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A theoretical study of the electronic structure of nitroethylene
311 Journal of Molecular Q Elsevier Scientific
Striicrure, Publishing
A THEORETICAL NtTROETHYLENE
TAE-KYU
2 1 (I 974) 3 I I-3 17 Company, Amsterdam
STUDY
OF
THE
- Printed
in The Netherlands
ELECTRONtC
STRUCTURE
OF
HA
PhJ*sical Chenrislry
Laboratory,
(Received
1973)
19 April
Swiss
Federol
Instirate
of Technolog_v,
Zmich
(Switzerland)
ABSTRACT
The electronic ground state of nitroethylene
in its planar and perpendicular conformations is studied by ab initio SCF calculations using Gaussian-lobe basis functions. The internal-rotation barrier of the nitro group has been calculated to be 6.02 kcal/mole. The dipole moment, the electric field gradient at the nitrogen and the diamagnetic contribution to the nuclear shielding for the protons have been calculated from the molecular wavefunction. Calculated and reported experimental values are in satisfactory agreement with each other. tn terms of the population analysis, the electronic charge distribution has also been studied.
INTRODUCTION
Extensive spectroscopic studies on nitroethylene have been reported by Giinthard and coworkers. They are infrared [l-3], microwave [4], NMR [5], and ultraviolet studies [6]. The internal-rotation barrier of the nitro group, the dipole moment, the quadrupole coupling constant of nitrogen, the nuclear magnetic shielding of protons and finally the n + z* and TC+ rc* electron transitions in nitroethylene have been studied. Various semi-empirical molecular-orbital treatments have also been reported with the main purpose of assigning the electronic transitions of the ultraviolet spectrum [6-81. Nitroethylene is of particular interest because it is the simplest member of the nitro-olefin series. The influence of a typical electron attracting group such as the nitro group to the unsaturated compound can be studied with regard to the possible ethylene z-electron delocalization through substitution. In this work, we report an ab initio SCF calculation of the electronic structure of nitroethylene in its electronic ground state and theoretically interpret vari-
312 ous molecular properties. A configuration interaction study of ground and electronically excited states for the assignment of the ultraviolet spectrum will be reported separately later [9].
CALCULATIONS
The approximate Hartree-Fock SCF atomic orbitals employed as a basis set for the ab initio SCF calculation in this work were the Gaussian lobe functions reported by Whitten [IO]. It consists of three linear combinations of 4, 3 and 3 primitive Gaussians respectively for s-orbitals and one linear combination of 5 pairs of primitive Gaussians for each of the three p-orbitals of the carbon, nitrogen and oxygen atoms. Each hydrogen Is-orbital is represented by a linear combina‘5 The size of the atomic basis set is tion of 5 primitive Gaussians scaled by J__ approximately equivalent to the double-zeta Slater-type orbital basis set in accuracy. For example, it gives the energies of -37.68052 a.u. for the 3P atomic state of carbon, - 54.388 15 a.u. for the “S state of nitrogen and - 74.791 54 a-u. for the 3P state of oxygen, while the corresponding energies from the double-zeta Slater-type orbital basis set are: -37.686 67 a-u., - 54.397 87 a-u., and - 74.804 18 a-u., respectively. Bond distances and bond angles were taken from the experimental values of the ref. 1, and were used for both the planar and the perpendicular conformations. Table 1 summarizes the atomic coordinates in nitroethylene. TABLE
1
COORDINATES
OF
Planar (q3 = OJ)
Cl
ATOMS
IN
NITROETHYLENE=
x
J
Z
0.000 00
0.00000
0.00000
CZ N 01 02 HI HZ
- 1.40543 2.77771 3.71384 3.71384 -0.51276 - 3.422 84
2.09940 0.000 00 -2.10256 2.10256 3.91353 1.965 39
0.00000 0.00000 0.00000 0.00000 0.00000
H3
-00.89267
-1.81415
0.00000 0.00000
’ Atomic units;
the coordinates for the perpendicular from the ones for the planar configuration by rotating
conformation (pl = 90”) may be derived the OIN02 group around the C,-N axis.
