solvent effects on the spin–spin coupling constants of acetylene revisited: supermolecular and...

MAGNETIC RESONANCE IN CHEMISTRYMagn. Reson. Chem. 2004; 42: S128–S137Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/mrc.1413

Solvent effects on the spin–spin coupling constantsof acetylene revisited: supermolecular and polarizablecontinuum model calculations†

Magdalena Pecul1,2 and Kenneth Ruud2∗

1 Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland2 Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway

Received 16 February 2004; Revised 11 March 2004; Accepted 11 March 2004

The solvent shifts of the spin–spin coupling constants of acetylene were calculated using the polarizablecontinuum model (PCM) for solvents ranging in polarity from cyclohexane to water, using both densityfunctional theory (DFT) and the complete active space self-consistent field (CASSCF) method. Thespin–spin coupling constants were also calculated for complexes of acetylene with water, acetonitrile,acetone and benzene using DFT/B3LYP. It is demonstrated that PCM reproduces the substantialexperimental solvent shifts of the 1J(C,C) and 1J(C,H) couplings with great accuracy. The sign andapproximate magnitude are also rendered correctly by the supermolecular method, in spite of thelimitation of the models, which included only one or two solvent molecules. Copyright 2004 John Wiley& Sons, Ltd.

KEYWORDS: NMR; acetylene; spin–spin coupling constants; solvent effects; polarizable continuum model; supermoleculareffects

INTRODUCTION

The influence of the environment on the parameters of NMRspectra is an important and widely researched subject,1 – 10

owing to the widespread application of NMR parametersin investigations of the structures of organic and biolog-ical molecules. Quantum chemical calculations are a veryuseful tool in these studies since all factors influencing anobservable NMR property can be investigated separately andquantitative correlations between the molecular structureand the environment can in principle be obtained. However,whereas numerous papers have been focused on environ-mental effects on the NMR shielding constants (see Ref. 5for a review and Refs 6 and 7 for recent references), ab ini-tio investigations of such effects on the spin–spin couplingconstants are still relatively scarce.1 – 4,10,11

The reason for this is that ab initio calculations ofindirect spin–spin coupling constants are a challengingtask. In the non-relativistic formulation of the theory asfirst derived by Ramsey,12 each nuclear magnetic momentperturbs the electron density through 10 different interactionmechanisms [six spin–dipolar (SD), three paramagneticspin–dipole (PSO) and one Fermi contact interaction], and

†Dedicated to Professor M. Barfield on the occasionof his 70th birthday.ŁCorrespondence to: Kenneth Ruud, Department of Chemistry,University of Tromsø, N-9037 Tromsø, Norway.E-mail: [email protected]/grant sponsor: Norwegian Research Council;Contract/grant number: 154 011/420.

a large number of response equations therefore need to besolved for each nucleus. Moreover, the presence of the Fermicontact interaction, which depends on the electron densityclose to the nuclei, puts severe demands on the quality ofthe basis set used. The triplet nature of the Fermi contactand the spin–dipolar operators also adds to the difficultiesfaced by theoretical calculations of these properties, sincespin-restricted approaches such as restricted Hartree–Fockfail completely, often giving results that are several orderof magnitudes too large, in addition to having incorrectsigns.13,14 Introducing electron correlation, for example bymeans of multiconfigurational self-consistent field (MCSCF)theory or density functional theory (DFT), in most casessolves the problem of triplet instabilities.

Both the MCSCF and the DFT methods have beenextended to include dielectric continuum effects described bythe polarizable continuum model (PCM)15 – 17 for spin–spincoupling constants calculations. In the PCM model, themolecule is placed in a molecule-shaped cavity in apolarizable dielectric medium, the polarization effects onthe solvated molecule being introduced through charges onthe cavity surface. The implementation is based on the recentextensions of the PCM model to a quadratically convergentscheme for optimizing PCM-MCSCF wavefunctions18 andsinglet linear response functions19 for solvated molecules.DFT reference states and triplet linear response functionshave been discussed.11

One of the systems for which solvent effects on thecoupling constants have been thoroughly investigated isacetylene.2,20,21 The coupling constants in acetylene, and in

Copyright 2004 John Wiley & Sons, Ltd.

Solvent effects on spin–spin coupling constants of acetylene S129

particular the 1J�C,C� coupling constant, have been foundto be very sensitive to solvent effects,2,20 and a seriesof experimental results obtained in different solvents isavailable.2,20 Acetylene is therefore an interesting moleculeto test a new implementation of the PCM for calculationsof spin–spin coupling constants using DFT. Moreover, thereare benchmark quality results available for the spin–spincoupling constants of the isolated acetylene molecule, bothcalculated theoretically22,23 and observed experimentally.20

Calculations of solvent effects on the NMR spectrum ofacetylene have previously been carried out at the MCSCFlevel using a reaction field method with a spherical cavityin a dielectric continuum.2 The reaction field model hasbeen shown to be useful for calculations of the trends inthe solvent effects on the spin–spin coupling constants,especially on 1J�C,C�, but the calculated changes wereseriously underestimated compared with experiment. Thisunderestimation could be due to the spherical shape of thecavity, which is not ideally suited for the cylindrically shapedacetylene molecule. Revisiting this subject once more, usinga more realistic PCM model where the cavity is adjusted tothe shape of the molecule, is therefore of interest.

The MCSCF method does not allow for calculationsof spin–spin coupling constants in extended systems, inparticular for molecular clusters. Calculations of spin–spincoupling constants for systems of substantial size havenowadays become feasible thanks to DFT, which usuallyperforms adequately for spin–spin coupling constants, issize extensive and scales favourably with molecular size.These features of DFT allow us to carry out, in additionto the PCM calculations, supermolecular calculations of theeffects of the formation of mixed dimers and trimers onthe spin–spin coupling constants of acetylene. Complexes ofacetylene with water, acetone, acetonitrile and benzene werestudied in this work. Not all of the structures investigatedhere are true minima on the respective potential energysurfaces, but this is of secondary importance, since the mainobject is to model structural arrangements which may occurwhen the acetylene molecule is solvated, rather than to studythe complexes per se.

