- Email: [email protected]
Vicinal proton—proton coupling constants. Basis set dependence in SCF ab initio calculations
Volume 206, number 1,2,3,4
30 April 1993
CHEMICALPHYSICS LETTERS
Vicinal proton-proton coupling constants. Basis set dependence in SCF ab initio calculations Jestis San-Fabian, Joaquin Guilleme, Ernest0 Diez Departamento a’eQuimica Fisica Apkada, Facultadde Ciencim C-2, Universidaddudnoma
deMadrid, 28049 Madrid, Spain
Paolo Lazzeretti, Massimo Malagoli and Riccardo Zanasi Dipartimento di Chimica, Universikidi Modena, Via Campi 183,411OOModena. Italy
Received 8 January 1993
An SCF ab initio study of the angular dependence and substituent effects upon the vicinal coupling constants has been carried out for the molecules U-I&H,, CHZFCHaand CHFQ-&. The four contributions to ‘.&,, (JFc, jSD, pD and p) have been computed using the STG-3G,6-3 1G, 6-3lG* and 6-3 1G” basis sets. The major contributions arise from the FC term. The magnitude of the SD contributions is very small and near independent of the size of the basis set. The magnitude of the orbital contributions OR (=OD+OP) decreases as the size of the basis set increases. The FC term slightly overestimates both the individual and the interaction substituent effects for basis sets larger than the STO-3G one. For this basis such effects are underestimated.
1. Introduction The vicinal proton-proton coupling constant 3JH~ is the most useful coupling encountered in *HNMR spectroscopy. The widespread application of this coupling to stereochemistry rests on its strong dependence upon the dihedral angle 4 between the coupled protons. The second important factor that determines the magnitude of the 3JHHcoupling is the effect of substituents attached to the HCCH fragment. An extended Karplus equation including the effect upon 3Jm.,of both main factors, angle @and substituent electronegativity, has been proposed in part 1 of this series [ 11. This equation is based on a substituent effect model and takes into account the effect upon 3JHHof interactions between substituents. In the particular case of the vi&al couplings to the methyl groups the interaction between geminal substituents gives substantial contributions to 3JHHwhich are proportional to the product of relative electronegativities of substituents [ 21. The development of accurate equations describing the angular dependence of ‘JHn proves to be a cumbersome process that needs to be based on theoret-
ical calculations for ethane derivatives. The results obtained from the analysis of the calculated values may be used then as a working hypothesis during the process of empirical parameterization of equations for 3JnH. The theory and methods of calculation of J couplings have been reviewed critically by Kowalewski [ 3 1, The semiempirical methods of calculation of J couplings INDO/FPT [4,5] and EHT/SOS [6,7 ] reproduce qualitatively a host of observed trends in the 3JHHcoupling due to substituents and stereochemicaleffects. Both economical methods have been used commonly to calculate the Fermi contribution JFc to 3JHH in ethane derivatives and large molecules. On the contrary, the expensive ab initio calculations of 3JHHare scarce and, to our knowledge, no studies of the angular dependence of 3JHHin ethane derivatives have been previously presented. Therefore, we have carried out some preliminary calculations of this kind in order to analyze the performance of the ab initio methods for calculating3JHH couplings at different levels of approximation. The results of this work are being used by us to select the most appropriate kinds of ab initio approaches to be
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
253
Volume 206,number 1,2,3,4
applied in order to develop an accurate equation for 3JHHbased, in part, upon reliable ab initio results for a large series of ethane derivatives. In this Letter, we report the results provided by an ab initio study of 3JHHfor the parent molecule of ethane, the monosubstituted derivative fluoroethane, and the geminal disubstituted derivative difluoroethane. The calculations have been carried out at the Hartree-Fock level of approximation using the STO-3G, 6-31G, 6-3lG* and 6-3lG** basis sets. The four contributionsJm (MN = FC, SD, OP, and OD) to the total couplingJro have been computed: Fermicontact ( JFc), spin dipolar (JsD ), orbital paramagnetic (Jop ) and orbital diamagnetic ( PD). For each of these contributions the angular dependence and substituent effects have been analyzed according to a substituent effect model.
2. Methods and calculations The angular dependence of the 3JHHcouplings is represented in the substituent effect model as a truncated Fourier series in the torsion angle $ of the form 3Jr.n.r(~)=CotC, cosdtCz cos@tC, +S, sin @tSa sin 245,
cos3@ (1)
which reduces to the Karplus equation 3Jr.,H(d)=COtC, cos+tC2cos2$,
254
H (+)S3
--!. -, I
L-J52 @
'
\t \ 51(t)
sL(-)
Fig. 1. Numbering for the position of substituents with respect to the coupled protons.
eq. ( 1) for CH2FCH3 may be expressed by the difference mr1n =KF’ n -Ko n>
(2)
(3)
where the KH ( =K;SO) are the Fourier coefficients for ethane. The interaction effect 6CFFZ (I 6C;T”) between the two geminal substituents upon the Cz’F*coefficient in eq. ( 1) for CHF2CH3is given by the deviation from additivity 8CFlF’ n = C:F* - (C; t AC; t AC?) .
(4)
In the case of the symmetrical molecule CHF&Ha the S, coefficients are equal to zero. Accordingto the above definitions, the KFv coefficient in eq. ( 1) for a disubstituted ethane with substituents X and Y in positions i and j, respectively, fulfis the equation Kx’ ” YI= p n + mxin + M> + SK>vi _
in the case of the ethane molecule if the term in cos 3$ neglected ( C3x 0). The molecular symmetry implies that S1= S, = 0 for ethane. The dependence of the 3JHHcouplings upon the substituents is embodied into the coefficients K, (C, and S, ) in eq. ( 1) . The formulation of equations accounting for the substituent effects requires the use of a notation that specifies the nature and position (see fig. 1) of substituents. Such a notation will be used in this section but hereinafter the superscripts relative to substituents will be omitted since these can be easily inferred for the’moleculesstudied here. The simplified notation is indicated in parentheses after the complete one. The individual effect AK:’ ( = @“) of a substituent F in position 1 upon the KE’coefficient in
is
30April1993
CHEMICAL PHYSICS LETTERS
(5)
The eqs. (3) to (5) can be rewritten for the ‘JoHH, ‘Jg$ and ‘J$$ couplings besides for the corre-
sponding Fourier coefftcients. The 3JHn ( =jr”) couplings can be expressed as a combination of four contributions J”“, JTo=JFCtJsDt~DtJoP,
(6)
Likewise the coefficients co, Go and 6K;f” can be expressed as a combination of the respective contributions KY, AK? and SKyN. The eqs. (3) to (5 ) can be rewritten for each of the MN contributions to the couplings or to the Fourier coefficients besides for the total values of these parameters. The ab initio calculations for the molecules CH3CH3,CH2FCH3,and CHF,CH3 were carried out at the SCF level [ 8-101 with the SYSMO (System Modena) program using the EOM (equation of mo-
30April 1993
CHEMICALPHYSICSLETTERS
Volume 206, number 1,2,3,4
tion) [ 111 method at the random phase approximation (RPA) [ 121. Three kinds of molecular geometries were used (i) experimental geometries, (ii ) optimized geometries at the 6-3lG* level, and (iii) standard geometries with tetrahedral bond angles and constant bond lengths (rcc= 1.54, rcH= 1.09 and
rc-= 1.36 A). The 3JuHcouplings depend upon the bond lengths and bond angles within the HCCH fragment (local geometry). Therefore, experimental couplings are compared to results for experimental and 6-31G* geometries while angular dependence is studied using a rigid rotor model. Both staggeredand eclipsed conformations were considered when using standard geometries providing values of 3JHHfor angles Q of O”, +60”, f 120”, and 180”. From these, the six K, coefficients in eq. ( 1) were calculated by Fourier inversion.
