the spin–spin coupling constants in the ammonia dimer

The spin–spin coupling constants in the ammonia dimer

Magdalena Pecul *, Joanna Sadlej

Department of Chemistry, University of Warsaw, ul. Pasteura 1, 02-093 Warsaw, Poland

Received 12 February 2002; in final form 15 May 2002

Abstract

The indirect spin–spin coupling constants have been calculated by means of the linear response MCSCF method for

the three stationary points of the ðNH3Þ2 dimer. The obtained intermolecular coupling constants and the dimerization-

induced changes of the intramolecular coupling constants are compared with the results for the ðHFÞ2 and ðH2OÞ2complexes and discussed as parameters of the hydrogen bond. The best correlation with the strength of the X–H � � �Yhydrogen bond is exhibited by the dimerization-induced change in the reduced intramolecular 1K(XH) coupling. The

reduced hydrogen-bond-transmitted 1hK(YH) coupling constant also correlates to some extent with the interaction

energy. No correlation with the interaction energy has been found for the reduced 2hKðXYÞ coupling constant. The

intermolecular coupling constants in ðNH3Þ2 seem to be determined primarily by the internuclear distances. � 2002

Elsevier Science B.V. All rights reserved.

1. Introduction

The experimental observation of the hydrogen-bond-transmitted indirect nuclear spin–spin cou-pling constants in several systems [1–4] hasinvoked much interest in these parameters amongtheoretical chemists [5–16]. In particular, thisdiscovery has raised once more the question ofthe covalent character of hydrogen bond [17,18].Recent theoretical studies [8,9,17] suggest thatintermolecular indirect spin–spin coupling con-stants may have measurable values not only inhydrogen-bonded complexes, but also in othervan der Waals molecules, including dimers of rare

gases [8]. This seems to indicate that the non-negligible value of the spin–spin coupling trans-mitted through an interaction is not connectedwith the covalent character of this interaction.This is supported by the analysis of the densitydistribution in the hydrogen bonds [17]. The othersource of interest in the intermolecular couplingconstants lies in their potential for localizing andcharacterizing hydrogen bonds in biomoleculesand thus for structure determination [3,4].

The coupling constants transmitted throughlow-barrier proton-shared hydrogen bonds havebeen recently frequently calculated [11–13,15,16].The medium-strength hydrogen bonds such asthose in water, ammonia or hydrogen fluoride di-mers are not as well investigated in this respect[5,6,9,10]. To fill this gap, our group has alreadystudied the spin–spin coupling constants in ðH2OÞ2

10 July 2002

Chemical Physics Letters 360 (2002) 272–282

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* Corresponding author. Fax: 48-22-822-59-96.

E-mail address: [email protected] (M. Pecul).

0009-2614/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0009-2614 (02 )00842-4

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and ðHFÞ2 dimers [5,9]. The hydrogen-bond-transmitted spin–spin coupling constants have alsobeen calculated for the mixed NH3–H2O dimer[10]. The collected data enable the comparison ofthe reduced hydrogen-bond-transmitted couplingconstants in different simple hydrogen-bonded di-mers and consequently an assessment of the ap-plicability of these parameters for the estimationof the hydrogen-bond strength.

Another motivation for the study of the cou-pling constants in ðNH3Þ2 is the singular potentialenergy surface of this system. The geometricstructure of ammonia dimer has arisen manycontroversies [19–23]. The most accurate calcula-tions [22] resulted in the conclusion that there aretwo minima, one nearly linear and one cyclic, veryclose in energy [22]. The conventional hydrogenbond is present in only one of them. Therefore thesystem is particularly appropriate for investigationof the role of a hydrogen bond in the transmissionof the spin–spin coupling constants.

This Letter is organized as follows. In Section 1,the method used for the calculation of spin–spincoupling constants is described. Next, the accuracyof the calculations is discussed on the basis of thespin–spin coupling constants obtained for theammonia monomer and the cyclic ammonia di-mer. In the next subsection the spin–spin couplingconstants calculated for three different stationarypoints of ðNH3Þ2 are reported and their depen-dence on the intermolecular distance is discussed.After that the intermolecular coupling constantsand the interaction-induced changes in the intra-molecular coupling constants obtained for thehydrogen-bonded structure of ðNH3Þ2 are com-pared with their counterparts in other hydrogen-bonded complexes: ðH2OÞ2 and ðHFÞ2. Finally, ashort summary and most important conclusionsare presented.

