22.1Introduction

Studies of the hydrogen bond have a long history, with the publication of the classicbook “The Hydrogen Bond” by Pimentel and McClellan [1] signaling the beginningof an era of intense experimental research on this subject. However, it was not untilthe late sixties and early seventies that ab initio quantum chemical studies of hydro-gen-bonded complexes were carried out in an effort to determine the structures andbinding energies of these complexes from first-principles calculations. During thelast 30 years of the twentieth century, developments in computational algorithmsand their implementation in software packages, the advent of more powerful com-puting machines, and methodological improvements have had a dramatic impacton ab initio computational quantum chemistry. Computed structures, binding ener-gies, and infrared (IR) vibrational spectral data, obtained at sophisticated levels oftheory, have achieved an accuracy which makes them complementary to experimen-tal data, and gives them predictive value in those cases for which experimental dataare not available. Studies of hydrogen-bonded complexes carried out at these levelshave led to a better understanding of the fundamental nature of the hydrogen bond.

In contrast, it was not until the last decade of the twentieth century that the firstexperimental measurements of NMR two-bond spin–spin coupling constants acrosshydrogen bonds were made. In a landmark paper [2], Dingley and Grzesiek reportedtwo-bond 15N–15N spin–spin coupling constants across N–H...N hydrogen bonds inAU and GC pairs. This paper generated a great deal of interest and excitement inthe chemical and biochemical communities, since it was suggested that such mea-surements might provide structural information about hydrogen-bonded complexesin solution. Subsequently, other experimental measurements of two-bond spin–spincoupling constants in hydrogen-bonded complexes have been made, and these aresummarized in recent review articles by Elguero and Alkorta [3], and by Grzesiek,Cordier, and Dingley [4].

Just as there had been no experimental measurements of two-bond spin–spincoupling constants across hydrogen bonds until the end of the twentieth century,there were also no published ab initio calculations on this subject until that time. Itwould not be unreasonable to state that just a few years prior to the end of the cen-

353

22

Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15NSpin–Spin Coupling Constants across Hydrogen Bonds Using AbInitio EOM-CCSD Calculations

Janet E. Del Bene

Calculation of NMR and EPR Parameters. Theory and Applications.Edited by Martin Kaupp, Michael B�hl, Vladimir G. MalkinCopyright � 2004 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 3-527-30779-6

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants

tury, the data base of knowledge related to spin–spin coupling constants for a pair ofhydrogen-bonded atoms based upon fundamental theoretical studies was compar-able to the data base of knowledge of the structures, binding energies, and vibra-tional spectra of such complexes based on ab initio calculations in the early 1970s.Hence, investigations of two-bond spin–spin coupling constants across hydrogenbonds are a new and exciting area of experimental and theoretical research. From acomputational viewpoint, there are many questions about spin–spin coupling con-stants across hydrogen bonds that need to be addressed at a level of theory capableof providing reliable answers. Among these questions are the following.

1. What is the relative importance of the paramagnetic spin–orbit, diamagneticspin–orbit, Fermi-contact, and spin–dipole contributions to the total couplingconstant?

2. How do spin–spin coupling constants vary with the nature of the atoms Xand Y, and the hybridization and bonding of these atoms?

3. To what extent do spin–spin coupling constants depend on the structure ofthe hydrogen-bonded complex, particularly on the X–Y distance and the ori-entation of the hydrogen-bonded pair?

4. What is the dependence of the coupling constant on hydrogen bond type andon the charge on the complex?

5. What can spin–spin coupling constants reveal about the nature of the hydro-gen bond?

This chapter contains a summary of the results of ab initio calculations carried outin this laboratory to determine 13C–15N, 15N–15N, and 19F–15N spin–spin couplingconstants across C–H–N, N–H–N, and F–H–N hydrogen bonds, respectively, inboth neutral and charged complexes. It is hoped that these results may providesome insights into the answers to the questions raised above.

22.2Methods

Recent computational studies of spin–spin coupling constants across hydrogenbonds have been carried out using both DFT and ab initio methods. A review ofthese calculations has been given by Elguero and Alkorta [3], so the reader isreferred to that paper for details. In this chapter the focus will be on studies carriedout in this laboratory, using equation-of-motion coupled-cluster singles and doublestheory (EOM-CCSD).

The first step is to determine the optimized structures of the complexes at sec-ond-order perturbation theory (MP2) [5–8] with the 6-31+G(d,p) basis set [9–12].This level of treatment employs an explicitly correlated wavefunction and a valencedouble-split basis set augmented with polarization functions on all atoms and dif-fuse functions on nonhydrogen atoms. It has been recommended as the level oftheory required to provide reliable structures and vibrational frequency shifts (if theharmonic approximation is appropriate) at minimum computational expense [13].

