J. Phys. Chem. 1988,92, 4869-4875
4869
Modified Oxidation Number As Applied to Carbon Compounds. Electron Number Analysis with ab Initio Molecular Orbital Wave Functions Keiko Takano, Mari Okamoto, and Haruo Hosoya* Department of Chemistry, Ochanomizu University, Bunkyo- ku, Tokyo 1 1 2, Japan (Received: September 14, 1987)
Accurate electron number analysis around the specified atoms in several series of acyclic and cyclic carbon compounds, Le., hydrocarbons, alcohols, ethers, and peroxides, was performed with ab initio Gaussian-type molecular orbital wave functions. Not only in inorganic but also in organic compounds the increment of the spherically averaged electron density, Ap,, was found to change stepwise and to be linearly proportional to the formally assigned oxidation number after a slight modification. Namely, the oxidation number of CH hydrogen atoms is assigned as half of that of OH hydrogen atoms. The modified oxidation numbers of the component atoms in acyclic and medium sized (>3) cyclic compounds containing C, H, and 0 atoms can well be assigned and interpreted by a set of a few simple additivity rules as long as electron migration and steric hindrance do not take place to a considerable extent.
Introduction The classical concept of the oxidation number is accepted as a kind of limiting index that sometimes overemphasizes the ionicity of bonds. However, in inorganic chemistry it has been widely used not only as a mnemonic device but also as a useful tool for synthetic Recently attempts have been made to elucidate its quantum chemical meaning by the use of detailed two- and three-dimensional analyses of the electron density,4-I0 instead of the conventional population According to our electron number analysis developed by Iwata with ab initio Gaussian-type wave functions,16 the deformation spherically averaged electron density, Ap,(R), around the specified atoms in a series of inorganic compounds actually shows subtle but stepwise changes in parallel with the classically assigned oxidation numb e r ~ . ' ~ , This ' ~ means that we can redefine the classical term "oxidation number'! as a relative measure of the polarization of ~~
~
(1) Jerrgensen, C. K. Oxidation Numbers and Oxidation States; Springer-Verlag: West Berlin, 1969. (2) Comprehensiue Inorganic Chemistry; Bailer, J. C., Jr., Emeleus, H.J., Nyholm, R., Trotman-Dickenson, A. F., Eds.; Pergamon: Oxford, 1973. (3) Turova, N. Ya. Spravochnye Tablitsy PO Neorganicheskoi Khimii (Reference Tables on Inorganic Chemistry); Khimiya: Leningrad, 1977. (4) Hirshfeld, F. L. Theor. Chim. Acta 1977, 44, 129-138. (5) Weber, J.; Roch, M. J . Mol. Graph. 1986, 4 , 145-160. (6) Gilbert, M. G.; Donn, J. J.; Peirce, M.; Sundberg, K. R.; Ruedenberg, K. J . Comput. Chem. 1985, 6, 209-215. (7) (a) Collins, J. B.; Streitwieser, A., Jr. J . Comput. Chem. 1980, I , 81-87. (b) McDowell, R. S.; Grier, D. L.; Streitwieser, A,, Jr. Comp. Chem. 1985. 9. 165-169. (8) Bader, R. F. W.; MacDougall, P. J. J . Am. Chem. SOC.1985, 107, 6788-6795, and the related papers. (9) Dean, S. M.; Richards, W. G. Nature (London) 1975, 256,473-475. (10) Smith, C. M.; Hall, G. G. Theor. Chim. Acta 1986.69.63-69.71-81. (11) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833-1840, 1841-1846. (12) Kern, C. W.; Karplus, M. J . Chem. Phys. 1964, 40, 1374-1389. (13) Greenberg, A,; Winkler, R.; Smith, B. L.; Liebman, J. F. J. Chem. Educ. 1982, 59, 367-370. (14) Fliszar, S.; rnt. J . Quantum Chem. 1986,29, 305-310, and others of the same series of papers. (1 5) Fliszar, S. Charge Distributions and Chemical Effects; SpringerVerlag: New York, 1983. (16) Iwata, S. Chem. Phys. Letr. 1980, 69, 305-312. (17) Takano, K.; Hosoya, H.; Iwata, S. J . Am. Chem. SOC.1982, 104, 3998-4005. (18) There is observed little meaningful difference among the N ( R ) (number of electrons) curves around the same kind of atoms in different oxidation states. They monotonously and uniformly increase with R up to . and thereafter scatter depending on the number of the total elecabout 1 & trons in the molecule. Although the difference among the po(R) (spherically averaged electron density) curves gets larger than the case with the N ( R ) curves, it is not large enough to analyze. The A N ( R ) analysis gives results similar to the case of Apo(R). The A N ( R ) curve, however, is liable to be affected by neighboring atoms.