2. Computational details

The indirect nuclear spin–spin coupling con-stants have been calculated for two hydrogen-bonded structures 1 and 3 and the cyclic structure2 of ðNH3Þ2. The structures are depicted in Fig. 1.The geometric parameters are taken from [22],

where they were obtained by means of the MP2/aug-cc-pVTZ geometry optimization. Structures 1and 2 (denoted as asymmetric and cyclic in [22])were established as minima on the potential energysurface of ðNH3Þ2, while structure 3 was found tobe a saddle point [22]. The structure of ammoniamonomer has been also optimized at the MP2/aug-cc-pVTZ level.

The nuclear spin–spin coupling constants havebeen calculated using multiconfigurational self-consistent field (MCSCF) linear response method,as described in [24,25]. We employed the Re-stricted Active Space (RAS) technique, dividingthe molecular orbitals into inactive space (here: 1snitrogen orbitals), RAS1 (here: empty), RAS2(here: the remaining orbitals occupied in SCF),RAS3 (here: lowest virtual orbitals, chosen ac-cording to their MP2 occupation numbers) and the

Structure 1 (asymmetric)

Structure 2 (cyclic)

Structure 3 (linear)

Fig. 1. The structures of the stationary points of ðNH3Þ2 dimer:

hydrogen-bonded global minimum (asymmetric structure 1),

cyclic local minimum (cyclic structure 2), and hydrogen-bonded

saddle point (linear structure 3).

M. Pecul, J. Sadlej / Chemical Physics Letters 360 (2002) 272–282 273

remaining, external orbitals. The resulting RASspace is denoted ðn1=n2=n3=n4 ne), where n1–4 rep-resents the number of orbitals in the inactive,RAS1, RAS2 and RAS3 spaces, respectively, andne indicates the maximum number of electronsallowed to be excited to the RAS3 space.

Several different wavefunctions have been testedfor the ammonia dimer (see Section 3.2.1). TheRAS space finally employed for the calculation ofthe spin–spin coupling constants is (2/-/8/8 4e). Thecore nitrogen orbitals have been kept inactive,expect for the RAS (-/-/10/8 4e) wave functionansatz. Since the employed computational tech-nique is not size-extensive, the dimerization-in-duced changes of the coupling constants have beencalculated by subtracting the results obtained forthe optimized structure of the dimer and thoseobtained for two monomers (with dimer-like ge-ometry) separated by the distance of 500 �AA. Theeffects of monomer relaxation during the dimerformation on the intramolecular coupling con-stants have been accounted for as a difference be-tween spin–spin coupling constants calculated (a)for the single NH3 molecule with deformed dimer-like geometry and (b) for the single NH3 moleculewith optimized geometry.

For the calculations of the spin–spin couplingconstants the aug-cc-pVDZ-su1 and aug-cc-pVTZ-su1 basis sets have been used for nitrogen, con-structed from the augmented correlation-consis-tent aug-cc-pVDZ and aug-cc-pVTZ basis sets ofDunning and coworkers [26,27] by decontractingthe s functions and adding one tight s orbital, aprocedure suggested in [28]. For hydrogen atomscc-pVDZ-su1 and cc-pVTZ-su1 basis sets havebeen used. The basis set constructed in this waywill be denoted aug-cc-pVDZ-su1/cc-pVDZ-su1(or aug-cc-pVTZ-su1/cc-pVTZ-su1, respectively),in this Letter. Former studies by the authors [5–7,9] indicate that this type of basis sets (containingboth a flexible set of core s functions, essential forthe calculation of the coupling constants, anddiffuse orbitals required for the proper descriptionof the intermolecular interactions) is suitable forthe calculations of the coupling constants in vander Waals complexes.

All terms contributing to the indirect nuclearspin–spin coupling constants, i.e., the Fermi con-

tact term FC, the spin–dipole term SD, the para-magnetic spin–orbit term PSO and thediamagnetic spin–orbit term DSO, have been cal-culated. In the case of the most extended calcula-tions the smallest but computationally expensiveSD term has been calculated at a lower level oftheory.

