the nuclear spin–spin coupling constants in the water dimer

30 July 1999

Ž .Chemical Physics Letters 308 1999 486–494www.elsevier.nlrlocatercplett

The nuclear spin–spin coupling constants in the water dimer

Magdalena Pecul, Joanna Sadlej )

Department of Chemistry, UniÕersity of Warsaw, Pasteura 1, 02-093 Warsaw, Poland

Received 30 March 1999; in final form 7 June 1999

Abstract

The nuclear spin–spin coupling constants have been calculated for the water dimer, as well as for the water monomer and< Ž . <dimer surrounded by the dielectric medium. The change due to condensation has been estimated at ;12 Hz for J O–H

< Ž . <and ;0.4 Hz for J H–H . The performance of different basis sets and electron correlation effects, as estimated by theŽ .MCSCF wavefunctions, have been investigated. The latter are particularly important for J H–H . The calculated changes in

Ž . Ž .both J O–H and J H–H coupling constants are dominated by the Fermi contact and paramagnetic spin–orbital terms.q 1999 Elsevier Science B.V. All rights reserved.

1. Introduction

The water dimer, in addition to its importance inchemistry, is one of the simplest examples of sys-tems with a weak O–H PPP O hydrogen bond. There-fore, it has been the subject of numerous theoreticalstudies, focused on determining the equilibrium ge-

Ž w xometry and the interaction energy see Refs. 1,2 for.the latest results . The molecular properties, includ-

ing the NMR shielding constants, have also beenw xcalculated 3,4 for this system. The nuclear spin–spin

coupling constants, although recently thoroughly in-w xvestigated theoretically for the water monomer 5–9 ,

Žtogether with the calculations of nuclear motionw x.effects 6 have not been calculated for the dimer.

Moreover, there is no theoretical work estimating the

) Corresponding author. Fax: q48 22 822 59 96; e-mail:[email protected]

influence of a molecular environment on the spin–spin coupling constants in water by any other method,although much effort has been dedicated to the in-vestigation of intermolecular effects on the water

w xshielding constants 10–12 . It is tempting then tocalculate the nuclear spin–spin coupling constants inthe water dimer, in particular 1J in the protonOH

donor molecule, the potentially excellent parameterof the O–H PPP O hydrogen bond.

Solvation effects on the nuclear spin–spin cou-pling constants: 1J and 2J in liquid water areOH HH

estimated here at three levels. Firstly, we discuss thechange in the spin–spin coupling constants in waterdue to dimer formation. This part focuses on themethodological aspects of the calculations: the choiceof the basis set, electron correlation effects, and therelative importance of the individual contributions tothe coupling constants. Secondly, the calculations arecarried out for a single water molecule embedded ina dielectric medium, an approach found useful forestimating solvent effects on the spin–spin coupling

0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0009-2614 99 00633-8

( )M. Pecul, J. SadlejrChemical Physics Letters 308 1999 486–494 487

w xconstants 13,14 . Finally, supermolecular and reac-tion field methods are employed simultaneously andcalculations are carried out for the water dimer em-bedded in a dielectric medium.

2. Computational details

The SCF method is quite useful in calculations ofthe energy and other properties of the water dimer.The proper evaluation of the spin–spin couplingconstants normally requires, however, a post-SCFtreatment. Electron correlation effects are investi-gated in this Letter using linear responce MCSCF

Ž w x w x .methods see Ref. 15 and 16 for review , imple-w xmented in the DALTON program system 17 . The

CASSCF and RASSCF wavefunctions employed areŽlisted in Tables 1 and 2. In the notation n1rn2r

.n3rn4 numbers in parentheses represent numbersŽof orbitals in, respectively, inactive space 1s orbitals

. Ž .of O in all MCSCF spaces , RAS1 space empty ,ŽRAS2 space, and RAS3 space empty for CASSCF