0022-3654/88/2092-4869$01.50/0
CHART I: Assignment of the Oxidation Number
classical
modified19
0-11 ~
chemical bonds or electron migration around atoms, although the actual amount of deformation of the electron cloud may be as small as one-tenth of the oxidation number. Further, we have shown that this concept can be extended to carbon compounds for understanding the series of stepwise oxidation-reduction reactions from methane to carbon dioxide by modifying the conventional assignment of the oxidation numbers.lg It reflects the difference in the extent of the charge displacement between inorganic and organic compounds. Namely, on the basis of our analytical electron number analysis, we could obtain a systematic and quantitative interpretation of the features of the oxidation state and oxidation number of many kinds of atoms in various series of inorganic and organic compounds in which a-electronic migration does not take place to a considerable extent.20*21 In some cases by the Ap, analysis we could also assign the oxidation numbers of atoms of the same kind but in different en~ironments.'~ Our electron number analysis for the series of compounds from methane to carbon dioxide (CH4, C H 3 0 H , HCHO, HC02H, C 0 2 ) shows that the hydrogen atom in a C H bond is oxidized to just half the extent of the hydrogen in an OH bond. Our modified oxidation number for the hydrogen atoms in C H bonds is assigned + O S , in contrast to the formal value of +1 for H in O H bonds. The carbon atoms will receive the residual number so that the sum of the oxidation numbers of the component atoms will be zero. For example, the C atom in CH4 is given -2 instead of -4 as the modified oxidation number (see Chart I). There may well arise the question is the mechanism determining the oxidation states in the majority of carbon compounds so simple and interpretable? The purpose of the present paper is to extend similar calculations to a variety of organic compounds composed of C, H, and 0 atoms including three- and four-membered ring compounds to ascertain (19) Takano, K.; Hosoya, H.;Iwata, S. J . Am. Chem. SOC.1984, 106, 2181-2792. (20) Takano, K.; Hosoya, H.;Iwata, S. Applied Quantum Chemistry; Smith, V. H., Schaefer, H. F., 111, Morokuma, K., Eds.; Reidel: Dordrecht, 1986; pp 375-393. (21) Takano, K.; Hosoya, H.; Iwata, S. J . Chem. SOC.Jpn. 1986, 11, 1395-1404.
0 1988 American Chemical Society
4870
Takano et al.
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988
how far the above mechanism is applicable. In this study those unsaturated systems such as acrolein are intentionally excluded, in which large ?r-electronic migration is expected. We can conclude from the systematic electron number analysis that these assignments of the oxidation number to the series of simple molecules from CH4 to C02can be extended to acyclic and cyclic compounds containing C, H, and 0 atoms as long as charge transfer and steric hindrance do not have a large effect. Simple rules are proposed for the assignment of the modified oxidation numbers for the component atoms in these molecules.
Method of Calculation The spherically averaged electron density, po(R) and its increment relative to the summed values of the component atoms, Apo(R),are defined as17,19
0
A130
MIDI-4
0.02
0.oc
i
-0.02
-I
H202
d
-R-QH, R-Q-R' - .- ..- - R-QQR'
atom
APO(R)= PO(R)-
PdR) 1
where N ( R ) is the number of electrons in a sphere with radius R , and the subscript i refers to the contribution of the component free atom i . The deformation electron number A N ( R ) is also defined as
AN(R) = N(R) -
N,(R) 1
The analytical expressions for these quantities from use of Gaussian-type functions (GTF) were obtained by Iwata.I6 The central position of the sphere for calculating these quantities can be moved to any point if necessary. In this paper the radius dependency of the Apo(R)values is mainly examined. The geometries of the compounds studied were taken from the experimentally determined data22-26and/or optimized parameters with ab initio calculations for the singlet ground state^.