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A coupled Hartree-Fock study on nuclear magnetic shielding in (HF)2 and (H2O)2
CHEMICAL
Volume 84, number 1
A COUPLED IN (m)2
HARTREE-FOCK
STUDY
PHYSICS LETTERS
ON NUCLEAR
MAGNETIC
SHlELDlNG
AND (H20)2
Robert HoLLER and Hans LISCHKA Instarut fur Tfuxwet~ciw C’?zermeund Strahlenchemle. Recelvcd
15 November 1981
8 June 1981, III tiil
form 6
August
Umverstiat Wen, A-1090
Vzenna. Austna
1981
Coupled Hat-tree-Fock ulclllatlons on susceptibltles and nuclear magnetic shleldmg constants have been performed for (HI3 and (H20j2 The apphcatlon the completeness rektlon m choosing a “best gauge” is a valuable ald but vekf large basis sets must be used to come close to the Htiree-Fock hnut Intermolecular effects of mducfd magnetic fields on the shwzklmg tensor are discussed
of
I. Introduction
2. Computational
The present mvestlgatlons on (HF)2 and (H20)2 are a direct continuation of our previous calculations on diamagnetic susceptibllitles and nucIear magnetic shleldmg constants for first- [l] and second-row [2] hydrides. Agam, we are usmg the coupled HartreeFock method and try to come as close as possible to the Hartree-Fock limit. As the molecular systems treated m tlus work are rather extended in space, the determination of an appropriate gauge orlgm is much more involved here than for the monomers As cntena for the choice of the ongm, completeness relations have been used for the nuclear magnetic slueldmg tensor a[3,4] and the maxunizatlon of X for the susceptlbility tensor [S]. The gauge ongms obtamed m this way are hereafter called “best or:gms”. To our knowledge, for @f20)2 onIy two ab nutlo calculations exist [6,7] and for @IF)2 only one [8]. The GLAO techmque was used by DItchfield for b water dimer calculations [7] whereas uncoupled Hartree-Fock calculations have been performed by Sadlej and co-workers [6,8]. Moreover, the changes in the shielding tensors due to hydrogen-bond formatlon are interpreted by Ditchfield by a method smular to the Mull&en populatron analysis in contrast to this, we analyze the calculated shifts m a more global way.
We use the coupled Hartree-Fock technique as formulated by Llpscomb [9 J. Since the computational 01
._.-_-_- ---_-FZ WI
FI
HZ
_;
bl L___________
e
S
L_____
..-
F
______
____
H
_
_____
e
-_
_
p2 =
cl
1’ &2________ F?_______
f
5
\ HZ d)
Fig
1 Geometry and geometry parameters for @IF)2 and (HzO)z- (Hi%. (a) h==Rq~~ = 53 au,+& =RF~H~ = 1.733 au; (c) eqtirium structure (Phil) RF,H, = 1.708 au* RF2Hz = 1 705 au, RF,F~ = 5 348 au, L HlFlFz = 6”, L FlF2Hl = 123 2” (d) (H2012: Rq02 = 5.669 au, 0 = 30”, ROH = 1809 au, L HOH = 104 5”. ROH and L HOH are the nme
94
details
in both water molecules.
0 00%2614/81/OOW-Owo/$O2.75
0 1981
North-Holland
Volume 84. number 1
procedures are identical ‘0 those of our pr&ious work [I ,2 1, we refer to them for mor& details. Foray _@culations the following Huzinaga basis sets have-been chosen [IO,1 1] I-IOs6p contracted to (4;6 X l/2,4 X 1) for F and 0, respectively, and 5s contra&d to (2, 3 X 1) for H. These basissets have been augmented by diffuse s and p and by polarization functibns. More information about orbital exponents is-given in the tables together with the results. For the linear and equilibrium &ctures of (HFh, geometries were taken from refs. 112,131 and for (H20)2 from ref. [143. Geometries and geometry parameters are given m fii 1.