In the next section, the theory and computational detailsare briefly summarized. In the subsequent section, the resultsof the calculations are discussed, starting from the couplingconstants of the isolated acetylene molecule and the solventeffects as estimated by the PCM model, and then proceedingto the effects of the formation of dimers and trimers. Finally,we give a brief summary and some concluding remarks.

THEORY AND COMPUTATIONAL DETAILS

For an isolated molecule, the indirect spin–spin couplingconstant between nuclei K and L, JKL, can be determined as thesecond derivative of the electronic energy with respect to thenuclear magnetic moments MK and ML.24 For a molecule insolution described by the PCM model, the indirect spin–spincoupling constants are determined as second derivatives ofthe free-energy functional G of the solute–solvent systemwith respect to the nuclear magnetic moments:

JKL D h�K

2�

�L

2�KKL D h

�K

2�

�L

2�

d2GdMKdML

�1�

where KKL is the reduced spin–spin coupling constant, h isPlanck’s constant and �K and �L are the magnetogyric ratiosof the nuclei.

The form of the free energy functional G appearingin the PCM has been discussed.11,15 – 17 Here we onlynote that for variational calculations, which includes theMCSCF wavefunction and Kohn–Sham DFT, the free energyfunctional can be symbolically represented as G�MK, �S, �T�,where �S and �T are two sets of variational parametersassociated with singlet and triplet variations of the electronicstate,25 and the spin–spin coupling constants can beevaluated by means of a procedure based on linear responsetheory for molecular solutes, i.e. a variational-perturbativescheme which ensures the stationarity condition of the free-energy functional to first order with respect to any value ofthe nuclear magnetic moments.

In the present work, the spin–spin coupling constantswere calculated using DFT employing the hybrid B3LYP26

functional. Collected computational experience25,27 indicatesthat B3LYP is the best choice of exchange-correlation func-tional for the calculation of spin–spin coupling constants. Toease the comparison with the results in Ref. 2, the CASSCF(complete active space self-consistent field) method was alsoemployed. The CAS space was constructed from 12 activeorbitals, with the 1s orbitals of C kept inactive, and corre-sponds to the active space denoted CAS1 in Ref. 2.

The PCM calculations were carried out using a staticsolvation model, using the same static dielectric constantsas in Ref. 2. The cavities in the PCM calculations wereconstructed from overlapping spheres centered on the nucleiof the acetylene molecule, with radius 1.7 A for the carbonatoms and 1.2 A for the hydrogen atoms. This choice of radiifor the spheres is based on the van der Waals radii of theatoms and collected computational experience.11,15 – 17

The PCM calculations of the solvent effects on thespin–spin coupling constants of acetylene were carried outusing the Huz-IIIsu3 or Huz-IVsu4 basis sets, constructedfrom van Wullen’s28 modification of Huzinaga’s basis sets29

by decontracting the s orbitals and adding three or fourtight s functions,30 respectively. For the supermolecularcalculations, two types of basis sets were used for thecalculation of the coupling constants: the acetylene moleculeis described using the IGLO Huz-IIsu2, Huz-IIIsu3 or Huz-IVsu4 basis sets, whereas a small 6–31GŁ basis set (or6–31GŁŁ in the case of the H2O complexes) is put on thesolvent molecules. This last scheme allows us to describethe electron density on the nuclei of interest (i.e. those of theacetylene molecule) with sufficient accuracy, keeping the sizeof the full basis set for the complex reasonably small. Theerrors resulting from such approximations are estimatedby comparison with the Huz-IIIsu3 results obtained forthe dimers.

In the PCM calculations, the geometry of acetylene wasin one set of calculations optimized using a first-ordergeometry optimization scheme31 at the DFT/B3LYP level inthe polarizable continuum environment, and in another set ofcalculations the geometry was kept fixed at the experimentalequilibrium values.32 For the supermolecular calculations,the geometry of the complexes was optimized using the MP2

Copyright 2004 John Wiley & Sons, Ltd. Magn. Reson. Chem. 2004; 42: S128–S137

S130 M. Pecul and K. Ruud

frozen core approach and the aug-cc-pVDZ or aug-cc-pVTZbasis sets.33,34 We decided not to use the DFT method forthe geometry optimization of the complexes, since DFT doesnot account for dispersion interactions. The MP2 method is,however, fairly reliable for calculations of the geometry ofweak molecular complexes.

The calculations of the coupling constants and PCMcalculations were carried out using a local version of theDALTON program,35 which has been extended to includethe PCM code for DFT and MCSCF calculations. The MP2geometry optimization of the acetylene complexes wasperformed using the Gaussian 9836 program.

RESULTS AND DISCUSSION

Coupling constants in the isolated acetylenemoleculeThe calculated coupling constants of the isolated acetylenemolecule are given in Table 1, together with theoretical andexperimental literature values. The coupling constants inthe isolated acetylene molecule were calculated using theMCSCF method with large active spaces and extended basissets by Jaszunski and Ruud,22 and we first compare theDFT/B3LYP results with these benchmark theoretical resultsand with experiment.20,23

The DFT/B3LYP method overestimates the one-bondcoupling constants 1J�C,C� and 1J�C,H� by about 10% incomparison with results obtained with the large RASSCFspaces22 and experiment.20,23 In the case of the one-bond couplings, even the use of a small CASSCF spaceleads to better results than those obtained by meansof DFT/B3LYP. For the 2J�C,H� coupling, both methodsyield results of comparable accuracy: the DFT/B3LYPoverestimates the 2J�C,H� coupling slightly, whereas theCASSCF space employed underestimates it. For the 3J�H,H�coupling, the DFT/B3LYP result is closer to the experimentaland theoretical benchmark value than the CASSCF result.Differences between the coupling constants obtained usingthe Huz-IIIsu3 and Huz-IVsu4 basis sets are small.

