J. Phys. Chem. A 2010, 114, 3713–3717
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Ab Initio Study of Nonadditivity Effects: Spin-Spin Coupling Constants for Tetrafluoroethene 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 Quı´mica Me´dica (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 electron donors X (X ) HLi, Cl-, CN-) and with the electron acceptor FH, and in ternary complexes FH:C2F4:X in which X and FH are located on opposite faces of the C2F4 π cloud. The electron donors X and the electron acceptor FH have opposite effects on 1J(C-C), 1J(C-F), 2J(C-F), and 3J(F-F) in binary complexes. Effects of X and FH on a particular coupling constant in a ternary complex are additive if the change in the coupling constant in this complex relative to C2F4 is within 1 Hz of the sum of the changes in the corresponding binary complexes. This is the case for 1J(C-F). Both positive and negative nonadditivities are computed for the remaining coupling constants. Although the values of most coupling constants lie between the values for FH:C2F4 and C2F4:X, that is not the case for 2J(C-F), and the effect of FH is enhanced by the presence of X. Moreover, values of 3J(F-F) trans and cis for FH:C2F4:X when X is Cl- or CN- bonded through C are within 1 Hz of the values for the corresponding binary complex C2F4:X. Significant differences can be found between the relative contributions of the PSO, FC, and SD terms to total J and to the nonadditivities of J in ternary complexes FH:C2F4:X. SCHEME 1
Introduction In recent years, a number of theoretical and experimental studies have reported the possibility of interaction between electron-rich moieties and the π clouds of electron-deficient systems.1 Among these, tetrafluoroethene, C2F4, is the smallest π-electron deficient molecule for which binary complexes with neutral and anionic electron-donor molecules X have been described.2-4 Moreover, although such systems usually are not good electron-pair donors, the binary systems C2F4:X are able to act as electron-pair donors to form hydrogen-bonded ternary complexes with molecules Y located on the opposite face of the C2F4 π system, as illustrated in Scheme 1. The properties of these complexes exhibit nonadditivity effects in the ground state.2,3 In the present article, we examine changes in spin-spin coupling constants of C2F4 in binary complexes with both electron donors and an electron acceptor, and ask whether nonadditivity effects can be seen in ternary complexes. For our study, EOM-CCSD spin-spin coupling constants have been evaluated for C2F4 and binary π complexes C2F4:X, with X the neutral molecule LiH with an electron-rich H which forms a hydride bond,5,6 or an anion Cl- or CN-, allowing for electron donation by CN- through either C or N. Coupling constants have also been evaluated for the π hydrogen-bonded complex FH:C2F4, and for ternary complexes FH:C2F4:X. In this paper we report and analyze the changes in the C2F4 coupling constants in these complexes, and ask whether or not the changes in the ternary complexes are additive. * Authors to whom correspondence should be addressed. E-mails: J.E.D.B.,
[email protected]; I.A.,
[email protected]. † Youngstown State University. ‡ Instituto de Quı´mica Me´dica (CSIC).
Methods The geometries of the monomers and complexes have been optimized at MP27-10 with the aug-cc-pVTZ basis set,11,12 as implemented in the Gaussian-03 program.13 Some of these complexes have been described previously.2,3 Two sets of complexes C2F4:X have been optimized, one with C2V and the other with Cs symmetry. This was done so that differences in coupling constants could be evaluated for the same complex with two different symmetries. This was a necessary step in this study because the computational demands of EOM-CCSD make coupling constant calculations on FH:C2F4:X complexes feasible only if they have C2V symmetry. FH:C2F4 and FH:C2F4:X were optimized at MP2/aug-cc-pVTZ under this constraint. These calculations were carried out on the computers at CSIC. The calculation of spin-spin coupling constants employed the equation-of-motion coupled-cluster singles and doubles method (EOM-CCSD) in the configuration interaction (CI)-like approximation14,15 with all electrons correlated. The Ahlrichs qzp basis set16 was used on 13C, 15N, and 19F atoms, and the qz2p basis set was used for 35Cl and 1H. Since an Ahlrichs qzp basis set is not available for 7Li, a previously constructed corresponding basis set was used for this atom.17 This basis set has the same number of contracted functions (6s, 4p, and 1d) as the Ahlrichs qzp basis for C, N, and F. This level of theory has been shown to produce coupling constants involving 13C and 19F that are in good agreement with experimental values.18
10.1021/jp1003159 2010 American Chemical Society Published on Web 02/17/2010
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Del Bene et al. TABLE 2: Coupling Constants (Hz) for C2F4 and Binary Complexes FH:C2F4 (C2W) and C2F4:X with Cs and C2W Symmetries
SCHEME 2: Cs and C2W structures
1
TABLE 1: MP2/aug-cc-pVTZ Interaction Energies (∆E) and Energy Barriers (E‡) (kJ mol-1) for Electron-Donors X with C2F4 in Cs and C2W Configurationsa C2F4:X
∆E (Cs)
∆E (C2V)
E‡
C2F4:HLi C2F4:ClC2F4:CNC2F4:NC-
-15.01 -35.17 -32.43 -35.70
-14.92 -35.17 -31.43 -33.49
0.08 0.00 1.00 2.21
a
The optimized C2V structure FH:C2F4 has a binding energy of -2.52 kJ mol-1.
