Exploring Structures and Energetics of Large OCS Clusters by

Article pubs.acs.org/JPCA

Exploring Structures and Energetics of Large OCS Clusters by Correlated Methods Nityananda Sahu, Gurmeet Singh, and Shridhar R. Gadre* Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur, 208016 India S Supporting Information *

ABSTRACT: An extensive minima search based on accurate estimation of binding energies in (OCS)n clusters for n = 2−5 is carried out employing MP2 and CCSD(T) levels of theory. Features of the molecular electrostatic potential of the OCS monomer are utilized for building the laterally shifted and linear aggregates of OCS. Trial structures generated through cluster building algorithm are subjected to geometry optimization at MP2 level using aug-cc-pvTZ (TZ) basis set. Molecular tailoring approach (MTA)-based single-point energies at MP2/QZ and CCSD(T)/TZ levels are calculated for the estimation of binding energy at complete basis set (CBS) limit. For a comparative study, benchmark calculations employing the dispersion-corrected B2PLYPD functional with TZ basis set are effected. The resulting geometrical parameters from which are found to be in excellent agreement with the experimental findings. With increasing cluster size, the calculated vibrational frequency at the MP2/DZ level of theory shows a substantial blue shift for the asymmetric C−O stretch. The results from the present study clearly bring out the feasibility of carrying out ab initio calculations on large-sized clusters on limited hardware with a minimal loss of accuracy.

I. INTRODUCTION The study of weakly bonded molecular clusters/complexes is a topic of active interest in contemporary science. Particularly, understanding the role of weak intermolecular forces1−4 on the stability, structural transitions and dynamics of clusters, has been a long-term issue in physics and chemistry. Carbonyl sulfide (OCS) clusters offer an example of weakly bonded molecular assemblies wherein the dispersion interactions are dominant. OCS aggregates, the most abundant sulfur compounds in the atmosphere, are found to play a vital role in the process of the global sulfur cycle.5 In the stratospheric sulfate layer, OCS clusters are oxidized to sulfuric acid which is responsible for the regulation of the energy balance during the process of light scattering.5 A small amount of OCS is naturally present in grains and seeds, but a high concentration (>1000 pm) can cause sudden collapse, unconsciousness, terminal asphyxia convulsion, and death from respiratory paralysis.6 Besides these, due to the difficulty of producing OCS inorganically, it is regarded as a possible indicator for life in the interstellar medium as well as in the atmosphere of Venus.7 On account of these extensive applications, the structures and vibrational spectra of OCS clusters have been investigated in great detail, both theoretically and experimentally.8−21 The experimental investigations for the structures and spectra of OCS dimers have been reported since 1980. In an earlier work, Ono et al.8 carried out the molecular beam photoionization study to deduce the structure of OCS dimer wherein OCS monomers were found to lie in a side-by-side arrangement. This was further supported through the infrared (IR) photodissociation study.9 Though OCS molecule is © 2013 American Chemical Society

isovalent to the CO2 molecule, the observation of a single peak in the IR photodissociation spectrum ruled out the possibility of the T-shaped isomer for the OCS dimer.9 The staggered-parallel structure with binding energy ∼230 cm−1 (approximately 0.66 kcal/mol) and a dipole moment value >0.1 D was the preferred structure of the dimer.10 Later, Randall et al.11 reported the first observed IR absorption spectrum for this nonpolar isomer wherein both the monomer units were found to have an antiparallel arrangement, at a center of mass distance of 3.65 Å, in agreement with the earlier experimental findings.9,10 For this nonpolar isomer, Afshari et al.12 recently observed six new infrared bands in the ν1 fundamental region of the OCS monomer (2062.20 cm−1) using a slit-jet supersonic expansion. The frequency for the fundamental vibrational bands, i.e., for the most intense asymmetric C−O stretch in the nonpolar dimer, was observed to be 2072.01 cm−1. Contrary to these experimental studies, a recent study13 revealed a new vibrational band at 2069.3 cm−1 in the IR spectrum, which was assigned to a polar isomer with an approximately parallel arrangement of the constituent monomers. On the basis of this finding, the microwave (MW) spectrum was further reported for the refinement of the structure of the recently observed polar OCS dimer.14 However, unlike the nonpolar isomer, the two monomers were slightly tilted with respect to each other through an angle of 16° with an intermonomeric center of mass distance of 3.88 Received: August 20, 2013 Revised: October 3, 2013 Published: October 3, 2013 10964

dx.doi.org/10.1021/jp408311c | J. Phys. Chem. A 2013, 117, 10964−10972

The Journal of Physical Chemistry A

Article

Å.15 In an ab initio calculation at MP2 level of theory,16 the nonpolar isomer with C2h symmetry was also found to be the global minimum on the potential energy surface (PES), in agreement with the experimental observations. However, after this investigation, there have been no theoretical investigations on OCS oligomers till 2012. Recently,17 a 4-dimensional PES for the intermolecular motions of (OCS)2 has been reported at the CCSD(T) level of theory for calculating the rovibrational wave functions wherein the nonpolar isomer is also observed to be the most stable one followed by its polar analogue. OCS trimers have been extensively probed by MW and IR spectroscopy. The MW spectrum for the trimer was first reported by Connelly et al.18 The OCS trimer was found to exhibit a distorted barrel-shaped structure wherein two out of the three constituent OCS monomers were aligned approximately parallel to each other with the remaining OCS being antiparallel. This structure can be identified as a combination of a nonpolar dimer with a OCS monomer stacked on the top. In an extensive study,19 the structure of the OCS trimer was investigated by analyzing the rotational spectrum. Geometrical parameters for trimers were investigated through the combination of the data from isotopic substitutions with the normal species data earlier reported by Connelly et al.18 The central carbon atoms of the monomer units were found to form three vertices of a triangle with the axes of the monomer units roughly parallel to each other. The lowest energy antiparallel barrel-shaped isomer was found to be similar to the earlier reported structure.18 Another new antiparallel structure, with the oxygen of one OCS interacting with the carbon of the adjacent OCS, was observed to be the second most stable conformer for the trimer. In a recent study,20 the infrared spectrum with peaks at 2047.44, 2053.95, and 2077.18 cm−1 for this barrel-shaped isomer was reported in the ν1 fundamental vibrational band region of the OCS trimer. In an earlier theoretical study,21 Valdés and Sordo had also searched for the minimum energy structures for the OCS trimer, employing MP2, MP4SDTQ and QCISD(T) levels along with 631G(d,p), cc-pvXZ (X = D, T, Q) and aug-cc-pvDZ basis sets. Six favorable conformers with different monomeric distributions, were located at these levels of theory wherein the most stable structure was found to be in agreement with the MW spectroscopic experiments.18,19 In spite of these extensive experimental studies on OCS dimers and trimers, no ab initio investigations on large-sized OCS clusters, e.g., tetramers and pentamers, have so far been reported in the literature. This lack of studies on large-sized OCS clusters may be due to the following three reasons. First, the investigations of the structural and spectral behavior of OCS clusters are very much sensitive to the type of experimental techniques18 as well as to the quantum chemical methods that are employed. Second, the number of local minima on the PES increasing rapidly with cluster size, particularly for large clusters, the number of nearly isoenergetics isomers is very large.22,23 The proper separation and characterization of such numerous structures is indeed prohibitively difficult through experimental techniques as well as through theoretical methods. Finally, the OCS clusters are known to be held through long-range dispersion interactions. Accurate estimation of such interactions generally requires high-level quantum chemical methods such as MP2 or CCSD(T) or dispersion-corrected density functionals along with correlated consistent basis sets.24−27 However, the calculations, especially the geometry optimization at these levels of theory are not

