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Nitrogen nuclear quadrupole coupling constants in heterocyclic molecules from ab initio molecular-orbital wavefunctions
V01ume 4, number 2
NITROGEN
CHEMICAL
NUCLEAR
PHYSICS
QUADRUPOLE
HETEROCYCLIC AZ3
LETTERS
COUPLING
MOLECULES
CONSTANTS
L969
IN
FROM
MOLECULAR-ORBITAL
ZNZTZO
1 October
WAVEFUNCTIONS
E. KOCHANSKI, J. M. LEHN Institut de Chimie,
1 rue Blaise
Pascal,
6?-Strasbowg.
France
and B. LEVY Laboratoire
de Chimie de 1’EX.S.. Received
24 rue Lhomond,
75Paris
G?me, France
31 July 1969
The nuclear quadrupole coupling components, the asymmetry parameter and the orientation of the corresponding principal axis system have been computed for the nitrogen nucleus in heterocyclic molecules, from a6 inifio wavefunctions using Gaussian basis sets. The results are discussed in terms of wavefuncticx accuracy and of moIecular structcre.
Nuclear quadrupole coupling constants (x = 5 e2@&‘h) result from the interaction of the nuclear quadrupole moment eQ with the electric field gradient eq at the site of the nucleus. These field gradients (which involve nuclear and electronic contributions) and the corresponding asymmetry parameters 17are a sensitive measure of the electronic charge distributions in the vicinity of the nucleus. Thus, they represent a means of probing the accuracy of molecular wavefunctions [1,2]. All electron ab initio SCF LCAO MO wavefunctions have become available in recent years for molecules oE moderate size. The calculation of x and q from these wavefunctions thus serves a double goal: testing wavefunctions and conversely predicting values of x, 17and of the quadrupole resonance frequencies. We have developed a program for calculating the components of q (qXX, qyy,qzZ ) and the orientation of the principal axis system of the field gradient tensor from ab initio wavefunctions using gaussian functions as basis set. We present here a preliminary account of a study of a number of heterocyclic nitrogen-containing molecules aimed at calculating the quadrupolar coupling constants of the nitrogen nucleus. Calculations of nitrogen quadrupolar constants from ab fnito wavefunctions employing gaussian-lobe [3] and Slater [4] basis functions have
been
published
recently
for
other
qyy and qzzS
for the following molecules are listed in the table: aziridine I: [5], diazirine 11 (61, pyrrole III [7], isoxazole IV [8], oxazole V [8]. pyrazole VI [8], imidazole M [S], pyridine VIII [9] and pyrazine IX [lo]. The structures of these molecules are schematically given in fig. 1. These results merit several comments: 1) Calculations done with the extended basis sets B1 and B3 (see table) lead to values in agreement with experiment within ca 20% both for the components of x and for the orientation of the principal axis system. When the minimal basis set B2 is used the agreement between experiment and theory is less good. 2) The agreement between calculated and experimental values is much worse for tricoordinated nitrogen (in III, VI (Nl), VII (Nl)) than for dicoordinated nitrogen (Vi (N2), VII (N3), VIII, IX). This indicates that the presently available wavefunctions do not describe accurately the nature of the bonding at the nitrogen in pyrrole and in similar systems. Because of the importance of this type of system in chemistry and biochemistry a more elaborate treatment is strongly needed. 3) The quadrupole coupling components are characteristic of the type of nitrogen site involved. Thus the dicoordinated nitrogens in t&e five-
membered heterocycles
ire easily recognized
systems.
The quadrupole coupling components xxx, XJJJJad xzz obtained from the calculated values of yxx,
f 6 :;2gen
nuclear quadrupole moment of 1.604 x
onx2 h=s beenemployed.
