Structures, Energies, and Spin−Spin Coupling Constants of Fluoro

ARTICLE pubs.acs.org/JPCA

Structures, Energies, and Spin
Spin Coupling Constants of Fluoro-Substituted 1,3-Diborata-2,4-diphosphoniocyclobutanes: Four-Member B
P
B
P Rings B2P2FnH8
n with n = 0, 1, 2, 4 Janet E. Del Bene,*,† Ibon Alkorta,*,‡ and Jos
e Elguero‡ † ‡

Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555, United States Instituto de Química M
edica (CSIC), Juan de la Cierva, 3, 28006-Madrid, Spain

bS Supporting Information ABSTRACT: An ab initio study has been carried out to determine the structures, relative stabilities, and spin
spin coupling constants of a set of 15 fluoro-substituted 1,3-diborata-2,4-diphosphoniocyclobutanes B2P2FnH8
n, for n = 0, 1, 2, 4, with fourmember B
P
B
P rings. Except for B2P2F4H4 with four fluorines bonded to two borons, these rings are puckered in a butterfly conformation. For a fixed number of fluorines, the isomers with B
F bonds are significantly more stable than those with P
F bonds. As the number of fluorines increases, the energy difference between the most stable isomer and the other isomers increases. Transition structures which interconvert axial and equatorial positions present relatively small inversion barriers. Coupling constants involving 31P, namely, 1J(B
P), 1J(P
F), 2J(P
P), 2J(P
F), and 3 J(P
F) are large and are capable of providing structural information. They are sensitive to the number of fluorines present and can discriminate between axial, equatorial, and geminal B
F and P
F bonds, although not all do this to the same extent. 1J(B
P) and 2 J(P
P) are similar in equilibrium and transition structures. Although transition structures no longer discriminate between axial and equatorial bonds, 1J(P
F) and 3J(P
F) remain sensitive to the number of fluorine atoms present.

’ INTRODUCTION In a recent study, Bertrand, Bourissou, et al.1 reported the preparation of the four 1,3-diborata-2,4-diphosphoniocyclobutanes which are illustrated in Figure 1. These authors described the crystal structures and selected NMR properties of these molecules. Although they noted that the NMR spectra of these molecules exhibit very broad 31P NMR signals, no spin
spin coupling constants were reported. We were intrigued by the results of ref 1 and asked what additional information spin
spin coupling constants might provide about these unusual molecules containing B
P
B
P rings. Because the molecules represented in Figure 1 are too large for high-level ab initio coupling constant calculations, we have investigated a series of smaller molecules containing the same B
P
B
P four-member ring structure, but with the groups bonded to B and P replaced by either H or F, giving a set of molecules represented as B2P2FnH8
n, for n = 0, 1, 2, 4. Based on the results of previous studies, it is likely that these molecules will exhibit large spin
spin coupling constants particularly for couplings involving 31P and 19F, and these should be experimentally measurable since both 31P and 19F are nuclei with spin 1 /2. In the present paper, we present the structures and relative stabilities of these molecules, estimates of the inversion barriers for some of these, and spin
spin coupling constants 1J(P
B), 1 J(B
F), 1J(P
F), 2J(B
B), 2J(P
P), 2J(B
F), 2J(P
F), 3 J(B
F), and 3J(P
F). We ask what effect does fluorine substitution have on these coupling constants, and how sensitive r 2011 American Chemical Society

are they to both the number of fluorines and the axial or equatorial positions of B
F and P
F bonds.

’ METHODS The structures of these molecules were initially optimized at second-order Møller
Plesset perturbation theory (MP2)2
5 with the 6-31þG(d,p)6
9 basis set. Frequency calculations were carried out at this level to confirm that the optimized structures correspond to either equilibrium structures (no imaginary frequencies) or transition structures (one imaginary frequency). These structures were then reoptimized at MP2 with the larger aug-cc-pVTZ basis set,10,11 and these structures were used for the subsequent coupling constant calculations. The optimization and frequency calculations were carried out using Gaussian 03.12 The molecules included in this study which have one or two fluorines have been restricted to those with Cs or higher symmetry, since coupling constant calculations with the method specified below are not feasible for fluoro-substituted B
P
B
P rings with only C1 symmetry. For molecules with four fluorines, C2v or higher symmetry has been required for the same reason. As a result, except for molecule 15 which has one fluorine atom bonded to each B and P in an equatorial position, the remaining Received: January 18, 2011 Revised: February 21, 2011 Published: April 01, 2011 4511

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Figure 1. The four 1,3-diborata-2,4-diphosphoniocyclobutanes reported in ref 1.