always feasible due to the inherent scaling and huge memory requirements. In view of this, the present article presents a high-level ab initio calculation for the structures, energetics and vibrational spectra of (OCS)n clusters for n = 2−5, at MP2 and CCSD(T) levels using correlation consistent basis sets. Initial geometries of the clusters are generated through the cluster building algorithm28 and the CCSD(T) level calculations on tetramers and pentamers have been performed within the state-of-the-art molecular tailoring approach (MTA).29−32 A comparison is made with the results obtained by employing Grimme’s dispersion corrected B2PLYPD functional.33 All the quantum chemical calculations reported in the present article are performed on Intel Core i7 CPUs @ 2.93 GHz machines with 16 GB RAM using the Gaussian package.34 In the present study, Dunning’s correlated basis sets,35,36 e.g., aug-cc-pvNZ (N = D,T,Q), are abbreviated as NZ.

II. METHODOLOGY AND COMPUTATIONAL DETAILS As the number of possible minima and nearly isoenergetic isomers grows rapidly with the cluster size,22,23 it is necessary to generate sufficient number of trial geometries for each cluster, for minimizing the possibility of missing out the energetically favorable ones. Since the molecular electrostatic potential (MESP) is known to play an important role in reactivity of molecules37−39 and energetics of weakly bonded molecular clusters,40 electrostatic features of OCS aggregates are explored for building larger clusters. The initial trial geometries of OCS cluster were generated through the molecular cluster building algorithm28 wherein a higher-sized cluster is generated from the smaller ones on the basis of electrostatics guidelines. Further, the energy minimization of these generated structures was performed employing the electrostatic potential for intermolecular complexation (EPIC) model.28,41,42 For example, the trimers were generated from the combination of dimer− monomer and similarly, tetramers were put together from either the combination of dimer−dimer or trimer-monomer. The pentamers were assembled from trimer-dimer and tetramer-monomer combinations. Thus, about 12 trial dimers and more than 30 trial geometries for each of the trimers, tetramers and pentamers, were generated and subjected to geometry optimization at MP2/TZ level of theory. The binding energies of these isomers were determined by employing the following formula ΔE = E(OCS)n − nE(OCS)

(1)

where E(OCS)n and E(OCS) stand for the total electronic energy of the n-mer and monomer of OCS respectively at same level of theory. In order to estimate the binding energies at the complete basis set (CBS) limit, employing the two-point formula proposed by Halkier and co-workers,43 single-point energy (ΔEQZ//TZ) calculations at MP2/QZ level of theory were further performed for the MP2/TZ geometries. ΔEMP2/CBS = (64ΔEQZ//TZ − 27ΔE TZ//TZ)/37

(2)

where ΔETZ//TZ stands for the binding energies for the geometries optimized at MP2/TZ level of theory. Due to the nonlinear scaling behavior and requirement of high computational resources, CCSD(T) level calculations are prohibitively difficult even with the high-end hardware. Due to this, the CCSD(T) level of calculations for the tetramers and pentamers were performed within MTA.29−32 MTA is a 10965



Article

fragment-based technique generally meant for the ab initio treatment of large molecular systems or clusters, wherein a large system is cut into a set of small overlapping fragments, on which the ab initio calculations are performed. Finally, the results from individual fragments are patched together by means of set inclusion-exclusion principle in order to get the result of the parent system. All the MTA-based calculations were done in parallel, in line with our earlier results on parallelization of quantum chemical codes.29,44 All the tetramers were cut into four trimeric fragments and pentamers were cut into seven trimeric fragments.45 It may be noted that full calculations on tetramers at the CCSD(T) level of theory is still a difficult task on the above-mentioned hardware. Furthermore, either full- or MTA-based calculations at the CCSD(T)/QZ level of theory is virtually impossible even on dimers and trimers. Therefore, the estimation of CBS binding energy at the CCSD(T) level employing eq 2 was not possible, and hence it is calculated through the CBS extrapolation46−48 from MP2 level of theory using eq 3.

Figure 1. (a) Molecular electrostatic potential (MESP) isosurface of value −0.0013 au around the oxygen and sulfur atoms for the OCS monomer evaluated at MP2/aug-cc-pvTZ level of theory. (b) The MESP isosurface of value −0.0066 au for the linear OCS dimer with end-on S···O interaction evaluated at MP2/aug-cc-pvTZ level of theory. See text for details.