75
Volume 4. number
CHEMICAL PHYSICS LETTERS
2
1 October 1969
Table 1 Calculated and experimental a) quadrupole coupling tensor componeats in the principal axis system XYZ (in MHZ). Molecule
Basis
XUY talc.
set b, Bl Bz
I
+3.356 +4.368
m
0.533
25%4’(x)
0.492 0.683 0.629
29011’(x) 00(y) 25’50’1~) O”&) 25025’(x) O”(y)
0.788 0.703
23O28’(x) 00(y) 29040’(x) 00(y)
+3.oi2 +3.004
+ 0.568 +0.685
*I B3 exp.e]
- 0.312 - 0.401
+2.938 +2.699
- 2.636 - 2.299
XAA < 1-O
XCC -XBB
= 6.2
B2 exp-
- 5.257 -2.67
+2.916 +1.43
1-2.341 i-l.%
0.109 0.071
OO(X) 00(Y)
+o_s92
-6.021
O-704
00~).57040'~)
<1
+5.123 <1
+ 1.576 1.58
zp.
e)
%
WI
-4.990
e3.414
0.314
- 3.99
+2.41
0.21
00(X) 51010’(y)
VI (at N1)
2pf.g)
- 4.928
+1.833
0.236
00(x) 15oo4’(y)
12.61
+3.045 -
VI (at N2)
B2
+ 1.305
t5.026
- 6.332 13.9951
0.588 0.657
O”(x) 61011’(y)
f 1.920
+2.395
0.110
00(x) 88035’1y)
- 5.046 13.2711
+3.595 -
0.425 0.129
00(x) 50043’(y)
+3.523 +3.45
- 6.315 -4.88
+2.733 +1.43
0.115 0.405
00(x) OoW
+3.479
- 6.636 14.8571
+3.157
0.040 0.536
00(x] 00(Y)
VII (at NI)
2.f.g)
VII (at N3) VIII
lx
-4.315 11.71 + 1.451
Ill]
1151
t
f)
[ll] [13]
t141
6xp.e)
=P.
Ref.
00(y)
B3
Iv
V
-4.377 - 5.856 - 3.530 - 3.639
_P.
II
+ 1.021 + 1.487
0 (axis) d) talc. exp.
X ZE
1171 1181
WI WI
WI [191
a) Gas phase unless indicated. b) Gaussian functions basis sets: gaussian type functions GTF/contracted functions: BI: 954/422 :vith respectively 3 and 2 GTF’s in the two contracted p functions B2: 733/2X B3: 1054/422with respectively 4 and 1 GTF’s in the two contracted p functions. C) Asymmetry parameter defined as T]= &__-x@&,,, with Ika 1 s Ix,, 1c lx& where xii =e2q&/h = @2V/&.2).
WI
and qii =
d) Rotation &gle for transforming a given coordinate axis x,y , t into the corresponding quadrupole tensor principal +xis XYZ (see also the molecular diagrams). e) Values for the inertial axis system. f) Values obtained from NQR measurements in solid phase. Gas phase vnlues are probably larger by 0.3 - 0.5 MHz. g) Values obtained from the single NQR resonance reported in [18] assuming the asymmetry parameter to be the same as in pyrrole.
from the tricoordinated nitrogens and display similar x components at similar sites (for inst.anceNinIVandN~inVX; NinVandNgin VII). The same holds for the six-membered hetezocycles VDI and IX 4) The largest component of 1x1 lies approximately in the direction of the classically defined nitrogen “lone pair”. $ .76
5) The calculation of the components of x may also be of help in determining the orientation of the inertial axis system in molecules where the components of x in that system are known from microwave studies. Thus the agreement between $ Escept in the case of diazirine II which will be discussed in detail in the final publication.
Volume 4, number 2
CHEMICAL PHYSICS LETTERS
I&
J?J/
__& H__:
em-
-__
-_-_
p
1 October
$
1969
_
____-p
Y i\
i\
,
I
II
I
5’1
‘I
L
III
VII
Y t
k
+TX
VIII
N
61 N
I%
Fig. 1.
calculated indicates
and experimental that the orientation
values for V (table) of the inertial
axis
system should not be very different from the field gradient system. In addition, in the case of IV values
of the components smaller than 1 MHz are obtained in an axis system characterized by a rotation angle of ca 150 (y), defining
thus an approximate axis system in IV.
orientation of the inertial
A more detailed discussion of these points, together with a study of various acyclic compounds (methylenimine, aminoborane, hydrazine, etc.) and of deuterium quadrupolar couplings will be given in the final account of this work. We thank Drs. H. Basch, J. L. Calais, J. F. Earrison and P. Pykkii for sending us test calcuIations for checking our program and Drs. H. Basch and G. Berthier for communicating to us the molecular wavefunctions of nitrogen containing heterocycles [S,ll,IZ].