Figure 2. Molecules 8 and 9 illustrating the butterfly conformation of the rings and the numbering of atoms in the ring. In this illustration, axial positions have even numbers and equatorial have odd numbers.

molecules have fluorines bonded to either B or P, but not to both, in the same molecule. Spin
spin coupling constants were evaluated using the equation-of-motion coupled cluster singles and doubles method (EOMCCSD) in the CI (configuration interaction)-like approximation,13,14 with all electrons correlated. The Ahlrichs qzp basis set was placed on 19F and the qz2p basis on 31P.15 Because an Ahlrichs qzp basis is not available for B, a corresponding basis set which had been constructed and used previously for studies of B
H, B
N, and B
Li coupling was placed on 11B.16 The Dunning cc-pVDZ basis set was placed on 1H, and no coupling constants involving H are reported. In the Ramsey approximation, the total coupling constant (J) is expressed as a sum of four terms: the paramagnetic spin
orbit (PSO), diamagnetic spin
orbit (DSO), Fermi contact (FC), and spin
dipole (SD).17 All terms have been computed for all molecules. The EOM-CCSD calculations were carried out with ACES II18 on the IBM cluster 1350 (Glenn) at the Ohio Supercomputer Center.

’ RESULTS AND DISCUSSION The molecules which have been investigated in this study include the parent molecule B2P2H8, four isomers B2P2F1H7, seven isomers B2P2F2H6, and three isomers B2P2F4H4. Equilibrium and transition structures are illustrated in Figure S1 of the Supporting Information, and total energies are given in Table S1. The numbering of P and B atoms is illustrated in Figure 2. Except for molecule 13 which has the four fluorines bonded to the two borons in a structure with D2h symmetry, these molecules have either Cs or C2v symmetry with puckered rings in a butterfly conformation, and axial and equatorial B
F and P
F bonds. The molecules are identified by number and are distinguished by the number and positions of the fluorine atoms, as indicated in Table 1. If there is only one F atom bonded to a P atom or two F atoms bonded to the same P, that atom is designated P1, as

Table 1. Symmetries and Relative MP2/aug-cc-pVTZ Energies and Inversion Barriers (kJ/mol) for Equilibrium Structures and Transition Structures of B2P2FnH8
n equilibrium structures formula

transition structures Erel

no. description

sym

B2P2H8

1 parent

C2v

0.0

B2P2F1H7

2 B-Fax

Cs

17.7

B2P2F2H6

3 B-Feq

Cs

0.0

4 P-Fax

Cs

65.9

5 P-Feq

Cs

60.5

6 B-Fgem 7 B-Feq,B-Feq

Cs C2v

0.0 49.2

sym

barrier

D2h

8.4

C2v

3.9

8 B2-Feq,B4-Fax

Cs

38.6

C2h

5.9

9 P-Fgem

Cs

116.2

C2v

8.5

C2v

165.1

11 P1-Fax,P3-Feq

Cs

160.4

C2h

13.4

12 P-Feq,P-Feq

C2v

162.0 D2h

7.0

10 P-Fax,P-Fax

B2P2F4H4 13 B-Fgem,B-Fgem D2h

0.0

C2v C2v

244.8 216.8

14 P-Fgem,P-Fgem 15 all eq

illustrated for molecule 9 in Figure 2; if there is only one F atom bonded to a B atom or two F atoms bonded to the same B, it is B2. Whenever necessary, molecules are named so as to avoid ambiguity, as for example, molecule 8 in Figure 2 is B2-Feq,B4Fax to indicate that the B2
F bond is equatorial while the B4
F bond is axial. Among the isomers with two F atoms bonded to boron, molecule B-Fax,B-Fax is missing, since this isomer coverts without a barrier to B-Feq,B-Feq. Similarly, B2P2H4F4 with all axial bonds converts without a barrier to the all-equatorial molecule 15. 4512

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Figure 3. Relative energies of isomers with 1, 2, and 4 F atoms. The zero of energy corresponds to the lowest-energy isomer in each group.