354

22.2 Methods

Obtaining reliable energetics requires a larger basis set, such as Dunning’s aug-cc-pVTZ basis [14, 15] without counterpoise corrections for binding energies [16].

Ab initio calculations to determine spin–spin coupling constants across hydrogenbonds have been carried out using the equation-of-motion coupled-cluster singlesand doubles (EOM-CCSD) formalism in the CI-like approximation [17–20]. EOM-CCSD with the Ahlrichs (qzp, qz2p) basis set [21] gives good agreement betweencomputed and experimental coupling constants in molecules [18], and good agree-ment with experimental data for hydrogen-bonded complexes when comparisonscan be made. It is this level of theory which has been used for all of the studies thatwill be discussed below. Early calculations employed the qz2p basis set on all hydro-gen atoms. However, subsequent studies indicated that replacing this basis set byDunning�s cc-pVDZ basis [14] on hydrogen atoms not involved in the hydrogenbond has little effect on computed X–Y coupling constants, but reduces the compu-tational cost.

Two-bond X–Y spin–spin coupling constants across X–H–Y hydrogen bonds aredesignated 2hJX–Y, where “2” indicates that the coupling is across two bonds, “h” indi-cates that the coupling is across a hydrogen bond, and “X–Y” are the hydrogen-bonded atoms that couple. In nonrelativistic theory, 2hJX–Y has four components: theparamagnetic spin–orbit (PSO), diamagnetic spin–orbit (DSO), Fermi-contact (FC),and spin–dipole (SD) terms. Because the calculation of spin–spin coupling con-stants across hydrogen bonds is a new area of research, we initially computed allterms that contribute to 2hJX–Y for a series of complexes in which X and Y are fixed,in order to evaluate the relative importance of each term for determining the X–Ycoupling constant for a particular pair of hydrogen-bonded atoms.

22.3Discussion

22.3.1Hydrogen Bond Types and 2hJX–Y

When examining both the IR and NMR spectral properties of hydrogen-bondedcomplexes, it is advantageous to classify X–H–Y hydrogen bonds into one of threetypes: traditional, proton-shared, or ion-pair [22–24]. A hydrogen bond is called tradi-tional if the X–H bond of the proton-donor group remains intact in the complex,and the X–Y distance is normal (as opposed to short). The IR spectrum of such acomplex is characterized by a strong X–H stretching band shifted to lower frequencyrelative to the X–H band in the monomer. The traditional hydrogen bond is by farthe most common type found in uncharged complexes in the gas phase. Examplesinclude (H2O)2, (HF)2, FH:NH3 and ClH:NH3. In this chapter, a traditional hydro-gen bond will be designated as X–H...Y.

In particular cases, the hydrogen-bonded proton can be transferred from X to Y,forming a hydrogen-bonded ion pair. In such a complex the X–Y distance is similarto the X–Y distance in a corresponding complex with a traditional hydrogen bond.

355

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants

The Y–H distance is elongated relative to the corresponding isolated cation, and theIR spectrum exhibits a strong Y–H stretching band shifted to lower frequency rela-tive to the cation. Such hydrogen bonds are depicted as X–...+H–Y. This type is notcommon in the gas phase, but can be formed if a very strong proton donor is com-plexed with a very basic proton acceptor. An ion-pair hydrogen bond stabilizes thecomplex formed between HBr and N(CH3)3 in the gas phase [25].

Intermediate between these two is the proton-shared hydrogen bond. A complexstabilized by such a hydrogen bond has a short X–Y distance, but long X–H andY–H distances. The proton-stretching band is very intense and appears at a very lowfrequency. Other strong bands may be observed, depending on the nature of thecomplex. A hydrogen bond of this type is designated as X...H...Y. The complex be-tween HCl and N(CH3)3 has a proton-shared hydrogen bond in the gas phase [25]. Ifin a proton-shared hydrogen bond the proton is shared equally between two equiva-lent atoms, the hydrogen bond is called symmetric. If the sharing is equal (as mea-sured by the forces exerted by X and Y on H) but X and Y are different atoms, thehydrogen bond is referred to as a quasi-symmetric proton-shared hydrogen bond.

356

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

12

10

8

6

4

2

0

−0.05

−0.10

−0.15

−0.20

−0.25

−0.30

6

5

4

3

2

1

0

−100

−200

−300

−400

−500

−600

Cl-H…NH3 Cl…H…NH3 Cl-…

+H-NH3

−1

Figure 22.1 The two-bond Cl–N spin–spincoupling constant, the chemical shift of thehydrogen-bonded proton, the anharmonic pro-ton-stretching frequency, and the Cl–N dis-tance for ClH:NH3 as a function of external

field strength. Values are plotted relative to 0.0for the zero-field values. Solid circle: couplingconstant; solid triangle: chemical shift; soliddiamond: proton-stretching frequency; solidsquare: Cl–N distance.