MOLECULAR ENERGIES AND INTERNAL-ROTATION
BARRIER
Table 2 summarizes molecu-ar SCF energy components energies for both the planar and perpendicular conformations
and the orbital of nitroethylene.
313
The total SCF energy difference (AET) between these two conformations is found to be 6.02 kcal/mole, the planar one being more stable. The experimental barrier height is reported to be not lower than 1690.6 cm-’ (= 4.83 kcal/mole) [3]. Agreement between the calculated and the experimental values is considered satisfactory. One notices that, excepting differences in the total SCF energies, all other ener_q components differ markedly from each other. tf we make use of the energy partitioning scheme, which has been introduced by Allen [13], the energy changes may be analyzed in terms of attractive (EN-,_,) and repulsive (EN, of the total SCF energy. We find that the difference in Et?,-.,, E,) components the attractive energy component (lAE,_,,j) is 1.5665 a-u., while the difference in the repulsive energy component (I AE,I -I-lAE,,_,,I + lAE,J) is 1.5570 a-u. According to this scheme, the barrier in nitroethylene is considered as an “attractive dominant barrier”, meaning that the change in the attractive energy components is larger than that of the repulsive energy components. This energy barrier is thus qualitatively similar to that of acetaldehyde [13], the larger barrier of hydroxylamine [l4], the cis-barrier of hydrogen peroxide [15], the cis-to-90” barrier of nitrous acid [16], and the cis-to-90” barrier of glyoxal [17]. It may also be noticed that all the repulsive energy components are smaller in the perpendicular conformation than those of the planar one in nitroethylene as shown in Table 2. TABLE MOLECULAR
2 ENERGIES
IN
NITROETHYLENE=
Energy
Planar
Perpendicular
Ek EN--cl E cl-Cl EN frE,
280.6314 - 994.4294 265.0868 167.6209 - 28 0.0000 1.0903
280.5786 - 992.8629 264.3034 166.900 I - 28 0.0096 I .0807
Orbital
energies
Planar
Perpendicular
Planar
Perpendicular
- 20.6094(
-20.6124(la’) -20.6123(2a’) - I6.0265(3a’) - I I .4602(4a’) - 1 I .4079(5a’) I .6529(6a’) 1.4476(1a”) l.l710(7a’) I .0094(8a’) - 0.8444(9a’)
-0.7941(1 la’) -0_7770(la”) -0.7365(12a’) -O-6975( I3a’) -0_6332(14a’) -O-5224( l5a’) -0.5037(16a’) -0.4821(2a”) -0.448 I (3a”)
- O-8029( I Oa’) -0.7700(1 la’) -0.7283(2a”) -0.6913(12a’) -0_6371(13a’) -OS439(3a”) -0.5011(14a’) - 0.4706(4a”) -0.4490(5a”)
-
I a’) 20.598 I (2a’) 16.0279(3a’) I I .4564(4a’) I I .4140(5a’) I.6501 (6a’) I .4458(7a’) I. 1704(8a’) l.O097(9a’) 0.8358( IOa’)
a Atomic units;
Ek = kinetic energy, EN_=, = nuclear-electron interaction energy, E=;I--cl = electron-electron repulsion energy, EN = nuclear-nuclear interaction energy and ET = total molecular electronic energy.