For the purpose of this study—the modelling of solventeffects—the accuracy obtained using the DFT/B3LYP model

Table 1. Spin–spin coupling constants (Hz) in the isolatedacetylene molecule (rigid MW geometry) calculated by meansof CASSCF and DFT methods used to model solvent effects

Method Basis 1J�C,C� 1J�C,H� 2J�C,H� 3J�H,H�

B3LYP Huz-IIIsu3 204.72 273.68 55.80 10.97B3LYP Huz-IVsu4 205.47 273.95 56.52 11.17CASSCF Huz-IIIsu3 194.13 259.48 50.56 13.29SOPPA(CCSD)a

189.995 254.946 51.727 11.311

RASSCFb 184.68 244.27 53.08 10.80Experimentc 184.52 242.4 53.76 10.11

a Ref. 23.b Ref. 22, RASSCF-4/cc-pCVQZsu2 results.c Gas-phase, extrapolated to zero density20 and corrected forvibrational effects.23

with the Huz-IIIsu3 basis sets suffices. However, the overes-timation of the coupling constants in the isolated acetylenemolecule by the DFT/B3LYP model may potentially lead toa similar overestimation of the solvent-induced changes ofthese coupling constants, which should be taken into accountwhen comparing them with the experimental solvent shifts.

Dielectric medium effects on the couplingconstantsThe solvent-induced shifts of the spin–spin coupling con-stants of acetylene are given in Table 2 and comparedwith previous thereotical values obtained using the spher-ical cavity model and a CASSCF wavefunction2 and withexperiment.2,20 The experimental solvent shifts in Table 2differ slightly from those reported in Ref. 2 since moreprecise measurements of the coupling constants of gaseousacetylene and extrapolation to zero density yielded slightlydifferent values20 than those quoted in Ref. 2. We discuss theeffects on the different coupling constants separately.

1J�C,C�The dielectric medium effects on the 1J�C,C� couplingconstant in acetylene are the largest in terms of absolutevalues and, as demonstrated before,2 change smoothly withthe dielectric constant of the solvent. The reaction fieldmodel using a spherical cavity reproduced the changesqualitatively, but underestimated their magnitude by about60%.2 This hiatus is rectified by the PCM model with amolecule-shaped cavity, as shown in Table 2. For highlypolar solvents such as acetone, acetonitrile and water, thecalculated changes of 1J�C,C�, in particular the CASSCFresults, are in perfect agreement with experiment, whereasthe DFT results are slightly overestimated, as were thecoupling constants for the isolated molecule (see Table 1).For less polar solvents, in particular for cyclohexane andchloroform, where dispersion interactions probably playa more significant role, the PCM results are somewhatoverestimated, although for benzene the PCM solvent shiftagrees very well with experiment.

The effects of geometry relaxation are negligible for thesolvent-induced changes of 1J�C,C�: the entire solvent effectseems to originate from the changes in electronic density ofthe molecule under the influence of the electric field of thesolvent. Solvent shifts calculated using the HuzIII-su3 andHuzIV-su4 basis sets are close to each other, as was the casefor the coupling constants of the free acetylene molecule.

1J�C,H�The solvent-induced changes of the 1J�C,H� coupling con-stant in acetylene obtained using a spherical cavity in adielectric medium have the right sign, but amount to lessthan 10% of the magnitude of the experimental results.2 Alsoin this case, the PCM model is a tremendous improvementon the spherical cavity model,2 and renders both the signand the magnitude of the solvent shifts mostly correct. Incontrast to 1J�C,C�, the effects of geometry relaxation areof paramount importance for the 1J�C,H� coupling constant:including geometry relaxation increases the solvent effect bya factor of two and significantly improves the agreement



Table 2. Comparison of the changes of the coupling constants (Hz) in acetylene calculated by means of PCM/B3LYP method withexperiment and previous reaction field results

This work, PCM/B3LYPPCM/CASSCF Ref. 2 Ref. 20

Coupling Solvent HIII-su3 HIV-su4 HIII-su3a HIII-su3 calc. exp.

1J�C,C� Cyclohexane �4.35 �4.30 �4.28 �3.72 �1.36 �1.2Benzene �4.89 �4.84 �4.81 �4.18 �1.55 �4.2Chloroform �7.95 �7.90 �7.85 �6.80 �2.50 �4.1Acetone �10.43 �10.38 �10.32 �8.92 �3.37 �9.0Acetonitrile �10.80 �10.75 �10.69 �9.24 �3.50 �8.4Water �11.06 �11.02 �10.95 �9.47 �3.59 �9.8b

1J�C,H� Cyclohexane 0.31 0.31 0.79 0.33 0.05 0.5Benzene 0.34 0.35 0.89 0.38 0.06 0.8Chloroform 0.55 0.57 1.43 0.60 0.09 1.3Acetone 0.72 0.75 1.85 0.79 0.11 0.7Acetonitrile 0.74 0.78 1.92 0.81 0.11 1.2Water 0.76 0.79 1.96 0.83 0.11 1.6b

2J�C,H� Cyclohexane 0.18 0.17 0.19 0.27 0.09 �0.4Benzene 0.20 0.19 0.21 0.30 0.10 �0.5Chloroform 0.33 0.31 0.34 0.49 0.16 �0.5Acetone 0.43 0.41 0.45 0.65 0.22 �0.2Acetonitrile 0.45 0.42 0.46 0.67 0.23 �0.2Water 0.46 0.43 0.47 0.69 0.23 �0.4b

3J�H,H� Cyclohexane �0.04 �0.04 0.01 �0.03 �0.01 �0.1Benzene �0.04 �0.05 0.01 �0.04 �0.01 �0.1Chloroform �0.07 �0.08 0.01 �0.06 �0.02 �0.1Acetone �0.10 �0.11 0.02 �0.09 �0.02 0.0Acetonitrile �0.10 �0.11 0.01 �0.09 �0.02 0.0Water �0.10 �0.12 0.01 �0.10 �0.02 0.1b

a Geometry reoptimized for each solvent.b Ref. 2, corrected for the gas-phase value from Ref. 20.

with experiment, the only exception being the case of ace-tone, where the experimental shift is much smaller than in theother solvent with a similar dielectric constant (acetonitrile),and thus is better reproduced when the geometry relaxationis not included. This is probably coincidental and due toeffects other than those arising from the dielectric medium.The CASSCF and B3LYP results are close to each other in thecase of the 1J�C,H� solvent shifts.

