JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 13 1 OCTOBER 2001
Structure and stability of fluorine-substituted benzene-argon complexes:The decisive role of exchange-repulsion and dispersion interactions
P. Tarakeshwar and Kwang S. KimNational Creative Research Initiative Center for Superfunctional Materials, Department of Chemistry,Pohang University of Science and Technology, San 31, Hyojadong, Pohang 790-784, Korea
Elfi Kraka and Dieter CremerDepartment of Theoretical Chemistry, Go¨teborg University, S-41320 Go¨teborg, Reutersgatan 2, Sweden
A large number of experimental and theoretical invesgations in the recent past have focused on van der Wheteroclusters consisting of rare gas atoms bound to mor poly-cyclic aromatic molecules,1–6 because of their utilityin understanding the structural and dynamic aspects ofsolvation processes, condensed-phase properties in liqand solids, and cluster dynamics. The experimental invegations, which have employed a wide variety of spectscopic methods, have rendered important information onstructure, binding energies, spectral shifts, intermolecularbrations, and ionization potentials of these rare gcomplexes.7–27 In addition, theoretical investigations, whicinclude high-levelab initio calculations, have probed thstructures, binding energies, and intermolecular vibratiofrequencies of these complexes.28–36However, none of thesetheoretical studies has quantitatively examined the interpof attractive and repulsive forces governing the interactiof the inert rare gas atom and thep-electron system of anaromatic or olefinic molecule.
There have been qualitative attempts to describemagnitude of the various attractive and repulsive forcestheir role in the formation of these complexes where thattempts have been based on the analysis of BSSE~basis setsuperposition error!-corrected electron difference densidistributionsr~r !.37–39 One of the crucial factors, which impedes quantitative investigations, is the high level of theneeded to accurately describe the interaction of an inert
6010021-9606/2001/115(13)/6018/12/$18.00
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gas and the diffusep electron clouds of the benzene ring6
This is because the major attractive component of theseteractions is predominantly dispersive in nature, which conly be adequately described at correlated levels of theo
At this juncture, it is useful to recall that attractive forceare mainly comprised of electrostatic, dispersive, and indtive interactions, while the repulsive forces are mostly dueexchange repulsions. Each of these components has a dent physical origin, magnitude, and directionality. Thus eletrostatic forces result from interactions between the permnent electric multipole moments of the complex partneinduction forces result from interactions of the permanelectric multipole moment of one monomer with the electmultipole moment induced in the other monomer; dispersforces result from the mutual polarization of the electrdensities of the two interacting monomers; repulsive forresult from the Pauli exclusion principle, which prevents telectrons of one monomer from penetrating into the occupspace of the other monomer. Exchange repulsion increwith increasing overlap and is always destabilizing.
The recent experimental binding energies of a numbeclosely related p systems ~benzene, fluorobenzenep-difluorobenzene! with argon seem to indicate that the preence of electron-withdrawing substituents on the ring dnot have a substantial effect on the observmagnitudes.13,14,16–20,39This is contrary to what was observed for the interactions of water with thesep systemswhere the binding energy of thep bonded complexes de
creases significantly as one progresses from benzenp-difluorobenzene.40–42 It should be noted that both electrostatic and dispersive interactions have a significant role inbinding of water with thesep systems. Thus it is interestinand desirable to determine the magnitude of each of thedividual interaction energy components ofp-argon com-plexes and explain both the observed equilibrium geometand the resulting binding energies. Given the earlier attemof some of the authors of this study to explain the stabilityp-rare gas complexes using a novel electron density analwe have also examined the efficacy of this analysis inplaining the stability of thesep-argon complexes.37–39
The argon complexes of various aromaticp systemshave been theoretically investigated by a number of groin the past.28–36 Thus Hobza and co-workers evaluated tgeometries, binding energies and vibrational stretchmodes of the benzene-argon, fluorobenzene-argon,p-difluorobenzene complexes at the second-order MøllPlesset~MP2! level of theory using a 6-311G(d) basis setto describe thep system and a@7s4p2d# basis set to de-scribe the argon atom.28–30,32Their calculated binding energies and geometries were fairly close to the experimevalues.30 They, however, conjectured that the stabilizationthe argon complexes of the fluorinated benzenes was pbly due to a charge transfer from thep system to argon.30
Kraka and co-workers, however, observed that the chatransfer is more of an artifact of calculations not includiBSSE corrections.37 The benzene-argon complex was rcently investigated by Kochet al. employing high-levelabinitio methods.33 These authors carried out CCSD~T! calcu-lations ~coupled cluster theory with single and double extations and a perturbative inclusion of triple excitations! witha large basis set of QZ quality for the experimentally detmined geometry of the benzene-argon complex and obtaa binding energy of 385 cm21 in reasonable agreement witthe experimental values13,16of (D05340,316 cm21), consid-ering that that zero point energy corrections are of the orof 50 cm21 ~see Sec. III!. Due to a fortuitous cancellation obasis set and correlation errors, the experimental estimathe binding energy is also close to the BSSE corrected bing energy of 394 cm21 evaluated at the MP2/aug-cc-pVDlevel.33
The experimental binding energies of the benzene-arcomplex merit special mention because of the presenctwo different experimental estimates.13,16 The earlier experi-mental estimate of an upper limit of (D05340 cm21) for theC6H6-Ar complex was obtained by Krause and Neusse13
However, based on the infrared spectra of jet-cooled C6H6
and C6D6 cations complexed with Ar, Satinket al. observethat aD0 of 316 cm21 would be a more stringent upper limfor the dissociation energy of the neutral C6D6-Ar complex.16
Therefore, in our comparisons of the calculated bindingergies to the experimental estimates, we use both the amentioned values.
