**

*Vibrational frequencies (in cm<sup>1</sup> ) computed at PBE0/aug1-cc-pVTZ optimized geometries for (H2O)n, n = 2, 3, and 4: Results for water monomer included for comparison. Values in the parentheses indicate intensities.*

the cyclic oligomers up to pentameric water clusters are energetically more favorable than their acyclic or linear chain counterparts. Also, these cyclic structures of tetramer, pentamer and hexamer form the basic building blocks for the energetically favorable larger clusters viz. (H2O)n, for n = 12, 15, 16, 20, 24, 25, 30 and so on. The hexameric ring even though energetically unfavorable as compared to prism and cage hexamers also forms the basic building blocks of higher clusters viz. (H2O)n, n = 12, 18, 20, 24, 30 and so on.

As concluded by the earlier studies [4], that one can anticipate several structures for a given water cluster (H2O)n, by changing the hydrogen bonding sequence. Hence, the number of possible energetically favorable isomers increase very fast with increase in the value of n. Considering all such isomers in a single study is beyond the scope of a single study.

### **4. Conclusions**

The present short review on investigation of water clusters employing DFTframework delineates the strength of DFT to study water clusters accurately and efficiently. The salient features of the present work are summarized as follows.

DFT in conjugation with appropriate triple zeta basis set can yield very accurate estimation of interaction energies and structures of water clusters. The results are at par with MP2/CBS or even CCSD(T)/CBS level of theory. The recommended density functionals for studying water clusters are MN15 [16, 54, 77], ωB97X-D, M06, M06-L, M06-2X and PBE0 where the recommended basis sets is aug-cc-pVTZ. The truncated basis set aug1-cc-pVTZ can also yield better agreement of interaction energies when compared with MP2/CBS and CCSD(T)/ CBS levels of theory. Hence, it is recommended for studying the larger clusters as well as lowering the computational exhaustiveness of the calculations. The cyclic structures of tetramer, pentamer and hexamer are the basic building blocks of larger clusters.

The performance of DFT in studying water clusters is indeed encouraging. It is expected that the initial guidelines from the present short-review can be gainfully employed to investigate larger water clusters and assessment of additional density functionals.

The investigations combined with the novel approaches like molecular tailoring approach will enable in obtaining the better understanding and accurate prediction of interaction energies within DFT-framework. Such studies are underway and will be undertaken in an independent venture.
