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Investigation of the counterpoise contribution to the variation of nuclear magnetic shielding constants with intermolecular interaction
Volume
io3, number2
CHEMICAL PHYSICS LETTERS
23 December 1983
INVESTIGATION OF THE COUNTERPOISE CONTRIBUTiON TO THE VAXIATiON OF NUCLEAR MAGNETIC SHIELDING CONSTANTS WITH INTERMOLECULAR INTERACTION S. FERCHIOU and C. GIESSNER-PRETTRE Institut de Bioiogie Physic+Orimique, Laboratoire de Biochimie i%!orique Associe’ au CNRS, I3 Rue Pierre et Marie Chic. 75005 Paris, France Received 1 September 1983;in fiial form 30 September 1983
The contribution of basisset extension to the calculated chemiulkift variation due to inr~rmolecular interaction is investigated for water and methane dimers and for the water-proton system. The results show that for protons the error due to the fiite size of the basis set is small enough to be neglected; however. it can be of measurable magnitude for the nuclei of non-hydrogen atoms. Therefore, the counterpoise correction should be taken into account. The variation of this correction with the basis set is e.wmined in the case of the water dimer.
1. Introduction
2. Method
The quantum-mechanical calculation of intermolecular interaction energies [l-4] and of the variation of physico-chemical quantities [5,6] with intermolecular interaction are subject, for the basis sets which can currently be used in this type of calculation, to errors due to basis-set extension if the counterpoise correction is not taken into account [7 81 i However, this correction has been neglected in previous studies of the variation of magnetic shielding constants with intermolecular interaction [g-18]. Since the number of non-empirical calculations of such variations is increasing rapidly, it appears not without interest to examine the contribution of basisset extension to the calculated chemical-shift variation in order to determine its magnitude for the different nuclei of rhe various systems. In the present study, we have evaluated the counterpoise effect on the variation of the magnetic shielding constants of the different nuclei of the water and methane molecules upon formation of dirners, treated as supermolecules [ 191.
For a nucleus N of a molecule A interacting with a molecule B, the counterpoise correction is given by the equation As?
= uL%n - uNX ,
(1)
where oNA is the magnetic shielding constant of nucleus N in the isolated molecule A and u”NpAu is the magnetic shielding constant of the same nucleus N of molecule A calculated with the total basis set of the AB complex. in a recent study [13] we have proposed, within the framework of ab initio SCF methods, a decomposition scheme for the calculated variation of nuclear magnetic shielding constants with intermolecular interaction which shows that A6 can be written as a sum of three contributions. The chemical&rift variation of nucleus N-due to the interaction of molecules A and B takes the form A6B =A6bBiA6r;iA6;+e,
(2)
where A@&, As& and &A” are the geometric, polarization and charge-transfer plus exchange contribu-
tions, respectively. If the counterpoise correction is taken into account, 156
0 009-2614/83/$03.00 0 Elsevier Science publishers B.V. (North-Holland Physics Publishing Division)
Volume103. number2
CHEMICAL
PHYSICS
the expression giving the total chemical-shift variation is then AS’N = AskB -I- Ask i- AG$+e
-
A&T
_
(3)
- AS3 is analogous to the correThe sum As$* sponding term AEL, obtained after an interaction energy decomposition taking into account the counterpoise correction 141. So eq. (3) takes the form A&~=A6~B+A~;+A8;t*‘,
3. Results and discussion We see from the values reported in table 1 for the water dimer that A6q calculated for an intermolecular geometrical arrangement close to equilibrium depends strongly upon the nucleus considered as well as upon the basis set used for the computation_ The values obtained for the oxygen nuclei are larger by an order of magnitude than those calculated for the protons_ Moreover, for the hydrogens we find not only that A6q is in eve-v case smaller (in absolute value) than 0.1 ppm, but also that we have in most cases As’/As CIJ> 10 _Therefore, it appears that for this type of nucleus the counterpoise correction could be neglected in the calculation of chemical-shift variations. On the contrary, for oxygen this correction can be several ppm, even when the largest basis set is used, and is therefore of measurable magnitude _In the case of 02 (see fg. 1 for the atom numbering) in particular, we see that A6cP and A6’ have comparable values. For this non-hydrogen nucleus which participates
1983
Table 1 Values (calculated with different basis sets) of the counterpoise correction (~6=p), the charge-transfer plus ewhange mntribution (ASct+e). the total chemiukhift variation (A6) and its corrected value (A&‘) for the water dimera) (in ppm) Atom b)
01
d)
(4)
where AS:* is the corrected charge-transfer ~1~s exchange contribution. The calculations have been carried out using nonempirical methods and gaussian basis functions. The elements of the magnetic shielding tensors are calculated using the self-consistent perturbation procedure developed by Ditchfield [20] for gauge invariant atomic orbitals (GIAO). Four different basis sets have been used: A: a minimal basis set currently in use in our laboratory [2 l] ; B: a split-valence basis set defmed in ref_ [21], C: the 4-31G basis set [22]; and D: the 9sSp basis set proposed by Dunning 13-31.
