Next Article in Journal
De Novo Potent Peptide Nucleic Acid Antisense Oligomer Inhibitors Targeting SARS-CoV-2 RNA-Dependent RNA Polymerase via Structure-Guided Drug Design
Next Article in Special Issue
Halogen Bond via an Electrophilic π-Hole on Halogen in Molecules: Does It Exist?
Previous Article in Journal
Injectable Xenogeneic Dental Pulp Decellularized Extracellular Matrix Hydrogel Promotes Functional Dental Pulp Regeneration
Previous Article in Special Issue
Intermolecular Interactions in 3-Aminopropyltrimethoxysilane, N-Methyl-3-aminopropyltrimethoxysilane and 3-Aminopropyltriethoxysilane: Insights from Computational Spectroscopy
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
IJMS
Volume 24
Issue 24
10.3390/ijms242417480
ijms-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory

by
Carly A. Rock
and
Gregory S. Tschumper
*
Department of Chemistry and Biochemistry, University of Mississippi, University, MS 38677-1848, USA
*
Author to whom correspondence should be addressed.
Int. J. Mol. Sci. 2023, 24(24), 17480; https://doi.org/10.3390/ijms242417480
Submission received: 29 November 2023 / Revised: 6 December 2023 / Accepted: 7 December 2023 / Published: 14 December 2023
(This article belongs to the Special Issue Noncovalent Interactions: New Developments in Experiment and Theory)
Browse Figure
Versions Notes

Abstract

:
This work systematically examines the interactions between a single argon atom and the edges and faces of cyclic H 2 O clusters containing three–five water molecules (Ar(H 2 O) n = 3 – 5 ). Full geometry optimizations and subsequent harmonic vibrational frequency computations were performed using MP2 with a triple- ζ correlation consistent basis set augmented with diffuse functions on the heavy atoms (cc-pVTZ for H and aug-cc-pVTZ for O and Ar; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the two-body–many-body (2b:Mb) and three-body–many-body (3b:Mb) techniques; here, high-level CCSD(T) computations capture up through the two-body or three-body contributions from the many-body expansion, respectively, while less demanding MP2 computations recover all higher-order contributions. Five unique stationary points have been identified in which Ar binds to the cyclic water trimer, along with four for (H 2 O) 4 and three for (H 2 O) 5 . To the best of our knowledge, eleven of these twelve structures have been characterized here for the first time. Ar consistently binds more strongly to the faces than the edges of the cyclic (H 2 O) n clusters, by as much as a factor of two. The 3b:Mb electronic energies computed with the haTZ basis set indicate that Ar binds to the faces of the water clusters by at least 3 kJ mol − 1 and by nearly 6 kJ mol − 1 for one Ar(H 2 O) 5 complex. An analysis of the interaction energies for the different binding motifs based on symmetry-adapted perturbation theory (SAPT) indicates that dispersion interactions are primarily responsible for the observed trends. The binding of a single Ar atom to a face of these cyclic water clusters can induce perturbations to the harmonic vibrational frequencies on the order of 5 cm − 1 for some hydrogen-bonded OH stretching frequencies.

1. Introduction

Noble gases are frequently used as carrier gases and as inert environments in a broad range of spectroscopic techniques. Supersonic expansions [1,2,3,4,5,6,7,8,9,10,11,12], cryogenic matrices [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35], and helium nanodroplets [36,37,38,39,40,41,42] are specific examples that continue to play important roles in the experimental characterization of weakly bound molecular complexes. Spectroscopic studies of neutral hydrogen-bonded clusters, including H 2 O clusters, sometimes utilize one or more noble gas atoms (typically Ar) as an experimental tag to probe structural features, enhance experimental signals and even examine the hydrophobic effect [43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71].
Although the noble gases are inert under these types of experimental conditions, they can still perturb the molecules and complexes being studied [3,7,31,51,55,72,73,74,75,76,77]. Several studies involving Ar-tagged complexes demonstrate the potential of Ar to engage in favorable intermolecular dispersion and induction interactions when utilized as an isotropic probe of electron density to provide insight into regions of a molecule or molecular cluster of interest [51,53,54,58,59,62,63,64,65,68,78].
The interaction between an Ar atom and a single H 2 O molecule has been studied in great detail [69,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93], but relatively few studies have looked at the interactions of Ar with the water dimer [69,87,94] or larger water clusters [95,96]. The present study systematically identifies the energetically favorable binding sites of a single Ar atom to the well-characterized structures of cyclic (H 2 O) n = 3 – 5 clusters [6,10,24,30,31,37,42,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136] while also tracking structural and vibrational perturbations that occur. Symmetry-adapted perturbation theory is used to analyze the interaction energies for the different binding motifs.

2. Computational Details

The lowest-energy binding sites of a single Ar atom around small water clusters with three–five water molecules (Ar(H 2 O) n = 3 – 5 ) were identified via full geometry optimizations and harmonic vibrational frequency computations using MP2 [137] and Dunning’s correlation-consistent cc-pVTZ [138] basis set for H atoms and aug-cc-pVTZ [139,140] for the “heavy atoms” (O and Ar), hereafter denoted as haTZ. A subsequent set of haTZ geometry optimizations and harmonic vibrational frequency computations were performed on the MP2/haTZ-identified stationary points with the highly efficient and accurate N-body–many-body (Nb:Mb) technique [134,141,142,143] that captures all leading dominant N-body contributions to the many-body expansion (MBE) of the interactions in a cluster using an accurate high-level method, whereas the remaining higher-order contributions are recovered with a less demanding low-level method. For this study, we have selected the 2b:Mb [142,143,144,145,146,147] and 3b:Mb [141,143] versions of the Nb:Mb procedure. In this implementation, CCSD(T) [148] is used as the high-level method to describe the one- and two-body terms in the MBE of the cluster energy for 2b:Mb (as well as the three-body interactions for 3b:Mb) while MP2 is used as the low-level method to recover the higher-order ≥ three-body contributions to the MBE (or ≥4-body for 3b:Mb) by means of a computation on the entire cluster. Analytic gradients were used for all geometry optimizations along with analytic Hessians for all harmonic vibrational frequency computations. MP2 computations were carried out using Gaussian16 while all CCSD(T) computations were performed with CFOUR [149,150].
The relative electronic energies ( ∆ E ) of the various complexes were calculated by comparing the total energies at each level of theory. The supramolecular approach was used to determine the MP2, 2b:Mb, and 3b:Mb binding energies ( E b i n d ) and interaction energies ( E i n t ) of the Ar atom to various water cluster isomers as shown in Equation (1).
E b i n d / i n t = E [ Ar ( H 2 O ) n ] − E [ ( H 2 O ) n ) ] − E [ Ar ]
E b i n d is obtained when E [ ( H 2 O ) n ] is evaluated using the fully optimized geometry of the isolated water cluster, whereas use of the geometry adopted in the full complex yields E i n t . The effects of the harmonic zero-point vibrational energy (ZPVE) were also assessed for all minima, and the ZPVE-inclusive relative and binding energies are denoted ∆ E 0 and  E b i n d 0   respectively.
By comparing the total energy of a complex to the sum of fragment energies computed with finite basis sets, Equation (1) introduces an inconsistency commonly referred to as basis set superposition error (BSSE) [151,152]. To assess the potential effects of this inconsistency, the Boys–Bernardi counterpoise (CP) procedure [153,154] was employed to compute for the MP2/haTZ-optimized Ar(H 2 O) n = 3 – 5 structures. This analysis utilized the protocol outlined elsewhere [155], which corresponds to the default CP scheme in Gaussian16, where the energies of the last two terms in Equation (1) are evaluated in the basis set of the entire cluster.
An additional analysis of the total interaction energies based on symmetry-adapted perturbation theory (SAPT) [156,157,158] was carried out on the 3b:Mb-optimized Ar(H 2 O) n = 3 – 5 structures. We used the higher-order SAPT2+3(CCD) method that includes a treatment of dispersion based on coupled-cluster doubles and has been shown to provide improvements for challenging cases such as the PCCP dimer [159,160]. The SAPT2+3(CCD) computations were carried out with the haTZ basis set using the efficient implementation in the PSI4 [161,162] quantum chemistry software package that employs natural orbital truncation [163]. Rather than just calculating the total interaction energies as described above, SAPT provides additional insight into how Ar interacts with the small water clusters by identifying the individual contributions from exchange repulsion, electrostatics, induction, and dispersion.

3. Results and Discussion

Twelve low-lying stationary points were identified for the Ar(H 2 O) n = 3 – 5 systems via full geometry optimizations using the haTZ basis set in conjunction with the MP2, 2b:Mb, and 3b:Mb methods, and these structures are shown in Figure 1. Both the faces and edges of small, cyclic water clusters were identified as favorable binding sites for a single Ar atom. These H 2 O stationary points include the well-characterized C 1 and C 3 trimers, S 4 , C i and C 4 tetramers, and C 1 pentamer. The distance between the Ar atom and the corresponding face or edge binding site ranges from approximately 3.4 to 3.7 Å across the various Ar(H 2 O) n = 3 – 5 binding motifs. Harmonic vibrational frequency computations confirm that these Ar(H 2 O) n = 3 – 5 stationary points are minima at all levels of theory presented in this work. Cartesian coordinates and harmonic vibrational frequencies for all identified structures are reported in the Supporting Information (Table S1–Table S36).
The naming scheme shown in Figure 1 beneath each structure includes the point group symmetry of the Ar(H 2 O) n cluster, the binding site of the Ar atom on the (H 2 O) n cluster (face or edge) and the number of free hydrogens pointing towards the Ar atom when additional distinction is needed. For example, the first two structures listed at the top left of Figure 1 for Ar(H 2 O) 3 (C 1 Face 1 and C 1 Face 2 , respectively) both have C 1 symmetry and Ar bound to the face of the water trimer. A subscript of 1 is added to the first structure name to indicate one free hydrogen pointing towards the Ar atom, while a subscript of 2 is added to the second structure name to indicate two free hydrogens pointing toward the Ar atom. This distinction is only necessary for some of the Ar(H 2 O) 3 and Ar(H 2 O) 5 clusters.