that around the sulfur atom viz. −0.0016 au. The nature of MESP of OCS is suggestive of the existence of the end-on (O··· S) and side-on (C···S and C···O) binding interactions in OCS aggregates. However, due to the ring-shaped MESP isosurface around S-atom with relatively large radius, the side-on C···S interaction is expected to be seen at longer sidewise contacts. Based on electrostatic complementarity, four low-lying OCS dimers with different monomeric orientations are generated and subjected to MP2/TZ level of geometry optimization. These dimers are displayed in Figure 2 and respective binding energies of all these isomers at different levels of theory are reported in Table 1. It may be noticed that (OCS)2-I and (OCS)2-II isomers have numerically higher binding energy values than other isomers. The former is found to have an antiparallel orientation of the monomers with two C···S interactions whereas the later shows a tilted but parallel orientation of the monomers. Similarly, the planar isomer-III is stabilized through two C···O interactions. At B2PLYPD/TZ level of theory, the overall dipole moment values of dimers are 0.0002, 0.090, 0.0006, and 0.020 D respectively, suggesting that both (OCS)2-I and (OCS)2-III are nonpolar and (OCS)2-II and (OCS)2-IV are polar in nature. The structures of (OCS)2-I and (OCS)2-II resemble the experimental nonpolar8−12 and polar13−15 structures reported earlier. For (OCS)2-I and (OCS)2-II, the energy rank ordering is unaltered on switching from MP2/CBS to CCSD(T)/CBS levels. Though isomer-IV is energetically more stable than the isomer-III at MP2/CBS levels, the trend is seen to be reversed at the CCSD(T)/CBS level. Similar trend is also noticed for B2PLYPD/CBS level of theory, reflecting the consistency of the results within these levels of theory. For the first two isomers, the rotational constants (A, B and C) are reported in Table 2 along with their experimental values.11−13,16 It may be seen that the values at MP2 level agree well with the respective experimental ones although the errors in A are somewhat large. On the other hand, the values derived from the B2PLYPD level of geometry optimization are in a better agreement with the experimental results11−16 as well as a recent theoretical study.17 Considering this good agreement, for (OCS)2-III and (OCS)2-IV, only the values corresponding to the B2PLYPD/TZ level optimized geometry are presented in Table 2. Looking at the MESP feature of the OCS units, especially the hole near the sulfur atom (cf. Figure 1), and the possibility of S···O (end-on) attractive interaction, the linear dimer ((OCS)2-V) is also considered in the present study, though it is found to be

ΔECCSD(T)/CBS = ΔECCSD(T)/TZ + ΔEMP2/CBS − ΔE TZ//TZ

(3)

where ΔETZ//TZ and ΔECCSD(T)/TZ represent the binding energies at MP2/TZ and CCSD(T)/TZ level of theory for the MP2/TZ optimized geometry and ΔEMP2/CBS represents the MP2 level CBS binding energy estimated from eq 2. As mentioned above, dispersion interactions are important for energetics of OCS clusters. For the proper estimation of binding interactions as well as the geometric parameters, a comparative study was taken up by employing the dispersioncorrected density functional B2PLYPD, developed by Grimme and co-workers.33 In a recent study due to Yeole et al.,49 this functional was explored for the investigation of the structures and energetic of (N2O)n, n = 4−6 clusters. For this purpose, all of the geometries obtained from the MP2/TZ level of geometry optimization, were further subjected to geometry optimization at B2PLYPD/TZ level of theory. Subsequently, the single point energy calculations for each of the optimized geometries were performed at same level of theory using QZ basis set, followed by the estimation of CBS binding energy at B2PLYPD level using eq 2. For this purpose, the binding energies from B2PLYPD level were considered rather than MP2 level calculations. Finally, the minimal nature of all the resulted isomers was established through the vibrational frequency calculations at MP2/DZ level of theory.

III. RESULTS AND DISCUSSION It is worthwhile exploring the geometry as well as the MESP features of OCS monomer before embarking on the study of OCS clusters. The MESP isosurface for the OCS monomer is calculated at the MP2/TZ level of theory and displayed in Figure 1 using the UNIVIS visualization package.50 At MP2/TZ level geometry optimization, the calculated C−O and C−S bond lengths are 1.17 and 1.56 Å, respectively. As expected, due to the presence of lone pairs, the O atom of the OCS monomer shows a balloon-like MESP isosurface at a distance of 1.54 Å from the nucleus along the internuclear axis (see Figure 1). To the contrary, S-atom exhibits an unusual ring-shaped degenerate isosurface with radius of 2.23 Å around the sulfur atom with a positive hole along the internuclear axis. However, the minimum value of MESP corresponding to the lone pairs of the oxygen atom is approximately −0.0256 au, in contrast to 10966



Article

Figure 2. Optimized geometries of low-lying structures of (OCS)2 and (OCS)3 clusters at MP2/aug-cc-pvTZ level of theory. Red, gray, and violet spheres represent the oxygen, carbon, and sulfur atoms, respectively. See text and Table 1 for details.

Table 1. Binding Energiesa (in kcal/mol) for the OCS Dimers (n = 2) and Trimers (n = 3) Optimized MP2/aug-cc-pvTZ (MP2/TZ) and B2PLYPD/aug-cc-pvTZ (B2/TZ) Level of Theoriesb (OCS)n

ΔEMP2/TZ

ΔEMP2/CBS

ΔECCSD(T)/TZ

ΔECCSD(T)/CBS

ΔEB2/TZ

ΔEB2/CBS

2-I 2-II 2-III 2-IV 2-V 3-I 3-II 3-III 3-IV

−2.53 −2.26 −1.94 −1.32 −1.58 −7.32 −6.71 −6.81 −6.20

−2.36 −2.03 −1.68 −2.03 −1.16 −6.63 −5.98 −6.08 −5.42

−1.83 −1.70 −1.65 −1.62 −1.35 −5.16 −4.97 −4.96 −4.83

−1.67 −1.47 −1.39 −1.32 −0.93 −4.47 −4.24 −4.23 −4.05

−1.39 −1.29 −1.30 −1.20 −1.06 −3.93 −3.81 −3.77 −3.78

−1.27 −1.19 −1.21 −1.08 −0.82 −3.58 −3.50 −3.49 −3.47

Optimized energy of OCS monomer at MP2/TZ, CCSD(T)/TZ, and B2/TZ levels of theory are −510.89645, −510.93011, and −511.40740 au, respectively. bComplete basis set (CBS) limit at MP2, CCSD(T), and B2PLYPD levels of theory. See text and Figure 2 for details. a