23 December
LETTERS
Basis set C)
A6cp
A&ct*e
A B C D
-0.37 -0.62
3.69 3.15 1 A4 -094 -0.48 -0.31 -059 -0.74
097
-0.60
HI e)
A B C D
0.01 -o_lo -0.06 -0.05
HI’
A B C D
-0.01 000 -0.01 0.02
02
A B C D
1 .I8 0.83 096
A B c D
H2
~6 697 7.36 7.36 5 -32 -1-75 -115 -2.x -1.45
Ali’
792 6.39 796 5.94 -1.76 -1.65 -221 -‘_-IO
053 0.70 0.63 055
05-l 0.70 0.64 053
-056
0.70 -2.49 -330 -394
3-09 036 1.30 -1.l6
191 -O.-l7 03-l -0.60
-01)6 0.05 0.01 01)l
-0.1 1 0.04 -0D7 0.00
330 -0.30 -0.42 -0.48
-0.N -0.35 -0.43 -0-49
026 0.44 029 0.1 7
a) R(O...0) = 3.9 and e = 150=‘. bJ See tig. 1 for the atom numbering. C) See texf for the definition of the basis sets. d) In the monomer, the v;ilue of 00 calculated with basis sets A-D is 384.7,3838,328.4 and 324.4 ppm,respectiwly. e) In the monomer, the value of oH ulculated with basis sets A-D is 32.6, 32.4. 32.8 and 32.4 ppm, respecthcly.
directly in the intermolecular hydrogen bond, the counterpoise correction must definitely be taken into account in the calculation of A6 if one wants a meaningful result _ If we consider the variation of the counterpoise correction, calculated with the extended basis set B, with the intermolecular distance, we see from fig_2 that it is a short-range effect since it is negligible for intermolecular distances larger than 4-5 X. The curves for the protons are not reported since A6 =IJremains
negligible for these nuclei in the entire range of intermolecular distances studied. For 01, we see that AScP becomes important only 157
CHEMICAL
Volume 103, nbmber 2
HIS
l------&&~H, ..
\
01
‘H’. -
2,
(a)
Hz
‘1
4
(6) Fig. 1. Atom numbering zmd geometrical arrangement in the water and methane dimen.
for very short intermolecular distances (close to the value of 2B A) and that the curves representing the variation of ASct* and A6ct+e’ have the same qualitative behavior_ For 02, the results reported in fq_ 2b clearly show that, for intermolecular distances from 35 to 5 A, the counterpoise effect is as equilibrium
23 December 1983
PH’YSICS LElTERS
large as the charge-transfer plus exchange contribution. Therefore, the qualitative as well as quantitative behavior of the uncorrected AclSct*_term and of the corrected value are completely different. For this range of intermolecular distance, the counterpoise effect is dominant since it decreases considerably the magnitude (ii absolute value) of the charge-transfer plus exchange contribution, however, this term remains the leading contribution to A&’ at the equilibrium intermolecular distance. Reported in fig_ 3 are the variations of ASet*, A&Cp, AS d*’ and AS’ for the equilibrium intermolecular distance of the water dimer as a function of the angle 0 defmed in fig. 1. For 01, the-value of A6 cP remains approximately constant (AacP = 090 ppm), and therefore the curves representing ASct* and A6ct+e’ are parallel_ For 02, the curves of fig. 3b show that the counterpoise correction is very sensitive to intermolecular orientation since we have AVP = -13 ppm for 0 = 130” and A6=P = +I 2 ppm for 13= 180’. However, since the absolute value of AScP is smaller than &ct+e,
the variation
of the corrected
and uncorrected charge-transfer plus exchange contributions are similar. The values for the methane dimer, which are re-
A6
P-r-
A6
P-Pm.