314 Orbital energies of the canonical SCF-MO’s given in Table 2 provide some semi-quantitative features to understand the electronic structure of nitroethylene in the frame of the Koopmans’ theorem [12]. Inspecting the expansion coefficients in the atomic orbital basis shows that, in both cases, the highest occupied molecular orbitals (3a” and 5a”) are the anti-bondin g 2p,-orbital and the anti-bonding linear combination of the 2p,,-orbitals of oxygen, respectively. This is in contrast to the semi-empirical results, where the highest occupied MO is predicted to be the n-orbital of oxygens [7, 81. Of course, the orbital ordering from the semiempirical MO calculation is dependent upon the empirical parameter sets employed [8]. The first ionization is thus predicted to come from the x-electrons of oxygen, the theoretical value of 12.19 eV being the first ionization potential of nitroethylene. The experimental ionization potential as well as the photoelectron spectroscopic data are not yet available. We notice further that the n-orbital of oxygens (l5a’ and 16a’ for the planar and 3a” and 14a’ for the perpendicular conformation) are nearly degenerate, the antisymmetric combinations (16a’ and 14a’) being slightly below the symmetric ones. Of particular interest are the 2a”- and 4a”-orbitals, which correspond to the bonding n-orbital of the ethylene molecule (I b,,-orbital of ethylene). Comparing with the lb,,- orbital energy of -0.4064 a-u., calculated by the same basis set contraction of the Gaussian lobe functions [l I], we notice that the 2a”- and 4a”-orbitals are stabilized by an amount of 2.04 eV and I .75 eV, respectively for the planar and the perpendicular conformations of nitroethylene. Small destabilization of the orbital energy in the perpendicular form is related to the diminishing delocalization of the ethylene x-electrons upon rotating the nitro group as the expansion coefficients show.
MOLECULAR
PROPERTIES
Table 3 summarizes the calculated dipole moment and the electric field gradient of nitrogen in nitroethylene. The calculated dipole moment of 4.429 D is approximately I6 o/0 larger than the reported experimental value of 3.70 D [4]. The electronic charge distribution at the site of nitrogen is almost spherically symmetric, judging from the relatively small value of the electric field gradient. The field gradient is smaller in the planar conformation than in the perpendicular one. The nuclear quadrupole coupling constant of 14N is calculated to be - 1.1 I MHz with the asymmetry parameter of 0.18, using the nuclear quadrupole moment Q(“N) = 1.56x 1O-26 cm2, obtained by O’Konski and Ha [ 181. This can be compared with the experimental value of - 1.25 MHz and 0.39, reported in ref. 4. The diamagnetic contribution to the nuclear magnetic shielding tensor at A is defined as [l9]
Q(A) = -
e2
2mC’
315 TABLE DIPOLE
3 hlOhlENT
AND
ELECTRIC
FIELD
Planar Dipole
moment
(Debye
PY
lctl Expt.” Electric
field
gradient
OF THE NITROGEN
units)
of the nitrogen
- 4.098 0.558 4.136
(atomic
units)
X’X’
-0.179
-0.162
_V’_V’
0.302 -0.123 0.18
-0.199 0.361 0.10
I'$ 77
IN NITROETHYLENE
Perpendicular
-4.370 0.722 4.429 3.70;0.03
Px
GRADIENT
= Ref. 4.
where yAi represents the distance of electron i from nucleus A, and Q, /3 = X, J’ and z. It is sufficient to calculate this quantity from the knowledge of the ground state wavefunction, Y. The paramagnetic contribution requires the excited state molecular wavefunctions. For protons, however, it is known that the diamagnetic term is the dominant term. Table 4 summarizes the shielding components calculated TABLE
4
DIAMAGNETIC
CONTRIBUTION
IN NITROETHY
LENE’
H3
HI HZ ’ Dimensionless for definition).
TO THE NUCLEAR
hlAGNETlC
SHlELDlNG
CONSTANTS
~,*x,
QP’J’
b,.,,
<%?
0.1 II9 0. I826 0.06 I I
0.1956 0.1106 0.2011
0.2582 0.246 1 0.2208
0.1886 0.1798 0.1610
units x
104; 2.66245
x IO-’
x natural
units
=
dimensionless
FOR THE PROTONS
units
(see
ref.