^'-^^ We have extensively studied the basis set dependency of these quantities, but in this paper only the results of the analysis of Apo at the restricted Hartree-Fock level with MIDI-4 basis of double-{ (DZ) quality proposed by Tatewaki and H ~ z i n a g aare ~ ~given. The electron number analysis was performed for the component atoms of the following 24 acyclic and cyclic compounds containing C, H, and 0 atoms: CH3CH2CH3,CH3CH2CHzCH3,CH2= C=CH2, CH2=CHCH=CH2, CH,CH20H, CHjCH2CH20H, HOCH,CH@H, CH3OCH3, CH3CH20CH3, CH,OOH, CH3OOCH3, C4Hs (cyclobutane), C4H6 (cyclobutene), C4H4 (cyclobutadiene), C3H60(oxetane), CZH4O2 (1,3-dioxetane), CZH4O2 (1,2-dioxetane), C3Hs (cyclopropane), C3H4 (cyclopropene), C2H4O (ethylene oxide), CH202(dioxirane) CH(CH3)3,C(CH3)4, (22) Landolt-Bornstein, Structure Data of Free Polyatomic Molecules; Springer-Verlag: West Berlin, 1976; New Series 11-7. (23) Hayashi, M.; Adachi, M. J . Mol. Struct. 1982, 78, 53-62. (24) Almennigen, A,; Bastriansen, 0.;Skanke, P. N. Acta Chem. Scand. 1961, 15, 711-712. (25) Cunningham, G. L.; Boyd, A. W.; Myers, R. J.; Gwinn, W. D.; Le Van, W. I. J . Chem. Phys. 1951, 19, 676-685. ( 2 6 ) Suenram, R. D.;Lovas, F.J. J . A m . Chem. SOC. 1978, 100, 5 117-5 122. (27) Wiberg, K. B. J . Am. Chem. SOC.1983, 105, 1227-1233. (28) Lotta, T.; Murto, J.; Rasanen, M.; Aspiala, A. Chem. Phys. 1984,86, 105-114. (29) Van Alsenoy, C.; Van Den Enden, L.; Schafer, L. J . Mol. Struct. (THEOCHEM)1984, 108, 121-128. (30) Bair, R. A,; Goddard, W. A., I11 J . Am. Chem. SOC.1982, 104, 27 19-2724, (31) Hess, B. A., Jr.; Carsky, P.; Schaad, L. J. J . Am. Chem. SOC.1983, 105, 695-701. (32) Skancke, P. N.; Fogarrasi, G . ;Boggs, J. E. J . Mol. Struct. 1980,62, 259-273. (33) Hotokka, M.; Roos, B.;Siegbahn, P. J . Am. Chem. SOC.1983, 105, 5263-5268. (34) Komornicki, A,; Pauzaut, F.; Ellinger, Y. J . Phys. Chem. 1983, 87, 3847-3857. (35) Tatewaki, H.; Huzinaga, S. J . Comput. Chem. 1980, 1, 205-228.
I
(
I
0.5
I
1.0
I
R [i]
Figure 1. Difference spherically averaged electron density Apo(R) around the oxygen atom in alcohols, ethers, and peroxides including the reference curves of H 2 0 and H 2 0 2with the MIDI-4 basis.
and C(OCH3)& Structural formulas of these molecules are shown in the left column in Table I. The computers used in this work are the HITAC M200H and HITAC M680H at the Institute for Molecular Science and the HITAC M280H/M200H and HITAC M682H/M680H at the University of Tokyo. The calculation of the Apo(R)values needs only a small amount of computer time. About 10 s are needed per 60 different R values around a given atom in typical molecules on HITAC M280H, if the Gaussian-type molecular wave functions are available.
Acyclic Compounds Figure 1 shows the radial dependency of Apo around the oxygen atom in a variety of acyclic compounds. The previously obtained results for H 2 0and H202are also included as references. In our previous study, it was found that the Apo values in the bonding region from 0.5 to 1.0 8, show quantitative information of the electron density distribution around the specified atom, which closely relates to its oxidation state.36 Let us concentrate on the shapes of the Apo curves in that region. A positive Ap,, value, Le., increment of the electron density, means that the atom is in a reduced state. On the contrary, a negative value, Le., decrement of the electron density, comes from an oxidized state. In Figure 1 we can see that the curves are grouped into two. Namely, the oxidation state of the oxygen atom either belongs to the HzO or around the H 2 0 2group. The numerical values of Apo(( oxygen atoms given in Table I show a quite similar trend, Le., the Apo( values in the former group have the range from 17 X lo-) to 20 X e/au3, and those in the latter group from 10 X lo-) to 12 X e/au3. The choice of (G)'12 for R is tentative, since practically the same parallelism can be observed for a different choice of R value in this bonding region. This, in turn, is a firm support for our modified oxidation number as a relative measure of electron migration around the atoms in molecules. As found in our previous paper, if we assign -2 for the oxidation number of the oxygen atom in H20, the oxygen atom in H202is given -1, in accordance with the classical assignment. Thus the modified oxidation number of the oxygen atoms in the chain compounds studied here can be assigned as follows: (1) -2 for the 0 atom in alcohols (ROH) and ethers (ROR');(2) -1 for the 0 atoms in peroxides (ROOR'). It should be kept in mind for the whole discussion in this study that although the assigned oxidation numbers are formal ones and the actual amount of (36) Though a comparison of the Apo values among the different elements is difficult, it gives the information, which has a close relationship with the oxidation state, within the same element.
