1440
J. Phys. Chem. 1988, 92, 1440-1444
-89.0 kcal/mol, while the ring nitrogen goes from -68.9 to -99.7 kcal/mol. Most significant, however, is that the sulfilimine VI1 does not show extended negative regions above and below the ring (Figure 6b). This is a striking difference between the two sulfilimines that are being studied and indicates that I11 should be considerably more reactive toward electrophiles than is VII. Summary and Conclusions The analysis that has been presented shows that the most negative regions in these molecules are associated with one of the ring nitrogens and not with the exocyclic nitrogen that is to be oxidized. This is true in the sulfilmine intermediates as well as in the original aminoazines. An important new feature in the case of sulfilimine I11 is that the exocyclic nitrogen has become much more accessible to electrophiles, now from both sides of the ring plane as well as in the plane, whereas the only channel of approach in the original azine I1 was from one side of the ring plane (compare Figures 3 and 4). The increase in accessibility is much greater for the exocyclic nitrogen than for the one in the ring; the latter could be approached from either side of the ring plane even before formation of the sulfilimine, since its lone-pair potential
extends above and below the ring plane, unlike that of the exocyclic nitrogen. Thus, while the most reactive site for initial electrophilic attack is the ring nitrogen, in I11 as well as in 11, the possibility of the reaction taking place at the exocyclic nitrogen is significantly greater in the sulfilimine. Indeed, as mentioned earlier, a 33% yield of 2-nitropyrimidine (V)was obtained from sulfilimine IIL3 The introduction of the -NOz group in position 5 prevents the development of extensive, relatively strong negative electrostatic potentials above and below the pyrimidine ring (Figure 6b). Accordingly, there does not occur, in VII,the considerable increase in electrophilic accessibility to the exocyclic sulfilimine nitrogen that is found in 111. We suggest that this is at least part of the reason why oxidation of the latter nitrogen in VI1 is not ob~erved.~
Acknowledgment. We greatly appreciate very helpful discussions with Dr. Jane S. Murray and Dr. Michael D. Coburn. We are grateful for the support of this work by the Office of Naval Research. Registry No. 11, 109-12-6; 111, 54214-58-3; VI, 3073-77-6; VII, 108733-91- 1.
An Analysis of ?r-Bond Formation Using Hartree-Fock Theory Hiroshi Ichikawa,* Yukiko Ebisawa, and Atsushi Shigihara Hoshi College of Pharmacy, Shinagawa. Tokyo 142, Japan (Received: June 1 1 , 1987)
A Hartree-Fock MO theoretical method of energy analysis of chemical binding which might be applied to large organic systems is proposed. An application of the method to the *-bond formation in the ethylene system shows that a release of the kinetic energy pressure of 2p valence electrons leads to delocalization between 2p atomic orbitals and, as a consequence, both carbon atoms move closer with a concomitant lowering of the potential energy and the total energy.
holds in chemical processes (unless it is applied to transition states), Seeking the reason for chemical binding has been a central the kinetic energy of nuclear motion may be considered separately. problem in chemistry. This extends to prediction of reactivity and Therefore, major and important energies in molecule are the reaction products in synthetic chemistry. The concept of atomic potential energy and the kinetic energy of electrons. or molecular orbital interaction has been prevalent in the theories Ruedenberg and his co-workers have performed a quantum of chemical binding (orbital interaction theories). Examples can be seen in molecular orbital theory,’ frontier orbital t h e ~ r y , ~ ? ~ mechanical analysis on the formation of the covalent bond in the hydrogen molecule ion.6-8 They came to the conclusion that charge-transfer theory, etc.