calculated rotational constants for the (OCS)3-I isomer, along with the earlier experimental findings,19,20 are reported in Table 2. Very similar to the observation regarding dimers, the rotational constants obtained from MP2 level of theory show somewhat larger errors, whereas the values from the B2PLYPD theory are in a better agreement with their experimental counterparts. The experimental values of A, B, and C of other isomers are not reported so far and hence only the corresponding B2PLYPD/TZ level theoretical values are shown in Table 2. Most of our calculated values of A, B, and C show a trend similar to that of the theoretical findings by Valdés and Sordo.21 It may, however, be pointed out that the studies in ref 21 are performed at MP2/cc-pvTZ level of theory. No high-level ab initio theoretical as well as experimental studies on OCS tetramers and pentamers are reported till date in the published literature. Out of more than 30 trial structures, optimized at a lower basis, four favorable ones for each of tetramers and pentamers are followed up at the MP2/TZ level of theory. Due to the inherent nonlinear scaling and requirement of large computational resources, the single point energy calculations on these clusters at CCSD(T)/TZ level of theory are prohibitively difficult with the contemporary off-the-shelf hardware. These calculations are rendered possible by employing MTA. Though MTA has been extensively

energetically less favorable than the above-reported isomers. For example, it is higher in energy by about 1.5 and 1.1 mH as compared to (OCS)2-I and (OCS)2-II, respectively. More importantly, this linear dimer represents a local minimum on the PES of OCS dimer. Out of 30 trimer geometries generated from the cluster building algorithm28 and EPIC-model geometry optimization,41,42 four low-lying barrel-like conformations (see Figure 2) are found at the MP2/TZ level of geometry optimization. Very similar to the dimers, the energy gap between the isomers decreases after the CBS extrapolation at CCSD(T) and B2PLYPD levels of theory (cf. Table 1). The (OCS)3-I isomer is found to have two sets of antiparallel arrangement of the monomers mainly through C···S interactions and resembles the global minimum geometry from earlier experimental19,20 and theoretical21 investigations. All the geometries found in the current work are also in agreement with those reported by Valdés and Sordo.21 Their second most stable isomer with three parallel arrangements of the monomers also ranks second at MP2/CBS level whereas at CCSD(T)/CBS and B2PLYPD/ CBS level of theory, this isomer ranks as the third most stable isomer. At B2PLYPD/TZ level of theory, the overall dipole moment values of these isomers are 0.036, 0.084, 0.135, and 0.102 D respectively, indicating their polar nature. The 10967



Article

Table 2. Rotational Constants (cm−1) for Four Low-Lying OCS Dimers (n = 2) and Trimers (n = 3) after the Geometry Optimization at MP2/aug-cc-pVTZ (MP2/TZ) and B2PLYPD/aug-cc-pVTZ (B2/TZ) Level of Theory along with the Corresponding Experimental Values of the Isomers I and II for Dimers and of the Isomer I for Trimersa (OCS)2 2-I

2-II

2-III 2-IV 3-I

3-II 3-III 3-IV

level of theory

A

B

C

MP2/TZ B2/TZ exptb,c MP2/TZ B2/TZ exptd expte B2/TZ B2/TZ MP2/TZ B2/TZ exptf,g B2/TZ B2/TZ B2/TZ

0.1009 0.1014 0.1026 0.1312 0.1346 0.1329 0.1350 0.2265 0.1133 0.0300 0.0288 0.0283 0.0328 0.0289 0.0315

0.0457 0.0427 0.0421 0.0371 0.0344 0.0344 0.0322 0.0263 0.0362 0.0259 0.0248 0.0246 0.0217 0.0243 0.0212

0.0315 0.0301 0.0298 0.0289 0.0274 0.0273 0.0260 0.0236 0.0351 0.0210 0.0195 0.0192 0.0164 0.0170 0.0145

(OCS)4-I isomer, four of the dimeric interactions out of the total of six are antiparallel (see Figure 3). Similarly, (OCS)4-II and (OCS)4-III are endowed with polar-nonpolar and polar− polar dimeric interactions whereas (OCS)4-IV has a polar and tilted nonpolar dimeric interactions. Due to these dimeric interactions, the rotational constants (cf. Table 4) of these isomers are found to be very close to each other even though the monomeric distributions are different from each other (cf. Table 4). At B2PLYPD/TZ level of theory, the overall dipole moments of these isomers are 0.074, 0.076, 0.0001, and 0.173 D, respectively, indicating that the (OCS)4-III isomer is almost nonpolar whereas other isomers are polar in nature. It may be noted that the dipole moments at this level of theory are, in general, in a good agreement with their MP2/TZ counterparts. Recently in a review, Ahmadi and McKellar51 have reported a symmetric top structure for the OCS tetramer [unpublished result]. The rotational constants values for this isomer are A ≈ 0.020 cm−1 and B ≈ C ≈ 0.0103 cm−1. However, a similar structure sent to the authors by Oliaee52 is found to lie around 1.0 kcal/mol higher than the present (OCS)4-I isomers and 0.5 kcal/mol higher than the (OCS)4-IV isomer at all levels of theory. In view of unfavorable energetics, this symmetric top isomer is not considered further in the present study. Similarly, four low-lying geometries of pentamers are displayed in Figure 3, and their binding energies at different levels of theory are reported in Table 3. In each of the isomers, one monomer seems to be placed over the two sets of dimers of OCS clusters (see Figure 3). Unlike the tetramers, the relative energy rank ordering of the isomers is changed with a change in level of theory. However, the most stable isomer at CCSD(T)/ CBS level of theory remains the most stable at B2PLYPD/CBS level of theory (cf. Table 3). The (OCS)5-I isomer exhibits a trigonal-planar (TBP) structure wherein the planar base consists of two S···O contacts and one C···S interaction. Very similar to the tetramers, the dimeric arrangements of the monomers are responsible for the overall stability of the isomers and rotational constants (cf. Table 4) are very close to each other. Due to the unavailability of experimental results for tetramer and pentamer, only the rotational constants corresponding to B2PLYPD/TZ level of theory are given in Table 4. However, we hope that our theoretical values will be of some use to future experimental investigations of tetramers and pentamers. A study of C···S and C···O contact distances in the OCS clusters is quite revealing (cf. Table S2 in the Supporting Information). Many of the C···S contact distances in clusters are found to be less than 3.55 Å, which is the sum of vdW radii of C and S atoms, indicating a strong C···S interaction.

a f

See text for details. bSee ref 11. cSee ref 12. dSee ref 14 eSee ref 15. See ref 19. gSee ref 20.

