the nuclear spin–spin coupling constants in methanol and methylamine: geometry and solvent effects

The nuclear spin±spin coupling constants in methanoland methylamine: geometry and solvent e�ects

Magdalena Pecul, Joanna Sadlej *

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

Received 17 January 2000

Abstract

The e�ects of internal rotation and bond stretching on the spin±spin coupling constants in CH3OH and CH3NH2

have been calculated on MCSCF level. The reaction ®eld theory has been used to simulate the e�ect of the water

environment. The internal rotation causes considerable changes not only in 3JHH but in 1JCH and 2JOH (2JNH) as well.

The coupling constants in the methyl group and some of the geminal couplings in polar moieties (2JOH, 2JNH and 2JHNH)

exhibit a di�erential sensitivity to bond length variations. This phenomenon does not emerge for the single bond

couplings involving nuclei with lone pairs. The simulation of the aqueous environment leads to the conclusion that

solvent e�ects are substantial for the single bond coupling constants and for some of the geminal coupling constants but

negligible for 3JHH. In the case of 1JCH and 2JHCH, solvent e�ects depend considerably on the molecular conformation.

All e�ects under study are dominated by the changes in the Fermi contact terms, with the exception of the internal

rotation e�ects on 1JCO and 1JCN. Ó 2000 Published by Elsevier Science B.V. All rights reserved.

1. Introduction

Recent advances in NMR spectroscopy haveincreased its role, already substantial, in thestructure elucidation. The scalar nuclear spin±spincoupling constants are of a particular interest asmeans of establishing the bond and dihedral angles[1±3]. On the other hand, the quantum-chemicalcalculations of the spin±spin coupling constantshave reached the stage in which, the modelling ofthe geometry e�ects and, to some extend, of thein¯uence of the molecular environment is possible.Ab initio calculations of geometry e�ects on thenuclear spin±spin coupling constants have lately

attracted a lot of attention [4±12]. The modellingof the nuclear spin±spin coupling constants inmolecules interacting with the environment is stilla new ®eld, but the interest in this subject isgrowing [13±18].

The spin±spin couplings constants, especially3JHH are basic parameters for estimating dihedralangles in biomolecules. In our previous paper [12],the geometry dependence of the spin±spin couplingconstants in ethane, the smallest system withH±C±C±H dihedral angle, was investigated. In thepresent study, the coupling constants in methanoland methylamine are investigated. These mole-cules are the smallest systems with H±C±N±H andH±C±O±H dihedral angles, therefore are applica-ble for modelling of geometry dependence ofcouplings in peptides and hydrocarbons, respec-tively. In order to simulate more closely the

Chemical Physics 255 (2000) 137±148

www.elsevier.nl/locate/chemphys

* Corresponding author. Fax: +48-22-822-5996.

E-mail address: [email protected] (J. Sadlej).

0301-0104/00/$ - see front matter Ó 2000 Published by Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 1 - 0 1 0 4 ( 0 0 ) 0 0 0 8 7 - 2

conditions in which the NMR spectra are usuallymeasured, the aqueous solvent e�ects are estimat-ed, using the reaction ®eld theory [14]. For thecomparison, calculations of solvent e�ects forethane, the reference non-polar molecule, are re-ported.

In addition to the study of internal rotation andbulk solvent e�ects, the e�ects of the changes inbond lengths are investigated. Keeping ®xed theremaining geometry parameters during the internalrotation may lead to unphysical results of compu-tational simulations. Therefore, to account for thegeometry relaxation, the molecular geometry hasbeen optimized for each value of the dihedral angle.For a better analysis of the results, the changes inthe coupling constants in CH3OH and CH3NH2

upon variation of the bond lengths have been ad-ditionally calculated. This presents an opportunityof investigating the problem of ``di�erential sensi-tivity'' [5] of the coupling constants to the bondlength changes, observed [19] and calculated[5,12,19] for hydrocarbons, but absent in smallmolecules containing lone pairs [4]. CH3OH andCH3NH2, in which both methyl and polar moietiesare present, are suitable for further inquiries intothe nature of the di�erential sensitivity.

2. Computational details

For the calculations of the nuclear spin±spincoupling constants, the linear response multi-con®gurational self consistent ®eld (MCSCF)method has been used, as described in Refs. [20,21].Because of the necessity to account, at least partly,for the dynamic correlation e�ects, the restrictedactive space (RAS) technique has been used. Thedetailed description of the employed wave func-tions is presented in Tables 1 and 2. The calcula-tions of the solvent and geometry e�ects have beencarried out in RAS 2/-/7/19 2e for CH3OH andCH3NH2 and RAS 2/-/7/20 2e for CH3CH3 (seefootnotes of Table 1 for the symbol explanation).

The basis sets listed in Tables 1 and 2, used forpreliminary calculations for the rigid and non-in-teracting molecules, are mostly modi®cations ofthe standard correlation-consistent basis sets [22±24]. cc-pVXZ-su-n denotes the cc-pVXZ basis setwith s functions decontracted and n tight s func-

tions added, with the exponents forming a geo-metric progression [25]. The examination ofgeometry e�ects has been carried out using themedium-size HIII IGLO basis set [26], appropriatefor the calculations of the nuclear spin±spin cou-pling constants [25,27]. For the calculations ofsolvent e�ects, the aug-cc-pVDZ-su-1 basis set hasbeen used, proved to be reliable for this type ofcalculation [16].