In the Ramsey approximation,19 the nuclear spin-spin coupling constant is composed of four terms: the paramagnetic spin-orbit (PSO), diamagnetic spin-orbit (DSO), Fermi-contact (FC), and spin-dipole (SD). All terms have been computed for all complexes. The EOM-CCSD calculations were carried out using ACES II20 on the Itanium cluster at the Ohio Supercomputer Center. Results and Discussion Binding Energies of Binary Complexes of C2F4. As noted previously, some complexes C2F4:X have Cs rather than C2V symmetry.2,3 The Cs structure is usually the minimum-energy structure, with the C2V structure being the transition structure for the interconversion of the Cs mirror images, as illustrated in Scheme 2. However, the interaction energies reported in Table 1 indicate that the transition-state barrier for interconversion of the two equivalent Cs structures is very low at less that 2.5 kJ mol-1. The small difference between the Cs and C2V structures reflects a very flat potential surface for translation of X above the C-C bond. Such small differences imply that zero-point vibrational motion would make the average ground-state structure C2V. Only a constrained C2V structure of FH:C2F4 has been optimized, given its very small stabilization energy and the preference for FH to interact with isolated C2F4 as an electron-donor through F.2,3 Coupling Constants: C2W vs Cs. Table 2 presents coupling constants 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 for 2 J(F-F), differences between corresponding coupling constants in the C2V and Cs structures of C2F4:X are small. These are usually less than 1 Hz except for 2J(C-C) for C2F4:CN-, in which case the difference is 3 Hz out of a total of 212 Hz. Such small differences provide justification for using the coupling constants for C2V structures in our analyses of nonadditivity effects. There is, however, a noticeable difference between the values of the two unique 2J(F-F) couplings in the Cs structures of C2F4:X compared to the C2V. Values of 2J(F-F) in the Cs structures are “split” relative to those for the C2V complex, with the C2V value being remarkably close to the average of the Cs values. However, there does not appear to be a pattern for this splitting. 2J(F-F) is greater for the CF2 group that is closer to Cl-; in the other three complexes it is greater for the CF2 group further removed from X. The largest splitting is 34 Hz for C2F4:
1
J(C-C)
J(C-F)
species
C2V
Cs
C2V
Csa
Csb
C 2F 4 C2F4:HLi C2F4:ClC2F4:CNC2F4:NCFH:C2F4
201.66 207.62 212.86 212.49 212.79 195.29
207.35 212.14 209.49 211.41
-274.64 -265.66 -257.41 -257.54 -258.26 -281.96
-265.02 -256.72 -258.24 -258.12
-266.24 -258.45 -256.27 -257.89
2
C2 F4 C2F4:HLi C2F4:ClC2F4:CNC2F4:NCFH:C2F4
a
b
J(C-F)
C2V
Cs
Cs
C2V
Csa
Csb
122.68 121.74 121.59 121.85 124.81 115.15
117.16 128.14 104.34 119.66
125.72 115.01 137.86 129.45
48.64 49.03 49.03 49.16 50.04 46.27
48.44 49.16 48.56 49.11
49.27 48.84 48.25 49.31
3
J(F-F) trans
C2V C2 F4 C2F4:HLi C2F4:ClC2F4:CNC2F4:NCFH:C2F4
2
J(F-F)
-111.00 -105.41 -102.07 -100.86 -102.33 -114.14
3
J(F-F) cis
Cs
C2V
Cs
-105.50 -102.10 -101.24 -102.20
67.58 63.37 60.40 60.82 61.84 69.66
63.23 60.32 59.60 60.71
a
In Cs symmetry, this is the value from the CF2 group which is closer to the atom that bonds the anion to the monomer. b In Cs symmetry, this is the value from the CF2 group which is further from the atom that bonds the anion to the monomer.