2J�C,H�The PCM model, performing very well in the case of theone-bond coupling constants of C2H2 [1J�C,C� and 1J�C,H�],fails completely to reproduce the experimental solvent shiftsof 2J�C,H�: the calculated shifts are in the wrong direction,and neither including the geometry relaxation effects [whichare negligible for 2J�C,H�] nor changing the wavefunctionmodel from B3LYP to CASSCF improves the situation. It ispossible that in the case of 2J�C,H�, effects other than theelectrostatic interactions play a more important role, sincethe experimental solvent shifts of 2J�C,H� do not changesmoothly with the dielectric constant of the solvent. Wenote at this point that for 2J�C,H� in acetylene even thebenchmark theoretical and experimental values are not inperfect agreement.22

3J�H,H�Experimentally measured solvent shifts of 3J�H,H� are small,negative for non-polar solvents and positive for water. Forthe rigid molecule approximation, the calculated solventshift is small, but in the wrong direction in comparisonwith experiment (at both B3LYP and CASSCF computationallevels). When geometry relaxation is included, the calculatedsolvent shift is close to zero, which is consistent withexperiment: the experimentally established shifts are of thesame order as the experimental error, which should be takeninto account when comparing the results.

Supermolecular effects on the coupling constantsChanges in the coupling constants in complexes withwaterThe changes in the acetylene coupling constants causedby the formation of the acetylene–water dimer (globalminimum D1) are reported in Table 3. The column denoted ccshows changes calculated using the counterpoise correctionmethod,37 and the column ncc contains the results obtainedwithout counterpoise correction. Table 3 also contains thegeometry relaxation effects, denoted gr, calculated as thedifference between the coupling constant calculated in theisolated C2H2 molecule with geometric parameters as inthe given complex and the result obtained for the isolatedacetylene molecule with the geometry optimized at the same



computational level. The total change is calculated as thesum of contributions cc and gr.

Molecular complexes studied using supermolecular cal-culations are, of course, large systems, and the calculationsare therefore more time consuming than modeling of sol-vent effects using dielectric continuum models. Therefore, areduction in the basis set size is desirable. For this reason, weused a basis set consisting of the Huz-IIsu2 set on the C2H2

molecule and the 6–31GŁŁ set on the solvent molecules forthe calculations of the largest complexes. Before consideringthe larger complexes, we will discuss some methodologicalissues on the basis of the interaction-induced changes in

Table 3. Changes in the spin–spin coupling constants (Hz) ofacetylene induced by formation of the acetylene–watercomplex D1, obtained by means of DFT/B3LYP with differentbasis sets: cc, counterpoise corrected changes; ncc,non-counterpose corrected changes; gr, geometry relaxationeffects (see text)

Coupling Basis set cc ncc gr Total

1J�C,C� Huz-IVsu4 �8.34 �8.34 0.14 �8.20Huz-IIIsu3 �8.42 �8.41 0.13 �8.28Huz-IIsu2a �9.47 �9.46 0.13 �9.34

1J�C,H��1�b Huz-IVsu4 1.70 1.69 1.63 3.33Huz-IIIsu3 1.72 1.70 1.64 3.36Huz-IIsu2a 2.06 2.01 1.60 3.66

1J�C,H��2�b Huz-IVsu4 1.62 1.62 0.06 1.68Huz-IIIsu3 1.65 1.64 0.06 1.71Huz-IIsu2a 1.80 1.82 0.06 1.87

2J�C,H��1�b Huz-IVsu4 �1.55 �1.55 0.01 �1.55Huz-IIIsu3 �1.56 �1.56 0.00 �1.55Huz-IIsu2a �1.83 �1.81 0.00 �1.83

2J�C,H��2�b Huz-IVsu4 �4.75 �4.75 0.50 �4.24Huz-IIIsu3 �4.78 �4.78 0.51 �4.27Huz-IIsu2a �5.46 �5.48 0.50 �4.97

3J�H,H� Huz-IVsu4 �0.11 �0.11 0.09 �0.02Huz-IIIsu3 �0.10 �0.10 0.09 �0.01Huz-IIsu2a �0.03 �0.05 0.09 0.06

a Huz-IIsu2 basis set on C2H2, 6–31GŁŁ on H2O.b Superscripts�1� and �2� denote couplings of protons closer to thesolvent molecule and further from it, respectively, here and insubsequent tables.

the acetylene coupling constants for the global minimumstructure of the C2H2 –H2O dimer obtained using differentbasis sets.

The changes in the coupling constants of C2H2 inducedby the formation of the C2H2 –H2O dimer D1 calculated usingthe Huz-IIIsu3 and Huz-IVsu4 basis sets are almost identical.Using the smaller basis set with the Huz-IIsu2 set on C2H2

and the 6–31GŁŁ set on H2O gives results which tend to beoverestimated by ca 10–20% compared with the Huz-IVsu4results. This adds to the overestimation caused by the use ofthe DFT/B3LYP method, which means that the interaction-induced changes in the coupling constants calculated usingthe DFT/B3LYP method and the Huz-IIsu2/6–31GŁŁ basisset may be too large by as much as 30%.

The basis set superposition errors (BSSEs), as estimatedusing the counterpoise correction method, are very smallfor all basis sets. As expected, they are more substantial forthe smallest Huz-IIsu2/6–31GŁŁ basis set than for the largerbasis sets, but even for the smaller basis sets they neverexceed 0.05 Hz. The negligible BSSEs probably originatefrom the fact that the coupling constants are very localizedproperties (especially the dominant FC contribution), and thedescription of the electron density in the outer regions doesnot influence them much. All interaction-induced changesin the coupling constants discussed later in this paperwere obtained using the counterpoise correction method,even though the results in Table 3 suggest that this isnot necessary.

The geometry relaxation effects are important in the caseof the interaction-induced changes in the 1J�C,H� couplingconstants, and constitute 10–15% of the interaction-inducedchanges in the 2J�C,H� coupling constants. For the othercouplings, geometry relaxation effects are negligible.