.wavefunctions . A notation ne indicates the maxi-mum number of electrons in RAS3 space. The activespaces have been chosen on the basis of MP2 orbitaloccupation numbers, with the exception of CAS2,where the last active orbital is an unoccupied orbital

Table 1Ž .The nuclear spin–spin coupling constants Hz in the water

monomer1 2Method Ref. J JOH HH

SCFrHIIIa this Letter y94.54 y21.18Ž .CAS 1r0r6r0 rHIIIa this Letter y83.15 y12.15Ž .CAS 1r0r7r0 rHIIIa this Letter y82.38 y11.71

aŽ .RAS1 2r0r8r6 2 erHIIIa this Letter y83.70 y12.65aŽ .RAS2 2r0r8r6 4erHIIIa this Letter y82.44 y11.75aŽ .RAS3 2r0r8r8 2 erHIIIa this Letter y83.88 y12.87

abŽ .RAS4 2r0r8r14 2 erHIIIa this Letter y77.12 y12.60Ž .CAS 1r0r14r0 rHIIIa this Letter y75.25 y9.29Ž . w xCAS 1r0r14r0 r 5 y77.23 y9.01

cc-pV5Z-su-0c w xSOPPA-CCSD 6 y77.22 y8.03

w xEOM-CCSD 7 y74.9 y10.81w xMP2 8 y74.73 y18.33

a Two water molecules separated by 1000 aub No SD term calculated.c The vibrationally averaged results.

of a lone pair of the proton acceptor. In CAS1 thisorbital is not active.

The basis sets employed are of small and mediumsize, selected with the intention of use for calcula-tions of intermolecular effects in larger systems. Thechoice of the basis sets has been influenced by twofactors: the need for a good description of coreorbitals in the spin–spin coupling constants calcula-

w xtions 5 and the requirement for a presence ofdiffuse orbitals in the calculation of the intermolecu-lar interaction energy. For our study we have chosenthus two types of basis sets: modifications of Huzi-

w xnaga’s basis sets 18 , giving good results for thespin–spin coupling constants in isolated moleculesw x5,16 , and modified standard correlation-consistentbasis sets. In the notation used throughout this work

Ž .HIII is the IGLO C:7s6p2d, H:4s2p modificationw x w x Ž19 of Huzinaga’s basis set 18 . HIIIa in which

.most of the calculations have been carried out isHIII with diffuse functions added: 1s, 1p, 1d on O,1s, 1p on H, following the pattern employed in Ref.w x20 . cc-pVDZ-su-n and aug-cc-pVDZ-su-n designateDunning’s basis sets with decontracted s orbitals andn tight s functions added, with the exponents form-

w xing a geometric progression 5 .The full Boys and Bernardi counterpoise correc-

w xtion 21 has been used for estimating the basis setŽ .superposition error BSSE for the spin–spin cou-

pling constants. In the case of the RASSCF methodŽ .which is non-size-consistent the counterpoise cor-rection could not be used and the coupling constantsin an isolated H O molecule have been obtained by2

calculations on the two H O molecules separated by2

1000 au.w xThe reaction field method 13 as implemented in

w xRef. 17 has been employed for the estimation ofbulk solvent effects on the spin–spin coupling con-stants in water. The radius of a spherical cavity hasbeen taken as a sum of the van der Waals radius ofhydrogen and a distance of the most external hydro-

Žgen from the molecular centre of mass coinciding.with the centre of cavity . This procedure has re-

sulted in cavity radius equal 3.94 au for the watermonomer and 6.31 au for the dimer. The order of themultipole expansion is 10 and the dielectric constantof water is 78.54.