Structures. It is difficult to precisely compare the experimental structures of the molecules illustrated in Figure 1 with the computed structures of molecules B2P2FnH8
n illustrated in Figure S1 in the Supporting Information. Geometric parameters are sensitive to the nature of the substituents, some of which are bulky organic groups in the molecules investigated experimentally, but only fluorine atoms in the molecules investigated in this study. Moreover, the experimental structures are derived from crystals which have packing requirements; the calculated structures refer to gas-phase molecules. Finally, the experimental distances and bond angles are ground-state values which are influenced by zero-point vibrational motion; the computed structures are equilibrium structures. Nevertheless, except for molecule 13, the computed structures of these molecules have puckered rings, in agreement with the experimental structures reported in ref 1. The computed B
P distances range from 1.92 to 2.05 Å, consistent with the experimental range of 1.97
2.01 Å. Experimental B
B distances range from 2.80 to 2.84 Å, while the computed values vary to a much greater extent from 2.57 to 2.82 Å, with the upper limit increased to 2.90 Å if molecule 13 with the planar ring is included. Similarly, experimental P
P distances range from 2.79 to 2.84 Å, while the computed range for molecules 1
12 and 14 is 2.79
2.88 Å. The shortest P
P distance is 2.65 Å in molecule 15 with four equatorial bonds. The upper limit increases to 2.97 Å when molecule 13 is included. Since the ring inversion barriers are low, it is reasonable to assume that zero-point motion tends to produce rings that approach a more nearly planar structure, and this motion would increase the upper values of both the B
B and the P
P distances. Energies. Relative energies of molecules 1 through 15 are reported in Table 1 and are illustrated in the scattergram of Figure 3.

Table 2. Computed and Experimental Coupling Constants Involving 31P, 11B, and 19F (Hz) molecule

coupling const

EOM-CCSD

exptl

PF3

1


1342

144119

PF5

1

1038 (P-Feq)

93819

PF(CH3)2 1,2-dihydro-1,2-azaborine

1

J(P
F) 1 J(B
H)


809 126

83019 13020

Borazine

1

131

13821

1,1-difluoro-ethene

2

31.9

32.722

J(P
F) J(P
F)

868 (P-Fax)

J(B
H) J(F
F)

In Table 1 and Figure 3, the energies are given relative to the lowest-energy isomer with a given number of fluorine atoms. As evident from Figure 3, for a fixed number of F atoms, isomers with F bonded to B are more stable than those with F bonded to P. For molecules B2P2F1H7 with only one F atom bonded to either B or P, the isomer with F in an equatorial position is more stable than that with F in an axial position. As the number of F atoms increases, the energy difference between the most stable isomer and the other isomers increases dramatically. That fluorine substitution has a more stabilizing effect on B compared to P is consistent with the experimental ΔHf° values of BH3 and BF3 (107 and
1136 kJ/mol, respectively) compared to PH3 and PF3 (5 and
958.4 kJ/mol, respectively).19 Of the seven isomers with the formula B2P2F2H6, the most stable is 6, B-Fgem, which has both fluorines bonded to the same boron. The remaining isomers with the two F atoms bonded to two different borons are less stable by 39 and 49 kJ/mol, with the more stable isomer having one F axial and the other equatorial. The four isomers with P
F bonds are much higher in energy. Of these, the most stable is P-Fgem which lies 4513

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116 kJ/mol above 6. Relative to P-Fgem, the remaining three isomers are less stable by 45
50 kJ/mol. The most stable of these three also has one F bonded in an axial position and the other equatorial. The final three molecules have the formula B2P2F4H4. Molecule 13 has four fluorines bonded to two borons, while 14 has the four fluorines bonded to two phosphorus. Not surprisingly, B-Fgem,B-Fgem is more stable than P-Fgem,P-Fgem by 245 kJ/mol. B-Fgem,B-Fgem is distinctive insofar as it is the only molecule which has a planar B
P
B
P ring with D2h symmetry, which removes the distinction between axial and equatorial bonds. Molecule 15 with two B
F and two P
F equatorial bonds is more stable than 14 by 28 kJ/mol. Table 3. One-Bond Spin
Spin Coupling Constants J(P
B) (Hz) 1

1

1

J(P
B)

identity

no.

1

57.3

P
B

8

2

64.5

P
B2

9

58.2

P
B4

64.7

P
B2

57.0

P
B4

4

66.5 55.7

P1
B P3
B

11

57.5 69.5

P1
B P3
B

5

72.3

P1
B

12

66.4

P
B

44.4

P3
B 13

107.5

P
B

no.