The calculations of the spin–spin couplingconstants have been performed using DALTON

[29] program package. The geometry optimizationhas been carried out by means of GAUSSIAN 98software [30].

3. Results and discussion

3.1. The coupling constants in ammonia monomer

The spin–spin coupling constants calculated forthe NH3 monomer for two basis sets and severalactive spaces are presented in Table 1. We wouldlike to focus on the comparison of the results ob-tained with the RAS space and basis set usedsubsequently for the calculations of the couplingconstants in the ðNH3Þ2 dimer (RAS (2/-/8/8 4e)with aug-cc-pVDZ-su1/cc-pVDZ-su1 basis set)with the results of more sophisticated calculations.For a better comparison with previous ab initiocalculations [31,32] the spin–spin coupling con-stants have been calculated additionally for theammonia monomer with the experimental geom-etry used therein. However, since the differencesbetween the results obtained with the optimizedand experimental geometry of ammonia monomerare less than 0.6%, they latter are not presented inTable 1.

The coupling constants calculated for the am-monia monomer with the RAS (1/-/4/4 2e) activespace are compared with the results obtained withRAS (2/-/8/8 4e) for the two NH3 molecules sep-arated by 500 �AA. The relevant numbers are pre-sented in the first two rows of Table 1. Thedifferences do not exceed 1% for the 1JðNHÞcoupling constant and 2% for 2JðHHÞ. This indi-cates that RAS (1/-/4/4 2e), in which monomerrelaxation effects on the intramolecular spin–spincoupling constants have been estimated, is practi-cally equivalent to RAS (2/-/8/8 4e) for the dimer.

274 M. Pecul, J. Sadlej / Chemical Physics Letters 360 (2002) 272–282

Unfortunately, the size-extensive CAS SCF ana-logue of RAS (2/-/8/8 4e), built from 16 activeorbitals, comprises more than 8� 107 determi-nants, which makes it untractable computation-ally.

The 1JðNHÞ coupling constant calculated withthe small active space and moderate basis setagrees well with the our best theoretical result(CAS with aug-cc-pVQZ-su1 basis set), which inturn is in a perfect agreement with experiment.This may be circumstantial to a some extent sincethe rovibrational effects are not taken into accountin our calculations. The consistency of the 1JðNHÞcoupling constant calculated at the RAS (1/-/4/42e)/aug-cc-pVDZ-su1/cc-pVDZ-su1 level with ex-periment is most probably caused by the cancel-lation of errors resulting from inadequacies of abasis set and lack of higher-order electron corre-lation effects. This conclusion is supported by thefact that an extension of the active space alone (toCAS (1/-/13/- 8e)) shifts down the calculated1JðNHÞ value, increasing the discrepancy with ex-periment, while the improvement of the basis set(to aug-cc-pVQZ-su1) shifts it in an opposite di-rection.

The calculated 2JðHHÞ coupling constant issensitive to the size of an active space, in accor-dance with the previous results [5] but does notdepend much on the employed basis set. The

value obtained with the small aug-cc-pVDZ-su1/cc-pVDZ-su1 basis set is in surprisingly goodagreement with the aug-cc-pVQZ-su1 result. Tosum up, the results for the ammonia monomerindicate that at least proton–nitrogen couplingconstants obtained for the dimer should be reli-able, if we assume that the computational re-quirements are similar for the covalent-bond andhydrogen-bond-transmitted spin–spin couplingconstants. Proton–proton coupling constants havesteeper computational requirements. The issue ofthe accuracy of our calculations will be pursuedfurther in the next subsection.

3.2. The coupling constants in ammonia dimer

3.2.1. Accuracy of the calculated coupling constantsThe cyclic ammonia dimer has the highest

symmetry. In consequence, it has been possibleto carry out more extensive MCSCF calculationsof the spin–spin coupling constants for thisstructure, too time-consuming in the case of theother two stationary points. The results, sum-marized in Table 2, are used to discuss the ac-curacy of the intermolecular coupling constantsobtained with the wavefunction finally employed,RAS (2/0/8/8 4e) with the aug-cc-pVDZ-su-1basis set on the N atoms and cc-pVDZ-su-1 onthe H atoms.