Table 4 contains the changes in the coupling constants inacetylene induced by the formation of dimers D1 and D2 ortrimers T1, T2, T3 and T4. The values for dimer D1 differ fromthose in Table 3 since the geometric parameters of the dimersfor which the coupling constants shown in Table 4 werecalculated were optimized using the aug-cc-pVDZ basis set,for the sake of consistency with the results for the trimers. Thecouplings reported in Table 3 were obtained for a geometryoptimized using the aug-cc-pVTZ basis set. All structures areminima on the potential energy surface for the C2H2 –H2Odimer and the C2H2 –�H2O�2 trimer, respectively.38 The

Table 4. Changes in the spin–spin coupling constants (Hz) of acetylene induced by formation of theacetylene-water complexes, calculated by means of DFT/B3LYP

Basis set 1J�C,C� 1J�C,H��1� 1J�C,H��2� 2J�C,H��1� 2J�C,H��2� 3J�H,H�

Huz-IIIsu3 D1 �8.76 2.00 �4.69 1.69 �1.69 �0.08Huz-IIIsu3 D2 �5.07 2.18 2.18 �0.03 �0.03 0.04Huz-IIsu2a D1 �9.79 3.45 �5.62 1.93 �2.01 0.02Huz-IIsu2a D2 �4.82 2.16 2.16 �0.05 �0.05 0.08Huz-IIsu2a T1 �17.78 6.60 �4.54 2.28 �3.06 0.00Huz-IIsu2a T2 �8.67 3.14 �2.64 1.39 �1.43 0.09Huz-IIsu2a T3 �18.42 �1.98 �1.98 �0.10 �0.10 0.05Huz-IIsu2a T4 �9.18 3.95 3.95 �0.06 �0.06 0.16

a Huz-IIsu2 basis set on C2H2, 6–31GŁŁ on H2O.



H1H2 C2 C1

2.173 Å

D1

H1H2 C2 C1

2.385 Å

D2

H1H2 C2 C1

2.362 Å

2.206 Å

T1

H1H2 C2 C1

2.215 Å

T3

2.403 Å

T4

H1H2 C2 C1

2.262 Å

2.696 Å

T2

Figure 1. Structures of the acetylene–water complexes.

structures of the acetylene–water complexes are shown inFig. 1. The energetics of the complexes have been discussedelsewhere.38

1J�C,C� is the coupling which is the most affected by thecomplexation, especially for the structures with a C—HÐ Ð ÐOhydrogen bond-like interaction (D1, T1, T3). In the trimer T2,the effect may be weakened by the fact that the oxygen atomdonates a second lone pair to the second water molecule,unlike in the trimer T1. The changes in 1J�C,C� are smallerfor the T-shaped complexes with an acidic proton of thewater molecule interacting with the carbon–carbon triplebond (D2 and T4) than with C—HÐ Ð ÐO interactions. The signand approximate magnitude of the changes of 1J�C,C� areconsistent with experiment (see Table 2).

Formation of the C—HÐ Ð ÐO hydrogen bond increases the1J�C,H� coupling of the proton engaged in the interaction[1J�C,H��1� in Table 4], but decreases, and to a larger extent,the 1J�C,H� coupling of the other proton [1J�C,H��2� incomplexes D1, T1, T2]. This explains the negative shift of1J�C,H� in the trimer T3. The proximity of the water proton tothe carbon–carbon triple bond gives a positive shift of severalhertz in 1J�C,H�. The net effect in solution would thereforebe positive, which again is consistent with experiment.

The 2J�C,H� coupling of C2H2 changes in a manner similarto 1J�C,H�: the shift in the coupling of the proton-forminghydrogen bond C—HÐ Ð ÐO is positive, whereas the couplingof the other proton shifts in the opposite direction. Theformation of a T-shaped complex D2 hardly affects 2J�C,H�.Judging from the results for the dimers, the net shift in 2J�C,H�in solution should be close to zero. However, in trimerT1 (the global minimum38), the negative shift in 2J�C,H� is

substantially larger than the positive one, which may accountfor the experimentally observed negative effect. This is theonly case where the supermolecular method reproduces theexperimental effect, whereas the PCM method does not.

The changes in 3J�H,H� are close to zero, in accordancewith the experimental findings. This applies to all complexesin this paper, so 3J�H,H� will not be discussed further.

Trimers T3 and T4 can be considered to be built fromdimers D1 and D2, respectively. An analysis of the datain Table 3 leads to the conclusion that the changes in thecoupling constants of acetylene caused by formation of thetrimers can be predicted using the changes in the couplingconstants in the respective dimers: the complexation effectson the coupling constants seem to be nearly additive.

Changes of the coupling constants in complexes withacetoneTable 5 collects the changes in the coupling constants ofacetylene induced by the formation of the complexes shownin Fig. 2: dimer D1 and trimer T with a hydrogen bond-likeinteraction C—HÐ Ð ÐO, and the ‘stacked’ dimer D2. Thesestructures are stationary points on the potential energysurface, but not minima (negative vibrational frequencies).

The differences between the results obtained with differ-ent basis sets are smaller than for the acetylene–water com-plexes, but using a smaller basis set leads also in this case tooverestimation of the changes. Like for the acetylene–watercomplex, the basis set superposition errors are small.

The changes in the coupling constants in the acety-lene–acetone dimer D1 are similar to the analogous acety-lene–water dimer D1. However, they are larger than in thewater dimer D1, which is opposite to the experimental obser-vation. The relative (although not absolute) magnitude of thechanges in the couplings of acetylene in water and acetone isrecovered only when comparing the effects in the analogoustrimers T (Table 5) and T3 (Table 4). The changes in the acety-lene couplings in the dimer D2 are basically similar to thoseof the dimer D1, probably because the proton in acetylene isin the proximity of the carbonyl oxygen atom of acetone inboth structures. The calculated changes in 1J�C,C� have mag-nitude and sign consistent with experiment when allowingfor the overestimation of the couplings due to the B3LYP

H1H2 C2 C1

2.127 Å

D1

H2H1 C2C1

2.543 Å

D2

H1H2 C2 C1

2.169 Å

T1

Figure 2. Structures of the acetylene–acetone complexes.