For the water monomer vibrationally averagedw xgeometrical parameters suggested in Ref. 22 have

( )M. Pecul, J. SadlejrChemical Physics Letters 308 1999 486–494488

Table 2Ž .The changes in the nuclear spin–spin coupling constants Hz in the water dimer calculated in HIIIa basis – electron correlation effects

1 1 1 2 1Ž . Ž . Ž . Ž . Ž .Active space J O2–H5 J O2–H6 J O1–H3 J H5–H6 J H3–H3a

Ž .SCF 10r0r0r0 y6.26 y0.93 y3.35 0.55 0.03a Ž .SCF 10r0r0r0 y6.37 y0.86 y3.34 0.48 y0.13

Ž .CAS1 2r0r12r0 y15.53 y3.04 y1.66 y4.93 0.19Ž .CAS2 2r0r13r0 y5.00 y0.84 y2.22 y0.29 y0.17

a Ž .CAS2 2r0r13r0 y5.13 y0.80 y2.20 y0.36 y0.32b Ž .RAS1 2r0r8r6 2 e y4.47 y0.71 y2.38 y0.14 y0.14

Ž .RAS2 2r0r8r6 4e y4.24 y0.69 y2.29 y0.21 y0.16Ž .RAS3 2r0r8r8 2 e y4.69 y0.70 y2.40 y0.07 y0.18

b Ž .RAS4 2r0r8r14 2 e y4.89 y0.79 y2.60 0.00 y0.14a The counterpoise-corrected results.b No SD term calculated.

been used. Experimental intermolecular geometricalw xparameters of the dimer are taken from Ref. 23 .

Ž .The H O structure with the numeration of atoms2 2

employed throughout this work is presented in Fig.1.

3. Results

3.1. The water monomer

Before any description of the changes in thespin–spin coupling constants caused by intermolecu-lar interactions the parameters in the isolated watermolecule are reported. The calculated nuclear spin–spin coupling constants in the water monomer arepresented in Table 1. The changes of the couplingconstants presented in the further parts of this Letterare given with respect to these values, unless statedotherwise.

Our results, in particular 2J , are in slightlyHHŽ .worse agreement with experiment see below than

Fig. 1. The numeration of atoms in the water dimer.

the best ab initio calculations. We attribute thisdiscrepancy to electron correlation effects, as the

Ž . Žcalculation in a larger CAS 1r0r14r0 much too.large, however, to employ for the dimer improves

considerably the agreement with experiment.The recent measurements of 1J in non-polarOH

w xsolvents gave y78.70 Hz 24 when the solvent wascyclohexane-d and y80.62 Hz for water in ni-12

w x 1tromethane-d 25 . J in gaseous water was esti-3 OHw xmated at y79 Hz 26 . The experimental estimation

1 w xof J in liquid water is y89.8 Hz 27 , althoughOH

there are some controversies concerning this valuew x28 . From these data we can estimate the gas-to-liquid shift in 1J at y10 Hz. The measurements ofOH2 w xJ in nitromethane-d 25 give a value of y7.342HH 3

Hz. We are not aware of any paper reporting 2J inHH

liquid water.

3.2. The water dimer

3.2.1. General considerationsThe changes of the nuclear spin–spin coupling

constants due to a formation of the water dimer,calculated in SCF and different MCSCF approaches,are presented in Table 2. First, we discuss the effectscaused by the formation of hydrogen bonding on thenuclear spin–spin coupling constants. Our discussionhere we will base on the RAS4 results, the most

Ž .reliable ones see Section 3.2.2 .The formation of the hydrogen bond influences

Ž . Žmost strongly the J O2–H5 coupling constant in-.volving the proton engaged in the H-bond . The

Ž .change of J O1–H3 in the proton acceptor molecule


Žfrom y77.12 Hz in monomer to y79.72 Hz in.dimer is considerable, too, and of the same sign.