Table 1

The nuclear spin–spin coupling constants (in Hz) in the NH3 monomer

RAS space Basis set 1JðNHÞ 2JðHHÞ

RAS (1/-/4/4 2e) aug-cc-pVDZ-su1/cc-pVDZ-su1 )62.2 )15.5RAS (2/-/8/8 4e)a aug-cc-pVDZ-su1/cc-pVDZ-su1 )61.7 )15.1CAS (1/-/13/- 8e) aug-cc-pVDZ-su1/cc-pVDZ-su1 )57.8 )11.5RAS (1/-/4/4 2e) aug-cc-pVQZ-su1 )66.6 )16.0CAS (1/-/13/- 8e) aug-cc-pVQZ-su1 )61.7 )11.4

Exp. )61.2b )10b

61:45� 0:02c

61:54� 0:03d

Other calc. )60.07e )19.9e

)58.65f )12.09f

aAn analogue of RAS (1/-/4/4 2e) for two monomers separated by 500 �AA.bExperimental results from [35].c Experimental liquid-phase results from [34].d Experimental gas-phase results from [33].e Finite field MP2 results from [32].f EOM-CCSD results from [31].


Firstly, the effect of including the core orbitalsof nitrogen in the active space are analyzed by acomparison of the RAS (2/-/8/8 4e) and RAS (-/-/10/8 4e) results. As one can see, it is practicallynegligible. Although the employed basis set is notoptimized for core correlation effects, the uncon-traction of the s orbitals increases its flexibility inthe core region, so this conclusion should notchange if a more complete basis set were used.Predictably, including a larger number of virtualorbitals in the active space has a more pronouncedeffect on the calculated coupling constants, as thecomparison of the RAS (2/-/8/8 2e) and RAS (2/-/8/18 2e) results shows. The couplings calculatedwith the active space extended in this way tend tobe smaller, but the effect is less than 10%. It turnsout that building the RAS wave function ansatz byincluding higher than double excitations from theRAS2 to RAS3 active space is necessary in par-ticular for the accurate rendering of the intermo-lecular 1hJðNNÞ coupling constant, as the

comparison of the RAS (2/-/8/8 2e) and RAS (2/-/8/8 4e) results indicates.

Extension of a basis set to a triple-zeta one haslittle effect on the couplings of nitrogen, but a verypronounced influence on the intermolecular pro-ton–proton coupling, which becomes more thantwice smaller. Our results for the intermolecularproton–proton couplings should therefore beviewed with caution. On the other hand, the use ofthe full aug-cc-pVDZ-su1 basis set, with diffusefunctions added also on hydrogen atoms, does notinfluence the calculated proton couplings much.Thus the lack of these functions in the appliedabbreviated basis set is not a source of significanterrors.

3.2.2. The coupling constants at the stationarypoints

The intermolecular spin–spin coupling con-stants calculated for all three stationary points ofðNH3Þ2 are summarized in Table 3. To facilitate

Table 2

The intermolecular spin–spin coupling constants (in Hz) in the cyclic structure 2 of the ðNH3Þ2 dimer obtained with various basis sets

and RAS active spaces

RAS space Basis set JðN1N10Þ JðN1H10Þ JðH1H10Þ

(2/-/8/8 2e) aug-cc-pVDZ-su1/cc-pVDZ-su1 2.54 0.50 0.57


(-/-/10/8 4e)a aug-cc-pVDZ-su1/cc-pVDZ-su1 2.56 0.43 0.57


(2/-/8/8 4e) aug-cc-pVDZ-su1 2.55 0.42 0.54

(2/-/8/8 4e)b aug-cc-pVTZ-su1/cc-pVTZ-su1 2.54 0.44 0.22

a SD term calculated at the RAS (2/-/8/8 4e) level with aug-cc-pVDZ-su1/cc-pVDZsu1.b SD term calculated at the RAS (2/-/8/8 2e) level with aug-cc-pVTZ-su1/cc-pVTZsu1.