01
02
Fig. 2. Variation h-ablated with basis tit B) of A6cP, ASct*, A&d* &d A6’ for the oxygen nuclei of the water-dimer as a function bf the CL.0 di&noe (0 = liO”). ..I counterpoke correction AbcP, - - - - - char&-transfer plk exchange contribution AI$‘e, -- - corn&ted charge-transfer plti ex&ange contribution A6&*‘, Lcorrected total cheniicalrhift vaktion 66’.
158
Volume 103, number 2
CHEMICAL
PHYSICS
23 December
LE-JXERS
1983
tances smaller than the equilibrium value (3 5 4.0 A 1241). The counterpoise correction is a short-range effect like the charge-transfer contribution. Thii susests that this term might be important for the nuclei of systems in which one of the entities is a cation since, in such cases, AE,, (3) [25] and Agct* [ 131 are particularly large. But results obtained (using basis set B) for water interacting with a proton show that the ratios A6/A6cP and A6 ct*e/A6cp are much larger than for the water dimer, as can be seen from table 3 _ Moreover, in the case of a cation for which AscP is not identically equal to zero (7J_i for example), the value of A6cP is, for the equilibrium distance. equal to zero at the precision of the iterative SCF procedure_ In conclusion, the results of the present study
show that the counterpoise correction to calculated
lb)
(0)
Fig. 3. Variation (calculated with basis set B) of A6cp, ASct+e, Agct+e’ and A6’ for the oxygen nuclei of the water dimer as a function of the angle @ (O...O distance = 2.8 A) (for legend see fig. 2).
ported in table 2, show clearly that for the carbon nucleus as well as for the protons the counterpoise contribution is negligible even at intermolecular dis-
Table 2 Values (calculated with basis set Ba)) of the counterpoise correction (AGP), the charge-transfer plus exchange contribution (A&ct+e), the total chemicalshift variation (A&) and its corrected value (AZ’) for the methane diier (in ppm)
d (CL)
Atom%
A6 cp
A&ct+e
A6
4
a) b) c) d)
cc) Hl d) H2 C Hl H2
-0.16 0.01 0.00 0.00 0.01 0.00
-10.62 -0-44 -0.09 -0.89 -0134 0.00
See text for defiition of the basis set. See fii. I for the atom numbering_ aC = 219.4 ppm in the monomer. cc = 33.2 ppm in the monomer.
definitely be taken into account even when a relatively extended basis set is used.
Table 3 Values (calculated with basis set Ba)) oDrrection (AfcP). the charge-transfer the total chemical-shift variaticn (A6) (As’) for the aater-proton systemb) d(O...H+) (A)
Atom
1
0 H
2
A6 cP
of the counterpoise contribution (~6ct), and its corrected value (in ppm)
4gct
46
45’
2.26 0.14
-23.72 -0.80
-23,9 -5.60
-2555 -5 -71
0 H
1x7 0.02
-86.48 -2.58
-77.45 12.49
-79.32 151
3
0 H
127 -0.01
-74 -08 -1.78
-68.26 -2.69
-6953 -2.68
4
0 H
0.02 0.00
-18.09 -039
-14.35 -092
-14.37 -092
6
0 H
-0.01 0.00
A&’
(X) 3
chemical-shift variations due to intermolecular interactions can be safely neglected in many cases, but that for the nuclei of non-hydrogen atoms which are directly engaged in a hydrogen bond this term should
-9.13 -0.25 -0.15
-897 -0.26 -0.15
-0.76 -0.01 0.00
-0.76 -0.02 0.00
-0.01 0.00
2.40 -037
2.41 -0.27
a) See text for definition of the basis set. b)The proton is located on the bisector of the HOH angle.