3. Results and discussion 3. I. The HF &mm
For the linear arrangement we have tested several basis sets. Table 1 shows that two sets of d functions on each F atom are required for a reasonable calculatron of <_ However, at least one further polarization
set is necessary in order to reduce the strong gauge dependence of e to a few pbm. Table 2 gives om resul!s fo! both the liriear and the equilibrium geometry obta&cd-&th our b_e.sti&is set (basis 4 in table I). The most interesting shielding tensor is the one for H1- the proton involved in the hydrogen bridge. The average shielding constant & decreases from 26.6 to 26.2 pGm when going from the linear to the bent eqtilibrium structure. Compared to the monomer & is decreased by 2.2 ppm in the dimer (equilibrium structure)_ Okn_inski and Sadlej [8] fmd in their uncoupled Hartree-Fock calculations -1.3 and -2.85 ppm, respectively. As pointed out by Ditchfield [7], changes in the anisotropy of e upon hydrogen-bond formation are larger than the sh&s of the average value of e. In the following we restricted ourselves to the linear geometry because it is easier to analyze. However. we lhink that the main conclusions are transferable to the nonlinear geometry of (HF)z and also with some restdctions to the Hz0 dimer. We define erel as the difference of edtier e mOnomeT_Simdarly to Ditchfield, we divide 6* into
TabIe I Perpend~cuIarnuclear shiekhng constants (ppm) for the HF dimer in the Imear arrangement. A comparison of dtierent baser setsa) Bans set
1
2
3
4
AddItional bass funtinsb)
Relative gauge origin=)
F
H
Owl
2d
1P
(O.O*O)
em2
-
-
@,O,f)
01
2d
O-E92
Id
IP 1P
@IF)1
2d
W=),
zu
(HF)L (HO2
lslp3d lslp3d
best origin
430.1 431.0 430.3
329.4 3649 332.8
8080 78.39 89.80
(O,OSO) (O,OJ) best origin
407.7 412 3 408.1
3835 4058 385.7
42.32 46.86 38.47
20.75 34.71 20.94
1P
(O,O,O)
IP
cw,u
best origin
397 8 404.0 398.4
391.5 394 3 392 0
29.12 36.02 23.61
20.77 30.86 20 91
(0,OP) (O.OJ) best ongin
397.6 395 -4 397.2
391.7 390.2 391.3
L8.17 20.39 15.46
18.44 22.18 i7.70
Zpld 2p
L.s.5 6S 1.87
a) A lOs6p (4,6 X 1/2,4X 1) basis set for F and a 5s (2.3 X 1) set for H was used throughout. b, Exponents for the additional funtions: 1dF (1.6),_2dF (1.6, O 15). 3dF (2.4.0.6.0.15), 19 (O-l), 1pF CO-06). 1pH (0.75) 2Ptf (1.6,0.4), 1dH (1.2). C) The gauge or&n is given in cartesian coordinates relative to the F atom of the pertaining HF mdeade. Only chaages atong the t axis arq c+sidered_ 95
two contributions (a,,* =aiel +&I). One of them (&) cornea from the currents which are induced by
Table 2
Results for the lmear and equiliinum geometr.,s of (HF)~ a)
OF1
Lmw
Equtlibrium
XX
397.2
397 0
YY
3v
397 2 483 1 0 0 425 9
395 5 482 3 82 78 4249
xx YY zz xz
391.3 391 3 4835 0
445.4 388 2 423 6 -29 6
ZX
0
-390
av
422 0
zz xz ZX
*FZ
=HI
eH2
xr .vY
15 46 15 46
ZZ
48
xz ZX av
0 0 26 60
xx YY zz rz ZX
17 70 17 70 45 47 0 2: 95
av x
.rcx YY
-24 -24 -20
ZZ
av
15 37 14 48 48 80 24 22 26 22
88
35 17 27 -28 -125 26
96 96 03
92 68 16 7
duced magnetic
92
-25 17 -23 88 -20 40 -0 30 -23 15
Component 1
II ;:*p
(ppm)arel
field of one molecule
=~&rr,er-(Imono~e.