19
for three different protons in nitroethylene after diagonalizing the tensors individually. The values are the isotropic averages for the diamagnetic contribution. Experimental chemical shifts are reported to be 7.21 ppm for H3, 6.65 ppm for H, and 6.01 ppm for Hz, respectively [5], which are in satisfactory agreement with the ratio of the calculated values of in Table 4, the sequence being also correct. Table 5 summarizes the electron population in nitroethylene, in its planar and perpendicular conformations. We obtain an overall gross population of
316 TABLE
5
ELECTRON
POPULATION
C,
s
P. PY Pr total
C2
S PI PY PZ total
N
S PX PY PZ total
IN
NITROETHYLENE
Planar
Perpendimlar
3.132 0.781 I.185 1.100 6.198
3.125 0.785 1.190 I .089 6.189
01
3.249 1.225 I.159 0.873 6.506
3.243 1.221 1.145 0.912 6.521
02
3.337 1.208 I .039 I.195 6.779
3.336 1.206 I.202 1.036 6.780
HI HZ H3
S
082.272
#.5’S
Hy.557
~7.570
H;.669
@.6S9
P% PY PZ total
~6,305
for the planar c5.189 1
N6.779
I
~6.780
S
S
Perpendicular
3.860 1.807 I.188 I.407 8.262
3.860 1.805 I.402 I.189 8.256
3.858 I.805 I.183 I .424 8.270
3.860 I .805 I .402 1.189 8.256
0.658 0.667 0.660
0.670 0.669 0.659
-_____07.252
conformation c;.52
S
P. PY PZ total
~~_I98
S
Planar
@.550
and 0;.;55 .
for the perpendicular one, which are quite similar to each other. Inspecting the detailed atomic orbital population of electron, however, we notice marked shifts of electrons from the p,-orbitals to the p,-orbitals especially for the N, 0, and O2 atoms upon rotating the nitro group. They are 0.159 e- for N, 0.218 e- for 0, and 0.235 e- for 02, respectively. These shifts of electrons reflect the diminishing TABLE AVERAGE
6 VALUE
OF
THE
INVERSE
OF
THE
ELECTRONIC
Planar
Perpendicrdar
16.09; 14.950 19.235 20.023 20.240 6.752 6.028 7.082
16.090 14.908 19.238 20.096 20.096 6.608 6.085 7.023
Cl CZ N 01 02 H, H2 Ha il Atomic
units.
DISTANCE
FROM
THE
NUCLEUS
()’
317 degree of the delocalization of ethylene n-electrons throughout the nitroethylene molecule and it is also related to the decrease in the partial double bond character of the C-N bond or the failure of x-electron conjugation in the perpendicular conformation. The failure of n-electron conjugation is, in turn, responsible for the relatively high barrier in nitroethylene. Table 6 summarizes the average values of the inverse of the electronic distance from the nucleus, which is defined as
where n stands for total number of electrons in a molecule. One notices that the resulting average distances between the nuclei and the electronic charge cloud becomes larger (xA < l/r*> value becomes smaller) through rotating the nitro group. This reflects, in turn, a large decrease in the electron-nuclear attraction energy in the perpendicular conformation and this attractive energy component is the dominant term in determining the barrier mechanism in nitroethylene as the energy partitioning scheme above as shown.
ACKNOWLEDGMENT
We express our sincere appreciation to the ETH-Zurich computer center for providing computer time and to Prof. Hs. H. Giinthard for his encouragement and advice.
