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Comparison of Calculated and Experimental Electron Difference Densities of Tetracyanoethylene.

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at equilibrium; cf. Fig. I), according to the Hammond postulate
the transition state in our case is more similar to the covalent
compound than on collapse of the high-energy system of
dissociated ions in dichloroethandB1.Dynamic NMR measurements therefore permit the study of barriers of ionization
equilibria, and should thus provide a deeper insight into
the transition state of ion recombinations in solution.
stat
Received: January 18, 1977 [ Z 658 IE]
German version: Angew. Chem. 89,266 (1977)
CAS Registry numbers:
Trityl chloride, 76-83-5
~
[l] NMR SpectroscopicStudies on Kinetics and Thermodynamics of Reversible Dissociation Reactions, Part 3. This work was supported by the
Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.-Part 2: M . Feigel, H . Kessler, Tetrahedron 32, 1575 (1976).
[2] D. J . Raber, J . M . Harris, P . u. R. SchkJJerin M . Szwarc: Ions and
Ion-pairs in Organic Reactions, Vol. 11. Wiley, New York 1974, pp.
247-374.
[3] a) C. D. Rifchie, Acc. Chem. Res. 5, 348 (1972); b) L. M . Dorfmann,
R. J . Sujdak, B. Bockrath, ibid. 9, 352(1976).
[4] J . I . Brauman, M! C . Archie, J. Am. Chem. SOC.92, 5981 (1970).
[5] The entropy of trityl chloride ion pairs in SO2 is not known exactly.
WhileK, hasbeendeterminedas0.014atO0C[6a], a value of K , =0.0025
can be calculated from the results of temperature-dependent conductivity
measurements [6b]. In [6b] AS? was determined as -34.5 e.u. Our
own concentration-dependent NMR measurements give AS?= - 37.5
e.u.forthedeuteratedcompound,butavalueofK, =0.0044on extrapolation to 0°C.
[6] a) N . N . Lichtin, Prog. Phys. Org. Chem. 1, 75 (1963); b) E. Clougherry,
Ph. D. Boston University 1966, Diss. Abstr. B 27, 1438.
[7] E . D. Huyhes, C. K . Inyold, S. F. Mok, S. Parai, I! Pocker, J. Chem.
SOC.1975, 1265.
kcal mol was determined by
[8] A recombination barrier of AG:,,=8.1
an indirect method for tri-p-tolylmethyl chloride in methylene chloride
[9a]; no change in line shape has been reported on direct measurement
of the ionization of this compound in SO,/CD2Cl2 [9b].
[9] a ) H. H. Freedman, A. E. Young, !I R . Sandel, J. Am. Cbem. SOC. 86,
4722 (1964); b) M . Nojima, M . Ishiyama, N . Tokura, Kogyo Kagaku
Zasshi 73. 2306 (1970).
Comparison of Calculated and Experimental Electron
Difference Densities of T e t r a c y a n o e t h y l e n e [ * * ]
By Hans-Lothar Hase, Karl- Wilheim Schulte, and Armin
Schweigr]
It is assumed[” that electron difference densities[*] in the
region of chem’ical bonds can be determined with an accuracy[31of 0.05 e/A3.We now report quantum chemical ab initio
results which cast doubt upon this expectationL4]for the standard example tetracyanoethylene (TCNE)[’].
D
.
,_
I
Fig. 1. Calculated (“4-31 G” basis) static ( s t a t ) and dynamic ( d y n ) and
experimental ( e x p ) electron difference densities in the molecular plane ( A )
and perpendicular to the molecular plane through the C=C ( B ) , C-C
(C), and C s N bonds (D) of tetracyanoethylene (TCNE). The contour
negative
lines mark differences of 0.1 e/A3 in all cases; positive lines (-),
experimental).
lines (----), zero line (.... calculated and
shows sections through the resulting static (star) and dynamic
( d y n ) densities and also through the experimental (exp)
densities [in the molecular plane ( A ) , perpendicular thereto
through the C=C (B), C-C (C), and C=N bonds ( D ) ] .