3.1. Structures, Harmonic Vibrational Frequencies, and Relative Energies

Table 1 reports the relative electronic and ZPVE-inclusive energies ( ∆ E and ∆ E 0 , respectively) obtained with the haTZ basis set and the MP2, 2b:Mb, and 3b:Mb methods for all Ar(H 2 O) n = 3 – 5 minima depicted in Figure 1. The reference values of 0.00 kJ mol − 1 correspond to the lowest-energy structure for each Ar(H 2 O) n (n = 3, 4 and 5) cluster, each of which is depicted in the leftmost image of each row in Figure 1). The first five rows of Table 1 also include ∆ E and ∆ E 0 values for the bare C 1 and C 3 water trimers and S 4 , C i and C 4 water tetramers for reference. The haTZ relative electronic and ZPVE-inclusive energies reported in Table 1 are remarkably consistent between all three methods utilized in this work. The 2b:Mb values differ only slightly from the 3b:Mb results (average absolute deviation of 0.06 kJ mol − 1 and never by more than ±0.32 kJ mol − 1 ). The deviations from the 3b:Mb ∆ E and ∆ E 0 values tend to be slightly larger for the MP2 method, but they always fall within ±0.43 kJ mol − 1 .
Note that ∆ E 0 values are not provided for the C 4 bare (H 2 O) 4 tetramer because it is a transition state (denoted by the superscript † symbol) with 1 imaginary vibrational frequency at all three levels of theory. The MP2, 2b:Mb, and 3b:Mb harmonic vibrational frequency computations with the haTZ basis set confirm that all of the other (H 2 O) n = 3 – 5 and Ar(H 2 O) n = 3 – 5 stationary points listed in Table 1 are minima. Shifts in the harmonic OH stretching frequencies induced by the binding of an Ar atom to a water trimer, tetramer, or pentamer (Ar(H 2 O) n = 3 – 5 ) relative to the OH stretching frequencies of the isolated water cluster ((H 2 O) n = 3 – 5 ) were also analyzed. The formation of the Ar(H 2 O) n = 3 – 5 complexes induces small shifts to lower energy (typically just 1 or 2 cm − 1 ) for every intramolecular vibrational mode relative to the isolated water clusters. However, the shifts grow as large as − 5 to − 7 cm − 1 for some of the hydrogen-bonded OH stretching frequencies when a single Ar atom binds to the face of these cyclic (H 2 O) n = 3 – 5 clusters. For comparison, the analogous experimental shifts induced by cryogenic Ar matrices and Ar nanocoatings range from approximately − 15 to − 35 cm − 1 . (see Table II from Ref. [96]). The shifts predicted with the haTZ basis set are quite consistent across the MP2, 2b:Mb, and 3b:Mb CCSD(T):MP2 methods, and the harmonic vibrational frequencies are reported in the Supporting Information for all Ar(H 2 O) n = 3 – 5 complexes identified in this work.

3.1.1. Ar(H 2 O) 3

Five structures were identified as minima for the Ar(H 2 O) 3 system in which Ar binds to either a face or an edge of the C 1 and C 3 water trimer isomers. All unique faces and edges were tested as potential binding sites for a single Ar atom, but the subsequent geometry optimizations always collapsed to one of the five structures reported here. The five binding motifs are shown in the first row of Figure 1; to the best of our knowledge, the rightmost C 3 Face 3 configuration is the only one that has been previously reported in the literature [95].
Ar binds to both unique faces of the C 1 water trimer, as well as the edge in which both free hydrogens are oriented in the same direction. Ar also binds to both unique faces of the C 3 water trimer, but does not bind to an edge. All five identified minima are separated by only a few kJ mol − 1 at all three levels of theory, as can be seen from the ∆ E and ∆ E 0 data near the middle of Table 1. The structure with the lowest energy has the single Ar on the face of the C 1 trimer with only one free hydrogen oriented towards the Ar atom (leftmost image in Figure 1). However, the structure with Ar bound to the other face (C 1 Face 2 ) is only higher in energy by a few tenths of a kJ mol − 1 . The energy increases more significantly when Ar binds to an edge of the cyclic water trimer in the C 1 Edge structure, where ∆ E grows to more than 1.2 kJ mol − 1 . The C 3 Face 0 and C 3 Face 3 structures also have the largest relative energies, but this difference does not necessarily indicate weak binding (which will be discussed in greater detail in Section 3.2). It is almost entirely due to the underlying energy difference between the C 1 and C 3 isomers of the water trimer as shown in the first two rows of Table 1.

3.1.2. Ar(H 2 O) 4

The second row of Figure 1 depicts the four minima identified for the Ar(H 2 O) 4 system in which Ar binds to the S 4 , C i and C 4 cyclic structures of (H 2 O) 4 . To the best of our knowledge, none of these complexes have been previously reported. The structure with the lowest energy has the Ar atom on the face of the S 4 global minimum of (H 2 O) 4 , which results in an Ar(H 2 O) 4 complex with C 2 symmetry (leftmost image in the second row of Figure 1). No minima were identified with Ar binding to the edge of the S 4 water tetramer at the levels of theory used in this work. However, when Ar is in the presence of the C i (H 2 O) 4 structure, minima were identified with Ar bound not only to the face but also to the edge with both free hydrogens oriented in the same direction (analogous to the situation for the Ar(H 2 O) 3 system). The resulting C 1 Face and C 1 Edge Ar(H 2 O) 4 complexes have electronic energies higher than the C 2 Face minimum by at least 3.5 and 5.6 kJ mol − 1 , respectively.
The highest-energy minimum identified (rightmost image in the second row of Figure 1) involves Ar binding to the face of the C 4 water tetramer structure with all free hydrogens on the opposite side of the ring, which gives an Ar(H 2 O) 4 complex that maintains C 4 symmetry. Interestingly, the C 4 structure of the isolated (H 2 O) 4 cluster is a transition state even though the corresponding complex with an Ar atom is a minimum at each level of theory reported here. Furthermore, scans of the Ar atom moving along the C 4 axis on the side of the ring with the four free H atoms yielded repulsive potential energy curves. As can be seen from the C 4 Face Ar(H 2 O) 4 row of data in in Table 1, the 2b:Mb and 3b:Mb ∆ E results grow beyond 8.7 kJ mol − 1 . As noted for the water trimer systems, however, large ∆ E and ∆ E 0 values do not necessarily indicate weak interactions between the Ar atom and the water cluster. (see Section 3.2). The large relative energies for C 4 Face Ar(H 2 O) 4 primarily reflect that the C 4 transition state of (H 2 O) 4 has an electronic energy approximately 9 kJ mol − 1 higher than the S 4 global minimum structure of the water tetramer (fifth row of data in Table 1).

3.1.3. Ar(H 2 O) 5

The last row of Figure 1 shows the three Ar(H 2 O) 5 minima identified with the MP2, 2b:Mb, and 3b:Mb methods in conjunction with the haTZ basis set. The two unique faces of the cyclic water pentamer provide similar binding sites for the Ar atom, but the electronic energy is slightly lower when it binds to the side with two free hydrogens (leftmost image in bottom row of Figure 1) rather than three (middle image in bottom row of Figure 1). The 3b:Mb ∆ E for the latter (Ar(H 2 O) 5 C 1 Face 3 ) is only 0.36 kJ mol − 1 . A minimum with Ar bound to an edge was also identified. As with the water trimer and tetramer clusters, a minimum for this motif was only found along the edge with both free hydrogens pointing to the same side of the (H 2 O) n ring. To the best of our knowledge, all three binding motifs are reported here for the first time. The last row of Table 1 shows the C 1 Edge Ar(H 2 O) 5 structure is noticeably higher in energy compared to the C 1 Face 2 minimum, with both ∆ E and ∆ E 0 growing larger than 2.3 kJ mol − 1 . Binding sites on the cyclic C 5 (H 2 O) 5 pentamer, analogous to those for the C 3 trimer and C 4 tetramer, were also investigated. However, all attempts to identify minima on the corresponding faces and edges collapsed to one of the C 1 structures shown in the bottom of row of Figure 1.

3.2. Binding and Interaction Energies

3.2.1. Binding Energies

The electronic and ZPVE-inclusive binding energies ( E b i n d and E b i n d 0 ) of the haTZ optimized Ar(H 2 O) n = 3 – 5 minima are reported in Table 2 for the MP2, 2b:Mb, and 3b:Mb methods. Note that E b i n d 0 values are not provided for the C 4 Ar(H 2 O) 4 complex as the bare (H 2 O) 4 tetramer fragment is a transition state at the associated levels of theory. All three methods are in remarkably good agreement for both quantities. The MP2 and 2b:Mb values (left and middle columns of Table 2) deviate by less than 0.3 kJ mol − 1 from the corresponding 3b:Mb E b i n d and E b i n d 0 data in the last two columns of Table 2. For comparison, the electronic binding energy of the ArH 2 O dimer computed with the same procedures is approximately −1.2 kJ mol − 1 .
Overall, the tabulated E b i n d and E b i n d 0 data show that Ar binds more strongly to the cyclic water clusters as the size increases from n = 3 (top 3 rows of data in Table 2) to n = 5 (bottom 3 rows of data in Table 2). Although the enhancement is quite modest when Ar binds to the edge of the cluster (less than 0.5 kJ mol − 1 ), the binding of Ar to a face of C 1 (H 2 O) 5 is approximately 2 kJ mol − 1 stronger than to a face of C 1 (H 2 O) 3 . The 3b:Mb E b i n d values in Table 2 clearly show that Ar binds more strongly to the faces of the water clusters than the edges, and due to the aforementioned trends, the energetic advantage of binding to a face becomes more pronounced as the cluster size increases (from 1.26 kJ mol − 1 (or 41%) for n = 3 to 2.07 and 2.71 kJ mol − 1 (or 50% and 56%) for n = 4 and 5). The C 1 Ar(H 2 O) 5 Face 2 and Face 3 complexes exhibit the strongest binding energies out of all of the Ar(H 2 O) n = 3 – 5 minima identified in this work with E b i n d exceeding − 5.3 kJ mol − 1 and approaching − 5.8 kJ mol − 1 . The electronic binding energies indicate that Ar binds slightly more strongly to faces that have fewer free hydrogens oriented towards the Ar atom (by approximately 0.3 kJ mol − 1 for C 1 Face 1 vs. Face 2 Ar(H 2 O) 3 , 0.8 kJ mol − 1 for C 3 Face 0 vs. Face 3 Ar(H 2 O) 3 , and 0.4 kJ mol − 1 for C 1 Face 2 vs. Face 3 Ar(H 2 O) 5 ).
When the CP procedure was employed to evaluate the potential impact of the BSSE on the binding energies for the Ar(H 2 O) n = 3 – 5 minima identified in this work, the MP2/haTZ binding energies were found to decrease in magnitude by approximately 1.1 kJ mol − 1 on average and never by more than 1.5 kJ mol − 1 for all 12 configurations. These relatively small differences suggest that the results presented in Table 2 are only slightly larger in magnitude that the corresponding values evaluated at the complete basis set limit, where by definition, the BSSE vanishes. All binding energies obtained with the CP procedure can be found in the Supporting Information (Tables S37–S39).