22.3 Discussion

Research in enzyme kinetics has suggested that proton-shared hydrogen bonds(sometimes called “low-barrier” hydrogen bonds) may play an important role indetermining reaction rates [26–32]. Could measurements of 2hJX–Y serve to prove theexistence of such hydrogen bonds? We have addressed the relationship between2hJX–Y and hydrogen bond type in a series of papers [22–24, 33–38]. We first recog-nized this relationship in a study of the ClH:NH3 complex. Our interest in this andthe related BrH:NH3 complex [39] was originally stimulated by their unusual low-temperature Ar matrix vibrational spectra, and by the failure of the harmonicapproximation to reproduce the large experimental low-frequency shifts of the Br–Hand Cl–H stretching bands in these complexes [40]. In the course of our studies, weobserved that an external electric field applied along the hydrogen-bonding axis wascapable of mimicking the matrix environment of these and related complexes, in-ducing proton transfer, and thereby changing hydrogen bond type from traditional,to proton-shared, to ion-pair [39–41]. The ClH:NH3 complex subsequently becameour workhorse system, allowing for detailed studies of IR and NMR properties as afunction of hydrogen bond type in a single chemical system. From such studies arich harvest of information concerning the variation of these properties with hydro-gen bond type has been obtained.

This variation is most succinctly illustrated in Fig. 22.1, which plots the equilibri-um Cl–N distance, the two-bond spin–spin coupling constant (2hJCl–N), the chemicalshift of the hydrogen-bonded proton, and the two-dimensional anharmonic proton-stretching frequency as functions of increasing field strength and therefore chang-ing hydrogen bond type. As is apparent from this figure, these properties are finger-prints of hydrogen bond type, exhibiting extremum values for a quasi-symmetricproton-shared hydrogen bond. The variation of 2hJX–Y with hydrogen bond type willbe seen in the subsequent discussion of coupling constants across N–H–N, C–H–N,and F–H–N hydrogen bonds.

22.3.2N–H–N Hydrogen Bonds

The experimental measurement of 15N–15N spin–spin coupling constants across theN–H...N hydrogen bonds in the AU and GC base pairs [2] generated a great deal ofexcitement. Hence, it seems fitting to begin this discussion of spin–spin couplingacross hydrogen bonds by considering 2hJN–N. Based on EOM-CCSD calculations fora series of complexes stabilized by N–H–N hydrogen bonds, we demonstrated that2hJN–N is determined solely by the Fermi-contact (FC) term. This is not due to a can-cellation of other terms, but arises because the FC term is more than an order ofmagnitude greater than any other term. Because the FC term approximates 2hJN–N

so well, calculations of 15N–15N coupling constants are feasible in relatively largesystems. Moreover, the Fermi-contact term and therefore total 2hJN–N are distancedependent, decreasing (in an absolute sense) with increasing N–N distance [34–36].This suggests that it should be possible to obtain intermolecular N–N distancesfrom experimentally measured N–N coupling constants. It was also our hope that

357

the innate simplicity of the Fermi-contact term might carry over and lead to generalrelationships between coupling constants and intermolecular distances.

Since the two-bond N–N coupling constant across an N–H...N hydrogen bondhad been directly measured [2], we computed 2hJN-N for the CNH:NCH complex atan N–N distance of 2.90 �, which corresponds to the N–N distance in the AU andGC pairs. The computed value is 7.2 Hz, in excellent agreement with the experi-mental value of about 7 Hz. This result was initially puzzling, since CNH:NCHwould not be expected to be a good model for base pairs, and suggests that 2hJN–N isnot very sensitive to the bonding at the nitrogens. Table 22.1 reports equilibrium N–N distances and 2hJN–N values computed at the equilibrium geometries of a series ofneutral and cationic complexes with N–H–N hydrogen bonds [34–36]. The nitrogenatoms may be sp, sp2, or sp3 hybridized, although no cationic complexes with sphybridized nitrogens as proton donors are included. The neutral complexes are sta-bilized by traditional hydrogen bonds, while the hydrogen bonds in the cationiccomplexes may be either traditional or proton-shared. Figure 22.2 shows a plot of2hJN–N versus the N–N distance for these 13 complexes. The value of 2hJN–N at2.90 � obtained from this curve is 7.5 Hz, in agreement with the value of 7.2 Hzobtained for the CNH:NCH complex at the same N N distance, and with the experi-mental value of about 7 Hz for the AU and GC base pairs. These results suggestthat two-bond 15N–15N spin–spin coupling constants across hydrogen bonds areinsensitive to the nature of the hybridization of the nitrogens, the nature of the sub-stituents bonded to nitrogens, and the presence or absence of a positive charge onthe complex. However, it should be emphasized that there is an indirect dependenceof 2hJN–N on the nature of the hybridization and bonding of the N atoms for a partic-ular complex, since these properties determine the equilibrium N–N distance,