a) for the linear mnf&Wation of (HF)z b)
aP3
60 13
-07 1.3
00 17
-09 15
-44 36
-19 38
-4.7 4.4
0.0 20
0.6 1.7
-0.1 24
-18 8.1
00 5.7
F2
=rel
al Monomer v;ilues a,,F = 481 8, oIF = 391 3. a,,H - 45
ht-
is connected to the small anrsotropy of x for HP (see e g. ref.1151). The parallel components of the shrelding constants m the drmer are well represented by the respective u:. Much larger ddferences, especrally for a:,, are found for the perpendrcular components In agreement wrth Drtchfield’s fmdmgs, we observe that the prominent part of the amsotropy change Au”,{ 1s brought about by the induced magnetic fields in the other molecule (compare_ Aa::= 5.7 ppm and A$ = 8.1 ppm)
Fl
OreI
contnbutes
tle to 0 of the nuclei on the other molecule. Tlus fact
Basis set 4 was used. The diagonal elements are gwen at the best orgm. the off&agonal ones at (O,O,O) AU values are in ppm Total energies HF monomer E = - 100 06553 au HF duner, Lear. E = -200 13588 au, equiliirmm stmcture: E = -200.13697 au
Table 3 Relatwe nudear sh=ldmg amstants
96
the external magnetrc fieId in the other molecule The other one (e&) comes from the changes of the electronic density due to the intermolecular interaction. These effects are discussed extensrvely in ref. 171. We compute =;I in the following way. We take one HF molecule and place magnetic test dipoles into those positions PI-P4 which represent the nuclei of the second HF molecule m the dirner. The srtuation is demonstrated m fig lb. For example, P4 takes the position of H,. For thrs arrangement the nuclear shielding constant2s apt (I = 1. 4) are calculated. areI 1s obtained simply by subtraction of aZ from ere,_ It should be mentioned at this point that our partitromng, although sirmlar to Ditchfield’s procedure, IS not equivalent to it. In our analysis we avoid the arbitrariness of basrs sets which is inherent rn ah populatron-type methods. Howeve;, we drd not attempt any further decomposrtron of urel and &I mto atomic contributions In table 3 the relatrve shrelding constants for the dimer are compared to the up1 values. The average values Cipl are all close to zero. Thrs means that the m-
419 1
0 -23 32
XZ
a)
15 November 1981
CHEMICAL PHYSICS LETI-ERS
Volume 84. number 1
aP1
26. OF = 19 89.
Hl
QIel
J’4
Hz erel
-2.2
&‘2
-04
02 -14 2.4
b, Pure1 = (01, - Ui)dimer --(u,, - u~)monomer.
0”:: 1.1
Volume 84, number 1
CFLEMICAL PHYSICS LETTERS
3.2. The H20 dmer For (H20)2 we performed only one calculation mth a basis set of comparable-quahty td basis 4 of HF. Results are collected in tables 4 and 5. For the decrease of the average tielding of the bridging proton we find -2 8 ppm (see table 5) -a value close to the one reported by Ditchfield 171. On the other hand, Sadlq and Jaszunsla [6] calculated a shift of only -1 ppm. We also computed the change of the shielding tensoraH between the water dimer and an isolated water molecule whch was III exactly the same postlon as in the dimer. As in the HF case, one finds that the changes in the indlvldual components of aHz are much
15 November I98L
Table 5 Relativeaverage &i&&g mmtants (ppm) r?&, = Zdimer -5 mommer fur (H&)2 a) Ref. [7j
This work
-01 OreI
-35
-02 Drd
0.9
-HI arel
-06
-Hz =re1
-30
-H3
Tel
7.7
-3.0
0.0
a) Monomer
values:
s1
0.8
= 329 1 ppm siiHt = 30 0
ppm
larger than the shift of the average values. Some disagreement between our and Dltchfield’s results is observed in the case of the oxygen atom. We obtain a much smaller change m Go2 than Ditchfield (0.8 ver-
4. Conclusions
sus 7 7 ppm).
Magnetic effects for hydrogen-bonded systems are certainly very difficult to treat in the coupled HartreeFock framework since very extended basis sets have to be used and since the effects one wants to compute are rather small. We find, in agreement with previous work of Ditchfield [7], that the aniso~ropy of the
Table 4 Results for (H20)2 a) X
uo1
xx YY zz XY xz YZ av xx
YY zz ZX
35 7.0 31s 7 -2.8 -3.6
aV
325.7
XZ
u”2
-29 81 -29 85 -27 92 0.0 -0 29 00 -29.19 304 3
xx
YY LZ XZ ZX
av
aH1
XY
YX XZ
zx YZ ZY av (IHf
XX
YY JZ
3369 304 6 348 1 -252 -28 9 3299
xx YY zz
XZ ZX
av GH3
x.x YY LZ XZ ZX
av
23 21 36 64 28 09 5_26 4.66 -3 32 -342 -8 40 -9.43 29.31 16.36 1694 48 -0 -2 27
28 94 43 19
41.38 2162 2656 -22.12 -6 58 29x5
elements are gwen at the best origins. the offdragonal ones at (O,O,O).AlI values are in ppm. Bass sets0, lOdp+lslp (0 08.0.05) + 3d(2 4.0 6.0.15); HI, H3. Ss+2p(I.6.0.4); Hz, Sti2p(1.6.0 4) + ld(1.6). Total energles- Hz0 monomer, E = -76 06233 au; Hz0 dimer, E = -152.13062 au.