The experimental equilibrium geometry pa-rameters [28±30] have been employed, except forcalculations with relaxed geometry, in which case,the geometric parameters have been optimized onMP2/HIII level, with dihedral angle ®xed at 0�, 30�

and 60�.In the study of the geometry dependence of the

coupling constants, the dihedral angle has beenvaried by every 30� and the bond lengths have beenvaried by �0.05 �A from their equilibrium values.

The reaction ®eld method [14] as implementedin Ref. [31] has been employed for the estimationof bulk solvent (water) e�ects on the spin±spincoupling constants. The radius of a sphericalcavity has been taken as a sum of the distance ofthe most external hydrogen from the molecularcentre of mass (coinciding with the centre of cav-ity) and hydrogen van der Waals radius. The orderof the multipole expansion is 10 and the dielectricconstant of water is 78.54.

The most time-consuming spin±dipole (SD)term of the spin±spin coupling constants has notbeen calculated in the study of geometry and sol-vent e�ects, unless explicitly stated otherwise. Ourpreliminary calculations con®rmed that the errorsintroduced by this omission are negligible.

All calculations of the coupling constants havebeen performed using the Dalton program system[31]. For MP2 optimization, GAUSSIAN 94GAUSSIAN 94 [32] hasbeen used.

3. Results

3.1. The nuclear spin±spin coupling constants for theisolated molecules in the staggered conformation

The nuclear spin±spin coupling constantsin CH3OH and CH3NH2 calculated for the

138 M. Pecul, J. Sadlej / Chemical Physics 255 (2000) 137±148

experimental geometries with di�erent basis setsand di�erent RAS wave functions are collected inTables 1 and 2. All coupling constants in this workare given for 1H, 13C, 15N and 17O isotopes. Thedata in Tables 1 and 2 cannot be considered as thebenchmark results: the basis set used are of smallto medium size, and electron correlation treatmentis also not complete. However, the tendencies areclear enough to allow for the qualitative estima-tion of the errors resulting from the basis set in-completeness and the underestimation of thecorrelation e�ects.

3.1.1. The electron correlation e�ectsThe electron correlation e�ects on the coupling

constants are usually very large, which originsmostly from the instability of SCF wave functionto the triplet Fermi contact and spin±dipole per-turbations [21]. This usually leads to considerableoverestimation of the calculated couplings [21,33].Our results in Tables 1 and 2 con®rm this ten-dency, with one exception: 1JCO in CH3OH ob-

tained at the SCF level is nearly ®ve timesunderestimated in comparison with the most reli-able RAS 2/-/7/27 2e results. This indicates that asign of the correlation correction can be di�erentfor various types of coupling. Therefore, the SCFresults should be treated with utmost caution.

The single bond coupling constants 1JCN inCH3NH2 and 1JCO in CH3OH are very sensitive tothe correlation e�ects and attain the agreementwith experiment (or the convergence with the RASextension for 1JCO, for which no experimental dataexist) only for RAS with fairly large number ofvirtual orbitals in RAS3 space. A similar patterncan be observed for the proton±proton geminalcoupling constants. The remaining coupling con-stants are in good agreement with the experimentor with the results of more advanced calculationsalready for the smallest MCSCF wave functions.This suggests that the static correlation e�ects areimportant for all coupling constants, but the roleof dynamic correlation depends on the type ofcoupling. On the basis of the results presented in

Table 1

The nuclear spin±spin coupling constants (Hz) in methanol in staggered conformation; electron correlation and basis set e�ects

Method 1JCO1JOH

1JCH2JHOC

2JHCO2JHCH

3JHOCH

ava ava ava ava

Active space dependence (HIII basis set)

SCF 2.35 ÿ98.34 165.55 ÿ9.45 ÿ5.21 ÿ21.26 6.25

2/-/7/7 2eb 6.79 ÿ86.30 141.27 ÿ4.86 ÿ5.09 ÿ15.96 5.27

2/-/7/7 4ec 7.30 ÿ84.95 138.18 ÿ4.36 ÿ5.06 ÿ15.16 5.18

2/-/7/14 2e 10.12 ÿ80.38 138.38 ÿ4.57 ÿ5.02 ÿ13.81 5.13

2/-/7/19 2e 10.90 ÿ80.15 135.38 ÿ4.40 ÿ4.91 ÿ12.85 5.11

2/-/7/21 2ed 10.94 ÿ80.22 134.70 ÿ4.38 ÿ4.89 ÿ12.74 5.10

2/-/7/27 2ed 11.05 ÿ78.55 134.24 ÿ4.25 ÿ5.00 ÿ12.44 5.10

Basis set e�ects (RAS 2/-/7/19 2e active space)