3

6 7

98.7

P
B2

59.5

P
B4

65.7

P
B

10

Transition structures have been located for six of these molecules. The energies of these structures provide the barriers to inversion which interchange axial and equatorial positions. Data for the transition structures are also given in Table 1. The barriers range from 4 (6) to 13 (11) kJ mol
1. The low ringinversion barriers indicate that, in solution, the NMR properties of these molecules should be averaged over interconvertible conformations. However, if the properties are measured in lowtemperature solids or in the gas phase at low temperature, differences should be detectable for coupling constants involving substituents in axial versus equatorial positions, provided that Table 4. Two-Bond Spin
Spin Coupling Constants 2J(P
P) and 2J(B
B) (Hz) no.

2

J(P
P)

no.

2

J(B
B)

J(P
B)

identity

65.5

P
B2

64.3

P
B4

78.2

P1
B

4

102.1

4

0.4

48.0

P3
B

5

322.5

5

0.8

65.2

P
B


1.3

1

139.3

1


0.7

2 3

292.5 233.0

2 3


1.3 0.9

6

474.2

6

7

319.9

7

5.0

8

361.2

8


0.3

9

286.1

9

3.0

10 11

86.1 307.9

10 11

1.6 1.9

12

605.3

12

1.9

13

779.5

13

0.0

14

78.8

P
B

14

713.1

14

6.8

15

83.6

P
B

15

964.8

15

12.4

Figure 4. 1J(B
P) for molecules 1
15. 4514

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Figure 5. 2J(P
P) for molecules 1
15.

these differences are large enough to be measured experimentally. Whether this is the case will be addressed below. Spin
Spin Coupling Constants. Comparisons with Experimental Data. Although no spin
spin coupling constants have been measured experimentally for the molecules investigated in this study, experimental20
23 and computed EOM-CCSD/(qzp, qz2p) values of 1J(P
F), 1J(B
H), and 2J(F
F) for related systems are available and are reported in Table 2. It should be noted that the range of both computed and experimental values of 1J(P
F) is large, and that the agreement between computed and experimental data is good. The largest difference is found for 1 J(P
F) in PF3, which has computed and experimental values of
1342 and
1441 Hz, respectively. The experimental value of 1 J(P
F) for PF5 is
938 Hz, which is in agreement with the average of
970 Hz for the computed three equatorial and two axial P
F couplings in this molecule. Similarly, good agreement is found for computed and experimental values of 1J(B
H) and 2 J(F
F). These comparisons and previous studies24 suggest that the EOM-CCSD method with the basis set used in these studies should provide reasonable values for the coupling constants arising in the B2P2FnH8
n molecules. 1 J(B
P). Values of 1J(B
P) are reported in Table 3, and the components of 1J(B
P) are given in Table S2 of the Supporting Information. From these data it can be seen that 1J(B
P) is dominated by the Fermi-contact term. The variation in this coupling constant due to the number of F atoms and the axial or equatorial positions of B
F and P
F bonds is illustrated in Figure 4. As evident from this figure, if the coupled B does not form a B
F bond, 1J(B
P) is similar to 1J(B
P) for the parent molecule 1; if the coupled B forms a B
F bond, 1J(B
P) increases relative to 1. For molecules with only one or two F atoms, this increase is insensitive to the number and positions (axial or equatorial) of these bonds provided that there are no geminal bonds. Molecule 6 with geminal B
F bonds has a

Table 5. One-Bond Spin
Spin Coupling Constants 1J(P
F) and 1J(B
F) (Hz) 1

J(P
F)

identity

no.

4


776.0

P1
Fax

5


965.4

P1
Feq

9


1114.3
1279.6

10 11

no.