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants358

Table 22.1 N–N distances (�) and 15N–15N spin–spin coupling constants (2hJN–N, Hz) inequilibrium structures of neutral and cationic complexes stabilized by N–H–N hydrogen bonds.

R(N–N) 2hJN–N

Neutral complexesCNH:pyridine 2.793 10.7CNH:NCLi 2.833 9.6CNH:NH3 2.846 8.7CNH:NCH 2.996 5.5Pyrrole:NCH 3.164 3.0Cationic complexes1,4-Diazinium:NCLi 2.633 16.5NH4

+:NCLi 2.634 16.1Pyridinium:NCLi 2.673 14.4NH4

+:NH3 2.705 12.9NH4

+:NCH 2.830 9.21,4-Diazinium:NCH 2.834 9.4Pyridinium:NCH 2.872 8.2NH4

+:N2 3.108 3.2

22.3 Discussion 359

2

4

6

8

10

12

14

16

18

2.6 2.7 2.8 2.9 3.0 3.1 3.2

2hN

-N

Figure 22.2 2hJN–N versus the N–N distance for the equilibriumstructures of neutral and cationic complexes with N–H–N hydro-gen bonds.

1

2

3

4

5

6

-60 -40 -20 0 20 40 60

d ao

2hN

-N

Figure 22.3 The variation of 2hJN–N as a function of thenonlinearity of the hydrogen bond in CNdH:NaCH. A value offf H–Nd–Na = 0.0� corresponds to a linear hydrogen bond.

which in turn, determines 2hJN–N. Figure 22.2 should be useful for estimating N–Ndistances from experimental 15N–15N coupling constants, and for predicting 2hJN–N

when experimental values are not available.All of the complexes in Table 22.1 have linear hydrogen bonds formed with a di-

rected lone pair of electrons on the proton-acceptor nitrogen atom. How does 2hJN–N

change if the hydrogen bond becomes nonlinear, or if the directed lone pair isremoved from the hydrogen bond? Figures 22.3 and 22.4 show the variation of2hJN–N graphically as such changes occur in CNdH:NaCH. To obtain 2hJN–N as a func-tion of the linearity of the hydrogen bond, a rotational axis was placed through Nd

perpendicular to the Nd–Na line, and CNdH was rotated about this axis, keeping allother coordinates fixed. Similarly, to obtain the variation in 2hJN–N as the lone pair isremoved from the hydrogen bond, an axis was placed through Na perpendicular tothe Nd–Na line, and NaCH was rotated about this axis, again keeping all other coor-dinates fixed. Figures 22.3 and 22.4 suggest that small perturbations which distortthe hydrogen bond from linearity or displace the directed lone pair from the hydro-gen bonding axis have relatively small effects on 2hJN–N. However, 2hJN–N decreasesrapidly as these perturbations become larger.

22.3.3C–H–N Hydrogen Bonds

In principle, it should be possible to measure spin–spin coupling constants acrossC–H–N hydrogen bonds. In anticipation of such experimental studies, we have car-

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants360

1

2

3

4

5

6

90 120 150 180 210 240 270

d ao

2hN

-N

Figure 22.4 The dependence of 2hJN–N on the orientation of thelone pair on the proton-acceptor nitrogen in CNdH:NaCH. Thelone pair is directed along the Nd–H–Na axis when ff Nd–Na–C =180.0�.

ried out systematic investigations of 13C–15N coupling constants in a series of neu-tral, cationic, and anionic complexes stabilized by C–H–N hydrogen bonds [42].These complexes include C and N atoms that are sp, sp2, and sp3 hybridized. All ofthese complexes are stabilized by traditional hydrogen bonds in which a C–H groupis the proton donor to N, except for pyridinium:CNH and NH4

+:CNH, which arestabilized by traditional N–H+...C hydrogen bonds.

C–N distances, the Fermi-contact term, and total 2hJC–N for the equilibrium struc-tures of 23 complexes with C–H–N hydrogen bonds are reported in Table 22.2. The

22.3 Discussion 361

Table 22.2 Equilibrium distances (�) and the Fermi-contact term (FC) and 2hJC–N (Hz) for com-plexes with C–H–N hydrogen bonds.

