Ab Initio Study of Nonadditivity Effects: Spin-Spin Coupling Constants forTetrafluoroethene in Ternary π Complexes

Janet E. Del Bene,*,† Ibon Alkorta,*,‡ and Jose Elguero‡

Department of Chemistry, Youngstown State UniVersity, Youngstown, Ohio 44555, and Instituto de QuımicaMedica (CSIC), Juan de la CierVa, 3; 28006-Madrid (Spain)

ReceiVed: January 12, 2010

C2F4 coupling constants have been evaluated at EOM-CCSD/(qzp,qz2p) in binary complexes with electrondonors X (X ) HLi, Cl-, CN-) and with the electron acceptor FH, and in ternary complexes FH:C2F4:X inwhich X and FH are located on opposite faces of the C2F4 π cloud. The electron donors X and the electronacceptor FH have opposite effects on 1J(C-C), 1J(C-F), 2J(C-F), and 3J(F-F) in binary complexes. Effectsof X and FH on a particular coupling constant in a ternary complex are additive if the change in the couplingconstant in this complex relative to C2F4 is within 1 Hz of the sum of the changes in the correspondingbinary complexes. This is the case for 1J(C-F). Both positive and negative nonadditivities are computed forthe remaining coupling constants. Although the values of most coupling constants lie between the values forFH:C2F4 and C2F4:X, that is not the case for 2J(C-F), and the effect of FH is enhanced by the presence ofX. Moreover, values of 3J(F-F) trans and cis for FH:C2F4:X when X is Cl- or CN- bonded through C arewithin 1 Hz of the values for the corresponding binary complex C2F4:X. Significant differences can be foundbetween the relative contributions of the PSO, FC, and SD terms to total J and to the nonadditivities of J internary complexes FH:C2F4:X.

Introduction

In recent years, a number of theoretical and experimentalstudies have reported the possibility of interaction betweenelectron-rich moieties and the π clouds of electron-deficientsystems.1 Among these, tetrafluoroethene, C2F4, is the smallestπ-electron deficient molecule for which binary complexes withneutral and anionic electron-donor molecules X have beendescribed.2-4 Moreover, although such systems usually are notgood electron-pair donors, the binary systems C2F4:X are ableto act as electron-pair donors to form hydrogen-bonded ternarycomplexes with molecules Y located on the opposite face ofthe C2F4 π system, as illustrated in Scheme 1. The propertiesof these complexes exhibit nonadditivity effects in the groundstate.2,3

In the present article, we examine changes in spin-spincoupling constants of C2F4 in binary complexes with bothelectron donors and an electron acceptor, and ask whethernonadditivity effects can be seen in ternary complexes. For ourstudy, EOM-CCSD spin-spin coupling constants have beenevaluated for C2F4 and binary π complexes C2F4:X, with X theneutral molecule LiH with an electron-rich H which forms ahydride bond,5,6 or an anion Cl- or CN-, allowing for electrondonation by CN- through either C or N. Coupling constantshave also been evaluated for the π hydrogen-bonded complexFH:C2F4, and for ternary complexes FH:C2F4:X. In this paperwe report and analyze the changes in the C2F4 coupling constantsin these complexes, and ask whether or not the changes in theternary complexes are additive.

Methods

The geometries of the monomers and complexes have beenoptimized at MP27-10 with the aug-cc-pVTZ basis set,11,12 asimplemented in the Gaussian-03 program.13 Some of thesecomplexes have been described previously.2,3 Two sets ofcomplexes C2F4:X have been optimized, one with C2V and theother with Cs symmetry. This was done so that differences incoupling constants could be evaluated for the same complexwith two different symmetries. This was a necessary step inthis study because the computational demands of EOM-CCSDmake coupling constant calculations on FH:C2F4:X complexesfeasible only if they have C2V symmetry. FH:C2F4 andFH:C2F4:X were optimized at MP2/aug-cc-pVTZ under thisconstraint. These calculations were carried out on the computersat CSIC.