12 14 15

2

J(B
F)

identity

2


96.7

B2
Fax

3


90.1

B2
Feq

P1
Fax P1
Feq

6


90.4
89.0

B2
Feq B2
Fax


812.8

P1
Fax

7


86.3

B
Feq


777.1

P1
Fax

8


88.3

B2
Feq


945.7

P3
Feq


918.4

P
Feq


1151.3

P
Fax


1236.9

P
Feq


941.9

P
Feq


92.9

B4
Fax

13


87.2

B
F

15


77.4

B
Feq

significantly increased value of 1J(B2
P). Molecule 13 with two geminal B
F bonds has the largest value of 1J(B
P). For molecules with P
F bonds, 1J(B
P) decreases relative to 1 if the coupled P is not bonded to F. For those molecules in which the coupled P is bonded to F, 1J(B
P) increases, although this increase is negligible for 1J(B
P1) in molecule 11 for the P1
F axial bond. The largest values of 1J(B
P) are found for molecules with geminal P
F bonds (9 and 14) and for the all equatorial arrangement (15). However, 1J(B
P) is much smaller for these molecules compared to molecules with geminal B
F bonds. Two-Bond Coupling Constants 2J(P
P) and 2J(B
B). Table 4 presents two-bond coupling constants 2J(P
P) and 2J(B
B), and Table S2 in the Supporting Information provides their components. The variation of 2J(P
P) with the number and positions of B
F and P
F bonds is illustrated in Figure 5. 2 J(P
P) values extend over a wide range from about 100 to 1000 Hz. In general, the presence of B
F or P
F bonds increases 4515

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Figure 6. 1J(P
F) for molecules 4
15. 2

J(P
P) relative to 1 except for 4 and 10, which have one and two axial P
F bonds, respectively. Except for 6 and 12, 2J(P
P) values for molecules with one or two F atoms are relatively similar and less than 400 Hz. What are the bonding characteristics that give rise to values of 2J(P
P) that are greater than 400 Hz? Two of the five molecules in this set have geminal B
F bonds and 2J(P
P) values of 474 (6) and 780 Hz (13). Although molecule 9 also has geminal P
F bonds, it has a value of 2J(P
P) which is less than 400 Hz. In contrast, 2J(P
P) for molecule 12 with two equatorial P
F bonds is 605 Hz. The remaining two molecules in this set, 14 (P-Fgem,PFgem) and 15 (all eq), also have two equatorial P
F bonds, and 2 J(P
P) values of 713 and 965 Hz, respectively. Thus, 2J(P
P) is most sensitive to the presence of geminal B
F bonds, and to a pair of equatorial P
F bonds. As evident from Table 5, values of 2J(B
B) are very small, not exceeding 12 Hz. Thus, two-bond B
B couplings are very inefficient in these B
P
B
P rings. The large differences between 2J(P
P) and 2J(B
B) are not due to the different magnetogyric ratios of 31P and 11B. This can be demonstrated by removing the dependence on the magnetogyric ratios by converting 2J(P
P) and 2J(B
B) to the corresponding reduced coupling constants 2K(P
P) and 2K(B
B), using molecule 14 as an example. For this molecule, the ratio 2K(P
P)/2K(B
B) is 80/1. Since both 2J(P
P) and 2J(B
B) are dominated by the Fermi-contact terms, it is s-electron densities in both the ground state and the excited states which couple to it which are the mediators of these two-bond couplings. The small B
B couplings may be attributed to relatively low s-electron densities on boron in these states. 1 J(P
F) and 1J(B
F). Table 5 presents the one-bond coupling constants 1J(P
F) and 1J(B
F). It is once again evident that coupling constants involving P are very large and extend

Table 6. Two-Bond Spin
Spin Coupling Constants 2 J(P
F), 2J(B
F), and 2J(F
F) (Hz) 2

J(P
F)

identity

no.

2

92.0

P-BFax

3

69.7

P-BFeq

6

96.7

P-BFeq

7

104.3 62.8

8

no.

2

J(B
F)

identity

4

9.1

B-PFax

5

11.8

B-PFeq

9

7.5

B-PFax

P-BFax P-BFeq

10

9.6 9.3

B-PFeq B-PFax

86.1

P-BFax

11

8.1

B-PFax

64.2

P-BFeq

13

106.2

15

60.7

B-PFeq

P-BF

12

10.2

B-PFeq

P-BFeq

14

7.7

B-PFax

9.7

B-PFeq

12.5

15 no.

11.3

2

J(F
F)

no.