REFERENCES 1 K. R. Loos and Hs. H. Gtinthard, J. Chem. Phys., 46 (1967) 1200. 2 K. R. Loos and Hs. H. Giinthard, J. Clrenr. Ph_w., 48 (1968) 4332. 3 R. Meyer, A. Gammeter, P. Smith, H. Kiihne, P. Nosberger and Hs. H. Giinthard, J. Mol. Spedrusc., 46 (1973) 397. 4 H. D. Hess, A. Bauder and Hs. H. Giinthard, J. ~Vfol. Specrrosc., 22 (1967) 208. 5 H. J. Friihlin, K. R. Loos and Hs. H. Giinthard, Helo. Clrin~. Acfa, 51 (1968) 1593. 6 K. R. Loos, U. P. Wild and Hs. H. Giinthard, Specrrochirrr. Acta, 25A (1968) 275. 7 C. Leibovici and J.-F. Labarre, J. Chir~r. Phys., 67 (1970) 1664. 8 J. Kuhn, W. Hug, R. Geiger and G. Wagniere, Nelc. C/rim. Acm, 54 (1971) 2260. 9 T.-K. Ha, Mol. Phys., to be published. 10 J. L. Whitten, J. Chem. Phys., 44 (1966) 359. 1 I R. J. Buenker, S. D. Peyerimhoff and J. L. Whitten, J. Clrenr. Phys., 46 (1967) 2029_ 12 T. A. Koopmans. Physicu, I (1933) 104. 13 L. C. Allen, Clrern. Phys. Lerr., 2 (1968) 597. 14 W. H. Fink, D. C. Pan and L. C. Allen, J. Clrelrr. Phys., 47 (1967) 895. 15 W. H. Fink and L. C. Allen, J. Chenr. Phys., 46 (1967) 2261. 2276. 16 M. E. Schwartz, E. F. Hayes and S. Rothenberg, Theor. Chim. Acra, 19 (1970) 98. 17 T.-K. Ha, J. Mol. Structure, 12 (1972) 171. 18 C. T. O’Konski and T.-K. Ha, J. Chem. Phys., 49 (1968) 5354. 19 H. J. Kolker and M. Karplus, J. Chew. Phys., 41 (1964) 1259.
Striicrure, Publishing
A THEORETICAL NtTROETHYLENE
TAE-KYU
2 1 (I 974) 3 I I-3 17 Company, Amsterdam
STUDY
OF
THE
- Printed
in The Netherlands
ELECTRONtC
STRUCTURE
OF
HA
PhJ*sical Chenrislry
Laboratory,
(Received
1973)
19 April
Swiss
Federol
Instirate
of Technolog_v,
Zmich
(Switzerland)
ABSTRACT
The electronic ground state of nitroethylene
in its planar and perpendicular conformations is studied by ab initio SCF calculations using Gaussian-lobe basis functions. The internal-rotation barrier of the nitro group has been calculated to be 6.02 kcal/mole. The dipole moment, the electric field gradient at the nitrogen and the diamagnetic contribution to the nuclear shielding for the protons have been calculated from the molecular wavefunction. Calculated and reported experimental values are in satisfactory agreement with each other. tn terms of the population analysis, the electronic charge distribution has also been studied.
INTRODUCTION
Extensive spectroscopic studies on nitroethylene have been reported by Giinthard and coworkers. They are infrared [l-3], microwave [4], NMR [5], and ultraviolet studies [6]. The internal-rotation barrier of the nitro group, the dipole moment, the quadrupole coupling constant of nitrogen, the nuclear magnetic shielding of protons and finally the n + z* and TC+ rc* electron transitions in nitroethylene have been studied. Various semi-empirical molecular-orbital treatments have also been reported with the main purpose of assigning the electronic transitions of the ultraviolet spectrum [6-81. Nitroethylene is of particular interest because it is the simplest member of the nitro-olefin series. The influence of a typical electron attracting group such as the nitro group to the unsaturated compound can be studied with regard to the possible ethylene z-electron delocalization through substitution. In this work, we report an ab initio SCF calculation of the electronic structure of nitroethylene in its electronic ground state and theoretically interpret vari-
312 ous molecular properties. A configuration interaction study of ground and electronically excited states for the assignment of the ultraviolet spectrum will be reported separately later [9].