The calculation of spin-spin coupling constants employedthe equation-of-motion coupled-cluster singles and doublesmethod (EOM-CCSD) in the configuration interaction (CI)-likeapproximation14,15 with all electrons correlated. The Ahlrichsqzp basis set16 was used on 13C, 15N, and 19F atoms, and theqz2p basis set was used for 35Cl and 1H. Since an Ahlrichs qzpbasis set is not available for 7Li, a previously constructedcorresponding basis set was used for this atom.17 This basis sethas the same number of contracted functions (6s, 4p, and 1d)as the Ahlrichs qzp basis for C, N, and F. This level of theoryhas been shown to produce coupling constants involving 13Cand 19F that are in good agreement with experimental values.18

* Authors to whom correspondence should be addressed. E-mails:J.E.D.B., jedelbene@ysu.edu; I.A., ibon@iqm.csic.es.

† Youngstown State University.‡ Instituto de Quımica Medica (CSIC).

SCHEME 1

J. Phys. Chem. A 2010, 114, 3713–3717 3713

10.1021/jp1003159 2010 American Chemical SocietyPublished on Web 02/17/2010

In the Ramsey approximation,19 the nuclear spin-spin couplingconstant is composed of four terms: the paramagnetic spin-orbit(PSO), diamagnetic spin-orbit (DSO), Fermi-contact (FC), andspin-dipole (SD). All terms have been computed for allcomplexes. The EOM-CCSD calculations were carried out usingACES II20 on the Itanium cluster at the Ohio SupercomputerCenter.

Results and Discussion

Binding Energies of Binary Complexes of C2F4. As notedpreviously, some complexes C2F4:X have Cs rather than C2Vsymmetry.2,3 The Cs structure is usually the minimum-energystructure, with the C2V structure being the transition structurefor the interconversion of the Cs mirror images, as illustratedin Scheme 2. However, the interaction energies reported in Table1 indicate that the transition-state barrier for interconversion ofthe two equivalent Cs structures is very low at less that 2.5 kJmol-1. The small difference between the Cs and C2V structuresreflects a very flat potential surface for translation of X abovethe C-C bond. Such small differences imply that zero-pointvibrational motion would make the average ground-statestructure C2V. Only a constrained C2V structure of FH:C2F4 hasbeen optimized, given its very small stabilization energy andthe preference for FH to interact with isolated C2F4 as anelectron-donor through F.2,3

Coupling Constants: C2W vs Cs. Table 2 presents couplingconstants 1J(C-C), 1J(C-F), 2J(C-F), 2J(F-F), and 3J(F-F)trans and cis for C2F4 and complexes FH:C2F4 (C2V) and C2F4:X(C2V and Cs symmetries). As evident from this table, except for2J(F-F), differences between corresponding coupling constantsin the C2V and Cs structures of C2F4:X are small. These areusually less than 1 Hz except for 2J(C-C) for C2F4:CN-, inwhich case the difference is 3 Hz out of a total of 212 Hz. Suchsmall differences provide justification for using the couplingconstants for C2V structures in our analyses of nonadditivityeffects.

There is, however, a noticeable difference between the valuesof the two unique 2J(F-F) couplings in the Cs structures ofC2F4:X compared to the C2V. Values of 2J(F-F) in the Cs

structures are “split” relative to those for the C2V complex, withthe C2V value being remarkably close to the average of the Cs

values. However, there does not appear to be a pattern for thissplitting. 2J(F-F) is greater for the CF2 group that is closer toCl-; in the other three complexes it is greater for the CF2 groupfurther removed from X. The largest splitting is 34 Hz for C2F4:

CN-; it is only 10 Hz for C2F4:NC-. Scheme 3 shows thestructures of C2F4:CN- and C2F4:NC-, with the former beingsimilar to the structure of C2F4:HLi with C2V symmetry. Thestructural differences suggest differences in the mode ofinteraction in these two complexes, which may indeed beresponsible for the significant differences in the splittings.Because of the differences observed between 2J(F-F) valuesin C2V and Cs structures, discussing changes in this couplingconstant in C2V structures is tenuous at best; hence, 2J(F-F)will not be included in the analyses that follow.