R(C–N) FC 2hJC–N

Neutral complexesHCCH...NCH 3.440 –5.24 –5.26ClCCH...NCH 3.413 –6.03 –6.06FCCH...NCH 3.412 –6.33 –6.35NCH...NCH 3.316 –7.31 –7.34

HCCH...NCLi 3.303 –8.34 –8.37FCCH...NCLi 3.272 –10.09 –10.09a

ClCCH...NCLi 3.268 –9.77 –9.77a

NCH...NCLi 3.160 –12.16 –12.21

NCH...pyridine 3.163 –12.66 –12.66a

HCCH...NH3 3.327 –8.13 –8.14ClCCH...NH3 3.303 –9.26 –9.26FCCH...NH3 3.301 –9.73 –9.73a

NCH...NH3 3.204 –10.95 –10.98

F(O)CH...NCH 3.466 –5.19 –5.19a

F(O)CH...NH3 3.340 –8.39 –8.39a

F3CH...NCH 3.456 –4.68 –4.68a

F3CH...NH3 3.341 –7.30 –7.30a

Cationic complexesPyridine–H+...CNH 2.974 –22.24 –22.24a

H3NH+...CNH 2.936 –26.40 –26.49

HNCH+...NCH 2.832 –40.03 –40.13

Anionic complexesHCCH...NC– 3.117 –16.19 –16.25FCCH...NC– 3.077 –20.09 –20.09a

NCH...NC– 2.940 –24.66 –24.77

a Estimated from the Fermi-contact term.

PSO, DSO, and SD terms make negligible contributions to the total coupling con-stant, and FC approximates 2hJC–N to 0.1 Hz in those complexes for which all termswere computed. Since the FC term is distance dependent, 2hJC–N also depends onthe C–N distance. As evident from Table 22.2, the equilibrium distances in thecharged complexes are relatively short compared to the neutral complexes, and thevalues of 2hJC–N are also greater.

2hJC–N values for the entire set of 23 complexes have been plotted in Fig. 22.5 as afunction of the C–N distance. There is some scatter in the data, as evident fromFig. 22.5 and the correlation coefficient of 0.97 for the best-fit quadratic curve. Thescatter is due primarily to the dependence of 2hJC–N on the hybridization and bond-ing at the proton-donor C–H group [42]. Since 2hJC–N is also relatively insensitive tosmall deviations which perturb the linearity of the hydrogen bond, the curve pre-sented in Fig. 22.5 should be useful for relating experimentally measured C–N cou-pling constants to C–N distances.

22.3.4F–H–N Hydrogen Bonds

Experimental measurements of 19F–15N spin–spin coupling constants across F–H...N hydrogen bonds are available, due primarily to the work of Limbach and hisassociates [43, 44]. We have investigated F–N coupling constants for neutral com-plexes with F–H...N hydrogen bonds [45] and cationic complexes with N–H+...F

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants362

-45

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-35

-30

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-15

-10

-5

02.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5

2hC

-N

Figure 22.5 2hJC–N versus the C–N distance for the equilibriumstructures of neutral and charged complexes stabilized byC–H–N hydrogen bonds.

hydrogen bonds [46]. Figure 22.6 presents 2hJF–N versus the F–N distance for theoptimized structures of 13 neutral and 18 cationic complexes. The best-fit quadraticcurve is not shown, but its low correlation coefficient of 0.62 is not unexpected giventhe scatter evident in these data. The scatter may be attributed primarily to the sig-nificantly greater values of coupling constants for cationic complexes compared toneutral complexes at the same F–N distance. This is apparent from Fig. 22.6, whichshows that when 2hJF–N for neutral and cationic complexes are plotted separatelyagainst the F–N distance, improved correlations are found, although there is stillsome scatter. There are two obvious questions to be addressed.

1. What causes the scatter in the plots of 2hJF–N versus the F–N distance, partic-ularly in the cationic complexes?

2. Why do the cationic complexes have larger coupling constants over the entirerange of F–N distances?

Table 22.3 lists the F–N distances, PSO, DSO, FC, and SD terms, and 2hJF–N forcomplexes stabilized by F–H...N and N–H+...F hydrogen bonds. The Fermi-contactterm is again a good approximation to 2hJF–N, although the differences between FCand 2hJF–N for the complexes of FH with ammonia and substituted amines aregreater than observed previously for other complexes. For FH:NHF2 and FH:NH2F,FC underestimates (in an absolute sense) 2hJF–N primarily because of the contribu-tion of the SD term. In contrast, for FH:NH3 and FH:NH2(CH3), FC overestimates2hJF–N primarily because of the relatively large positive value of the PSO term.