SCHEME 3: Optimized Cs Structures of C2F4:CN- and C2F4:NC-
CN-; it is only 10 Hz for C2F4:NC-. Scheme 3 shows the structures of C2F4:CN- and C2F4:NC-, with the former being similar to the structure of C2F4:HLi with C2V symmetry. The structural differences suggest differences in the mode of interaction in these two complexes, which may indeed be responsible for the significant differences in the splittings. Because of the differences observed between 2J(F-F) values in C2V and Cs structures, discussing changes in this coupling constant 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 Symmetry. Because some coupling constants of C2F4 are positive while others are negative, the effects of X and FH on these coupling constants will be evaluated in terms of whether their absolute 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
J. Phys. Chem. A, Vol. 114, No. 10, 2010 3715 TABLE 3: Coupling Constants (Hz) for Ternary Complexes FH:C2F4:X of C2W Symmetry 3
FH:C2F4:X X ) HLi X ) ClX ) CNX ) NC-
1
J(C-C)
1
200.14 203.90 203.76 203.95
-272.77 -264.82 -264.46 -266.10
J(C-F)
2
J(F-F)
108.88 103.59 103.69 108.34
2
J(C-F)
J(C-F) trans
45.25 43.47 43.65 44.92
-106.90 -103.22 -100.84 -103.55
3
J(C-F) cis 64.82 61.10 61.67 63.37
1
J(C-C) and 2J(C-F) but increasing 1J(C-F) and 3J(F-F) trans and cis. This is really not surprising, given that X and FH play very different roles in complex formation with X an electron donor 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. Since this term is a contact term dependent on s-electron densities in both the ground state and the excited states that couple to it through the FC operator, it is obvious that although interactions with both FH and X occur through the π-electron system of C2F4, these π interactions induce significant changes in the s-electron densities of C2F4 in these states. 2J(C-F) is also dominated by the FC term and this term is a good approximation to 2J(C-F), but only because the non-negligible contributions from the PSO and SD terms cancel. The negative PSO contribution to 3J(F-F) trans dominates and is an order of magnitude greater than the positive SD term. 3J(F-F) cis arises from similar positive contributions from the PSO and SD terms. These terms are noncontact terms dependent on p-electron densities, which increase in importance particularly when fluorine lone pairs are present.21 The roles played by the various terms in nonadditivities will be discussed below. Nonadditivities in Ternary Complexes. Table 3 presents coupling constants for complexes FH:C2F4:X, and Table 4 provides 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 changes in a coupling constant J in FH:C2F4 and C2F4:X relative to its value in C2F4. A positive sign indicates that the sum gives an increase in J, whereas a negative sign means that the sum leads to a decrease in J. Similarly, δJ(FH:C2F4:X) is the change in J in the ternary complex FH:C2F4:X relative to C2F4, given as a positive number if the absolute value of J increases, and negative if J decreases. Nonadditivity is evaluated as the difference between [δJ(FH:C2F4) + δJ(C2F4:X)] and δJ(FH:C2F4:X), with a positive sign indicating nonadditivity in a positive sense; that is, the change in J is greater than anticipated from the sum of the changes for the corresponding binary complexes. A negative nonadditivity indicates that the change in J in the ternary complex is less than the sum of the changes for the corresponding binary complexes. Since FH and X have opposite effects on C2F4 coupling constants, it might be anticipated that the value of J in a ternary complex will lie between the values in the corresponding binary complexes. Whether this is the case or not will comprise part of the nonadditivity assessment. A comparison of the values of 1J(C-C) in Table 2 with those in Table 3 shows that the value of this coupling constant for FH:C2F4:X does lie between the values for the corresponding binary complexes, as anticipated. A detailed assessment of nonadditivity can be easily illustrated using 1J(C-C) as an example. 1J(C-C) decreases (δJ ) -6.4 Hz) upon formation of FH:C2F4; in contrast, it increases (δJ ) +6.0 Hz) upon formation of C2F4:HLi. As evident from Table 4, simultaneous interaction of the two neutral molecules FH and HLi with C2F4 leads to a positive nonadditivity for 1J(C-C), since the change in 1J(C-C) in the ternary complex is greater than the sum of the changes in the corresponding binary complexes. In this case, the effect of FH is dominant. In contrast, changes in the binary
