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Bonding in carbonyl and thiocarbonyl compounds: an ab initio charge density study of H2CX and HC(X)YH (X,Y O or S)
THEO CHEM Journal of Molecular Structure (Theochem) 315 (1994) 123- 136
__---___-__
Bonding in carbonyl and thiocarbonyl compounds: an ab initio charge density study of H2C=X and HC(=X)YH (X, Y = 0 or S) Rui Faust0 Departamento de Quimica, Universidade de Coimhra, P-3049 Coimbra, Portugal
Received 25 March 1994; accepted 14 April 1994
Abstract Ab initio 6-31G* SCF-MO calculations have been carried out for formaldehyde, thioformaldehyde, and for both the scis and s-trans conformers of formic acid and their sulphur-containing analogues (thiol-, thiono- and dithioformic acids). The calculated wavefunctions were used to perform a detailed charge density analysis based on both the Mulliken and Bader partitioning schemes. Particular emphasis was given to the study of the effects of substitutions of oxygen-bysulphur on the electronic distributions of the whole set of molecules and to the conformational effects due to the s-cis --+ s-trans rotamerization in the acids and thiolacids studied. The calculated electronic properties are successfully correlated with several geometric features exhibited by the molecules and used to explain the relative differences in energy between the s-cis and s-trans forms in formic acid and its sulphur derivatives.
1. Introduction Equilibrium geometries and relative energies of a series of molecules containing the -C(=X)Y(X, Y = 0 or S) fragment, determined by ab initio SCF-MO methods, have been reported in previous publications from this laboratory [l-7]. Besides the series of molecules considered here, those previously studied include acetic and propionic acids, their methyl and ethyl esters, and the corresponding sulphur analogues [l-7]. Though a number of important questions were answered by those studies where the emphasis was given either to the analysis of the conformational dependence of relevant geometrical features or to the effects of oxygen-by-sulphur substitution on geometries - some important questions still remain open. Indeed, to further our understanding of these families of molecules, it is fundamental to carry out a detailed analysis of the
electronic structure of a series of representative molecules. Thus, in this article, we report the results of ab initio 6-3 lG* SCF-MO charge density analyses carried out by both Mulliken [8] and Bader [9-l l] methods on formaldehyde (F), formic acid (FA), and their sulphur-containing analogues, thioformaldehyde (TF), thiolformic acid (TLFA), thionoformic acid (TNFA) and dithioformic acid (DTFA). In particular, the following problems are analysed in detail: (i) How is the structural chemistry of the carbonyl and thiocarbonyl groups affected by the electronic properties of substituents like -H, -OH and -SH? (ii) How does the oxygen-by-sulphur substitution affect the electronic distribution in the molecules studied and, in particular, how does it affect their bonding?
0166-1280/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0166-1280(94)03787-L
(
(s-h)
Fig. 1. The s-cis and s-trans (X. Y = 0 or S) molecule.
conformers
.r-l,
at2.s)
of an HC(=X)YH
(iii) What are the relevant electronic features which are responsible for the different relative energies of the s-cis and s-trans conformers (Fig. 1) of the HC(=X)YH (X, Y = 0 or S) molecules? Besides its fundamental importance, the precise characterization, in electronic terms, of the differences between carbonyl and thiocarbonyl compounds achieved in the present study may also provide an important contribution to the understanding, at a molecular level, of a series of complex processes involving such groups in enzyme catalysis, such as catalytic hydrolysis of proteins by serine or cysteine proteases (e.g. chymotrypsin, papain), which have been studied by resonance Raman (RR) spectroscopy using a technique that involves an in situ generation of a thiocarbonyl RR chromophore differing from the natural substrate by a single atom substitution (=0 + =S) [12-141.