a) The diagonal
nuclear
shielding
tensor is more sensitive to effects
of
intermolecularrntemtlons than the averagevalue. Acknowledgement The cakulatlons were performed on the CDC CYBER 73/74 computers of the University and the Techrucal University of Vienna_ We are grateful for a generous
supply of computer
time.
References [I] R. HBlkr and H. Lischka, Mol. Phys 41 (1980) 1017. 121 R. Hbtler and H. Lischka. Mol. Phys. 41 (1980) 1041. [3J [4] [S ] [6]
AJ. Sadlej, Chem. Phys Letters 36 (1975) L29. R. Yans, Chem. Phys. Letters 38 (1976) 460. R. Moccia, Chem. Phys. Letters S (1970) 260. M. Jasunski and A. Sad& Theoret Cbim. Acta 30 (1973) 257. [7] R. DtchfAd, J. Chenx Pbys. 65 (1976) 3123. [8] A. Okninskiand A. Sadkj,Acta Phys. Polon A48
(1975) 45s*
[9] W N. Lipsoomb. Advances III magnetic resonance. VoL 2 (Academic Press, New York. 1966) p. 137.
97
Volume 84, number I
CHEMICAL
[tOI S. Huzies. J.Chem. Phys. 42 (1965)1293 [ 111S. Huzinaga.Approbate Atomic FunUIChons, Unwxsity of AIkrta,
Canada (1971).
[It] H. Lischka. 3. Am Chem Sot 96 (1974) 4761 [13] H. LxM&a,Chem Phys Letters66 (1979) 108.
98
PHYSICS
LSZTJTERS
15
November‘1981
f 141H. Popkie, H. Kstenmacher and E. Clement&J. Chem. Phys. 59 (1973)
[ 15 ] D.W
Davtes, The
1325.
theory of the electrrc and magnetic properties of molecules (Wiley, New York, 1967) p 183
Volume 84, number 1
A COUPLED IN (m)2
HARTREE-FOCK
STUDY
PHYSICS LETTERS
ON NUCLEAR
MAGNETIC
SHlELDlNG
AND (H20)2
Robert HoLLER and Hans LISCHKA Instarut fur Tfuxwet~ciw C’?zermeund Strahlenchemle. Recelvcd
15 November 1981
8 June 1981, III tiil
form 6
August
Umverstiat Wen, A-1090
Vzenna. Austna
1981
Coupled Hat-tree-Fock ulclllatlons on susceptibltles and nuclear magnetic shleldmg constants have been performed for (HI3 and (H20j2 The apphcatlon the completeness rektlon m choosing a “best gauge” is a valuable ald but vekf large basis sets must be used to come close to the Htiree-Fock hnut Intermolecular effects of mducfd magnetic fields on the shwzklmg tensor are discussed
of
I. Introduction
2. Computational
The present mvestlgatlons on (HF)2 and (H20)2 are a direct continuation of our previous calculations on diamagnetic susceptibllitles and nucIear magnetic shleldmg constants for first- [l] and second-row [2] hydrides. Agam, we are usmg the coupled HartreeFock method and try to come as close as possible to the Hartree-Fock limit. As the molecular systems treated m tlus work are rather extended in space, the determination of an appropriate gauge orlgm is much more involved here than for the monomers As cntena for the choice of the ongm, completeness relations have been used for the nuclear magnetic slueldmg tensor a[3,4] and the maxunizatlon of X for the susceptlbility tensor [S]. The gauge ongms obtamed m this way are hereafter called “best or:gms”. To our knowledge, for @f20)2 onIy two ab nutlo calculations exist [6,7] and for @IF)2 only one [8]. The GLAO techmque was used by DItchfield for b water dimer calculations [7] whereas uncoupled Hartree-Fock calculations have been performed by Sadlej and co-workers [6,8]. Moreover, the changes in the shielding tensors due to hydrogen-bond formatlon are interpreted by Ditchfield by a method smular to the Mull&en populatron analysis in contrast to this, we analyze the calculated shifts m a more global way.