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
1
J(C–C)
FH:C2F4:HLi FH:C2F4:Cl– FH:C2F4:CN– FH:C2F4:NC– 1
J(C–F)
FH:C2F4:HLi FH:C2F4:Cl– FH:C2F4:CN– FH:C2F4:NC– 2
J(C–F)
FH:C2F4:HLi FH:C2F4:Cl– FH:C2F4:CN– FH:C2F4:NC– 3
J(F–F) trans
FH:C2F4:HLi FH:C2F4:Cl– FH:C2F4:CN– FH:C2F4:NC– 3
FH:C2F4:HLi FH:C2F4:Cl– FH:C2F4:CN– FH:C2F4:NC–
J(F–F) cis
–6.4a + 6.0b 11.2 10.8 11.1
–0.4c 4.8 4.4 4.7
–1.5 2.2 2.1 2.3
1.1 –2.6 –2.3 –2.4
+7.3 + (–9.0) –17.2 –17.1 –16.4
–1.7 –9.9 –9.8 –9.1
–1.9 –9.8 –10.2 –8.5
0.2 –0.1 0.4 –0.6
–2.4 + 0.4 0.4 0.5 1.4
–2.0 –2.0 –1.9 –1.0
–3.4 –5.2 –5.0 –3.7
1.4 3.2 3.1 2.7
+3.1 + (–5.6) –8.9 –10.1 –8.7
–2.5 –5.8 –7.0 –5.6
–4.1 –7.8 –10.2 –7.5
1.6 2.0 3.2 1.9
+2.1 + (–4.2) –7.2 –6.8 –5.7
–2.1 –5.1 –4.7 –3.6
–2.8 –6.5 –5.9 –4.2
0.7 1.4 1.2 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 the absolute 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 changes in J in the corresponding binary complexes. d The change in J in the ternary complex relative to isolated C2F4. e A positive nonadditivity indicates 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 the changes in the corresponding binary complexes. A negative nonadditivity indicates that the effects are less than the sum of the changes.
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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 the complex with FH. However, as evident from Table 3, the change in a ternary complex is less than the sum of the changes in the corresponding binary complexes. Since 1J(C-C) increases in the ternary complexes, the anions have the dominant effect, but this effect is attenuated by the effect of FH, and the two effects are 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 coupling constant additive? We could set an arbitrary limit of 1 Hz. The nonadditivities for 1J(C-F) are all smaller than 1 Hz, so for the complexes FH:C2F4:X the effects of FH and X on 1J(C-F) are additive. However, the situation for 2J(C-F) is quite different. Although FH decreases 2J(C-F) in FH:C2F4 by only -2.4 Hz, the electron donors only slightly increase 2J(C-F) in C2F4:X by 0.4 to 1.4 Hz. However, in the ternary complexes 2 J(C-F) decreases by -3.4 to -5.2 Hz; that is, the decrease in 2 J(C-F) is greater than the decrease found for FH:C2F4. The effects of FH and X are nonadditive, with the effect of FH not only dominant but also enhanced by the presence of X. For complexes FH:C2F4, 3J(F-F) trans and cis increase by 3.1 and 2.1 Hz, respectively. The decreases in 3J(F-F) trans and cis in complexes C2F4:X range from -5.6 to -10.1 Hz and from -4.2 to -7.2 Hz, respectively. In the ternary complexes these two coupling constants are reduced relative to C2F4, so that the effects of the electron donors dominate. For FH:C2F4:HLi and FH:C2F4:NC-, the effects of FH and X on 3 J(F-F) cis are additive. However, for the remaining ternary complexes the effects of FH and X are nonadditive in a positive sense; that is, the change in 3J(F-F) trans and cis in a ternary complex is greater than anticipated from the sum of the changes in the corresponding binary complexes. Moreover, when X is Cl- or CN- with interaction occurring through C, the decrease in 3J(F-F) in FH:C2F4:X is within 1 Hz of the decrease in the corresponding binary complexes C2F4:X; that is, the effect of X is essentially independent of the presence of FH. Finally, what roles do the various terms that contribute to total J play in nonadditivities? Not surprisingly, just as the FC term dominates 1J(C-C), this term also dominates and is a good approximation to the nonadditivities computed for 1J(C-C). In contrast, although the FC term is also by far the dominant term contributing to the total coupling constant 1J(C-F), and the effects of FH and X are additive as reported in Table 