3. Results and discussion Angular dependence for ethane. The observed vicinal couplings to methyl groups are average couplings. The calculated contributions JMN to the average coupling in ethane are entered in table 1. The terms OP and OD have been added together to get the orbital term OR (only the sum OP + OD is invariant to the choice of origin for the electromagnetic vector potential [ 18] ) . Comparison of SCF results obtained by us for different basis sets (rows 2
to 5) shows that: (1) the FC term gives the major contribution and its magnitude depends unsystematically upon the size of the used basis set, (2) the OR term gives a contribution important in principle, but its magnitude decreases as the size of the basis set increases, and ( 3) the SD contribution is unimportant and close to 0.1 Hz, independently of the used basis set. The calculated SCF contributions to the FC term JFc given in table 1 are larger than the experimental value Jm = 8.02 Hz for ethane [ 131. On the other hand, Laaksonen et al. [ 19,201 found that the SCF values are reduced in magnitude by including correlation and that the correlation contribution CI to JFc is of importance. The primitive Gaussian basis set in this study was 9s5p for carbon and 4s for hydrogen contracted to C: 4s2p/I-I:2s (double zeta). Finite perturbation calculations at the unrestricted Hartree-Fock (UHF) and configuration interaction (CI) levels of approximation were carried out. The UHF contribution to JFc of 10.5 reduces to an UHF+CI one of 7.0 which is 1.0 Hz smaller than Jm of ethane. According to the results reported by Galasso (row 7 in table 1) [ I 7 1, this difference cannot be attributed to the negligible contribution calculated for the noncontact terms. This author calculated the four contributions JMN for an experimental staggered conformation of ethane using the EOM method with the 6-31G” basis set. The EOM formalism is more economical than CHF-CI
Table 1 Contributions JMN (to the vicinal couplings in CH,CH3), AJMN(to the substituent effect in CH,FCH,), and 8JMN(to the effect of interaction between substitucnts in CHFaCHs) calculated for the indicated methods Method
exp. a’ SCF(STG-3G) ‘) SCF(6-31G) b, SCF(6-3lG*) b, SCF(6-3lG#) b’
AJm
Jm
&F
TO
FC
SD
OR
TO
FC
OR
TO
FC
8.02 6.94 10.87 9.05 9.19
8.21 11.87 9.80 9.70
0.08 0.09 0.07 0.07
- 1.35 - 1.09 -0.82 -0.58
-1.02 -0.34 -1.28 -1.33 -1.29
-0.54 -1.45 -1.41 -1.38
0.19 0.16 0.07 0.08
- 1.46 -1.01 -1.86 - 1.64 - 1.66
-0.96 - 1.84 - 1.63 - 1.65
-1.07
-1.15
0.07
-1.54
-1.52
SCF(6-31Gh) c,
9.26
9.75
0.07
-0.56
EOM *) INDO/FPT ‘i
6.50
4.56 8.97
0.08
-0.14 -0.80
-0.80
I) Ref. [ 131. ‘) Optimized 6-3lG* geometry. cr Experimental structures taken from ref. [ 141 for ethane, [ 15] for fluoroethane and [ 161 for difluoroethane. The bond angles HCC and HCH for dlfluoroethane were taken from the optimized 6-3lG* geometry. d, Ref. 1171.
255
Volume206,number 1,2,3,4
30 April 1993
CHEMICALPHYSICSLETTERS
-cPRX _ 0.6 Hz. When correlation is taken into account (tables 1 and 2) the importance of the OR term is further reduced. (4) The FC term gives the major contributions to the calculated couplings.The C$ contribution is the largest one and near coincides with the averagevalue JFC ( = C$ - Cgc) . The Ctc values are smaller than Crc ones x 3 Hz (STO-3G and 6-31G) and 2 Hz (6-3lG* and 6-3lG”). Both the Crc and C!c coefficients increase going from STO-3G minimal to 63 1G split valence basis set and decrease going from 6-31G to 6-31G* polarization basis set. On the other hand, near the same results are obtained for the 63 lG* and 6-31G” basis sets. The addition of a single Gaussian p-type function to each hydrogen (to get 6-3lG** from 6-31G*) has, therefore, a very small effect upon the calculated values for Czc and C!c. The Cy” coefficient is close to -0.8 Hz except for the STO-3G basis set. The empirical values given in table 3 for C, and C, have been obtained by us fitting to a generalized Karplus equation a large set of 3JHHvalues measured for different molecules.The CT0 coefficient explains the well known difference between the 3JHH(4) values for trans and cis orientations (J( ISO’)J( 0’) = 2CT”) which, according to our estimation, amounts to 2.4? 0.8 Hz. The Laaksonen calculations give values of - 1.4 (UHF) and - 1.1 Hz (UHF+ CI) for CT”in good agreement with the empirical value of - 1.2f 0.4 Hz. Our SCF results for Cyc are in reasonable agreement with this empirical data, However, our values for the total contribution
procedures. The EOM values by Galasso are listed in table 2 together with the SCF values by us and the corresponding differences CI giving the correlation contributions. For the FC term the CI contribution is of similar importance to that calculated by Laaksonen (in parentheses in table 2). Probably, both the EOM and the UHF+CI calculations overestimate the negative correlation contribution [ 191 givinglow values of JTOfor ethane (6.5 Hz the EOM method). The contributions Cy” to the Fourier coefficients calculated for ethane with standard geometries are entered in table 3 for the four used basis sets. Comparison of the SCF results for different basis sets indicates that: ( 1) The coefficients Cy are unimportant. Their absolute values are smaller than 0.1 Hz for the FC term and than 0.02 for the remaining terms. (2) The SD contributions CE”, (n=O, 1, 2), are of little importance. All of them are close to 0.1 Hz independently of the used basis set. (3) The OD and OP contributions to the OR term are important in principle. The Cz” coefficients are near independent of the used basis set (CtD x-C$)~Z--~.~ Hz, C$‘DxO.l Hz). On the contrary, the magnitude of the CZp coefficients increases with the size of the basis set being C8” x C$“. For a given n the signs of CfD and C$’ are different and the sum Cz” of both of these decreases as the size of the basis set increases. For the 6-3lG** basis set the OR contributions reduce to CgRx
Table 2 Contributions JMN($) to the coupling constants in staggeredethane obtained from calculations at the SCF and EOM levels of theory‘) MN
SCF b, FC (FC) ‘) OD OP SD To exp.