CALCULATIONS
The approximate Hartree-Fock SCF atomic orbitals employed as a basis set for the ab initio SCF calculation in this work were the Gaussian lobe functions reported by Whitten [IO]. It consists of three linear combinations of 4, 3 and 3 primitive Gaussians respectively for s-orbitals and one linear combination of 5 pairs of primitive Gaussians for each of the three p-orbitals of the carbon, nitrogen and oxygen atoms. Each hydrogen Is-orbital is represented by a linear combina‘5 The size of the atomic basis set is tion of 5 primitive Gaussians scaled by J__ approximately equivalent to the double-zeta Slater-type orbital basis set in accuracy. For example, it gives the energies of -37.68052 a.u. for the 3P atomic state of carbon, - 54.388 15 a.u. for the “S state of nitrogen and - 74.791 54 a-u. for the 3P state of oxygen, while the corresponding energies from the double-zeta Slater-type orbital basis set are: -37.686 67 a-u., - 54.397 87 a-u., and - 74.804 18 a-u., respectively. Bond distances and bond angles were taken from the experimental values of the ref. 1, and were used for both the planar and the perpendicular conformations. Table 1 summarizes the atomic coordinates in nitroethylene. TABLE
1
COORDINATES
OF
Planar (q3 = OJ)
Cl
ATOMS
IN
NITROETHYLENE=
x
J
Z
0.000 00
0.00000
0.00000
CZ N 01 02 HI HZ
- 1.40543 2.77771 3.71384 3.71384 -0.51276 - 3.422 84
2.09940 0.000 00 -2.10256 2.10256 3.91353 1.965 39
0.00000 0.00000 0.00000 0.00000 0.00000
H3
-00.89267
-1.81415
0.00000 0.00000
’ Atomic units;
the coordinates for the perpendicular from the ones for the planar configuration by rotating
conformation (pl = 90”) may be derived the OIN02 group around the C,-N axis.
MOLECULAR ENERGIES AND INTERNAL-ROTATION
BARRIER
Table 2 summarizes molecu-ar SCF energy components energies for both the planar and perpendicular conformations
and the orbital of nitroethylene.
313
The total SCF energy difference (AET) between these two conformations is found to be 6.02 kcal/mole, the planar one being more stable. The experimental barrier height is reported to be not lower than 1690.6 cm-’ (= 4.83 kcal/mole) [3]. Agreement between the calculated and the experimental values is considered satisfactory. One notices that, excepting differences in the total SCF energies, all other ener_q components differ markedly from each other. tf we make use of the energy partitioning scheme, which has been introduced by Allen [13], the energy changes may be analyzed in terms of attractive (EN-,_,) and repulsive (EN, of the total SCF energy. We find that the difference in Et?,-.,, E,) components the attractive energy component (lAE,_,,j) is 1.5665 a-u., while the difference in the repulsive energy component (I AE,I -I-lAE,,_,,I + lAE,J) is 1.5570 a-u. According to this scheme, the barrier in nitroethylene is considered as an “attractive dominant barrier”, meaning that the change in the attractive energy components is larger than that of the repulsive energy components. This energy barrier is thus qualitatively similar to that of acetaldehyde [13], the larger barrier of hydroxylamine [l4], the cis-barrier of hydrogen peroxide [15], the cis-to-90” barrier of nitrous acid [16], and the cis-to-90” barrier of glyoxal [17]. It may also be noticed that all the repulsive energy components are smaller in the perpendicular conformation than those of the planar one in nitroethylene as shown in Table 2. TABLE MOLECULAR
2 ENERGIES
IN
NITROETHYLENE=
Energy
Planar
Perpendicular
Ek EN--cl E cl-Cl EN frE,
280.6314 - 994.4294 265.0868 167.6209 - 28 0.0000 1.0903
280.5786 - 992.8629 264.3034 166.900 I - 28 0.0096 I .0807
Orbital
energies
Planar
Perpendicular
Planar
Perpendicular
- 20.6094(
-20.6124(la’) -20.6123(2a’) - I6.0265(3a’) - I I .4602(4a’) - 1 I .4079(5a’) I .6529(6a’) 1.4476(1a”) l.l710(7a’) I .0094(8a’) - 0.8444(9a’)
-0.7941(1 la’) -0_7770(la”) -0.7365(12a’) -O-6975( I3a’) -0_6332(14a’) -O-5224( l5a’) -0.5037(16a’) -0.4821(2a”) -0.448 I (3a”)
- O-8029( I Oa’) -0.7700(1 la’) -0.7283(2a”) -0.6913(12a’) -0_6371(13a’) -OS439(3a”) -0.5011(14a’) - 0.4706(4a”) -0.4490(5a”)
-
I a’) 20.598 I (2a’) 16.0279(3a’) I I .4564(4a’) I I .4140(5a’) I.6501 (6a’) I .4458(7a’) I. 1704(8a’) l.O097(9a’) 0.8358( IOa’)
a Atomic units;
Ek = kinetic energy, EN_=, = nuclear-electron interaction energy, E=;I--cl = electron-electron repulsion energy, EN = nuclear-nuclear interaction energy and ET = total molecular electronic energy.