As shown by the figure, overall agreement between the calculated and the experimental difference densities is surprisingly
good. However, some considerable discrepancies (0.5 e/A3 for
W N and 0.4e/A3 for C-C) are found for the difference
densities in the bonds (Table 1).
The deviations of the calculated values to be expected as
a result of using the incomplete “4-31 G” basis have been
estimated for the model compound cyanogen (NCCN). For
Table 1. Peak heights in the difference densities of tetracyanoethylene (TCNE).
Peak heights in the difference densities
r431
Difference density type
4-31
G
experimental
For this purpose the static and dynamic electron difference
densities were calculated in “4-31 G quality[61.Figure 1
C=-N
C=C
C-C
lone pair
static
dynamic
0.7
0.4
0.5
0.3
0.6
0.2
1.1
0.3
dynamic
0.9
0.4
0.6
0.4
Table 2. Peak heights in the difference densities of cyanogen (NCCN).
Peak heights in the difference densities
[*] Prof. Dr. A. Schweig, Dr. H.-L. Hase, Dipl.-Chem. K.-W. Schulte
Fachbereich Physikalische Chemie der Universitat
Auf den Lahnbergen, D-3550 Marburg (Germany)
p’] Part 3 of “Comparison of Observed and Calculated Electron Densities”,
DFG-Sonderforschungsbereich 127 (“Crystal Structure and Chemical Bonding”). Presented in part at the “Sagamore V” conference, Killjava (Finland),
August 1 6 2 0 , 1976.-Part 2: H . Imgartinger, H . L. Hase, K.-W Schulte,
A. Schweig, Angew. Chem. 89, 194 (1977); Angew. Chem. Int. Ed. Engl.
16, 187 (1977).
Angew. Chem. l n t . Ed. Engl. 16 ( 1 9 7 7 ) No. 4
~
~
3
1
-
Difference density type
C=N
C-C
lone pair
DZ+P
(near HF)
static
dynamic
1.0
0.65
0.6
0.4
1.1
0.35
4--31
static
dynamic
0.8
0.47
0.4
0.24
0.40
1.1
257
this molecule the static difference density is known in “near
HF” quality[’]. As shown by comparison of the corresponding
dynamic difference densities in the bonds with the corresponding “4-31 G”values[’] (Table 2 ) the mutual deviation between
the two calculations does not exceed 0.16 (C-C) or 0.18e/A3
( e N ) . “4-31 G ’ calculations thus prove to be surprisingly
reliable for calculations of difference densities.
[7] A . D. McLean, M . Yoshiminel Tables of Linear Molecule Wave Functions,
IBM 1967; F. L. Hirshfeld, Acta Crystallogr. 827, 769 (1971).
[8] P. C o p p e n s , Acta Crystallogr. 830,255 (1974). According to this method
the maximum bond densities in NCCN are represented by a Gaussian
function p= Aexp( - ar’) perpendicular to the bonds and subsequently
“smeared out” in simple manner. Our “4-31 G” difference densities
give A = 0 . 8 , 0.4, and l.le/A’ and x=6.365, 7.354, and 12.237.k’ for
C-N, C-C, and the lone pair, respectively.
[9] J. Rudfoff,Elektron. Rechenanl. 16, 18 (1974).
An Economic Basis for Electron Difference Density
CalculationsC‘*l
By Hans-Lothar Hase and Armin Schweig[*]
Experimental electron difference densities are already available for large polyatomic molecules. RHF (Restricted HartreeFock) calculations have so far proved impossible for such
systems, and calculations with drastically limited basis sets
are therefore unavoidable. In this communication we propose
such a basis which leads to results of “near RHF” quality
and therefore appears very promising for difference density
calculations on large molecules.
Fig. 2. Perspective representation of the three-dimensional static ( A ) and
dynamic ( B ) “4-31 G” difference electron densities of tetracyanoethylene
and -0.1 e/A3 (-).