The complexes of oxazole, isoxazole, and chlorobenzwith argon were at the focus of a series of theoretical invtigations by Kraka and co-workers.37–39 In their investiga-tions, which were carried out using Spackman’s 6-33(1sd,1sp) basis set to describe thep system and a
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(14s10p2d1 f )@7s4p2d1 f # basis to describe the argoatom,43–45 the rotational constants of the equilibrium geometries of these complexes were evaluated. Their studiesinvolved an innovative use of electron density maps toravel the electronic factors determining the stability andconfiguration of the equilibrium geometry. Thus an analyof the Laplace concentration of the monomers enabled thto detect regions of strong contraction of negative chargesmall exchange repulsion.
In this work, we will combine three different theoreticamethods to analyze the complex stability of benzene-ar~BAr!, fluorobenzene-argon~FAr!, and p-difluorobenzene-argon~DAr! in terms of dispersive, inductive, and exchanrepulsion forces. First, we will apply the conventional supmolecular ~SM! approach to determine various compleproperties, but in particular the complex stabilization enerThen, we will decompose the latter into dispersive, indutive, and repulsive contributions employing symmetadapted perturbation theory~SAPT!.46 Finally, we will mergethe SM and SAPT results with the electron density analyof Kraka and Cremer37–39 to obtain a unified description othe three complexes where we will concentrate specificon the following questions:
~1! Does theory confirm the experimental observation ofmost identical complex binding energies for BAr, FAand DAr?
~2! How is the accuracy of calculated complex binding eergies influenced by basis set size, BSSE correctioand vibrational corrections? How do calculated geoetries compare with the available experimental data?
~3! What are the dominant interaction terms determiningcomplex stability? Does the analysis of these terms lto an explanation for the insensitivity of complex bining energies to F substitution?
~4! Do SAPT and the electron density analysis lead tosame, complementary, or controversial descriptionsthe complex properties? Can one use the latter as asaving qualitative alternative for the time consuming aexpensive SAPT description?
~5! How does F substitution influence the complex propties and can these electronic influences be explaiwithin a simple model?
~6! What predictions can be made for otherp-rare gas com-plexes on the basis of what is learned from the currinvestigation?
The paper is organized as follows: In the next sectiwe briefly describe the computational details. Then, in SIII, we present and discuss the results obtained from thecomposition of the binding energies of thep-argon com-plexes BAr, FAr, and DAr. Furthermore, we also examineresults obtained from the electron density distributionsthese complexes. Finally, we compare the results obtafrom both methods.
II. METHODS
In most theoretical investigations of van der Waals coplexes, the interaction energy is evaluated either using
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6020 J. Chem. Phys., Vol. 115, No. 13, 1 October 2001 Tarakeshwar et al.
SM variational method or the perturbational SAPT method46
In the SM method, the interaction energy is the differenbetween the energy of the complex and the energies ofisolated systems. Although the SM method is conceptuand computationally simple, it can not provide a clear pictof the interaction forces. However, the SAPT method47 com-putes the interaction energy directly as a sum of theelectro-static, exchange, dispersion, and inductioncontributions,which provide a physical interpretation of the interactiobetween the complex monomers.
Given the aims of this study, we initially carried ouconventional SM calculations to obtain the optimized geoetries, binding energies, and vibrational frequencies of BFAr, and DAr. SAPT calculations were then performeddecompose the binding energy of these complexes into ividual interaction energy components.48 The details of thecalculations are briefly elaborated to aid the discussion ofresults.
A. Supermolecular calculations
Complete geometry optimization of all the complexinvestigated in this study were carried out at the MP2 leof theory using Pople’s 6-311G(d) basis44 as well as Dun-ning’s aug-cc-pVDZ and and aug-cc-pVTZ basis sets.49 Vi-brational frequencies were then evaluated for all the omized structures at the MP2/aug-cc-pVDZ level. Whilethe electrons were explicitly included in the calculations cried out with VDZP basis sets, only the valence electrowere correlated in the MP2/aug-cc-pVTZ calculations.
The zero point vibrational energy~ZPVE! correctionswere computed from the frequencies evaluated atMP2/aug-cc-pVDZ level of theory. The BSSE correctionsthe SM calculations were computed using the counterp~CP! method of Boys and Bernardi50 according to the follow-ing calculational strategy. First, calculated binding energDEe
N were corrected by referencing them to BSSE-correcmonomer energies, which led to binding energiesDEe
B . Al-though this leads to an improvement of calculated values,binding energies are still flawed by a geometry error cauby the fact that geometries also suffer from BSSEs.37–39,51
Hence, in a second step, binding energiesDEeB were recal-
culated for BSSE-corrected complex geometry thus yieldfinal binding energiesDEe
F , which represent the most relable values.
The correction of complex geometries by the CP methwas carried out in three steps.~i! The geometries of thepsystems were initially optimized at the MP2/aug-cc-pVTlevel of theory.~ii ! The binding energies of the complexefor different intermolecular separations were then obtainat the MP2 level using a@7s4p2d1 f /4s3p1d/3s1p#basis which is based on Spackman’s 6-31G(1sd,1sp)basis set43,44 to describe the p system and the(14s10p2d1 f )@7s4p2d1 f # basis set of Chalasin´ski andco-workers45 to describe the argon atom. For this purpothe MP2/aug-cc-pVTZ optimized geometry of thep systemwas frozen and the location of the Ar atom above the rwas varied. For the sake of brevity, this calculation whenceforth be denoted as MP2/@7s4p2d1 f /4s3p1d/3s1p#.~iii ! BSSE-corrected binding energies were fitted to a po
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nominal depending on the position of the Ar atom, andequilibrium geometry was determined as the geometryleads to a maximum binding energy.