159
Volume 103. number 2
CHEMICAL PHYSICS LETTERS
Although the method used for the calculation of AGcP gives art upper limit to this quantity [3 81, we can reasonably expect that the information obtained
frpm such calctiations is qualitatively meaningful. This assumption gains support from the comparable magnitude of the vahxs obtained for the counterpoise correction to intermolecular interaction energies obtained from the procedure used in the present study and from one which introduces only the virtual molecular orbitals of the second molecule [26].
23 December 1983
[JO] Th. Wellcr.W. Meiier, HJ. KohIer. H. lischka and R. HBBer, Chem. Phys. Letters 98 (1983) 541_ [Ill J.S.Tse,Chem.Phys.Letters92(1982) 144. [I 21 C. hlcMichael Rohlfmg, L.C. ABen and R Ditchfield, Chem. Phys. Letters 86 (I 982) 380. [ 13) C. Giessner-Prettre and S. Ferchiou, J. Magn. Reson., to
be published. [14] hf. Jaszunski and AJ. Sadlej, Chem. Phys. Letters 15 (1972)
41_
[IS] M. Jaszunski and A-l. SadIej. Theoret. Chim. Acta 30 (1973) 257. [16] R. Ditchtield. J. Chem. Phys. 65 (1976)
3123. R. Ditchtield and R-E. McKinney, Chem. Phys. 13 (1976) 187. [ 181 R. HBBer and H. Lischka, them. Phys. Letters 84 (I 981) 94. [19] A. Pullman in: Structure and conformations of nucleic acids and proteic and nucleic acid interactions, eds. M. Sundaralingam and S.T. Baa (University Park Press, Baltimore, 1975) p_ 457. ’ [20] R. Ditchfield, hlol. Phys. 27 (1974) 789_ [21] F. Ribas Prado and C. Giessner-F’rettre, J. Map. Reson. [17]
References [I] W.Kotbs,Theoret.Chim.ActaSJ (1979)219. 121 J.-P. Daudey. Intern. J. Quantum Chem. 8 (1974) 29. i3] H. Bethod and A. Pullman,J. Comput. Chem. 2 (1981) 87. [4] N. Cresh, P. CIawxie and A. Pullman. Intern. J. Quantum Chem. 22 (1982) 199. [S] MD. Newton and N_R_Kestner, Chem. Phys. Letters 94 (1983) 198. [6] JM. Leclercq. M. AJlavena and Y. Bouteiller. J. Chem. Phys. 78 (1983) 4606. [7] SF. Boys and F. Bernardi, Mot Phys 19 (1970) 553. [S] J.-P. Daudey, P. CJaverieand J.-P. Mahieu, Intern. J.
Quantum Chem. 8 (1974) 1_ 191 K. Jackowski, W-T. Raynes and AJ. Sadlej, Chem. Phys. Letters 54 (1978) 128.
-160
47 (1982) 103. R. Ditchtield, WJ. Hehre and J.A. Pople, J. Chem. Phys. 54 (1971) 724. 1231 J-R. Dunning and H-Thorn. J.Chem. Phys. 53 (1970) 7. [24] W. Kdbs, G. Ranghino, E. Clementi and 0. Novaro, Intern. J. Quantum Chem. 17 (1980) 429. [25] H. Berthod and A. Pullman, Chem. Phys. Letters 70
[22]
(1980) 434. [26]
A. hfeunnier, B. Levy and G. Berthier. Theoret.
Acta 29 (1973) 49.