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988 4871
Modified Oxidation Number: Carbon Compounds
MIDI-4 0.0 2
-0.02
t
-
i
€H3CH3
-
CH3CHzCH3
-+-
CH&H&CH3
i , -
0.0
0.5
1.0
-OH
&kfCH2
-CH
- - - --
1.5R[S]
Figure 2. Difference spherically averaged electron density Apo(R)around the hydrogen atom in the following alcohols: C2H50H,C3H70H,and HOC2H40H,including the reference curve of CH30H with the MIDI-4
basis. displacement of electron around the atoms is of the order of one-tenth of these numbers, the obtained results well reflect the relative magnitudes of electron displacement within a molecule. In Figure 2 are plotted the Apo curves of the hydrogen atoms in several alcohols studied, together with the two reference curves of the O H and CH hydrogen atoms in methanol, whose oxidation numbers were assigned respectively as +I and +OS. The hydrogen atoms of the former have been shown to be in the same oxidation state as the majority of OH hydrogen atoms in inorganic compounds. The distinctive two groupings of hydrogen atoms in Figure 2 clearly support the assignment of + I for O H and + O S for C H hydrogens in aliphatic alcohols. From the comparison of the Apo curves these assignments were found to be applicable also to hydrocarbons, ethers, peroxides, and several four-membered ring compounds.37 The Apo( ( r2)'I2) values around hydrogen atoms in Table I also show the distinctive differences between OH (from -9 X lo-, to -6 X e/au3) and C H (from -4 X to -2 X lo-, e/au3). That the shapes of the Apo curves of O H and C H hydrogen atoms are rather different from each other can be ascribed to the fact that the electronic cloud of the hydrogen atoms is embedded in that of the heavier atoms. The sum of the oxidation numbers of all the component atoms should be 0 in the case of neutral molecules. Then, the sum of the oxidation numbers of the carbon atoms in the acyclic compounds studied may be estimated as their residual values. However, we cannot always uniquely assign the oxidation number to the carbon atoms, because, as is usually the case with organic compounds, not all the carbon atoms are equivalent. The Apo curves around carbon atoms for two hydrocarbons, Le., propane and n-butane, are drawn in Figure 3. Dashed curves are the references for methane (C-"H,), ethane (C-1.SH3CH3), ethylene (C-'H2=CH2), and methanol (C4'.SH30H) from the upper to the lower, respectively. Propane (CH3CH2CH3)and n-butane (CH3CH2CH2CH3)both have two kinds of carbons. The Apo(R) curves for these four different carbon atoms are grouped into two, Le., those similar to the carbon atoms of ethane (C-'.5H3CH3)and ethylene (c-'H2=CH2). The primary (-CH3) and secondary (=CH2) carbon atoms belong to the former and latter groups, respectively, without exception. Thus, the oxidation numbers of the carbon atoms of these two types in hydrocarbons are assigned as in Chart II(a), where the numbers in parentheses (37) The assignment of +0.5 to H in CH bond is the most probable from the cross reference with the assignment to carbon atoms based on the Apo curves, even though it seems to be tentative.
tk3OH
CH3(CH&CH3
0.0 0.5 1.o l.5 R [A] Figure 3. Difference spherically averaged electron density Apo(R)around the carbon atom in the two hydrocarbons CH3CH2CH3and CH3(CH2)2CH3,including the reference curves of CH4,CH3CH3,CHz=CH2, and CH30H with the MIDI-4 basis.
CHART I1 -1.5
(c)
-I 0 CH,=C=CH (0) -0.5
(4
-I
(0)
-1
-I
CH3-Q-Q-R
Fl) (-1)(-1)
show the sum of the oxidation numbers in each group. It is interesting to note that such a partial sum of the oxidation numbers for each unit of the functional groups becomes 0. This is also the case with the unsaturated hydrocarbons studied as listed in Chart II(b) and (c). The oxidation states of the carbon atoms in three alcohols and two ethers were also interpreted by referring to the data for methane (C-"H4), ethane (C-1.SH3CH3),ethylene (C-'H2=CH2), and methanol (C4.'H3OH). The carbon atom not adjacent to the oxygen atom is in the same oxidation state as the corresponding carbon atoms in hydrocarbons. Namely, for primary carbon atoms the oxidation number is assigned -1.5, and for secondary carbons -1. On the other hand, from the Apo values of primary and secondary carbon atoms adjacent to an oxygen atom we get the values of -0.5 and 0, respectively. The Apo value of primary carbon atom (ROCH,) is similar to that of the carbon atom in C4'.'H30H The Ap0 value of the secondary carbon atom (ROCH2R') is between those of C4.SH,0H and HC+'HO, just closer to the former. Therefore, a tentative assignment of the oxidation number of this carbon atom is 0. The carbon atom adjacent to an oxygen atom is shown to be actually oxidized as expected. Also, for the component atoms in the peroxides, we could obtain the oxidation numbers of the atoms by comparing the Apo curves with the whole family of previous results. The oxygen atoms in methyl peroxide ( C H m H ) and dimethyl peroxide (CH3= CH3) were given -1 for the oxidation number as in the case of hydrogen peroxide (see Figure 1). The oxidation numbers for all the carbon atoms in these two molecules were shown to be -0.5, giving the net (or partial sum of) oxidation number of methyl group (-CH,) the value +1 (see Chart II(d)).