“ However, such theories raise further electron sharing leads to chemical binding as the result of a subtle questions regarding the physical sources of attractive or repulsive interplay between the uncertainty principle and the nuclear atinteraction between orbitals. Although orbital interaction theories tractions: “Delocalization of the valence electrons from one atom are useful in application, it is fruitful to proceed beyond this level to other atoms leads to a lowering of the kinetic energy pressure and to look for explanations in terms of fundamental physical and, as a consequence, there results a firmer attachment of these quantities. electrons to the nuclei with a concomitant lowering of the potential Chemical phenomena always involve energetic changes in a as well as the total energy”. given system. The basic energies which govern chemical pheWe consider their method of approach to be the most fundanomena are electrostatic potentials (between electrons, between mental one among those so far proposed since it clarifies the roles electrons and nuclei, and between nuclei) and kinetic energies of of the potential energy and the kinetic energy of electrons in nuclei and electrons. Since the Bom-Oppenheimer approximation5 chemical binding. We also believe this kind of analysis to be effective for the fundamental interpretation of chemical phe(1) Early history of molecular orbital theory is summarized in: Parr, R. nomena. However, it does not seem to be widely known among G. Quantum Theory of Molecular Electronic Structure; Benjamin: New organic chemists. This may be because it is difficult to apply the York, 1963; Slater, J. C. Quantum Theory of Molecules and Crystals; same method or similar methods9 to large systems such as those McGraw-Hill: New York, 1963; Vol. 1. (2) (a) Fukui, K.; Yonezawa, T.; Shingu, H. J . Chem. Phys. 1952, 20,722. (b) Fukui, K.; Yonezawa, T.; Nagata, C.; Shingu, H. J. Chem. Phys. 1954, 22, 1433. (c) Fukui, K.; Yonezawa, T.; Nagata, C. Bull. Chem. Soc. Jpn. 1954, 27, 423. (3) (a) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965,87,395. (b) Longuet-Higgins, H. C.; Abrahamson, E. W. J. Am. Chem. SOC.1965, 87, 2045. (4) (a) Mulliken, R. S. J . Am. Chem. SOC.1952, 74, 811. (b) Mulliken, R. S.J . Chem. Phys. 1951, 19, 514. (c) Briegelb, C. Elektronen-DonarorAcceptor-Komplexe; Springer-Verlag: Berlin, 196 1.
0022-3654/88/2092-1440$01.50/0
( 5 ) Born, M.; Oppenheimer, J. R. Ann. Phys. 1927,84, 457. (6) Ruedenberg, K. Rev. Mod. Phys. 1962, 34, 326. (7) Feinberg, M. J.; Ruedenberg, K. J. Chem. Phys. 1971, 54, 1495. (8) Feinberg, M. J.; Ruedenberg, K.; Mehler, E. L. Adu. Quantum Chem. 1970, 5, 27. (9) (a) Wilson, Jr., C. W.; Goddard 111, W. A. Theor. Chim. Acta 1972, 26, 195. (b) Goddard 111, W. A,; Wilson, Jr., C. W. Theor. Chim. Acta 1972, 26, 21 1.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1441
Analysis of a-Bond Formation
SCHEME I1
SCHEME I
A
C
A TOTAL
in which organic chemists are interested. We have therefore tried to find a convenient energy-component analysis using MO theories. As an application, this paper deals with a simple analysis of the a-bond formation in the ethylene molecule and its ion.
( h b l e t Cry) ENERGY
-77 685869
AU
C
(Doublet 0 2 ~ )
T c r a ~E N E R G Y -77 731980
$2
because it is generally impossible to obtain such SCF intermediate wave functions as those where one of chemical bindings is forced to cease. Therefore, we treated the problem differently as follows. An M O theoretical calculation provides a convenient means Partitioning of Molecular Energy to analyze chemical phenomena by creating models such that the cause and the result(s) can be considered separately. We created We adopted the LCAO SCF MO theory based on the Hara reactant model where the a-bond does not exist between the tree-Fock equationlo since, so far, this theory has been the only two methylene groups. Since the methyl radical and the methyl one that can be applied, with comprehensive accuracy, to sizable cation have planar s t r u c t u r e ~ , ' ~the J ~structure of such ethylene systems. There are some problems regarding electron correlation system may have a C, (in the doublet state) or DZdsymmetries and the S2operator when it is applied to open-shell systems. The (in the singlet or triplet biradical) as shown in Scheme IA: The latter may be solved if one uses a large size basis set." The former plane of one methylene group is orthogonal (0 = 90°) to the other problem becomes crucial when the discussion concerns narrow one due to the least interatomic repulsion. The real ethylene or gaps of relevant energies, since a bond formation is not generally ethylene ion, however, may have a planar structure with a D2h an isodesmic reaction. We will comment on those questions in symmetry because of existence of a a-bond (Scheme IC). connection with the calculated results. Consider the process when A becomes C through the minimum The Hamiltonian of the molecular system is composed of openergy path. As 0 decreases to zero, the bond length between two erators referring to the kinetic energy of the electron, the potential carbons and the geometries around the CH2 groups may be energy between the electrons and nuclei, and the repulsion energy changed. Since angular coordinates do not