HIII 10.90 ÿ80.15 135.38 ÿ4.40 ÿ4.91 ÿ12.85 5.11

cc-pVDZ-su-0 11.50 ÿ63.64 117.07 ÿ3.78 ÿ4.65 ÿ10.66 3.49

cc-pVDZ-su-1 12.16 ÿ70.55 130.29 ÿ4.30 ÿ5.06 ÿ12.60 4.27

aug-cc-pVDZ-su-1 10.67 ÿ76.73 131.31 ÿ4.44 ÿ4.50 ÿ13.08 4.31

cc-pVTZ-su-0 10.07 ÿ74.80 126.90 ÿ4.09 ÿ4.60 ÿ12.24 4.52

cc-pVTZ-su-1e 10.59 ÿ78.67 135.62 ÿ4.37 ÿ4.92 ÿ13.45 5.00

Expt.f ÿ85 (10) 141 ÿ7.5 ÿ10.8 5.0

a The arithmetically averaged results for the staggered conformation.b n0/n1/n2/n3 ne denotes: n0 a number of inactive orbitals, n1 a number of orbitals in RAS1 space (here empty), n2 a number of orbitals

in RAS2 space (all occupation allowed), n3 a number of orbitals in RAS3 space (up to ne electrons excited to RAS3).c SD term calculated in the 2/-/7/7 2e active space.d SD term calculated in the 2/-/7/19 2e active space.e SD term calculated in the cc-pVTZ-su-0 basis set.f Experimental results quoted from Ref. [35].

M. Pecul, J. Sadlej / Chemical Physics 255 (2000) 137±148 139

this paper and additional calculations forCH3CH3, we conclude that the dynamic correla-tion e�ects are the largest for geminal couplingconstants and single bond coupling constants be-tween nuclei of atoms bearing lone pairs.

The RAS 2/-/7/19 2e results are fairly reliable.Their deviations from the coupling constants cal-culated by means of RAS 2/-/7/27 2e (considerablymore demanding computationally) are less than5% for the geminal coupling constants and lessthan 3% for the others. The e�ects of includinghigher than double excitations in RAS wavefunction would probably be more substantial, asthe comparison of RAS 2/-/7/7 2e and RAS 2/-/7/74e results indicates. However, this extention ofRAS in 2/-/7/19 2e leads to the active space in-tractable computationally. On these consider-ations, the RAS 2/-/7/19 2e wave function modelhas been employed for the study of the basis sete�ects and the further investigations of geometryand solvent e�ects.

3.1.2. The basis set e�ectsThe data in Tables 1 and 2 illustrate three types

of basis set e�ects: the e�ect of an increase of thecardinal number X in cc-pVXZ sequence, the e�ectof an addition of tight s orbital, and the e�ect of anaddition of di�use orbitals. The performance ofHIII IGLO basis set and the modi®ed correlation-consistent basis sets can also be compared.

Most of the calculated coupling constants areincreased (in terms of reduced coupling constants)with any extension of the basis set. 1JCO in CH3OHis again an exception; an addition of one tight sorbital causes its increase, but an addition of po-larization functions (i.e. an extension of cc-pVDZto cc-pVTZ or of cc-pVDZ to aug-cc-pVDZ) hasthe opposite e�ect. In general, any addition to theinner shell functions in¯uences primarily the cou-pling constants involving protons, which indicatesthat the correlation-consistent basis sets for hy-drogen are too small in this respect for the cou-pling constants calculations. The addition of

Table 2

The nuclear spin±spin coupling constants (Hz) in methylamine in staggered conformation; electron correlation and basis set e�ects

Method 1JCN1JNH

1JCH2JHNC

2JHNH2JHCN

2JHCH3JHNCH

ava ava ava ava

Active space dependence (HIII basis set)

SCF ÿ15.30 ÿ78.11 159.24 ÿ9.91 ÿ20.87 0.51 ÿ22.66 8.19

2/-/7/7 2eb ÿ10.21 ÿ68.31 135.00 ÿ5.48 ÿ14.61 ÿ0.29 ÿ17.06 6.60

2/-/7/7 4ec ÿ9.65 ÿ67.17 132.03 ÿ4.98 ÿ13.86 ÿ0.39 ÿ16.27 6.41

2/-/7/14 2e ÿ7.30 ÿ65.60 132.39 ÿ4.73 ÿ11.58 ÿ0.52 ÿ14.70 6.46

2/-/7/19 2e ÿ6.82 ÿ65.63 129.75 ÿ4.46 ÿ11.64 ÿ0.55 ÿ13.78 6.38

2/-/7/21 2ed ÿ6.71 ÿ65.74 129.03 ÿ4.44 ÿ11.67 ÿ0.56 ÿ13.67 6.40

2/-/7/27 2ed ÿ6.46 ÿ65.04 128.28 ÿ4.43 ÿ10.83 ÿ0.69 ÿ13.30 6.33

Basis set e�ects (RAS 2/-/7/19 2e active space)

