Methanol clusters (CH3OH)n, n = 3–6 in external electric fields: Densityfunctional theory approachDhurba Rai, Anant D. Kulkarni, Shridhar P. Gejji, and Rajeev K. Pathak Citation: J. Chem. Phys. 135, 024307 (2011); doi: 10.1063/1.3605630 View online: http://dx.doi.org/10.1063/1.3605630 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v135/i2 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS 135, 024307 (2011)

Methanol clusters (CH3OH)n, n = 3–6 in external electric fields:Density functional theory approach

Dhurba Rai,1,a) Anant D. Kulkarni,2,3,b) Shridhar P. Gejji,2 and Rajeev K. Pathak1,b)

1Department of Physics, University of Pune, Pune - 411007, India2Department of Chemistry, University of Pune, Pune - 411007, India3Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA

(Received 2 April 2011; accepted 9 June 2011; published online 11 July 2011)

Structural evolution of cyclic and branched-cyclic methanol clusters containing three to sixmolecules, under the influence of externally applied uniform static electric field is studied withinthe density functional theory. Akin to the situation for water clusters, the electric field is seen tostretch the intermolecular hydrogen bonds, and eventually break the H-bonded network at certaincharacteristic threshold field values of field strength in the range 0.009–0.016 a.u., yielding linear orbranched structures with a lower energy. These structural transitions are characterized by an abruptincrease in the electric dipole moment riding over its otherwise steady nonlinear increase with theapplied field. The field tends to rupture the H-bonded structure; consequently, the number of hydro-gen bonds decreases with increasing field strength. Vibrational spectra analyzed for fields appliedperpendicular to the cyclic ring structures bring out the shifts in the OH ring vibrations (blueshift)and the CO stretch vibrations (redshift). For a given field strength, the blueshifts increase with thenumber of molecules in the ring and are found to be generally larger than those in the correspondingwater cluster counterparts. © 2011 American Institute of Physics. [doi:10.1063/1.3605630]

I. INTRODUCTION

Understanding the nature of the hydrogen-bonded liq-uids from a molecular standpoint has attracted a great dealof interest.1–5 Water and methanol, being hydrogen-rich, con-stitute important prototypes of such liquids with markedlydifferent hydrogen bonding patterns due to the presence ofhydrophobic methyl group in the latter amphiphilic species.Despite numerous investigations,6–17 no general consensushas been reached to date, whether the predominant structuralmotifs in liquid water and methanol are chains, or small orlarge ring structures. Conventional description of liquid wateras a tetrahedrally coordinated network has evoked many in-tense discussions.18–20 However, both experiments and theo-retical studies10, 13, 21–28 have abandoned the traditional view29

of water-methanol mixture in which the normal water struc-tures in the immediate surroundings of methyl headgroups getenhanced upon mixing, thereby forming microscopic “ice-bergs” around the methyl headgroups. The x-ray emissionspectroscopic study by Guo et al.10 and the neutron diffrac-tion experiment by Dixit et al.26 provide conclusive evi-dence that the hydrophilic OH end of methanol forms anordered hydrogen-bonded network with water molecules ac-commodating the methyl headgroups within the water struc-ture. The hydrogen-bonded network in water is thus notlost upon mixing up with methanol, and the diminutive en-tropy increase (which, for decades, was believed to be dueto iceberg formation) is actually attributed to this peculiar

a)Present address: School of Chemistry, Tel-Aviv University, Tel-Aviv 69978,Israel.

b)Authors to whom correspondence should be addressed. Electronic ad-dresses: akulkarn@umn.edu and pathak@physics.unipune.ac.in.

property of ordered and incomplete mixing at the molecularlevel.

Since methanol differs only in the presence of a methylgroup in place of a hydrogen atom in water molecules,the lowest energy structure of small methanol clusters,(CH3OH)n, n = 2–5, are markedly similar to the water clus-ter counterparts.30–32 Methanol dimer exhibits a linear hy-drogen bond, while trimer, tetramer, and pentamer are ringstructures with dangling methyl groups oriented alternately“up” (u) and “down” (d) from the ring formed by the oxy-gen atoms.33, 34 The optimized potential for liquid simulation(OPLS) model35 predict36–38 the results that are contradic-tory with the high-level ab intio and the density functionaltheory (DFT) calculations.31, 39–42 Quantum chemical calcula-tions predict C1 and S4 symmetries for trimer and tetramerthat are in confirmation with the experimental33, 34 infrared(IR) spectra in the OH stretching region. The lowest energyconfigurations for hexamer through decamer are found to bering structures;30, 40–43 in particular, the hexamer and the oc-tamer exhibit, respectively, the S6 and S8 symmetries, whileheptamer, nanomer, and decamer manifest themselves as dis-torted rings; whereas the other cyclic ring hexamer possessesa C2 symmetry. In tetramer and pentamer, the branched cyclicstructures are determined to correspond to the next lowest en-ergy configurations.36, 40 Such a tetramer has actually beenidentified in laser irradiated44 methanol aggregates trapped ina solid nitrogen matrix.