Ž .The change of J O2–H6 is much smaller, but also1 Žnegative. It seems then that J should increase asOH

.far as the absolute value is concerned by severalhertz when going from an isolated molecule to abulk liquid, where each molecule acts at the sametime as proton donor and proton acceptor. Thisestimation is consistent with most experimental data,although the rigorous experimental gas-to-liquid shiftof 1J in water has not yet been reported. TheOH

Ž . Ž .changes of J H5H6 and J H3H3a depend stronglyon the method of calculation but on the whole thehydrogen-bond formation appears to increase slightlythe absolute value of 2J .HH

The intermolecular spin–spin coupling constantsŽin the water dimer i.e., involving nuclei belonging

.to the different monomers are summarised in TableŽ .3. J O1–H5 is, according to our results, positive

Ž .and equal ;4 Hz. The difference in J O1–H6 andŽ .J O2–H3 values can be attributed to the difference

Ž .in dihedral angles: O1H5O2H6 1808 andŽ . Ž .O2H5O1H3 57.28 . The intermolecular J O1–O2

coupling constant is equal ;1 Hz but its value isvery sensitive to the electron correlation effects.Ž . Ž .J H3–H6 is -0.5 Hz and J H3–H6 is negligible.

Ž .It seems from our results that J O1–H5 is largeenough to be interesting from the experimental pointof view. The measurement of it in liquid water is notpossible, but the solid state experiment is probablyworth undertaking.

3.2.2. Electron correlation effectsIn this section we discuss electron correlation

effects on the changes of the coupling constants in

water due to the dimer formation, calculated in theŽ .HIIIa basis set Table 2 . The changes in the water

coupling constants upon the formation of the dimercalculated at the SCF level have the right sign in thecase of 1J , but they are, like the coupling con-OH

stants themselves, overestimated when comparedwith the MCSCF results. This overestimation is dif-ferent for 1J in the acceptor and donor molecule,OH

so a simple scaling does not seem practical. Thechanges of the 2J coupling constants has differentHH

sign and magnitude when calculated by SCF andcorrelated methods.

The changes of the coupling constants calculatedŽwith CAS1 active space lacking the unoccupied

.orbital of the proton acceptor lone pair differ veryconsiderably from the results obtained with CAS2and RAS methods. The discrepancies are even largerthan in the case of SCF results. This indicates thatthe incorporation of the unoccupied orbital of theproton acceptor in an active space is crucial for aproper description of hydrogen bonds.

The results obtained with all RAS spaces aresimilar. The inclusion of deeper than double excita-

Ž .tions extension of RAS1 to RAS2 lowers slightlythe calculated changes in the case of 1J couplingOH

constants and increases them in the case of 2JHH

coupling constants. The addition of more virtualŽ .orbitals extension of RAS1 to RAS4 modifies the

changes of 1J and 2J in the opposite directionOH HH

than the extension of RAS1 to RAS2. The errorsshould then partially cancel and the RAS1 resultsshould give quite a reliable estimation of the changesin the coupling constants. On this basis, for testcalculations with basis sets other than HIIIa, we haveemployed the SCF and RAS1 methods

Table 3Ž .The intermolecular spin–spin coupling constants Hz in the water dimer calculated in HIIIa basis

Ž . Ž . Ž . Ž . Ž . Ž .Active space J O1–O2 J O1–H5 J O1–H6 J O2–H3 J H3–H5 J H3–H6

Ž .SCF 10r0r0r0 1.8771 6.6856 0.7732 0.3238 0.5674 y0.0619Ž .CAS2 2r0r13r0 1.8246 4.8217 0.5832 0.1972 0.3172 y0.0795Ž .RAS1 2r0r8r6 2 e 1.6051 4.4475 0.5361 0.2087 0.3287 y0.0818

a Ž .RAS2 2r0r8r6 4e 2.0268 3.7444 0.448 0.0982 0.4187 0.0269Ž .RAS3 2r0r8r8 2 e 1.3014 4.3106 0.5006 0.224 0.3292 y0.0836

b Ž .RAS4 2r0r8r14 2 e 0.9387 4.2847 0.491 0.199 0.2869 y0.0921a The SD term calculated in RAS1.b The SD term calculated in RAS3.


As far as the basis set superposition error isconcerned, the data in Table 2 indicate that thedifference between counterpoise-corrected and un-corrected results is nearly the same for SCF andCASSCF wavefunctions. Following this observation,BSSE is estimated at the SCF level only in thesuccessive studies of basis set effects on the calcu-lated changes of the spin–spin coupling constants.