3.2.2. Interaction Energies

The first three columns of Table 3 report the interaction energies ( E i n t in kJ mol − 1 ) calculated for the haTZ optimized Ar(H 2 O) n = 3 – 5 minima depicted in Figure 1 using the MP2, 2b:Mb and 3b:Mb methods, respectively. The remaining columns report the individual energy components of and the total interaction energy (in kJ mol − 1 ) obtained from SAPT2+3(CCD) computations with the haTZ basis set for the 3b:Mb/haTZ-optimized Ar(H 2 O) n = 3 – 5 minima. Utilizing SAPT to compute the total interaction energy directly provides the physical contributions from exchange repulsion, electrostatics, induction and dispersion, which are reported in the last four columns of Table 3, respectively.
The MP2, 2b:Mb, and 3b:Mb E i n t values reported in the left half of Table 3 are in remarkably good agreement with the corresponding binding energies reported in Table 2, with differences never exceeding 0.14 kJ mol − 1 across all of the different structures examined and methods utilized in this study. The consistency between E i n t and E b i n d values suggest that the binding of an Ar atom to a cyclic water trimer, tetramer or pentamer does not induce any significant geometric changes to the (H 2 O) n cluster itself. This observation is consistent with the small perturbations to the intramolecular vibrational frequencies that occur upon binding as noted in Section 3.1.
While the SAPT2+3(CCD) interaction energy values in Table 3 are somewhat smaller in magnitude than the MP2, 2b:Mb, and 3b:Mb E i n t values, they are also slightly larger than the corresponding MP2 results obtained with the CP procedure that are tabulated in the Supporting Information (Tables S37–S39) which is to be expected because SAPT does not suffer from the BSSE issues introduced via Equation (1). All computations reveal stronger interactions for complexes in which Ar is bound to a face of the water cluster rather than an edge, and the SAPT analysis provides some insight into the underlying factors. The penultimate column of data in Table 3, for example, shows that induction consistently has the smallest contribution to E i n t . Additionally, the attractive induction component is only slightly smaller in magnitude for the C 1 Edge structures than the analogous C 1 Face minima (by ca. 0.1 to 0.3 kJ mol − 1 ). The electrostatic contributions, which include short-range terms from the overlap of the electron cloud of Ar with that of the water cluster, are larger than those from induction and also favor the face-binding motifs over the edge-binding ones by approximately 0.6 to 1.3 kJ mol − 1 . In all cases, dispersion (last column of Table 3) is the dominant attractive contribution to E i n t for these systems in which Ar binds to the edge or face of a cyclic water trimer, tetramer or pentamer. The dispersion components from the SAPT2+3(CCD) computations also exhibit the largest energetic differences between the C 1 Edge and corresponding C 1 Face structures, being more attractive in the latter by ca. 2 to 5 kJ mol − 1 . Although all attractive contributions from the SAPT analysis (electrostatics, induction and dispersion) favor the face-binding motifs, the situation is reversed for exchange repulsion, which is smaller for the C 1 Edge structures than the corresponding C 1 Face motifs by approximately 2 to 4 kJ mol − 1 . Nevertheless, the contributions from exchange repulsion are not enough to offset the attractive components, and the total SAPT2+3(CCD) E i n t values are larger in magnitude for the lowest-energy C 1 Face minima of the Ar(H 2 O) n clusters than the C 1 Edge structures by 1.09, 1.80 and 2.41 kJ mol − 1 for n = 3 , 4 , 5 , respectively.

4. Conclusions

This work systematically identifies the energetically favorable binding sites of a single Ar atom to the well-characterized structures of the cyclic (H 2 O) n = 3 – 5 trimer, tetramer and pentamer clusters using the haTZ basis set and a variety of methods including MP2 and the highly efficient and accurate 2b:Mb and 3b:Mb methods. Twelve unique Ar(H 2 O) n = 3 – 5 stationary points have been identified in which Ar binds to either a face or an edge on the water cluster via full geometry optimizations and have been confirmed as minima by harmonic vibrational frequency computations at all three levels of theory. Five, four and three unique stationary points have been identified in which Ar binds to the C 1 and C 3 water trimers, S 4 , C i and C 4 water tetramers and C 1 water pentamer, respectively. To the best of our knowledge, all of these structures are characterized here for the first time with the exception of the C 3 Face 3 complex. [95]
Although multiple minima were identified with the Ar bound to a face of each water cluster (9 total), only a single minimum was identified for each value of n with Ar bound to an edge (3 total). In every case, a face provided a more energetically favorable binding site for the Ar atom than an edge of the same (H 2 O) n cluster. Relative electronic energies (with and without ZPVE correction) ranged from approximately 1 to 3 kJ mol − 1 higher in energy for the latter complexes. The binding energies ( E b i n d and E b i n d 0 ) also show that Ar consistently binds more strongly to the faces of the water clusters than the edges (by ca. 1 to 3 kJ mol − 1 ).
The MP2, 2b:Mb, and 3b:Mb electronic interaction energies ( E i n t ) computed with the haTZ basis set are nearly identical to the corresponding E b i n d values, suggesting that the binding of an Ar atom has no significant effect on the geometries of the bare (H 2 O) n = 3 – 5 clusters. The small differences between E b i n d and E i n t are also consistent with the very small changes to (nearly) all intramolecular harmonic vibrational frequencies of the water clusters after Ar binds to an edge or face. However, the frequency shifts can be on the order of − 5 cm − 1 for some of the hydrogen-bonded OH stretching frequencies when a single Ar atom binds to a face of these small cyclic water clusters.
The haTZ total interaction energies computed with SAPT2+3(CCD) qualitatively support these findings, resulting in stronger interaction energies for complexes with Ar bound to a face rather than an edge, with the differences between the SAPT2+3(CCD) values exceeding 2 kJ mol − 1 between the two potential binding sites. Notably, using SAPT to compute the total interaction energy provides further insight into the nature of these favorable interactions between Ar and small cyclic water clusters by providing a breakdown of the total interaction energy into physically meaningful components (electrostatics, exchange repulsion, induction and dispersion).
SAPT2+3(CCD) computations with the haTZ basis set indicate that dispersion overwhelmingly provides the dominant attractive component to E i n t in all cases. It also exhibited the greatest difference between the edge- and face-binding motifs, favoring the latter by just over 2 kJ mol − 1 for the trimer and growing to more than 5 kJ mol − 1 for the pentamer.
The results presented here for 2-dimensional hydrogen-bonded networks provide some guidelines for the expected binding patterns that Ar will exhibit in larger 3-dimensional water clusters. In the case of (H 2 O) 6 , for example, an Ar atom is expected to preferentially bind to the faces rather than the edges edges of the low-lying minima (prism, cage, etc.). Additionally, the interaction strength should increase with the size of the face (from triangular to rectangular and pentagonal), but the overall perturbations to the relative energetics and vibrational frequencies of the hexamer isomers will likely remain quite small and similar in magnitude to those reported here.

Supplementary Materials

The supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ijms242417480/s1.

Author Contributions

Conceptualization, methodology, and funding acquisition, G.S.T.; Investigation and data curation, C.A.R.; Writing—original draft, C.A.R.; Writing—review & editing, G.S.T. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported in part by the National Science Foundation (CHE-2154403).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article and Supplementary Materials.