benchmarked on a variety of systems, it is worthwhile to further benchmark the accuracy of the MTA-based results for OCS clusters. In view of this, a comparison of the MP2 energies obtained from the full geometry optimization is made to that of the MP2 energies obtained from the MTA-based single point energy calculation, employing trimeric fragments. For both of the tetramers and pentamers, these values are found to differ from each other typically only by 0.06 mH, confirming the accuracy of MTA energetics. Since MP2 level energy is a significant part of the CCSD(T) level calculation and since the CCSD(T) calculations are performed employing the same set of fragments, the CCSD(T) results are also hoped to be accurate to a similar extent. Four different tertameric isomers are investigated at MP2 and B2PLYPD levels of theory. The binding energies of these geometries at each level of theory are reported in Table 3. The (OCS)4-III and (OCS)4-IV isomers, though structurally quite different, are energetically nearly undistinguishable at each level of theory (cf. Table 3). Though the energy gap between the isomers decreases upon the CBS extrapolation at CCSD(T) and B2PLYPD levels, the overall rank ordering of these isomers remains unaltered for all the levels of theory. In the most stable

Table 3. Binding Energies (in kcal/mol) for the OCS Tetramers (n = 4) and Pentamers (n = 5) Optimized at MP2/aug-cc-pvTZ (MP2/TZ) and B2PLYPD/aug-cc-pvTZ (B2/TZ) Levels of Theorya

a

(OCS)n

ΔEMP2/TZ

ΔEMP2/CBS

ΔECCSD(T)/TZ

ΔECCSD(T)/CBS

ΔEB2/TZ

ΔEB2/CBS

4-I 4-II 4-III 4-IV 5-I 5-II 5-III 5-IV

−11.97 −11.66 −11.63 −11.67 −16.45 −16.40 −16.31 −16.53

−10.65 −10.34 −10.33 −10.32 −14.29 −14.15 −14.08 −14.26

−8.65 −8.51 −8.31 −8.34 −11.92 −11.93 −11.87 −11.83

−7.33 −7.19 −7.01 −6.99 −9.76 −9.68 −9.64 −9.56

−6.58 −6.46 −6.38 −6.40 −9.19 −8.88 −9.17 −9.10

−5.97 −5.85 −5.78 −5.78 −8.12 −6.96 −7.98 −7.78

Complete basis set (CBS) limit at MP2, CCSD(T), and B2PLYPD levels of theory. See text and Figure 3 for details. 10968



Article

Figure 3. Optimized geometries of low-lying structures of (OCS)4 and (OCS)5 clusters at MP2/aug-cc-pvTZ level of theory. Red, gray, and violet spheres represent the oxygen, carbon, and sulfur atoms, respectively. See text and Table 3 for details.

Table 4. Rotational Constants (cm−1) for the Low-Lying OCS Tetramers (n = 4) and Pentamers (n = 5) after the Geometry Optimization at the B2PLYPD/aug-cc-pVTZ Level of Theorya

a

(OCS)4

A

B

C

4-I 4-II 4-III 4-IV 5-I 5-II 5-III 5-IV

0.0228 0.0156 0.0214 0.0185 0.0103 0.0125 0.0107 0.0116

0.0113 0.0148 0.0114 0.0128 0.0096 0.0084 0.0083 0.0090

0.0094 0.0114 0.0091 0.0010 0.0069 0.0076 0.0074 0.0071

does our MTA-based approach perform for larger clusters? As a test case, both MP2/DZ and MP2/TZ level geometry optimizations are performed for an (OCS)8 cluster. Within the MTA-framework, the MP2/DZ level job takes only 24 min per cycle whereas the full calculation requires 75 min on three Intel Core i7 CPUs @ 2.93 GHz machines with 16 GB RAM each. However, the full geometry optimization at MP2/TZ level for (OCS)8 cluster is not possible on the above-mentioned hardware. To the contrary, MTA-based MP2/TZ level calculation is indeed feasible (by employing tertameric fragments) and takes 3 h for each optimization cycle, clearly bringing out the feasibility of the calculations at higher levels of theory without significant loss of accuracy. As expected, the many-body decomposition analysis53,54 of the tetramers and pentamers at both MP2/TZ and B2PLYPD/ TZ levels of theory reveals that the two-body interaction energies are mainly responsible for the overall binding of the clusters, contributing more than 95% of the total interaction energy (cf. Table 5). Due to the adjustment of the intermonomeric distances, the percent contribution from twobodies is seen to increase from MP2/TZ level to B2PLYPD/ TZ level of theory. For example, at these levels, for (OCS)4-I isomer, the two-body contributions are 96.41% and 97.43%, respectively, whereas for (OCS)5-I isomer, these are 98.05%

See text for details.

However, many of the C···O contact distances in OCS clusters are greater than 3.10 Å, the sum of the vdW radii of C and O atoms. This implies that the side-on C···S interactions contribute significantly toward the overall stability of the OCS aggregates. Furthermore, isomers with large number of C···S contacts represent the low-energy structures. Both MP2 and B2PLYPD level calculations require high computational cost, as these are known to scale as O(N5). How

Table 5. Many-Body Decomposition Analysis and Total Interaction Energies (in kcal/mol) of Four Low-Lying Isomers Each of the (OCS)4 and (OCS)5 Clusters at MP2/aug-cc-pvTZ (MP2/TZ) and B2PLYPD/aug-cc-pvTZ (B2/TZ) Levels of Theorya (OCS)4 isomers