2. Computational
methods
The ab initio SCF-MO calculations were carried out with the 6-31G* basis set [ 151 using the GAUSSIAN 92 program system [16] running on a Molecular geometries VAX9000 computer. were fully optimized by the force gradient method using Berny’s algorithm [17]. The largest residual internal coordinate forces were always less than 3 x 10m4 hartree bohr-’ (1 hartree = 1 bohr = 5.29177 x lo-” m) 2625.5001 kJmol-‘; or hartree rad-’ , for bond stretches and angle bends, respectively. The analysis of the wavefunctions in terms of the charge distribution was carried out both by Mulliken’s method [8], using
the standard GAUSSIAN 9: built-in procedures, and Bader’s topological method, using the PROAIMS program package [9- 111. The principles and fundamentals of Bader’s topological method, as well as a series of practical applications to different chemical problems, can be found in the original articles of the author [9- 11,1&24] or in a series of more recent reviews [25,26]. Essentially, in this electron density partitioning scheme, an atom in a molecule is defined as a quantum mechanical subspace, obeying the generalized variational principle [23], which is uniquely defined in real space by a surface of zero-flux in the gradient vector of the charge density [9-l 1,231. Indeed, because of the principal topological property of a charge distribution for a many-electron system -~~ that it exhibits local maxima only at the positions of the nuclei ~ the quantum boundary condition above yields a partitioning of the real space of a molecule into a disjointed set of mononuclear regions, or atoms. As a result of this quantum description of an atom, any property of a molecule may be partitioned into a sum of atomic contributions, i.e. all the properties of an atom in a molecule, including energy, are uniquely defined and their average values may be calculated from the corresponding one-electron density distribution defined in real space by integration over the associated atomic volume defined by the zero-flux surface. Another important result derived from Bader’s theory of atoms in molecules is the unique definition of a bond between a pair of atoms as the path of maximum electron density joining the two nuclei (bond path) [lo]. The angles formed by bond paths are called bond path angles and, in general, as a result of steric interactions between substituents around a given atom, are different from the geometrical bond angles. A negative value of AU (Aa = a(bond path)- (lY(geometrlc) ) suggests a repulsive interaction between the outer atoms of those forming the angle. A positive value could indicate an attractive interaction, but it is more likely that it reflects a smaller repulsion than at other angles. Negative Acvs are generally found with small bond path angles that would tend to bring the end atoms close together, and positive Aas are generally found with large angles where the repulsion between the end atoms would be small.
R. Fuusto/Journal of Molecular Structure (Theochem)
315 11994) 123-136
Table 1 Calculated equilibrium geometries and conformational relative energies for H$=X Parameter
c=x C-Y C-H Y-H H-C=X X-C-Y H-C-Y C-Y-H
H&=0
H,C=S
118.4
159.7
109.2
107.8
122.1
122.3
AEb
125
and HC(=X)YH (X, Y = 0
or S)” HCSSH
s-cis
s-trans
HC(=O)SH ______ s-cis s-trans
118.2 132.3 108.4 95.3
117.6 132.8 109.9 94.8
118.0 177.4 108.9 95.4
117.9 177.1 109.0 94.9
161.9 130.7 107.6 132.5
160.0 131.6 108.1 132.6
161.0 173.6 107.9 132.5
160.8 174.2 107.8 132.6
124.7 124.9 110.4 108.7
124.1 122.0 113.9 III.6
123.4 125.1 111.5 95.9
123.2 122.4 114.4 96.7
123.0 126.7 110.3
121.6 124.3 114.1 111.8
120.9 128.8 110.3 97.6
121.1 124.7 114.2 97.5
HCOOH
25.84
HC(=S)OH s-cis
s-trans
s-cis
s-trans
110.0
6.29
27.40
7.50
a Bond lengths in pm; angles in degrees. b Relative energies (kJ mol-’ ) to the most stable conformer (s-cis)I_
3. Results and discussion
3.1. How are the C=O and C=S groups qflected by the -H,
Table 1 shows the 6-31G* energies and optimized geometries for the molecules studied. For all the HC(=X)YH (X, Y = 0 or S) molecules, the s-cis conformer is more stable than the s-trans form, the energy difference reaching a minimum for X = 0 and Y = S, and a maximum for X = S and Y = 0. It is clear that while the =0 -+ =S substitution only slightly affects the relative energies of the conformers (a slight increase in is observed), the -0+ -SAE(,-rr,,,)-(,-,i,) substitution produces a large decrease in this energy difference. Indeed, the higher degree of similarity between properties of the pairs of molecules having equal -Y- and different X= atoms, when compared with the pairs of molecules having equal =X and different -Y - atoms, has also been found for other series of molecules containing the -C(=X)Yfragment [1,5-71, which seems to indicate that the nature of the -Y- atom determines to a large extent the properties exhibited by this kind of molecule. As noted for the energies, structural changes associated with the rotational isomerism reveal well-defined trends. For instance, the changes in the C=X bond length upon (s-cis) --+ (s-trans) isomerization increase along the series TLFA < DTFA << FA < TNFA calculated values are 0.08, (AC=X/C=Xc,_,is) 0.12, 0.51 and 0.62%, respectively).