Acknowledgments

The Mississippi Center for Supercomputing Research (MCSR) is thanked for a generous allocation of time on their computational resources.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Liu, K.; Brown, M.G.; Carter, C.; Saykally, R.J.; Gregory, J.K.; Clary, D.C. Characterization of a cage form of the water hexamer. Nature 1996, 381, 501–503. [Google Scholar] [CrossRef]
  2. Liu, K.; Brown, M.G.; Saykally, R.J. Terahertz Laser Vibration-Rotation Tunneling Spectroscopy and Dipole Moment of a Cage Form of the Water Hexamer. J. Phys. Chem. A 1997, 101, 8995–9010. [Google Scholar] [CrossRef]
  3. Klots, T.D.; Ruoff, R.S.; Gutowsky, H.S. Rotational spectrum and structure of the linear CO2-HCN dimer: Dependence of isomer formation on carrier gas. J. Chem. Phys. 1989, 90, 4216–4221. [Google Scholar] [CrossRef]
  4. Ruoff, R.S.; Klots, T.D.; Emilsson, T.; Gutowsky, H.S. Relaxation of conformers and isomers in seeded supersonic jets of inert gases. J. Chem. Phys. 1990, 93, 3142–3150. [Google Scholar] [CrossRef]
  5. Emilsson, T.; Germann, T.C.; Gutowsky, H.S. Kinetics of molecular association and relaxation in a pulsed supersonic expansion. J. Chem. Phys. 1992, 96, 8830–8839. [Google Scholar] [CrossRef]
  6. Steinbach, C.; Andersson, P.; Melzer, M.; Kazimirski, J.K.; Buck, U.; Buch, V. Detection of the book isomer from the OH-stretch spectroscopy of size selected water hexamers. Phys. Chem. Chem. Phys. 2004, 6, 3320–3324. [Google Scholar] [CrossRef]
  7. Pérez, C.; Muckle, M.T.; Zaleski, D.P.; Seifert, N.A.; Temelso, B.; Shields, G.C.; Kisiel, Z.; Pate, B.H. Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy. Science 2012, 336, 897–901. [Google Scholar] [CrossRef] [PubMed]
  8. Pérez, C.; Lobsiger, S.; Seifert, N.A.; Zaleski, D.P.; Temelso, B.; Shields, G.C.; Kisiel, Z.; Pate, B.H. Broadband Fourier transform rotational spectroscopy for structure determination: The water heptamer. Chem. Phys. Lett. 2013, 571, 1–15. [Google Scholar] [CrossRef]
  9. Pérez, C.; Zaleski, D.P.; Seifert, N.A.; Temelso, B.; Shields, G.C.; Kisiel, Z.; Pate, B.H. Hydrogen Bond Cooperativity and the Three-Dimensional Structures of Water Nonamers and Decamers. Angew. Chem. 2014, 53, 14368–14372. [Google Scholar] [CrossRef]
  10. Otto, K.E.; Xue, Z.; Zielke, P.; Suhm, M.A. The Raman spectrum of isolated water clusters. Phys. Chem. Chem. Phys. 2014, 16, 9849–9858. [Google Scholar] [CrossRef]
  11. Richardson, J.O.; Pérez, C.; Lobsiger, S.; Reid, A.A.; Temelso, B.; Shields, G.C.; Kisiel, Z.; Wales, D.J.; Pate, B.H.; Althorpe, S.C. Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism. Science 2016, 351, 1310–1313. [Google Scholar] [CrossRef] [PubMed]
  12. Cole, W.T.S.; Farrell, J.D.; Wales, D.J.; Saykally, R.J. Structure and torsional dynamics of the water octamer from THz laser spectroscopy near 215 μm. Science 2016, 352, 1194–1197. [Google Scholar] [CrossRef]
  13. Thiel, M.V.; Becker, E.D.; Pimentel, G.C. Infrared Studies of Hydrogen Bonding of Water by the Matrix Isolation Technique. J. Chem. Phys. 1957, 27, 486–490. [Google Scholar] [CrossRef]
  14. Redington, R.L.; Milligan, D.E. Infrared Spectroscopic Evidence for the Rotation of the Water Molecule in Solid Argon. J. Chem. Phys. 1962, 37, 2162–2166. [Google Scholar] [CrossRef]
  15. Redington, R.L.; Milligan, D.E. Molecular Rotation and Ortho-Para Nuclear Spin Conversion of Water Suspended in Solid Ar, Kr and Xe. J. Chem. Phys. 1963, 39, 1276–1284. [Google Scholar] [CrossRef]
  16. Ayers, G.P.; Pullin, A.D.E. The i.r. spectra of matrix isolated water species-I. Assignment of bands to (H2O)2, (D2O)2 and HDO dimer species in argon matrices. Spectrochim. Acta Part A 1976, 32, 1629–1639. [Google Scholar] [CrossRef]
  17. Bentwood, R.M.; Barnes, A.J.; Orvill-Thomas, W.J. Studies of intermolecular interactions by matrix isolation vibrational spectroscopy: Self-association of water. J. Mol. Struct. 1980, 84, 391–404. [Google Scholar] [CrossRef]
  18. Engdahl, A.; Nelander, B. On the structure of the water trimer. A matrix isolation study. J. Chem. Phys. 1987, 86, 4831–4837. [Google Scholar] [CrossRef]
  19. Knözinger, E.; Schuller, W.; Langel, W. Structure and dynamics in pure and doped rare-gas matrices. Faraday Discuss. Chem. Soc. 1988, 86, 285–293. [Google Scholar] [CrossRef]
  20. Engdahl, A.; Nelander, B. Water in krypton matrices. J. Mol. Struct. 1989, 193, 101–109. [Google Scholar] [CrossRef]
  21. Forney, D.; Jacox, M.E.; Thompson, W.E. The Mid- and Near-Infrared Spectra of Water and Water Dimer Isolated in Solid Neon. J. Mol. Spectrosc. 1993, 157, 479–493. [Google Scholar] [CrossRef]
  22. Perchard, J.P. Anharmonicity and hydrogen bonding. III. Analysis of the near infrared spectrum of water trapped in argon matrix. Chem. Phys. 2001, 273, 217–233. [Google Scholar] [CrossRef]
  23. Michaut, X.; Vasserot, A.M.; Abouaf-Marguin, L. Temperature and time effects on the rovibrational structure of fundamentals of H2O trapped in solid argon: Hindered rotation and RTC satellite. Vib. Spectrosc. 2004, 34, 83–93. [Google Scholar] [CrossRef]
  24. Ceponkus, J.; Karlström, G.; Nelander, B. Intermolecular Vibrations of the Water Trimer, a Matrix Isolation Study. J. Phys. Chem. A 2005, 109, 7859–7864. [Google Scholar] [CrossRef]
  25. Hirabayashi, S.; Yamada, K.M.T. Infrared spectra of the H2O-Kr and H2O-Xe complexes in argon matrices. Chem. Phys. Lett. 2005, 418, 323–327. [Google Scholar] [CrossRef]
  26. Coussan, S.; Roubin, P.; Perchard, J.P. Infrared induced isomerizations of water polymers trapped in nitrogen matrix. Chem. Phys. 2006, 324, 527–540. [Google Scholar] [CrossRef]
  27. Abouaf-Marguin, L.; Vasserot, A.M.; Pardanaud, C.; Michaut, X. Nuclear spin conversion of water diluted in solid argon at 4.2 K: Environment and atmospheric impurities effects. Chem. Phys. Lett. 2007, 447, 232–235. [Google Scholar] [CrossRef]
  28. Pardanaud, C.; Vasserot, A.M.; Michaut, X.; Abouaf-Marguin, L. Observation of nuclear spin species conversion inside the 1593 cm-1 structure of H2O trapped in argon matrices: Nitrogen impurities and the H2O:N2 complex. J. Mol. Struct. 2008, 873, 181–190. [Google Scholar] [CrossRef]
  29. Ceponkus, J.; Uvdal, P.; Nelander, B. Acceptor switching and axial rotation of the water dimer in matrices, observed by infrared spectroscopy. J. Chem. Phys. 2010, 133, 074301. [Google Scholar] [CrossRef]
  30. Ceponkus, J.; Uvdal, P.; Nelander, B. Water Tetramer, Pentamer, and Hexamer in Inert Matrices. J. Phys. Chem. A 2012, 116, 4842–4850. [Google Scholar] [CrossRef]
  31. Ceponkus, J.; Engdahl, A.; Uvdal, P.; Nelander, B. Structure and dynamics of small water clusters, trapped in inert matrices. Chem. Phys. Lett. 2013, 581, 1–9. [Google Scholar] [CrossRef]
  32. Mukhopadhyay, A.; Cole, W.T.S.; Saykally, R.J. The water dimer I: Experimental characterization. Chem. Phys. Lett. 2015, 633, 13–26. [Google Scholar] [CrossRef]
  33. Pogorelov, V.Y.; Doroshenko, I.Y. Vibrational spectra of water clusters, trapped in low temperature matrices. Low Temp. Phys. 2016, 42, 1163–1166. [Google Scholar] [CrossRef]
  34. Oswald, S.; Suhm, M.A.; Coussan, S. Incremental NH stretching downshift through stepwise nitrogen complexation of pyrrole: A combined jet expansion and matrix isolation study. Phys. Chem. Chem. Phys. 2019, 21, 1277. [Google Scholar] [CrossRef] [PubMed]
  35. Oswald, S.; Coussan, S. Chloroform-nitrogen aggregates: Upshifted CH and downshifted CCl stretching vibrations observed by matrix isolation and jet expansion infrared spectroscopy. Low Temp. Phys. 2019, 45, 639–648. [Google Scholar] [CrossRef]
  36. Nauta, K.; Miller, R.E. Formation of Cyclic Water Hexamer in Liquid Helium: Smallest Piece of Ice. Science 2000, 287, 293–295. [Google Scholar] [CrossRef]
  37. Burnham, C.J.; Xantheas, S.S.; Miller, M.A.; Applegate, B.E.; Miller, R.E. The formation of cyclic water complexes by sequential ring insertion: Experiment and theory. J. Chem. Phys. 2002, 117, 1109–1122. [Google Scholar] [CrossRef]
  38. Lindsay, C.M.; Douberly, G.E.; Miller, R.E. Rotational and vibrational dynamics of H2O and HDO in helium nanodroplets. J. Mol. Struct. 2006, 786, 96–104. [Google Scholar] [CrossRef]
  39. Kuyanov-Prozument, K.; Choi, M.Y.; Vilesov, A.F. Spectrum and infrared intensities of OH-stretching bands of water dimers. J. Chem. Phys. 2010, 132, 014304. [Google Scholar] [CrossRef]