Jy
JMN(600)
5.33 (6.1) -0.92 0.60 0.10 5.1I
CI c’ -2.04 (-2.7) 0.01 0.11 0.00 -1.92
EOM d’
SCF b,
CI c,
EOM d’
3.29
19.05 (19.4) - 3.05 1.99 0.02 18.01
-5.94 (-5.3) 0.00 1.05 0.01 -4.88
13.11 (14.1) -3.05 3.04 0.03 13.13 16.2(S)
(3.4) -0.91 0.71 0.10 3.19 3.9(S)
‘) Experimental structure taken from ref. [ 2 11. b, This work. c) Difference between the EOM and SCF values. d, Ref. [ 171. ‘) Ref. [ 191.
256
180”)
Volume 206, number 1,2,3,4 Table 3 Calculated Fourier coefficients Cy Basis set
in ethane, eq. ( 1), for the indicated basis sets JK
Jrn P
CT
exp. ” STO-3G 6-31G 6-31G’ 6-31G” INDO/FPT UHF b, UHFtCI b,
8.02 6.70 10.42 8.37 8.71
-1.2(4) -0.35 0.35 -0.10 -0.05
Basis set
JD CF
STO-3G 6-31G 6-31G’ 6-31G” Basis set
0.08 0.10
0.08 0.08
STO-3G 6-31G 6.31G* 6-31G” ‘) Ref.
CF 7.0(4) 5.26 8.22 7.39 7.36
CP
0.26 0.46 0.74 1.02
Cf”
0.07 0.01 -0.05 -0.06
7.89 11.36 9.28 9.17 8.38 10.8 6.9
CT”
CT”
CF
-1.65 -0.77 -0.86 -0.77 -2.82 -1.4 -1.1
5.08 8.07 7.24 7.22 7.43 7.4 6.1
0.07 0.02 -0.05 -0.06 0.00
CP”
CFR
CpR
PR C$ 0.06 0.12 0.14 0.14
CY 0.12 0.09 0.09 0.09
Cs” 0.00 0.00 0.00 0.00
w - 1.27 - 1.03 -0.78 -0.54
1.24 1.oo 0.62 0.58
0.06 0.05 0.06 0.06
0.01 0.00 0.00 0.00
PD
JOP Cfj-
30 April 1993
CHEMICAL PHYSICS LETTERS
Cpp
CP’
CP
w
-0.35 -0.59 -0.98 -1.02
-0.03 -0.04 -0.03 - 0.04
0.00 -0.01 -0.01 -0.01
-
CP” 1.53 1.49 1.53 1.57
1.60 1.59 1.60 I .60
CP
CYD
0.09 0.09 0.09 0.09
0.01 0.01 0.01 0.01
[ 141. b, Ref. [ 181.
CT0 are too small due mainly to the positive contribution of CpR. The INDO/FPT value for C:” of -2.8 Hz is too large. The difference CT0 - CT0 is equal to J( 90 ’) . The calculations by Laaksonen give differences CFCg” of 3.4 (UHF) and 0.8 (UHF+ CI). The second is in good agreement with the empirical data of 1.O? 0.4 Hz while the UHF value is too large. Our SCF values for the 6-31G’and 6-31G” basis sets are close to 2 Hz. On the other hand, the 6-31G basis set provides a value of 3.3 Hz close to the UHF one. The total contribution CT” is close to Cg” but CT0 is smaller than C!c due mainly to the negative contribution of CcR. In consequence, the differences CP-CZ” (1.3 at the 6-3lG” level) are smaller than the corresponding differences CF - CTc and in better agreement with the empirical data. The INDO/FPT difference of 1.0 Hz is satisfactory.
Individual substituent eficts. The calculated individual effects AJMNof a substituent F in fluoroethane appear in table 1 for the FC and OR terms. The magnitude of the SD contribution AJsD,not included in this table, is smaller than 0.02 Hz. The FC term gives the major contribution. Excepting at the STO-3G level, the magnitude of AJFc is near independent of the basis set ( - 1.4 Hz for 6-3lG* geometries and - 1.15 Hz for experimental geometries at the 6-31G*+level) and larger than the experimental value ( - 1.0 Hz). On the other hand, the small magnitude of the OR contribution JoR decreases as the size of the basis set increases, except when comparing 6-31G’and 6-31G” results. The contributions AKFN to the Fourier coefflcients calculated for fluoroethane using standard geometries are entered in table 4. The ACf;” (except ACFc) and ACSyD contributions, not included in this
257
Volume206,number 1,2,3,4
CHEMICALPHYSICSLETTERS
30April 1993
Table4 CalculatedFouriercoeflicientsAK? in fluoroethane for the indicated basis sets Basisset
hKT” n
AKx n
ACp
ACT0
ACS”
AGo
ASTo
ASF
AC$
ACT
STO-3G 6-31G
-0.61 - 1.57
-0.35
-0.57
-0.06
-0.11
0.80
-0.81
-0.46
-0.55
6-31G* 6-31G*
- 1.60 - 1.56
-0.30 -0.34 -0.30
-1.49 - 1.50 - 1.50
-0.13 -0.09
-0.08 -0.11
2.46 2.24
-1.74 -1.68
-0.40 -0.37
- 1.47 - 1.47
-0.09
-0.08
2.24
-1.65 -0.96
-0.34 -0.41
- 1.47 -0.97
- 0.08 0.00
INDO/FPT Basisset
AQR ACgR
STO-3G 6-31G 6-3lG’ 6-3lG”
AC?’
ACtc z ACcc z -@S:” .