contribute to the virial between electrons. The electronic energy (Eel), therefore, consists relation~hip,'~ the equation V = -2T holds exactly in this process. of the kinetic ( E )and potential energies. The latter is further The geometrical change on the minimum energy path comes about partitioned into the attractive one-electron potential (Ev) and the as the result of three primary effects: the change of interatomic repulsive two-electron potential ( E J )energies. distances (steric effect), the loss of hyperconjugation, and the Since, in LCAO M O theory, each M O is expanded in terms formation of a-bond, each of which involves an energetic change. of a linear combination of atomic orbitals (AO's), the total energy Shortening of the C-C bond length is clearly produced by the ( E ) based on either the restricted or unrestricted Hartree-Fock a-bond formation. Ih order to study the cause of the a-bond equation12 is expressed by the sum of monocentric (EA) and formation, one must eliminate the geometrical effect which results bicentric ( E A B ) terms from the a-bond formation. To this end we considered a planar intermediate structure (B) for which all geometrical parameters were those of A except that 0 has the same value as in C, usually zero. The molecular energies at B still include the effects of the differences in the steric environment and of the diminished hyperconjugation. The former can be handled by the energy partitioning technique. The latter will be discussed in connection with the calculated energies. where EABNis the nuclear repulsion energy between atoms A and Elimination of the geometrical effect due to the a-bond forB. The detailed method of calculation is found e l ~ e w h e r e . ' ~ - ' ~ mation causes an imbalance in the virial relationship which one It has been reported that both the kinetic and potential energies must carefully analyze. This is the way we studied the a-bond on an atom are dependent on the electron density of the atom as formation in ethylene and its ion. they are supposed to be.I5 It is, however, important to note that As an M O method we adopted 6-31 1G** method20 which is the energy quantities thus obtained as well as the atomic charges considered to be close to the Hartree-Fock limit. Since energy obtained in a Mulliken population analysis16 must be dependent components may be critically dependent on the geometry of the on the basis set since any assignment of charges to atoms in a given system,21 the threshold of geometry optimization was set molecule is necessarily arbitrary. We considered that the values to be 0.000 03 (maximum) and 0.000 02 (rms) hartree/bohr or obtained by eq 2 and 3 are effective as long as they are compared radian,22 which are one-tenth of standard optimization. in the same basis set as well as the same system.
Method of Analysis In the analysis on the covalent bond formation in H2+, Ruedenberg et al. used the wave functions before and after bond formation and analyzed the changes of energy components between them.&* This method is difficult to apply to the present problem (10) (a) Hall, G. G . Proc. R. Soc. London, Ser. A 1951, ,4205, 541. (b) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (11) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York; 1986; Chapter 6. (12) Pople, J. A.; Nesbet, R. K. J. Chem. Phys. 1954, 22, 571. (13) Kollmar, H. Theor. Chim. Acta 1978,50, 235. (14) Ichikawa, H.; Ebisawa, Y. J . Am. Chem. Soc. 1985, 107, 1161. (15) Ichikawa, H.; Sameshima, K.; Ebisawa, Y. Bull. Chem. Soc. Jpn. 1986,59, 2729. (16) Mulliken, R. S. J. Chem. Soc. 1955,23, 1822; 1955 23, 1841; 1955, 23, 2338; 1955, 23, 2343.
Results and Discussion Ethylene Zon. Mulliken and Roothaan predicted that the ethylene ion has a twist angle of 30' from a plane.23 This is the (17) Herzberg, G. Electronic Spectra of Polyatomic Molecule; Van Nostrand: Princeton, NJ, 1967. (18) Walsh, A. D. J. Chem. Soc. 1953, 2260. (19) (a) Nelander, B. J . Chem. Phys. 1969, 51, 469. (b) Srebrenik, S . ; Messer, R. J. Chem. Phys. 1975, 63, 2768. (20) Krishnan, R.; Binkley, J. S.;Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. (21) The energy components were proved to be largely dependent on the scale factor (Pedersen, L.; Morokuma, K. J . Chem. Phys. 1967, 46, 3941). Since a scale factor applies to the electronic coordinates as well as the nuclear coordinates, the energy components naturally are influenced by the condition or threshold of geometry optinlization. (22) We have used the GAUSSIAN-SOH program (Hitac Version of GAUSSIAN-EO (QCPE 437, 1982)) at the Computer Center of the University of Tokyo.