Coupling Constants in Binary Complexes of C2W Sym-metry. Because some coupling constants of C2F4 are positivewhile others are negative, the effects of X and FH on thesecoupling constants will be evaluated in terms of whether theirabsolute values increase or decrease. As evident from Table 2,the interaction of X with C2F4 increases 1J(C-C) and 2J(C-F)but decreases 1J(C-F) and 3J(F-F) trans and cis. In contrast,interaction of FH with C2F4 has opposite effects, decreasing

SCHEME 2: Cs and C2W structures

TABLE 1: MP2/aug-cc-pVTZ Interaction Energies (∆E)and Energy Barriers (E‡) (kJ mol-1) for Electron-Donors Xwith C2F4 in Cs and C2W Configurationsa

C2F4:X ∆E (Cs) ∆E (C2V) E‡

C2F4:HLi -15.01 -14.92 0.08C2F4:Cl- -35.17 -35.17 0.00C2F4:CN- -32.43 -31.43 1.00C2F4:NC- -35.70 -33.49 2.21

a The optimized C2V structure FH:C2F4 has a binding energy of-2.52 kJ mol-1.

TABLE 2: Coupling Constants (Hz) for C2F4 and BinaryComplexes FH:C2F4 (C2W) and C2F4:X with Cs and C2WSymmetries

1J(C-C) 1J(C-F)

species C2V Cs C2V Csa Cs

b

C2F4 201.66 -274.64C2F4:HLi 207.62 207.35 -265.66 -265.02 -266.24C2F4:Cl- 212.86 212.14 -257.41 -256.72 -258.45C2F4:CN- 212.49 209.49 -257.54 -258.24 -256.27C2F4:NC- 212.79 211.41 -258.26 -258.12 -257.89FH:C2F4 195.29 -281.96

2J(F-F) 2J(C-F)

C2V Csa Cs

b C2V Csa Cs

b

C2F4 122.68 48.64C2F4:HLi 121.74 117.16 125.72 49.03 48.44 49.27C2F4:Cl- 121.59 128.14 115.01 49.03 49.16 48.84C2F4:CN- 121.85 104.34 137.86 49.16 48.56 48.25C2F4:NC- 124.81 119.66 129.45 50.04 49.11 49.31FH:C2F4 115.15 46.27

3J(F-F) trans 3J(F-F) cis

C2V Cs C2V Cs

C2F4 -111.00 67.58C2F4:HLi -105.41 -105.50 63.37 63.23C2F4:Cl- -102.07 -102.10 60.40 60.32C2F4:CN- -100.86 -101.24 60.82 59.60C2F4:NC- -102.33 -102.20 61.84 60.71FH:C2F4 -114.14 69.66

a In Cs symmetry, this is the value from the CF2 group which iscloser to the atom that bonds the anion to the monomer. b In Cs

symmetry, this is the value from the CF2 group which is furtherfrom the atom that bonds the anion to the monomer.

SCHEME 3: Optimized Cs Structures of C2F4:CN- andC2F4:NC-

3714 J. Phys. Chem. A, Vol. 114, No. 10, 2010 Del Bene et al.

1J(C-C) and 2J(C-F) but increasing 1J(C-F) and 3J(F-F) transand cis. This is really not surprising, given that X and FH playvery different roles in complex formation with X an electrondonor and FH an electron acceptor.

Both 1J(C-C) and 1J(C-F) are dominated by the FC term,as evident from Table S1 of the Supporting Information. Sincethis term is a contact term dependent on s-electron densities inboth the ground state and the excited states that couple to itthrough the FC operator, it is obvious that although interactionswith both FH and X occur through the π-electron system ofC2F4, these π interactions induce significant changes in thes-electron densities of C2F4 in these states. 2J(C-F) is alsodominated by the FC term and this term is a good approximationto 2J(C-F), but only because the non-negligible contributionsfrom the PSO and SD terms cancel. The negative PSOcontribution to 3J(F-F) trans dominates and is an order ofmagnitude greater than the positive SD term. 3J(F-F) cis arisesfrom similar positive contributions from the PSO and SD terms.These terms are noncontact terms dependent on p-electrondensities, which increase in importance particularly whenfluorine lone pairs are present.21 The roles played by the variousterms in nonadditivities will be discussed below.