HIII ÿ6.82 ÿ65.63 129.75 ÿ4.46 ÿ11.64 ÿ0.55 ÿ13.78 6.38

cc-pVDZ-su-0 ÿ6.23 ÿ54.84 112.40 ÿ3.94 ÿ9.56 ÿ0.67 ÿ11.56 4.49

cc-pVDZ-su-1 ÿ6.42 ÿ61.05 125.09 ÿ4.43 ÿ11.55 ÿ0.71 ÿ13.64 5.43

aug-cc-pVDZ-su-1 ÿ6.87 ÿ63.59 125.79 ÿ4.51 ÿ11.81 ÿ0.38 ÿ13.93 5.53

cc-pVTZ-su-0 ÿ6.60 ÿ61.17 121.75 ÿ4.25 ÿ10.54 ÿ0.53 ÿ13.12 5.62

cc-pVTZ-su-1e ÿ6.79 ÿ65.03 130.08 ÿ4.53 ÿ11.65 ÿ0.58 ÿ14.44 6.21

Expt.f ÿ4.50

(0.5)

ÿ65.00

(0.2)

132.50

(0.2)

ÿ1.00

(0.1)

7.10

(0.1)

a The arithmetically averaged results for the staggered conformation.b n0/n1/n2/n3 ne denotes: n0 a number of inactive orbitals, n1 a number of orbitals in RAS1 space (here empty), n2 a number of orbitals

in RAS2 space (all occupation allowed), n3 a number of orbitals in RAS3 space (up to ne electrons excited to RAS3).c SD term calculated in the 2/-/7/7 2e active space.d SD term calculated in the 2/-/7/19 2e active space.e SD term calculated in the cc-pVTZ-su-0 basis set.f Experimental results quoted from Ref. [36].


di�use functions has the largest e�ect on the cou-pling constants involving lone-pair atoms, aswould be expected intuitively. The e�ect of theuniform extension of cc-pVDZ to cc-pVTZ issimilar for all the coupling constants under inves-tigation.

The results obtained with HIII IGLO are sim-ilar to the cc-pVTZ-su-1 ones, in spite of thesmaller size of the HIII IGLO basis set. For thisreason, HIII IGLO has been employed for thestudy of the geometry e�ects, similarly as in theformer work on ethane [12]. Also the aug-cc-pVDZ-su-1 basis set gives reliable results forCH3OH and CH3NH2. Moreover, it is suitable forthe calculations of the electric ®eld e�ects on thecoupling constants [16] because of the presence ofboth di�use functions and tight s orbitals. Ac-cordingly, the investigation of the solvent e�ectshas been conducted using the aug-cc-pVDZ-su-1basis set.

In the subsequent discussion of the geometryand solvent e�ects, the changes of the spin±spincoupling constants in CH3NH2 and CH3OH dueto geometry deformations are given with respect tothe values obtained by means of RAS 2/-/7/19 2eand the basis set HIII, given in Tables 1 and 2,respectively. The solvation-induced changes of thespin±spin coupling constants are given with re-spect to the values calculated with RAS 2/-/7/19 2eand the basis set aug-cc-pVDZ-su-1, also present-ed in Tables 1 and 2.

3.2. The geometry and solvent e�ects on single bondcoupling constants

In this subsection, the single bond couplingconstants are discussed. For each type of singlebond coupling constants, the geometry e�ects arediscussed in the following order: the dependence ofthe coupling on the dihedral angle, the e�ects of thegeometry relaxation on this dependence, andthe variation of the coupling with the bondlengths. Finally, the estimated solvation e�ects arepresented.

3.2.1. 1JCO and 1JCN coupling constantsNow, the e�ects of the internal rotation on the

spin±spin coupling constants through the bond

around which the molecule is rotated will be dis-cussed. It should be kept in mind that the axis ofrotation is not exactly collinear with the bond axis;the experimental tilt angle is equal to 3� in CH3OH[29] and 2.9� in CH3NH2 [28].

The changes in the single bond coupling con-stants through the bond around which the mole-cule is rotated are not very large. 1JCO in methanoldecreases by 0.50 Hz when going from the stag-gered to eclipsed form, while the absolute value of(negative) 1JCN in methylamine increases then by0.30 Hz. It means that the changes are, in terms ofreduced coupling constants, of a similar magni-tude, but of the opposite sign: the internal rotationcauses an decrease in reduced 1JCO, but an increasein reduced 1JCN. In the previous paper on ethane,the analogous reduced 1JCC was found to increaseupon internal rotation [12], but the change wastwo times smaller than those of 1JCN in methyl-amine.

The calculated internal rotation e�ect on 1JCO inmethanol is approximately the same when the ge-ometry is relaxed. In methylamine, however, re-laxation of the geometry increases the e�ect ofinternal rotation on 1JCN from 0.30 to 0.90 Hz.This additional increase can be caused by a con-siderable change in the tilt angle (4.9� for thestaggered conformation and 0.4� for the eclipsedone). The e�ects of the internal rotation on 1JCN

and 1JCO are dominated by the paramagnetic spin±orbital term, similarly as that on 1JCC in ethane.This contrasts with the other geometry e�ects,where the changes in the Fermi contact term pre-vail.

1JCO in methanol and 1JCN in methylamine donot exhibit a di�erential sensitivity to the bondlengths changes: the e�ects (highly non-linear in-crease of the reduced coupling constants with thebond elongation) are the largest when CO or CNbonds are stretched. It distinguishes them from1JCC in ethane, where the di�erential sensitivitywas observed.