314 Orbital energies of the canonical SCF-MO’s given in Table 2 provide some semi-quantitative features to understand the electronic structure of nitroethylene in the frame of the Koopmans’ theorem [12]. Inspecting the expansion coefficients in the atomic orbital basis shows that, in both cases, the highest occupied molecular orbitals (3a” and 5a”) are the anti-bondin g 2p,-orbital and the anti-bonding linear combination of the 2p,,-orbitals of oxygen, respectively. This is in contrast to the semi-empirical results, where the highest occupied MO is predicted to be the n-orbital of oxygens [7, 81. Of course, the orbital ordering from the semiempirical MO calculation is dependent upon the empirical parameter sets employed [8]. The first ionization is thus predicted to come from the x-electrons of oxygen, the theoretical value of 12.19 eV being the first ionization potential of nitroethylene. The experimental ionization potential as well as the photoelectron spectroscopic data are not yet available. We notice further that the n-orbital of oxygens (l5a’ and 16a’ for the planar and 3a” and 14a’ for the perpendicular conformation) are nearly degenerate, the antisymmetric combinations (16a’ and 14a’) being slightly below the symmetric ones. Of particular interest are the 2a”- and 4a”-orbitals, which correspond to the bonding n-orbital of the ethylene molecule (I b,,-orbital of ethylene). Comparing with the lb,,- orbital energy of -0.4064 a-u., calculated by the same basis set contraction of the Gaussian lobe functions [l I], we notice that the 2a”- and 4a”-orbitals are stabilized by an amount of 2.04 eV and I .75 eV, respectively for the planar and the perpendicular conformations of nitroethylene. Small destabilization of the orbital energy in the perpendicular form is related to the diminishing delocalization of the ethylene x-electrons upon rotating the nitro group as the expansion coefficients show.
MOLECULAR
PROPERTIES
Table 3 summarizes the calculated dipole moment and the electric field gradient of nitrogen in nitroethylene. The calculated dipole moment of 4.429 D is approximately I6 o/0 larger than the reported experimental value of 3.70 D [4]. The electronic charge distribution at the site of nitrogen is almost spherically symmetric, judging from the relatively small value of the electric field gradient. The field gradient is smaller in the planar conformation than in the perpendicular one. The nuclear quadrupole coupling constant of 14N is calculated to be - 1.1 I MHz with the asymmetry parameter of 0.18, using the nuclear quadrupole moment Q(“N) = 1.56x 1O-26 cm2, obtained by O’Konski and Ha [ 181. This can be compared with the experimental value of - 1.25 MHz and 0.39, reported in ref. 4. The diamagnetic contribution to the nuclear magnetic shielding tensor at A is defined as [l9]
Q(A) = -
e2
2mC’
315 TABLE DIPOLE
3 hlOhlENT
AND
ELECTRIC
FIELD
Planar Dipole
moment
(Debye
PY
lctl Expt.” Electric
field
gradient
OF THE NITROGEN
units)
of the nitrogen
- 4.098 0.558 4.136
(atomic
units)
X’X’
-0.179
-0.162
_V’_V’
0.302 -0.123 0.18
-0.199 0.361 0.10
I'$ 77
IN NITROETHYLENE
Perpendicular
-4.370 0.722 4.429 3.70;0.03
Px
GRADIENT
= Ref. 4.
where yAi represents the distance of electron i from nucleus A, and Q, /3 = X, J’ and z. It is sufficient to calculate this quantity from the knowledge of the ground state wavefunction, Y. The paramagnetic contribution requires the excited state molecular wavefunctions. For protons, however, it is known that the diamagnetic term is the dominant term. Table 4 summarizes the shielding components calculated TABLE
4
DIAMAGNETIC
CONTRIBUTION
IN NITROETHY
LENE’
H3
HI HZ ’ Dimensionless for definition).