Chim.
io3, number2
CHEMICAL PHYSICS LETTERS
23 December 1983
INVESTIGATION OF THE COUNTERPOISE CONTRIBUTiON TO THE VAXIATiON OF NUCLEAR MAGNETIC SHIELDING CONSTANTS WITH INTERMOLECULAR INTERACTION S. FERCHIOU and C. GIESSNER-PRETTRE Institut de Bioiogie Physic+Orimique, Laboratoire de Biochimie i%!orique Associe’ au CNRS, I3 Rue Pierre et Marie Chic. 75005 Paris, France Received 1 September 1983;in fiial form 30 September 1983
The contribution of basisset extension to the calculated chemiulkift variation due to inr~rmolecular interaction is investigated for water and methane dimers and for the water-proton system. The results show that for protons the error due to the fiite size of the basis set is small enough to be neglected; however. it can be of measurable magnitude for the nuclei of non-hydrogen atoms. Therefore, the counterpoise correction should be taken into account. The variation of this correction with the basis set is e.wmined in the case of the water dimer.
1. Introduction
2. Method
The quantum-mechanical calculation of intermolecular interaction energies [l-4] and of the variation of physico-chemical quantities [5,6] with intermolecular interaction are subject, for the basis sets which can currently be used in this type of calculation, to errors due to basis-set extension if the counterpoise correction is not taken into account [7 81 i However, this correction has been neglected in previous studies of the variation of magnetic shielding constants with intermolecular interaction [g-18]. Since the number of non-empirical calculations of such variations is increasing rapidly, it appears not without interest to examine the contribution of basisset extension to the calculated chemical-shift variation in order to determine its magnitude for the different nuclei of rhe various systems. In the present study, we have evaluated the counterpoise effect on the variation of the magnetic shielding constants of the different nuclei of the water and methane molecules upon formation of dirners, treated as supermolecules [ 191.
For a nucleus N of a molecule A interacting with a molecule B, the counterpoise correction is given by the equation As?
= uL%n - uNX ,
(1)
where oNA is the magnetic shielding constant of nucleus N in the isolated molecule A and u”NpAu is the magnetic shielding constant of the same nucleus N of molecule A calculated with the total basis set of the AB complex. in a recent study [13] we have proposed, within the framework of ab initio SCF methods, a decomposition scheme for the calculated variation of nuclear magnetic shielding constants with intermolecular interaction which shows that A6 can be written as a sum of three contributions. The chemical&rift variation of nucleus N-due to the interaction of molecules A and B takes the form A6B =A6bBiA6r;iA6;+e,
(2)
where A@&, As& and &A” are the geometric, polarization and charge-transfer plus exchange contribu-
tions, respectively. If the counterpoise correction is taken into account, 156
0 009-2614/83/$03.00 0 Elsevier Science publishers B.V. (North-Holland Physics Publishing Division)
Volume103. number2
CHEMICAL
PHYSICS
the expression giving the total chemical-shift variation is then AS’N = AskB -I- Ask i- AG$+e
-
A&T
_
(3)
- AS3 is analogous to the correThe sum As$* sponding term AEL, obtained after an interaction energy decomposition taking into account the counterpoise correction 141. So eq. (3) takes the form A&~=A6~B+A~;+A8;t*‘,
3. Results and discussion We see from the values reported in table 1 for the water dimer that A6q calculated for an intermolecular geometrical arrangement close to equilibrium depends strongly upon the nucleus considered as well as upon the basis set used for the computation_ The values obtained for the oxygen nuclei are larger by an order of magnitude than those calculated for the protons_ Moreover, for the hydrogens we find not only that A6q is in eve-v case smaller (in absolute value) than 0.1 ppm, but also that we have in most cases As’/As CIJ> 10 _Therefore, it appears that for this type of nucleus the counterpoise correction could be neglected in the calculation of chemical-shift variations. On the contrary, for oxygen this correction can be several ppm, even when the largest basis set is used, and is therefore of measurable magnitude _In the case of 02 (see fg. 1 for the atom numbering) in particular, we see that A6cP and A6’ have comparable values. For this non-hydrogen nucleus which participates
1983
Table 1 Values (calculated with different basis sets) of the counterpoise correction (~6=p), the charge-transfer plus ewhange mntribution (ASct+e). the total chemiukhift variation (A6) and its corrected value (A&‘) for the water dimera) (in ppm) Atom b)
01
d)
(4)
where AS:* is the corrected charge-transfer ~1~s exchange contribution. The calculations have been carried out using nonempirical methods and gaussian basis functions. The elements of the magnetic shielding tensors are calculated using the self-consistent perturbation procedure developed by Ditchfield [20] for gauge invariant atomic orbitals (GIAO). Four different basis sets have been used: A: a minimal basis set currently in use in our laboratory [2 l] ; B: a split-valence basis set defmed in ref_ [21], C: the 4-31G basis set [22]; and D: the 9sSp basis set proposed by Dunning 13-31.