The estimated gas-to-aqueous solution shift of1JCO in methanol is equal to ÿ1:0 Hz and dependsvery little on the molecular conformation. Inmethylamine, the solvent-induced change of 1JCN

varies from ÿ0:5 Hz for the staggered conforma-tion to ÿ0:6 Hz for the eclipsed conformation. In


ethane, this e�ect on 1JCC is barely 0.1 Hz andnearly independent on the dihedral angle. To sumup, the reduced coupling constant 1J�CX�(X � O;N;C) increases upon embedding in thedielectric medium, the e�ect is intensi®ed withpolarity of the molecule, and the slight dependenceon the conformation can be observed in methyl-amine only.

3.2.2. 1JOH and 1JNH coupling constantsThe single bond coupling constants in the polar

groups: 1JOH in methanol and 1JNH in methylaminedo not seem very sensitive to the internal rotationwhen the geometry relaxation is not taken intoaccount. 1JOH changes from ÿ80:1 Hz in thestaggered conformation to ÿ80:9 Hz in theeclipsed conformation. For 1JNH in methylamine,the e�ect is similar; ÿ65:6 Hz in the staggeredconformation and ÿ66:0 Hz in the eclipsed con-formation. In the intermediate asymmetric con-formation, there is nearly no di�erence betweentwo non-equivalent 1JNH coupling constants inCH3NH2, both are ÿ65:8 Hz. The e�ect of theinternal rotation is considerably intensi®ed whenthe in¯uence of the geometry relaxation is includ-ed; 1JOH and 1JNH then change by as much as 2.1and 2.5 Hz, respectively. This additional e�ectemerges from shortening of the OH (and NH)bond, accompanying the rotation, and probablyfrom the change in the tilt angle. The changes ofthe other geometric parameters should not in¯u-ence much 1JOH and 1JNH (see below).

The investigation of the dependence of 1JOH and1JNH on the bond lengths shows that 1JOH and1JNH, similarly as 1JCO and 1JCN, do not exhibit adi�erential sensitivity to the bond lengths changes.1JOH is extremely sensitive to the changes inR�OH�; it increases by nearly 13 Hz when the bondis stretched by 0.05 Hz. In CH3NH2, stretching ofR�NHa� by 0.05 Hz causes an increase in 1JNHa by3.4 Hz and a decrease in 1JNHb by only 0.4 Hz. Thestretching of CO and CN bonds does not intro-duce substantial changes in 1JOH and 1JNH. Itseems from the present results that the di�erentialsensitivity of the single bond nuclear spin±spincoupling constants can be observed only in cou-plings between atoms without lone pairs [4].

Surrounding the molecules by a dielectric me-dium increases 1JOH and 1JNH (in terms of theirabsolute values) by approximately 2.75 and1.15 Hz, respectively. These e�ects do not dependon the dihedral angles.

3.2.3. 1JCH coupling constantsThe dependence of the 1JCH coupling constants

in methanol and methylamine on the conforma-tion is shown in Fig. 1(a) and (b), respectively. Thesolid lines correspond to the results for ®xed ex-perimental geometric parameters and the dashedlines to the results for relaxed MP2 optimized ge-ometries. h1 is a dihedral angle between the givenCH bond and the polar group (i.e. the OH bond inmethanol and the C2 axis of NH2 in methylamine).

1JCH is very sensitive to the conformationalchanges in both CH3OH and CH3NH2, especiallyin the latter, where it changes by nearly 10 Hzupon the staggered±eclipsed transition. For thecomparison, the calculated change upon internal

Fig. 1. The dependence of 1JCH coupling constants in (a)

methanol (b) methylamine on the conformation. h1 is CH-polar

group dihedral angle.


rotation in 1JCH in CH3CH3 is equal only 0.4 Hz[12]. The relaxation of geometric parameters otherthan the dihedral angle introduces some irregu-larities, but does not change the general trend;1JCH increases with increase of the CH-polar groupdihedral angle.

The changes in 1JCH coupling constants inmethanol and methylamine upon variations of thebond lengths are summarized in Table 3. Theyexhibit a di�erential sensitivity: the change of 1JCH

is much larger when CO (or CN) or nearby CHbond length is stretched than when the CH dis-tance between the nuclei engaged in the coupling isvaried. It resembles the situation in hydrocarbons[5,12,19] and contrasts with the reported behav-iour of the single bond coupling constants in polarmoieties of CH3OH and CH3NH2. The phenom-enon of the di�erential sensitivity of 1JCH inCH3OH and CH3NH2 emerges only at the corre-lated level of the calculations; the SCF results arecompletely incorrect, again in analogy to hydro-carbons.

The 1JCH coupling constants in methanol arenot very sensitive to the variation of the OH bondlength. In analogy to ethane, the changes are dif-ferent for 1JCH in trans and gauche positions withrespect to the OH bond. In methylamine, the e�ect

of the NH bond length variation is the largest on1JCH in gauche position, outside the ±NH2 group.

The next point of the discussion is the solvente�ect on 1JCH. According to our estimation, themagnitude and the sign of solvent e�ects on 1JCH inmethanol and methylamine depend strongly on themolecular conformation. It is visualized in Fig. 2.For both systems under study, the e�ects arepositive and substantial when the dihedral angle issmall, negligible for h1 approaching 100� andagain quite considerable, but negative, for h1 ap-proaching 180�. It follows from the comparison ofFigs. 1 and 2 that the solvent e�ect reduces thee�ect of the internal rotation.