-OH
and -SH
suhstituents?
Before looking in detail at the electronic factors which are the origin of both the energetic and structural differences mentioned above, it would appear desirable to examine the nature of the interactions between the carbonyl and thiocarbonyl groups and their substituents (-H, -OH and -SH). A very useful and convenient way of doing this is by considering the relative degrees of p character in the different bonds formed by the carbonyl (or thiocarbonyl) carbon atom [27]. In turn, an estimate of the fractional p character may be obtained either by a direct analysis of the electron populations at each atom on an MO by MO basis or, indirectly, from the calculated bond path angles around the carbonyl (thiocarbonyl) carbon atom (Table 2) considering that these angles correspond to the undeformed bond angles [lo]. In order to convert the angles to fractional p character, the following procedure, outlined in detail elsewhere [28], is adopted: the carbon orbitals involved in the molecular a-system are written as +c=x = (3 +
~PI)IJNl
&A
= (s + hP2JlJN2
4C-B
=
(s +
fP3)/@3
126 Table 2 Bond path angles and hybridization Molecule
A
H2C=0 H2C=S HCOOH s-cis HCOOH s-/rans HC(=O)SH s-cis HC(=O)SH s-tram HC(=S)OH s-ck HC(=S)OH .s-trans HCSSH s-cis HCSSH s-trans
H H OH OH SH SH OH OH SH SH
H H H H H H H H H H
in carbonyl
114.39 116.59 109.49 108.40 108.62 109.58 110.67 109.90 110.90 112.45
and thiocarbonyl
-1.41 1.19 -0.90 -5.50 -2.88 -4.83 0.37 -4.10 0.59 - 1.?S
a Angles in degrees; AN = (bond path angle - geometric C-B bond, respectively; X = 0= or S=.
AF= -l/
(a])
cos (CQ)
& = -l/cos
122.80 121.70 129.07 128.97 127.88 127.85 128.23 127.68 125.67 126.02
AU,
(xi
A%
Px
PA
Pa
0.70 -0.60 4.37 4.87 4.48 4.65 5.23 6.07 4.77 4.92
122.80 121.70 121.43 122.62 123.49 122.57 121.09 122.42 123.43 121.53
0.70 -0.60 -3.47 0.62 -1.61 0.17 -5.61 -1.88 -5.38 -3.18
0.57 0.61 0.58 0.45 0.46 0.48 0.50 0.48 0.50 0.53
0.71 0.70 0.81 0.82 0.80 0.80 0.80 0.79 0.76 0.77
0.71 0.70 0.71 0.73 0.74 0.72 0.70 0.72 0.73 0.70
angle); px. PA, pa, are the percentage
where the p orbials are aligned with the bond directions. Hence, the orthogonality requirement leads to AS = -l/cos
derivatives”
(cuj)
with the cys being the three bond path angles at the carbonyl carbon. The equations are then solved for A, S and c, and the carbon orbitals obtained by normalizing the $s (i.e. by obtaining the values of Ni, NZ and Nj). Finally, the fractions of p character shown in Table 2 (px, PA and ~a) are obtained by squaring the normalized p coefficients. From the calculated fractional p characters, the following conclusions can be drawn: (i) Both for the carbonyl and thiocarbonyl groups, the p fractional character of the 0 C=X bond is fairly small, when compared with those of the C-H or C-Y single bonds. (ii) The p fractional character of the g thiocarbonyl bond is slightly larger than that of the 0 carbonyl bond (for instance, in TF pZs is 0.61, while in F pZo is 0.57). (iii) The relative values of the p fractional characters of the C-S and C-O bonds are similar (very slightly higher values were found for the C-O bonds), while the p fractional character of the C-H bond is considerably lower than that associated with both the C-S and C-O bonds.