Some investigations in the context of electro-wettinghave been carried out on the effect of an externally appliedelectric field on alcohols.45 A study by Bateni et al.45 re-veals that the applied electrostatic field deforms an alcoholdrop, causing the angle of contact to increase with the field.Besides, the shift in angle of contact and the change in sur-

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024307-2 Rai et al. J. Chem. Phys. 135, 024307 (2011)

face tension due to applied field are found to be larger foralcohols with long chain of molecules. Thus, applied elec-tric fields have significant, macroscopically observable effecton the structural and dynamical properties of H-bonded liq-uids. On the other hand, a detailed study of field effects at themolecular level is thus indispensable for understanding the in-teresting macroscopic phenomena exhibited by H-bonded liq-uids, such as the “water bridge”46, 47 and others.48, 49 Molecu-lar dynamics simulation study50 employing an OPLS modelpotential35 predicts an enhancement of methanol hydrogenbond structure with increasing electric field strength in therange 0.000–0.019 a.u. Moreover, the linear distribution prob-ability of the O–H···O unit was found to increase with fieldstrength. A recent investigation51 based on a statistical molec-ular model suggests that the average number of H-bonds inmethanol increases up to the field strength of 0.017 a.u. Be-yond this, the H-bond structure gets disrupted due to break-ing of the H-bonds owing to the high-degree dipolar align-ment leading to decrease in the average number of hydrogenbonds.

Effects and structural reformations brought about by anexternally imposed electric field on the water clusters (H2O)n,where n = 3–8 have been described by means of model po-tential studies52–54 and also within the DFT framework.55–57

It is found that the applied field weakens the hydrogen-bondnetwork and “opens up” the water cluster at threshold fieldto form a (local) energy-minimum configuration comprised alinear, branched, or netlike structure with the electric dipolemoment aligned along the field axis, exhibiting an abruptincrease in the dipole moment for certain critical field val-ues, characterizing structural transitions. A very recent work58

purports that alignment of the dipoles with electric field isstronger in the liquid phase than in the vapor phase due toenhanced cooperative effects in the liquid phase.

The spirit underlying our present DFT calculations is toprovide detailed insights into the effects the static and uni-form electric fields have on the energy-minimum cyclic andbranched-cyclic (CH3OH)n, n = 3–6 clusters, with regardsto structure, energetics, and the vibrational frequencies. Also,of particular importance, in view of both methanol and waterbeing H-bonded liquids with widespread applications, will bethe comparison of the field effects on water and methanol atthe molecular-cluster level.

II. METHODOLOGY

We have employed the GAUSSIAN-03 suite ofprograms59 with the popular black-box type B3LYP hybridexchange-correlation functional60 to investigate the structuraltransitions, changes in the dipole moment, and the energeticsof cyclic and branched-cyclic methanol clusters (CH3OH)n,n = 3–6 under the influence of uniform static externally ap-plied bipolar electric fields. All calculations were carried outby fully optimizing the cluster geometry in the presence offield using the 6–311++G(2d,2p) basis set. This basis setis found to be adequate for investigating hydrogen bondedmolecular clusters61–64 and clusters in presence of externalelectric field.65, 66 We have performed vibrational frequencycalculations in presence of field to ascertain the optimized

structures indeed represent local minima on the potential en-ergy surface (PES). A cluster during its evolution under theinfluence of applied field may pass through a transition state(TS; a first order saddle point on the PES) essentially a criti-cal point with vanishing energy-gradient, characterized by ex-actly one pure imaginary vibrational frequency. Unless men-tioned otherwise, the vibrational frequencies of the clusterscomputed in the presence of electric field were all found to bereal, confirming local minimal nature on the PES.

Throughout the work, we have employed atomic units forfield strengths; 1 a.u. of electric field strength = 51.42 V/Å.The applied bipolar field strength was increased graduallyfrom zero in steps of 0.001 a.u. along the direction of per-manent electric dipole moment of a cluster and also alonga specified direction in the clusters having negligible dipolemoment. In view of inherent perturbative nature of the theo-retical description, we have considered rather low or moder-ate fields of magnitude in the range (∼10−3–10−2 a.u.), henceavoiding numerically large field strengths. Fields in this rangeare found to exist in zeolite67 and protein cavities,68 and inthe vicinity of nano-tips employed in scanning tunneling andatomic force microscopy.69 Thus, in the present work, wehave explored the offshoot of applied fields far away from thevery-high field regime that may cause fragmentation of theclusters.

III. RESULTS

A. Structural evolution of methanol clusters

We consider energetically stable cyclic (p) and thebranched-cyclic (p)+q methanol clusters comprising 3–6molecules. Here, “p” denotes the number of methanols in thecyclic structure and “q” denotes the number of methanols ina branch. The representative structures include a ring struc-ture (C1 symmetry) for trimer, a cyclic (S4), and a branchedcyclic ((3)+1) structure for tetramer, four pentamers (C1,(3)+2, (4)+1, (3)+1+1) and hexamers, namely, S6, C2,(5)+1, (4)+2. We first consider the energy-minimum cyclicconformers for fields applied perpendicular (F⊥) and paral-lel (F||) to the cyclic ring, followed by that on the branched-cyclic structures for field applied along the permanent dipolemoment.

1. Cyclic clusters

The minimum-energy cyclic methanol clusters consistof molecules with dangling methyl headgroups oriented al-ternately “up” (u) and “down” (d) with reference to thering formed by oxygen atoms. Figures 1(a)–1(d) depict thefield free configurations namely (udd), (udud), (ududu) and(ududud) for trimer, tetramer, pentamer, and hexamer, respec-tively, leading to Sn symmetry for even size clusters and C1 forodd ones. The next lowest energy conformer of cyclic hex-amer (not shown herein) exhibits C2 symmetry with a (ud-dudd) configuration.