B-PFeq 2

J(F
F)

6

66.5

13

86.7

9

62.0

14

68.1

over a range of 500 Hz. Figure 6 illustrates the variation of J(P
F) as a function of the number and positions of P
F bonds. For molecules with one or two P
F bonds in which a given P is bonded to only one F atom and the P
F bond is axial (4, 10, 11), 1J(P
F) is approximately
800 Hz. If a given P forms only one P
F bond and it is in an equatorial position (5, 11, 12, 15), then 1J(P
F) increases in absolute value to between
900 and
1000 Hz. The largest absolute values of 1J(P
F) are
1300 and
1250 Hz for the P
F equatorial bonds in molecules 9 (P-Fgem) and 14 (P-Fgem,P-Fgem), respectively. These two molecules also have the largest absolute 1

4516

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Figure 7. 2J(P
F) for molecules 3
15.

values (
1100 and
1150 Hz, respectively) for P
F couplings involving axial bonds. Thus, values of 1J(P
F) can easily discriminate between P
F axial and P
F equatorial bonds, as well as the presence or absence of geminal P
F bonds. All 1J(P
F) are negative, in violation of the Dirac vector model25 which states that reduced one-bond coupling constants are positive. Such is often the case for coupling involving 19 F. The data of Table S2 (Supporting Information) show that, although the FC term is the dominant term, both the PSO and SD terms make small but nonnegligible contributions to 1 J(P
F). On the other hand, 1J(B
F) does not provide much structural information. The largest absolute value of 1J(B
F) is found for 2, which has only one B
F bond in an axial position. For molecules with two or four B
F bonds but no P
F bonds, 1J(B
F) is
89 ( 4 Hz, independent of the axial or equatorial positions of these bonds. The smallest absolute value of 1J(B
F) is
77 Hz for the equatorial B
F bonds in molecule 15 which also has two equatorial P
F bonds. 2 J(P
F), 2J(B
F), 2J(F
F). Table 6 provides coupling constants 2J(P
F), 2J(B
F), and 2J(F
F), and Figure 7 illustrates the variation in 2J(P
F), the coupling between P and an F atom bonded to B. For molecules that have either one or two B
F bonds but in which a given B forms only one of these, 2 J(P
F) has its smallest values between 60 and 70 Hz if the B
F bond is equatorial (3, 7, 8, 15). If a given B forms only one B
F bond and it is in an axial position (2, 8), then 2J(P
F) increases to approximately 90 Hz. Note that 2J(P
F) values are larger when coupling involves P and an F bonded to B in an axial position; 1J(P
F) couplings have larger absolute values when the P
F bonds are equatorial. The largest values of 2 J(P
F) are found for molecules 6 (B-Fgem) and 13 (B-Fgem, B-Fgem). For 6, 2J(P
F) is approximately 100 Hz, with the coupling constant involving the axial B
F bond greater than

Table 7. Three-Bond Spin
Spin Coupling Constants 3 J(P
F) and 3J(B
F) (Hz) 3

3

J(P
F)

identity

4


21.0

P3-Fax

2


2.2

B4-Fax

5

209.3

P3-Feq

3

2.9

B4-Feq

9

6.7

P3-Fax

6

2.5

B4-Feq

10

208.7
17.1

P3-Feq P3-Fax

7


1.3 11.2

B4-Fax B-Feq

11


16.9

P3-Fax

8

214.2

P1-Feq

no.

no.

J(B
F)

identity

3.4

B4-Feq


3.8

B2-Fax

12

211.4

P-Feq

13

7.4

B
F

14

66.5

P-Fax

15

13.2

B-Feq

299.1

P-Feq

256.6

P-Feq

15

that for the equatorial B
F bond. The two-bond P
F coupling constants in 13, for which axial and equatorial are no longer distinct, have the largest values of 106 Hz. Not surprisingly, 2 J(B
F) coupling constants are significantly smaller than 1 J(B
F) with values between 8 and 12 Hz. Once again, these contain little structural information. Finally, there are only four molecules with geminal bonds (6, 9, 13, 14) which provide values of 2 J(F
F). For three of these, 2 J(F
F) lies between 60 and 70 Hz, while 2 J(F
F) increases to 87 Hz for 13, which has the unique planar B
P
B
P ring. 3 J(P
F) and 3J(B
F). Coupling constants 3J(P
F) and 3 J(B
F) are reported in Table 7. Values of 3J(B
F) are relatively small, with 3J(B-Fax) negative and 3J(B-Feq) positive. Not surprisingly, it is 3J(P
F) which again provides structural information. Figure 8 illustrates that values of 3J(P
F) 4517

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Figure 8. 3J(P
F) for molecules 4
15.