23 December
LETTERS
Basis set C)
A6cp
A&ct*e
A B C D
-0.37 -0.62
3.69 3.15 1 A4 -094 -0.48 -0.31 -059 -0.74
097
-0.60
HI e)
A B C D
0.01 -o_lo -0.06 -0.05
HI’
A B C D
-0.01 000 -0.01 0.02
02
A B C D
1 .I8 0.83 096
A B c D
H2
~6 697 7.36 7.36 5 -32 -1-75 -115 -2.x -1.45
Ali’
792 6.39 796 5.94 -1.76 -1.65 -221 -‘_-IO
053 0.70 0.63 055
05-l 0.70 0.64 053
-056
0.70 -2.49 -330 -394
3-09 036 1.30 -1.l6
191 -O.-l7 03-l -0.60
-01)6 0.05 0.01 01)l
-0.1 1 0.04 -0D7 0.00
330 -0.30 -0.42 -0.48
-0.N -0.35 -0.43 -0-49
026 0.44 029 0.1 7
a) R(O...0) = 3.9 and e = 150=‘. bJ See tig. 1 for the atom numbering. C) See texf for the definition of the basis sets. d) In the monomer, the v;ilue of 00 calculated with basis sets A-D is 384.7,3838,328.4 and 324.4 ppm,respectiwly. e) In the monomer, the value of oH ulculated with basis sets A-D is 32.6, 32.4. 32.8 and 32.4 ppm, respecthcly.
directly in the intermolecular hydrogen bond, the counterpoise correction must definitely be taken into account in the calculation of A6 if one wants a meaningful result _ If we consider the variation of the counterpoise correction, calculated with the extended basis set B, with the intermolecular distance, we see from fig_2 that it is a short-range effect since it is negligible for intermolecular distances larger than 4-5 X. The curves for the protons are not reported since A6 =IJremains
negligible for these nuclei in the entire range of intermolecular distances studied. For 01, we see that AScP becomes important only 157
CHEMICAL
Volume 103, nbmber 2
HIS
l------&&~H, ..
\
01
‘H’. -
2,
(a)
Hz
‘1
4
(6) Fig. 1. Atom numbering zmd geometrical arrangement in the water and methane dimen.
for very short intermolecular distances (close to the value of 2B A) and that the curves representing the variation of ASct* and A6ct+e’ have the same qualitative behavior_ For 02, the results reported in fq_ 2b clearly show that, for intermolecular distances from 35 to 5 A, the counterpoise effect is as equilibrium
23 December 1983
PH’YSICS LElTERS
large as the charge-transfer plus exchange contribution. Therefore, the qualitative as well as quantitative behavior of the uncorrected AclSct*_term and of the corrected value are completely different. For this range of intermolecular distance, the counterpoise effect is dominant since it decreases considerably the magnitude (ii absolute value) of the charge-transfer plus exchange contribution, however, this term remains the leading contribution to A&’ at the equilibrium intermolecular distance. Reported in fig_ 3 are the variations of ASet*, A&Cp, AS d*’ and AS’ for the equilibrium intermolecular distance of the water dimer as a function of the angle 0 defmed in fig. 1. For 01, the-value of A6 cP remains approximately constant (AacP = 090 ppm), and therefore the curves representing ASct* and A6ct+e’ are parallel_ For 02, the curves of fig. 3b show that the counterpoise correction is very sensitive to intermolecular orientation since we have AVP = -13 ppm for 0 = 130” and A6=P = +I 2 ppm for 13= 180’. However, since the absolute value of AScP is smaller than &ct+e,
the variation
of the corrected
and uncorrected charge-transfer plus exchange contributions are similar. The values for the methane dimer, which are re-
A6
P-r-
A6
P-Pm.