Table 3

The changes in the 1JCH coupling constants (Hz) in CH3OH and

CH3NH2 induced by the bond variations

CH3OH 1JCH11JCH2

1JCH3

DR�OH�� 0.05 ÿ0.07 0.07 0.07

DR�OH��ÿ0.05 0.07 ÿ0.04 ÿ0.04

DR�CO�� 0.05 2.31 3.48 3.48

DR�CO��ÿ0.05 ÿ2.38 ÿ3.70 ÿ3.70

DR�CH1�� 0.05 3.09 3.33 3.33

DR�CH1��ÿ0.05 ÿ2.94 ÿ3.39 ÿ3.39

DR�CH2�� 0.05 3.52 1.70 3.75

DR�CH2��ÿ0.05 ÿ3.60 ÿ1.75 ÿ3.84

CH3NH2

DR�NHa�� 0.05 0.06 0.01 0.25

DR�NHa��ÿ0.05 ÿ0.05 0.01 ÿ0.23

DR�CN�� 0.05 2.80 3.18 3.18

DR�CN��ÿ0.05 ÿ2.96 ÿ3.28 ÿ3.28

DR�CH1�� 0.05 0.67 3.57 3.57

DR�CH1��ÿ0.05 ÿ0.87 ÿ3.66 ÿ3.66

DR�CH2�� 0.05 3.40 2.33 3.02

DR�CH2��ÿ0.05 ÿ3.46 ÿ2.27 ÿ3.08

Fig. 2. (a) The change in 1JCH upon embedding CH3OH in the

dielectric (� � 78:54) medium as a function of the conformation

of CH3OH. (b) The change in 1JCH upon embedding CH3NH2

in the dielectric (� � 78:54) medium as function of the confor-

mation of CH3NH2.


Because of an opposite sign of the solvent ef-fects for small and large dihedral angles, the av-eraged e�ect observed in NMR spectroscopy canbe small when internal rotation is not hindered. Itmay also be di�erent in sign for methylamine andmethanol, as an examination of Fig. 2 indicates.These theoretical predictions are supported by theexperiment [34]. The basic features of the 1JCH

dependence on the dihedral angle and the solventpolarity were correctly predicted previously by thesemi-empirical INDO method [34].

Contrary to what is found for CH3OH andCH3NH2, the solvent e�ect on 1JCH in CH3CH3 issmall (ÿ0:2 Hz) and nearly independent on theconformation. This indicates that the pattern ob-served in CH3OH and CH3NH2 originates fromthe in¯uence of lone pairs in the polar groups.

3.3. The geometry and solvent e�ects on geminalcoupling constants

This subsection contains a discussion of thegeometry and solvent e�ects on the geminal cou-pling constants. As before, at the beginning, theinternal rotation e�ects are presented. Then, thein¯uence of the geometry relaxation on the de-pendence of the coupling on the dihedral angle isdiscussed. Next, the e�ects of the changes in thebond lengths are described. In the end, the aque-ous solvent e�ects are reported.

3.3.1. 2JOH and 2JNH coupling constants2JOH is di�cult to measure and 2JNH is usually

very small. Therefore, they are of little importancein NMR spectroscopy. Nevertheless, they areworth discussing because of two interesting prop-erties: they are extremely sensitive to the internalrotation and they exhibit a di�erential sensitivityto the bond stretching.

2JOH in CH3OH varies from 0.1 to ÿ10:5 Hzwhen the dihedral angle h1 between CH bond inthe coupling path and the polar group is changedfrom 0� to 180�. The behaviour of 2JNH in thisrange of h1 is similar; it varies from 1.17 to ÿ5:15Hz. In contrast to 2JOH, 2JNH exhibits a shallowmaximum for h1 equal �60°. The inclusion of thegeometry relaxation introduces only slight altera-tions to this pattern.

2JOH and 2JNH are more sensitive to the changesin the OH (or NH) bond length than to those inthe CH bond length in the coupling path. Thedi�erential sensitivity exhibited by these couplingconstants means that this property is not limited tothe coupling constants between nuclei without lonepairs. 2JOH in methanol is di�erentially sensitivealso to the stretching of CH bonds; 2JOH of aproton in the gauche position with respect to theOH bond is more a�ected by the stretching of theCH bond in the trans position than by the changein the CH bond in the coupling path. The reverse,however, is not true; 2JOH of a proton in the transposition is primarily a�ected by the stretching ofthe trans CH bond. The change in the CO (or CN)bond length a�ects 2JOH (or 2JNH) to the similarextend as the change in the OH (NH) bond does,but the sign of this e�ect is opposite.

The estimated solvent e�ect on 2JOH in CH3OHis small (max. 0.2 Hz). 2JNH in CH3NH2 is moresensitive to the polar environment (max. 0.6 Hz).The dependence of the solvent e�ect on the con-formation is similar to that observed for 1JCH; thee�ect is large for the h1 dihedral angle approaching0� and 180�, and nearly zero for h1 equal 90�.However, in the case of 2JOH and 2JNH, the solvente�ect is always positive, in contrast to 1JCH.