Nonadditivities in Ternary Complexes. Table 3 presentscoupling constants for complexes FH:C2F4:X, and Table 4provides a summary of data needed to evaluate nonadditivity

effects for the ternary complexes FH:C2F4:X. In Table 4,[δJ(FH:C2F4) + δJ(C2F4:X)] represents the sum of the changesin a coupling constant J in FH:C2F4 and C2F4:X relative to itsvalue in C2F4. A positive sign indicates that the sum gives anincrease in J, whereas a negative sign means that the sum leadsto a decrease in J. Similarly, δJ(FH:C2F4:X) is the change in Jin the ternary complex FH:C2F4:X relative to C2F4, given as apositive number if the absolute value of J increases, and negativeif J decreases. Nonadditivity is evaluated as the differencebetween [δJ(FH:C2F4) + δJ(C2F4:X)] and δJ(FH:C2F4:X), witha positive sign indicating nonadditivity in a positive sense; thatis, the change in J is greater than anticipated from the sum ofthe changes for the corresponding binary complexes. A negativenonadditivity indicates that the change in J in the ternarycomplex is less than the sum of the changes for the correspond-ing binary complexes. Since FH and X have opposite effectson C2F4 coupling constants, it might be anticipated that the valueof J in a ternary complex will lie between the values in thecorresponding binary complexes. Whether this is the case ornot will comprise part of the nonadditivity assessment.

A comparison of the values of 1J(C-C) in Table 2 with thosein Table 3 shows that the value of this coupling constant forFH:C2F4:X does lie between the values for the correspondingbinary complexes, as anticipated. A detailed assessment ofnonadditivity can be easily illustrated using 1J(C-C) as anexample. 1J(C-C) decreases (δJ ) -6.4 Hz) upon formationof FH:C2F4; in contrast, it increases (δJ ) +6.0 Hz) uponformation of C2F4:HLi. As evident from Table 4, simultaneousinteraction of the two neutral molecules FH and HLi with C2F4

leads to a positive nonadditivity for 1J(C-C), since the changein 1J(C-C) in the ternary complex is greater than the sum ofthe changes in the corresponding binary complexes. In this case,the effect of FH is dominant. In contrast, changes in the binary

TABLE 3: Coupling Constants (Hz) for Ternary ComplexesFH:C2F4:X of C2W Symmetry

FH:C2F4:X 1J(C-C) 1J(C-F) 2J(F-F) 2J(C-F)3J(C-F)

trans3J(C-F)

cis

X ) HLi 200.14 -272.77 108.88 45.25 -106.90 64.82X ) Cl- 203.90 -264.82 103.59 43.47 -103.22 61.10X ) CN- 203.76 -264.46 103.69 43.65 -100.84 61.67X ) NC- 203.95 -266.10 108.34 44.92 -103.55 63.37

TABLE 4: Nonadditivity Effects of FH and X on Spin-Spin Coupling Constants (Hz) in FH:C2F4:X

complex J [δJ(FH:C2F4)a + δJ(C2F4:X)b]c δJ(FH:C2F4:X)d nonadditivitye

1J(C–C)FH:C2F4:HLi –6.4a + 6.0b –0.4c –1.5 1.1FH:C2F4:Cl– 11.2 4.8 2.2 –2.6FH:C2F4:CN– 10.8 4.4 2.1 –2.3FH:C2F4:NC– 11.1 4.7 2.3 –2.4

1J(C–F)FH:C2F4:HLi +7.3 + (–9.0) –1.7 –1.9 0.2FH:C2F4:Cl– –17.2 –9.9 –9.8 –0.1FH:C2F4:CN– –17.1 –9.8 –10.2 0.4FH:C2F4:NC– –16.4 –9.1 –8.5 –0.6

2J(C–F)FH:C2F4:HLi –2.4 + 0.4 –2.0 –3.4 1.4FH:C2F4:Cl– 0.4 –2.0 –5.2 3.2FH:C2F4:CN– 0.5 –1.9 –5.0 3.1FH:C2F4:NC– 1.4 –1.0 –3.7 2.7

3J(F–F) transFH:C2F4:HLi +3.1 + (–5.6) –2.5 –4.1 1.6FH:C2F4:Cl– –8.9 –5.8 –7.8 2.0FH:C2F4:CN– –10.1 –7.0 –10.2 3.2FH:C2F4:NC– –8.7 –5.6 –7.5 1.9