4, these effects are nonadditive when evaluated from the PSO and FC terms individually. In particular, the changes in the FC component in the ternary complex are more negative than the sum of the changes in the corresponding binary complexes, while changes in the PSO component are more positive. When these are combined they cancel, and the effects of HF and X on 1J(C-F) are additive in the ternary complexes. For 2J(C-F), the FC term is again the dominant term, and the nonadditivities evaluated from this term also approximate the nonadditivities computed for this coupling constant to within 0.5 Hz. However, the situation for 3J(F-F) trans and cis that involve coupling of two F atoms is dramatically different. As evident from Table S1 (Supporting Information) and the discussion above, the PSO terms dominate 3J(F-F) trans and the FC contributions are negligible. However, the FC contributions to the nonadditivities are not negligible. For example, nonadditivities evaluated for FH:C2F4:HLi and FH:C2F4:CNfrom the FC terms are 1.1 and 2.2 Hz, respectively, while the PSO contributions are 0.5 and 0.8 Hz, respectively. For
Del Bene et al. FH:C2F4:Cl- and FH:C2F4:NC- the relative importance of the contributions from these two terms are reversed, with the PSO terms contributing 1.4 and 1.1 Hz, respectively, and the FC terms contributing 0.5 and 0.6 Hz, respectively. For 3J(F-F) cis the PSO and SD terms make comparable contributions to the total J and the FC term is again negligible. Nonadditivities evaluated for 3J(F-F) cis from the PSO term are dominant, followed by the FC contribution, with the SD contribution very small. The analysis of nonadditivities in terms of the components of total J provides another insight into the subtle changes in both sand p-electron densities in ground and excited states of C2F4 due to the interaction of this molecule through its π-electron system 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 necessarily correspond to their importance in determining the nonadditivities in 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 as in ternary complexes FH:C2F4:X in which X and FH are located on opposite faces of the C2F4 π cloud. The following statements are supported by the results of these calculations. 1. Coupling constants for C2F4:X in binary complexes with C2V and Cs symmetries are similar, except for 2J(F-F). 2. Opposite effects of X and FH on C2F4 coupling constants are observed in binary complexes. The interaction of X with C2F4 increases the absolute values of 1J(C-C) and 2J(C-F) but decreases the absolute values of 1J(C-F) and 3J(F-F) trans and cis. 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 are within 1 Hz of the sum of the changes for the corresponding binary complexes. Thus, the effects of X and FH on 1J(C-F) are additive. 4. The remaining coupling constants in ternary complexes exhibit both positive and negative nonadditivity effects. The values of most of these coupling constants lie between the values for FH:C2F4 and C2F4:X. However, that is not the case for 2 J(C-F), and the effect of FH is enhanced by the presence of X. Moreover, although the effects of FH and X on 3J(F-F) cis are additive when X is either HLi or NC-, values of 3J(F-F) trans and cis are nonadditive when X is Cl- or CN- bonded through C, and are within 1 Hz of the values for the corresponding binary complexes C2F4:X. 5. Significant differences can be found between the relative contributions of the PSO, FC, and SD terms to total J and to the nonadditivities of J in ternary complexes FH:C2F4:X. Acknowledgment. This work has been financed by the Spanish MICINN (CTQ2009-13129-C02-02) and Comunidad Auto´noma de Madrid (Project MADRISOLAR, ref S-0505/PPQ/ 0225). The continuing support of the Ohio Supercomputer Center and CTI-CSIC is gratefully acknowledged. Supporting Information Available: PSO, DSO, FC, and SD components of 1J(C-C), 1J(C-F), 2J(C-F), 2J(F-F), 3 J(F-F) cis and trans, and the full refs 13 and 20. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Schottel, B. L.; Chifotides, H. T.; Dunbar, K. R. Chem. Soc. ReV. 2008, 37, 68.
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