of p character
of the g(C=X),
C-A
or
(iv) In the studied acids and thiolacids, the conformational isomerization does not produce important changes in the relative p fractional characters of the bonds formed by the carbonyl (or thiocarbonyl) carbon atom. It is a general rule for single bonds that the larger the electronegativity of a substituent, the larger the fractional p character of the bond formed with this substituent. Indeed, this rule is obeyed in the systems studied for C-H, C-S and C-O single bonds (conclusion (iii) above), although it could be expected that the p characters of the C-O bonds would be significantly larger than those of the C-S bonds. However, considering the relative values found for either pEo or pZs and those associated with the C-H bonds, it must be concluded that the above rule does not seem to be valid in the case of a double bond. Indeed, this conclusion is supported by the direct analysis of the electron populations at each atom on an individual MO basis, as presented in Table 3 for F and TF. For both molecules, this analysis reveals that the p fractional character of the CTcomponent of the double bond is fairly small. In F, the percentage of p character of the (TC=O bond can be estimated from the carbon atom contributions to the electron populations of MO 3 and MO 6, which are formed using the carbon 2s and 2p, orbitals, respectively. The carbon contributions to each orbital are about the same, and the value obtained from Table 3, 0.460/(0.460 + 0.417) = 0.52, is similar to that derived from the bond path angles (0.57,
H. FaustolJournal Table 3 MO electron
populations
for H2C=0
of MolecularStructure
and H2C=Sa
MO
0
C
H
H2C=0 1 @I) 2 (AI)
2.000 0.000
0.000 2.000
0.000 0.000
0 1s c 1s
0.417 1.122 0.863 0.460 0.582
0.003 0.146 0.205 0.041 0.000
g(C-0);
7 @I)
1.576 0.586 0.726 1.459 1.417
8
1.334
0.137
0.264
01,
3 (AI) 4 (AI) 5 U32) 6 (AI)
(B2)
S
Type
01,
4CH2) 74CH2)
fl(C-0); K(C-0)
01,
H2C=S
16%)
0.000
0.000
2 (AI) 3 (AI)
2.000 0.000
0.000 0.000
4 5 6 7 8 9
(AI) 0%)
0.000 0.000
0.000 0.000
U-32)
0.000
0.000
(AI) (AI)
116%)
0.792 0.680 1.189 0.524 0.654
12
0.033
(B2)
10 (A,)
032)
2.000 0.000 2.000
s 1s c 1s s 2s
0.030 0.110 0.326 0.033 0.000
2.000 2.000 2.000 1.148 1.099 0.158 1.409 1.346
S 2P S 2P S 2P dC-Sk
0.099
1.769
SI,
S,,
dCH2) 74’332)
g(C-S); x(C-S)
S,,
a Units of e (e = 1.6021892 x lo-l9 C).
Table 2). On the contrary, in TF, the p fractional character of the 0 component of the double bond, as derived from the carbon electron populations of MO 7 and MO 10 (Table 3), amounts to only 0.40. Table 4 Results of Mulliken
H2C=0 C 0 H c=o C-H H2C=S C S H
5.866 8.415 0.859
6.382 16.056 0.781
electron
population
0.670 1.297
0.796 3 177
partitioning
for H2C=0
5.196 7.118 0.859
5.586 12.879 0.781
4.571 7.981 0.612
5.194 15.720 0.510
(Theochem)
Thus, this result also supports the conclusions derived from the above analysis based on the bond path angles with regard to the general small p character exhibited by the o component of double bonds (conclusion (i) above). It is. however, important to note that the relative values of the fractional p characters of the CTC=O and C-S bonds obtained from direct inspection of the MO electron populations on the atoms and based on the bond path angles give results in opposite directions, with the first method predicting a larger p character for the IT C=O bond and the second a larger p character for the 0 C=S bond (conclusion (ii) above). This apparent discrepancy can be easily overcome if we take into consideration the corresponding 0 C=X overlap opulations, o0 (C==X) (Table 4), as well as the carbon electron population in the MOs involved in the g C=X bonds in F and TF (respectively MOs 3 and 6, and MOs 7 and 10). The absolute values of the total carbon p electron populations in the relevant orbitals (MO 6 in F; 0.460e, and MO 10 in TF; 0.524e, see Table 3) follow the order predicted by the bond path angle analysis. However, the total carbon s electron population in MO 3 of F (0.417e) is much smaller than the corresponding population in the MO 7 of TF (0.792e) which leads both to a larger value for the sum of the carbon atom electron populations in the two relevant MOs in TF than in F (1.316e vs. 0.877e) and to a relative p and H2C=S”
0.449 1.073
0.571 2.952
c=s C-H a Units of e (e = 1.6021892 x lo-l9 C); Total populations,
121
315 11994) 123-136
X, = xf + ui, where
4.122 6.098 0.612 1.086 0.752
0.441
0.646 0.752
0.890 0.742
0.450
0.440 0.742
4.624 12.768 0.510
i is gross (g). net (n) or overlap (0) electron populations.