T a k a n o et al.
4872 The Journal of Physical Chemistry, Vol. 92, No. 17, 1988
TABLE I: A p o ( ( r 3 ’/’) ) Values with MIDI-4 Basis and the Modified Oxidation Numbers, Listed in Parentheses, for 0, H, and C Atoms
H, 0.843 A
0, 0.590 8,
compound
C, 0.702 8,
ref“
b b’ a a’ CH3--CHl--CH3
a’ b’
-2.6 (+0.5) -2.7 (+0.5)
a b
9.3 (-1.5) 8.1 (-1)
22
b a‘ a a’ CH3--CH2-CHZ-CH3
a‘
-2.8’ ( + O S )
a b
9.6 (-1.5) 8.6 (-1)
27
-3.0 (+0.5)
a b
8.6 (-1) 4.4 (0)
22
a‘
-3.1’ (+0.5)
a b
7.9 (-1) 7.1 (-0.5)
22
18.5 (-2)
a’ b‘
-7.3 (+1) -2.9 ( + O S )
a b
3.5 (0) 9.8 (-1.5)
22
19.2 (-2)
a’ b’
-6.0 (+1) -3.3’ (+0.5)
a b
4.1 (0) 9.1 (-1) 9.8 (-1.5)
28
-6.8 ( + I ) -3.6 (+0.5)
4.5 (0)
29
-3.4 (+0.5)
4.4 (-0.5)
22
4.7 (-0.5) 3.5 (0) 9.6 (-1.5)
23
-9.6 (+1) -3.4 (+0.5)
4.5 (-0.5)
30
-3.4 (+0.5)
4.5 (-0.5)
30
-2.4 (+0.5)
8.3 (-1)
24 27
b
a
CH ,=C=CH
2
ba’
aa‘
CH2=CH--CH=CH2 b b‘ a b’ CH3-CH2-H
a’
c bf b b‘ a b’ CH,-CH2--CH,--OH
a’
C
b’
a’
18.8 (-2)
HO--CH,--CHZ--OH CH,-O--CH,
17.8 (-2)
c a’ b a’ a a’ CH,-CH,--O-CH3
18.1 (-2)
a’ b‘
a‘
-3.1b (+0.5)
a b C
a b
11.2 (-1) 10.2 (-1)
a’ b’
10.8 (-1)
a‘
-2.6’ (+0.5)
a b
-3.1 (+0.5)
7.2 (-0.5) 7.6 (-I)
22
6.4 (-0.5)
31
3.6 (0) 9.3 (-1)
22
CH CH
17.7 (-2)
n
a‘
-2.7b (+0.5)
a b
17.6 (-2)
-4.1 (+0.5)
-0.5 (+1)
32
9.9 (-1)
-3.7 (+0.5)
5.0 (0)
33
-2.3
7.3
22
6.0 5.7
22
a’
b’
-2.9 -2.2
a b
14.4
-3.0
3.5
25 34
7.7
-3.7
-1.2
26
a‘ b‘
-2.5 -2.2
a b
8.7 6.9
22
-2.5
a b
8.6 7.1
22
The Journal of Physical Chemistry, Vol. 92, No. 17, I988
Modified Oxidation Number: Carbon Compounds
4873
TABLE I (continued) 1o3aP,, efau
H, 0.843 8,
0, 0.590 8,
compound
17.5 (-2)
C, 0.702 8, a
-2.5'
ref"
5.4 -11.1
b
22
Reference Compoundsc H20
19.5 (-2)
-7.2 (+1)
22
H202
11.0 (-1)
-9.9 (+1)
22
CH4 br a' CH3OH HCHO br b a a' HCOOH
co2
18.8 (-2)
a' b'
14.2 (-2)
a b
16.5 (-2) 17.2 (-2)
a' b'
-2.7 (+0.5)
9.8 (-2)
22
-6.3 (+1) -3.6 (+0.5)
4.4 (-0.5)
22
-3.5 (+0.5)
-1.7 (+1)
22
-8.3 (+1) -4.3 (+0.5)
-6.9 (+2.5)
22
-14.9 (+4)
14.6 (-2)
22
CH3-CH3
-2.7 (+0.5)
8.7 (-1.5)
22
CH2=CH2
-3.2 (+0.5)
7.8 (-1)
22
CH=CH
-4. Od
7.7d
22
References related to the geometry. 'Averaged value. 'Reference 19. dHydrogen in methyne group (=C-H) is examined extensively. CHART 111
A1501
0
MIDI-4
0.02
0.00
It is interesting to note that if we take the partial sum of the oxidation numbers around each carbon atom, all the modified oxidation numbers obtained for the compounds composed of C, H, and 0 atoms are found to obey a simple rule. This is illustrated in Chart 111. The values in parentheses give the partial sum of the oxidation number. Later we will discuss this problem in more detail.