Table 3

The intermolecular spin–spin coupling constants (in Hz) in the ðNH3Þ2 dimer; RAS (2/-/8/8 4e) results

Structure 1 J(N1N2) J(H4N1) J(H1H4) J(H2H4)

aug-cc-pVDZ-su1/cc-pVDZ-su1 2.07 1.62 0.56 )0.01aug-cc-pVTZ-su1/cc-pVTZ-su1a 2.07 1.70 0.37 0.03

Structure 2 JðN1N10Þ JðN1H10Þ JðH1H10Þ JðH1H20Þaug-cc-pVDZ-su1/cc-pVDZ-su1 2.56 0.43 0.57 )0.23aug-cc-pVTZ-su1/cc-pVTZ-su1b 2.54 0.44 0.22 )0.16

Structure 3 J(N1N2) J(H4N1) J(H1H4) J(H2H4)

aug-cc-pVDZ-su1/cc-pVDZ-su1 1.90 1.73 )0.19 0.46

aug-cc-pVTZ-su1/cc-pVTZ-su1b 1.90 1.83 )0.11 0.39

a SD term calculated at the RAS1 (2/-/8/8 2e) level.


the interpretation of the results, the interactionenergies and selected geometric parameters ofðNH3Þ2, taken from [22], are presented in Table 4.

The calculated 2hJðNNÞ coupling constant islargest in the cyclic structure 2, although the in-teraction energy is smaller for this structure thanfor the asymmetric structure 1. It means that thisintermolecular coupling constant correlates withthe internuclear R(NN) distance, which is shorterfor the structure 2 than for the structure 1, ratherthan with the interaction energy. This observationis confirmed by the smallest value of 2hJðNNÞcalculated for the linear structure 3, which ischaracterized by the longest nitrogen–nitrogendistance.

The internuclear distance seems also to be thedominant factor determining the value of the1hJðNHÞ coupling constant. The value is the larg-est for the linear structure 3, only slightly smallerfor the structure 1, and significantly smaller for thestructure 2, which corresponds to the nitrogen–proton distances of 2.273, 2.283, and 2.515 �AA, re-spectively. Again, the intermolecular energy doesnot correlate with the intermolecular coupling.Using the aug-cc-pVTZ-su1 basis set instead of theaug-cc-pVDZ-su1 one does not change noticeablythe calculated 2hJðNNÞ and 1hJðNHÞ couplings, asit has been already discussed on the basis of theresults from Table 2.

The intermolecular proton–proton couplingsare positive and relatively significant when bothprotons are engaged in the intermolecular inter-action, for example J(H1H4) in the structure 1 orJðH1H10Þ in the structure 2. It is probably due to alarge extent to the spatial proximity of the coupledprotons since the J(H4H2) coupling in the struc-ture 3 is also positive and substantial in contrast to

the J(H1H4) coupling when the protons are fur-ther away from each other. Significant values ofthe proton–proton couplings between protonsforming adjacent hydrogen bonds have been al-ready discussed in [6,7]. However, these valuesmay be overestimated since it has been shownabove that the intermolecular proton–protoncouplings are sensitive to the basis set size, and thebasis sets applied here are clearly not saturated.

3.2.3. The dependence of the coupling constants onthe internuclear distance

The dependence of the intermolecular couplingconstants on the nitrogen–nitrogen distanceR(NN), calculated for five distances using RAS(2/-/8/8 4e) and the aug-cc-pVDZ-su1/cc-pVDZ-su1 basis set, is depicted in Fig. 2. For the2hJðNNÞ and 1hJðNHÞ couplings the dependence issteep, and it resembles the exponential trends al-ready reported for the coupling constants of thistype in the other complexes [7]. In contrast to that,the intermolecular proton–proton couplings de-pend only slightly on the intermolecular distance.This difference between those two types of inter-molecular coupling can be explained by an anal-ysis of the terms contributing to them: the2hJðNNÞ and 1hðNHÞ couplings are dominated bythe strongly distance-dependent Fermi contactterm, while the proton–proton couplings are de-termined by the balance between the para- anddiamagnetic spin–orbit terms, which are much lessdistance-dependent. A weak distance-dependenceof the proton–proton intermolecular couplingconstants has been already reported before [6,7].