R. FausfoiJournal of Molecular Structure (Throchem
128
Table 5 Results of Mulliken
HCOOH C =o -oH H(O)
5.475 8.511 8.662 0.819 0.534
electron
population
0.643 1.445 1.853
partitioning
for the s-cis conformers
4.832 7.065 6.808 0.819 0.534
4.196 8.039 8.293 0.530 0.283
0.405 1.258 1.813
J315 i 1994) 123~ 136
of HC(=X)YH
3.791 6.781 6.480 0.530 0.283
c=o c-o C-H O-H
HC(=O)SH C =o -sH H(S)
5.838 8.444 16.033 0.815 0.869
0.692 1.369 3.894
5.146 7.075 12.139 0.815 0.869
4.684 8.039 15.608 0.557 0.609
0.450 1.174 3.871
5.899 16.208 8.624 0.756 0.513
0.712 3.420 1.820
5.186 12.788 6.803 0.756 0.513
4.828 15.858 8.245 0.476 0.263
0.477 3.246 1.793
6.356 16.102 15.924 0.748 0.870
0.817 3.303 3.842
5.539 12.799 12.081 0.748 0.870
c=s c-s C-H S-H a Units of e (e = 1.6021892 x lo-l9 C); Total populations,
5.339 15.824 15.540 0.487 0.608
0.574 3.129 3.837
0.388 0.088
0.807 0.472 0.818 0.489
1.034 0.582 0.737 0.553
0.41 I 0.073
0.623 0.509 0.737 0.553
0.934 0.511 0.746 0.511
0.252 0.078
0.682 0.433 0.746 0.511
0.835 0.522 0.732 0.561
0.415 0.070
0.420 0.452 0.732 0.561
4.351 12.611 6.453 0.476 0.263
c=s c-o C-H O-H
HCSSH C =s -SH H(S)
1.195 0.560 0.818 0.489
4.234 6.865 11.736 0.557 0.609
c=o c-s C-H S-H
HC(=.S)OH C =s -OH H(O)
(X, Y = 0 or S)”
4.76 12.695 11.703 0.487 0.608
xi = xI + ci, where i is gross (g), net (n), or overlap
(0) electron
populations.
R. Fausto/Journal of Molecular Structure (Theochem)
character associated with such MOs that is smaller for TF than for F (0.40 vs. 0.52), as mentioned above. Thus, it is the s component that varies to a greater extent. On the contrary, o0 (C=O) in F is larger than go (C=S) in TF (0.646e vs. 0.440e, see Table 4), indicating that the g electrons are more localized in the C=O bond in F than in the C=S bond in TF, while they are more localized in the carbon atom in TF than in F. This conclusion is in consonance with the expected greater electronegativity of oxygen when compared with sulphur, which makes this atom more efficient in attracting electrons by the inductive effect. Indeed, in F, the large inductive effect of the oxygen substituent requires a more extensive participation of the carbon s electrons in the bonding than in TF. Such a conclusion receives support from the observation given above, that it is the carbon s electrons that are mainly affected by the 0 ---f S substitution, with these migrating from the u C=X bond towards the carbon atom. Therefore, the fractional p character associated with the P C=S bond must be considerably larger than that directly obtained from the MOs as made above (without considering the effective contribution of the electrons to the bonding, i.e. without distinguishing between the net and overlap populations), thus being in consonance with the results derived from the bond path angles. From the results presented in Table 3, some other interesting conclusions can be obtained: (i) Im F, MO 3 and MO 6 have nearly identical contributions from the 0 atom, indicating that this atom distributes equally its s and p electrons by the lone pair and by the u C=O bond. On the contrary, in TF, MO 10 has a much larger contribution from the S atom than MO 7, clearly showing that MO 10 relates to a greater extent to the sulphur lone pair than MO 7, which participates more in the c C=S bonding. As MO 10 has a larger p character, it can be concluded that the sulphur atom lone electron pair has a fairly large p character, being certainly larger than that of the carbony1 lone electron pair in F. (ii) The large fraction of the hydrogen electron population derived from MO 8 in F (0.264e)
315 11994) 123-136
129
shows the importance of back-donation from the oxygen lone pairs into the hydrogens. This effect have been considered to explain both the observed values of the stretching frequencies of isolated CH groups in similar molecules [29] and the charges on hydrogen atoms, as evaluated from infrared intensities in F and ethene [30]. However, the fraction of the electron population derived from MO 12 in TF due to the hydrogen atoms is small (O.O99e), indicating that back-donation is not important in this molecule. (iii) Finally, the carbon and X= electron populations derived from MO 7 in F and MO 11 in TF (7r C=X MOs) clearly show that, as in the case of the 0 electrons, the 7r electrons associated with the C=X moiety are also more localized on the 0 atom in F than on the S atom in TF. 3.2. What is the relative importance of the effects of the 0 + S substitutions on the CTand the YTsystems in the studied molecules?