All the SM calculations reported in this study were caried out using theGAUSSIAN52 andCOLOGNE2000programs.53
B. Symmetry-adapted perturbation theorycalculations
SAPT47 provides a rigorous quantitative quantum mchanical description of the intermolecular forces and aenables one to identify the physically meaningful termoriginating from classical theories of intermolecular forceUnlike most other decomposition procedures, SAPT allofor a natural description of the interaction energy in the foof a sum ofelectrostatic, induction, dispersion, andexchangeinteractions. One can also examine the changes obtainestepwise inclusion of electron correlation effects on theforces. In this study, the SAPT calculations were carriedusing theoretical~obtained from SM calculations! or experi-mental geometries of the complexes. The SAPT interacenergy accurate to third order,Eint
~SAPT! , is given by Eq.~1!
Eint~SAPT)5Eelst
~1!1Eexch~1! 1Eind
~2!1Eexch-ind~2! 1Edisp
~2!
1Eexch-disp~2! 1dint
HF , ~1!
whereEelst(1) is the electrostatic energy of the monomers w
the unperturbed electron distribution,Eexch(1) is their first-order
valence repulsion energy due to the Pauli exclusion pciple, Eind
(2) stands for the second-order energy gain resultfrom the induction interaction,Eexch-ind
(2) represents the repulsion change due to the electronic cloud deformation,Edisp
(2) denotes thesecond-order correction for a coupling between the excharepulsion and the dispersion interaction, andd int
HF includes thehigher order induction and exchange corrections.
The SAPT interaction energy can also be representethe sum ofEint
~HF) andEint~corr) , whereEint
~HF) is the sum of all theenergy components evaluated at the Hartree–Fock levelEint
~corr) is the sum of all the energy components evaluatedthe correlated level. Given the size of the systems invegated and the level of theory employed in this study to evaate the various energy components, it was not feasibleevaluate the computationally demanding higher order coponents. Hence, one should expect a slight deviation oftotal interaction energies evaluated using SAPT and SMculations. This, however, does not affect our conclusiobased on the magnitude of the individual interaction enecomponents, as was shown in a recent paper.54 A detaileddescription of SAPT and some of its applications canfound in some recent references.41,42,55–59
III. RESULTS AND DISCUSSION
A. Geometries and energies
The optimization of thep-Ar complexes BAr, FAr, andDAr at the MP2/aug-cc-pVDZ level of theory yielded thstructures shown in Fig. 1. An analysis of the optimized gometries shown in Fig. 1 of both the uncomplexed~p mono-mers! and complexed forms~p-Ar complexes! reveals that
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there is no perceptible change in the geometries of thpsystem upon complex formation~changes in bond lengths,0.001 Å; similarly small deviations from planarity!. This isalso evident from experiments of Weberet al.7 In order toevaluate the effect of the individual interaction energy coponents on the observed geometries, we have also carriecalculations on the forms shown in Fig. 2.
While in the case of both the BAr and DAr complexethe argon atom is directly located over the center ofaromatic ring, it is slightly shifted toward the C–F bonin the FAr complex. This is in line with experimentaobservations8–11 and, therefore, no attempts were madelocate other plausible conformers. It can be seen frTables I, II, and III that as one progresses from the BArthe DAr complex, there is a gradual decrease in the inmolecular distanceRpCM-Ar defined as the distance betwethe Ar atom and the the center-of-mass of the~substituted!benzene. This decrease ranges from about 0.014(MP2/@7s4p2d1 f /4s3p1d/3s1p#), 0.03 Å ~MP2/aug-cc-
FIG. 1. MP2/aug-cc-pVTZ geometries of the benzene-Ar~BAr!,fluorobenzene-Ar~FAr!, andp-difluorobenzene-Ar~DAr! complexes. Valuesin parentheses correspond to MP2/aug-cc-pVDZ calculations. The posof the Ar atom was determined at the MP2/@7s4p2d1f /4s3p1d/3s1p# levelof theory using BSSE corrections as described in the text. CM denotecenter-of-mass for the monomer, CR the center-of-ring for fluorobenzExperimental~exp! values from Refs. 7, 9, and 10. All distances in Å.
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pVDZ!, 0.018 Å~MP2/aug-cc-pVTZ! to about 0.032 Å~ex-perimental values!.7,9,10
The calculated intermolecular separationsRpCM-Ar
@aug-cc-pVDZ: 3.364~BAr!; 3.335 ~DAr!, Table I; aug-cc-pVTZ: 3.373~BAr!; 3.355 Å ~DAr!, Table III# are compara-tively smaller than the experimentally determined distan~BAr: 3.582; DAr: 3.550 Å!.7,9,10 This is due to the BSSEwhich becomes obvious when considering BSSE-correcgeometry optimizations~Table II!. Thus in case of the BArcomplex, the BSSE-corrected geometry optimization atMP2/aug-cc-pVDZ level yielded an intermolecular sepation RpCM-Ar of 3.534 Å and a binding energyDEe
F of 399cm21. However, the computational effort involved in detemining BSSE-corrected geometries with extended basisfor FAr and DAr is considerable and, therefore, these callations were carried out at the MP2 level using t@7s4p2d1 f /4s3p1d/3s1p# basis set.
As can be seen from Table II, the intermolecular sepations RpCM-Ar ~BAr: 3.592; DAr: 3.578 Å! obtained at thislevel are close to the experimental values. Moreover, a cparison of the sum of the calculated rotational constantsA1B52220 MHz) of DAr with the experimentally determined sum of (A1B52234.662 MHz) indicates that thecalculated structure closely resembles the experimentallyserved structure.12 For FAr it is useful to give the intermolecular separation in terms ofR' , which is the perpendiculadistance of the argon atom from the ring plane of fluorobzene, andRi , which is the distance between the geometcenter of the C6-ring and the intersection ofR' with the ringplane. Values of 3.588 and 0.154 Å were determined atMP2/@7s4p2d1 f /4s3p1d/3s1p# level of theory ~withoutBSSE-corrections at MP2/aug-cc-pVTZ: 3.364 and 0.300!,
on
hee.