The comparison of the dependence of the2hJðNNÞ coupling on the nitrogen–nitrogen dis-tance for any of the three structures with the

Table 4

The interaction energy DE and selected geometry parameters of the ðNH3Þ2 dimer; DE obtained at the counterpoise corrected MP2/

aug-cc-pVQZ level, for MP2/aug-cc-pVTZ optimized geometrya

DE R(NN) R(NH)b aðNNHÞb(kJ/mol) (�AA) (�AA) (deg)

Structure 1 )12.92 3.235 2.283 17.1

Structure 2 )12.89 3.166 2.515 42.6

Structure 3 )12.39 3.258 2.273 12.0

aAll data taken from [22].b The hydrogen-bond length and the hydrogen-bond angle, respectively.


values reported in Table 3 supports the conclusionthat this coupling is determined mainly by the in-ternuclear distance. For example, interpolating thedependence of 2hJðNNÞ on R(NN) calculated for

the structure 1 for the values of R(NN) corre-sponding to structures 2 and 3 reproduces therelevant values from Table 3 with acceptable ac-curacy. The same reproducibility is observed forthe 1hJðNHÞ coupling. The authors find this factsurprising since it means that in the ðNH3Þ2 dimerthe intermolecular couplings are determined pri-marily by the internuclear distance, with little an-gular dependence, while in the strongly interactingcomplexes the hydrogen-bond-transmitted cou-plings depend significantly on the intermolecularangles [9,14,16].

3.2.4. The dimerization-induced changes of theintramolecular coupling constants in NH3

The complexation-induced shifts of the intra-molecular coupling constants in NH3 are summa-rized in Table 5. The first observation is that in theproton donor molecule the 1JðNHÞ coupling con-stant of a proton engaged in the hydrogen bondð1JðH4N2Þ in structure 1 and in structure 3) in-crease significantly (as far as the absolute value isconcerned), while the remaining two equivalent1JðNHÞ coupling constants decrease in their ab-solute values. An increase in the 1J (H1N1) cou-pling constant in the structure 1 (in the protonacceptor) is probably due to the proximity of theN2 nitrogen atom, since this effect is much smallerfor the structure 3 where H2 is far from N2. In thecyclic structure the dimerization-induced changesof 1JðNHÞ couplings are smaller than in the hy-drogen-bonded structures but the basic pattern isthe same: a coupling of the proton in the imme-diate vicinity of the other molecule increases itsabsolute value while the couplings of the other twoprotons decrease.

Taking into account the monomer relaxationeffects does not change much the calculated hy-drogen-bond-induced changes of the 1JðNHÞcoupling constants. The monomer relaxation ef-fects are larger for the changes of the 2JðHHÞcoupling, in some cases changing the sign of thenet shift, but the dimerization effects on the2JðHHÞ couplings are not significant anyway. Wehave not accounted in these calculations for thebasis set superposition error since in the RAS SCFcalculations the counterpoise correction methodcannot be applied. However, the study of the

Fig. 2. The dependence of the selected intermolecular coupling

constants on the nitrogen–nitrogen R(NN) distance for (a)

asymmetric structure 1, (b) cyclic structure 2, (c) linear structure

3.


coupling constants in ðH2OÞ2 [5] suggests that us-ing the basis set of the aug-cc-pVXZ-su1 type en-sures that BSSE is small.

There are no experimental data available for thedimerization-induced changes of the spin–spincoupling constants. The only experimental refer-ence that can be made are the gas-to-liquid shiftsof the coupling constants of NH3. The measure-ments of Wielog�oorska [33] in the gas phase to-gether with the liquid-phase results of Wasylishenand Friedrich [34] indicate that the gas-to-liquidshifts for both 1JðNHÞ and 2JðHHÞ (actually,2JðDHÞ) couplings are positive, but practicallywithin the experimental error. The calculated di-merization-induced changes would suggest a smallnet increase in the absolute value of 1J (NH) and adecrease in 2JðHHÞ, which does not agree with theexperimental gas-to-liquid shifts. However, oneshould keep in mind that rigid dimers are a verycrude approximation for the dynamic structure ofthe liquid. Moreover, the measurements for the gasphase and for the liquid were carried out in dif-ferent temperatures, which complicates the com-parison further since the gas-to-liquid andtemperature shifts are interrelated.

3.3. The comparison of ðHF Þ2, ðH2OÞ2 and ðNH3Þ2dimers

The interaction energy in ðHFÞ2, ðH2OÞ2 andðNH3Þ2 [21], the reduced X–H � � �Y hydrogen-bond-transmitted couplings, and the interaction-induced changes of the reduced intramolecular1JðXHÞ coupling in the proton donor and1JðYHÞ in the proton acceptor (averaged valuein the case of the ðNH3Þ2 dimer) are collected inTable 6. We refer to the symmetry adaptedperturbation theory (SAPT) interaction energies[21] since [21] provides the interaction energiescalculated at a uniform level of theory for allcomplexes under study. The coupling constantsfor all the complexes have been obtained at theRAS (2/0/8/8 4e)/aug-cc-pVDZ-su1 level, withouttaking into account the monomer relaxationeffects.