This is another fundamental question which has not yet been clearly answered and which has important structural and chemical implications. To answer it requires a detailed electronic analysis carried out by using a suitable o/r electron distribution partitioning scheme. Since the results obtained by both the Bader and Mulliken partitioning schemes were found to exhibit a general qualitative agreement, we have decided to discuss in detail here those obtained by the more widely used Mulliken method (Tables 4-6). For the HC(=X)YH molecules, the following analysis is based on the results obtained for the most stable s-cis conformers, though identical conclusions can also be derived from the s-trans data. In the case of the O= + S= substitution, the general pattern of changes observed in the electron populations may be summarized as follows. The total, CJ,and n electron populations on the carbon atom (x,(C), g,(C) and n,(C), respectively) increase, while the corresponding electron populations of the X= atom decrease (see also Fig. 2). These results can be easily correlated with the different electronegativities of the 0 and S atoms.
130
R. Fuusto/Journul
Table 6 Results of Mulliken
HCOOH C =o -OH H(O)
5.476 8.479 8.652 0.855 0.538
electron
population
0.667 1.417 1.858
qf .Moleculrrr Structure
partitioning
for the s-tram
4.809 7.062 6.794 0.855 0.538
4.209 7.992 8.301 0.593 0.290
i Theo&m
conformers
0.427 1.225 1.823
I 315 ( 1994) 123 136
of HC(=X)YH
3.783 6.766 6.478 0.593 0.290
c=o c-o C-H O-H
HC(=O)SH C =o -SH H(S)
5.839 8.439 15.989 0.818 0.914
0.698 1.360 3.896
5.141 7.079 12.093 0.818 0.914
4.677 8.022 15.588 0.576 0.677
0.456 1.165 3.876
5.919 16.156 8.606 0.790 0.529
0.746 3.384 1.823
5.173 12.772 6.783 0.790 0.529
4.854 15.791 8.254 0.532 0.290
0.511 3.205 1.800
6.366 16.085 15.891 0.751 0.907
0.829 3.284 3.847
5.536 12.801 12.044 0.751 0.907
c=s c-s C-H S-H a Units of e (e = 1.6021892 x IO-l9 C); Total populations,
5.350 15.792 15.539 0.503 0.672
0.587 3.111 3.848
0.399 0.080
0.834 0.432 0.808 0.507
1.054 0.579 0.723 0.498
0.414 0.071
0.641 0.509 0.723 0.498
0.963 0.446 0.750 0.508
0.403 0.068
0.559 0.378 0.750 0.508
0.861 0.487 0.720 0.508
0.420 0.064
0.441 0.422 0.720 0.508
4.343 12.586 6.454 0.532 0.290
c=s c-o C-H O-H
HCSSH C =s -SH H(S)
1.233 0.513 0.808 0.507
4.221 6.857 11.713 0.576 0.677
c=o c-s C-H S-H
HC(=S)OH C =s -OH H(O)
(X, Y = 0 or S)”
4.763 12.681 11.691 0.503 0.672
xi = ri + ui, where i is gross (g), net (n) or overlap
(0) electron
populations.