FIG. 2. Various forms of the benzene-Ar andp-difluorobenzene-Ar com-plexes, whose interaction energies are decomposed in Tables II and III.values ofRp-Ar for the BAr and DAr complexes are 3.364 and 3.335 Åthe MP2/aug-cc-pVDZ level of theory and 3.592 and 3.578 Å atMP2/@7s4p2d1f /4s3p1d/3s1p# level of theory.
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6022 J. Chem. Phys., Vol. 115, No. 13, 1 October 2001 Tarakeshwar et al.
TABLE I. Total binding energies and binding energy components calculated at the MP2/aug-cc-pVDZ level of theory for different forms of the bfluorobenzene-, andp-difluorobenzene-argon complexes.a
aAll energies are in cm21; distances are in Å. See Figs. 1 and 2 for a description of the various complex forms. Form I corresponds to the MP2/aug-coptimized geometry, form V to the experimental geometry. ‘ ‘DEe
N’ ’ and ‘‘ DEeB’ ’ represent the supermolecular binding energies without and with basis
BSSE correction, respectively.DEo is the ZPVE-correctedDEeB . The frequencies for ZPVE were evaluated at the MP2/aug-cc-pVDZ level. The ele
correlation energyDEcor is the value of theEe(MP2) subtracted byEe(HF) at the MP2 optimized geometry.RpCM-Ar is the distance from the center-of-masof benzene, fluorobenzene, andp-difluorobenzene to the argon atom. A, B, C are the rotational constants in MHz.
bEint~SAPT) is the interaction energy of the complex form evaluated using SAPT according to Eq.~1! ~see text!.
cEint~corr) is the sum of all the energy components evaluated at the correlated level.
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which indicates that BSSE corrections increaseR' of FAr toa value between the two correspondingR'5RpCM-Ar valuesfor BAr and DAr. With increasingR' the horizontal shiftparameterRi becomes smaller because the electronic effeof the F atom are less experienced by the Ar atom.
The influence of the BSSE is also reflected by the cculated binding energies~2653,2679,2698 cm21, Table I!.Errors are in the range of 339–349 cm21 with the complexstabilities doubled because of an unbalanced descriptiothe monomers. They become smaller for the aug-cc-pVbasis ~,200 cm21, Table III! in line with the well-knownfact that the BSSE decreases with increasing basis setThe BSSE-corrected SM binding energiesDEe
B at theMF2/aug-cc-pVDZ level~365, 353, and 349 cm21, Table I!are 40–60 cm21 smaller than the corresponding energDEe
F evaluated at the MP2/@7s4p2d1 f /4s3p1d/3s1p# level~408, 409, 408 cm21, Table II!. One has to correct calculated binding energies by ZPVEs to obtain quantitiesDEo
which are directly comparable with experimental bindienergies (D0). MP2/aug-cc-pVDZ values ofDEo ~314, 295,305 cm21, Table I! and MP2/@7s4p2d1 f /4s3p1d/3s1p#values ~357, 351, 364 cm21, Table II! both agree reasonably with experimental values of 340~BAr!, 344 ~FAr!,and 339 cm21 ~DAr!,13,17–20 where the MP2/aug-cc-pVDZvalues are 26–59 cm21 too small and theMP2/@7s4p2d1 f /4s3p1d/3s1p# values 7–25 cm21 toolarge. If one employs the experimental estimates of 3cm21 ~BAr!,16 in the comparison, the MP2/aug-cc-pVDvalues are 2–59 cm21 too small and theMP2/@7s4p2d1 f /4s3p1d/3s1p# values 7–41 cm21 toolarge. Actually, the latter binding energies are closer to
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perimental values in line with the fact that this approach agives a better account of the experimental geometries.
The binding energies obtained using VDZ basis setscombination with the BSSE-corrected geometries are in bter agreement with experimental values than those obtawith large basis sets for BSSE-uncorrected geometrHence, MP2/VDZ calculations, in general, but in particuthe MP2/@7s4p2d1 f /4s3p1d/3s1p# approach provide auseful description of the complex properties due to a foritous cancellation of basis set truncation and correlationrors, as pointed out previously by Kraka anco-workers.37–39 Noteworthy in this connection is the facthat the most accurate estimate of the binding energy ofBAr complex obtained at the CCSD~T!/aug-cc-pVQZ levelof theory yielded a value of 385 cm21 corresponding toDEo5334 cm21.33
Although the ZPVE corrections employed in thstudy, i.e., 51~BAr!, 58 ~FAr!, 44 ~DAr!, were obtainedusing the harmonic vibrational frequencies evaluated atMP2/aug-cc-pVDZ level, it is useful to illustrate the effectthe inclusion of both BSSE and anharmonic effects onmagnitude of the ZPVE corrections. A few studies have dcussed the effect of the BSSE corrections on the calculaforce constants and zero point vibrational energies.51,60 Al-though the intermolecular vibrational frequencies or forconstants are influenced upon optimization using BSSErections, the extent of the effects varies from extremely smto quite large depending on the complex and the calcutional method. In the case of these weakly bound complethese effects are expected to be very small. Furthermoreintermolecular stretching and bending frequencies exh
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TABLE II. Total binding energies and binding energy components calculated atMP2/@7s4p2d1f /4s3p1d/3s1p# level of theory for different forms of the benzene-, fluorobenzene-,p-difluorobenzene-argon complexes.a
aAll energies are in cm21; distances in Å. See Figs. 1 and 3 for a description of the various complex foForm I corresponds to the MP2/@7s4p2d1f /4s3p1d/3s1p# optimized geometry, form V to the experimentageometry.DEe
F represents the supermolecular binding energy including BSSE corrections and being calcat the BSSE-corrected geometry.DEo is the ZPVE-correctedDEe
F . Frequencies for ZPVE were evaluatedthe MP2/aug-cc-pVDZ level. The electron correlation energyDEcor is given by the differenceEe(MP2)2Ee(HF) calculated at the MP2 geometry.RpCM-Ar is the distance from the center-of-mass of benzene, flrobenzene, andp-difluorobenzene to the argon atom. A, B, C are the rotational constants in MHz.
bEint~SAPT) is the interaction energy of the complex form evaluated using SAPT according to Eq.~1! ~see text!.
cEint~corr) is the sum of all the energy components evaluated at the correlated level.