As a consequence of the leading −�μ · �F interaction fornonzero dipole moments �μ of the cluster, the “up” dan-gling methyl headgroup flips to “down” along the field (F⊥),

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024307-3 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

FIG. 1. Structural evolution of cyclic methanol clusters (p) (p = 3–6) under the action of fields applied perpendicular and parallel to the cyclic ring. Insetsdepict the field free structures on which fields are applied as indicated. Solid arrow represents the electric dipole moment of the cluster.

when applied perpendicular to the cyclic ring, resulting intothe structural transition from (udd) → (ddd) (C3), (udud)→ (dddd) (C4), (dudud) → (ddddd) bowl configurations at therespective threshold field strengths (Fd) of 0.004 a.u., 0.004a.u., and 0.005 a.u. The nearly C3 symmetric (ddd) bowl con-figuration is retained up to 0.026 a.u. beyond which the geom-etry gets distorted but still maintains the ring structure evenfor the field strength of 0.034 a.u. applied in the same direc-tion (cf. Fig. 1(a)). The transformed bowl configuration withall methyl headgroups aligned roughly along the applied fieldis a local minimum on its PES. It is gratifying that such a con-figuration has actually been identified experimentally34 and isfound to be energetically less stable than the global energy-minimal configuration (udd).39, 41 The C4 symmetric (dddd)configuration is retained up to the field strength of 0.038 a.u.which, however, slips into a first order saddle point charac-terized by one imaginary frequency on its PES for the fieldstrength of 0.034 a.u. and above, while still sustaining the ringstructure for a field strength as large as 0.040 a.u. The struc-tures for fields between 0.038 a.u. and 0.040 a.u. are all saddlepoints with exactly one imaginary frequency. Beyond 0.040a.u., however, the cluster starts to fragment. In contrast to theother two configurations, the (ddddd) “bowl” configuration isnot symmetric at low field values, however, becomes nearlyC5 symmetric for the field strength of 0.012 a.u. onward, afeature preserved up to 0.024 a.u. (cf. Fig. 1(c)). Local minima

on the PES with all five methyl headgroups aligned roughlyalong the field direction have been obtained even for slightlyhigher field values in the range ∼0.026–0.030 a.u. These fieldinduced structural transitions are very similar to those in waterclusters52, 53, 55 and are discernible with a characteristic abruptincrease in the dipole moment profile (elaborated in Subsec-tion B).

As in the clusters discussed above, the dangling “up”(u) methyl headgroups in S6 and C2 symmetric cyclic hex-amers are all forced by the field to align themselves down-ward (d) for F⊥ at the field strengths (Fd) of 0.004 a.u. and0.008 a.u, respectively, leading to a structural transition from(dududu) → (dddddd) (C3) (refer Fig. 1(d)) and (uddudd) →(dddddd) (C2) configuration. In contrast to the cyclic waterhexamer, the S6 methanol cluster retains the transformed C3

symmetric structure even for the field strength of 0.024 a.u.For fields in the range (∼0.026–0.028 a.u), the optimum struc-ture amounts to a slight distortion of the C3 symmetric struc-ture. The nearly C2 symmetric (dddddd) configuration holdsup to the field strength of 0.018 a.u. Beyond this field, thecluster gets distorted but still maintains the ring configura-tion up to field of 0.026 a.u. Summing up, the effect of theperpendicular field F⊥ does not lead to a sharp distortion ofthe cyclic structure but rather to a conformational transitionto another cyclic cluster, namely, bowl configuration of lowerenergy. Unlike F⊥, the field (F||) applied in the plane of the

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024307-4 Rai et al. J. Chem. Phys. 135, 024307 (2011)

clusters distorts the cyclic ring forcing one of the bonds toconsiderably weaken. This triggers structural transitions fromcyclic to linear chains at the threshold field strengths (Ft);0.009 a.u., 0.013 a.u., 0.014 a.u., and 0.016 a.u. for trimerthrough hexamer (S6), respectively. The linear chain struc-tures get aligned along the field direction, and the orienta-tions of each pair of methanol molecules in the chains resem-ble somewhat the structure of the methanol dimer. Through-out their evolution (ring · · · → chain), the structures turn outto be local minima on the multi-dimensional PES. Interest-ingly, such a ring opening to linear chain in case of trimerupon IR laser irradiation has been studied in Ref. 44. Vi-brational excitation of OH stretching modes by IR irradia-tion around 3450 cm−1 breaks one of the H-bonds leadingto the conversion of (uud) and (ddd) configurations to variouschain structures. However, the field induced structural transi-tion, namely, ring → chain, is once again due to the domi-nant −μ · �F interaction prevailing over the intermolecular in-teraction energy that defines the structure at zero or very lowfields. Alignment of monomer dipoles along the applied fieldbecomes ubiquitous: the cyclic structure eventually opens upto form a linear chain at threshold field, Ft. The threshold fieldvalues (Fd and Ft) for cyclic trimer through hexamer alongwith that for branched-cyclic conformers are summarized inTable I.

Figure 2 depicts the variation of average electroniccharge density ρc at the O···H bond critical point (bcp) asa function of F⊥. Bader’s theory70 of “Atoms in Molecules,”and extensions due to Cioslowski and co-workers,71 imple-mented in GAUSSIAN suite of programs were used to calculatethe charge densities at bcp. It is noteworthy from the figuresthat ρc increases as we go from trimer to hexamer due to en-

TABLE I. Comparison between the threshold values of the electric fields Fd,and Ft for methanol and water clusters. Fd: Minimum field at which dangling-OH and CH3 groups in cyclic water and methanol clusters get aligned inthe direction of the applied field without breaking the hydrogen bonds. Ft:Minimum field required to induce a configurational (geometry) transforma-tion by breaking a hydrogen bond. (Note that 1 a.u. of electric field strength= 51.42 V/Å).