3.2.3. Basis set effectsThe changes of the coupling constants upon the

formation of the water dimer, calculated by means ofSCF and RAS1 methods and with different basissets, together with the values of SCF interactionenergy are summarised in Table 4.

The relative conformity of changes in the cou-pling constants obtained by means of HIIIa and thestandard cc-pVDZ basis is rather fortuitous, consid-ering the very discrepant interaction energy, largeBSSE of both the interaction energy and the cou-pling constants, and large effects of decontractionand addition of the s-orbitals. The latter procedure,performing well for the coupling constants in the

w xisolated molecule 5 , does not improve either thecalculated changes in the coupling constants, or the

Žinteraction energy the discrepancy is even more.pronounced .

The aug-cc-pVDZ basis set, giving far better re-sults for the interaction energy, is better than cc-pVDZ for the construction of the final basis set forour purpose. The changes of the coupling constantsobtained with unmodified aug-cc-pVDZ are too smallin the case of 1J and of different sign for 2J .OH HH

However, the decontraction of s-orbitals improvesconsiderably the agreement with HIIIa results, reduc-

Žing at the same time BSSE already smaller than for.cc-pVDZ by one order of magnitude. The addition

of tight s-orbitals leads to results in very goodagreement with HIIIa. These extensions of the innershell do not influence the interaction energy. Thegood performance of aug-cc-pVDZ-su-1 has beenconfirmed by additional CAS calculations in thisbasis, giving the results similar to the HIIIa ones.

The addition of diffuse orbitals to basis sets of thecc-pVDZ type lowers the calculated changes of thecoupling constants. A similar effect can be noticedwhen extending HIII to HIIIa, but it is relativelysmaller because of a larger dimension of this basis

set. The cc-pVTZ basis set gives the counterpoise-corrected changes in the coupling constants in satis-factory agreement with HIIIa, but BSSE is large.

The general conclusion from this methodologicalpart is: a basis set employed for calculations of thechanges in the coupling constants caused by a hydro-gen-bond formation should be a balanced one, withboth diffuse functions and flexible description ofinner shell orbitals. The lack of the former leads tooverestimated changes of 1J , as well as largeOH

BSSE. The lack of the latter leads to underestimatedchanges of 1J and large BSSE, too. A good per-OH

formance of a basis set for the interaction energy orfor the coupling constants in the isolated moleculealone does not automatically ensure correctly calcu-lated changes of the coupling constants due to inter-molecular interactions. According to our results, ba-sis sets of the aug-cc-pVXZ-su-n type can be recom-mended for that type of calculation.

3.2.4. The changes in the indiÕidual contributions tothe coupling constants

There are four terms contributing to the isotropicnuclear spin–spin coupling constant: the Fermi con-

Ž . Ž .tact FC , the paramagnetic spin–orbital PSO , theŽ .spin–dipole SD , and the diamagnetic spin–orbital

Ž . w xDSO term. The FC term was previously found 29to be the most sensitive to the intermolecular interac-tions. In the present work the change in the FC term

Ž . Ž .is predominant for J O2–H5 and J O1–H3 only,being ; y7 Hz and ; y3 Hz, respectively. Evenin those cases, however, the changes in the PSO termŽ .of opposite sign to the total change are consider-able, being ;2 Hz and ;0.4 Hz, respectively. The

Ž .change in J O2–H6 is dominated by the PSO term,overestimating the total effect by 15%. The changes

Ž .in the spin–dipole SD term are smaller than in theŽ .PSO term, the largest being 0.15 Hz for J O2–H5 .

The changes in the diamagnetic spin–orbit term arenegligible.

In the case of the 2J coupling constants theHHŽtotal effect is an interplay of the FC, PSO the largest

. Žchanges and DSO the changes partially canceling.the ones in PSO terms, the changes in the SD terms

are the smallest ones. However, the total effect is toosmall to draw any definite conclusions.