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differing trends, with the former generally decreasing andlatter generally increasing, upon BSSE corrections. Thisdicates that the magnitude of the ZPVE correction issignificantly effected when the force constants are correcfor BSSE.51
In the case of anharmonic effects, earlier efforts to evaate accurate ZPVE corrections inclusive of them hayielded values of 59 cm21,35 and 54 cm21,15 for the BArcomplex. These values indicate that the noninclusion ofharmonic effects in the evaluation of ZPVE corrections donot significantly influence the magnitude of the calculabinding energies in these complexes. Hobza and co-worhave arrived at similar conclusions in their investigationanharmonic effects in the more strongly bound wadimer.60
The MP2/@7s4p2d1 f /4s3p1d/3s1p# data listed inTable II confirm that complexes BAr, FAr, and DAr possea complex binding energyDEe
B of 40861 cm21, which isslightly varied when adding ZPVE corrections. This similaity is remarkable in view of the calculated variation in thdistanceRp-Ar of 0.03 Å ~BSSE-corrected: 0.014 Å, TablII !. As it is hardly possible that all interaction terms aresensitive to F substitution of the benzene ring, the ratioattractive and repulsive forces in complexes BAr, FAr, aDAr must be conserved in some way, despite changeindividual interaction terms. Therefore, it has to be clarifihow this balance of attractive and repulsive forces is retaifor the three complexes.
Such an analysis must be based on BSSE-correSAPT values obtained at BSSE-corrected geometries
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cause a comparison of the data in Tables I and II revealsthe former~calculated for BSSE-uncorrected geometries! dif-fer considerably from the latter~calculated for BSSE-corrected geometries!. The magnitude of all the interactioenergy components is significantly higher in the structuoptimized at the~not BSSE-corrected! MP2/aug-cc-pVDZlevel of theory. Even though this increase can be readattributed to the decreased intermolecular separationserved for these structures as a consequence of the BSScan be seen that the increase observed in the attractiveponents is partially balanced by an equally large increasthe repulsive components.
Changes in the magnitude of electrostatic, dispers
TABLE III. Total binding energies and binding energy components callated at the MP2/aug-cc-pVTZ level of theory for different forms of thbenzene-, fluorobenzene-, andp-difluorobenzene-argon complexes.a
B 2501 2505 2502DEo 2450 2446 2458DEcor 21210 21200 21220
aAll energies are in cm21; distances are in Å. See Figs. 1 and 3 fordescription of the various complex forms. The frequencies for ZPVE wevaluated at the MP2/aug-cc-pVDZ level. See footnote of Table I for otdefinitions.
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6024 J. Chem. Phys., Vol. 115, No. 13, 1 October 2001 Tarakeshwar et al.
and exchange-repulsion interaction energy componcaused by the F substituent~s! also depend on how thgeometry optimizations were carried out. Thus in tMP2/aug-cc-pVDZ calculations without BSSE correctio~Table I!, one observes an increase in these componentone progresses from BAr to DAr, with the increase bemore pronounced in the case of dispersion energies, thathe exchange-repulsion and electrostatic energies. A decris, however, observed in the calculations~Table II! carriedout at the MP2/@7s4p2d1 f /4s3p1d/3s1p# level, with thedecrease being more pronounced in the case of excharepulsion than dispersive energies. Although the trends innet interaction energies are very similar for both calcutional procedures, one notes that the noninclusion of BSin the geometry optimization dramatically alters the trenobserved in the case of individual interaction energy comnents.The altered trends can also be attributed to the diffent distance dependencies of the individual interactionergy components because the intermolecular separationthe BSSE-uncorrected geometries are far smaller thancorrected geometries. Therefore, we will base the followingdiscussion~if not otherwise noted! on energy data based othe BSSE-corrected geometries of Table II.
It can be seen from the magnitude of the total interactenergyEint
~SAPT) and the sum of all the interaction energy components evaluated at the correlated level~Eint
~corr) , Tables I andII ! that all p-Ar complexes are strongly repulsive at thHartree–Fock level of theory. However, for both the HF acorrelation corrected contributions it holds that BAr, FAand DAr do not differ much~Table II!. The magnitude of theelectrostatic energiesEelst
(1) ~2199, 2192, 2192 cm21, TableII ! has little effect on the relative magnitudes of total inteaction energies. The major attractive force in all of thecomplexes is the dispersive interactionEdisp
(2) ~2772, 2759,2761 cm21, Table II! with its contribution being nearly foutimes larger than that of the corresponding electrostaticteraction. The dominance of dispersive interactions inattractive forces ofp-Ar complexes BAr, FAr, and DAr is inmarked contrast to the dominance of electrostatic and indtive interactions observed in the case of conventional hydgen bonded systems. The magnitude of the repulsive cobution, which predominantly emerges from the exchanrepulsive term Eexch
(1) , is of particular interest for theequilibrium geometry of these complexes, an issue whwill be examined in more detail when analyzing the electrdensity distributions of BAr, FAr, and DAr~see Sec. III B!.
A fluorine substituent leads to a contraction of tp-density of the ring, which can be made visible by subtraing ther~r ! of benzene fromr~r ! of p-difluorobenzene~seeFig. 3!. If one keeps the geometry of benzene fixed to thap-difluorobenzene~apart from the C–X bonds in paraposition!, differences in the electron density can be direcanalyzed for regions far from the C–X bonds. Thus thesubstituents diminish thep-density above and below the sixmembered ring~dashed contour lines! and contract it towardthe C atoms~solid contour lines!. The s-electron withdraw-ing power of the F substituents is reflected by the decreasthe electron density in the ring plane~in particular the ringcenter! and is actually responsible for the changes in
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p-space. For the complex formation, however, the mostportant effect of the F substituents is the reduction ofdensity above and below the ring plane.