The couplings in ðHFÞ2 and ðH2OÞ2, calculatedfor the experimental geometries of the dimers,have been already discussed in [5,9].T

able

5

Thechanges

intheammonia

intramolecularspin–spin

couplingconstants

(inHz)

causedbythedim

erform

ation;RAS(2/-/8/84e)/(aug-cc-pVDZ-su1/cc-pVDZ-su1)

results

Structure

11J(H4N2)

1J(H5N2)

1J(H1N1)

1J(H2N1)

2J(H5H4)

2JðH5H50 Þ

2J(H2H1)

2JðH2H20 Þ

Inter

)3.11

0.67

)0.46

)0.03

)0.41

0.11

)0.23

)0.32

+Mon.relax.

)3.43

0.48

)0.47

)0.02

)0.10

)0.08

)0.19

)0.35

Structure

2–

–1J(H1N1)

1J(H2N1)

––

2J(H2H1)

2JðH2H200 Þ

Inter

––

)1.85

0.31

––

)0.38

)0.22

+Mon.relax.

––

)2.16

0.16

––

)0.14

)0.35

Structure

31J(H4N2)

1J(H5N2)

1J(H1N1)

1J(H2N1)

2J(H5H4)

2JðH5H50 Þ

2J(H2H1)

2JðH2H20 Þ

Inter

)3.26

0.74

)0.13

)0.16

)0.39

0.18

)0.21

)0.22

+Mon.relax.

)3.53

0.57

)0.20

0.01

)0.09

)0.03

)0.15

)0.42


The first observation from Table 6 is that thereduced 2hKðXYÞ coupling constant has little incommon with the interaction energy in the se-quence of dimers under study. Even the sign of2hKðXYÞ varies, from positive in ðH2OÞ2 andðNH3Þ2 to negative in ðHFÞ2 (dominated by theparamagnetic spin–orbit term [9]). The sign re-mains constant when only the Fermi contact termis analyzed, but the value of 2hKðXYÞ still does notcorrelate with the interaction energy. It is furtherconfirmed by the fact that the reduced 2hKðNOÞcoupling in H2O–NH3 dimer calculated by Ja-nowski and Jaszu�nnski [10] is 18:73� 1019 T2 J�1, avalue similar to the one obtained by us for ðNH3Þ2,although the interaction energy in H2O–NH3 isapproximately 2.5 times larger than that inðNH3Þ2.

The 1hKðHYÞ coupling seems to be a bettergeneral parameter of the strength of the hydrogenbond. Its value in ðHFÞ2 is larger than in ðH2OÞ2,which is opposite to what one will expect from thecomparison of the interaction energies, but thediscrepancy is not substantial. The reduced1hKðNHÞ coupling in the trans form of theH2O–NH3 dimer calculated by Janowski and Jas-zu�nnski is �2:89� 1019 T2 J�1, while the interactionenergy is approximately )26.8 kJ/mol. It fitstherefore in the tendency described here.

Much better correlation with the interactionenergy is observed for the XH � � �Y hydrogen-bond-induced changes in the Fermi contact termsof the intramolecular one-bond coupling 1KðXHÞ(of the hydrogen-bond-forming proton) than forthe intermolecular coupling constants. The chan-ges in the total 1KðXHÞ couplings do not corre-spond so well to the interaction energy since in

ðHFÞ2, unlike in ðH2OÞ2 and ðNH3Þ2, dimerizationchanges to a large extent the PSO term. In theH2O–NH3 dimer the corresponding reduced cou-pling 1KðOHÞ increases by approximately5:4� 1019 T2 J�1, which correlates well with theinteraction energy )26.8 kJ/mol. Predictably, thehydrogen-bond-induced change in reduced cou-pling constant between non-hydrogen-bondedproton and proton acceptor 1KðXHÞ exhibits nocorrelation with the hydrogen-bond strength.