3.3.2. 2JCH coupling constants2JCNH in methylamine and 2JCOH in methanol

are not susceptible to the internal rotation: thestaggered±eclipsed transition increases them (interms of reduced coupling constants) by only 0.2Hz. Taking into account the geometry relaxationreverses this e�ect and, in the case of 2JCNH inmethylamine, considerably increases its magni-tude. This origins primarily from the shortening ofthe OH (NH) bond and the lengthening of the CO(CN) bond accompanying the internal rotation.These e�ects reinforce each other in CH3NH2, butpartially cancel in CH3OH (see below), thus thedi�erence in the magnitude of the total e�ect.

The behaviour of 2JCOH and 2JCNH when thebond lengths are changed is complicated. 2JCNH

does not exhibit the di�erential sensitivity to thechanges of NH bond length. However, both 2JCNH

and 2JCOH increase (in terms of reduced couplingconstants) considerably when the CH bond in


a gauche position is stretched, in analogy to whatwas observed for 2JCCH in ethane. For CH3OH,this change (ÿ0:53 Hz when the bond is stretchedby 0.1 �A) exceeds the e�ect of the CO bondstretching (ÿ0:39 Hz), although it is smaller thanthe e�ect of the OH bond stretching (ÿ0:88 Hz). InCH3NH2, a lengthening of the CH gauche bond by0.1 �A causes the change of ÿ0:78 Hz in 2JCNH

(ÿ0:51 Hz when the stretched bond is outside theNH2 group). The equal stretching of the CN andNH bonds in the coupling path causes changes of1.03 and ÿ0:55 Hz, respectively. To sum up, 2JCH

in CH3NH2 and CH3OH exhibits a di�erentialsensitivity to the changes in the bond lengths in themethyl groups, but not in the polar moieties.

The estimated e�ect of the aqueous environ-ment on 2JCH is negligible for all systems underinvestigation.

3.3.3. 2JHH coupling constantsIn this section, we discuss the in¯uence of the

geometry changes and polar environment on thegeminal proton±proton coupling constants: 2JHCH

in CH3OH, 2JHCH and 2JHNH in CH3NH2.2JHCH in CH3OH depends signi®cantly on the

dihedral angle and varies from ÿ10:37 (the leastnegative value) to ÿ14:50 Hz (the most negativevalue). The analogous coupling in CH3NH2 variesfrom ÿ12:97 to ÿ17:06 Hz. In both molecules,2JHCH achieves the most negative values when thelone pairs are in syn or anti position to the C2 axisof coupled H±C±H. The least negative couplingsoccur for their gauche position. This results in abell-shaped dependence of 2JHCH on the dihedralangle. This pattern is little changed by inclusion ofa geometry relaxation.

2JHNH in CH3NH2 varies from ÿ12:34 Hz in thestaggered conformation to ÿ12:93 Hz in theeclipsed conformation. Inclusion of a geometryrelaxation practically cancels this e�ect. This iscaused by the stretching of the CN bond accom-panying the eclipsed±staggered transition (seebelow).

2JHCH exhibits a di�erential sensitivity to thechanges in CH bond lengths in both CH3OH andCH3NH2. Similar to what was found for 2JOH and2JNH, the e�ect of CH bond stretching varies withthe CH-polar group dihedral angle. 2JHCH be-

comes, on the average, more negative with thelengthening of CO or CN bond, but this e�ect isnot signi®cant (0.2 Hz in CH3OH, even smaller inCH3NH2). The changes in OH or NH bondlengths have negligible in¯uence on 2JHCH.

2JHNH in CH3NH2 changes similarly with CNand NH bond variations; the shortening of the CNor NH bond increases the absolute value of 2JHNH

by 0.2 Hz. Noteworthy is the fact that the elon-gation of the CN bond decreases the absolutevalue of 2JHNH more than the equal stretching ofthe NH bond does. Hence, rather unexpectedly,2JHNH also exhibits a di�erential sensitivity.

The in¯uence of the dielectric environment on2JHCH strongly depends on the molecular confor-mation. In both molecules under investigation, theshift of 2JHCH to more negative values is largest(ÿ0:55 Hz in CH3OH and ÿ0:25 Hz in CH3NH2)when the polar groups are near syn positions withrespect to the C2 axis of coupled H±C±H. In thecase of 2JHNH in CH3NH2, the estimated solvente�ect is approximately ÿ0:4 Hz and does notchange with the molecular conformation.

3.4. The geometry and solvent e�ects on vicinalcoupling constants

Now, we shall discuss the calculated depen-dence of 3JHH coupling constants on the dihedralangle, bond lengths, and solvent polarity. Fig. 3aand b depict the calculated 3JHH coupling con-stants in CH3OH and CH3NH2, respectively, asfunctions of the dihedral angle h. The couplingconstants have been calculated for experimentalgeometries (exp. geom.) and geometries optimizedfor each value of a dihedral angle (opt. geom.). Forcomparison, Fig. 3 also contains the experimentalcurves (quoted from Ref. [2]) derived for sets ofcompounds containing ±CH2OH and CHNH2

groups, respectively. The discrepancy betweentheoretical and experimental 3JHH coupling con-stants is substantial, but it should be kept in mindthat they are derived for di�erent systems.