Table 5. Changes in the spin–spin coupling constants (Hz) of acetylene induced by formation of theacetylene–acetone complexes, calculated by means of DFT/B3LYP


Huz-IIIsu3 D1 �9.26 4.53 �5.80 2.07 �1.86 �0.05Huz-IIIsu3 D2 �6.23 5.57 �2.43 1.17 �0.96 0.11Huz-IIsu2a D1 �9.46 4.71 �5.90 2.09 �1.97 0.06Huz-IIsu2a D2 �6.25 5.94 �2.44 1.22 �0.96 0.20Huz-IIsu2a T �16.81 �0.48 �0.48 0.16 0.16 0.16

a Huz-IIsu2 basis set on C2H2, 6–31GŁ on �CH3�2CO.

functional and the use of a small basis set. For 1J�C,H�, thenet positive shift is recovered only in dimer D2. None of thecalculated structures recover the experimental net negativeshift of 2J�C,H�, but this is probably because the configurationspace of the trimer has not been sufficiently probed.

Changes of the coupling constants in complexes withacetonitrileThe changes in the coupling constants of acetylene causedby formation of the complexes with acetonitrile are shownin Table 6, and Fig. 3 presents the structures. The dimerstructures obtained are basically similar to the complexeswith acetone (see above): D1 with a linear hydrogen bond-like C—HÐ Ð ÐN interaction and a ‘stacked’ D2 structure.However, unlike the acetylene–acetone complexes, allacetylene–acetonitrile structures are minima.

The changes in the coupling constants of the acety-lene–acetonitrile complexes are almost the same as for theanalogous acetylene–acetone complexes (see above). Thechange in 1J�C,C� is larger in the dimer D1 with acetonitrilethan in the corresponding complex with acetone, which isopposite to the observed experimental solvent shifts (seeTable 2). In the case of the ‘stacked’ dimer D2, the relativemagnitude of the changes is the same as in experiment. Asfor the acetone complexes, the net changes in 1J�C,H� arenegative for the linear dimer D1 and trimer T and positivefor the ‘stacked’ dimer D2. This might be an indication thatthe latter arrangement is on average favored in both solu-tions, although the structural space probed here is certainlytoo small to allow any definite conclusions to be drawn. Thesmall negative solvent shift in 2J�C,H� is not reproduced byany of the acetylene–acetonitrile complexes studied here. Inthe linear �CH3CN�2 –C2H2 trimer (see Fig. 3), the changesin the coupling constants can be extrapolated from thosein the linear CH3CN–C2H2 dimer: the contributions arenearly additive.

As was the case for the complexes with water and acetone,geometry relaxation effects are small for 1J�C,C� and 3J�H,H�.However, they need to be taken into account for the 2J�C,H�couplings and in particular for the 1J�C,H� couplings. Thedifferences between the changes in the acetylene couplingscalculated with the smaller HuzII-su2/6–31GŁ set and thelarger HuzIII-su3 basis set are small and, similarly to theother complexes, the use of the smaller basis set leads tooverestimated interaction-induced changes.

Changes of the coupling constants in complexes withbenzeneThe interaction-induced changes in the spin–spin couplingconstants were calculated for three acetylene–benzenecomplexes: dimer D1 with C6v symmetry with the acetylenemolecule on the main axis of the benzene molecule, (as foundpreviously39), dimer D2 with C2v symmetry and trimer Twith D6h symmetry. The optimized structures are shown inFig. 4, and the calculated changes in the spin–spin couplingconstants are presented in Table 7.

When compared with experiment, the interaction-induced change in 1J�C,C� in dimer D1 has the correct sign,but its magnitude is somewhat overestimated (and evenmore so in the trimer), which probably is due to the system-atic errors inherent in the computational methods used. Inthe dimer D2, on the other hand, the change is negligible.D1 and D2 represent, in a sense, boundary structures whichmay occur in solution, so an averaging would probably yieldresults consistent with experiment. This is also the case for1J�C,H�, although in this case it is dimer D2 for which thecoupling is overestimated when compared with experiment,whereas it is underestimated for dimer D1.

The supermolecular results for the solvent shifts of2J�C,H� are inconclusive. The 2J�C,H� coupling of theproton close to the benzene ring in the D1 dimer hasa negative solvent shift, which may support the notion

Table 6. Changes in the spin–spin coupling constants (Hz) of acetylene induced by formation of theacetylene–acetonitrile complexes, calculated by means of DFT/B3LYP


Huz-IIIsu3 D1 �9.59 4.50 �5.79 2.07 �1.97 �0.03Huz-IIIsu3 D2 �5.86 5.50 �2.54 1.06 �0.97 0.05Huz-IIsu2a D1 �9.86 4.70 �6.01 2.10 �2.10 0.06Huz-IIsu2a D2 �5.87 5.78 �2.55 1.08 �0.99 0.12Huz-IIsu2a T �17.25 �0.62 �0.62 0.08 0.08 0.14

a Huz-IIsu2 basis set on C2H2, 6–31GŁ on CH3CN.



H1H2 C2 C1

2.253 Å

D1

2.769 Å

H1H2 C2 C1

D2

H1H2 C2 C1

2.302 Å

T1

Figure 3. Structures of the acetylene–acetonitrile complexes.

Table 7. Changes in the spin–spin coupling constants (Hz) of acetylene induced by formation of the acetylene–benzenecomplexes, calculated by means of DFT/B3LYP


Huz-IIIsu3 D1 �6.20 4.21 �3.84 1.45 �1.28 0.03Huz-IIsu2a D1 �7.02 4.79 �4.32 1.71 �1.36 0.13Huz-IIsu2a D2 �0.24 1.19 1.19 �0.17 �0.17 0.18Huz-IIsu2a T1 �13.13 0.62 0.62 0.33 0.33 0.28

a Huz-IIsu2 basis set on C2H2, 6–31GŁ on C6H6.