total

2-body

3-body

total

2-body

3-body

4-body

MP2/TZ B2/TZ MP2/TZ B2/TZ MP2/TZ B2/TZ MP2/TZ B2/TZ

−12.01 −6.61 −11.70 −6.48 −11.66 −6.40 −11.68 −6.43

−11.58 −6.44 −11.39 −6.33 −11.26 −6.28 −11.28 −6.27

−0.43 −0.17 −0.31 −0.14 −0.40 −0.12 −0.40 −0.16

−16.42 −9.16 −16.39 −8.86 −16.28 −9.15 −16.50 −9.12

−16.10 −9.04 −15.93 −8.65 −15.83 −8.95 −16.07 −8.94

−0.45 −0.22 −0.55 −0.32 −0.55 −0.29 −0.53 −0.23

0.13 0.10 0.09 0.11 0.10 0.09 0.11 0.04

I II III IV

a

(OCS)5

level of theory

See text for details. 10969



Article

and 98.69%, respectively. The corresponding three-body contributions are very small and seen to decrease in magnitude on going from MP2/TZ to B2PLYPD/TZ level (cf. Table 5). For the pentamers, the four-body interactions at both MP2/TZ and B2PLYPD/TZ levels are repulsive in nature and destabilize the overall stability of the isomers. However, these values are negligible in comparison to the total two- and three-body interactions, and hence, the overall stability of the isomers is unaffected by these interactions. Finally, for the prototypical cases, the minimal nature of all the isomers is established through the vibrational frequency calculations at MP2/DZ level of theory. OCS monomer exhibits55,56 three normal modes viz., bending mode around 540 cm−1, C−S stretch around 850 cm−1, and an asymmetric stretch C−O around 2050−2150 cm−1. Among these three modes, the asymmetric C−O stretch mode is the most intense one and regarded as the characteristic band in the vibrational spectrum of the OCS monomer and hence also for OCS clusters. For the OCS monomer, the C−O asymmetric stretching frequency at the MP2/DZ level is found to be 2061.85 cm−1 against the experimental55,56 value of 2062.20 cm−1. Thus, after the comparison of these two values, the scaling factor for MP2/DZ level of theory is taken as 1. At this level of theory, the calculated asymmetric C−O stretching frequencies for the two low-lying nonpolar and polar dimers are 2072.44 and 2068.60 cm −1 , respectively, whereas the experimental values for the nonpolar12,17 and polar13 isomers are 2072.01 and 2069.3 cm−1, respectively. Similarly, the calculated vibrational frequency for the most intense asymmetric C−O stretch for the (OCS)3-I is 2078.5 cm−1, whereas the reported experimental value20 is 2077 cm−1, indicating a good agreement of the experimental findings to those of the calculated ones. For the most stable isomer of each of the clusters, the vibrational spectrum is shown in Figure 4. With increasing cluster size, the most intense peak corresponding to the asymmetric C−O stretch exhibits a substantial blue shift, indicating the agreement with the trends shown by experiments on clusters. For both of the tetramers as well as the pentamers, all the reported isomers are almost isoenergetics in nature. Besides this, the rotational constant values of some of them are similar to each other. For investigating the similarity between the isomers, the IR frequency calculations in the asymmetric C−O frequency region are performed at MP2/DZ level of theory. These data are given in the Supporting Information (Figure S1 and Figure S2). The spectral patterns of the isomers are seen to differ from each other, although the corresponding energy values are close. For example, for the isomer pairs (OCS)4-I and (OCS)4-III and (OCS)5-I and (OCS)5-III, the peak distributions in the vibrational spectra are substantially different from each other, although the isomers are almost indistinguishable based on their rotational constant values. From the above discussion, it may be noticed that the antiparallel orientations are more dominant in small OCS clusters. However, looking at the nature of the MESP isosurfaces on OCS monomer units, antiparallel arrangements can be anticipated to be energetically less favorable in crystal structures of OCS. Hence, the parallel but shifted arrangements of the monomer units, exhibiting both end-on S···O and sideon C···S and C···O interactions, are expected to exist in the OCS crystal system. A look at the experimental crystal structure57 is indeed in agreement with this anticipation. However, the total energetics of parallel stacked linear chains,

Figure 4. Most intense (KM/mol) asymmetric C−O vibrational stretching frequency (cm−1) of the (OCS)n clusters, for n = 2−5 at MP2/aug-cc-pvDZ level of theory, shows a substantial blue shift with respect to that of the asymmetric C−O stretch (2061.85 cm−1) in the OCS monomer. See text for details.

as seen in the crystal, is computationally arduous task and is beyond the scope of the present study.

IV. CONCLUDING REMARKS Capturing the energetically low-lying geometries of molecular clusters employing correlated ab initio computations is a challenging task. A highlight of the present work is the use of molecular electrostatic potential (MESP) for systematic growth of clusters from monomers to oligomers. MESP is indeed known to capture the direction of weak interactions, as shown by the studies in our group over the past decade. The MESPguided cluster building algorithm28 is employed for the generation of the initial trial geometries of the (OCS)n cluster for n = 2−5. All of the CCSD(T) level calculations on tetramers and pentamers are indeed made possible on routinely available hardware, employing the powerful tool of molecular tailoring approach (MTA). Actual full CCSD(T) calculations on systems beyond (OCS)3 are not possible on the hardware used. In order to explore the suitability of dispersion-corrected density functional theory for studying molecular clusters, a follow-up is done at B2PLYPD level of theory. These calculations led to more accurate values of rotational constants of (OCS)n clusters for n = 2−5, than those obtained from MP2 10970



Article

Commission (UGC), New Delhi and Council of Scientific and Industrial Research (CSIR), New Delhi for the award of Senior Research Fellowships, respectively. Authors are thankful to Dr. Oliaee for his useful communication and Dr. McMeeking for sending us the CIF of OCS structure.

level of theory. Five low-lying geometries for dimers and four each for the trimers, tetramers and pentamers have been reported at these levels of theory. The structural parameters of dimers and trimers derived from these calculations are in agreement with those derived from earlier experimental as well as theoretical investigations. Generally the dimeric OCS (mostly antiparallel) patterns are found to be retained in tetramers and pentamers and are responsible for the overall stability of these clusters. The rotational constants of the isomers of (OCS)5 are found to be very close to each other even though the arrangements of the monomers in these isomers are different. With increasing cluster size, the most intense peak corresponding to the asymmetric C−O stretch exhibits a substantial blue shift with respect to the monomer asymmetric stretch, in agreement with the experimental results.51 We also notice the presence of the ring-shaped degenerate MESP isosurface in the vicinity of sulfur atom in OCS monomer units (as seen in Figure 1) leading to the long-range C...S interactions rather than C···O interactions. Hence, small aggregates endowed with antiparallel arrangement of monomers with more number of C···S contacts represent the most favorable conformers. A further noteworthy outcome of the present study is the existence of linear chains in OCS aggregates, showing end-on S···O contacts. Such an interaction may be termed as the sulfur bond, following the trend in the current literature, to name such weak interactions as halogen or carbon bonds etc. Such linear chains are indeed noticed in the crystal structure.57 However, the computational treatment of large aggregates showing parallel-displaced linear chain arrangements is a formidable task at present. In summary, it may be concluded that a judicious combination of the cluster building algorithm coupled with the state-of-the-art molecular tailoring approach and use of dispersion-corrected density functionals can be profitably used for the ab initio treatment of large molecular clusters. Further, the estimation of the binding energies at complete basis set limit (CBS), especially within the contemporary “gold standard” of quantum chemistry viz. CCSD(T)/CBS level theory, is within reach with the use of molecular tailoring approach.