The electron correlation effects influence mostlythe changes in the FC terms of the coupling con-

()

M.P

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Table 4Changes in the nuclear spin–spin coupling constants in the water dimer and the interaction energy–basis seta effects

1 2 bŽ . Ž . Ž . Ž . Ž .Basis set Changes in J O–H Hz Changes in J H–H Hz E kcalrmolint

1 1 1 2 2Ž . Ž . Ž . Ž . Ž .J O2–H5 J O2–H6 J O1–H3 J H5–H6 J H3–H3ac c c c c cSCF SCF RAS SCF SCF RAS SCF SCF RAS SCF SCF RAS SCF SCF RAS SCF SCF

Ž .HIII 108 y6.42 y6.43 y4.61 y0.97 y0.84 y0.77 y3.57 y3.41 y2.55 0.46 0.49 y0.23 y0.03 y0.13 y0.18 y3.844 y3.825Ž .HIIIa 144 y6.26 y6.37 y4.47 y0.93 y0.86 y0.71 y3.35 y3.34 y2.38 0.55 0.48 y0.14 0.03 y0.13 y0.14 y3.933 y3.845

Ž .cc-pVDZ 48 y5.91 y5.03 y4.74 y1.46 y0.57 y1.37 y5.03 y2.84 y3.88 0.30 0.41 y0.29 y0.51 y0.20 y0.54 y5.942 y3.936Ž .cc-pVDZ-su0 68 y7.12 y6.73 y5.06 y0.96 y0.66 y0.94 y6.11 y3.65 y4.43 0.32 0.41 y0.18 y0.47 y0.16 y0.47 y6.269 y4.210Ž .cc-pVDZ-su1 74 y8.16 y7.71 y5.83 y0.96 y0.60 y0.93 y6.87 y4.14 y5.00 0.42 0.52 y0.18 y0.53 y0.15 y0.53 y6.264 y4.204Ž .cc-pVDZ-su2 80 y8.86 y8.39 y6.37 y0.94 y0.56 y0.91 y7.37 y4.43 y5.37 0.47 0.58 y0.19 y0.57 y0.16 y0.57 y6.261 y4.201Ž .aug-cc-pVDZ 82 y4.58 y3.31 y4.02 y0.42 y0.93 y0.16 y3.44 y2.43 y2.95 0.53 0.64 y0.09 0.24 0.05 0.07 y3.967 y3.752

aug-cc-pVDZ-su0 y5.29 y5.40 y3.72 y0.93 y0.86 y0.71 y2.95 y2.91 y2.08 0.42 0.42 y0.13 y0.09 y0.10 y0.23 y3.988 y3.814Ž .102aug-cc-pVDZ-su1 y6.23 y6.24 y4.47 y0.83 y0.84 y0.59 y3.33 y3.28 y2.35 0.54 0.54 y0.12 y0.07 y0.09 y0.24 y3.981 y3.807Ž .108aug-cc-pVDZ-su2 y6.72 y6.79 y4.84 y0.86 y0.83 y0.64 y3.58 y3.53 y2.54 0.61 0.61 y0.11 y0.08 y0.08 y0.26 y3.98 y3.806Ž .114

Ž .cc-pVTZ 116 y8.92 y6.65 y6.56 y1.29 y0.73 y1.04 y4.49 y3.56 y3.06 0.51 0.56 y0.13 y0.19 y0.07 y0.27 y4.575 y3.748

a The basis set dimension given in parentheses in the first column.b w x w xThe estimated SCF limit ranges from y3.52 kcalrmol 1 to y3.69 kcalrmol 30 , depending on the geometry employed.c The counterpoise-corrected results.