1442 The Journal of Physical Chemistry, Vol. 92, No. 6 , 1988
Ichikawa et al. TABLE I: Kinetic Energies on Atoms and between Atoms
difference* ~
A
doublet
C, C2 CI-C, H Cl-H H'
Cl-H'
triplet C, C1-C2 H C-H
C2"
37.250877 36.974518 0.494 238 0.341 650 0.374 258 0.365631 0.401 416 D2d
A
B
C
Figure 1. Relative energy levels of the total, potential, and kinetic en-
ergies between A, B, and C in the doublet ethylene system. The dotted lines at B indicate the energy levels for which the difference of steric effect between A and B is cancelled out. result of compromise between normal *-bonding (planar structure) and hyperconjugative *-bonding (orthogonal structure). This prediction was supported by ultraviolet studies regarding a series of Rydberg states of ethylene which converge to the ethylene ionz4 A single report stated that a nonplane structure could be reproduced by using the ab initio SCF MO CI method.zs Recently, we have tried to reproduce this structure optimizing all of the geometrical parameters using MP3/6-3 1G**? However, like all other reports based on reasonably extensive S C F MO C I calculations, a planar ion was found to be the most stable and to ~ ~ means that the degree of hyhave a DZh~ y m m e t r y . ~ ' , This perconjugation is not large enough to seriously affect the formation of a normal ?r-bond. A structure with C, symmetry was found to be the most stable in orthogonal structure:26 The nonequivalent geometries of the two methylene groups are caused by a configurational difference in which the unpaired electron occupies only one of the methylene groups. The structure with a Cz, symmetry could be reproduced by 6-311G**, which is shown in Scheme 11. We regarded this structure as the reactant structure. The planar structure with 0 = 0, but all other geometrical parameters equal to those found in A, was regarded as the intermediate structure (B). Finally, all geometrical parameters of the planar structure were optimized with respect to the total energy to give the product structure (C). The difference of the steric effect between A and B was estimated as follows. Since both A and B have a Czusymmetry, the difference of the steric effect (AES') is expressed as Al?' = 4E,390 - 2E1? - 2E1: where E1390represents EABvalue between HI and H3 at 0 = 90° etc. The AEst value can be partitioned into the potential energy and kinetic energy fractions. Figure 1 displays the total, kinetic, and potential energies of the structures A, B, and C. The dotted lines for B show the energy levels for which the change of steric effect is compensated, Le., the steric effect at B is the same as that of A. It is seen that the (23) Mulliken, R. S.; Roothaan, C. C. J. Chem. Rev. 1947, 41, 219. (24) Koppel, H.; Domcke, W.; Cederbaum, L. S.; v. Niessen, W. J. Chem. Phys. 1978,69, 4252. (25) Buenker, R. J.; Peyerimhoff, S. D.; Hsu, H. L. Chem. Phys. Lett. 1971, 11, 65. (26) Ichikawa, H.; Ebisawa, Y.; Shigihara, A. Bull. Chem. SOC.Jpn. 1985, 58, 3619. (27) Foo, P. D.; Innes, K. K. J . Chem. Phys. 1974, 60, 4582. (28) Rodwell, W. R.; Guest, M. F.; Clark, D. T.; Shuttlesworth, D. Chem. Phys. Lett. 1977, 45, 50.
C2"
37.009866 37.013466 0.540 544 0.360 673 0.404726 0.361 175 0.402 196
~
C
ET(B) - ET(C) ET(A) ET(B)
D2h
37.029672 0.570 790 0.363 008 0.410 302
-633 102 122 50 80 -1 2 2
52 43 79 6 15 5 21
-735 467 2 10
219 561 16 13
-751 462 -10 23
221 551 17 18
DZh
37.169263 0.398 538 0.410947 0.406 490
36.889487 0.576 302 0.41 1881 0.410 452
37.174473 0.403938 0.415 244 0.399636
36.888500 0.580074 0.411 448 0.408410
singlet C, Cl-C2 H C-H
structureQ B
D2h
D2h
36.972847 0.790092 0.417 853 0.415260
OThe energies are expressed in hartrees (1 hartree = 2625.5 kJ/ kJ/mol.
mol).