22.3 Discussion 363

-120

-100

-80

-60

-40

-20

02.5 2.6 2.7 2.8 2.9 3.0 3.1

2hN

-F

Figure 22.6 2hJF–N versus the F–N distance for the optimizedstructures of neutral and cationic complexes stabilized byF–H–N hydrogen bonds. Solid square: cations; solid triangle:neutrals.

The equilibrium structures of all of the neutral complexes have linear hydrogenbonds formed with directed lone pairs of electrons, while the equilibrium structuresof the cationic complexes do not necessarily have this ideal structure. However, forcomparison purposes, the structures of the cationic complexes were constrainedduring optimization so that N–H+...F–H are collinear. These constraints are not

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants364

Table 22.3 Equilibrium distances (�) and two-bond spin–spin coupling constants (2hJF–N) andcomponentsa of 2hJF–N (Hz) for complexes with F–H...N and N–H+...F hydrogen bonds.

F–N PSO DSO FC SD 2hJF–N

Neutral complexesFH:NF3 3.095 –4.2 –4.2b

FH:NCCN 2.895 0.2 0.0 –13.1 –0.5 –13.4FH:NHF2 2.869 –0.5 –0.1 –16.1 –1.2 –17.9FH:NCF 2.846 0.4 0.0 –18.1 –0.4 –18.1FH:NCH 2.817 0.3 0.0 –21.2 –0.6 –21.5FH:NH2F 2.721 0.3 0.0 –32.4 –1.6 –33.7FH:1,3,5-triazine 2.684 –40.3 –40.3b

FH:NCLi 2.660 0.6 0.0 –47.5 –0.9 –47.8FH:1,4-diazine 2.638 –49.1 –49.1b

FH:NH3 2.637 2.8 0.0 –45.2 –1.3 –43.7FH:pyridine 2.611 –57.0 –57.0b

FH:NH2(CH3) 2.598 2.9 0.0 –53.3 –1.7 –52.1FH:4-Li-pyridine 2.572 –70.5 –70.5b

Cationic complexes4-Li-Pyridinium:FH 2.933 –21.7 –21.7b

Pyridinium:FH 2.882 –26.9 –26.9b

(CH3)H2NH+:FH 2.872 –23.8 –23.8b

1,4-Diazinium:FH 2.855 –30.1 –30.1b

H2C=NH2+:FH 2.838 –33.5 –33.5b

H3NH+...FH 2.835 0.5 0.0 –28.7 –0.2 –28.4

1,3,5-Triazinium:FH 2.834 –32.2 –32.2b

(F)HC=NH2+:FH 2.814 –36.9 –36.9b

LiCNH+:FH 2.795 0.4 –0.1 –47.1 –0.1 –46.91,2,4,6-Tetrazinium:FH 2.785 –49.7 –49.7b

F H2NH+:FH 2.762 0.3 –0.1 –42.3 –0.3 –42.4

H2C=N(F)H+:FH 2.748 –56.4 –56.4b

(CH3)CNH+:FH 2.696 –78.7 –78.7b

F2HNH+:FH 2.687 0.0 –0.1 –64.1 –0.5 –64.7HCNH+:FH 2.647 0.4 –0.1 –94.5 –0.2 –94.3FCNH+:FH 2.632 0.5 –0.1 –109.1 –0.1 –108.8NCCNH+:FH 2.627 0.4 –0.1 –105.4 –0.2 –105.3F3NH

+:FH 2.612 –102.3 –102.3b

a PSO = paramagnetic spin–orbit; DSO = diamagnetic spin–orbit;FC = Fermi-contact, SD = diamagnetic spin–orbit.

b Estimated from the Fermi-contact term.

unreasonable, as discussed in detail in ref. 46. Although the quadratic correlationbetween 2hJF–N and the F–N distance for the neutral complexes is good, there is stillsome scatter in the data, as evident from Fig. 22.6. This scatter can be traced to thedependence of 2hJF–N on the hybridization of the nitrogen, as evident from Fig. 22.7.If the proton-acceptor molecules are grouped according to the nitrogen hybridiza-tion, excellent quadratic correlations between 2hJF–N and the F–N distance arefound, with correlation coefficients between 0.99 and 1.00. Similarly, the greaterscatter in the data for the cationic complexes can also be attributed to the hybridiza-tion of the nitrogen, as evident from Fig. 22.8. It is interesting to note that 2hJF–N forcationic complexes in which the proton donors are sp3 hybridized have lower abso-lute values than 2hJF–N for complexes with sp and sp2 nitrogens over the entirerange of F–N distances.