ASF
-0.06
-0.10
0.78
-0.12 - 0.09
-0.07 -0.10
2.45 2.25
-0.08 -0.48
2.25 1.61
ACpr’ 0.11 0.11 0.11 0.11
0.10
-0.01
-0.01
0.21
0.11
-0.02
-0.01
0.19
0.08 0.08
0.05 0.05
-0.12 -0.11
-0.07 -0.06
0.19 0.19
(7)
ASF
AG=
0.17
Interaction substituent e&ts. The calculated interaction effects We between two geminal F substituents appear in table 1. The magnitude of the SD and OR contributions, not included in this table, is smaller than 0.03 Hz. Like in the case of the individual substituent effect AJMN,excepting the STO3G basis set, the magnitude of the interaction substituent effect SJFc is near independent of the basis set ( - 1.7 for 6-31G’geometries and - 1.5 for experimental geometries at the 6-31G** level) and 258
ACpp
0.20
table, are smaller than 0.02 Hz in magnitude. For the orbital terms OD, OP, and OR, only the ACFN and ACY” contributions are given in table 1. The magnitude of the remaining orbital contributions ACF, ASY and ASY”, is smaller than 0.04 Hz. Among the FC contributions, the less important one are near independent of the basis set: AC:e x -0.4 Hz, A@ x-O.1 Hz, and ASgcx - 0.1 Hz. The main FC contributions scarcely depend upon the basis set (excepting the STO-3Gone): ACgcz - 1.7 Hz, AC;‘x - 1.5 Hz, and AS:” x2.3 Hz. The magnitude of these contributions is smaller at the STO-3G level than at higher levels. The values calculated using the INDO/FPT method for the main FC contributions are smaller in magnitude than those calculated at the 6-31GbClevel but show the same trend,
AC?
tiD
WP ACR
ACT
slightly larger than the experimental value ( - 1.5 Hz). The contributions SJFC to the Fourier coefficients calculated for 1,l-difluoroethane using standard geometries are given in table 5. The magnitude of the FC contributions scarcely depends upon the basis set @x&Wing the STO-3G one): 6Cgcc - 1.2 Hz, 2 w-O.3 Hz, 6C:C=C;Ca0.1 Hz. As in the case of individual effects ACfcc,the values calculated for interaction effects SC$c using the INDO/FPT method are smaller in magnitude than those calculated at the 6-31G” level but show the same trend, i.e. the main contribution is SCgc.
4. Conclusions The main conclusions of a detailed analysis of the results obtained in this work at the SCF level using different basis sets are: (1) The calculated Jr0 and JFc values for the symmetrical moleculesof ethane and difluoroethane fit wellthe Karplus relation (2). For the molecule of fluoroethane the term S, sin 24 in eq. ( 1) is also of importance. (2) The FC term gives the major contributions in ethane overestimating the average coupling. The OD contributions are near independent of the used basis set and the magnitude of the OP contributions in-
Volume 206, number I ,2,3,4
30 April 1993
CHEMICALPHYSICSLETTERS
Table 5 Calculated Fourier coefficients SKY in difluoroethane for the indicated basis sets Basisset
STO-3G 6-31G 6-3lG” 6-31GP INDO/FPT
6CFC
8Crn C$
CP
C$
CP
C;c
C:c
CF”
CF
-0.56 -1.36 -1.19 -1.22
-0.04 0.10 0.09 0.07
-0.17 -0.40 -0.31 -0.32
0.04 0.15 0.13 0.12
-0.56 -1.38 -1.20 -1.22 -0.52
-0.04 0.12 0.10 0.09 0.02
-0.17 -0.42 -0.32 -0.34 -0.02
0.04 0.15 0.13 0.12 0.00
creases as the size of the basis increases. The sum of both terms OR decreases at the size of the basis increases being further reduced when correlation is taken into account. The SD contributions are unimportant and near independent of the basis set. (3) The agreement for the substituent effects between our SCF calculations of the FC term at the 63 1G and higher levels and the experimental data may be considered satisfactory. The individual substituent effect in fluoroethane and the interaction substituent effect in difluoroethane are slightly overestimated. On the other hand the STO-3G basis underestimates both effects but provides analogous trends to larger basis sets. (4) The development
of empirical
equations
for
3Jr.,Hmay be based, in part, upon ab initio results at
the SCF level of approximation for the FC term. The STO-3G basis may be used, together with semiempirical methods, for extensive calculations of ethane derivatives trying to find general trends. Then, larger basis sets may be used to get more quantitative results for selected molecules.
Acknowledgement This work was supported in part by the Direction General de Investigation Cientifica y Tecnica of Spain (Proyecto PS88-0014).
References [ 1] E. Diez, J. San-Fabian, I. Guilleme, C. Altona and L.A. Donders, Mol. Phys. 68 (1989) 49. [2] J. Guilleme, J. San-Fabian, E. Diez, F. Bermejo and A. Esteban, Mol. Phys. 68 (1989) 65. [ 31 J. Kowalewski,Ann. Rept. NMR Spectry. 12 (1982) 81. [4] J.A. Pople, J.W. McIver and N.J. Ostlund, J. Chem. Phys. 49 (1968) 2960. [ 51J.A. Pople, D.L. Beveridgeand P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [6] R. Hoffman, J. Chem. Phys. 39 (1963) 1397. [7] J.A. Pople and D.P. Santry, Mol. Phys. 8 (1964) 1. [ 81 P. Lazzemttiand R. Zanasi,J. Chem. Phys. 77 ( 1982) 2448. [9] P. Lazzeretti, Intern. J. Quantum. Chem. 15 (1979) 181. [lo] P. Lazzeretti, J. Chem. Phys. 71 (1979) 2514. [ll]C.V. McCurdy Jr., T.N. Rex&o, D.L. Yaeger and V. McKay, Methods of electron structure theory, Vol. 3, eds. H.F. Schaefer III (Plenum Press, New York, 1977) p. 339. [ 121J. Oddershede, Advan. Quantum Chem. 11 (1978) 275. [ 131C. Altona, J.H. Ippel, A.J.A.WcstraHoclczema,C. Erkelens, M. Groesbeek and L.A. Donders, Magn. Reson. Chem. 27 ( 1989) 564. [ 14] E. Hirota, Y. Endo, S.Saito and J.L. Duncan, J. Mol.Spectry. 89 (1981) 285. [ 15 ] M. Hayashi,M. Fujitake,T. Inagusaand S. Miyazaki,J. Mol. Stmct. 216 (1990) 9. [ 161B. Beagley,M.O. Jones and N. Houldsworth, J. Mol. Struct. 62 (1980) 105. [17] V. Galasso, J. Chem.Phys. 82 (1985) 899. [18] W.S. Lee and J.M. Schulman, J. Chem. Phys. 70 (1979) 1530. [ 19] A. Laaksonen,J. Kowalewskiand P. Siegbabn,Chem. Phys. Letters 69 (1980) 109. [20] A. Laaksonen and J. Kowalewski,J. Am. Chem. Sot. 103 (1981) 5277. [21] DE. Shaw, D.W. Lepard and H.L. Welsh, J. Chem. Phys.