TABLE II: Potential Energies on Atoms and between Atoms
differenceb
A doublet
C, C2
C,-Cz H Cl-H H' C2-H'
triplet Cl CI-C,
H C-H singlet CI CI-CZ
H C-H
C2" -83.183992 -81.588805 9.258424 -1.501 204 -0.416044 -1.656 694 -0.464050
structure" B Cl"
C D2h
-81.823289 -81.956476 -81.884496 8.714 128 8.848456 -1.603445 -1.619222 -0.557646 -0.574292 -1.608 026 -0.547 106
O2d O2h -82.21 5 328 -80.742 657 7.090624 9.523516 -2.021 890 -2.031 433 -0.459010 -0.454732 D2d
D2h
-82.236 848 -80.747470 7.112406 9.488 172 -2.068 122 -2.020672 -0.413430 -0.460560
______ Ep(B) - Ep(C) Ep(A) Ep(B)
O2h -81.297942 7.841 754 -2.102876 -0.569356
3573 -776 -1429 -268 -372 128 -218
-350 -189 353 -4 1 -44 -29 -7 1
3866 -6388 25 -11
-1458 1972 -213 -290
3910 -6238 125 -124
-1445 1915 -216 -286
"The energies are expressed in hartrees. In kJ/mol. EP = E'
+ E'
f
EN.
steric effects appear mostly in the potential energy. The virial theorem requires that the energy differences between A and C obey the relationship, AV = -2AT. The diagram shows that this requirement is reasonably well satisfied. As stated, the energy changes between A and B may be regarded as those caused by the formation of a r-bond between two methylene groups. The total energy dropped by 118 kJ/mol in this process. The changes of its components are significant: Although the potential energy increases, the kinetic energy decreases even more lowering the total energy. Table I shows the kinetic energies on atom (EAT)and between atoms (EABT) for the structures A, B, and C, while Table I1 shows the potential energies. At the reactant structure (A) the kinetic energy of C , is larger than that of C,, indicating the existence of an unpaired electron at C,. The change from A to B lowers the kinetic energy at C I and increases the kinetic energies at C2 and between CI and C2, showing that the kinetic energy pressure at C1is released by forming a ?r bond. Although the change of the total potential energy from A to B (38 kJ/mol) is less than that of the kinetic energy (-156 kJ/mol), the individual potential energy components show drastic changes: a large increase at C1 and considerable decrease at C2 and H, and for C,-C2 all cor-
Analysis of r-Bond Formation
The Journal of Physical Chemistry, Vol. 92, No. 6, 1988 1443
SCHEME 111
respond to the situation that the unpaired electron at C1delocalizes itself to form the T bond. Geometry optimization of B lowers the total energy only by 3 kJ/mol but its components encounter dramatic changes: The potential energy drops by 266 kJ/mol while the kinetic energy rises 263 kJ/mol. The comparison of the bond lengths between the structures B and C indicates that the optimization shrinks the whole system and that a firmer attachment of the two methylene groups is due to a lowering of the potential energy. Tables I and I1 show the detail of this process. Geometry optimization lowers most components of the potential energy partitioning, except the one between the carbon atoms which is increased because of a large increase of the internuclear repulsion (EccN(C) - EccN(B) = 301 kJ/mol). This means that a firmer attachment of the two methylene groups; Le., a shrinking of the double bond is caused not by the lowering of the potential energy in the double bond but by those of other parts of the molecule. All parts of the partitioned kinetic energies are increased as B is changed to C, corresponding to a shrinking of the whole system. From the described results, we naturally reach a conclusion that is very similar to that obtained Ruedenberg et aL6* in the analysis of the covalent bond in the hydrogen molecule ion. Namely, the release of the kinetic energy pressure of the unpaired electron of one methylene, when it is delocalized between the two methylene groups, leads to a lowering of the kinetic energy. The virial theorem is then reestablished by a firmer attachment of the methylene groups to each other because the formation of a more compact system, while causing an increase in the kinetic energy, leads to a larger lowering in the potential energy with a resulting lowering of the total energy. Ethylene Molecule. Since in the neutral ethylene system the B is neither isodesmic nor isogyric, the difference reaction A in the correlation energy may be a significant fraction of the n-bond energy. One would expect the rotational barrier obtained by the Hartree-Fock model to be less than the true value because the energy lowering due to electron correlation is larger for geometry C with paired electrons. The various states of an ethylene molecule have been thoroughly studied by experimentsz9and theoretical calculation^.^^^^^ The rotational barrier of an ethylene molecule has been observed to be 273 kJ/mol. The maximum energy of the barrier occurs for the orthogonal structure. In this state, there are two spin states: the singlet and the triplet state. Their total calculated energies are given in Scheme I11 together with the calculated geometries. The calculated barriers are 168 and 179 kJ/mol for the singlet and triplet spin state, respectively. The difference between the observed and calculated values, ca. 100 kJ/mol, is considered to be the change in the correlation energy due to electron pairing by r-bond formation.