for an axial P
F bond may be positive or negative and are relatively small. The largest among these is 67 Hz for 14 (PFgem,P-Fgem). In contrast, 3J(P
F) increases significantly to about 210 Hz for coupling involving equatorial P
F bonds in molecules with one or two fluorine atoms. The largest values of 3 J(P
F) are 299 and 257 Hz for molecules 14 (P-Fgem,P-Fgem) and 15 (all eq), respectively. Thus, 3J(P
F) readily discriminates between axial and equatorial P
F bonds. It is interesting to note that both 1J(P
F) and 3J(P
F) are greater for corresponding equatorial P
F bonds, while 2J(P
F) is greater for corresponding axial B
F bonds. Coupling Constants for Transition Structures. How do coupling constants change in going from an equilibrium structure to a transition structure? The data needed to answer this question are reported in Table 8. This analysis has been restricted to 1 J(B
P), 2J(P
P), 1J(P
F), and 3J(P
F) which illustrate three different patterns of change in going from equilibrium to transition structures. For the molecules listed in Table 8, if the ground state has C2v symmetry, the transition structure has D2h symmetry (molecules 1 and 14) and 1J(B
P) has only one unique value in each structure. The difference between 1J(B
P) in the two structures is not large, with 1J(B
P) in the transition structure increasing by 3 Hz for 1 and decreasing by 4 Hz for 14. The remaining molecules for which transition structures are available have Cs symmetry in the ground state, and two unique values of 1J(B
P) for the equilibrium structure. Among these, molecules 8 and 11 have equivalent B
P bonds in the transition structures and thus only one value of 1J(B
P). For 8, this value is several hertz larger in the transition structure; for 11, the transition structure value is intermediate between the values for the equilibrium structure. Molecules 6 and 9 have two values of 1J(B
P) in both structures, with the largest difference being 5 Hz. Thus, values of 1J(B
P), which are

between 50 and 100 Hz in the equilibrium structures, are similar in the transition structures. In going from the equilibrium structure to the transition structure, 2 J(P
P) increases by 50 Hz for molecule 1. If the molecule has B
F bonds (6 and 8), 2 J(P
P) decreases by about 20 Hz in the transition structure. In contrast, when P
F bonds are present, 2J(P
P) increases by about 80 Hz for 11, and 110 Hz for 9 and 14 which have geminal P
F bonds. Thus, differences between equilibrium and transition structure values of 2J(P
P) are sensitive to the presence of B
F or P
F bonds and to the presence of P
F geminal bonds. 1 J(P
F) values for equilibrium and transition structures are available for molecules 9, 11, and 14. For each molecule, two large negative values of 1 J(P
F) in the equilibrium structure become one value in the transition structure. From Table 8 it can be seen that this value is very close to the average of the two equilibrium values. This is reminiscent of the comparison between the computed and experimental values of 1J(P
F) for PF5 noted above. It is important to note that, in the equilibrium structures, 1 J(P
F) easily discriminates between P
F axial and P
F equatorial bonds and is sensitive to the presence of geminal P
F bonds. Discrimination between axial and equatorial bonds is lost in the transition structures, but sensitivity to geminal P
F bonds remains. A similar situation occurs for 3J(P
F). The two values of 3 J(P
F) for the equilibrium structures (9, 11, 14) become a single value for the transition structures, and so the ability to discriminate between axial and equatorial bonds is lost. However, the transition structures do discriminate between the presence of one or two versus four P
F bonds. As is the case for 1J(P
F), values of 3J(P
F) for the transition structures approach the average of the two values for the corresponding equilibrium structures. 4518

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ARTICLE

Table 8. 1J(B
P), 2J(P
P), 1J(P
F), and 3J(P
F) (Hz) for Equilibrium and Transition Structures

present and can discriminate between axial, equatorial, and geminal B
F and P
F bonds, although not all do this to the same extent. 5. Coupling constants 1J(B
P) and 2J(P
P) are similar in equilibrium and transition structures. However, 1J(P
F) and 3J(P
F) no longer discriminate between axial and equatorial P
F bonds, but remain sensitive to the number of fluorine atoms present.