42 (1965) 3736.
259
30 April 1993
CHEMICALPHYSICS LETTERS
Vicinal proton-proton coupling constants. Basis set dependence in SCF ab initio calculations Jestis San-Fabian, Joaquin Guilleme, Ernest0 Diez Departamento a’eQuimica Fisica Apkada, Facultadde Ciencim C-2, Universidaddudnoma
deMadrid, 28049 Madrid, Spain
Paolo Lazzeretti, Massimo Malagoli and Riccardo Zanasi Dipartimento di Chimica, Universikidi Modena, Via Campi 183,411OOModena. Italy
Received 8 January 1993
An SCF ab initio study of the angular dependence and substituent effects upon the vicinal coupling constants has been carried out for the molecules U-I&H,, CHZFCHaand CHFQ-&. The four contributions to ‘.&,, (JFc, jSD, pD and p) have been computed using the STG-3G,6-3 1G, 6-3lG* and 6-3 1G” basis sets. The major contributions arise from the FC term. The magnitude of the SD contributions is very small and near independent of the size of the basis set. The magnitude of the orbital contributions OR (=OD+OP) decreases as the size of the basis set increases. The FC term slightly overestimates both the individual and the interaction substituent effects for basis sets larger than the STO-3G one. For this basis such effects are underestimated.
1. Introduction The vicinal proton-proton coupling constant 3JH~ is the most useful coupling encountered in *HNMR spectroscopy. The widespread application of this coupling to stereochemistry rests on its strong dependence upon the dihedral angle 4 between the coupled protons. The second important factor that determines the magnitude of the 3JHHcoupling is the effect of substituents attached to the HCCH fragment. An extended Karplus equation including the effect upon 3Jm.,of both main factors, angle @and substituent electronegativity, has been proposed in part 1 of this series [ 11. This equation is based on a substituent effect model and takes into account the effect upon 3JHHof interactions between substituents. In the particular case of the vi&al couplings to the methyl groups the interaction between geminal substituents gives substantial contributions to 3JHHwhich are proportional to the product of relative electronegativities of substituents [ 21. The development of accurate equations describing the angular dependence of ‘JHn proves to be a cumbersome process that needs to be based on theoret-
ical calculations for ethane derivatives. The results obtained from the analysis of the calculated values may be used then as a working hypothesis during the process of empirical parameterization of equations for 3JnH. The theory and methods of calculation of J couplings have been reviewed critically by Kowalewski [ 3 1, The semiempirical methods of calculation of J couplings INDO/FPT [4,5] and EHT/SOS [6,7 ] reproduce qualitatively a host of observed trends in the 3JHHcoupling due to substituents and stereochemicaleffects. Both economical methods have been used commonly to calculate the Fermi contribution JFc to 3JHH in ethane derivatives and large molecules. On the contrary, the expensive ab initio calculations of 3JHHare scarce and, to our knowledge, no studies of the angular dependence of 3JHHin ethane derivatives have been previously presented. Therefore, we have carried out some preliminary calculations of this kind in order to analyze the performance of the ab initio methods for calculating3JHH couplings at different levels of approximation. The results of this work are being used by us to select the most appropriate kinds of ab initio approaches to be
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
253
Volume 206,number 1,2,3,4
applied in order to develop an accurate equation for 3JHHbased, in part, upon reliable ab initio results for a large series of ethane derivatives. In this Letter, we report the results provided by an ab initio study of 3JHHfor the parent molecule of ethane, the monosubstituted derivative fluoroethane, and the geminal disubstituted derivative difluoroethane. The calculations have been carried out at the Hartree-Fock level of approximation using the STO-3G, 6-31G, 6-3lG* and 6-3lG** basis sets. The four contributionsJm (MN = FC, SD, OP, and OD) to the total couplingJro have been computed: Fermicontact ( JFc), spin dipolar (JsD ), orbital paramagnetic (Jop ) and orbital diamagnetic ( PD). For each of these contributions the angular dependence and substituent effects have been analyzed according to a substituent effect model.
2. Methods and calculations The angular dependence of the 3JHHcouplings is represented in the substituent effect model as a truncated Fourier series in the torsion angle $ of the form 3Jr.n.r(~)=CotC, cosdtCz cos@tC, +S, sin @tSa sin 245,
cos3@ (1)
which reduces to the Karplus equation 3Jr.,H(d)=COtC, cos+tC2cos2$,
254
H (+)S3
--!. -, I
L-J52 @
'
\t \ 51(t)
sL(-)
Fig. 1. Numbering for the position of substituents with respect to the coupled protons.
eq. ( 1) for CH2FCH3 may be expressed by the difference mr1n =KF’ n -Ko n>
(2)
(3)
where the KH ( =K;SO) are the Fourier coefficients for ethane. The interaction effect 6CFFZ (I 6C;T”) between the two geminal substituents upon the Cz’F*coefficient in eq. ( 1) for CHF2CH3is given by the deviation from additivity 8CFlF’ n = C:F* - (C; t AC; t AC?) .
(4)
In the case of the symmetrical molecule CHF&Ha the S, coefficients are equal to zero. Accordingto the above definitions, the KFv coefficient in eq. ( 1) for a disubstituted ethane with substituents X and Y in positions i and j, respectively, fulfis the equation Kx’ ” YI= p n + mxin + M> + SK>vi _
in the case of the ethane molecule if the term in cos 3$ neglected ( C3x 0). The molecular symmetry implies that S1= S, = 0 for ethane. The dependence of the 3JHHcouplings upon the substituents is embodied into the coefficients K, (C, and S, ) in eq. ( 1) . The formulation of equations accounting for the substituent effects requires the use of a notation that specifies the nature and position (see fig. 1) of substituents. Such a notation will be used in this section but hereinafter the superscripts relative to substituents will be omitted since these can be easily inferred for the’moleculesstudied here. The simplified notation is indicated in parentheses after the complete one. The individual effect AK:’ ( = @“) of a substituent F in position 1 upon the KE’coefficient in
is
30April1993
CHEMICAL PHYSICS LETTERS
(5)
The eqs. (3) to (5) can be rewritten for the ‘JoHH, ‘Jg$ and ‘J$$ couplings besides for the corre-
sponding Fourier coefftcients. The 3JHn ( =jr”) couplings can be expressed as a combination of four contributions J”“, JTo=JFCtJsDt~DtJoP,
(6)
Likewise the coefficients co, Go and 6K;f” can be expressed as a combination of the respective contributions KY, AK? and SKyN. The eqs. (3) to (5 ) can be rewritten for each of the MN contributions to the couplings or to the Fourier coefficients besides for the total values of these parameters. The ab initio calculations for the molecules CH3CH3,CH2FCH3,and CHF,CH3 were carried out at the SCF level [ 8-101 with the SYSMO (System Modena) program using the EOM (equation of mo-
30April 1993
CHEMICALPHYSICSLETTERS
Volume 206, number 1,2,3,4
tion) [ 111 method at the random phase approximation (RPA) [ 121. Three kinds of molecular geometries were used (i) experimental geometries, (ii ) optimized geometries at the 6-3lG* level, and (iii) standard geometries with tetrahedral bond angles and constant bond lengths (rcc= 1.54, rcH= 1.09 and
rc-= 1.36 A). The 3JuHcouplings depend upon the bond lengths and bond angles within the HCCH fragment (local geometry). Therefore, experimental couplings are compared to results for experimental and 6-31G* geometries while angular dependence is studied using a rigid rotor model. Both staggeredand eclipsed conformations were considered when using standard geometries providing values of 3JHHfor angles Q of O”, +60”, f 120”, and 180”. From these, the six K, coefficients in eq. ( 1) were calculated by Fourier inversion.