Fd Ft

(a.u.) (a.u.)

Cluster n Structure code Methanol Watera Methanol Watera

3 (3)⊥ 0.004 0.004(3)|| . . . . . . 0.009 0.007

4 (4)⊥ 0.004 0.005(4)|| . . . . . . 0.013 0.012

(3) + 1 . . . . . . 0.0105 (5)⊥ 0.005 0.005

(5)|| . . . . . . 0.014 0.014(4) + 1 . . . . . . 0.014(3) + 2 . . . . . . 0.006

(3) + 1 + 1 . . . . . . 0.0086 (6)⊥ 0.004 0.004

(6)|| . . . . . . 0.016 0.012(6′) 0.008

(5) + 1 . . . . . . 0.016(4) + 2 . . . . . . 0.012

aThreshold field values calculated at the 6–311++G(2p,2d) basis set (see Ref. 56).

hancement in hydrogen bonding cooperativity with the clustersize and also that the field free (ρc)methanol > (ρc)water. How-ever, when the field is applied perpendicularly, ρc is seen todecrease gradually, and then falls abruptly at F⊥ = Fd be-yond which it once again decreases steadily. Interestingly,

FIG. 2. Variation of average electronic charge density ρc(e/a3o ) (in a.u.) calculated at the hydrogen bond critical points for field applied perpendicular to the

plane of the cyclic ring methanol (M) clusters. The lower curve depicts the same for cyclic water (W) clusters under similar field orientation.

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024307-5 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

FIG. 3. Representative cluster configurations depicting the structural transition of branched-cyclic clusters brought about by the fields applied along the dipolemoment shown by the solid arrowheads. Dagger (†) denotes a hydrogen bond in which C–H acts as a proton donor.

although the trends in variation of ρc with field are similar inboth methanol and water cluster, (ρc)methanol decreases com-paratively faster than (ρc)water does. This suggests that themethanol clusters may open up at slightly lesser magnitudeof applied field than the corresponding water clusters for suf-ficiently high field; F⊥ � Fd and Ft. Unlike F||, F⊥ may causefragmentation of cluster into smaller units by rupturing two ormore H-bonds.

2. Branched-cyclic clusters

We consider six branched-cyclic clusters, tetramerthrough hexamer, with the field applied in the directionof permanent dipole moment. As shown in Fig. 3(a), thebranched-cyclic tetramer, (3)+1, is comprised of (udd) con-figured cyclic trimer with a monomer H-bonded to one ofthe methanols oriented downward “d” in the ring. While thisfeature is seen to be preserved up to 0.009 a.u., the clusteropens up at the 0.010 a.u. field to form energetically favorablebranched-chain labeled by 2+22. We number the chain fromthe free OH end, and the point of hydrogen bonding of the“branch” to the principal chain (indicated by the underscore)is labeled by a subscript on the branch. Thus, the 2+22 struc-ture is a branched-chain tetramer composed of a dimer withtwo branched methanols attached to the second methanol hav-ing no free hydroxyl end. As in cyclic clusters, this structuraltransformation is accompanied by abrupt jumps in the electricdipole moment, riding over its steady and nonlinear rise withthe applied field. Once again, the transformed branched-chainstructure has all vibrational frequencies real.

The lowest branched-cyclic pentamer, namely, (4)+1, iscomprised (udud) cyclic tetramer with a monomer H-bondedto the cyclic ring. The applied field distorts the ring structure

and weakens one of the bonds in the ring considerably forfield strength above 0.010 a.u., causing the structure to openout to form a 3+23 branched-chain at the field strength of0.014 a.u. The chain gets aligned roughly along the field di-rection (cf. Fig. 3(b)). The next lowest energy branched-cyclicpentamer, (3)+2, is an extension of the (3)+1 structure witha methanol attached to the branch monomer H-bonded to thecyclic ring. This structure is seen to open out to form a linearchain at field strength, Ft = 0.006 a.u. The (3)+1+1 pentamerconsists of a (3)+1 structure with a monomer attached to themethanol oriented upward “u” in the (udd) configuration ofcyclic trimer. As shown in Fig. 3(d), this structure is retainedup to the field strength of 0.007 a.u., and opens up at 0.008a.u. to form a cyclic tetramer with a monomer attached on it,i.e., (4′)+1. The ring configuration in the transformed struc-ture (which is primed for distinction from the actual cyclicstructure) contains intermolecular hydrogen bond (indicatedby a dagger (†)) formed between C–H of a methanol and theoxygen of the other methanol in the ring. Not surprisingly, theC–H···O H-bond length is comparatively longer than that forthe O–H···O hydrogen bond. For instance, at the field strengthof 0.008 a.u., the C–H···O hydrogen bond length is 2.509Å against an average of 1.897 Å for the O–H···O hydrogenbonds. Throughout their evolution under the influence of thefield, these structures manifest local minima on the PES.