The theoretical curves in Fig. 3 obtained withand without the geometry relaxation are practi-cally indistinguishable. A better insight into thegeometry relaxation e�ects can be obtained when


the calculated 3JHH coupling constants are ®tted inthe extended Kaplus-type relation:

3JHH�h� � C0 � C1 cos�h� � C2 cos�2h�� C3 cos�3h� � S1 sin�h�� S2 sin�2h� � S3 sin�3h�� S1=2 sin�0:5h�: �1�

The parameters of Eq. (1) are presented in Table 4.It can be seen from these data that the 3JHH cou-plings for the optimized relaxed geometry areslightly smaller than those for the experimentalone, for both methanol and methylamine. This canbe rationalized by investigating the dependence of

3JHH on the bond lengths. For methanol 3JHH in-creases with the increase of OH and CH bondlengths (in the coupling path) and decreases withthe stretching of the CO bond. This explains theobserved di�erence between 3JHH calculated withthe experimental and MP2 optimized geometry;MP2 optimization leads to the shorter CH and OHdistances, but overestimates the CO bond length.The source of the e�ect observed in methylamine isanalogous.

In analogy to what was observed in CH3CH3,the 3JHH coupling constants in CH3OH andCH3NH2 do not exhibit a di�erential sensitivity,the bond stretching has a considerable in¯uence on3JHH only when the bond in the coupling path isstretched.

The estimated solvent e�ects on the 3JHH cou-pling constants in CH3OH and CH3NH2 are small.In CH3OH, the solvent e�ect is negative and itsmagnitude mirrors that of 3JHH itself; the largestchanges (approximately ÿ0:1 Hz) are observed forthe dihedral angles 0� and 180�. In CH3NH2, thee�ects are smaller (the largest of them does norexceed 0.07 Hz) and on the average positive al-though their sign depends on the molecular con-formation. In CH3CH3, the solvent e�ect does notexceed 0.05 Hz, and its sign also depends on themolecular conformation.

4. Conclusions

The dependence of the coupling constants onmolecular geometry and solvent polarity has beencalculated at MCSCF level for two model polarmolecules with the methyl group: CH3OH andCH3NH2. The most important results of the cal-culations are summarized below.

The calculations for the rigid and isolatedmolecules indicate that electron correlation e�ectsare the largest for the geminal couplings and thesingle bond couplings between nuclei in atomsbearing lone electron pairs. Also, the extension ofthe basis set by di�use functions has the largeste�ect on the couplings between nuclei in atomsbearing lone electron pairs.

It is demonstrated in the present and previous[12] studies of geometry e�ects that a ``di�erential

Fig. 3. The dependence of 3JHH (Hz) on the dihedral angle h(deg) in (a) CH3OH and (b) CH3NH2. Comparison of the

theoretical and experimental curves.


sensitivity'' of the coupling constants to thechanges in the bond lengths is a phenomenoncommon for methyl groups, the molecular envi-ronment notwithstanding. It is not observed forsingle bond coupling constants between nuclei inatoms with lone pairs, but may occur for manybond couplings, even in polar moieties (e.g. 2JOCH

in methanol, 2JNCH and 2JHNH in methylamine).The internal rotation in¯uences considerably

the single bond carbon±proton couplings inCH3OH and CH3NH2, particularly in the latter.Very large e�ects are also observed on 2JOH and2JNH couplings. The dependence of 3JHH on a di-hedral angle is bell-shaped and the asymmetryobserved in CH3NH2 is not substantial. Allowingthe other geometry parameters to relax during theinternal rotation does not change much the patternfound for the above couplings. However, the ge-ometry relaxation introduces some modi®cationsfor the other couplings, which are less dependenton a dihedral angle (e.g. 1JOH and 1JNH).

The changes of the nuclear spin±spin couplingconstants induced by variations in geometry aredominated by the FC term. The exception is avariation of single bond coupling constantsthrough the bond collinear with the axis of internalrotation (i.e. 1JCC in ethane, 1JCO in methanol, 1JCN

in methylamine), in which case the PSO termprevails. The SCF method gives correct trends forthe variation of the spin±spin coupling constantswith dihedral angles, but does not reproduce the

MCSCF dependence of the coupling constants onbond lengths.

The water environment e�ects estimated by re-action ®eld theory are considerable for the singlebond coupling constants and the geminal 2JNH and2JHH coupling constants. For the other geminalcouplings and 3JHH, they are negligible. In the caseof the coupling constants in methyl groups of thepolar molecules, the e�ect of the uniform dielectricenvironment depends considerably on the confor-mation. It is probably connected with the changesin orientation of the dipole moment and the cou-pling tensor. All the solvent e�ects under study aredominated by the FC term.

Acknowledgements

We would like to thank Prof. Michal Jaszu�nskifor his helpful comments. This work was sup-ported by the 3 TO9A 121 16 KBN Grant.

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the nuclear spin–spin coupling constants in methanol and methylamine: geometry and solvent effects

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