3J(F–F) cisFH:C2F4:HLi +2.1 + (–4.2) –2.1 –2.8 0.7FH:C2F4:Cl– –7.2 –5.1 –6.5 1.4FH:C2F4:CN– –6.8 –4.7 –5.9 1.2FH:C2F4:NC– –5.7 –3.6 –4.2 0.6

a Change in J in the binary complex FH:C2F4. The changes are given in terms of absolute values, with the sign indicating whether theabsolute value of J has increased (+) or decreased (-) relative to C2F4. b Change in J in the binary complex C2F4:X. c The sum of the changesin J in the corresponding binary complexes. d The change in J in the ternary complex relative to isolated C2F4. e A positive nonadditivityindicates that the effects of FH and X together are nonadditive in a positive sense; that is, the change in J is greater than the sum of thechanges in the corresponding binary complexes. A negative nonadditivity indicates that the effects are less than the sum of the changes.

J. Phys. Chem. A, Vol. 114, No. 10, 2010 3715

complexes when X is an anion are large and positive (11.2,10.8, and 11.1 Hz for X ) Cl-, CN-, and NC-, respectively),and much greater than the -6.4 Hz decrease in 1J(C-C) in thecomplex with FH. However, as evident from Table 3, the changein a ternary complex is less than the sum of the changes in thecorresponding binary complexes. Since 1J(C-C) increases inthe ternary complexes, the anions have the dominant effect, butthis effect is attenuated by the effect of FH, and the two effectsare nonadditive in a negative sense.

How similar should δJ(FH:C2F4:X) and [δJ(FH:C2F4) +δJ(C2F4:X)] be to make the effects of FH and X on a couplingconstant additive? We could set an arbitrary limit of 1 Hz. Thenonadditivities for 1J(C-F) are all smaller than 1 Hz, so forthe complexes FH:C2F4:X the effects of FH and X on 1J(C-F)are additive. However, the situation for 2J(C-F) is quitedifferent. Although FH decreases 2J(C-F) in FH:C2F4 by only-2.4 Hz, the electron donors only slightly increase 2J(C-F) inC2F4:X by 0.4 to 1.4 Hz. However, in the ternary complexes2J(C-F) decreases by -3.4 to -5.2 Hz; that is, the decrease in2J(C-F) is greater than the decrease found for FH:C2F4. Theeffects of FH and X are nonadditive, with the effect of FH notonly dominant but also enhanced by the presence of X.

For complexes FH:C2F4, 3J(F-F) trans and cis increase by3.1 and 2.1 Hz, respectively. The decreases in 3J(F-F) transand cis in complexes C2F4:X range from -5.6 to -10.1 Hzand from -4.2 to -7.2 Hz, respectively. In the ternarycomplexes these two coupling constants are reduced relative toC2F4, so that the effects of the electron donors dominate. ForFH:C2F4:HLi and FH:C2F4:NC-, the effects of FH and X on3J(F-F) cis are additive. However, for the remaining ternarycomplexes the effects of FH and X are nonadditive in a positivesense; that is, the change in 3J(F-F) trans and cis in a ternarycomplex is greater than anticipated from the sum of the changesin the corresponding binary complexes. Moreover, when X isCl- or CN- with interaction occurring through C, the decreasein 3J(F-F) in FH:C2F4:X is within 1 Hz of the decrease in thecorresponding binary complexes C2F4:X; that is, the effect ofX is essentially independent of the presence of FH.

Finally, what roles do the various terms that contribute tototal J play in nonadditivities? Not surprisingly, just as the FCterm dominates 1J(C-C), this term also dominates and is a goodapproximation to the nonadditivities computed for 1J(C-C). Incontrast, although the FC term is also by far the dominant termcontributing to the total coupling constant 1J(C-F), and theeffects of FH and X are additive as reported in Table 4, theseeffects are nonadditive when evaluated from the PSO and FCterms individually. In particular, the changes in the FCcomponent in the ternary complex are more negative than thesum of the changes in the corresponding binary complexes,while changes in the PSO component are more positive. Whenthese are combined they cancel, and the effects of HF and Xon 1J(C-F) are additive in the ternary complexes.