The two branched-hexamers considered here are (5)+1and (4)+2. The lowest energy structure, (5)+1, is com-prised (dudud) configured cyclic pentamer with a monomerH-bonded to one of the methanols oriented downward in thering. The applied field distorts the ring structure and consid-erably weakens one of the bonds in the ring for field strengthabove 0.010 a.u. The resultant structure opens up, at the field

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024307-6 Rai et al. J. Chem. Phys. 135, 024307 (2011)

strength of 0.016 a.u. yielding a linear chain with a cyclictrimer at the end. As in the (4′) + 1 structure, the cyclic trimerunit H-bonded to the chain in the (3′) + 3 structure contains ahydrogen bond in which C–H of methyl group acts as a pro-ton donor. As a consequence, herein too the C–H···O H-bondlength is comparatively longer than that of the O–H···O hy-drogen bonds. The (4)+2 structure is an extension of (4)+1with a methanol attached to the branch monomer. Field ap-plied along its permanent dipole moment distorts the ringstructure leading one of its bonds to weaken for the fieldstrength of 0.080 a.u.; the resultant structure still continuesto be a local minimum on the potential energy surface. Com-paratively the high field strength of 0.012 a.u., however, co-erces the structure to open up to form a 5+13 branched-chainstructure. The threshold field values (Fd, and Ft) for cyclicand branched-cyclic methanol conformers along with that forcyclic water counterparts are presented in Table I. A closerlook at the table reveals that Fd for both H-bonded clustersare nearly equal but Ft is marginally higher for methanol.

It should be noted that the field induced bowl struc-tures upon optimization in absence of field need not neces-sarily lead to their respective global minimal configurations.Pentamer and hexamer bowl structures revert to the globalminimum configurations, viz., (dudud) and (dududu); how-ever, trimer and tetramer retain their bowl configurations. Theenergetically stable bowl trimer (vibrational frequencies allpositive) is ∼0.84 kcal mol−1 above the global minimum con-figuration (udd), whereas bowl tetramer configuration (dddd)is locked into the saddle point with exactly one purely imagi-nary vibrational frequency.

B. Hydrogen-bond lengths and dipole moments

The average H-bond lengths during the structural evolu-tion driven by applied field are presented in Tables S1 andS2 (in the supplementary information),75 whence the aver-age H-bond length increases with the field intensity as ex-pected. The stretching of H-bonds is due to enhancement inthe orientation of dipole moment of each methanol moleculein the direction of applied field. Once the dipole-field interac-tions overwhelm the intermolecular interactions that governthe structure at zero and low fields, the hydrogen bond lengthsincrease rapidly. This takes place just before the thresholdfield (Ft) corresponding to the breakdown of the H-bonding“network,” and thus the average H-bond length attains a max-imum value. At the threshold field, the structure opens upto form a linear or a branched chain structure with breakingof already weakened H-bonds, and the structure gets alignedroughly along the field direction. With an increase in the fieldstrength along the length of linear or branched chain structure,the O···O separation decreases while the O–H bonds get elon-gated leading a consistent decrease in H-bond lengths withthe field, a feature also observed for water clusters.55, 56 Thus,the net effect is shortening of chain length with increase infield strength. Figure 4 depicts the variation of average hy-drogen bond length with the field strength in global minimumcyclic trimer through hexamer for field applied in the plane ofthe cyclic ring. The cluster opens up to form a linear chain atthreshold field (Ft) indicated in the figure. Recently, molecu-lar dynamics simulations50 carried out in liquid methanol pre-dict an enhancement of H-bond structure with increasing fieldstrength in the range 0–0.019 a.u. However, the separations of

FIG. 4. Variation of average H-bond length in the global minimum cyclic methanol (M) clusters for field applied parallel to the plane of the cyclic ring. Theupper curve depicts the same for cyclic water (W) clusters for similar field orientation. Transition threshold fields (Ft) are indicated in the pictures.

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024307-7 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

the (O, O) and O–H atoms in O–H···O alignment are found tobe insensitive to the applied field, and thus it is deduced thatthe enhancement and the change in the H-bond structure isdue to reorientation of molecules caused by the external field.

A property of a molecule of primal importance in the de-scription of its response to an external electric field is its elec-tric polarizability αi j and higher order polarizabilities. Theseelectrical properties enter in general, the total electrostatic en-ergy expression for a system of a (static) charge distributionas72, 73

E = E0 − μi Fi − 1

2αi j Fi Fj − 1

6βi jk Fi Fj Fk

− 1

24γi jkl Fi Fj Fk Fl − · · · . (1)

Here, the first term on the right is the energy of the system inthe absence of the field, the second contribution is the leadingcontribution by virtue of its dipole moment; the next one infact defines the electric polarizability. The higher order termsresult from higher order polarizabilities.

The components of the electric dipole moment �μ has thecontributions,

μi = μ0i + αi j Fj + 1

2βi jk Fj Fk + 1

6γi jkl Fj Fk Fl + · · · .

(2)

The first term is a possible permanent dipole moment;and all the latter terms together represent the induced dipolemoment. These involve the electric polarizability αi j (linearcoupling) and higher order polarizabilities with higher-ordercouplings (quadratic, cubic, and so on) with the electric field.

It evidently is a “disruptive” nonlinear response since thevariation is almost linear except at the threshold fields (Fd andFt), at which the dipole-moment jumps signifying a nontriv-ial structural transition due to opening of the clusters afterbreaking of some bonds. The charge distribution and bondorientation do not always take place in the field direction,which also is a cause of nonlinearity. For moderate enoughfields not near threshold, the linear term suffices. The struc-tural transition brought about by the threshold field results ina decrease in the number of hydrogen bonds, which may beunderstood in terms of reduction in orientational freedom ofeach dipolar methanol molecule in the presence of field. Sincethe applied fields rupture the H-bonding, it is expected thatthe number of hydrogen bonds, in general, should decreasefor larger clusters as well. A recent investigation51 based onthe three H-bonding sites molecular model for methanol alsosuggests that the average number of H-bonds in methanol in-creases up to the field strength of 0.017 a.u. beyond whichthe H-bond network gets disrupted leading to a decrease inthe number of hydrogen bonds. The net electric dipole mo-ments of methanol clusters during structural evolution causedby the external electric field are presented in Tables S3 and S4(cf. supplementary information).75 The variation in the elec-tric dipole moment is, as expected, phenomenal. For exam-ple, for the cyclic hexamer “6,” which is nonpolar at zerofield, develops a dipole moment of 24.7 D (Debye) for parallelfield. On the other hand, application of electric field along thepermanent dipole moment for polar cyclic hexamer 6′, a (ud-