Four-Membered Ring Compounds Similar calculations were also performed for four-membered ring compounds composed of C, H, and 0 atoms. Let us compare the results of the ring compounds with those of the corresponding compounds of open structure, e.g., the oxygen and carbon atoms of 1,2-dioxetane with dimethyl peroxide and ethylene glycol, respectively. The carbon atoms in the isomeric 1,2- and 1,3-dioxetanes are expected to be in rather different states. Figure 4 shows the Apo curves around the oxygen atoms in these two isomers. The oxidation numbers of the oxygen atoms in 1,2- and 1,3-dioxetanes can be assigned, respectively, to be -1 and -2, because the curves for these two cases are quite similar to those of the reference curves of the corresponding acyclic compounds, Le., dimethyl peroxide (CH3Q-*QCH3)and ethyl methyl ether ( C H 3 C H Q t 1 C H 3 ) . The oxygen atom in oxetane is also given -2 because the Apo curve is very similar to that of ethyl methyl ether as in the case of the oxygen atom in 1,3-dioxetane. Note that not only in the acyclic compounds but also in the cyclic compounds the oxidation number of the oxygen atom in the peroxide structure can be assigned -1 instead of -2. For the oxidation number of the hydrogen atom attached to a carbon atom, the previously assigned value of +0.5 is consistent with the present results (see Table I). Once the oxidation numbers of the oxygen and hydrogen atoms are fixed, the oxidation numbers of the two equivalent carbon
-0.02
I
I
I
0.0
0.5
1.0
I
1.5 R [ i
Figure 4. Difference spherically averaged electron density Apo(R) around the oxygen atom in oxetane and 1,3- and 1,2-dioxetanes,including the reference curves of CH3CH20CH3and CH300CH3with MIDI-4 basis.
atoms in 1,2- and 1,3-dioxetanes can be assigned, respectively, as 0 and 1, because the sum of the oxidation numbers for atoms in a neutral molecule are assumed to be 0. Independently from the above discussion, the oxidation numbers of the carbon atoms in these compounds can also be assigned from a comparison of the Apo curves. The oxidation number assigned to the carbon atoms is zero for 1,2-dioxetane because of the close similarity of the Apo curve with that of ethylene glycol (HOCoH&H20H). ) are 5.0 X and 4.5 X e/au3, The A p o ( ( P ) 1 / 2values respectively, as listed in Table I. By comparing the Apo curves around the carbon atom in 1,3-dioxetane with the already assigned we can curves in ethyl methyl ether (C-'.5H3CoHzOC~,5H3), estimate its oxidation number to be +1, in complete agreement with our former assignment (see Figure 5 ) . This is also the case for cyclobutane and cyclobutadiene. The oxidation numbers of the four equivalent carbon atoms in cyclobutane and cyclobutadiene are expected to be -1 and -0.5, respectively, by assuming the oxidation number of H in CH bonds to be +OS. This is again concordant with the conclusion deduced from the calculated Apo values. The oxidation numbers of the carbon atoms can safely
+
4874
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988
C
Takano et al. I
MI DI-4
i
‘i
I
I
j .-.. ,/’
n nnl
r
,
i
\
/:I/
b 1
1
I
1.o
1.5 R[A, Figure 5. Difference spherically averaged electron density Apo(R)around the carbon atom in 1,3-dioxetaneand ethyl methyl ether (CH3CH20CH,) with MIDI-4 basis.