  40. Schwan, R.; Kaufmann, M.; Leicht, D.; Schwaab, G.; Havenith, M. Infrared spectroscopy of the ν2 band of the water monomer and small water clusters (H2O)n=2,3,4 in helium droplets. Phys. Chem. Chem. Phys. 2016, 18, 24063–24069. [Google Scholar] [CrossRef]
  41. Douberly, G.E.; Miller, R.E.; Xantheas, S.S. Formation of Exotic Networks of Water Clusters in Helium Droplets Facilitated by the Presence of Neon Atoms. J. Am. Chem. Soc. 2017, 139, 4152–4156. [Google Scholar] [CrossRef]
  42. Schwan, R.; Qu, C.; Mani, D.; Pal, N.; Schwaab, G.; Bowman, J.M.; Tschumper, G.S.; Havenith, M. Observation of the Low-Frequency Spectrum of the Water Trimer as a Sensitive Test of the Water-Trimer Potential and the Dipole-Moment Surface. Angew. Chem. 2020, 59, 11399–11407. [Google Scholar] [CrossRef]
  43. Anderson, D.T.; Davis, S.; Nesbitt, D.J. Sequential solvation of HCl in argon: High resolution infrared spectroscopy of ArnHCl (n = 1, 2, 3). J. Chem. Phys. 1997, 107, 1114–1127. [Google Scholar] [CrossRef]
  44. Leung, H.O.; Gangwani, D.; Grabow, J.U. Nuclear Quadrupole Hyperfine Structure in the Microwave Spectrum of Ar-N2O. J. Mol. Spectrosc. 1997, 184, 106–112. [Google Scholar] [CrossRef]
  45. Häber, T. FTIR-Spectroscopy of isolated and argon coated (HBr)n≤4 clusters in supersonic slit-jet expansions. Phys. Chem. Chem. Phys. 2003, 5, 1365–1369. [Google Scholar] [CrossRef]
  46. Gregoire, G.; Brinkmann, N.R.; van Heijnsbergen, D.; Schaefer, H.F.; Duncan, M.A. Infrared Photodissociation Spectroscopy of Mg+(CO2)n and Mg+(CO2)nAr Clusters. J. Phys. Chem. A 2003, 107, 218–227. [Google Scholar] [CrossRef]
  47. Bochenkova, A.V.; Suhm, M.A.; Granovsky, A.A.; Nemukhin, A.V. Hybrid diatomics-in-molecules-based quantum mechanical/molecular mechanical approach applied to the modeling of structures and spectra of mixed molecular clusters Arn(HCl)m and Arn(HF)m. J. Chem. Phys. 2004, 120, 3732–3743. [Google Scholar] [CrossRef]
  48. Walker, N.R.; Walters, R.S.; Tsai, M.K.; Jordan, K.D.; Duncan, M.A. Infrared Photodissociation Spectroscopy of Mg+(H2O)Arn Complexes: Isomers in Progressive Microsolvation. J. Phys. Chem. A 2005, 109, 7057–7067. [Google Scholar] [CrossRef] [PubMed]
  49. Douberly, G.E.; Walters, R.S.; Cui, J.; Jordan, K.D.; Duncan, M.A. Infrared Spectroscopy of Small Protonated Water Clusters, H+(H2O)n (n = 2–5): Isomers, Argon Tagging, and Deuteration. J. Phys. Chem. A 2010, 114, 4570–4579. [Google Scholar] [CrossRef]
  50. Carnegie, P.D.; Bandyopadhyay, B.; Duncan, M.A. Infrared Spectroscopy of Mn+(H2O) and Mn2+(H2O) via Argon Complex Predissociation. J. Phys. Chem. A 2011, 115, 7602–7609. [Google Scholar] [CrossRef]
  51. Marshall, M.D.; Leung, H.O.; Calvert, C.E. Molecular structure of the argon-(Z)-1-chloro-2-fluoroethylene complex from chirped-pusle and narrow-band Fourier transform microwave spectroscopy. J. Mol. Spectrosc. 2012, 280, 97–103. [Google Scholar] [CrossRef]
  52. Fujii, A.; Mizuse, K. Infrared spectroscopic studies on hydrogen-bonded water networks in gas phase clusters. Int. Rev. Phys. Chem. 2013, 32, 266–307. [Google Scholar] [CrossRef]
  53. Leung, H.O.; Marshall, M.D.; Mueller, J.L.; Amberger, B.K. The molecular structure of and interconversion tunneling in the argon-cis-1,2-difluoroethylene complex. J. Chem. Phys. 2013, 139, 134303. [Google Scholar] [CrossRef]
  54. Leung, H.O.; Marshall, M.D.; Messinger, J.P.; Knowlton, G.S.; Sundheim, K.M.; Cheung-Lau, J.C. The microwave spectra and molecular structures of 2-chloro-1,1-difluoroethylene and its complex with the argon atom. J. Mol. Spectrosc. 2014, 305, 25–33. [Google Scholar] [CrossRef]
  55. Kaledin, M.; Adedeji, D.T. Driven Molecular Dynamics Studies of the Shared Proton Motion in the H5O2+·Ar Cluster: The Effect of Argon Tagging and Deuteration on Vibrational Spectra. J. Phys. Chem. A 2015, 119, 1875–1884. [Google Scholar] [CrossRef] [PubMed]
  56. Li, J.W.; Morita, M.; Takahashi, K.; Kuo, J.L. Features in Vibrational Spectra Induced by Ar-Tagging for H3O+Arm, m=0-3. J. Phys. Chem. A 2015, 119, 10887–10892. [Google Scholar] [CrossRef] [PubMed]
  57. Leung, H.O.; Marshall, M.D.; Wronkovich, M.A. The microwave spectrum and molecular structure of Ar-2,3,3,3-tetrafluoropropene. J. Mol. Spectrosc. 2017, 337, 80–85. [Google Scholar] [CrossRef]
  58. Marshall, M.D.; Leung, H.O. The microwave spectrum and molecular structure of 3,3-difluoro-1,2-epoxypropane and its complex with the argon atom. J. Mol. Spectrosc. 2018, 350, 18–26. [Google Scholar] [CrossRef]
  59. Marshall, M.D.; Leung, H.O.; Wang, K.; Acha, M.D. Microwave Spectrum and Molecular Structure of the Chiral Tagging Candidate, 3,3,3-Trifluoro-1,2-epoxypropane and Its Complex with the Argon Atom. J. Phys. Chem. A 2018, 122, 4670–4680. [Google Scholar] [CrossRef] [PubMed]
  60. Makarewicz, J.; Shirkov, L. Theoretical study of the complexes of dichlorobenzene isomers with argon. I. Global potential energy surface for all the isomers with application to intermolecular vibrations. J. Chem. Phys. 2019, 150, 074301. [Google Scholar] [CrossRef] [PubMed]
  61. Shirkov, L.; Makarewicz, J. Theoretical study of the complexes of dichlorobenzene isomers with argon. II. SAPT analysis of the intermolecular interaction. J. Chem. Phys. 2019, 150, 074302. [Google Scholar] [CrossRef] [PubMed]
  62. Marshall, M.D.; Leung, H.O.; Febles, O.; Gomez, A. The microwave spectra and molecular structures of (E)-1,3,3,3-tetrafluoropropene and its complex with the argon atom. J. Mol. Spectrosc. 2020, 374, 111379. [Google Scholar] [CrossRef]
  63. Leung, H.O.; Marshall, M.D.; Stuart, D.J. Microwave Spectrum and Molecular Structure of 3-fluoro-1,2-epoxypropane and the Unexpected Structure of Its Complex with the Argon Atom. J. Phys. Chem. A 2020, 124, 1798–1810. [Google Scholar] [CrossRef]
  64. Leung, H.O.; Marshall, M.D.; Horowitz, J.R.; Stuart, D.J. The microwave spectrum and molecular structure of the gas-phase heterodimer formed between argon and glycidol. J. Mol. Spectrosc. 2021, 375, 111407. [Google Scholar] [CrossRef]
  65. Leung, H.O.; Marshall, M.D.; Bozzi, A.T.; Horowitz, J.R.; Nino, A.C.; Tandon, H.K.; Yoon, L. The microwave spectra and molecular structures of (E)-1-chloro-1,2-difluoroethylene and its complex with the argon atom. J. Mol. Spectrosc. 2021, 381, 111520. [Google Scholar] [CrossRef]
  66. Punyain, W.; Takahashi, K. Evaluation of Ar tagging toward the vibrational spectra and zero point energy of X-HOH, X-DOH, and X-HOD, for X = F, Cl, Br. Phys. Chem. Chem. Phys. 2021, 23, 9492–9499. [Google Scholar] [CrossRef] [PubMed]
  67. Marks, J.H.; Miliordos, E.; Duncan, M.A. Infrared spectroscopy of RG-Co+(H2O) complexes (RG = Ar, Ne, He): The role of rare gas “tag” atoms. J. Chem. Phys. 2021, 154, 064306. [Google Scholar] [CrossRef]
  68. Leung, H.O.; Marshall, M.D.; Ahmad, T.Z.; Borden, D.W.; Hoffman, C.A.; Kim, N.A. The microwave spectra and molecular structures of the chiral and achiral rotamers of 2,3,3-trifluoropropene and their gas-phase heterodimers with the argon atom. J. Mol. Spectrosc. 2022, 387, 111656. [Google Scholar] [CrossRef]
  69. Das, A.; Arunan, E. Measurement of Donor-Acceptor Interchange Tunnelling in Ar(H2O)2 using Rotational Spectroscopy and a Re-look at Its Structure and Bonding. J. Mol. Struct. 2022, 1252, 132094. [Google Scholar] [CrossRef]
  70. Ito, Y.; Kominato, M.; Nakashima, Y.; Ohshimo, K.; Misaizu, F. Fragment imaging in the infrared photodissociation of the Ar-tagged protonated water clusters H3O+-Ar and H+(H2O)2-Ar. Phys. Chem. Chem. Phys. 2023, 25, 9404–9412. [Google Scholar] [CrossRef]
  71. Leung, H.O.; Marshall, M.D.; Hong, S.; Hoque, L. The microwave spectra and molecular structures of (Z)-1-chloro-3,3,3-trifluoropropene and its gas-phase heterodimer with the argon atom. J. Mol. Spectrosc. 2023, 394, 111779. [Google Scholar] [CrossRef]
  72. Wassermann, T.N.; Luckhaus, D.; Coussan, S.; Suhm, M.A. Proton tunneling estimates for malonaldehyde vibrations from supersonic jet and matrix quenching experiments. Phys. Chem. Chem. Phys. 2006, 8, 2344–2348. [Google Scholar] [CrossRef] [PubMed]
  73. Wassermann, T.N.; Zielke, P.; Lee, J.J.; Cezard, C.; Suhm, M.A. Structural preferences, argon nanocoating, and dimerization of n-alkanols as revealed by OH stretching spectroscopy in supersonic jets. J. Phys. Chem. A 2007, 111, 7437–7448. [Google Scholar] [CrossRef]
  74. Wassermann, T.N.; Suhm, M.A. Ethanol monomers and dimers revisisted: A raman study of conformational preferences and argon nanocoating effects. J. Phys. Chem. A 2010, 114, 8223–8233. [Google Scholar] [CrossRef]