We use the coupled Hartree-Fock technique as formulated by Llpscomb [9 J. Since the computational 01
._.-_-_- ---_-FZ WI
FI
HZ
_;
bl L___________
e
S
L_____
..-
F
______
____
H
_
_____
e
-_
_
p2 =
cl
1’ &2________ F?_______
f
5
\ HZ d)
Fig
1 Geometry and geometry parameters for @IF)2 and (HzO)z- (Hi%. (a) h==Rq~~ = 53 au,+& =RF~H~ = 1.733 au; (c) eqtirium structure (Phil) RF,H, = 1.708 au* RF2Hz = 1 705 au, RF,F~ = 5 348 au, L HlFlFz = 6”, L FlF2Hl = 123 2” (d) (H2012: Rq02 = 5.669 au, 0 = 30”, ROH = 1809 au, L HOH = 104 5”. ROH and L HOH are the nme
94
details
in both water molecules.
0 00%2614/81/OOW-Owo/$O2.75
0 1981
North-Holland
Volume 84. number 1
procedures are identical ‘0 those of our pr&ious work [I ,2 1, we refer to them for mor& details. Foray _@culations the following Huzinaga basis sets have-been chosen [IO,1 1] I-IOs6p contracted to (4;6 X l/2,4 X 1) for F and 0, respectively, and 5s contra&d to (2, 3 X 1) for H. These basissets have been augmented by diffuse s and p and by polarization functibns. More information about orbital exponents is-given in the tables together with the results. For the linear and equilibrium &ctures of (HFh, geometries were taken from refs. 112,131 and for (H20)2 from ref. [143. Geometries and geometry parameters are given m fii 1.
3. Results and discussion 3. I. The HF &mm
For the linear arrangement we have tested several basis sets. Table 1 shows that two sets of d functions on each F atom are required for a reasonable calculatron of <_ However, at least one further polarization
set is necessary in order to reduce the strong gauge dependence of e to a few pbm. Table 2 gives om resul!s fo! both the liriear and the equilibrium geometry obta&cd-&th our b_e.sti&is set (basis 4 in table I). The most interesting shielding tensor is the one for H1- the proton involved in the hydrogen bridge. The average shielding constant & decreases from 26.6 to 26.2 pGm when going from the linear to the bent eqtilibrium structure. Compared to the monomer & is decreased by 2.2 ppm in the dimer (equilibrium structure)_ Okn_inski and Sadlej [8] fmd in their uncoupled Hartree-Fock calculations -1.3 and -2.85 ppm, respectively. As pointed out by Ditchfield [7], changes in the anisotropy of e upon hydrogen-bond formation are larger than the sh&s of the average value of e. In the following we restricted ourselves to the linear geometry because it is easier to analyze. However. we lhink that the main conclusions are transferable to the nonlinear geometry of (HF)z and also with some restdctions to the Hz0 dimer. We define erel as the difference of edtier e mOnomeT_Simdarly to Ditchfield, we divide 6* into
TabIe I Perpend~cuIarnuclear shiekhng constants (ppm) for the HF dimer in the Imear arrangement. A comparison of dtierent baser setsa) Bans set
1
2
3
4
AddItional bass funtinsb)
Relative gauge origin=)
F
H
Owl
2d
1P
(O.O*O)
em2
-
-
@,O,f)
01
2d
O-E92
Id
IP 1P
@IF)1
2d
W=),
zu
(HF)L (HO2
lslp3d lslp3d
best origin
430.1 431.0 430.3
329.4 3649 332.8
8080 78.39 89.80
(O,OSO) (O,OJ) best origin
407.7 412 3 408.1
3835 4058 385.7
42.32 46.86 38.47
20.75 34.71 20.94
1P
(O,O,O)
IP
cw,u
best origin
397 8 404.0 398.4
391.5 394 3 392 0
29.12 36.02 23.61
20.77 30.86 20 91
(0,OP) (O.OJ) best ongin
397.6 395 -4 397.2
391.7 390.2 391.3
L8.17 20.39 15.46
18.44 22.18 i7.70
Zpld 2p
L.s.5 6S 1.87