For 2J(C-F), the FC term is again the dominant term, andthe nonadditivities evaluated from this term also approximatethe nonadditivities computed for this coupling constant to within0.5 Hz. However, the situation for 3J(F-F) trans and cis thatinvolve coupling of two F atoms is dramatically different. Asevident from Table S1 (Supporting Information) and thediscussion above, the PSO terms dominate 3J(F-F) trans andthe FC contributions are negligible. However, the FC contribu-tions to the nonadditivities are not negligible. For example,nonadditivities evaluated for FH:C2F4:HLi and FH:C2F4:CN-

from the FC terms are 1.1 and 2.2 Hz, respectively, while thePSO contributions are 0.5 and 0.8 Hz, respectively. For

FH:C2F4:Cl- and FH:C2F4:NC- the relative importance of thecontributions from these two terms are reversed, with the PSOterms contributing 1.4 and 1.1 Hz, respectively, and the FC termscontributing 0.5 and 0.6 Hz, respectively. For 3J(F-F) cis thePSO and SD terms make comparable contributions to the totalJ and the FC term is again negligible. Nonadditivities evaluatedfor 3J(F-F) cis from the PSO term are dominant, followed bythe FC contribution, with the SD contribution very small. Theanalysis of nonadditivities in terms of the components of totalJ provides another insight into the subtle changes in both s-and p-electron densities in ground and excited states of C2F4

due to the interaction of this molecule through its π-electronsystem with an electron donor X and an electron acceptor FH.What is striking is that the relative importance of the PSO, FC,and SD terms in determining total J does not necessarilycorrespond to their importance in determining the nonadditivitiesin J evaluated for the ternary complexes.

Conclusions

C2F4 coupling constants have been evaluated at EOM-CCSD/(qzp,qz2p) in binary complexes with electron donors X (X )HLi, Cl-, CN-) and with the electron acceptor FH, as well asin ternary complexes FH:C2F4:X in which X and FH are locatedon opposite faces of the C2F4 π cloud. The following statementsare supported by the results of these calculations.

1. Coupling constants for C2F4:X in binary complexes withC2V and Cs symmetries are similar, except for 2J(F-F).

2. Opposite effects of X and FH on C2F4 coupling constantsare observed in binary complexes. The interaction of X withC2F4 increases the absolute values of 1J(C-C) and 2J(C-F) butdecreases the absolute values of 1J(C-F) and 3J(F-F) trans andcis. In contrast, interaction of FH with C2F4 decreases 1J(C-C)and 2J(C-F) but increases 1J(C-F) and 3J(F-F) trans and cis.

3. Changes in 1J(C-F) computed for ternary complexes arewithin 1 Hz of the sum of the changes for the correspondingbinary complexes. Thus, the effects of X and FH on 1J(C-F)are additive.

4. The remaining coupling constants in ternary complexesexhibit both positive and negative nonadditivity effects. Thevalues of most of these coupling constants lie between the valuesfor FH:C2F4 and C2F4:X. However, that is not the case for2J(C-F), and the effect of FH is enhanced by the presence ofX. Moreover, although the effects of FH and X on 3J(F-F) cisare additive when X is either HLi or NC-, values of 3J(F-F)trans and cis are nonadditive when X is Cl- or CN- bondedthrough C, and are within 1 Hz of the values for the corre-sponding binary complexes C2F4:X.

5. Significant differences can be found between the relativecontributions of the PSO, FC, and SD terms to total J and tothe nonadditivities of J in ternary complexes FH:C2F4:X.

Acknowledgment. This work has been financed by theSpanish MICINN (CTQ2009-13129-C02-02) and ComunidadAutonoma de Madrid (Project MADRISOLAR, ref S-0505/PPQ/0225). The continuing support of the Ohio SupercomputerCenter and CTI-CSIC is gratefully acknowledged.

Supporting Information Available: PSO, DSO, FC, andSD components of 1J(C-C), 1J(C-F), 2J(C-F), 2J(F-F),3J(F-F) cis and trans, and the full refs 13 and 20. This materialis available free of charge via the Internet at http://pubs.acs.org.

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