FIG. 5. Net electric dipole moment as a function of field applied parallel toring in the cyclic clusters (trimer, teramer) while applied along the permanentdipole moment in the branched cyclic (tetramer, pentamer) clusters.

dudd) configuration possessing a 0.92 D moment at zero fieldhas its dipole moment enhanced to 14.7 D just at threshold(field value = 0.026 a.u.) accompanied by a (dddddd) struc-tural change. Branched cyclic methanol clusters also evincethis remarkable effect: the (4)+2 cluster with the 2.55 D mo-ment is elevated to 22.7 D for at the threshold field of 0.022a.u. The fine variations in the dipole moment are detailed outin Tables S3 and S4.

In summary, the dipole moment varies nonlinearly withan applied field and increases abruptly at the threshold val-ues, Fd and Ft. The abrupt increment is due to reorienta-tion of molecules so as to minimize −�μ. �F interaction, ordue to rupture of H-bond structure yielding extended linearor branched chain structures with larger dipole moments. Asin the water clusters, methanol clusters show a disrupted non-linear response to the applied field: characteristic variation ofdipole moment in the cyclic trimer “(3),” tetramer “(4),” andbranched cyclic tetramer “(3)+1” and pentamer “(4)+1” clus-ters is displayed in Fig. 5.

C. Energetics

We now present the energetics for the methanol clus-ters during their electric field-induced structural transitions.The cyclic ring cluster, where each molecule acts as protondonor and acceptor, represents the global energy-minimumstructures followed by the branched-cyclic and the linear orbranched chain structures. In trimer and hexamer, the mini-mum energy structures next to minimum are the C3 and C2

symmetric cyclic ring structures, respectively. In the presentcalculation, the latter structure is 1.03 kcal mol−1 above theglobal minimum S6 symmetric cyclic hexamer. While the ap-plied field upon a cluster distorts the geometry inducing struc-tural transitions to lower energies, a major change in the en-ergy is associated with the dipolar interactions with the ex-ternal field, which is further enhanced by mutual polarizationin response to the applied field. Figures 1(a)–1(d) presentedearlier depict the variation of relative energy (with respect to

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024307-8 Rai et al. J. Chem. Phys. 135, 024307 (2011)

FIG. 6. Relative energy as a function of the applied field in the branched-cyclic methanol clusters. Refer Fig. 3 for the representative structures in the fieldrange indicated.

the field-free value) in the cyclic ring clusters, in response tothe applied field. An abrupt decrease in energy takes placewhen the structure undergoes conformational transition at thethreshold field values. As displayed in the figure that for fieldvalues, F ≥ Fd, the bowl and linear chain structures are en-ergetically favorable than the field free cyclic rings. Figure 6portrays similar observations on the branched-cyclic clusters,where (3)+1 is 6.43 kcal mol−1 above the S4 symmetric cyclictetramer, and that the (4)+1, (3)+2, and (3)+1+1 struc-tures have energies 3.33, 8.26, and 9.38 kcal mol−1 above thecyclic pentamer, respectively. The branched-cyclic hexamers,namely, (5)+1 and (4)+2 are each 3.15 and 4.96 kcal mol−1

above the global energy-minimum S6 symmetric cyclic hex-amer. In these clusters, breaking of cyclic ring structure com-pels the structure to open up to form linear or branched chainstructures of low energies. Reorganization of cyclic ring, how-ever, leads to a branched chain structure, which can be viewedas a cyclic ring consisting of a C–H···O hydrogen bond withmethanols attached on the cyclic structure. Similarly, the fieldinduced linear chain structures upon optimization in the ab-sence of field need not necessarily lead to the ring structures.Tetramer chain, for instance, recoils back to form the globalminimum S4 symmetric (udud) ring structure, whereas trimerand hexamer chains lead to ring structures consisting of an

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024307-9 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

FIG. 7. Influence of field on the OH ring vibrations in cyclic water (light gray) and methanol (black) (a) trimer and (b) tetramer, for the field applied per-pendicular to the plane of the ring. Dagger (†) shows the position of side bands with low intensity. The numbers in cm−1 in the top panel indicate the shiftsnecessary to match the intense bands in cyclic methanol clusters with that calculated in the anharmonic approximation (Ref. 43), which are positioned towardlower frequencies.

intermolecular hydrogen bond between the C–H of amethanol and the oxygen of the other methanol in the ring.These stable ring structures (vibrational frequencies all pos-itive) are 3.06 kcal mol−1 and 8.95 kcal mol−1 above therespective global minimum configurations, viz., (udd) and(dududu). However, pentamer chain retains its structure withvibrational frequencies all positive, which is 10.43 kcal mol−1

above the global minimum structure (dudud). All these obser-vations add up to culminate into a picture that the predominantstructural motifs in methanol in the presence of an externalfield are preferably linear or branched chain conformers.