-
H.0.;Kessler, H. Top. Srereochim. 1973, 7, 295. (30) Said, M.; Maynau, D.; Molrieu, J.-P.;Bach, M.-A. B. J . Am. Chem. SOC.1984, 106, 571. (31) Kohler, H. J.; Lischka, H. J . Am. Chem. SOC.1982, 104, 5884. ( 2 9 ) Kalinowski,
w 11-9541
A
B
C
Figure 2. Relative energy levels of the total, potential, and kinetic energies between A, B, and C in the ethylene system with the singlet biradical at A. The dotted lines at B indicate the energy levels for which the difference of steric effect between A and B is cancelled out.
A
B
C
Figure 3. Relative energy levels of the total, potential, and kinetic energies between A, B, and C in the ethylene system with the triplet biradical a t A. The dotted lines a t B indicate the energy levels for which the difference of steric effect between A and B is cancelled out.
The electron-correlation energy is regarded as a correction to the two-electron potential energy calculated by means of the Hartree-Fock theory. Since the electron-correlation energies in B and C are expected to be similar in magnitude,32the correct potential energy at B should be about 100 kJ/mol lower than that actually calculated. However, we did not make this correction in order to avoid confusion. Fortunately, the quantity of correction was not large enough to affect the conclusion. The stabilization energies of CH3 for CH2+and CHI have been It is, therefore, reported to be 122 and 8 kJ/mol, re~pectively.~~ expected that the hyperconjugation between an unpaired electron and the C-H bond is far less than that between a cation center (32) It is accepted that within either isodesmic or isogyric reaction the difference of electron-correlation energies in different geometries remains negligible (ref 11, Chapter 6 ) . (33) Reference 1 1 , Chapter 7.
1444
J . Phys. Chem. 1988, 92, 1444-1451
and the C-H bond. We, therefore, neglected the effect of such a small hyperconjugation which might take place on changing A to B. Figures 2 and 3 show the energy diagrams for the reactant, intermediate, and product structures of the biradical singlet and triplet states, respectively. Dotted lines are those energy levels for which the difference due to the steric effect is compensated. Again it is seen that the steric effects appear only in the potential energy arid that the virial relationship between the reactant and product structures hold reasonably well in both electronic configurations. Similarly to the results for the ethylene ion, the kinetic energy decreases and the potential energy increases at each intermediate structure. One- and two-center terms of the kinetic energy of electrons behave in a manner similar to those in the doublet state: The change from A to B lowers the kinetic energy at both carbon atoms and increases the potential energy between the carbon atoms. Since the total energy of B is lower than that of A, the kinetic energy, or equivalently the kinetic energy pressure, on the carbon atoms is interpreted as the driving force that causes to form a A bond. As Scheme I11 shows, the optimization of structure B to give structure C leads to a shortening of the C-C bond by more than 0.15 A. Figures 2 and 3 indicate that such a shortening lowers the potential energy, overwhelming the increase of the kinetic
energy and resulting in a lowering of the total energy. Concluding Remarks An MO theoretical calculation is essentially a model calculation in terms of both the calculated system and the adopted basis set. We made use of these characteristics and studied certain models with the aim of separating the cause of chemical binding from other concomitant energy changes. This kind of approach may be useful for the analysis of other types of chemical bonds, including multimolecular chemical reactions. The results obtained show that the behavior of the energy components in the *-bond formation is very similar to that found for the u bond in the H2 molecule: The release of the kinetic energy pressure when the A bond comes into existence is the initial driving force in forming the bond. Concomitantly the virial theorem is maintained by shortening of the C-C bond length which represents an overall contraction that lowers the potential as well as the total energy. Although further studies are called for, we are confident that, in any kind of covalent bond formation, the kinetic energy plays the role of the “horse” and the potential energy is “the cart that is pulled by the horse”-to use Mulliken’s form ~ l a t i o nof~Ruedenberg’s ~ analysis. (34) Mulliken, R. S.; Ermler, W. C. Diaromic Molecules; Academic: New York, 1977; p 42.