H1H2 C2 C1

2.281 Å

D1

H1

H2

C2

C1 2.730 Å

D2

H1H2 C2 C1

2.285 Å

T1

Figure 4. Structures of the acetylene–benzene complexes.

that it is the influence of the ring currents which causesthis experimentally established sign of the solvent shift.However, it should be noted that the interaction-inducedshift on the other 2J�C,H� coupling in the D1 structure islarger, and positive, so the averaged effect would be positive.The interaction-induced shift on 2J�C,H� is also positive inthe trimer T1. In the flat structure D2, 2J�C,H� has negativeshift, consistent with experiment.

The interaction-induced changes in 3J�H,H� are positivefor all structures, which apparently is inconsistent withexperiment ��0.1 Hz�. This is not necessarily the case,however, since both the experimental and theoretical valuesare burdened with errors: the experimental shift is of theorder of the experimental error and basis set incompletenesseffects are significant for this coupling, leading to an

overestimation of the shift, as the comparison of theHuz-IIIsu3 and Huz-IIsu2/6–31GŁ results indicate. Forthe shifts in the other couplings, the relative differencesbetween the Huz-IIIsu3 and the Huz-IIsu2/6–31GŁ resultsare much smaller.

The basis set superposition errors for the changes inthe coupling constants of acetylene are small also for thecomplexes with benzene and the geometry relaxation effectsare significant for the 1J�C,H� coupling constants only: infact, for 1J�C,H� in the trimer, the geometry relaxation effectdetermines the total complexation-induced change of thecoupling. As for the other complexes under study, theinteraction-induced shifts in the trimer T1 ‘composed’ of thetwo dimers D1 can be approximately extrapolated from theshifts in the dimer, with the exception of the 2J�C,H� coupling.

CONCLUSION

The solvent shifts in the spin–spin coupling constantsof acetylene were calculated using the PCM for solventsranging in polarity from cyclohexane to water, and comparedwith available experimental data and previous resultsobtained using a spherical cavity.2 Spin–spin couplingconstants were also calculated for complexes of acetylenewith water, acetonitrile, acetone and benzene, in order tocheck the performance of the supermolecular method. TheDFT/B3LYP method was used in both sets of calculations. Inthe case of the PCM method, CASSCF calculations were alsocarried out. The main findings can be summarized as follows.

For both one-bond coupling constants, 1J�C,C� and1J�C,H�, the PCM model is a tremendous improvement onthe spherical cavity model2 and gives both the sign and



magnitude of the solvent shifts in almost perfect agreementwith experiment, especially for highly polar solvents. For lesspolar solvents, in particular for cyclohexane and benzene,where dispersion interactions and, in the case of benzene,the influence of ring currents may play may a moresignificant role, the PCM results are slightly further awayfrom experiment, although the agreement is still good. ThePCM model fails completely to reproduce the experimentalsolvent shifts of 2J�C,H�: the calculated shifts are in thewrong direction. This may indicate that for this couplingspecific interactions are more important than electrostaticinteractions. However, this failure does not seem to be amajor hiatus of the PCM model, since the solvent shiftsof 2J�C,H� are small and not likely to be of much interest.Experimental solvent shifts for 3J�H,H� are close to zero, andthis is correctly reproduced by the PCM model.

In the case of the supermolecular method, we are limitedby the higher cost of the calculations, so only a few structureshave been studied for each solvent, including only one or twosolvent molecules. The sign and approximate magnitude ofthe changes in 1J�C,C� calculated in this way are consistentwith experiment, although the size of the changes seems tobe overestimated in most cases. The changes in the 1J�C,H�coupling can be in both directions depending on the positionof the solvent molecule with respect to the coupled protonand, in the case of complexes with acetone and acetonitrile,the experimental net positive shift is reproduced only forthe ‘stacked’ dimers, whereas for the benzene complexes thecalculated change in 1J�C,H� seems to agree with experimentfor all complexes. Changes in both directions are alsoobserved for 2J�C,H�, and while the calculated net effectis in the same direction as the experimental shift for thecomplexes with water and benzene, this is not the case forthe complexes with acetone and acetonitrile. The changesin 3J�H,H� calculated using the supermolecular method areclose to zero, in agreement with experiment.

Individual contributions to the spin–spin couplingconstants of acetylene have not been discussed here. Weonly note that, as previously observed,40,41 for the one-bond and geminal coupling constants, the changes in theFC terms determine the total effect in both the PCM andthe supermolecular calculations, whereas for the vicinalcoupling 3J�H,H�, the interplay between the spin–orbitterms PSO and DSO determines the total (practicallynegligible) shift.

Geometry relaxation effects are important in the caseof the interaction-induced changes in the 1J�C,H� couplingconstants, and they are typically about 10–15% of thetotal interaction-induced changes in the 2J�C,H� couplingconstants (in the supermolecular calculations). For the othercouplings, geometry relaxation effects are negligible.

The DFT/B3LYP method overestimates the one-bondcoupling constants 1J�C,C� and 1J�C,H� by about 10% incomparison with benchmark theoretical results and withexperiment. Inadequacies of the basis set used for the largercomplexes tend to produce errors in the same direction,which to some extent accounts for the overestimation of thechanges in the couplings in the supermolecular calculations.The basis set superposition errors, as estimated using the

counterpoise correction method,37 are very small for allbasis sets.

We have demonstrated the very good performance ofthe PCM model for the calculations of solvent shifts in theacetylene spin–spin coupling constants, particularly for thecouplings which change significantly upon solvation. Thesupermolecular method requires much more computationaleffort, but may be helpful in cases when specific interactionsplay a more significant role, and it facilitates physicalinterpretation of the shifts.

AcknowledgmentsThis work was supported by the Norwegian Research Councilthrough a Strategic University Program in Quantum Chemistry(Grant No. 154011/420) and through a grant of computer time fromthe Supercomputing Programme.