1

J(P
B) (Hz)

description

no.

sym

eq

TS

B2P2H8

1

C2v/D2h

57

60

B-Fgem

6

Cs/C2v

97, 61

99, 60

B-Fax,B-Feq P-Fgem

8 9

Cs/C2h Cs/C2v

64, 66 78, 48

68 75, 53

P-Fax,P-Feq

11

Cs/C2h

70, 58

65

P-Fgem,P-Fgem

14

C2v/D2h

79

75

bS

2

J(P
P) (Hz)

description

’ ASSOCIATED CONTENT Supporting Information. MP2/aug-cc-pVTZ equilibrium and transition structures and total energies; PSO, DSO, FC, and SD components of coupling constants. This material is available free of charge via the Internet at http://pubs.acs.org.

no.

sym

eq

TS

B2P2H8

1

C2v/D2h

139

188

’ AUTHOR INFORMATION

B-Fgem

6

Cs/C2h

498

474

Corresponding Author

B-Fax,B-Feq

8

Cs/C2h

361

341

*E-mail: [email protected] (J.E.D.B.); [email protected] (I.A.).

P-Fgem P-Fax,P-Feq

9 11

Cs/C2v Cs/C2h

286 308

393 386

P-Fgem,P-Fgem

14

C2v/D2h

713

819

1

description

no.

sym

eq

J(P
F) (Hz) TS

9

Cs/C2v


1114,
1280


1217

P-Fax,P-Feq

11

Cs/C2h


946,
777


849

P-Fgem,P-Fgem

14

C2v/D2h


1151,
1236


1202

P-Fgem

3

J(P
F) (Hz)

description

no.

sym

eq

TS

P-Fgem P-Fax,P-Feq

9 11

Cs/C2v Cs/C2h

7, 209
17, 214

108 99

P-Fgem,P-Fgem

14

C2v/D2h

67, 299

183

’ CONCLUSIONS Ab initio calculations have been carried out to determine the structures, relative stabilities, and spin
spin coupling constants of a set of 15 fluoro-substituted 1,3-diborata-2,4-diphosphoniocyclobutanes B2P2FnH8
n, for n = 0, 1, 2, 4. The following statements are supported by the results of these calculations. 1. Except for the molecule having four fluorines bonded to two borons, the four-member B
P
B
P rings are puckered in a butterfly conformation and have axial and equatorial B
F and P
F bonds. 2. For a fixed number of F atoms, isomers with B
F bonds are more stable than those with P
F bonds. As the number of F atoms increases, the energy difference between the most stable isomer and the remaining isomers increases. 3. Transition structures and their energies relative to the corresponding equilibrium structures have been obtained for six of these molecules. These energies indicate that the barriers to interchanging axial and equatorial bonds are relatively low. 4. Coupling constants involving P, namely, 1J(B
P), 1 J(P
F), 2J(P
P), 2J(P
F), and 3J(P
F) are large and are capable of providing structural information about these molecules. They are sensitive to the number of fluorines

’ ACKNOWLEDGMENT The support provided by the Ohio Supercomputer Center for this project and the support of CTI-CSIC are gratefully acknowledged. This work has been financed by the Spanish MICINN (CTQ2009-13129-C02-02) and Comunidad Aut
onoma de Madrid (Project MADRISOLAR2, ref S2009/PPQ-1533). ’ REFERENCES (1) Fuks, G.; Saffon, N.; Maron, L.; Bertrand, G.; Bourissou, D. J. Am. Chem. Soc. 2009, 131, 13681. (2) Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J. Quantum Chem., Quantum Chem. Symp. 1976, 10, 1. (3) Krishnan, R.; Pople, J. A. Int. J. Quantum Chem. 1978, 14, 91. (4) Bartlett, R. J.; Silver, D. M. J. Chem. Phys. 1975, 62, 3258. (5) Bartlett, R. J.; Purvis, G. D. Int. J. Quantum Chem. 1978, 14, 561. (6) Hehre, W. J.; Ditchfield, R.; Pople, J. J. Chem. Phys. 1982, 56, 2257. (7) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta. 1973, 28, 213. (8) Spitznagel, G. W.; Clark, T.; Chandrasekhar, J.; Schleyer, P. v. R. J. Comput. Chem. 1982, 3, 363. (9) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. (10) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007. (11) Woon, D. E; Dunning, T .H., Jr. J. Chem. Phys. 1995, 103, 4572. (12) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C. Pople, J. A. Gaussian 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (13) Perera, S. A.; Sekino, H.; Bartlett, R. J. J. Chem. Phys. 1994, 101, 2186. 4519

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