0.0
0.5
be assigned as -1 for cyclobutane and as -0.5 for cyclobutadiene on the basis of the similarity of its Apo curve to that of the carbon atom of CH2 group in a chain compound, butane, and that of C H group in butadiene, respectively. On the other hand, there arises some arbitrariness in the assignment of the oxidation number of the carbon atoms in oxetane because of their nonequivalent environments. At this stage we know only that the sum of the oxidation numbers of the three carbon atoms in oxetane should be -1. Fortunately, the Apo curves in this analysis give us individual information on the oxidation number of each atom. The carbon atoms in oxetane were given zero for the a-position and -1 for the &position due to the close analogy with the carbon atom, respectively, in ethyl methyl ether (CH3CoH20CH3)and butanol (CH&-’H2CH20H). The similarity of the Apo( ( r2)’I2)values can also be seen in Table I. The sum of these assigned numbers of the three carbon atoms is -1, again in concordance with the previous estimate. The advantage of our analysis of the oxidation states based on Ap0 has already been exemplified for the case with nonequivalent sulfur atoms in S=SF,.”
Highly Strained Compounds We have performed similar analyses on the oxidation numbers of atoms in three-membered cyclic compounds. However, the results are not as simple as described above. The Apo curves for hydrogen atoms in the three-membered ring compounds are almost the same as those in many other organic molecules. On the other hand, the Apo values around the C and 0 atoms in the threemembered ring compounds are smaller than the corresponding values of the other groups of compounds with similar structures. Before going on to extend the discussion based on the Apo analysis, one has to realize the following point. That is, the Apo value is a one-dimensional quantity obtained by averaging over all the directions. Angular dependency of the electron distribution should duly be taken into consideration especially for the analysis of highly strained compounds. Thus, the electron distribution around the atoms and bonds was examined by drawing the contour map of the electron density. In Figure 6 are compared the contour maps of deformation electron density for the three-membered ring compounds (a) cyclopropane and (b) ethylene oxide and for the four-membered ring compound (c) oxetane. In the three-membered ring compounds three local maxima of electron density can be seen in the regions a small distance from the three CC bonds, revealing the formation of so-called “banana” bonds. Further, it is noteworthy that the lone-pair electrons of the oxygen atom in the three-membered ring are spread out in a wider region and are less concentrated than those in the four-membered ring and chain compounds. Because of their highly strained structure simple
E
I
Figure 6. Contour plots of the deformation electron density in the plane of the carbon and oxygen atoms in (a) cyclopropane, (b) ethylene oxide,
and (c) oxetane with MIDI-4 basis. Positive contours (electron excess) and zero contours are drawn as solid lines, and negative contours (electron deficiency) are dashed. The contours show the values of 0 and f0.004 X 2” ( n = 0, 1, 2, .. .) e/au3. The positions of atoms in the plane are denoted by 0 , and the projection of atoms into the plane are denoted by
x.
analysis by the use of the spherically averaged electron density cannot describe the detailed features of the electron density in small-sized ring compounds. A series of methyl derivatives of methane, Le., methane (CH,), ethane (CH3Me),propane (CH2Me2),isobutane (CHMe3), and neopentane (CMe,) were also studied with the electron number
J. Phys. Chem. 1988, 92, 4875-4880 analysis. The oxidation numbers of C and H atoms in each methyl group could be assigned as -C-1.5H3+o.5in just the same way as (0)
for the other acyclic compounds shown in Chart II(a). However, the simple rules as summarized in Chart I11 are not applicable to isobutane and neopentane. The Apo values for the central carbon atoms of these two molecules are almost the same (see Table I). Further, comparison with other Apo values suggests that the central carbon atoms are a little more reduced (C-3/4HMe3, C-3/4Me4) than what is expected from the above rules (C4.5HMe3, C0Me4).38 For the case of tetramethoxymethane (C(OMe),), the assignment based on the Apo values is contradictory to that deduced from the electroneutrality principle.
Concluding Remarks After a slight modification the classically assigned oxidation numbers for C, H, and 0 atoms in the hydrocarbons and their oxides, as long as large electronic migration and steric hindrance are not expected, give us systematic understanding of the oxidation states of the component atoms. The modified oxidation number for these molecules can be obtained by simple additivity rules as follows: Step 1: divide the molecule into units of oxygen, oxygenated hydrogen, and/or hydrogenated carbon. Step 2: assign -2 for the oxygen and 0 for the -CH, groups not directly bonded to oxygen. Step 3: assign +1 or +2 to the direct neighbors of the oxygens to attain the electroneutrality around each oxygen. (38) In the bonding region both the Apo curves around the central carbon atoms in CHMe, and CMe, molecules lie just in between the Apo curves of C-'H2=CH2 and C4,SH30H.