a) A lOs6p (4,6 X 1/2,4X 1) basis set for F and a 5s (2.3 X 1) set for H was used throughout. b, Exponents for the additional funtions: 1dF (1.6),_2dF (1.6, O 15). 3dF (2.4.0.6.0.15), 19 (O-l), 1pF CO-06). 1pH (0.75) 2Ptf (1.6,0.4), 1dH (1.2). C) The gauge or&n is given in cartesian coordinates relative to the F atom of the pertaining HF mdeade. Only chaages atong the t axis arq c+sidered_ 95
two contributions (a,,* =aiel +&I). One of them (&) cornea from the currents which are induced by
Table 2
Results for the lmear and equiliinum geometr.,s of (HF)~ a)
OF1
Lmw
Equtlibrium
XX
397.2
397 0
YY
3v
397 2 483 1 0 0 425 9
395 5 482 3 82 78 4249
xx YY zz xz
391.3 391 3 4835 0
445.4 388 2 423 6 -29 6
ZX
0
-390
av
422 0
zz xz ZX
*FZ
=HI
eH2
xr .vY
15 46 15 46
ZZ
48
xz ZX av
0 0 26 60
xx YY zz rz ZX
17 70 17 70 45 47 0 2: 95
av x
.rcx YY
-24 -24 -20
ZZ
av
15 37 14 48 48 80 24 22 26 22
88
35 17 27 -28 -125 26
96 96 03
92 68 16 7
duced magnetic
92
-25 17 -23 88 -20 40 -0 30 -23 15
Component 1
II ;:*p
(ppm)arel
field of one molecule
=~&rr,er-(Imono~e.
a) for the linear mnf&Wation of (HF)z b)
aP3
60 13
-07 1.3
00 17
-09 15
-44 36
-19 38
-4.7 4.4
0.0 20
0.6 1.7
-0.1 24
-18 8.1
00 5.7
F2
=rel
al Monomer v;ilues a,,F = 481 8, oIF = 391 3. a,,H - 45
ht-
is connected to the small anrsotropy of x for HP (see e g. ref.1151). The parallel components of the shrelding constants m the drmer are well represented by the respective u:. Much larger ddferences, especrally for a:,, are found for the perpendrcular components In agreement wrth Drtchfield’s fmdmgs, we observe that the prominent part of the amsotropy change Au”,{ 1s brought about by the induced magnetic fields in the other molecule (compare_ Aa::= 5.7 ppm and A$ = 8.1 ppm)
Fl
OreI
contnbutes
tle to 0 of the nuclei on the other molecule. Tlus fact
Basis set 4 was used. The diagonal elements are gwen at the best orgm. the off&agonal ones at (O,O,O) AU values are in ppm Total energies HF monomer E = - 100 06553 au HF duner, Lear. E = -200 13588 au, equiliirmm stmcture: E = -200.13697 au
Table 3 Relatwe nudear sh=ldmg amstants
96
the external magnetrc fieId in the other molecule The other one (e&) comes from the changes of the electronic density due to the intermolecular interaction. These effects are discussed extensrvely in ref. 171. We compute =;I in the following way. We take one HF molecule and place magnetic test dipoles into those positions PI-P4 which represent the nuclei of the second HF molecule m the dirner. The srtuation is demonstrated m fig lb. For example, P4 takes the position of H,. For thrs arrangement the nuclear shielding constant2s apt (I = 1. 4) are calculated. areI 1s obtained simply by subtraction of aZ from ere,_ It should be mentioned at this point that our partitromng, although sirmlar to Ditchfield’s procedure, IS not equivalent to it. In our analysis we avoid the arbitrariness of basrs sets which is inherent rn ah populatron-type methods. Howeve;, we drd not attempt any further decomposrtron of urel and &I mto atomic contributions In table 3 the relatrve shrelding constants for the dimer are compared to the up1 values. The average values Cipl are all close to zero. Thrs means that the m-
419 1
0 -23 32
XZ
a)
15 November 1981
CHEMICAL PHYSICS LETI-ERS
Volume 84. number 1
aP1
26. OF = 19 89.
Hl
QIel
J’4
Hz erel
-2.2
&‘2
-04
02 -14 2.4
b, Pure1 = (01, - Ui)dimer --(u,, - u~)monomer.