The decrease in the outerp-electron density of FAr fa-cilitates a closer approach of the argon atom because oduced exchange-repulsion interactions~Table II!. The pres-ence of an electron-withdrawing substituent such as F aleads to a decrease in the magnitude of the induction enEind
(2) which can be readily attributed to the diminishep-electron density above the ring as one progresses fbenzene top-difluorobenzene. Sincep-s* interactions alsocontribute to the induction energies, the enhanced stabilitthe highest occupied molecular orbitals~HOMOs! in the flu-orinated benzenes also decreases the induction energytribution in their argon complexes.
A contraction of the p-electron density in theF-substituted complexes also influences the magnitude odispersion energy, which becomes smaller~less stabilizing!~Table II!. Although the corresponding water monomer coplexes of thesep systems also exhibit a similar decreasethe magnitudes of the various interaction energy comnents, the decrease is much more pronounced therein ain sharp contrast to what is observed in case of thep-Arcomplexes.40,61 Thus as one progresses from benzenep-difluorobenzene, the magnitude of the total binding eneof their water monomer complexes decreases by about 6electrostatic by about 60%, exchange-repulsion by ab40%, induction by about 40%, and dispersion by ab20%.61
Given the definition of exchange-repulsion,62 its magni-
FIG. 3. Contour line diagram of the MP2 difference electron density disbution Dr~r !5r~p-difluorobenzene!-r~benzene! calculated with the@4s3p1d/3s1p# basis at MP2/aug-cc-pVTZ optimized geometries. Refence plane is the plane perpendicular to the benzene ring that containC–X bonds ~X5H or F!. Contour lines range from 231026 to 231021@e/Bohr3#. Solid lines correspond to an increase of the electron dsity upon change from benzene top-difluorobenzene, dashed lines to a dcrease.
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tude can be directly correlated to both the magnitude ofoverlap of the filled orbitals of thep system and the argoatom ~four-electron repulsion effects! and the extent ofpenetration of negative charge. Since the magnitude ofoverlap increases exponentially with decreasing inmolecular separations, it is of interest to examine on howsubstitution would influence the energetics and hence thesition of the argon atom over the ring. In order to do so,carried out calculations on forms II, III, and IV~Fig. 2! ofthe BAr and DAr complexes. While calculations on form Iwere carried out using both the aug-cc-pVDZ a@7s4p2d1 f /4s3p1d/3s1p# basis sets, forms II and III wereinvestigated using only the aug-cc-pVDZ basis set.
It can be seen from Tables I and II that a shift of targon atom from the center of the aromatic ring~form I! to aposition directly above one of the aromatic carbon ato~form IV! leads to a decrease in the~stabilizing! dispersiveenergiesEdisp
(2) for both the BAr and DAr complexes~by 111from 2772 to2661 and by 117 from2761 to2664 cm21,Table II!. The magnitude of the exchange-repulsion eneEexch
(1) , however, distinguishes between the BAr and Dcomplexes in the way that BAr is destabilized~by 5522533544 cm21, Table II!, while DAr is stabilized~by 47925075228 cm21! when converting the complex from I intIV. There are also changes in the electrostatic eneEelst
(1) @21772~2366!52189 cm21, Table II# and the induc-tion energyEind
(2) @21502~2250!52100 cm21#, however,the latter is largely canceled out by an accompanyingcrease in the exchange-induction energyEexch-ind
(2) ~355215951196 and 24921465103 cm21, Table II!. The changes inthe electrostatic energies do not compensate for the obsereduction of the stabilizing dispersive energies by 111 a117 cm21, respectively, and, as a result, the net bindingergy of form IV is lower than that of form I in both the BAand DAr complexes@by 137522832~2420! and 92523242~2416! cm21, Table II#.
Calculations on forms II and III~Table I! also distinguishbetween the characteristics of the BAr and DAr complexThus while stabilizing dispersive interactions become larfor DAr @219232~21133!52790 cm21, Table I# than forBAr @218882~21110!52778 cm21#, the increase in destabilizing exchange-repulsion is more pronounced in the cof BAr ~41462108453062 versus 38362110152735 cm21,Table I!. This is parallel to the fact that exchange interactiodistinguish between BAr and DAr, as discussed above fordifferenceEexch
~1! ~IV) 2Eexch~1! ~I).
An important point, which emerges from the above dcussion, is that the magnitude of both the exchange-repuland dispersion interactions have a crucial role in determinthe equilibrium geometry of thesep-argon complexes. Asthe dispersive effects are maximized both by a decreasthe intermolecular separation and an increase in the numof p-electrons participating in the interaction, the decreobserved in the exchange-repulsion of DAr as one progrefrom form I to form IV also explains the shifting of the argoatom toward the C–F bond in the case of FAr.
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B. Electron density analysis
Changes accompanying the complex formation can abe investigated by calculating difference electron density dtributions
Dr~r !5r~complex!2(i
r i~monomer!DCBS, i 51,2,
~2!
where the monomer density distributionsr i(monomer!DCBS
are calculated in the dimer-centered basis set~DCBS! to cor-rect for BSSE. In Fig. 4, MP2/@7s4p2d1 f /4s3p1d/3s1p#difference density distributionsDr~r ! determined for BAr,FAr, and DAr at their equilibrium geometries are shown wregard to a plane containing the Ar atom, the center ofbenzene ring, and the C–X bonds~X5H or F! in para-position. An increase of the difference density due to coplex formation is indicated by solid contour lines, a decreaby dashed contour lines.