It is also apparent from Fig. 22.6 that at a given F–N distance, 2hJF–N is signifi-cantly greater for a cationic complex, a reflection of its greater proton-shared charac-ter. One way to measure the degree of proton-sharing is to examine the differencebetween the F–H and N–H distances in a pair of neutral and cationic complexesthat have similar F–N distances. (This comparison is not strictly valid, since the vander Waals radii for N and F are different. However, the radii are similar enough at1.55 and 1.47 �, respectively, to warrant such a comparison.) Table 22.4 presentsdata for three sets of neutral and cationic complexes that have similar N–F distances.It is evident from these data that the absolute value of the difference between theF–H and N–H distances is smaller in the cationic complexes, and these complexes

22.3 Discussion 365

-80

-60

-40

-20

02.5 2.6 2.7 2.8 2.9 3.0 3.1

2hF

-N

Figure 22.7 2hJF–N versus the F–N distance for neutral com-plexes with F–H...N hydrogen bonds grouped according to thehybridization of the nitrogen. Solid triangle: sp; solid circle: sp2 ;solid square: sp3.

have significantly larger coupling constants. Perhaps an even more compellingargument can be made from the data in Table 22.4 that provide absolute values ofthe difference between the F–H and N–H distances for pairs of neutral and cationiccomplexes that have similar coupling constants but different F–N distances. It isevident from these data that when the degree of proton sharing is approximately thesame (as measured by the difference between the F–H and N–H distances in thepair), then the coupling constants for the pair are very similar. Even though thehydrogen bonds in these complexes are traditional hydrogen bonds, they have a sim-ilar degree of proton-shared character.

Another feature of complexes with F–H–N hydrogen bonds is the very large val-ues of F–N coupling constants. While the maximum N–N and C–N coupling con-stants computed are about 20 Hz and 45 Hz, respectively, F–N coupling constantscan exceed 100 Hz. (Although reduced coupling constants 2hKX–Y should be usedwhen comparing coupling constants for different atoms, it is 2hJX–Y that is measuredexperimentally, hence the large differences are significant.) An interesting conse-quence of the large range of values for N–F coupling constants is that a neutral anda cationic complex with similar F–N distances can have coupling constants that dif-fer by more than 50 Hz!

In some recent experimental studies, Limbach and his associates investigated thetemperature dependence of coupling constants across hydrogen bonds [43, 44, 47–49]. They observed that as a function of decreasing temperature, two-bond spin–spin coupling constants initially increase, exhibit a maximum absolute value, and

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants366

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-202.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95

2hN

-F

Figure 22.8 2hJF–N versus the F–N distance for cationic com-plexes with N–H+...F hydrogen bonds grouped according to thehybridization of the nitrogen. Solid triangle: sp; solid circle: sp2 ;solid square: sp3.

then decrease. They interpreted their results in terms of solvent ordering and protontransfer. They suggested that as the temperature decreases, the type of hydrogenbond changes from traditional, to proton-shared, to ion-pair. Thus, they came to thesame conclusions about the relationship between 2hJX–Y and hydrogen bond typebased on experimental data as we did based on EOM-CCSD calculations. That reli-able ab initio calculations can assist in the interpretation of experimental couplingconstants for hydrogen-bonded complexes is illustrated below using the FH:colli-dine complex.

In a recent experimental study of the temperature dependence of 2hJF–N for theFH:collidine (FH:2,4,6-trimethylpyridine) complex between 100 and 200 K [43],Limbach and co-workers noted that as the temperature decreased, proton transferoccurred and hydrogen bond type changed from traditional, to proton-shared, toion-pair. As the temperature decreased, they observed that the one-bond F–H cou-pling constant (1JF–H) decreased, the absolute value of the H–N coupling constant(1hJH–N) increased, but the two-bond F–N coupling constant remained essentiallyconstant at –96 € 5 Hz. This is puzzling, given their and our previous results. To

22.3 Discussion 367

Table 22.4 2hJN–F values (Hz) and differences between F–H and N–H distances (�) for selectedneutral and cationic complexes with F–H–N hydrogen bonds.