Table 5Ž .The changes in the nuclear spin–spin coupling constants Hz of

the water molecule in bulk water, as assessed by means of thereaction field method

SCF CAS CASŽ . Ž .1r0r7r0 1r0r14r0

1 Ž .J Hz :OH

HIIIa y6.73 y4.49 y4.99cc-pVDZ y4.98 y3.72 y4.05aug-cc-pVDZ y4.45 y3.29 y3.36aug-cc-pVDZ-su-1 y6.54 y4.33 y4.85

2 Ž .J Hz :HH

HIIIa 0.25 y0.51 y0.38cc-pVDZ y0.26 y0.81 y0.72aug-cc-pVDZ 0.46 y0.25 y0.15aug-cc-pVDZ-su-1 0.21 y0.51 y0.39

stants. It explains a small sensitivity of the change inŽ . ŽJ O2–H6 in which case the PSO term is the domi-

.nant one to the correlation effects. The changes inFC term are also most strongly distorted by BSSE.

3.3. The water monomer in bulk solÕent

The changes of the coupling constants in thewater molecule obtained by means of the reactionfield method, taking into account long-range electro-static effects, are presented in Table 5. The influenceof the bulk water changes the value of 1J by 5 HzOHŽ Ž . .CAS 1r0r14r0 rHIIIa results and affects it to asimilar extent as the formation of the hydrogen bonddoes. The absolute value of 2J is increased byHH

several tenths of hertz.Similarly as in the case of the supermolecular

method, the change in 1J calculated at the SCFOH

level has the right sign, but it is overestimated, whilein the case of the change in 2J the inclusion ofHH

correlation effects results in an opposite sign of thecalculated value.

The change in 1J in the water molecule sur-OH

rounded by the dielectric medium is dominated bythe FC term. The PSO term, second in magnitude,

Žcontributes 0.7 Hz to the total change with the.opposite sign , the SD term contributes 0.1 Hz. In

the case of the change in 2J the PSO term is theHH

most important one, at least at the correlated level ofthe calculations. The wrong SCF value is caused bythe overestimation of the change in the FC term. Onthe whole, the electron correlation affects most sub-stantially the change in FC term.

The usefulness of the aug-cc-pVDZ-su-1 basis setfor the evaluation of the changes in the couplingconstants resulting from intermolecular interations isconfirmed by the data in Table 5. Similarly as for thesupermolecular method unmodified cc-pVDZ andaug-cc-pVDZ basis sets do not perform well in thecalculations of solvent effects on the coupling con-stants.

3.4. The water dimer in bulk solÕent

The influence of bulk water approximated as adielectric medium on the nuclear spin–spin coupling

Žconstants in the water dimer the numeration of.atoms as in Fig. 1 is presented in Table 6. It follows

from these results that the long-range electrostaticŽinteractions in water cause a further increase in

. 1terms of an absolute value of the J couplingOH

constants by ;2 Hz, as well as a slight modification

Table 6Ž .The changes in the nuclear spin–spin coupling constants Hz of the water dimer in the bulk water, as assessed by means of the reaction

field method1 1 1 2 1Ž . Ž . Ž . Ž . Ž .J O2–H5 J O2–H6 J O1–H3 J H5–H6 J H3–H3a

In relation to the dimer:SCFrHIIIa y3.70 y2.96 y2.95 0.06 0.12SCFraug-cc-pVDZ-su-1 y3.64 y2.86 y2.88 0.06 0.10RAS1rHIIIa y2.79 y2.02 y2.08 y0.20 y0.23RAS1raug-cc-pVDZ-su-1 y2.74 y1.96 y2.02 y0.19 y0.23

In relation to the monomer:SCFrHIIIa y9.96 y3.88 y6.30 0.61 0.15SCFraug-cc-pVDZ-su-1 y9.88 y3.68 y6.20 0.60 0.03RAS1rHIIIa y7.26 y2.73 y4.47 y0.35 y0.37RAS1raug-cc-pVDZ-su-1 y7.21 y2.55 y4.38 y0.31 y0.47


of the 2J coupling constants. Interestingly, theHH

interaction with a bulk solvent modifies to the largestŽ . Žextent J O2–H5 nuclei directly engaged in the

hydrogen bonding, placed near the centre of the. Ž . Žcavity , not the more external J O1–H3 and J O2–