Complex formation leads to an increase of the electdensity distribution in regions 1 and 3, however, to a dcrease in regions 2 and 4, i.e., regions of positiveDr~r ! arefollowed by regions of negativeDr~r ! in a regular pattern.This pattern is similar for complexes BAr, FAr, and DAr ancan be explained in the following way. The Ar atom pushp-electron density out of the intermolecular region 2~Fig. 4!toward and through the center of the benzene ring~region 3!.The benzene ring, in turn, pushes the density of the Ar atoward its back~region 1!, however, part of this density isstopped by the Ar nucleus so that a build up of electrdensity in a small region in front of the Ar nucleus canobserved~region 2c!. Overall the calculatedDr~r ! indicatesthat complex formation leads to polarization of both the desity at Ar and thep-density of the benzene ring. Small dipomoments are induced for both the Ar atom and the benzring @see Fig. 4~a!# thus creating some attractive inductioforces.
The calculated difference electron density distributiDr~r ! reflects the important role of exchange repulsiowhich leads to a polarization of the charge distribution of tmonomers upon complex formation. For BAr and DAr, tenergetically favorable position is above the ring centercause the destabilizing exchange-repulsion effects are smIn this position, the Ar atom can approach the ring closelythat stabilizing dispersion effects involving the electronsthe six C atoms become large.
Comparison of Figs. 4~a! and 4~c! shows that less electron density is pushed out of region 2 in the case of DAccordingly, the polarization of the density at Ar and at tbenzene ring is smaller, which can be verified by inspectof Fig. 4~b!. There, the density at the Ar atom is distortedthe way that the stronger effect of thep-density associatedwith C4H ~as compared to that associated with C1F! be-comes visible@see arrows indicating polarization directionof the density in Fig. 4~b!#. While a quantification of theseeffects is difficult, they can be better illustrated when depiing the changes in the electron density distribution causeda variation of complex formation due to substituent effec
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reesity
theof
1
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tri-
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6026 J. Chem. Phys., Vol. 115, No. 13, 1 October 2001 Tarakeshwar et al.
FIG. 4. Contour line diagram of the MP2 difference electron density disbution Dr~r ! @see Eq.~2!# of ~a! benzene-argon~BAr!, ~b! fluorobenzene-argon ~FAr!, and ~c! p-difluorobenzene-argon~DAr! calculated with a@7s4p2d1f /4s3p1d/3s1p# basis at optimized geometries. The referenplane is the plane perpendicular to the benzene ring containing Ar andC–X bonds ~X5H or F!. Contour lines range from 231026 to 231021@e/Bohr3#. Solid lines correspond to an increase of electron denupon complex formation, dashed lines to a decrease. Regions of incand decrease of electron density are marked by small numbers. Locaduced dipole moments are schematically indicated by arrows where theof the arrow indicates the negative end of the dipole~chemical notation!.
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Differences between the density distributions of the thcomplexes are analyzed by calculating the difference dendistribution:
DDr~r !5Fr~complex 1!2(i
r i~1,monomeriDCBS!G
2Fr~complex 2!2(j
r j~2,monomerjDCBS!G ,
~3!
where 1 and 2 denote complexes BAr, FAr, and DAr andmonomers of a given complex correspond to Ar and onethe three benzenes. For the purpose of determiningDDr~r !,complex 2 is recalculated in the geometry of complex
-
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FIG. 5. Contour line diagram of the MP2 difference electron density disbution DDr~r ! @see Eq.~3!# of ~a! DAr-BAr and ~b! DAr-FAr calculatedwith a @7s4p2d1f /4s3p1d/3s1p# basis at optimized geometries. The reerence plane is the plane perpendicular to the benzene ring that contaiand the C–X bonds~X5H or F!. Contour lines range from 231026 to 231021@e/Bohr3#. Solid lines correspond to an increase of electron denupon complex formation, dashed lines to a decrease. Regions of incrand decrease of electron density are marked by small numbers.
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~apart from the C–X bond lengths with X5H or F!. In thisway, the differences caused by the replacement of H bbecome visible@see Figs. 5~a! and 5~b!#. In DAr, there ismore density in the region between the monomers~region 2!,which means that exchange-repulsion is smaller for Dthan for BAr ~533 versus 507 cm21, Table II!. Accordingly,the polarization of the electron density of the complex paners of DAr is also smaller. There is less density in regionand 2c, more in region 2@Figure 5~a!#, thus decreasing theabsolute magnitude of the induction term relative to thatBAr ~2177 versus2150 cm21, Table II!.
The decrease in exchange-repulsion calculated for Dleads also to a decrease in the coupling termsEexch-ind
(2) andEexch-disp
(2) ~159 versus 146, 59 versus 55 cm21, Table II! thusstabilizing complex DAr relative to complex BAr. Thtighter binding of thep-density toward the nuclear framework does not only decrease exchange repulsion butstabilizing dispersion interactions~from 2772 to 2761cm21, Table II!. This is due to the fact that tighter bindinof the density reduces thep-component of the dipole polarizability ~benzene: 6.33; fluorobenzene: 6.18; difluorobzene: 6.04 Å3, MP2/@7s4p2d1 f /4s3p1d/3s1p#, Table IV!.Hence, in total the changes in exchange repulsion~see Figs.4 and 5!, which increase the stability of DAr, are compesated by changes in the induction and the dispersion tewhich decrease the stability of DAr. Accordingly, complexBAr and DAr possess the same stability.
Complex FAr takes an intermediate position as tochanges in the various interaction terms@see Fig. 4~b! andTable II# and, therefore, similar considerations as in the cof BAr and DAr apply to explain the fact that the complestability does not change significantly. The Ar atom is shifttoward the F atom because of the decrease in excharepulsion~also, the Ar atom can interact with seven raththan six atoms possessingp-electrons!. The shift in theposition of Ar leads to some asymmetry in the charge poization in regions 1, 2, and 3. The charge build up in 1shifted slightly from 1b toward 1a. Also, there is more eletron density depleted from region 2b than from 2c while tbuild up of density is somewhat stronger in region 3b thin region 3a.