(TCNE) for the values 0.1 e/A3 (-)
These results suggest that the “4-31 G” bond difference
densities of Table 1 are falsified by no more than 0.2e/A3
in the critical bonds G N and C-C. Thus, the corresponding
experimental densitiesare probably more erroneous than hitherto assumed (0.07 e/A3). The large experimental values may
possibly be explicable in terms of erroneous scaling[’].
Our results pose the challenge to compare calculated and
experimental difference electron densities for other compounds
in order to better appreciate their accuracy. The present
demonstration of the very good (if not yet optimum) quality
of the “4-31 G” difference densities attainable with reasonable
effort is an encouraging step in this direction. These densities
(static and dynamic) are shown in perspective[’] for TCNE
in Figure 2. Corresponding representations of experimental
difference densities have not so far been employed in any
case.
Received: January 20, 1977 [Z 655a IE]
German version: Angew. Chem. 89, 263 (1977)
1.157~
NC
-C
-N
-
1.3808
As shown by a comparison“], the “4-31 G C zdifference
1
densities of cyanogen (NCCN) are of surprisingly high quality
relative to the “near RHF” densities[31.However, discrepancies
do occur in thepeak heights in thedifference densities (0.2 e/A3)
and in the detailed shape of the densities (cf. Fig. 1). As
a corrective measure we have tentatively extended the “431 G” basis by admixture of limited sets of atomic or bond
polarization functions (henceforth abbreviated as AP or BP).
Four basis sets were tested explicitly: STO-3GC4’
( A ) ; 4-31 G
( B ) ; 4-31 G + A P [AP: six d functions at each
(C); and 4-31 G + B P [BP: one s and two p functions in
the middle of each
(D).
Table 1. Peak heights in the difference densities of cyanogen (NCCN).
CAS Registry number:
Tetracyanoethylene, 670-54-2
I
~
[l] P . Coppens, Acta Crystallogr. ,431, S218 (1975).
[2] The electron difference density of a molecule is defined as the difference
between the total molecular electron density and the superposed atomic
densities of the atoms of which the molecule considered is composed.
[3] Standard deviation in the electron difference densities resulting from
statistical errors (in the structure factors, the positional and temperature
factors of the atoms, and in the scale factor). Systematic errors (due
to approximation corrections of the experimental values or to crystal
forces) are not considered.
141 A somewhat greater standard deviation (0.07 e/A3) was estimated for
TCNE [5].
[5] P. Beckeu, P . Coppens, F . K . Ross, J. Am. Chem. SOC.95, 7604 (1973).
[6] R . Ditchfield, W J. Hehre, J. A. Pople, J. Chem. Phys. 54, 724 (1971).
The total static electron density was calculated with the POLYATOM
program system (QCPE, No. 199) on the basis of the experimental
geometry [5]. The atomic densities were determined with the RHF
program section using the same basis set. In order to determine the
dynamic difference electron density according to H.-L. Hase, H . Reitz,
and A. Schwriq, Chem. Phys. Lett. 39, 157 (1976), an orthorhombic
unit cell was constructed with the dimensions a = & h=9, c = 5 A , into
which a molecule of TCNE just fits. The temperature factors obtained
by neutron diffraction were used [ 5 ] .
258
Basis sets
A
B
C
D
E
STO-3 G
4-31 G
4-31 G + A P
4-31 G BP
DZ+AP
+
j
Peak heights in the difference densities
[e/A31
N; ;
0.8
0.9
c;
;;pair
0.4
0.5
0.6
0.6
1.1
1.1
1.1
1.1
Sections through the resulting static electron difference
densities A-D are shown in Figure 1 and through the corresponding “near RHF” density ( E ) for comparison. Table 1
contains the maximum difference densities in the bonding
[*] Prof. Dr. A. Schweig, Dr. H.-L. Hase
Fachbereich Physikalische Chemie der Universitat
Auf den Lahnbergen, D-3550 Marburg (Germany)
Part 4 of “Comparison of Observed and Calculated Electron Densities”,
DFG-Sonderforschungsbereich 127 (“Crystal Structure and Chemical Bonding”).-Part 3: ref. [!].
[**I
Angew. Chem. Int. Ed. Engl. 16 (1977) N o . 4
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