3. Results and discussion Angular dependence for ethane. The observed vicinal couplings to methyl groups are average couplings. The calculated contributions JMN to the average coupling in ethane are entered in table 1. The terms OP and OD have been added together to get the orbital term OR (only the sum OP + OD is invariant to the choice of origin for the electromagnetic vector potential [ 18] ) . Comparison of SCF results obtained by us for different basis sets (rows 2
to 5) shows that: (1) the FC term gives the major contribution and its magnitude depends unsystematically upon the size of the used basis set, (2) the OR term gives a contribution important in principle, but its magnitude decreases as the size of the basis set increases, and ( 3) the SD contribution is unimportant and close to 0.1 Hz, independently of the used basis set. The calculated SCF contributions to the FC term JFc given in table 1 are larger than the experimental value Jm = 8.02 Hz for ethane [ 131. On the other hand, Laaksonen et al. [ 19,201 found that the SCF values are reduced in magnitude by including correlation and that the correlation contribution CI to JFc is of importance. The primitive Gaussian basis set in this study was 9s5p for carbon and 4s for hydrogen contracted to C: 4s2p/I-I:2s (double zeta). Finite perturbation calculations at the unrestricted Hartree-Fock (UHF) and configuration interaction (CI) levels of approximation were carried out. The UHF contribution to JFc of 10.5 reduces to an UHF+CI one of 7.0 which is 1.0 Hz smaller than Jm of ethane. According to the results reported by Galasso (row 7 in table 1) [ I 7 1, this difference cannot be attributed to the negligible contribution calculated for the noncontact terms. This author calculated the four contributions JMN for an experimental staggered conformation of ethane using the EOM method with the 6-31G” basis set. The EOM formalism is more economical than CHF-CI
Table 1 Contributions JMN (to the vicinal couplings in CH,CH3), AJMN(to the substituent effect in CH,FCH,), and 8JMN(to the effect of interaction between substitucnts in CHFaCHs) calculated for the indicated methods Method
exp. a’ SCF(STG-3G) ‘) SCF(6-31G) b, SCF(6-3lG*) b, SCF(6-3lG#) b’
AJm
Jm
&F
TO
FC
SD
OR
TO
FC
OR
TO
FC
8.02 6.94 10.87 9.05 9.19
8.21 11.87 9.80 9.70
0.08 0.09 0.07 0.07
- 1.35 - 1.09 -0.82 -0.58
-1.02 -0.34 -1.28 -1.33 -1.29
-0.54 -1.45 -1.41 -1.38
0.19 0.16 0.07 0.08
- 1.46 -1.01 -1.86 - 1.64 - 1.66
-0.96 - 1.84 - 1.63 - 1.65
-1.07
-1.15
0.07
-1.54
-1.52
SCF(6-31Gh) c,
9.26
9.75
0.07
-0.56
EOM *) INDO/FPT ‘i
6.50
4.56 8.97
0.08
-0.14 -0.80
-0.80
I) Ref. [ 131. ‘) Optimized 6-3lG* geometry. cr Experimental structures taken from ref. [ 141 for ethane, [ 15] for fluoroethane and [ 161 for difluoroethane. The bond angles HCC and HCH for dlfluoroethane were taken from the optimized 6-3lG* geometry. d, Ref. 1171.
255
Volume206,number 1,2,3,4
30 April 1993
CHEMICALPHYSICSLETTERS
-cPRX _ 0.6 Hz. When correlation is taken into account (tables 1 and 2) the importance of the OR term is further reduced. (4) The FC term gives the major contributions to the calculated couplings.The C$ contribution is the largest one and near coincides with the averagevalue JFC ( = C$ - Cgc) . The Ctc values are smaller than Crc ones x 3 Hz (STO-3G and 6-31G) and 2 Hz (6-3lG* and 6-3lG”). Both the Crc and C!c coefficients increase going from STO-3G minimal to 63 1G split valence basis set and decrease going from 6-31G to 6-31G* polarization basis set. On the other hand, near the same results are obtained for the 63 lG* and 6-31G” basis sets. The addition of a single Gaussian p-type function to each hydrogen (to get 6-3lG** from 6-31G*) has, therefore, a very small effect upon the calculated values for Czc and C!c. The Cy” coefficient is close to -0.8 Hz except for the STO-3G basis set. The empirical values given in table 3 for C, and C, have been obtained by us fitting to a generalized Karplus equation a large set of 3JHHvalues measured for different molecules.The CT0 coefficient explains the well known difference between the 3JHH(4) values for trans and cis orientations (J( ISO’)J( 0’) = 2CT”) which, according to our estimation, amounts to 2.4? 0.8 Hz. The Laaksonen calculations give values of - 1.4 (UHF) and - 1.1 Hz (UHF+ CI) for CT”in good agreement with the empirical value of - 1.2f 0.4 Hz. Our SCF results for Cyc are in reasonable agreement with this empirical data, However, our values for the total contribution
procedures. The EOM values by Galasso are listed in table 2 together with the SCF values by us and the corresponding differences CI giving the correlation contributions. For the FC term the CI contribution is of similar importance to that calculated by Laaksonen (in parentheses in table 2). Probably, both the EOM and the UHF+CI calculations overestimate the negative correlation contribution [ 191 givinglow values of JTOfor ethane (6.5 Hz the EOM method). The contributions Cy” to the Fourier coefficients calculated for ethane with standard geometries are entered in table 3 for the four used basis sets. Comparison of the SCF results for different basis sets indicates that: ( 1) The coefficients Cy are unimportant. Their absolute values are smaller than 0.1 Hz for the FC term and than 0.02 for the remaining terms. (2) The SD contributions CE”, (n=O, 1, 2), are of little importance. All of them are close to 0.1 Hz independently of the used basis set. (3) The OD and OP contributions to the OR term are important in principle. The Cz” coefficients are near independent of the used basis set (CtD x-C$)~Z--~.~ Hz, C$‘DxO.l Hz). On the contrary, the magnitude of the CZp coefficients increases with the size of the basis set being C8” x C$“. For a given n the signs of CfD and C$’ are different and the sum Cz” of both of these decreases as the size of the basis set increases. For the 6-3lG** basis set the OR contributions reduce to CgRx
Table 2 Contributions JMN($) to the coupling constants in staggeredethane obtained from calculations at the SCF and EOM levels of theory‘) MN
SCF b, FC (FC) ‘) OD OP SD To exp.