REFERENCES [1] E. A. C. Lucken, Nuclear quadrupole coupling con-
stants (Academic Press, London-New York, 1969).
[Z] E. Scrocco. in: Advan. Chem. Phys. 5 (1963) 318. [3: C.T.O’Konski and T.-K.Hn. J.Chem.Phys.49 !1968) 5354.
[4] R. Bonaccorsi, E.Scrocco and J.Tomasi, J.Chem. Phys. 50 (1969) 2940. [S] J. M. Lehn. B. Munsch. Ph. Millie and A. VeiLLard. Theoret. Chim. Acta 13 (1969) 313. [S] E. Kochanski and J. M. Lehn, Theoret. Chim. Acta (1969) in press. [i] E. Clementi, H.Clementi and D. R. Davis. 3. Chem. Phys.46 (1967) 4725. [8] G.Berthier, L. Praud and J. Serre. in: In:. Conf. on Quantum Aspects of Heterocyclic Conpounds in Chemistry and Biochemistry, Jerusalem. Israel, March 31 - Aaril 5. 1969. E.Clementi. i.Chem.Phys.46 (1967) 4731. E. Clementi, J.Chem. Phys.46 (1967) 4737. H. Basch, M.B. Robin. N.A. Kuebler, C. Baker and D.W.Turner. in press. H. Basch. private communication. hl. K. Kemp and W. H. Flygare. J.Am. Chew Sac. 90 (1968) 6267. L. Pierce and V. Dobyns, J. Am. Chem.Soc. 64 (1962) 2651. B. Bak and L. Nygaard. cited in ref. [Is]. D. W. Davies and W. C. Mackrodt, Chem. Commun. (1967) 1226. W. C. Mackrodt , A. Wardley. P. A. Curmuck, K_ L. Owen and J. Sheridan, Chem. Commun. (L966) 692. L.GuiM and E.A.C.Lucken. hToL.Phys.14 (1968) 73;
V&me
4, number 2
CHEMICAL
E.Schem& and D. J-Bray, Phys.Letters 25A (1967) 414. [X3] G.O.Sbrensen. J.Mol.Spectry. 22 (1967) 325.
FHYSiCS LETTERS (201 L.Guibe 273.
1 October 1969 and E.A.C.Lucken.
Mol.Phys.10
(1966)
NITROGEN
CHEMICAL
NUCLEAR
PHYSICS
QUADRUPOLE
HETEROCYCLIC AZ3
LETTERS
COUPLING
MOLECULES
CONSTANTS
L969
IN
FROM
MOLECULAR-ORBITAL
ZNZTZO
1 October
WAVEFUNCTIONS
E. KOCHANSKI, J. M. LEHN Institut de Chimie,
1 rue Blaise
Pascal,
6?-Strasbowg.
France
and B. LEVY Laboratoire
de Chimie de 1’EX.S.. Received
24 rue Lhomond,
75Paris
G?me, France
31 July 1969
The nuclear quadrupole coupling components, the asymmetry parameter and the orientation of the corresponding principal axis system have been computed for the nitrogen nucleus in heterocyclic molecules, from a6 inifio wavefunctions using Gaussian basis sets. The results are discussed in terms of wavefuncticx accuracy and of moIecular structcre.