REFERENCES1. Mikkelsen KV, Ruud K, Helgaker T. J. Comput. Chem. 1999; 20:

1281.2. Pecul M, Sadlej J. Chem. Phys. 1998; 234: 111.3. Pecul M, Sadlej J. Chem. Phys. 2000; 255: 137.4. Pecul M, Sadlej J. Chem. Phys. Lett. 1999; 308: 486.5. Jameson CJ, de Dios AD. In Nuclear Magnetic Shieldings and

Molecular Structure, Tossell JA (ed). Kluwer: Dordrecht, 1993;95–116.

6. Cossi M, Crescenzi O. J. Chem. Phys. 2003; 118: 8863.7. Mennucci B, Martinez JM, Tomasi J. J. Phys. Chem. A 2001; 105:

7287.8. Barfield M, Johnston MD Jr. Chem. Rev. 1973; 73: 53.9. Ando I, Webb GA. Org. Magn. Reson. 1981; 15: 111.

10. Astrand P-O, Mikkelsen KV, Jørgensen P, Ruud K, Helgaker T.J. Chem. Phys. 1998; 108: 2528.

11. Ruud K, Frediani L, Cammi R, Mennucci B. Int. J. Mol. Sci. 2003;4: 119.

12. Ramsey NF. Phys. Rev. 1953; 91: 303.13. Barszczewicz A, Helgaker T, Jaszunski M, Jørgensen P, Ruud K.

J. Magn. Reson. A 1995; 114: 212.14. Jaszunski M, Helgaker T, Ruud K. Magn. Reson. Chem. 1996; 34:

646.15. Miertus S, Scrocco E, Tomasi J. Chem. Phys. 1981; 55: 117.16. Tomasi J, Cammi R. J. Comput. Chem. 1995; 16: 1449.17. Mennucci B, Cances E, Tomasi J. J. Phys. Chem. B 1997; 101:

10 506.18. Cammi R, Frediani L, Mennucci B, Tomasi J, Ruud K,

Mikkelsen KV. J. Chem. Phys. 2002; 117: 13.19. Cammi R, Frediani L, Mennucci B, Ruud K. J. Chem. Phys. 2003;

119: 5818.20. Jackowski K, Wilczek M, Pecul M, Sadlej J. J. Phys. Chem. A 2000;

104: 5955.21. Pecul M, Sadlej J. Chem. Phys. 1999; 248: 27.22. Jaszunski M, Ruud K. Chem. Phys. Lett. 2001; 336: 473.23. Wigglesworth RD, Raynes WT, Kirpekar S, Oddershede J,

Sauer SPA. J. Chem. Phys. 2000; 112: 3735.24. Helgaker T, Jaszunski M, Ruud K. Chem. Rev. 1999; 99: 293.25. Helgaker T, Watson M, Handy NC. J. Chem. Phys. 2000; 113: 9402.26. Becke AD. J. Chem. Phys. 1993; 98: 5648.27. Lantto P, Vaara J, Helgaker T. J. Chem. Phys. 2002; 117: 5998.28. van Wullen C. PhD Thesis, Ruhr-Universitat Bochum, 1992.29. Huzinaga S. Approximate Atomic Functions. Technical Report,

University of Alberta, Edmonton; 1971.30. Helgaker T, Jaszunski M, Ruud K, Gorska A. Theor. Chem. Acc.

1998; 99: 175.31. Frediani L, Cammi R, Pomelli CS, Tomasi J, Ruud K. J. Comput.

Chem. 2004; 25: 375.32. Landolt-Bornstein, Zahlenwerte und Funktionen, Band 2. Springer:

Berlin, 1976; Chapt. 7.33. Dunning TH. J. Chem. Phys. 1989; 90: 1007.



34. Kendall RA, Dunning TH, Harrison RJ. J. Chem. Phys. 1992; 96:6796.

35. Helgaker T, Jensen HJA, Jørgensen P, Olsen J, Ruud K, Agren H,Auer AA, Bak KL, Bakken V, Christiansen O, Coriani S, Dahle P,Dalskov EK, Enevoldsen T, Fernandez B, Hattig C, Hald K,Halkier A, Heiberg H, Hettema H, Jonsson D, Kirpekar S,Kobayashi R, Koch H, Mikkelsen KV, Norman P, Packer MJ,Pedersen TB, Ruden TA, Sanchez A, Saue T, Sauer SPA,Schimmelpfenning B, Sylvester-Hvid KO, Taylor PR, Vahtras O.Dalton, an ab initio electronic structure program, Release 1.2, 2001;http://www.kjemi.uio.no/software/dalton/dalton.html.

36. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA,Cheeseman JR, Zakrzewski VG, Montgomery JA, Stratmann RE,Burant JC, Dapprich S, Millam JM, Daniels AD, Kudin KN,Strain MC, Farkas O, Tomasi J, Barone V, Cossi M, Cammi R,Mennucci B, Pomelli C, Adamo C, Clifford S, Ochterski J,

Petersson GA, Ayala PY, Cui Q, Morokuma K, Malick DK,Rabuck AD, Raghavachari K, Foresman JB, Cioslowski J,Ortiz JV, Stefanov BB, Liu G, Liashenko A, Piskorz P,Komaromi I, Gomperts R, Martin RL, Fox DJ, Keith T,Al-Laham MA, Peng CY, Nanayakkara AA, Gonzalez C,Challacombe M, Gill PMW, Johnson BG, Chen W, Wong MW,Andres JL, Head-Gordon M, Replogle ES, Pople JA. Gaussian 98,Revision A.1. Gaussian: Pittsburgh, PA, 1998.

37. Boys SF, Bernardi F. Mol. Phys. 1970; 19: 553.38. Tzeli D, Mavridis A, Xantheas SS. J. Phys. Chem. A 2002; 106:

11 327.39. Sundararajan K, Viswanathan KS, Kulkarni AD, Gadre SR.

J. Mol. Struct. 2002; 613: 209.40. Pecul M, Leszczynski J, Sadlej J. J. Chem. Phys. 2000; 112: 7930.41. Pecul M, Leszczynski J, Sadlej J. J. Phys. Chem. A 2000; 104: 8105.


solvent effects on the spin–spin coupling constants of acetylene revisited: supermolecular and...

Documents