4. Summary and conclusions

The Letter reports the results of the calculationsof the spin–spin coupling constants in the ðNH3Þ2dimer, carried out by means of the MCSCF linearresponse method. The obtained intermolecularcoupling constants and the dimerization-inducedchanges of the intramolecular coupling constantsare compared with the results for the ðHFÞ2 andðH2OÞ2 complexes and discussed in the context oftheir correlation with the complex structure andinteraction energies.

The assessment of the quality of the final resultson the basis of the calculations of the couplings inmonomer and in the most symmetric structure ofthe dimer leads to the conclusion that the obtainedvalues should be reliable, although perhaps not ofpredictive quality. The core correlation effects, asestimated in a relatively small basis set, are negli-gible. The basis set effects are unlikely to changequalitative conclusions, with a possible exception ofthose concerning the intermolecular proton–protoncoupling constants. The most significant source oferror are therefore the valence correlation effects

Table 6

The comparison of the interaction energies DE, the reduced intermolecular coupling constants 2hKðXYÞ and 1hKðHYÞ, and the changes

in the reduced coupling constants in the proton donor D1KðXHÞ and proton acceptor D1KðYHÞ in the X–H � � �Y hydrogen-bonded

complexes

DE a 2hKðXYÞ 1hKðHYÞ D1KðXHÞ D1KðYHÞ(kJ/mol) (10�19 T2 J�1) (10�19 T2 J�1) (10�19 T2 J�1) (10�19 T2 J�1)

ðNH3Þ2 )10.46 16.76 (17.04)b )1.31 ()1.40) 2.53 (2.90) 0.13 (0.15)

ðHFÞ2 )15.69 )0.58 (1.63) )2.44 ()2.65) 1.65 (3.55) 2.94 (3.84)

ðH2OÞ2 )17.66 5.41 (6.09) )2.27 ()2.46) 2.75 (3.92) 1.38 (1.61)

a SAPT results from [21].b Fermi contact term in parenthesis.


unaccounted for by the RAS wave functionemployed.

The analysis of intermolecular coupling con-stants calculated for the three stationary points onthe potential energy surface indicates that thesecouplings are determined primarily by the inter-nuclear distances, with surprisingly little angulardependence. This is confirmed further by theanalysis of the dependence of the intermolecularnitrogen–nitrogen, nitrogen–proton and proton–proton coupling constants on the nitrogen–nitro-gen distance. It seems therefore that the presenceof a nearly linear hydrogen bond is not paramountfor the significant value of the intermolecularcoupling constant, as the example of the cyclicstructure of ðNH3Þ2 indicates. It should be noted,however, that in this case there are two NH � � �Ncontacts which may magnify the coupling. None ofthe intermolecular coupling constants exhibit acorrelation with the interaction energy of ðNH3Þ2.

Predictably, the intermolecular 2hJðNNÞ and1hJðNHÞ coupling constants are the only couplingshaving significant values. The intermolecular pro-ton–proton couplings are relatively substantialwhen the protons are close, but their calculatedvalues are less reliable than in the case of the othercoupling constants because of the large basis setdependence. The 2hJðNNÞ and 1hJðNHÞ couplingconstants are more distance-dependent than theproton–proton ones because the intermolecularcouplings of nitrogen are determined primarily bythe Fermi contact term while in the other cou-plings the spin–orbit terms dominate.

The comparison of ðHFÞ2, ðH2OÞ2 and ðNH3Þ2dimers indicate that the best parameter of theX–H � � �Y hydrogen-bond strength is the changein the Fermi contact term of the reduced 1JðXHÞcoupling constant. Also the reduced couplingconstant between proton and proton acceptorcorrelates approximately with the interaction en-ergy. The reduced coupling constant betweenproton donor and proton acceptor 2hKðXYÞ ex-hibits no correlation with the hydrogen-bondstrength, since even the sign of 2hKðXYÞ changes inthe sequence of complexes under study. No cor-relation with the interaction energy is observedeven when only the Fermi contact term of 2hK(XY)is considered.

Acknowledgements

We acknowledge the support from the 7 TO9A11121 KBN Grant. In 2001 M.P. was a recipient ofDomestic Grant for Young Researchers foundedby Foundation for Polish Science.

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http://www.kjemi.uio.no/software/dalton/dalton.html

the spin–spin coupling constants in the ammonia dimer

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