IV. CONCLUSIONS
A number of conclusions can be drawn from this invetigation.
TABLE IV. Polarizabilities of benzene~B!, fluorobenzene~F!, and difluo-robenzene~D! evaluated at the MP2/@7s4p2d1f /4s3p1d/3s1p# level oftheory.a
PolarizabilityÅ3 ~B! ~F! ~D!
ap 6.33 6.18 6.04as1 11.81 11.88 11.96as2 11.81 11.70 11.67a iso 9.98 9.91 9.89aexp 10.0 10.3
aThe polarizability components are given for the principle axis systewhere one axis complies with thep direction and the other two with thein-plane directions.
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~i! BSSE- and ZPVE-corrected binding energiesDEo
calculated at the MP2/@7s4p2d1 f /4s3p1d/3s1p# level oftheory ~357, 351, 364 cm21, Table II! agree reasonably~de-viations between 7 and 25 cm21! with experimental bindingenergies of 340 ~BAr!, 344 ~FAr!, and 339 cm21
~DAr!.13,17–20We note that the inclusion of BSSE correctioimproves binding energies by 80% and more, but at leanother 10% improvement is due to ZPVE correctiowhich is often overlooked.
~ii ! BSSE-corrected complex geometries are in line wexperimentally determined geometries. In particular,MP2/@7s4p2d1 f /4s3p1d/3s1p# values of the distanceRpCM2Ar @3.592~BAr!; 3.588~R' for FAr; Ri50.154!; 3.578Å ~DAr!# agree well with the corresponding experimenvalues of 3.582, 3.572~0.228!, and 3.550 Å.7,9,10 BSSE-uncorrected geometry optimizations, however, underestimthis parameter by;0.03 Å.
~iii ! The BSSE also has serious consequences forSAPT analysis of binding energies. The noninclusionBSSE corrections in the geometry optimizations influenthe magnitude and trends of the various interaction enecomponents. The absolute magnitude of the calculated ctributions to the binding energy is exaggerated, whichmainly due to an underestimation of the distanceRpCM2Ar .
~iv! The presence of electron-withdrawing substituesuch as F in the aromatic ring has a strong effect onelectronic structure of the benzene ring and, by this, oncomplex formation. As shown in Fig. 3, thep-density aboveand below the ring is depleted by contraction toward theatoms of the ring. This leads to a reduction of exchanrepulsion and explains the shorterR' values for FAr~3.588!and DAr ~3.578 compared to 3.592 Å for BAr!.
~v! The contraction of thep-density caused by F substituents also has consequences for stabilizing inductiondispersion forces. Both are reduced where in the first casedecrease in exchange repulsion decreases also the polapower of the benzene monomer. Induced moments at abecome smaller and hence the induction contribution. Tdecrease of dispersion interactions results from the factwith a tighter binding of thep-density thep-component ofthe polarizability becomes smaller~Table IV!.
~vi! Both the exchange-repulsion and dispersion engies influence the location of the argon atom in the equirium geometries of these complexes, albeit in different waThus the diminished electron density of the fluorobenzeleads to a much closer approach of the argon atom tofluorine atom in its attempt to maximize the dispersive intactions. Since the smaller intermolecular separation aleads to an increase in the exchange-repulsion terms, thebinding energies are similar for both benzene and the flunated benzenes.
~vii ! Using results obtained in this work, we can predthat with increasing F substitution the complex stabilshould not change strongly because there will be a balabetween decreasing exchange-repulsion effects and decing dispersion interactions. This balance is more pronounfor highly symmetrical complexes. Similar predictions dnot hold for other halogen-substituted benzene-argon cplexes because in these cases the polarizability increases
,
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6028 J. Chem. Phys., Vol. 115, No. 13, 1 October 2001 Tarakeshwar et al.
nificantly in the series of F-, Cl-, Br-, and I-substituted bezenes, as well as with the number of halogen substitueThis leads to larger dispersion forces accompanied only bsmall increase in exchange-repulsion so that the overall cplex stability increases.
~viii ! In the halogen-substituted benzene-argon coplexes, exchange-repulsion and dispersion effects dominAn adequate description of the latter requires correlation crected methods. Conventional methods such as HF thcan only be used for predicting complex properties if theare dominated by electrostatic and exchange forces,63,64as isthe case for conventional hydrogen bonded complexes.
~ix! The SAPT and electron density descriptions, if crectly carried out, after considering BSSE corrections, leto similar, largely complementary descriptions of the coplexes investigated in this work. This supports argumethat the density description can be used~a! for a qualitativerationalization of complex properties such as equilibriumometry, binding energy, dipole moment, etc., and~b! for theinterpretation of SM binding energies and the SAPT decoposition of binding energies.
~x! Analysis of difference electron density distributionreflects, in particular, exchange-repulsion effects by indicing areas with a decrease or an increase of electron decaused by complex formation. The pattern of depletion aconcentration regions indicates induced dipole~multipole!moments and can be used to estimate induction forces.persion forces are proportional to the dipole polarizabilitof the monomers, as volume quantities are related tospace filled out by the density of the monomer~as, e.g.,given by the 0.001 a.u. contour line of the electron densi!.By comparing this space with the help of the difference eltron density distribution of closely related monomersthose in the current case, the relative polarizabilities andrelative magnitude of dispersion forces can be estimated
ACKNOWLEDGMENTS
Two of the authors~P.T.! and ~K.S.K.! thank MOST/STEPI~CRIP! for financial support. E.K. and D.C. acknowedge support by the Swedish Natural Science ReseCouncil ~NFR! and the Nationellt Superdatorcentrum~NSC!,Linkoping, Sweden. We thank Professor Bernhard Brutsfor helpful discussions on the experimental aspects ofFBz-Ar and DFBz-Ar complexes. We thank ProfessKrzysztof Szalewicz for providing us with a copy of SAP
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