  75. Lee, J.J.; Hofener, S.; Klopper, W.; Wassermann, T.N.; Suhm, M.A. Origin of the argon nanocoating shift in the OH stretching fundamental of n-propanol: A combined experimental and quantum chemical study. J. Phys. Chem. C 2009, 113, 10929–10938. [Google Scholar] [CrossRef]
  76. Vasylieva, A.; Doroshenko, I.; Doroshenko, O.; Pogorelov, V. Effect of argon environment on small water clusters in matrix isolation. Low Temp. Phys. 2019, 45, 627–633. [Google Scholar] [CrossRef]
  77. Vasylieva, A.; Doroshenko, I.; Stepanian, S.; Adamowicz, L. The influence of low-temperature argon matrix on embedded water clusters. A DFT theoretical study. Low Temp. Phys. 2021, 47, 242–249. [Google Scholar] [CrossRef]
  78. Kisiel, Z.; Fowler, P.W.; Legon, A.C. Rotational spectra and structures of van der Waals dimers of Ar with a series of fluorocarbons. J. Chem. Phys. 1991, 95, 2283–2291. [Google Scholar] [CrossRef]
  79. Cohen, R.C.; Busarow, K.L.; Laughlin, K.B.; Blake, G.A.; Havenith, M.; Lee, Y.T.; Saykally, R.J. Tunable far infrared laser spectroscopy of van der Waals bonds: Vibration-rotation-tunneling spectra of Ar-H2O. J. Chem. Phys. 1988, 89, 4494–4504. [Google Scholar] [CrossRef]
  80. Cohen, R.C.; Busarow, K.L.; Lee, Y.Y.; Saykally, R.J. Tunable far infrared laser spectroscopy of van der Waals bonds: The intermolecular stretching vibration and effective radial potentials for Ar-H2O. J. Chem. Phys. 1990, 92, 169–177. [Google Scholar] [CrossRef]
  81. Fraser, G.T.; Lovas, F.J.; Suenram, R.D.; Matsumura, K. Microwave spectrum of Ar-H2O: Dipole moment, isotopic studies, and 17O quadrupole coupling constants. J. Mol. Spectrosc. 1990, 144, 97–112. [Google Scholar] [CrossRef]
  82. Chałasiński, G.; Szczȩs̀niak, M.M.; Scheiner, S. Ab initio study of the intermolecular potential of Ar-H2O. J. Chem. Phys. 1991, 94, 2807–2816. [Google Scholar] [CrossRef]
  83. Cohen, R.C.; Saykally, R.J. Multidimensional intermolecular dynamics from tunable far-infrared laser spectroscopy: Angular-radial coupling in the intermolecular potential of argon-H2O. J. Chem. Phys. 1991, 95, 7891–7906. [Google Scholar] [CrossRef]
  84. Suzukí, S.; Bumgarner, R.E.; Stockman, P.A.; Green, P.G.; Blake, G.A. Tunable far-infrared laser spectroscopy of deuterated isotopomers of Ar-H2O. J. Chem. Phys. 1991, 94, 824–825. [Google Scholar] [CrossRef]
  85. Germann, T.C.; Gutowsky, H.S. Nuclear hyperfine interactions and dynamic state of H2O in Ar-H2O. J. Chem. Phys. 1993, 98, 5235–5238. [Google Scholar] [CrossRef]
  86. Tao, F.M.; Klemperer, W. Accurate ab initio potential energy surfaces of Ar-HF, Ar-H2O, and Ar-NH3. J. Chem. Phys. 1994, 101, 1129–1145. [Google Scholar] [CrossRef]
  87. Borges, E.; Ferreira, G.G.; Braga, J.P. Structures and energies of ArnH2O (n = 1–26) clusters using a nonrigid potential surface: A molecular dynamics simulation. Int. J. Quantum Chem. 2008, 108, 2523–2529. [Google Scholar] [CrossRef]
  88. Liu, X.; Xu, Y. New rovibrational bands of the Ar-H2O complex at the ν2 bend region of H2O. J. Mol. Spectrosc. 2014, 301, 1–8. [Google Scholar] [CrossRef]
  89. Zou, L.; Weaver, S.L.W. Direct measurement of additional Ar-H2O vibration-rotation-tunneling bands in the millimeter-submillimeter range. J. Mol. Spectrosc. 2016, 324, 12–19. [Google Scholar] [CrossRef]
  90. Hou, D.; Ma, Y.T.; Zhang, X.L.; Li, H. The origins of intra- and inter-molecular vibrational couplings: A case study of H2O-Ar on full and reduced-dimensional potential energy surface. J. Chem. Phys. 2016, 144, 014301. [Google Scholar] [CrossRef]
  91. Vanfleteren, T.; Földes, T.; Herman, M.; Liévin, J.; Loreau, J.; Coudert, L.H. Experimental and theoretical investigations of H2O-Ar. J. Chem. Phys. 2017, 147, 014302. [Google Scholar] [CrossRef]
  92. Yang, D.; Liu, L.; Xie, D.; Guo, H. Full-dimensional quantum studies of vibrational energy transfer dynamics between H2O and Ar: Theory assessing experiment. Phys. Chem. Chem. Phys. 2022, 24, 13542–13549. [Google Scholar] [CrossRef]
  93. Liu, L.; Yang, D.; Guo, H.; Xie, D. Full-Dimensional Quantum Dynamics Studies of Ro-vibrationally Inelastic Scattering of H2O with Ar: A Benchmark Test of the Rigid-Rotor Approximation. J. Phys. Chem. A 2023, 127, 195–202. [Google Scholar] [CrossRef]
  94. Arunan, E.; Emilsson, T.; Gutowsky, H.S. Rotational Spectra, Structure, and Dynamics of Arm-(H2O)n Clusters: The Ar-(H2O)2 trimer. J. Chem. Phys. 2002, 116, 4886–4895. [Google Scholar] [CrossRef]
  95. Arunan, E.; Emilsson, T.; Gutowsky, H.S. Rotational Spectra, Structure, and Dynamics of Arm-(H2O)n Clusters: Ar2-H2O, Ar3-H2O, Ar-(H2O)2 and Ar-(H2O)3. J. Am. Chem. Soc. 1994, 116, 8418–8419. [Google Scholar] [CrossRef]
  96. Moudens, A.; Georges, R.; Goubet, M.; Makarewicz, J.; Lokshtanov, S.E.; Vigasin, A.A. Direct absorption spectroscopy of water clusters formed in a continuous slit nozzle expansion. J. Chem. Phys. 2009, 131, 204312. [Google Scholar] [CrossRef] [PubMed]
  97. Mó, O.; Yáñez, M.; Elguero, J. Cooperative (nonpairwise) effects in water trimers: An ab initio molecular orbital study. J. Chem. Phys. 1992, 97, 6628–6638. [Google Scholar] [CrossRef]
  98. Pugliano, N.; Saykally, R.J. Measurement of Quantum Tunneling Between Chiral Isomers of the Cyclic Water Trimer. Science 1992, 257, 1937–1940. [Google Scholar] [CrossRef]
  99. Schütz, M.; Bürgi, T.; Leutwyler, S.; Bürgi, H.B. Fluxionality and low-lying transition structures of the water trimer. J. Chem. Phys. 1993, 99, 5228–5238. [Google Scholar] [CrossRef]
  100. Wales, D.J. Theoretical study of water trimer. J. Am. Chem. Soc. 1993, 115, 11180–11190. [Google Scholar] [CrossRef]
  101. Xantheas, S.S.; Dunning, T.H. The structure of the water trimer from abinitio calculations. J. Chem. Phys. 1993, 98, 8037–8040. [Google Scholar] [CrossRef]
  102. Xantheas, S.S.; Dunning, T.H. Ab initio studies of cyclic water clusters (H2O)n, n = 1–6. I. Optimal structures and vibrational spectra. J. Chem. Phys. 1993, 99, 8774–8792. [Google Scholar] [CrossRef]
  103. Xantheas, S.S. Ab initio studies of cyclic water clusters (H2O)n, n = 1–6. II. Analysis of many-body interactions. J. Chem. Phys. 1994, 100, 7523–7534. [Google Scholar] [CrossRef]
  104. Pribble, R.N.; Zwier, T.S. Size-Specific Infrared Spectra of Benzene-(H2O)n Clusters (n = 1 through 7): Evidence for Noncyclic (H2O)n Structures. Science 1994, 265, 75–79. [Google Scholar] [CrossRef] [PubMed]
  105. Liu, K.; Loeser, J.G.; Elrod, M.J.; Host, B.C.; Rzepiela, J.A.; Pugliano, N.; Saykally, R.J. Dynamics of Structural Rearrangements in the Water Trimer. J. Am. Chem. Soc. 1994, 116, 3507–3512. [Google Scholar] [CrossRef]
  106. Xantheas, S.S. Ab initio studies of cyclic water clusters (H2O)n, n = 1–6. III. Comparison of density functional with MP2 results. J. Chem. Phys. 1995, 102, 4505–4517. [Google Scholar] [CrossRef]
  107. Schütz, M.; Klopper, W.; Lüthi, H.P.; Leutwyler, S. Low-lying stationary points and torsional interconversions of cyclic (H2O)4: An abinitio study. J. Chem. Phys. 1995, 103, 6114–6126. [Google Scholar] [CrossRef]
  108. Fowler, J.E.; Schaefer, H.F.I. Detailed Study of the Water Trimer Potential Energy Surface. J. Am. Chem. Soc. 1995, 117, 446–452. [Google Scholar] [CrossRef]
  109. Wales, D.J.; Walsh, T.R. Theoretical study of the water pentamer. J. Chem. Phys. 1996, 105, 6957–6971. [Google Scholar] [CrossRef]
  110. Huisken, F.; Kaloudis, M.; Kulcke, A. Infrared spectroscopy of small size-selected water clusters. J. Chem. Phys. 1996, 104, 17–25. [Google Scholar] [CrossRef]
  111. Cruzan, J.D.; Braly, L.B.; Liu, K.; Brown, M.G.; Loeser, J.G.; Saykally, R.J. Quantifying Hydrogen Bond Cooperativity in Water: VRT Spectroscopy of the Water Tetramer. Science 1996, 271, 59–62. [Google Scholar] [CrossRef] [PubMed]
  112. Liu, K.; Brown, M.G.; Cruzan, J.D.; Saykally, R.J. Vibration-Rotation Tunneling Spectra of the Water Pentamer: Structure and Dynamics. Science 1996, 271, 62–64. [Google Scholar] [CrossRef]
  113. Paul, J.B.; Collier, C.P.; Saykally, R.J.; Scherer, J.J.; O’Keefe, A. Direct Measurement of Water Cluster Concentrations by Infrared Cavity Ringdown Laser Absorption Spectroscopy. J. Phys. Chem. A 1997, 101, 5211–5214. [Google Scholar] [CrossRef]
  114. Wales, D.J.; Walsh, T.R. Theoretical study of the water tetramer. J. Chem. Phys. 1997, 106, 7193–7207. [Google Scholar] [CrossRef]