■

■

(1) Keutsch, F. N.; Cruzan, J. D.; Saykally, R. J. The Water Trimer. Chem. Rev. 2003, 103, 2533−2578. (2) Kim, K. S.; Tarakeshwar, P.; Lee, J. Y. Molecular Clusters of πSystems: Theoretical Studies of Structures, Spectra and Origin of Interaction Energies. Chem. Rev. 2000, 100, 4145−4186. (3) Felker, P. M.; Maxton, P. M.; Schaeffer, M. W. Nonlinear Raman Studies of Weakly Bound Complexes and Clusters in Molecular Beams. Chem. Rev. 1994, 94, 1787−1805. (4) Celii, F. G.; Janda, K. C. Vibrational Spectroscopy, Photochemistry and Photophysics of Molecular Clusters. Chem. Rev. 1989, 86, 507−520. (5) Seinfeld, J. Atmospheric Chemistry and Physics; J. Wiley: London, 2006. (6) Gosselin, R. E.; Smith, R. P.; Hodge, H. C. Clinical Toxicology of Commercial Products, 5th ed.; Williams and Wilkins: Baltimore, 1984; pp III−201. (7) Landis, G. A. Astrobiology: The Case for Venus. J. Br. Interplanet. Soc. 2003, 56, 250−254. (8) Ono, Y.; Osuch, E. A.; Ng, C. Y. Molecular Beam Photoionization Study of OCS, (OCS)2, (OCS)3 and OCS•CS2. J. Chem. Phys. 1981, 74, 1645−1651. (9) Hoffbauer, M. A.; Liu, K.; Glese, C. F.; Gentry, W. R. Infrared Photodissociation of Ar•OCS, (OCS)2 and (OCS)3 in Pulsed Molecular Beams: Spectroscopy and Dynamics. J. Phys. Chem. 1983, 87, 2096−2102. (10) Lobue, J. M.; Riocand, J. K.; Novick, S. E. Qualitative structure of (CO2)2 and (OCS)2. Chem. Phys. Lett. 1984, 112, 376−380. (11) Randell, R. W.; Wilkie, J. M.; Howard, B. J.; Muenter, J. S. Infrared Vibration-Rotation Spectrum and Structure of OCS Dimer. Mol. Phys. 1990, 69, 839−852. (12) Afshari, M.; Dehghany, M.; McKellar, A. R. W.; MoazzenAhmadi, N. New Infrared Bands of Nonpolar OCS Dimer and Experimental Frequencies for Two Intermolecular Modes. J. Chem. Phys. 2012, 137, 054304. (13) Afshari, M.; Dehghani, M.; Abusara, Z.; Moazzen-Ahmadi, N.; McKellar, A. R. W. Observation of the “Missing” Polar OCS Dimer. J. Chem. Phys. 2007, 126, 071102. (14) Minei, A. J.; Novick, S. E. Microwave Observation of the “Recently Found” Polar OCS Dimer. J. Chem. Phys. 2007, 126, 101101. (15) Afshari, M.; Dehghani, M.; Abusara, Z.; Moazzen-Ahmadi, N.; McKellar, A. R. W. Infrared Spectra of the Polar Isomer of the OCS Dimer: (16O12C32S)2, (16O12C34S)2 and (16O13C32S)2. Chem. Phys. Lett. 2007, 442, 212−216. (16) Bone, R. G. A. An Investigation of the Structure of Weakly Bound (OCS)2. Chem. Phys. Lett. 1993, 206, 260−270. (17) Brown, J.; Wang, X. -G.; Dawes, R.; Carrington, T., Jr. Computational Study of the Rovibrational Spectrum of (OCS)2. J. Chem. Phys. 2012, 136, 134306. (18) Connelly, J. P.; Bauder, A.; Chisholm, A.; Howard, B. Internal Motion Effects in the Microwave Spectrum of OCS Trimer. Mol. Phys. 1996, 88, 915−929. (19) Peebles, R. A.; Kuczkowski, R. L. The OCS Trimer: Isotopic Studies, Structure and Dipole Moment. J. Phys. Chem. A 1999, 103, 6344−6350. (20) Afshari, M.; Dehghani, M.; Abusara, Z.; Moazzen-Ahmadi, N.; McKellar, A. R. W. Infrared Spectra of the OCS Trimer. J. Chem. Phys. 2007, 127, 144310. (21) Valdés, H.; Sordo, J. A. (OCS)3 van der Waals Complex: A Theoretical Study. J. Phys. Chem. A 2003, 107, 7845−7851.

ASSOCIATED CONTENT

S Supporting Information *

The detailed electronic energies, Cartesian coordinates for each of the isomers of the (OCS)n cluster for n = 2−5, for optimized (at both MP2/aug-cc-pVTZ and B2PLYPD/aug-cc-pVTZ level of theory) geometries, table for number of side-on C···S and C···O contacts and contact distances and the IR spectra for tetramers and pentamers are given. This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS S.R.G. is thankful to the Department of Science and Technology (DST) for the award of a J. C. Bose National Fellowship. N.S. and G.S. are thankful to the University Grants 10971