4875
Step 4: assign + O S to the hydrogens attached to carbon. Step 5: the carbon atoms will receive all the rest of the charge so as to obey all the above rules. For a set of nonequivalent carbon atoms in a molecule, assignment is given by the aid of the Apo curves in the bonding The absolute values of region, say the Apo value at R = (s)1/2. these modified oxidation numbers are just the formal numbers as they stand, but they surely reflect not only the subtle but also the stepwise polarization of valence electrons in those carbon compounds, about which most organic chemists have been skeptical in applying the concept of the oxidation number. For conjugated a-electronic systems a clear-cut assignment of the oxidation number becomes difficult. Study is under way along the present analysis to see if, and how far, electrons migrate in organic molecules as predicted from the conventional organic resonance theory.
Acknowledgment. We thank Professor Suehiro Iwata of Keio University for his helpful advice to our calculations. We also thank the Computer Center, Institute for Molecular Science, Okazaki National Research Institute for the use of the HITAC M200H and HITAC M680H computers. Registry No. CH,CH2CH,, 74-98-6; CH3(CH2)2CH3,106-97-8; CH24=CH2,463-49-0; C H 2 4 H C H 4 H 2 , 106-99-0;CH$HZOH, 64-17-5;CH,(CH2)2OH, 71-23-8; HO(CH2)20H, 107-21-1;CH30CH3, 115-10-6;CH3CH20CH3,540-67-0;CHSOOH, 3031-73-0;CH300CH3, 690-02-8; CH2CH2CH2CH2, 287-23-0; CH=CHCH2CH2, 822-35-5; CH=CHCH+H. 1120-53-2: OCH,CHXH,. 503-30-0: OCH~OCHI,287-50-3; OCH2CH20.6788-84-7; CH2CH2CH2, 75-194; CH-CHCHZ, 278 1-85-3; OCH2CH2, 75-21-8; OCH20, 157-26-6; CH(CH3)3, 75-28-5; C(CH3)4, 463-82-1; C(OCH3)4, 1850-14-2.
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6-31IG(MC)(d,p): A Second-Row Analogue of the 6-31 IG(d,p) Basis Set. Calculated Heats of Formation for Second-Row Hydrides Ming Wah Wong, Peter M. W. Gill, Ross H. Nobes, and Leo Radom* Research School of Chemistry, Australian National University, Canberra, A.C.T. 2601, Australia (Received: November 5, 1987)
Optimized d-function exponents have been obtained for first- and second-row atoms in various environments. The best values at Hartree-Fock and correlated levels are found to differ significantly in many cases. Optimum correlated exponents have been used in constructing the 6-31lG(MC)(d,p) basis set, defined for H, He, and first- and second-row atoms, and recommended as a starting point for large-basis-set correlated calculations. The 6-31Gft basis set has also been defined for H, He, and first- and second-row atoms and is recommended for smaller-basis-setcorrelated calculations. Heats of formation for second-row hydrides, calculated at the fourth-order Moller-Plesset level by using an augmented 6-31lG(MC)(d,p) basis set and an isogyric correction, are generally in good agreement with experimental values. In cases where experimental information is either uncertain or lacking, the present calculated heats of formation are probably the most reliable values currently available.
Introduction The most widely usGd basis sets in current electronic structure calculations are undoubtedly those that have been developed over the years by Pople and co-workers.' Descriptions such as STO-3G have become part of the chemical idiom and are familiar not only to practicing quantum chemists but also to many in the wider chemical community. The simplest such basis sets are STO-3G and 3-21G.l At the other end of the scale, large basis sets for H, He and the first-row ( 1 ) For a detailed description, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
0022-3654/88/2092-4875$01.50/0
atoms are based on the triple-{-valence 6-311G set,2 supplemented by one or more sets of polarization and/or diffuse functions, as r e q ~ i r e d . ~Basis sets of this type, in conjunction with a fourthorder Mdler-Plesset perturbation theory treatment of electron correlation4 and with an isogyric correction, have been founds to yield heats of formation for first-row hydrides to an accuracy of about f8 kJ mol-'. (2) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J . Chem. Phys. 1980, 72, 650. ( 3 ) Frisch, M. J.; Pople, J. A,; Binkley, J. S. J . Chem. Phys. 1984, 80, 3265. (4) Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244. (5) Pople, J. A,; Luke, B. T.; Frisch, M. J.; Binkley, J. S. J . Phys. Chem. 1985, 89, 2198.
0 1988 American Chemical Society