  115. Nielsen, I.M.B.; Seidl, E.T.; Janssen, C.L. Accurate structures and binding energies for small water clusters: The water trimer. J. Chem. Phys. 1999, 110, 9435. [Google Scholar] [CrossRef]
  116. Xantheas, S.S.; Burnham, C.J.; Harrison, R.J. Development of transferable interaction models for water. II. Accurate energetics of the first few water clusters from first principles. J. Chem. Phys. 2002, 116, 1493–1499. [Google Scholar] [CrossRef]
  117. Taketsugu, T.; Wales, D.J. Theoretical study of rearrangements in water dimer and trimer. Mol. Phys. 2002, 100, 2793–2806. [Google Scholar] [CrossRef]
  118. Anderson, J.A.; Crager, K.; Fedoroff, L.; Tschumper, G.S. Anchoring the potential energy surface of the cyclic water trimer. J. Chem. Phys. 2004, 121, 11023–11029. [Google Scholar] [CrossRef]
  119. Day, M.B.; Kirschner, K.N.; Shields, G.C. Global Search for Minimum Energy (H2O)n Clusters, n = 3–5. J. Phys. Chem. A 2005, 109, 6773–6778. [Google Scholar] [CrossRef]
  120. Dunn, M.E.; Evans, T.M.; Kirschner, K.N.; Shields, G.C. Prediction of Accurate Anharmonic Experimental Vibrational Frequencies for Water Clusters, (H2O)n, n = 2–5. J. Phys. Chem. A 2006, 110, 303–309. [Google Scholar] [CrossRef]
  121. Slipchenko, M.N.; Kuyanov, K.E.; Sartakov, B.G.; Vilesov, A.F. Infrared intensity in small ammonia and water clusters. J. Chem. Phys. 2006, 124, 241101. [Google Scholar] [CrossRef] [PubMed]
  122. Hirabayashi, S.; Yamada, K.M.T. Infrared spectra and structure of water clusters trapped in argon and krypton matrices. J. Mol. Struct. 2006, 795, 78–83. [Google Scholar] [CrossRef]
  123. Hirabayashi, S.; Yamada, K.M.T. The monocyclic water hexamer detected in neon matrices by infrared spectroscopy. Chem. Phys. Lett. 2007, 435, 74–78. [Google Scholar] [CrossRef]
  124. Pérez, J.F.; Hadad, C.Z.; Restrepo, A. Structural Studies of the Water Tetramer. Int. J. Quantum Chem. 2008, 108, 1653–1659. [Google Scholar] [CrossRef]
  125. Watanabe, Y.; Maeda, S.; Ohno, K. Intramolecular vibrational frequencies of water clusters (H2O)n (n = 2–5): Anharmonic analyses using potential functions based on the scaled hypersphere search method. J. Chem. Phys. 2008, 129, 074315. [Google Scholar] [CrossRef] [PubMed]
  126. Kang, D.; Dai, J.; Hou, Y.; Yuan, J. Structure and vibrational spectra of small water clusters from first principles simulations. J. Chem. Phys. 2010, 133, 014302. [Google Scholar] [CrossRef] [PubMed]
  127. Bégué, D.; Baraille, I.; Garrain, P.A.; Dargelos, A.; Tassaing, T. Calculation of IR frequencies and intensities in electrical and mechanical anharmonicity approximations: Applications to small water clusters. J. Chem. Phys. 2010, 133, 034102. [Google Scholar] [CrossRef] [PubMed]
  128. Shields, R.M.; Temelso, B.; Archer, K.A.; Morrell, T.E.; Shields, G.C. Accurate Predictions of Water Cluster Formation, (H2O)n=2--10. J. Phys. Chem. A 2010, 114, 11725–11737. [Google Scholar] [CrossRef]
  129. Ramirez, F.; Hadad, C.Z.; Guerra, D.; David, J.; Restrepo, A. Structural Studies of the Water Pentamer. Chem. Phys. Lett. 2011, 507, 229–233. [Google Scholar] [CrossRef]
  130. Temelso, B.; Archer, K.A.; Shields, G.C. Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections. J. Phys. Chem. A 2011, 115, 12034–12046. [Google Scholar] [CrossRef]
  131. Temelso, B.; Shields, G.C. The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters. J. Chem. Theory Comput. 2011, 7, 2804–2817. [Google Scholar] [CrossRef]
  132. Yoo, S.; Xantheas, S.S. Structures, Energetics and Spectroscopic Fingerprints of Water Clusters n = 2–24. In Handbook of Computational Chemistry; Leszczynski, J., Ed.; Springer: New York, NY, USA, 2012; Volume 2, pp. 761–792. [Google Scholar]
  133. Howard, J.C.; Tschumper, G.S. Wavefunction methods for the accurate characterization of water clusters. WIREs Comput. Mol. Sci. 2014, 4, 199–224. [Google Scholar] [CrossRef]
  134. Howard, J.C.; Tschumper, G.S. Benchmark Structures and Harmonic Vibrational Frequencies Near the CCSD(T) Complete Basis Set Limit for Small Water Clusters: (H2O)n=2,3,4,5,6. J. Chem. Theory Comput. 2015, 11, 2126–2136. [Google Scholar] [CrossRef] [PubMed]
  135. Miliordos, E.; Xantheas, S.S. An accurate and efficient computational protocol for obtaining the complete basis set limits of the binding energies of water clusters at the MP2 and CCSD(T) levels of theory: Application to (H2O)m, m = 2–6, 8, 11, 16, and 17. J. Chem. Phys. 2015, 142, 234303. [Google Scholar] [CrossRef]
  136. Malloum, A.; Fifen, J.J.; Dhaouadi, Z.; Engo, S.G.N.; Conradie, J. Structures, relative stability and binding energies of neutral water clusters, (H2O)2-30. New J. Chem. 2019, 43, 13020–13037. [Google Scholar] [CrossRef]
  137. Møller, C.; Plesset, M.S. Note on an Approximation Treatment for Many-electron Systems. Phys. Rev. 1934, 46, 618–622. [Google Scholar] [CrossRef]
  138. Dunning, T.H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007. [Google Scholar] [CrossRef]
  139. Kendall, R.A.; Dunning, T.H.; Harrison, R.J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796–6806. [Google Scholar] [CrossRef]
  140. Woon, D.E.; Dunning, T.H. Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon. J. Chem. Phys. 1993, 98, 1358. [Google Scholar] [CrossRef]
  141. Bates, D.M.; Smith, J.R.; Janowski, T.; Tschumper, G.S. Development of a 3-body:many-body integrated fragmentation method for weakly bound clusters and application to water clusters (H2O)n=3–10,16,17. J. Chem. Phys. 2011, 135, 044123. [Google Scholar] [CrossRef]
  142. Bates, D.M.; Smith, J.R.; Tschumper, G.S. Efficient and Accurate Methods for the Geometry Optimization of Water Clusters: Application of Analytic Gradients for the Two-Body:Many-Body QM:QM Fragmentation Method to (H2O)n, n = 3–10. J. Chem. Theory Comput. 2011, 7, 2753–2760. [Google Scholar] [CrossRef] [PubMed]
  143. Howard, J.C.; Tschumper, G.S. N-body:Many-body QM:QM vibrational frequencies: Application to small hydrogen-bonded clusters. J. Chem. Phys. 2013, 139, 184113. [Google Scholar] [CrossRef] [PubMed]
  144. Hopkins, B.W.; Tschumper, G.S. A multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen-bonded systems. J. Comput. Chem. 2003, 24, 1563–1568. [Google Scholar] [CrossRef]
  145. Tschumper, G.S. Multicentered integrated QM:QM methods for weakly bound clusters: An efficient and accurate 2-body:many-body treatment of hydrogen bonding and van der Waals interactions. Chem. Phys. Lett. 2006, 427, 185–191. [Google Scholar] [CrossRef]
  146. Elsohly, A.M.; Shaw, C.L.; Guice, M.E.; Smith, B.D.; Tschumper, G.S. Analytic gradients for the multicentered integrated QM:QM method for weakly bound clusters: Efficient and accurate 2-body:many-body geometry optimizations. Mol. Phys. 2007, 105, 2777–2782. [Google Scholar] [CrossRef]
  147. Tschumper, G.S.; Ellington, T.L.; Johnson, S.N. Chapter Two—Dissociation in Binary Acid/Base Clusters: An Examination of Inconsistencies Introduced Into the Many-Body Expansion by Naíve Fragmentation Schemes. Annu. Rep. Comput. Chem. 2017, 13, 93–115. [Google Scholar] [CrossRef]
  148. Purvis, G.D., III; Stanton, R.J.. A full coupled-cluster singles and doubles model: The inclusion of disconnected triples. J. Chem. Phys. 1982, 76, 1910–1918. [Google Scholar] [CrossRef]
  149. Stanton, J.F.; Gauss, J.; Cheng, L.; Harding, M.E.; Matthews, D.A.; Szalay, P.G. CFOUR, Coupled-Cluster Techniques for Computational Chemistry, a Quantum-Chemical Program Package. With Contributions from A.A. Auer, R.J. Bartlett, U. Benedikt, C. Berger, D.E. Bernholdt, Y.J. Bomble, O. Christiansen, F. Engel, R. Faber, M. Heckert, O. Heun, M. Hilgenberg, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, T. Kirsch, K. Klein, W.J. Lauderdale, F. Lipparini, T. Metzroth, L.A. Mück, D.P. O’Neill, D.R. Price, E. Prochnow, C. Puzzarini, K. Ruud, F. Schiffmann, W. Schwalbach, C. Simmons, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J.D. Watts and the Integral Packages MOLECULE (J. Almlöf and P.R. Taylor), PROPS (P.R. Taylor), ABACUS (T. Helgaker, H.J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen. Current Version. Available online: http://www.cfour.de (accessed on 1 December 2023).
  150. Matthews, D.A.; Cheng, L.; Harding, M.E.; Lipparini, F.; Stopkowicz, S.; Jagau, T.C.; Szalay, P.G.; Gauss, J.; Stanton, J.F. Coupled-cluster techniques for computational chemistry: The CFOUR program package. J. Chem. Phys. 2020, 152, 214108. [Google Scholar] [CrossRef]