.H6 .The changes in the nuclear spin–spin coupling

constants in water due to the influence of the dielec-Žtric medium and hydrogen-bond formation Table 6,

.in relation to the monomer , although substantial, aresmaller than the sum of the changes due to the dimer

Ž .formation Table 2 and the influence of the dielec-Ž .tric medium on the water monomer Table 5 . The

automatic summation of the results of supermolecu-Žlar calculations describing mostly the short-range,

.specific interactions and the results of reaction-fieldŽcalculations taking into account the long-range in-

.teractions leads therefore, as expected, to consider-ably overestimated changes in the coupling con-stants.

The influence of a dielectric medium on the cou-pling constants in the water dimer calculated at theSCF level is, as before, overestimated in the case ofthe 1J coupling constants, and of the wrong signOH

in the case of the 2J coupling constants. TheHH

results of calculations with HIIIa and aug-cc-pVDZ-su-1 basis sets are again in excellent agreement.

4. Conclusions

The nuclear spin–spin coupling constants havebeen calculated in the following systems: the waterdimer, the water monomer surrounded by a dielectricmedium, and the water dimer surrounded by thedielectric medium. Attention has been paid to thebasis set and electron correlation effects. The mostimportant results are summarised below.

The formation of the hydrogen bonding causes aconsiderable increase in absolute values of the 1JOH

coupling constants in both donor and acceptor watermolecules. The largest changes occur for 1JOH

through the bond directly engaged in the hydrogenbonding. A change of comparative magnitude andthe same sign results from the interactions with thebulk water, approximated by the reaction fieldmethod. By considering the changes in the couplingconstants due to the monomer–dimer transition andthe effects of embedding the dimer in the dielectric

medium the total change in 1J in water uponOH

condensation can be estimated at ;12 Hz, i.e., 15%1 Žof J itself taking into account that in the liquidOH

each water molecule acts as both proton donor and.proton acceptor .

The sign and magnitude of the change in 2JHH

depend strongly on the method of calculation. Calcu-lations with the most complex wavefunctions suggest

Ž .that both short-range supermolecular method andŽ .long-range reaction field method intermolecular in-

teractions with other water molecules cause a slightincrease of 2J in water. The total effect can beHH

Ž 2 .roughly estimated at ;0.4 Hz 5% of J .HH

The intermolecular spin–spin coupling constantsŽ .in the water dimer were calculated. J O1–H5 equals

Ž Ž ..;4 Hz, the other are 1 Hz J O1–O2 and smaller.The changes in 1J due to the hydrogen-bondOH

formation calculated at the SCF are overestimated,but not very different from the results obtained withmore sophisticated wavefunctions. In the case of thechanges in 2J the SCF method gives completelyHH

wrong results. This indicates that a calculation of thechanges in the spin–spin coupling constants due tohydrogen bonding by means of SCF method may, insome cases, be useful for qualitative considerations,but the results should be treated with caution.

It is necessary to include in calculations of thechanges in the coupling constants induced by theformation of the hydrogen bonding not only the FCterm, but at least the PSO term as well. However, theBSSE and correlation effects are small for the termsother than FC, so that they can be calculated at thelower level of theory. The latter conclusion holds forreaction field calculations, too.

The basis sets of the aug-cc-pVXZ-su-n type canbe recommended for calculations of the changes inthe spin–spin coupling constants due to intermolecu-lar interactions. The aug-cc-pVDZ-su-1 basis set per-

Žforms well in the supermolecular method givingvalues in agreement with the larger HIIIa basis set

.and small BSSE and in the reaction field method.

Acknowledgements

We thank K. Ruud for providing us with theDALTON program and K. Kamienska-Trela and M.´Jaszunski for many helpful suggestions. This work´was supported by the 3 TO9A 121 16 KBN Grant.


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