01
02
Fig. 2. Variation h-ablated with basis tit B) of A6cP, ASct*, A&d* &d A6’ for the oxygen nuclei of the water-dimer as a function bf the CL.0 di&noe (0 = liO”). ..I counterpoke correction AbcP, - - - - - char&-transfer plk exchange contribution AI$‘e, -- - corn&ted charge-transfer plti ex&ange contribution A6&*‘, Lcorrected total cheniicalrhift vaktion 66’.
158
Volume 103, number 2
CHEMICAL
PHYSICS
23 December
LE-JXERS
1983
tances smaller than the equilibrium value (3 5 4.0 A 1241). The counterpoise correction is a short-range effect like the charge-transfer contribution. Thii susests that this term might be important for the nuclei of systems in which one of the entities is a cation since, in such cases, AE,, (3) [25] and Agct* [ 131 are particularly large. But results obtained (using basis set B) for water interacting with a proton show that the ratios A6/A6cP and A6 ct*e/A6cp are much larger than for the water dimer, as can be seen from table 3 _ Moreover, in the case of a cation for which AscP is not identically equal to zero (7J_i for example), the value of A6cP is, for the equilibrium distance. equal to zero at the precision of the iterative SCF procedure_ In conclusion, the results of the present study
show that the counterpoise correction to calculated
lb)
(0)
Fig. 3. Variation (calculated with basis set B) of A6cp, ASct+e, Agct+e’ and A6’ for the oxygen nuclei of the water dimer as a function of the angle @ (O...O distance = 2.8 A) (for legend see fig. 2).
ported in table 2, show clearly that for the carbon nucleus as well as for the protons the counterpoise contribution is negligible even at intermolecular dis-
Table 2 Values (calculated with basis set Ba)) of the counterpoise correction (AGP), the charge-transfer plus exchange contribution (A&ct+e), the total chemicalshift variation (A&) and its corrected value (AZ’) for the methane diier (in ppm)
d (CL)
Atom%
A6 cp
A&ct+e
A6
4
a) b) c) d)
cc) Hl d) H2 C Hl H2
-0.16 0.01 0.00 0.00 0.01 0.00
-10.62 -0-44 -0.09 -0.89 -0134 0.00
See text for defiition of the basis set. See fii. I for the atom numbering_ aC = 219.4 ppm in the monomer. cc = 33.2 ppm in the monomer.
definitely be taken into account even when a relatively extended basis set is used.
Table 3 Values (calculated with basis set Ba)) oDrrection (AfcP). the charge-transfer the total chemical-shift variaticn (A6) (As’) for the aater-proton systemb) d(O...H+) (A)
Atom
1
0 H
2
A6 cP
of the counterpoise contribution (~6ct), and its corrected value (in ppm)
4gct
46
45’
2.26 0.14
-23.72 -0.80
-23,9 -5.60
-2555 -5 -71
0 H
1x7 0.02
-86.48 -2.58
-77.45 12.49
-79.32 151
3
0 H
127 -0.01
-74 -08 -1.78
-68.26 -2.69
-6953 -2.68
4
0 H
0.02 0.00
-18.09 -039
-14.35 -092
-14.37 -092
6
0 H
-0.01 0.00
A&’
(X) 3
chemical-shift variations due to intermolecular interactions can be safely neglected in many cases, but that for the nuclei of non-hydrogen atoms which are directly engaged in a hydrogen bond this term should
-9.13 -0.25 -0.15
-897 -0.26 -0.15
-0.76 -0.01 0.00
-0.76 -0.02 0.00
-0.01 0.00
2.40 -037
2.41 -0.27
a) See text for definition of the basis set. b)The proton is located on the bisector of the HOH angle.
159
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CHEMICAL PHYSICS LETTERS
Although the method used for the calculation of AGcP gives art upper limit to this quantity [3 81, we can reasonably expect that the information obtained
frpm such calctiations is qualitatively meaningful. This assumption gains support from the comparable magnitude of the vahxs obtained for the counterpoise correction to intermolecular interaction energies obtained from the procedure used in the present study and from one which introduces only the virtual molecular orbitals of the second molecule [26].
23 December 1983
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