  151. Kestner, N.R. He-He Interaction in the SCF-MO Approximation. J. Chem. Phys. 1968, 48, 252–257. [Google Scholar] [CrossRef]
  152. Liu, B.; McLean, A.D. Accurate calculation of the attractive interaction of two ground state helium atoms. J. Chem. Phys. 1973, 59, 4557–4558. [Google Scholar] [CrossRef]
  153. Jansen, H.B.; Ros, P. Nonempirical molecular orbital calculations on the protonation of carbon monoxide. Chem. Phys. Lett. 1969, 3, 140–143. [Google Scholar] [CrossRef]
  154. Boys, S.F.; Bernardi, F. The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors. Mol. Phys. 1970, 19, 553–566. [Google Scholar] [CrossRef]
  155. Tschumper, G.S. Reliable Electronic Structure Computations for Weak Non-Covalent Interactions in Clusters. In Reviews in Computational Chemistry; Lipkowitz, K.B., Cundari, T.R., Eds.; Wiley-VCH, Inc.: Hoboken, NJ, USA, 2008; Volume 26, Chapter 2; pp. 39–90. [Google Scholar] [CrossRef]
  156. Jeziorski, B.; Moszynski, R.; Szalewicz, K. Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes. Chem. Rev. 1994, 94, 1887–1930. [Google Scholar] [CrossRef]
  157. Hohenstein, E.G.; Sherrill, C.D. Wavefunction methods for noncovalent interactions. WIREs Comput. Mol. Sci. 2012, 2, 304–326. [Google Scholar] [CrossRef]
  158. Szalewicz, K. Symmetry-adapted perturbation theory of intermolecular forces. WIREs Comput. Mol. Sci. 2012, 2, 254–272. [Google Scholar] [CrossRef]
  159. Hohenstein, E.G.; Sherrill, C.D. Density fitting of intramonomer correlation effects in symmetry-adapted perturbation theory. J. Chem. Phys. 2010, 133, 014101. [Google Scholar] [CrossRef]
  160. Hohenstein, E.G.; Jaeger, H.M.; Carrell, E.J.; Tschumper, G.S.; Sherrill, C.D. Accurate Interaction Energies for Problematic Dispersion-Bound Complexes: Homogeneous Dimers of NCCN, P2 and PCCP. J. Chem. Theory. Comput. 2011, 7, 2842–2851. [Google Scholar] [CrossRef] [PubMed]
  161. Turney, J.M.; Simmonett, A.C.; Parrish, R.M.; Hohenstein, E.G.; Evangelista, F.A.; Fermann, J.T.; Mintz, B.J.; Burns, L.A.; Wilke, J.J.; Abrams, M.L.; et al. PSI4: An open-source ab initio electronic structure program. WIREs Comput. Mol. Sci. 2012, 2, 556–565. [Google Scholar] [CrossRef]
  162. Smith, D.G.A.; Burns, L.A.; Simmonett, A.C.; Parrish, R.M.; Schieber, M.C.; Galvelis, R.; Kraus, P.; Kruse, H.; Di Remigio, R.; Alenaizan, A.; et al. PSI4 1.4: Open-source software for high-throughput quantum chemistry. J. Chem. Phys. 2020, 152, 184108. [Google Scholar] [CrossRef]
  163. Parrish, R.M.; Sherrill, C.D. Tractability gains in symmetry-adapted perturbation theory including coupled double excitations: CCD+ST(CCD) dispersion with natural orbital truncations. J. Chem. Phys. 2013, 139, 174102. [Google Scholar] [CrossRef]
Ijms 24 17480 g001
Figure 1. Minima identified for the Ar(H 2 O) n = 3 – 5 complexes (H white; O red; Ar cyan).
Figure 1. Minima identified for the Ar(H 2 O) n = 3 – 5 complexes (H white; O red; Ar cyan).
Ijms 24 17480 g001
Table 1. Relative electronic and ZPVE-inclusive energies ( ∆ E and ∆ E 0 , respectively) in kJ mol − 1 obtained for the haTZ-optimized (H 2 O) n = 3 , 4 and Ar(H 2 O) n = 3 – 5 structures using the MP2, 2b:Mb, and 3b:Mb methods.
Table 1. Relative electronic and ZPVE-inclusive energies ( ∆ E and ∆ E 0 , respectively) in kJ mol − 1 obtained for the haTZ-optimized (H 2 O) n = 3 , 4 and Ar(H 2 O) n = 3 – 5 structures using the MP2, 2b:Mb, and 3b:Mb methods.
MP22b:Mb3b:Mb
ComplexLabel ∆ E ∆ E 0 ∆ E ∆ E 0 ∆ E ∆ E 0
(H 2 O) 3 C 1 0.000.000.000.000.000.00
(H 2 O) 3 C 3 3.241.723.451.973.431.95
(H 2 O) 4 S 4 0.000.000.000.000.000.00
(H 2 O) 4 C i 3.882.963.923.003.912.98
(H 2 O) 4 C 4 † 9.11…  a 9.34…  a 9.31…  a
Ar(H 2 O) 3 C 1 Face 1 0.000.000.000.000.000.00
Ar(H 2 O) 3 C 1 Face 2 0.360.230.270.170.270.17
Ar(H 2 O) 3 C 1 Edge1.340.901.390.981.260.87
Ar(H 2 O) 3 C 3 Face 0 3.101.753.402.003.371.98
Ar(H 2 O) 3 C 3 Face 3 4.172.284.182.414.162.39
Ar(H 2 O) 4 C 2 Face b 0.000.000.000.000.000.00
Ar(H 2 O) 4 C 1 Face c 3.502.703.552.733.562.74
Ar(H 2 O) 4 C 1 Edge c 5.704.505.884.655.634.43
Ar(H 2 O) 4 C 4 Face8.305.508.755.828.735.77
Ar(H 2 O) 5 C 1 Face 2 0.000.000.000.000.000.00
Ar(H 2 O) 5 C 1 Face 3 0.490.300.360.220.360.22
Ar(H 2 O) 5 C 1 Edge2.902.443.032.582.712.31
a C 4 † (H 2 O) 4 is a transition state (harmonic vibrational frequencies in Supporting Information); b Ar bound to S 4 (H 2 O) 4 ; c Ar bound to C i (H 2 O) 4 .
Table 2. Electronic and ZPVE-inclusive binding energies ( E b i n d and E b i n d 0 , respectively) in kJ mol − 1 for the haTZ-optimized Ar(H 2 O) n = 3 – 5 complexes with the MP2, 2b:Mb, and 3b:Mb methods.
Table 2. Electronic and ZPVE-inclusive binding energies ( E b i n d and E b i n d 0 , respectively) in kJ mol − 1 for the haTZ-optimized Ar(H 2 O) n = 3 – 5 complexes with the MP2, 2b:Mb, and 3b:Mb methods.
MP22b:Mb3b:Mb
Label E bind E bind 0 E bind E bind 0 E bind E bind 0
        Binding Process: C 1 (H 2 O) 3 + Ar → C 1 Ar(H 2 O) 3
C 1 Face 1 −3.88−3.10−3.99−3.21−3.84−3.09
C 1 Face 2 −3.52−2.87−3.73−3.04−3.57−2.92
C 1 Edge−2.54−2.20−2.60−2.23−2.58−2.23
        Binding Process: C 3 (H 2 O) 3 + Ar → C 3 Ar(H 2 O) 3
C 3 Face 0 −4.02−3.07−4.04−3.18−3.90−3.06
C 3 Face 3 −2.95−2.53−3.26−2.77−3.11−2.65
        Binding Process: S 4 (H 2 O) 4 + Ar → C 2 Ar(H 2 O) 4
C 2 Face−4.65−3.92−4.84−4.08−4.62−3.90
        Binding Process: C i (H 2 O) 4 + Ar → C 1 Ar(H 2 O) 4
C 1 Face−5.03−4.18−5.21−4.34−4.98−4.16
C 1 Edge−2.82−2.39−2.88−2.42−2.91−2.46
        Binding Process: C 4 † (H 2 O) 4 + Ar → C 4 Ar(H 2 O) 4
C 4 Face−5.46…  a −5.43…  a −5.20…  a
        Binding Process: C 1 (H 2 O) 5 + Ar → C 1 Ar(H 2 O) 5
C 1 Face 2 −5.85−4.92−6.03−5.09−5.75−4.86
C 1 Face 3 −5.36−4.61−5.67−4.87−5.39−4.64
C 1 Edge−2.95−2.47−3.01−2.51−3.04−2.55
a C 4 † (H 2 O) 4 is a transition state (harmonic vibrational frequencies in Supporting Information).
Table 3. Interaction energies ( E i n t in kJ mol − 1 ) calculated for the Ar(H 2 O) n = 3 – 5 minima using the MP2, 2b:Mb, and 3b:Mb methods with the haTZ basis set as well as the SAPT2+3(CCD) total interaction energies computed with the haTZ basis set for the 3b:Mb/haTZ optimized structures followed by the individual contributions from exchange repulsion, electrostatics, induction, and dispersion (in kJ mol − 1 ).
Table 3. Interaction energies ( E i n t in kJ mol − 1 ) calculated for the Ar(H 2 O) n = 3 – 5 minima using the MP2, 2b:Mb, and 3b:Mb methods with the haTZ basis set as well as the SAPT2+3(CCD) total interaction energies computed with the haTZ basis set for the 3b:Mb/haTZ optimized structures followed by the individual contributions from exchange repulsion, electrostatics, induction, and dispersion (in kJ mol − 1 ).
E int SAPT Components
LabelMP22b:Mb3b:MbSAPTExchElectIndDisp
        Binding Process: C 1 (H 2 O) 3 + Ar → C 1 Ar(H 2 O) 3
C 1 Face 1 −3.90−4.00−3.85−3.13+5.62−1.73−0.66−6.37
C 1 Face 2 −3.53−3.74−3.58−2.92+5.42−1.71−0.55−6.08
C 1 Edge−2.54−2.60−2.58−2.04+3.66−1.09−0.40−4.22
        Binding Process: C 3 (H 2 O) 3 + Ar → C 3 Ar(H 2 O) 3
C 3 Face 0 −4.03−4.04−3.90−3.08+5.41−1.63−0.53−6.33
C 3 Face 3 −2.95−3.26−3.11−2.43+4.96−1.60−0.20−5.59
        Binding Process: S 4 (H 2 O) 4 + Ar → C 2 Ar(H 2 O) 4
C 2 Face−4.71−4.90−4.66−3.71+6.94−2.17−0.39−8.08
        Binding Process: C i (H 2 O) 4 + Ar → C 1 Ar(H 2 O) 4
C 1 Face−5.05−5.23−4.99−4.08+7.20−2.23−0.77−8.28
C 1 Edge−2.83−2.89−2.91−2.28+4.05−1.23−0.44−4.65
        Binding Process: C 4 † (H 2 O) 4 + Ar → C 4 Ar(H 2 O) 4
C 4 Face−5.48−5.44−5.20−4.09+7.30−2.16−0.53−8.69
        Binding Process: C 1 (H 2 O) 5 + Ar → C 1 Ar(H 2 O) 5
C 1 Face 2 −5.97−6.15−5.84−4.79+8.51−2.64−0.57−10.01
C 1 Face 3 −5.50−5.81−5.50−4.42+8.29−2.63−0.45−9.62
C 1 Edge−2.96−3.01−3.05−2.38+4.28−1.31−0.49−4.86
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Rock, C.A.; Tschumper, G.S. Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory. Int. J. Mol. Sci. 2023, 24, 17480. https://doi.org/10.3390/ijms242417480

AMA Style

Rock CA, Tschumper GS. Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory. International Journal of Molecular Sciences. 2023; 24(24):17480. https://doi.org/10.3390/ijms242417480

Chicago/Turabian Style

Rock, Carly A., and Gregory S. Tschumper. 2023. "Insight into the Binding of Argon to Cyclic Water Clusters from Symmetry-Adapted Perturbation Theory" International Journal of Molecular Sciences 24, no. 24: 17480. https://doi.org/10.3390/ijms242417480

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop