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Calculation of the electronic structure of saturated nitogen-containing compounds by the method of geminals
Volume
23. number
CHEhllCAL PHYSICS
3
LETTERS
1 December
1973
CALCULATION OF THE ELECTRONIC STRUCTURE OF SATURATED NITROGEN-CONTAINING COMPOUNDS BY THE MJZTHODOF GEMlNALS Insrirure
ofChenrisrry
1.Ts. LVAST of IlIe Bashkinm Branch ofrhe Received Revised manuscript
12 June received
Acaden~y
of Sciences.
Ufa.
USSR
1973
10 Seprember
1973
A non-empirical all-v;llence electron calculation on Ihe CzHsNH2 molecule and the polyethylene chain in which one H a!om is subsfiluted by an NIIz group has been carried out using wavsfuncrions conslrucred from geminals. It is shown that the intemction between notvncighbour bonds separated by one C-C bond plays the main role in the transmission of the induclive rffecl.
I.
The localized geminals
Molecules of saturated compounds can be described with the method of geminals [I, 21. According to this method. which was developped in earlier papers [3-S] _ each geminal describing a u-bond is constructed as a bilinear expansion in terms of two atomic orbitals forming this bond
AZ2 are the coefficients of the ionic terms, whereAll, and the term in A 12 is the covalent (Heitler-London) one. The factors A are determined by means of the selfconsistent field procedure. Tile geminals are nonorthogonad, but the overlap integrals are small. In this case one can approximate the energy of the system by means of a convergent series, each term of which consists of integrals with a certain exchange parameter q [6] which is equal to the number of electronic indices belonging to different geminals in these integrals. In our method exchange integrals with II = 2 on!y are taken into account .!?I = - 2 c
~,(12)$,(34)&
- @$)I
432
-,
n
g’t 3 n-c-c-il-
(2)
n
Ii
1’ 4 ..61 12’ H
k
X Jlk(23)3r1(14)d(l)...d(4),
where fik, is the effective 4electron hamiltonian, I$!) is the coulombic energy. Tfle geminals of the bonds of the saturated nitrogencontaining compounds are constructed from the Is orbitals of the H atoms and sp3 orbit& of the C and N atoms. In accordance with the assumed sp3 character of the hybridization, the valence angles at the N atom are taken to be equal to the tetrahedron angles. It is assumed that the lone pair occupies the fixed (sP~)~ orbital. Each orbital is represented by a linear combination of gaussian lobe functions. As an example we give in table 1 the parameters of the bonds of the molecules C2Hg and C,H,NH, (conformation with the plane of symmetry) [S] . The numbering of the bonds and their conventional direction are shown in fig.1 _In each bond the orbital qpl belongs to the atom at the base of the atiow, q2 to the atom at its end. The dipole moment is positive when negative charge is shifted in the arrow directior?.
3
H
H
Volume 23, number 3
CHEbl!CAL Table
PHYSICS
I December 1973
LETTERS
1
Table 2 The dipole moments
Molecule
Bond
C2Hs
c-c
C-H N-H
CzHsNHz
a)
k
E; A
P
2.
- the
As2
PC)
- CH(NHz)
0.449
0.152
0
P)
lb)
0.408
0.124
1.880
0.333
0.404
0.034
1.251
3
0.100
0.440
0.233
4
0.143
0.447
0.165
0.257
0.408
0.105
1.843
7-8
0.238
0.408
0.126
1.964
9
0.242
0.408
0.121
1.938
@)
A,lb)
AI2
-
0.152
-
0.240
1-2
C-N c-c C-H
5-6
C-H C-H
bond number
The inductive
KHz),,
bonds
in the molecule
zc)
3d)
1
0.05072
0.05294
0.05294
0.649
0.00443 0.000361
0.01192 0.00354
0.01183 0.00442
0.069
4
0.000031
0.00073
0.00092
(1).
effect
When investigating the inductive effect in saturated compounds the field effect and the effect of successive transmission of polarity through a chain of bonds resulting from the interaction between neighbour bonds are usually taken into account [7]. Also the effect ought to be taken into account which can be called “the effect of successive polarity of the non-neighbour bonds”. This effect is due to the fact that each bond is influenced via the field by the polarized non-neighbour bond which is situated two bonds nearer to the substituent in the chain. The inductive effect is investigated in the polyethylene chain in which one H atom is substituted by an NH, group: - (CH2),, - CH(NH2) - (CH2)n -. The axis of the lone pair and the C-C and C-N bonds form one plane. One can assume that the fesults obtained for this system must be valid for all saturated atiphatic compounds [7] _ The influence of the substituent is estimated quantitatively by the dipole moments of the C-C bonds. In table 2 we give the results of three calculations. In the fitit calculation (see column 1 in table 2) only the effect of successive polarity of the neighbour bonds is taken into account. As is seen, the dipole moments fall off exponentially as the distance from the substiWent increases. When the distance from the substituent increases by one bond the dipole moment becomes 12 times less. In the second calculation (column 2 ) the effect of
- (CHz),,
-
2 3
(see fig. 1).
- coefficients of normalized geminals -dipole moment of bond (in debye).
-
of C-C
a) X_
- the C-C bond number, counting from the C-N bond. b) Column 1 - effect of successive polarity of the ncighbour bonds. ‘) Column 2 - effect of succcssivc polarity of the neighbour and non-neighbour bonds. d, dolumn 3 - eKec[ of successive polarity of the neighbour and non-neighbour bonds and the field effect.
successive polarity of the nearest non-neighbour bonds is also taken into account. The interaction between the non-neighbour bonds separated by one C-C bond is averaged according to all three ~urzs configurations. According to our results, when the distance from the substituent increases by one bond, the dipole moment becomes 4.2 times less in average. In the third calculation (column 3) all three effects are taken into account. The field effect is averaged according to the all-trms configuration. The configurations of the chain in which the distance between nonneighbour atoms is less than 4 au were excluded from consideration. It is assumed that all other configurations have an equal probability. The dielectric constant is taken to be equal to 2. According to our results, when the distance from the substituent increases by one bond, the dipole moment becomes 4 times less. The corresponding experimental figure is 2.8 [7] .
References [I] W.A. Fock, Dokl. Aknd. Nnuk [2] A.C. Hurley, J.E. Leonard-Jones Sot. A220 (1953) 446. [3] l.Ts. Lyast, Zh. Stiukt..Khim. [4] I.Ts. Lyast. Zh. Strukt. Khim. [S] I.Ts, Lyast, Zh. Strukt. Khim. [6] 1.Ts. Lyast, Zh. Strukt. Khim. [7] R.W. Taft, in: Steric effects in Newman (1956) ch. 13.
USSR 73 (195Oj 735. and J.A. Pople. Rot.
Roy.
USSR 7 (1966) 80. USSR 14 (1973) 141. USSR 14 (1973) 340. USSR 5 (1964) 94. organic chemistry, ed. MS.
433
23. number
CHEhllCAL PHYSICS
3
LETTERS
1 December
1973
CALCULATION OF THE ELECTRONIC STRUCTURE OF SATURATED NITROGEN-CONTAINING COMPOUNDS BY THE MJZTHODOF GEMlNALS Insrirure
ofChenrisrry
1.Ts. LVAST of IlIe Bashkinm Branch ofrhe Received Revised manuscript
12 June received
Acaden~y
of Sciences.
Ufa.
USSR
1973
10 Seprember
1973
A non-empirical all-v;llence electron calculation on Ihe CzHsNH2 molecule and the polyethylene chain in which one H a!om is subsfiluted by an NIIz group has been carried out using wavsfuncrions conslrucred from geminals. It is shown that the intemction between notvncighbour bonds separated by one C-C bond plays the main role in the transmission of the induclive rffecl.
I.
The localized geminals
Molecules of saturated compounds can be described with the method of geminals [I, 21. According to this method. which was developped in earlier papers [3-S] _ each geminal describing a u-bond is constructed as a bilinear expansion in terms of two atomic orbitals forming this bond
AZ2 are the coefficients of the ionic terms, whereAll, and the term in A 12 is the covalent (Heitler-London) one. The factors A are determined by means of the selfconsistent field procedure. Tile geminals are nonorthogonad, but the overlap integrals are small. In this case one can approximate the energy of the system by means of a convergent series, each term of which consists of integrals with a certain exchange parameter q [6] which is equal to the number of electronic indices belonging to different geminals in these integrals. In our method exchange integrals with II = 2 on!y are taken into account .!?I = - 2 c
~,(12)$,(34)&
- @$)I
432
-,
n
g’t 3 n-c-c-il-
(2)
n
Ii
1’ 4 ..61 12’ H
k
X Jlk(23)3r1(14)d(l)...d(4),
where fik, is the effective 4electron hamiltonian, I$!) is the coulombic energy. Tfle geminals of the bonds of the saturated nitrogencontaining compounds are constructed from the Is orbitals of the H atoms and sp3 orbit& of the C and N atoms. In accordance with the assumed sp3 character of the hybridization, the valence angles at the N atom are taken to be equal to the tetrahedron angles. It is assumed that the lone pair occupies the fixed (sP~)~ orbital. Each orbital is represented by a linear combination of gaussian lobe functions. As an example we give in table 1 the parameters of the bonds of the molecules C2Hg and C,H,NH, (conformation with the plane of symmetry) [S] . The numbering of the bonds and their conventional direction are shown in fig.1 _In each bond the orbital qpl belongs to the atom at the base of the atiow, q2 to the atom at its end. The dipole moment is positive when negative charge is shifted in the arrow directior?.
3
H
H
Volume 23, number 3
CHEbl!CAL Table
PHYSICS
I December 1973
LETTERS
1
Table 2 The dipole moments
Molecule
Bond
C2Hs
c-c
C-H N-H
CzHsNHz
a)
k
E; A
P
2.
- the
As2
PC)
- CH(NHz)
0.449
0.152
0
P)
lb)
0.408
0.124
1.880
0.333
0.404
0.034
1.251
3
0.100
0.440
0.233
4
0.143
0.447
0.165
0.257
0.408
0.105
1.843
7-8
0.238
0.408
0.126
1.964
9
0.242
0.408
0.121
1.938
@)
A,lb)
AI2
-
0.152
-
0.240
1-2
C-N c-c C-H
5-6
C-H C-H
bond number
The inductive
KHz),,
bonds
in the molecule
zc)
3d)
1
0.05072
0.05294
0.05294
0.649
0.00443 0.000361
0.01192 0.00354
0.01183 0.00442
0.069
4
0.000031
0.00073
0.00092
(1).
effect
When investigating the inductive effect in saturated compounds the field effect and the effect of successive transmission of polarity through a chain of bonds resulting from the interaction between neighbour bonds are usually taken into account [7]. Also the effect ought to be taken into account which can be called “the effect of successive polarity of the non-neighbour bonds”. This effect is due to the fact that each bond is influenced via the field by the polarized non-neighbour bond which is situated two bonds nearer to the substituent in the chain. The inductive effect is investigated in the polyethylene chain in which one H atom is substituted by an NH, group: - (CH2),, - CH(NH2) - (CH2)n -. The axis of the lone pair and the C-C and C-N bonds form one plane. One can assume that the fesults obtained for this system must be valid for all saturated atiphatic compounds [7] _ The influence of the substituent is estimated quantitatively by the dipole moments of the C-C bonds. In table 2 we give the results of three calculations. In the fitit calculation (see column 1 in table 2) only the effect of successive polarity of the neighbour bonds is taken into account. As is seen, the dipole moments fall off exponentially as the distance from the substiWent increases. When the distance from the substituent increases by one bond the dipole moment becomes 12 times less. In the second calculation (column 2 ) the effect of
- (CHz),,
-
2 3
(see fig. 1).
- coefficients of normalized geminals -dipole moment of bond (in debye).
-
of C-C
a) X_
- the C-C bond number, counting from the C-N bond. b) Column 1 - effect of successive polarity of the ncighbour bonds. ‘) Column 2 - effect of succcssivc polarity of the neighbour and non-neighbour bonds. d, dolumn 3 - eKec[ of successive polarity of the neighbour and non-neighbour bonds and the field effect.
successive polarity of the nearest non-neighbour bonds is also taken into account. The interaction between the non-neighbour bonds separated by one C-C bond is averaged according to all three ~urzs configurations. According to our results, when the distance from the substituent increases by one bond, the dipole moment becomes 4.2 times less in average. In the third calculation (column 3) all three effects are taken into account. The field effect is averaged according to the all-trms configuration. The configurations of the chain in which the distance between nonneighbour atoms is less than 4 au were excluded from consideration. It is assumed that all other configurations have an equal probability. The dielectric constant is taken to be equal to 2. According to our results, when the distance from the substituent increases by one bond, the dipole moment becomes 4 times less. The corresponding experimental figure is 2.8 [7] .
References [I] W.A. Fock, Dokl. Aknd. Nnuk [2] A.C. Hurley, J.E. Leonard-Jones Sot. A220 (1953) 446. [3] l.Ts. Lyast, Zh. Stiukt..Khim. [4] I.Ts. Lyast. Zh. Strukt. Khim. [S] I.Ts, Lyast, Zh. Strukt. Khim. [6] 1.Ts. Lyast, Zh. Strukt. Khim. [7] R.W. Taft, in: Steric effects in Newman (1956) ch. 13.
USSR 73 (195Oj 735. and J.A. Pople. Rot.
Roy.
USSR 7 (1966) 80. USSR 14 (1973) 141. USSR 14 (1973) 340. USSR 5 (1964) 94. organic chemistry, ed. MS.
433