Jy
JMN(600)
5.33 (6.1) -0.92 0.60 0.10 5.1I
CI c’ -2.04 (-2.7) 0.01 0.11 0.00 -1.92
EOM d’
SCF b,
CI c,
EOM d’
3.29
19.05 (19.4) - 3.05 1.99 0.02 18.01
-5.94 (-5.3) 0.00 1.05 0.01 -4.88
13.11 (14.1) -3.05 3.04 0.03 13.13 16.2(S)
(3.4) -0.91 0.71 0.10 3.19 3.9(S)
‘) Experimental structure taken from ref. [ 2 11. b, This work. c) Difference between the EOM and SCF values. d, Ref. [ 171. ‘) Ref. [ 191.
256
180”)
Volume 206, number 1,2,3,4 Table 3 Calculated Fourier coefficients Cy Basis set
in ethane, eq. ( 1), for the indicated basis sets JK
Jrn P
CT
exp. ” STO-3G 6-31G 6-31G’ 6-31G” INDO/FPT UHF b, UHFtCI b,
8.02 6.70 10.42 8.37 8.71
-1.2(4) -0.35 0.35 -0.10 -0.05
Basis set
JD CF
STO-3G 6-31G 6-31G’ 6-31G” Basis set
0.08 0.10
0.08 0.08
STO-3G 6-31G 6.31G* 6-31G” ‘) Ref.
CF 7.0(4) 5.26 8.22 7.39 7.36
CP
0.26 0.46 0.74 1.02
Cf”
0.07 0.01 -0.05 -0.06
7.89 11.36 9.28 9.17 8.38 10.8 6.9
CT”
CT”
CF
-1.65 -0.77 -0.86 -0.77 -2.82 -1.4 -1.1
5.08 8.07 7.24 7.22 7.43 7.4 6.1
0.07 0.02 -0.05 -0.06 0.00
CP”
CFR
CpR
PR C$ 0.06 0.12 0.14 0.14
CY 0.12 0.09 0.09 0.09
Cs” 0.00 0.00 0.00 0.00
w - 1.27 - 1.03 -0.78 -0.54
1.24 1.oo 0.62 0.58
0.06 0.05 0.06 0.06
0.01 0.00 0.00 0.00
PD
JOP Cfj-
30 April 1993
CHEMICAL PHYSICS LETTERS
Cpp
CP’
CP
w
-0.35 -0.59 -0.98 -1.02
-0.03 -0.04 -0.03 - 0.04
0.00 -0.01 -0.01 -0.01
-
CP” 1.53 1.49 1.53 1.57
1.60 1.59 1.60 I .60
CP
CYD
0.09 0.09 0.09 0.09
0.01 0.01 0.01 0.01
[ 141. b, Ref. [ 181.
CT0 are too small due mainly to the positive contribution of CpR. The INDO/FPT value for C:” of -2.8 Hz is too large. The difference CT0 - CT0 is equal to J( 90 ’) . The calculations by Laaksonen give differences CFCg” of 3.4 (UHF) and 0.8 (UHF+ CI). The second is in good agreement with the empirical data of 1.O? 0.4 Hz while the UHF value is too large. Our SCF values for the 6-31G’and 6-31G” basis sets are close to 2 Hz. On the other hand, the 6-31G basis set provides a value of 3.3 Hz close to the UHF one. The total contribution CT” is close to Cg” but CT0 is smaller than C!c due mainly to the negative contribution of CcR. In consequence, the differences CP-CZ” (1.3 at the 6-3lG” level) are smaller than the corresponding differences CF - CTc and in better agreement with the empirical data. The INDO/FPT difference of 1.0 Hz is satisfactory.
Individual substituent eficts. The calculated individual effects AJMNof a substituent F in fluoroethane appear in table 1 for the FC and OR terms. The magnitude of the SD contribution AJsD,not included in this table, is smaller than 0.02 Hz. The FC term gives the major contribution. Excepting at the STO-3G level, the magnitude of AJFc is near independent of the basis set ( - 1.4 Hz for 6-3lG* geometries and - 1.15 Hz for experimental geometries at the 6-31G*+level) and larger than the experimental value ( - 1.0 Hz). On the other hand, the small magnitude of the OR contribution JoR decreases as the size of the basis set increases, except when comparing 6-31G’and 6-31G” results. The contributions AKFN to the Fourier coefflcients calculated for fluoroethane using standard geometries are entered in table 4. The ACf;” (except ACFc) and ACSyD contributions, not included in this
257
Volume206,number 1,2,3,4
CHEMICALPHYSICSLETTERS
30April 1993
Table4 CalculatedFouriercoeflicientsAK? in fluoroethane for the indicated basis sets Basisset
hKT” n
AKx n
ACp
ACT0
ACS”
AGo
ASTo
ASF
AC$
ACT
STO-3G 6-31G
-0.61 - 1.57
-0.35
-0.57
-0.06
-0.11
0.80
-0.81
-0.46
-0.55
6-31G* 6-31G*
- 1.60 - 1.56
-0.30 -0.34 -0.30
-1.49 - 1.50 - 1.50
-0.13 -0.09
-0.08 -0.11
2.46 2.24
-1.74 -1.68
-0.40 -0.37
- 1.47 - 1.47
-0.09
-0.08
2.24
-1.65 -0.96
-0.34 -0.41
- 1.47 -0.97
- 0.08 0.00
INDO/FPT Basisset
AQR ACgR
STO-3G 6-31G 6-3lG’ 6-3lG”
AC?’
ACtc z ACcc z -@S:” .