Article

(22) Maillet, J. -B.; Boutin, A.; Buttefey, S.; Calvo, F.; Fuchs, A. H. From Molecular Clusters to Bulk Matter. I. Structure and Thermodynamics of Small CO2, N2 and SF6 Clusters. J. Chem. Phys. 1998, 109, 329−337. (23) Tokmachev, A. M.; Tchougreeff, A. L.; Dronskowski, R. Hydrogen-Bond Networks in Water Clusters (H2O)20: An Exhaustive Quantum-Chemical Analysis. Chem. Phys. Chem. 2010, 11, 384−388. (24) Muenter, J. S. An Intermolecular Potential Function Model Applied to Acetylene Dimer, Carbon Dioxide Dimer and Acetylene. J. Chem. Phys. 1991, 94, 2781−2793. (25) Tsuzuki, S.; Klopper, W.; Lüthi, H. -P. High-level ab initio Computations of Structures and Relative Energies of Two Isomers of the CO2 Trimer. J. Chem. Phys. 1999, 111, 3846−3854. (26) Helgaker, T.; Klopper, W.; Tew, D. P. Quantitative Quantum Chemistry. Mol. Phys. 2008, 106, 2107−2143. (27) Dawes, R.; Wang, X. G.; Jasper, A. W.; Carrington, T., Jr. Nitrous oxide dimer: A New Potential Energy Surface and Rovibrational Spectrum of the Nonpolar Isomer. J. Chem. Phys. 2010, 133, 134304. (28) Yeole, S. D.; Gadre, S. R. Molecular Cluster Building Algorithm: Electrostatic Guidelines and Molecular Tailoring Approach. J. Chem. Phys. 2011, 134, 084111. (29) Ganesh, V.; Dongare, R. K.; Balanarayan, P.; Gadre, S. R. Molecular Tailoring Approach For Geometry Optimization of Large Molecules: Energy Evaluation and Parallelization Strategies. J. Chem. Phys. 2006, 125, 104109. (30) Gadre, S. R.; Ganesh, V. Molecular Tailoring Approach: Towards PC-Based ab initio Treatment of Large Molecules. J. Theor. Comput. Chem. 2006, 5, 835−855. (31) Rahalkar, A. P.; Ganesh, V.; Gadre, S. R. Enabling ab initio Hessian and Frequency Calculations of Large Molecules. J. Chem. Phys. 2008, 129, 234101. (32) Rahalkar, A. P.; Yeole, S. D.; Ganesh, V.; Gadre, S. R. In Linear Scaling Techniques in Computational Chemistry and Physics; Zalesny, R., Papadopoulos, M. G., Mezey, P. G., Leszczynski, J., Eds.; Springer: Heidelberg, 2011. (33) Schwabe, T.; Grimme, S. Double-hybrid Density Functionals with Long-Range Dispersion Corrections: Higher Accuracy and Extended Applicability. Phys. Chem. Chem. Phys. 2007, 9, 3397−3406. (34) Frisch, M. J.; et al. Gaussian 09, revision A.1; Gaussian, Inc.: Wallingford, CT, 2009. (35) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (36) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (37) Mehta, G.; Gunasekaran, G.; Gadre, S. R.; Shirsat, R. N.; Ganguly, B.; Chandrasekhar, J. Electrophilic Additions to 7Methylenenorbornenes and 7-Isopropylidenenobornenes: Can Remote Substituents Swamp Electrostatic Control of π−Face Selectivity? J. Org. Chem. 1994, 59, 1953−1955. (38) Suresh, C. H.; Koga, N.; Gadre, S. R. Molecular Electrostatic Potential and Electron Density Topography: Structure and Reactivity of (Substituted Arene) Cr(CO)3 Complexes. Organometallics 2000, 19, 3008−3015. (39) Suresh, C. H.; Koga, N.; Gadre, S. R. Revisiting Markovnikov Addition to Alkenes via Molecular Electrostatic Potential. J. Org. Chem. 2001, 66, 6883−6890. (40) Gadre, S. R.; Bhadane, P. K. Patterns in Hydrogen Bonding via Electrostatic Potential Topography. J. Chem. Phys. 1997, 107, 5625− 5626. (41) Gadre, S. R.; Pundlik, S. S. Complementary Electrostatics for the Study of DNA Base-Pair Interactions. J. Phys. Chem. B 1997, 101, 3298−3303. (42) Pundlik, S. S.; Gadre, S. R. Structure and Stability of DNA Base Trimers: An Electrostatic Approach. J. Phys. Chem. B 1997, 101, 9657−9662.

(43) Halkier, A.; Klopper, W.; Helgaker, T.; Jørgensen, P.; Taylor, P. R. Basis Set Convergence of the Interaction Energy of Hydrogen Bonded Complexes. J. Chem. Phys. 1999, 111, 9157−9167. (44) Limaye, A. C.; Gadre, S. R. A General Parallel Solution to the Integral Transformation and Second-Order Møller-Plesset Evaluation on Distributed Memory Parallel Machines. J. Chem. Phys. 1994, 100, 1303−1307. (45) Ganesh, V. MeTA studio: A Cross Platform, Programmable IDE for Computational Chemist. J. Comput. Chem. 2009, 30, 661−672. (46) Sinnokrot, M. O.; Sherrill, C. D. Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer: Sandwich, TShaped and Parallel-Displaced Configurations. J. Phys. Chem. A 2004, 108, 10200−10207. (47) Sherrill, C. D.; Takatani, T.; Hohenstein, E. G. An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H2S. J. Phys. Chem. A 2009, 113, 10146−10159. (48) Bates, D. M.; Tschumper, G. S. CCSD(T) Complete Basis Set Limit Relative Energies for Low-Lying Water Hexamer Structures. J. Phys. Chem. A 2009, 113, 3555−3559. (49) Yeole, S. D.; Sahu, N.; Gadre, S. R. High-Level ab initio Investigations on Structures and Energetics of N2O Clusters. J. Phys. Chem. A 2013, 117, 8591−8598. (50) Limaye, A. C.; Gadre, S. R. UNIVIS-2000: A Comprehensive Visualization Package. Curr. Sci. (India) 2001, 80, 1296−1301. (51) Moazzen-Ahmadi, N.; McKellar, A. R. W. Spectroscopy of Dimers, Trimers and Large Clusters of Linear Molecules. Int. Rev. Phys. Chem. 2013, 32, 1−40. (52) Oliaee, J. N. Private Communication. (53) 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. (54) Kulkarni, A. D.; Ganesh, V.; Gadre, S. R. Many-Body Interaction Analysis: Algorithm Development and Application to Large Molecular Clusters. J. Chem. Phys. 2004, 121, 5043−5050. (55) Forbes, G. S.; Cline, J. E. The Photolysis and Extinction Coefficients of Gaseous Carbonyl Sulfide. J. Am. Chem. Soc. 1939, 61, 151−154. (56) McCarthy, M. I.; Vaida, V. Electronic Spectrum of OCS at 62000−72000 cm−1. J. Phys. Chem. 1988, 92, 5875−5879. (57) Overell, J. S. W.; Pawley, G. S.; Powell, B. M. Powder Refinement of Carbonyl Sulphide. Acta Cryst. B 1982, 38, 1121−1123.

10972


Exploring Structures and Energetics of Large OCS Clusters by

Recommend Documents