D. Vibrational spectra

The applied field perturbs the geometry upon which thevibrational energy levels have a direct bearing. This manifestsin shifts in the vibrational bands, accompanied by modifica-tions in the intensity distribution in the entire spectrum. Wepresent here the field effects in the OH and CO stretching

region of the IR spectra of cyclic methanol clusters for thefield applied perpendicular to the plane of the cyclic rings.The number of bands in the OH and CO stretching regions ofa spectrum corresponds to the cluster size, since each OH andCO oscillator contributes to the spectrum. However, some ofthe bands are degenerate and thus overlap due to symmetry ofthe structure. Influence of field in the OH stretching region ofmethanol clusters will be compared with that of cyclic waterclusters for similar field orientations.

1. OH stretching region

Schematic diagrams of the field free and field per-turbed OH stretch spectra calculated for the cyclicmethanol clusters, trimer through hexamer, are displayed inFigs. 7 and 8 along with that of the corresponding water clus-ter counterparts with OH stretch bands of indicated intensi-ties (red bars). The field perturbed spectra displayed for eachcluster corresponds to the field strengths of 0.010, 0.020,

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024307-10 Rai et al. J. Chem. Phys. 135, 024307 (2011)

FIG. 8. Influence of the external electric field on the OH ring vibrations in cyclic water (light gray) and methanol (black) (a) pentamer and (b) hexamer, forthe field applied perpendicular to the plane of the ring. Dagger (†) marks the position of side bands with low intensity. The numbers in cm−1 indicate the shiftsnecessary to match the intense bands in cyclic methanol clusters with that calculated in the anharmonic approximation (Ref. 43), which are positioned towardlower frequencies.

0.030 a.u. A particularly salient feature tangible in the fieldfree spectra is that most of the OH-stretch IR intensity iscarried by the pair of out-of-phase OH stretch modes, whichincreases as one moves from trimer to hexamer due to the en-hancement in coupling of the OH ends in the ring. Moreover,the symmetry of the cyclic tetramer and hexamer make the“out-of-phase” mode degenerate but strongly inhibit the lowerfrequency “in-phase” OH stretch mode, while the asymmet-ric trimer and pentamer produce weak transitions in the lat-ter mode. The weak bands as well as the strong bands in thehigher frequency region, all corresponding to the out-of-phaseOH stretch modes, in methanol clusters lie ∼12 cm−1 belowthat of respective bands in the water clusters.

Fields applied perpendicular to the plane of the ring in-duce conformational transition, at the threshold fields (re-fer Table I), to the symmetric bowl conformers with allmethyl headgroups in methanol and OH groups in waterclusters aligning downward in the direction of field. Conse-quently, the non-degenerate pair of out-of-phase OH stretch

modes in water trimer and pentamer become degenerate lead-ing to a single strong band as in tetramer and hexamer(Figs. 7(b) and 8(b)). These bands, however, remain non-degenerate in methanol trimer and pentamer because the bowlconformers so formed are not perfectly symmetric. Signif-icant up-shift (blueshift) in the OH stretch bands is to benoted in methanol clusters, as compared to the correspond-ing water cluster counterparts, when field strength is in-creased. For instance, the degenerate strong band in methanoltetramer is blueshifted by 40 cm−1 from the field free position(3451 cm−1) for the field strength of 0.020 a.u., against the up-shift of 24 cm−1 in water tetramer for the same field strength.Table II presents the vibrational frequency shifts of the strongOH stretching models in methanol and water clusters for var-ious field strengths. The amount of blueshift for a given ex-ternal field increases as we go from trimer to hexamer, withan exception in the methanol hexamer, in which case the out-of-phase OH stretch ring-vibrations hardly show any shift al-though the other “weak” bands corresponding to the in-phase

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024307-11 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

FIG. 9. Influence of field on the CO stretch vibrations in cyclic methanol (a) pentamer and (b) hexamer (S6 symmetry), for the field applied perpendicular tothe plane of the ring. Dagger (†) shows the position of satellites.

OH stretch ring-vibrations get shifted appreciably. Highfield, however, deforms the symmetric H-bonded cyclic ringstructure, thereby causing distortion in the OH ring vibrations.As a consequence, the OH stretch bands spread out in both di-rections and the intensity gets redistributed with almost equalproportion of intensity carried away by the otherwise weaksatellites as shown in Figs. 7 and 8 for the field strength of0.030 a.u. This effect is more pronounced in methanol hex-amer followed by pentamer and to a somewhat lesser extentin trimer than that in the corresponding water cluster coun-terparts because for the sufficiently high field, F⊥ � Fd, themethanol ring structures get distorted appreciably and mayopen up at a slightly lesser magnitude of field than the corre-sponding water clusters, an inference consistent with the ear-lier one on the basis of variation of electronic charge densityat the H-bond critical point.

2. CO stretching region

Fields applied perpendicular to the plane of the cyclicring markedly influence the CO stretch modes. As a result, the

CO stretch bands are redshifted significantly with modifiedintensities even for low fields; Fig. 9 depicts these featuresfor the pentamer and the hexamer. Unlike the H-bonded OHbonds in the ring, the CO bonds are roughly oriented alongthe field whose polarity is conducive to the CO bond to elon-gate and hence the redshift. Due to the S6 symmetry, the fieldfree spectrum of hexamer consists of two strong, almost de-generate bands (1048 cm−1, 1056 cm−1) corresponding to thecoupled symmetric and antisymmetric motion of CO oscilla-tors, whereas three strong non-degenerate bands (1046 cm−1,1052 cm−1, and 1056 cm−1) of comparable intensities areobserved for pentamer that correspond to broad unstructuredband in the experimental spectra.43 With an increase in fieldapplied perpendicular to the plane of the cyclic ring, the bandsare consistently redshifted with varying intensities. A similareffect is observed in trimer (not presented herein) in which thefield free weak band shares comparable intensities as the othertwo bands when field strength is increased. However, in thecase of the tetramer, intensity is shared between the coupledsymmetric-antisymmetric CO stretch modes and the purelysymmetric CO stretch vibration in a complementary manner,