TO THE NUCLEAR
hlAGNETlC
SHlELDlNG
CONSTANTS
~,*x,
QP’J’
b,.,,
<%?
0.1 II9 0. I826 0.06 I I
0.1956 0.1106 0.2011
0.2582 0.246 1 0.2208
0.1886 0.1798 0.1610
units x
104; 2.66245
x IO-’
x natural
units
=
dimensionless
FOR THE PROTONS
units
(see
ref.
19
for three different protons in nitroethylene after diagonalizing the tensors individually. The
316 TABLE
5
ELECTRON
POPULATION
C,
s
P. PY Pr total
C2
S PI PY PZ total
N
S PX PY PZ total
IN
NITROETHYLENE
Planar
Perpendimlar
3.132 0.781 I.185 1.100 6.198
3.125 0.785 1.190 I .089 6.189
01
3.249 1.225 I.159 0.873 6.506
3.243 1.221 1.145 0.912 6.521
02
3.337 1.208 I .039 I.195 6.779
3.336 1.206 I.202 1.036 6.780
HI HZ H3
S
082.272
#.5’S
Hy.557
~7.570
H;.669
@.6S9
P% PY PZ total
~6,305
for the planar c5.189 1
N6.779
I
~6.780
S
S
Perpendicular
3.860 1.807 I.188 I.407 8.262
3.860 1.805 I.402 I.189 8.256
3.858 I.805 I.183 I .424 8.270
3.860 I .805 I .402 1.189 8.256
0.658 0.667 0.660
0.670 0.669 0.659
-_____07.252
conformation c;.52
S
P. PY PZ total
~~_I98
S
Planar
@.550
and 0;.;55 .
for the perpendicular one, which are quite similar to each other. Inspecting the detailed atomic orbital population of electron, however, we notice marked shifts of electrons from the p,-orbitals to the p,-orbitals especially for the N, 0, and O2 atoms upon rotating the nitro group. They are 0.159 e- for N, 0.218 e- for 0, and 0.235 e- for 02, respectively. These shifts of electrons reflect the diminishing TABLE AVERAGE
6 VALUE
OF
THE
INVERSE
OF
THE
ELECTRONIC
Planar
Perpendicrdar
16.09; 14.950 19.235 20.023 20.240 6.752 6.028 7.082
16.090 14.908 19.238 20.096 20.096 6.608 6.085 7.023
Cl CZ N 01 02 H, H2 Ha il Atomic
units.
DISTANCE
FROM
THE
NUCLEUS
()’
317 degree of the delocalization of ethylene n-electrons throughout the nitroethylene molecule and it is also related to the decrease in the partial double bond character of the C-N bond or the failure of x-electron conjugation in the perpendicular conformation. The failure of n-electron conjugation is, in turn, responsible for the relatively high barrier in nitroethylene. Table 6 summarizes the average values of the inverse of the electronic distance from the nucleus, which is defined as
where n stands for total number of electrons in a molecule. One notices that the resulting average distances between the nuclei and the electronic charge cloud becomes larger (xA < l/r*> value becomes smaller) through rotating the nitro group. This reflects, in turn, a large decrease in the electron-nuclear attraction energy in the perpendicular conformation and this attractive energy component is the dominant term in determining the barrier mechanism in nitroethylene as the energy partitioning scheme above as shown.
ACKNOWLEDGMENT
We express our sincere appreciation to the ETH-Zurich computer center for providing computer time and to Prof. Hs. H. Giinthard for his encouragement and advice.
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