ASF
-0.06
-0.10
0.78
-0.12 - 0.09
-0.07 -0.10
2.45 2.25
-0.08 -0.48
2.25 1.61
ACpr’ 0.11 0.11 0.11 0.11
0.10
-0.01
-0.01
0.21
0.11
-0.02
-0.01
0.19
0.08 0.08
0.05 0.05
-0.12 -0.11
-0.07 -0.06
0.19 0.19
(7)
ASF
AG=
0.17
Interaction substituent e&ts. The calculated interaction effects We between two geminal F substituents appear in table 1. The magnitude of the SD and OR contributions, not included in this table, is smaller than 0.03 Hz. Like in the case of the individual substituent effect AJMN,excepting the STO3G basis set, the magnitude of the interaction substituent effect SJFc is near independent of the basis set ( - 1.7 for 6-31G’geometries and - 1.5 for experimental geometries at the 6-31G** level) and 258
ACpp
0.20
table, are smaller than 0.02 Hz in magnitude. For the orbital terms OD, OP, and OR, only the ACFN and ACY” contributions are given in table 1. The magnitude of the remaining orbital contributions ACF, ASY and ASY”, is smaller than 0.04 Hz. Among the FC contributions, the less important one are near independent of the basis set: AC:e x -0.4 Hz, A@ x-O.1 Hz, and ASgcx - 0.1 Hz. The main FC contributions scarcely depend upon the basis set (excepting the STO-3Gone): ACgcz - 1.7 Hz, AC;‘x - 1.5 Hz, and AS:” x2.3 Hz. The magnitude of these contributions is smaller at the STO-3G level than at higher levels. The values calculated using the INDO/FPT method for the main FC contributions are smaller in magnitude than those calculated at the 6-31GbClevel but show the same trend,
AC?
tiD
WP ACR
ACT
slightly larger than the experimental value ( - 1.5 Hz). The contributions SJFC to the Fourier coefficients calculated for 1,l-difluoroethane using standard geometries are given in table 5. The magnitude of the FC contributions scarcely depends upon the basis set @x&Wing the STO-3G one): 6Cgcc - 1.2 Hz, 2 w-O.3 Hz, 6C:C=C;Ca0.1 Hz. As in the case of individual effects ACfcc,the values calculated for interaction effects SC$c using the INDO/FPT method are smaller in magnitude than those calculated at the 6-31G” level but show the same trend, i.e. the main contribution is SCgc.
4. Conclusions The main conclusions of a detailed analysis of the results obtained in this work at the SCF level using different basis sets are: (1) The calculated Jr0 and JFc values for the symmetrical moleculesof ethane and difluoroethane fit wellthe Karplus relation (2). For the molecule of fluoroethane the term S, sin 24 in eq. ( 1) is also of importance. (2) The FC term gives the major contributions in ethane overestimating the average coupling. The OD contributions are near independent of the used basis set and the magnitude of the OP contributions in-
Volume 206, number I ,2,3,4
30 April 1993
CHEMICALPHYSICSLETTERS
Table 5 Calculated Fourier coefficients SKY in difluoroethane for the indicated basis sets Basisset
STO-3G 6-31G 6-3lG” 6-31GP INDO/FPT
6CFC
8Crn C$
CP
C$
CP
C;c
C:c
CF”
CF
-0.56 -1.36 -1.19 -1.22
-0.04 0.10 0.09 0.07
-0.17 -0.40 -0.31 -0.32
0.04 0.15 0.13 0.12
-0.56 -1.38 -1.20 -1.22 -0.52
-0.04 0.12 0.10 0.09 0.02
-0.17 -0.42 -0.32 -0.34 -0.02
0.04 0.15 0.13 0.12 0.00
creases as the size of the basis increases. The sum of both terms OR decreases at the size of the basis increases being further reduced when correlation is taken into account. The SD contributions are unimportant and near independent of the basis set. (3) The agreement for the substituent effects between our SCF calculations of the FC term at the 63 1G and higher levels and the experimental data may be considered satisfactory. The individual substituent effect in fluoroethane and the interaction substituent effect in difluoroethane are slightly overestimated. On the other hand the STO-3G basis underestimates both effects but provides analogous trends to larger basis sets. (4) The development
of empirical
equations
for
3Jr.,Hmay be based, in part, upon ab initio results at
the SCF level of approximation for the FC term. The STO-3G basis may be used, together with semiempirical methods, for extensive calculations of ethane derivatives trying to find general trends. Then, larger basis sets may be used to get more quantitative results for selected molecules.
Acknowledgement This work was supported in part by the Direction General de Investigation Cientifica y Tecnica of Spain (Proyecto PS88-0014).
References [ 1] E. Diez, J. San-Fabian, I. Guilleme, C. Altona and L.A. Donders, Mol. Phys. 68 (1989) 49. [2] J. Guilleme, J. San-Fabian, E. Diez, F. Bermejo and A. Esteban, Mol. Phys. 68 (1989) 65. [ 31 J. Kowalewski,Ann. Rept. NMR Spectry. 12 (1982) 81. [4] J.A. Pople, J.W. McIver and N.J. Ostlund, J. Chem. Phys. 49 (1968) 2960. [ 51J.A. Pople, D.L. Beveridgeand P.A. Dobosh, J. Chem. Phys. 47 (1967) 2026. [6] R. Hoffman, J. Chem. Phys. 39 (1963) 1397. [7] J.A. Pople and D.P. Santry, Mol. Phys. 8 (1964) 1. [ 81 P. Lazzemttiand R. Zanasi,J. Chem. Phys. 77 ( 1982) 2448. [9] P. Lazzeretti, Intern. J. Quantum. Chem. 15 (1979) 181. [lo] P. Lazzeretti, J. Chem. Phys. 71 (1979) 2514. [ll]C.V. McCurdy Jr., T.N. Rex&o, D.L. Yaeger and V. McKay, Methods of electron structure theory, Vol. 3, eds. H.F. Schaefer III (Plenum Press, New York, 1977) p. 339. [ 121J. Oddershede, Advan. Quantum Chem. 11 (1978) 275. [ 131C. Altona, J.H. Ippel, A.J.A.WcstraHoclczema,C. Erkelens, M. Groesbeek and L.A. Donders, Magn. Reson. Chem. 27 ( 1989) 564. [ 14] E. Hirota, Y. Endo, S.Saito and J.L. Duncan, J. Mol.Spectry. 89 (1981) 285. [ 15 ] M. Hayashi,M. Fujitake,T. Inagusaand S. Miyazaki,J. Mol. Stmct. 216 (1990) 9. [ 161B. Beagley,M.O. Jones and N. Houldsworth, J. Mol. Struct. 62 (1980) 105. [17] V. Galasso, J. Chem.Phys. 82 (1985) 899. [18] W.S. Lee and J.M. Schulman, J. Chem. Phys. 70 (1979) 1530. [ 19] A. Laaksonen,J. Kowalewskiand P. Siegbabn,Chem. Phys. Letters 69 (1980) 109. [20] A. Laaksonen and J. Kowalewski,J. Am. Chem. Sot. 103 (1981) 5277. [21] DE. Shaw, D.W. Lepard and H.L. Welsh, J. Chem. Phys.
42 (1965) 3736.
259