Nuclear quadrupole coupling constants (x = 5 e2@&‘h) result from the interaction of the nuclear quadrupole moment eQ with the electric field gradient eq at the site of the nucleus. These field gradients (which involve nuclear and electronic contributions) and the corresponding asymmetry parameters 17are a sensitive measure of the electronic charge distributions in the vicinity of the nucleus. Thus, they represent a means of probing the accuracy of molecular wavefunctions [1,2]. All electron ab initio SCF LCAO MO wavefunctions have become available in recent years for molecules oE moderate size. The calculation of x and q from these wavefunctions thus serves a double goal: testing wavefunctions and conversely predicting values of x, 17and of the quadrupole resonance frequencies. We have developed a program for calculating the components of q (qXX, qyy,qzZ ) and the orientation of the principal axis system of the field gradient tensor from ab initio wavefunctions using gaussian functions as basis set. We present here a preliminary account of a study of a number of heterocyclic nitrogen-containing molecules aimed at calculating the quadrupolar coupling constants of the nitrogen nucleus. Calculations of nitrogen quadrupolar constants from ab fnito wavefunctions employing gaussian-lobe [3] and Slater [4] basis functions have
been
published
recently
for
other
qyy and qzzS
for the following molecules are listed in the table: aziridine I: [5], diazirine 11 (61, pyrrole III [7], isoxazole IV [8], oxazole V [8]. pyrazole VI [8], imidazole M [S], pyridine VIII [9] and pyrazine IX [lo]. The structures of these molecules are schematically given in fig. 1. These results merit several comments: 1) Calculations done with the extended basis sets B1 and B3 (see table) lead to values in agreement with experiment within ca 20% both for the components of x and for the orientation of the principal axis system. When the minimal basis set B2 is used the agreement between experiment and theory is less good. 2) The agreement between calculated and experimental values is much worse for tricoordinated nitrogen (in III, VI (Nl), VII (Nl)) than for dicoordinated nitrogen (Vi (N2), VII (N3), VIII, IX). This indicates that the presently available wavefunctions do not describe accurately the nature of the bonding at the nitrogen in pyrrole and in similar systems. Because of the importance of this type of system in chemistry and biochemistry a more elaborate treatment is strongly needed. 3) The quadrupole coupling components are characteristic of the type of nitrogen site involved. Thus the dicoordinated nitrogens in t&e five-
membered heterocycles
ire easily recognized
systems.
The quadrupole coupling components xxx, XJJJJad xzz obtained from the calculated values of yxx,
f 6 :;2gen
nuclear quadrupole moment of 1.604 x
onx2 h=s beenemployed.
75
Volume 4. number
CHEMICAL PHYSICS LETTERS
2
1 October 1969
Table 1 Calculated and experimental a) quadrupole coupling tensor componeats in the principal axis system XYZ (in MHZ). Molecule
Basis
XUY talc.
set b, Bl Bz
I
+3.356 +4.368
m
0.533
25%4’(x)
0.492 0.683 0.629
29011’(x) 00(y) 25’50’1~) O”&) 25025’(x) O”(y)
0.788 0.703
23O28’(x) 00(y) 29040’(x) 00(y)
+3.oi2 +3.004
+ 0.568 +0.685
*I B3 exp.e]
- 0.312 - 0.401
+2.938 +2.699
- 2.636 - 2.299
XAA < 1-O
XCC -XBB
= 6.2
B2 exp-
- 5.257 -2.67
+2.916 +1.43
1-2.341 i-l.%
0.109 0.071
OO(X) 00(Y)
+o_s92
-6.021
O-704
00~).57040'~)
<1
+5.123 <1
+ 1.576 1.58
zp.
e)
%
WI
-4.990
e3.414
0.314
- 3.99
+2.41
0.21
00(X) 51010’(y)
VI (at N1)
2pf.g)
- 4.928
+1.833
0.236
00(x) 15oo4’(y)
12.61
+3.045 -
VI (at N2)
B2
+ 1.305
t5.026
- 6.332 13.9951
0.588 0.657
O”(x) 61011’(y)
f 1.920
+2.395
0.110
00(x) 88035’1y)
- 5.046 13.2711
+3.595 -
0.425 0.129
00(x) 50043’(y)
+3.523 +3.45
- 6.315 -4.88
+2.733 +1.43
0.115 0.405
00(x) OoW
+3.479
- 6.636 14.8571
+3.157
0.040 0.536
00(x] 00(Y)
VII (at NI)
2.f.g)
VII (at N3) VIII
lx
-4.315 11.71 + 1.451
Ill]
1151
t
f)
[ll] [13]
t141
6xp.e)
=P.
Ref.
00(y)
B3
Iv
V
-4.377 - 5.856 - 3.530 - 3.639
_P.
II
+ 1.021 + 1.487
0 (axis) d) talc. exp.
X ZE
1171 1181
WI WI
WI [191
a) Gas phase unless indicated. b) Gaussian functions basis sets: gaussian type functions GTF/contracted functions: BI: 954/422 :vith respectively 3 and 2 GTF’s in the two contracted p functions B2: 733/2X B3: 1054/422with respectively 4 and 1 GTF’s in the two contracted p functions. C) Asymmetry parameter defined as T]= &__-x@&,,, with Ika 1 s Ix,, 1c lx& where xii =e2q&/h = @2V/&.2).