Modeling the Configuration about the Nitrogen Atom in Methyl- and Silyl-Substituted Amines Maureen M. Julian* and G. V. Gibbs Department of Geological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 (Received: June 25, 1987)
Bond lengths, angles, energies, and electron density maps were calculated for a substituted series of four amines, N(CH3)”(SiH3)>,, ( n = 0, 1, 2, 3). When n = 0, 1, or 3, the amine crystallizes at about 115 K as a monomer. However, when n = 2, while the molecules in the gas phase are monomeric, at room temperature, the molecules in the crystal phase are pentamers. In the monomeric form for each amine in the series, the average calculated values of LSiNSi, LSiNC, and LCNC tend to be preserved at 120.0°, 117.8’, and 112.2O, respectively. The nonbonded cation-cation distances also tend to be preserved. Reaction energies for six double-replacementreactions within the series indicate that the pentamer-forming compound occurs on the less stable side of the calculated reactions. The electronegativity of the nitrogen increases as methyl is substituted for silyl. The lengthening of the bonds associated with the change in electronegativity is ascribed to the relatively large buildup of electron density in the neighborhood of the nitrogen in N(SiH3)3. A unique angle, 0,was defined in terms of line LN making the same angle with each bond such that, for a given amine NRR’R”, 0 = LLNR = LLNR’ = LLNR”. From the deformation maps, each lone pair lies along LN. Finally, the maps show that the bonding electron density peak is located interior to the bond for all nonplanar configurations. The molecule that forms the pentamer shows the largest displacement of the peak off the SiN bond, perhaps representing a pathway for nucleophilic attack.
Introduction
In an earlier paper’ on bonding in framework and molecular silicon nitrides, a planar NSi3skeleton was observed. The NGe, skeleton of trigermylamine* is also planar. Planarity about the nitrogen is also observed in the nitrates and in F2PN(CH3),, where the planar NPC2group has been ascribed to PN multiple bonding.3 Moreover, there are a few isolated cases such as N(Ir(S0,)2)3” where a nitrogen atom bridges three metal atoms to produce a planar NIr, group.4 (1) Julian, M. M.; Gibbs, G. V. J . Phys. Chem. 1985, 89, 5476. (2) Glidewell, C.; Rankin, D. W. H.;Robiette, A. G. J . Chem. SOC.A 1970. 2935. ( 3 ) Morris, E. D.; Nordman, C. E. Inorg. Chem. 1969, 8, 1673.
0022-3654/88/2092-1444$01 S O / O
On the other hand, molecules5 such as NH3, NF,, N(CH3)3, and NC13 have pyramidal geometry. Most amines of the form NRR’R’’, while pyramidal, are not chira16 because they undergo rapid inversion about the nitrogen. Optical isomers have only been isolated in unusual circumstances such as where the nitrogen has been incorporated into a strained ring.’ Most amines form in (4) Ciechanowicz, M. Chem. Commun. 1971, 876. (5) Taurian, 0. E.; Lunell, S. J . Chem. Phys. 1987, 91, 2249. Holte, P. Inorg. Chem. 1971, 10, 210. Beagley, B.; Robiette, A. G.; Sheldrick, G. M. J . Chem. SOC.A 1968, 3002. (6) Cotton, F. A,; Wilkinson, G. Advanced Inorganic Chemistry, 4th ed.; Interscience Publishers: New York, 1980; p 341. (7) Rauk, A,; Allen, L. C.; Mislow, K. Angew. Chem., Int. Ed. Engl. 1970, 9, 400. Mislow, K. Tetrahedron Lerf. 1971, 3437.
0 1988 American Chemical Society