0”:: 1.1
Volume 84, number 1
CFLEMICAL PHYSICS LETTERS
3.2. The H20 dmer For (H20)2 we performed only one calculation mth a basis set of comparable-quahty td basis 4 of HF. Results are collected in tables 4 and 5. For the decrease of the average tielding of the bridging proton we find -2 8 ppm (see table 5) -a value close to the one reported by Ditchfield 171. On the other hand, Sadlq and Jaszunsla [6] calculated a shift of only -1 ppm. We also computed the change of the shielding tensoraH between the water dimer and an isolated water molecule whch was III exactly the same postlon as in the dimer. As in the HF case, one finds that the changes in the indlvldual components of aHz are much
15 November I98L
Table 5 Relativeaverage &i&&g mmtants (ppm) r?&, = Zdimer -5 mommer fur (H&)2 a) Ref. [7j
This work
-01 OreI
-35
-02 Drd
0.9
-HI arel
-06
-Hz =re1
-30
-H3
Tel
7.7
-3.0
0.0
a) Monomer
values:
s1
0.8
= 329 1 ppm siiHt = 30 0
ppm
larger than the shift of the average values. Some disagreement between our and Dltchfield’s results is observed in the case of the oxygen atom. We obtain a much smaller change m Go2 than Ditchfield (0.8 ver-
4. Conclusions
sus 7 7 ppm).
Magnetic effects for hydrogen-bonded systems are certainly very difficult to treat in the coupled HartreeFock framework since very extended basis sets have to be used and since the effects one wants to compute are rather small. We find, in agreement with previous work of Ditchfield [7], that the aniso~ropy of the
Table 4 Results for (H20)2 a) X
uo1
xx YY zz XY xz YZ av xx
YY zz ZX
35 7.0 31s 7 -2.8 -3.6
aV
325.7
XZ
u”2
-29 81 -29 85 -27 92 0.0 -0 29 00 -29.19 304 3
xx
YY LZ XZ ZX
av
aH1
XY
YX XZ
zx YZ ZY av (IHf
XX
YY JZ
3369 304 6 348 1 -252 -28 9 3299
xx YY zz
XZ ZX
av GH3
x.x YY LZ XZ ZX
av
23 21 36 64 28 09 5_26 4.66 -3 32 -342 -8 40 -9.43 29.31 16.36 1694 48 -0 -2 27
28 94 43 19
41.38 2162 2656 -22.12 -6 58 29x5
elements are gwen at the best origins. the offdragonal ones at (O,O,O).AlI values are in ppm. Bass sets0, lOdp+lslp (0 08.0.05) + 3d(2 4.0 6.0.15); HI, H3. Ss+2p(I.6.0.4); Hz, Sti2p(1.6.0 4) + ld(1.6). Total energles- Hz0 monomer, E = -76 06233 au; Hz0 dimer, E = -152.13062 au.
a) The diagonal
nuclear
shielding
tensor is more sensitive to effects
of
intermolecularrntemtlons than the averagevalue. Acknowledgement The cakulatlons were performed on the CDC CYBER 73/74 computers of the University and the Techrucal University of Vienna_ We are grateful for a generous
supply of computer
time.
References [I] R. HBlkr and H. Lischka, Mol. Phys 41 (1980) 1017. 121 R. Hbtler and H. Lischka. Mol. Phys. 41 (1980) 1041. [3J [4] [S ] [6]
AJ. Sadlej, Chem. Phys Letters 36 (1975) L29. R. Yans, Chem. Phys. Letters 38 (1976) 460. R. Moccia, Chem. Phys. Letters S (1970) 260. M. Jasunski and A. Sad& Theoret Cbim. Acta 30 (1973) 257. [7] R. DtchfAd, J. Chenx Pbys. 65 (1976) 3123. [8] A. Okninskiand A. Sadkj,Acta Phys. Polon A48
(1975) 45s*
[9] W N. Lipsoomb. Advances III magnetic resonance. VoL 2 (Academic Press, New York. 1966) p. 137.
97
Volume 84, number I
CHEMICAL
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98
PHYSICS
LSZTJTERS
15
November‘1981
f 141H. Popkie, H. Kstenmacher and E. Clement&J. Chem. Phys. 59 (1973)
[ 15 ] D.W
Davtes, The
1325.
theory of the electrrc and magnetic properties of molecules (Wiley, New York, 1967) p 183