WI
and qii =
d) Rotation &gle for transforming a given coordinate axis x,y , t into the corresponding quadrupole tensor principal +xis XYZ (see also the molecular diagrams). e) Values for the inertial axis system. f) Values obtained from NQR measurements in solid phase. Gas phase vnlues are probably larger by 0.3 - 0.5 MHz. g) Values obtained from the single NQR resonance reported in [18] assuming the asymmetry parameter to be the same as in pyrrole.
from the tricoordinated nitrogens and display similar x components at similar sites (for inst.anceNinIVandN~inVX; NinVandNgin VII). The same holds for the six-membered hetezocycles VDI and IX 4) The largest component of 1x1 lies approximately in the direction of the classically defined nitrogen “lone pair”. $ .76
5) The calculation of the components of x may also be of help in determining the orientation of the inertial axis system in molecules where the components of x in that system are known from microwave studies. Thus the agreement between $ Escept in the case of diazirine II which will be discussed in detail in the final publication.
Volume 4, number 2
CHEMICAL PHYSICS LETTERS
I&
J?J/
__& H__:
em-
-__
-_-_
p
1 October
$
1969
_
____-p
Y i\
i\
,
I
II
I
5’1
‘I
L
III
VII
Y t
k
+TX
VIII
N
61 N
I%
Fig. 1.
calculated indicates
and experimental that the orientation
values for V (table) of the inertial
axis
system should not be very different from the field gradient system. In addition, in the case of IV values
of the components smaller than 1 MHz are obtained in an axis system characterized by a rotation angle of ca 150 (y), defining
thus an approximate axis system in IV.
orientation of the inertial
A more detailed discussion of these points, together with a study of various acyclic compounds (methylenimine, aminoborane, hydrazine, etc.) and of deuterium quadrupolar couplings will be given in the final account of this work. We thank Drs. H. Basch, J. L. Calais, J. F. Earrison and P. Pykkii for sending us test calcuIations for checking our program and Drs. H. Basch and G. Berthier for communicating to us the molecular wavefunctions of nitrogen containing heterocycles [S,ll,IZ].
REFERENCES [1] E. A. C. Lucken, Nuclear quadrupole coupling con-
stants (Academic Press, London-New York, 1969).
[Z] E. Scrocco. in: Advan. Chem. Phys. 5 (1963) 318. [3: C.T.O’Konski and T.-K.Hn. J.Chem.Phys.49 !1968) 5354.
[4] R. Bonaccorsi, E.Scrocco and J.Tomasi, J.Chem. Phys. 50 (1969) 2940. [S] J. M. Lehn. B. Munsch. Ph. Millie and A. VeiLLard. Theoret. Chim. Acta 13 (1969) 313. [S] E. Kochanski and J. M. Lehn, Theoret. Chim. Acta (1969) in press. [i] E. Clementi, H.Clementi and D. R. Davis. 3. Chem. Phys.46 (1967) 4725. [8] G.Berthier, L. Praud and J. Serre. in: In:. Conf. on Quantum Aspects of Heterocyclic Conpounds in Chemistry and Biochemistry, Jerusalem. Israel, March 31 - Aaril 5. 1969. E.Clementi. i.Chem.Phys.46 (1967) 4731. E. Clementi, J.Chem. Phys.46 (1967) 4737. H. Basch, M.B. Robin. N.A. Kuebler, C. Baker and D.W.Turner. in press. H. Basch. private communication. hl. K. Kemp and W. H. Flygare. J.Am. Chew Sac. 90 (1968) 6267. L. Pierce and V. Dobyns, J. Am. Chem.Soc. 64 (1962) 2651. B. Bak and L. Nygaard. cited in ref. [Is]. D. W. Davies and W. C. Mackrodt, Chem. Commun. (1967) 1226. W. C. Mackrodt , A. Wardley. P. A. Curmuck, K_ L. Owen and J. Sheridan, Chem. Commun. (L966) 692. L.GuiM and E.A.C.Lucken. hToL.Phys.14 (1968) 73;
V&me
4, number 2
CHEMICAL
E.Schem& and D. J-Bray, Phys.Letters 25A (1967) 414. [X3] G.O.Sbrensen. J.Mol.Spectry. 22 (1967) 325.
FHYSiCS LETTERS (201 L.Guibe 273.
1 October 1969 and E.A.C.Lucken.
Mol.Phys.10
(1966)