R(N–F) |R(N–H) – R(F–H)| 2hJN–F

Complexes with similar N–F distancesFH:NCH 2.817 0.941 –21.5(F)HC=NH2

+:FH 2.814 0.767 –36.9

FH:1,3,5-triazine 2.684 0.778 –40.3F2HNH+:FH 2.687 0.595 –64.7

FH:NH3 2.637 0.711 –43.7FCNH+:FH 2.632 0.560 –108.8

Complexes with similar N–F coupling constantsFH:pyridine 2.611 0.678 –57.0H2C=N(F)H

+:FH 2.748 0.683 –56.4

FH:1,4-diazine 2.638 0.718 –49.11,2,4,6-tetrazinium:FH 2.785 0.721 –49.7

FH:NCLi 2.660 0.750 –47.8LiCNH+:FH 2.795 0.763 –46.9

FH:NH2F 2.721 0.824 –33.7H2C=NH2

+:FH 2.838 0.792 –33.5

FH:NCH 2.817 0.941 –21.54-Li-pyridinium:FH 2.933 0.899 –21.7

gain insight into these experimental results, we computed 1JF–H,1hJH–N, and

2hJF–Nin two model systems, FH:NH3 and FH:pyridine [50]. For each system we systemati-cally varied the F–H distance, optimized the complex at each distance, and thencomputed the coupling constant for each optimized structure. Figure 22.9 showsthe variation of 1JF–H,

1hJH–N and 2hJF–N as a function of the F–H distance, and there-fore changing hydrogen bond type, for FH:pyridine. As the F–H distance increases,the F–N distance decreases to a minimum when the hydrogen bond is proton-shared, and then increases as the ion-pair hydrogen bond is formed. These distancechanges are intimately related to the variation of 2hJF–N that is seen in Fig. 22.9. Itshould be noted that since collidine is a stronger base than pyridine, the equilibriumstructure of FH:collidine has greater proton-shared character, even in the gas phase.Our data suggest that at the highest temperatures investigated experimentally in so-lution, the hydrogen bond in FH:collidine is proton-shared, being on the traditionalside of quasi-symmetric. At the lowest temperature, the hydrogen bond is still pro-ton-shared, but is now on the ion-pair side. Thus, the vertical bars in Fig. 22.9 aredrawn to correspond to the region of the potential surface probed by the experi-ments. In this region, the potential surface for proton motion is relatively flat. Thisallows the proton to move freely while the F–N distance remains constant. It is theconstancy of this distance that gives rise to the constancy of 2hJF–N.

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants368

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

100.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

-80

-30

20

70

120

170

220

270

320

Figure 22.9 2hJF–N,1hJH–N, and

1JF–H for FH:pyridine as afunction of the F–H distance. The values of the couplingconstants (estimated from the FC terms) were computed forthe optimized structures at these distances. Open square:F–N; open diamond: H–N; open triangle: F–H.

Although Limbach et al. were not able to specifically identify the temperature atwhich the complex is stabilized by a quasi-symmetric proton-shared hydrogen bonddue to the constancy of 2hJF–N, they presented their estimates of the values of F–H,F–N, and H–N coupling constants that might characterize such a complex. Theseare given in Table 22.5, along with our computed values for FH:pyridine in the pro-ton-shared region. Given that pyridine is not as basic as collidine, and that 2hJF–Nhas been estimated only by the Fermi-contact term, the computed results are ingood agreement with the experimental, and provide insight into the interpretationof the experimental findings.

22.4Concluding Remarks

This chapter presents a summary of EOM-CCSD calculations carried out in this lab-oratory to characterize two-bond spin–spin coupling constants across N–H–N, C–H–N, and F–H–N hydrogen bonds in neutral and charged complexes. From thecomputed results, we have constructed curves for 2hJX–Y as a function of the X–Ydistance for each set of hydrogen-bonded complexes. These curves are presented astools for extracting X–Y distances from experimentally-measured coupling con-stants, and for predicting these constants in the absence of experimental data. Thecomputed results have led to new insights into the factors that determine 2hJX–Y.Future work will expand on these results, with the aim of providing a systematiccharacterization of spin–spin coupling constants across various types of X–H–Yhydrogen bonds.

Acknowledgments

This work was supported by the National Science Foundation through NSF grantCHE-9873815. This support and that of the Ohio Supercomputer Center are grate-fully acknowledged. It is a pleasure to acknowledge the many research collaboratorswho made important contributions to the work reported in this chapter.

22.4 Concluding Remarks 369

Table 22.5 NMR spin–spin coupling constants (Hz) for quasi-symmetric proton-shared hydrogenbonds in FH:collidine and FH:pyridine.

FH:collidineExperimental

FH:pyridineEOM-CCSDa

F–H (�) 1.15 1.20 1.25F–N (�) 2.489 2.480 2.4842hJF–N –96 –89 –90 –871JF–H 30 68 24 –81hJH–N –50 –21 –31 –41

a Estimated from the Fermi-contact term.

22 Characterizing Two-Bond NMR 13C–15N, 15N–15N, and 19F–15N Spin–Spin Coupling Constants370

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