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024307-12 Rai et al. J. Chem. Phys. 135, 024307 (2011)

TABLE II. Calculated frequency shifts (in cm−1) of the two strong bands corresponding to out-of-phase OH ringvibration in the cyclic methanol (M) and water (W) clusters at various field strengths. The entries for zero field strengthare the field free position (unscaled) of the strong bands calculated in the harmonic approximation. These bands aredegenerate in tetramer and hexamer due to symmetry of the structure.a

Trimer (3) Tetramer (4) Pentamer (5) Hexamer (6)

Electric field �νM �νW �νM �νW �νM �νW �νM �νW

(a.u.) (cm−1) (cm−1) (cm−1) (cm−1) (cm−1) (cm−1) (cm−1) (cm−1)

0.000 3612 3618 3451 3464 3394 3404 3380 33913623 3629 3451 3464 3404 3413 3380 3391

0.005 0 0 19 8 15 20 2 100 − 4 27 11

0.010 − 4 2 21 13 25 24 0 202 − 8 32 15

0.015 0 6 28 17 38 28 0 387 0 36 19

0.020 5 12 41 24 52 39 4 − 4916 2 52 33

0.025 17 18 54 36 58 51 − 12 6536 8 82 46 − 7

0.030 . . . 31 71 51 . . . 67 − 31 90. . . 20 . . . 65 − 20

aField free position of the strong bands in anharmonic approximation are: (3510, 3518) cm−1 in trimer, 3400 cm−1 in tetramer, (3352,3345) cm−1 in pentamer, and 3305 cm−1 in hexamer (Ref. 43). The experimental values for trimer are: 3472, 3503 cm−1 (Ref. 33); 3469and 3474 cm−1 (Ref. 74).

so that the field free weak band corresponding to the lattermode becomes intense when the field strength is increased.Due to the symmetry, only two strong lines in the CO stretch-ing region are observed even for field as large as 0.036 a.u.,in agreement with the quiescence of a strong line in the OHstretching region shown in Fig. 7(b).

IV. CONCLUDING REMARKS

Electric field induced structural transitions in cyclic andbranched-cyclic methanol clusters (CH3OH)n, n = 3–6 arepresented.

1. The most salient effect of the applied field is the “open-ing up” of cyclic ring yielding linear or branched struc-tures at the characteristic threshold fields (F|| = Ft) ap-plied parallel to the cyclic ring structures or along thepermanent electric dipole moment in branched-cyclicstructures.

2. These structural transitions are accompanied by anabrupt increase in their electric dipole moments, reveal-ing the characteristic disrupted nonlinear response oftypical hydrogen-bonded clusters to the applied electricfield.

3. In particular, the field applied perpendicular to the cyclicmethanol clusters aligns the “dangling” CH3 groupsalong the field direction at threshold field, F⊥ = Fd,transforming the structures to “bowl” configurations oflower energy, which once again manifest with an abruptincrement in the net electric dipole moment.

4. Despite the fairly “intense” field (F⊥∼ 0.032–0.040 a.u.)applied perpendicular to cyclic methanol trimer throughhexamer, conformational transition to linear chain havenot been observed, which is also the case for cyclic waterclusters for similar field orientations.

5. It is found that the threshold field (Fd) at which “dan-gling” OH and CH3 groups in cyclic water and methanolclusters get aligned in the direction of F⊥ is nearly equal,but Ft is marginally higher for methanol.

6. The estimation of electron densities at the hydrogen-bond critical points shows comparatively a rapid de-crease in methanol than in the corresponding water clus-ters for F⊥ > Fd. This suggests that the methanol clus-ters may “open out” at a slightly lesser magnitude of ap-plied field than do the corresponding water clusters forF⊥ >> Fd.

7. Since the applied field breaks the H-bonding, the numberof hydrogen bonds decreases with an increase in the fieldstrength and is expected in larger clusters as well.

8. Analysis of vibrational spectrum provides yet anotherway to gauge the effect of the applied electric field,which brings out shifts in the vibrational bands accom-panied by modifications in the intensity distribution. Forinstance, the out-of-phase OH stretch ring-vibrations inboth water and methanol clusters show blueshift, whilethe coupled symmetric-antisymmetric CO stretch vibra-tions in the methanol clusters show redshift for fieldapplied perpendicular to the cyclic ring. However, theshifts in the out-of-phase OH ring-vibrational bands inmethanol clusters are found to be larger than in the cor-responding water cluster counterparts.

It is gratifying that the present study based on B3LYP-functional unravel similarities in the response of the typicalhydrogen-bond methanol and water clusters to the externalfield. However, further studies and comparison with the ex-perimental observations and/or other theoretical methods mayprovide insights into the refinement of the theoretical descrip-tion of field effects on the molecular clusters or molecular

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024307-13 Methanol clusters in external electric fields J. Chem. Phys. 135, 024307 (2011)

assembly, such as molecular wires, and are underway in ourgroup.

ACKNOWLEDGMENTS

R.K.P. is indebted to Professor Robert G. Parr during avisit to Chapel Hill, NC (March 2011) for discussions andencouragement.

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