R. FaustolJournal of Molecular Structure (Theochem)
315 (1994) 123-136
131
b
Fig. 2. Contour maps of the molecular charge density (p) in the molecular plane of (a) F and (b) TF, and the trajectories of the corresponding gradients. The points marked with the symbol l correspond to saddle points in p and are named bond critical points,as the presence of a bond between two atoms in a molecule leads to the appearance of such a critical point in p [lO,ll]. The two unique gradient paths which originate at infinity and terminate at a bond critical point define the boundary between a pair of bonded atoms, in the considered plane. Note that the position of the bond critical point associated with the C=X bond deviates markedly towards the C atom on going from TF to F, in agreement both with a decrease in the electron population of this atom and an increase in the electron population of the X= atom. Contour values(u) in this figure are 2 x lo”, 4 x 10” and 8 x 10”. where n starts at -3 and increases in steps of unity.
On going from F to TF, both the total and c C=X overlap populations (x,(C=X) and CJ~(C=X), respectively) decrease, while r,(C=X) increases. This reflects a weakening of the g C=X bond upon the 0= -+ S= substitution which is partially compensated by a slight strengthening of the 7r bond, which receives electronic charge from the less electronegative S= atom. However, both a,(H) and G,(C-H) decrease, mainly due to the absence in TF of the back-donation charge transfer from the X= atom to the hydrogens, which in turn is observed in F, as shown in the previous section. In the HC(=X)SH molecules (i.e. in TLFA and DTFA) the patterns of variation with the 0= + S= substitution followed by the C=X and C-H overlap populations and by a,(H) are the same as on going from F to TF, and have the same origin. However, the observed increase in
rr,(C=X) is very small, and in the HC(=X)OH molecules (i.e. in FA and TNFA) r,(C=X) decreases. These results may be correlated with the well-known greater ability of the S= atom to accept electronic charge by mesomerism when compared with the 0= atom [l-7]. Note that in F and TF the mesomeric interaction involving the -C(=X)Yfragment (Fig. 3) cannot take place, and that this effect is considerably more important in the HC(=X)OH than in the HC(=X)SH molecules, as it will be shown in detail below.
/i H-C ‘YH
Fig. 3. Canonical with the -C(=X)Y-
forms showing the mesomerism group (X, Y = 0 or S).
associated
Both the total, 0 and rr net electron populations on the Y atom and the total, c and 7r overlap populations of the C-Y bond decrease. Thus. the C-Y bond becomes weaker and the Y atom becomes less negative. The reduction of the considered 7r populations is also in consonance with the above-mentioned greater ability of the S= atom to accept electronic charge by mesomerism. In turn, the changes found in the case of the (T populations are more difficult to interpret, but it seems that the electronic charge is transferred from both -Yand C-Y to either the Y-H overlap or a,(C). Considering now the changes observed in the electron populations due to the -0+ -S- substitution, the following conclusions can be drawn. The total and r C-Y overlap populations increase, while the rr C-Y overlap population decreases. However, the overlap populations associated with the C=X bond change in the opposite direction, i.e. the total and 0 C=X overlap populations reduce, while the rr C=X overlap population increases. Such results indicate that the mesomerism within the -C(=X)Ygroup is more important when Y is an oxygen atom, thus reinforcing the conclusions of previous studies on related molecules [l-7]. In addition, they show that the overall electronic effect of the -04 -Ssubstitution, resulting from both rr and (T effects, leads to a weakening of the C-Y bond and to a strengthening of the C=X bond, as the changes in the P system (inductive effects) are opposite to and larger than those occurring in the rr system. Indeed, the most relevant electronic changes due to the -0+ -Ssubstitution occur in the ~7 system. In consonance with the results found for the C-Y and C=X overlap populations, the total Table 7 Conformer relative energies, s-cis u,(X= with the (s-cis) + (s-trans) isomerization”
H(Y)) overlap
Molecule
A%,ran+j\+c,i~
An,(C-Y)
HCOOH HC(=O)SH HC(=S)OH HCSSH
25.84 6.29 27.40 7.50
7.48 2.50 9.66 6.14
AEnergies in kJ mol
ml’, Electron populations
populations
x 103
and (T net electron populations of the Y atom reduce and those of the X atom increase, while the 7r net electron populations of these atoms vary inversely (i.e. r,(Y) increases and T,,(X) reduces). The total. ~7and 7r net electron populations of the carbon atom and the electron populations of the hydrogen atoms increase, due to the reduction of the electronegativity of the substituent. The Y-H overlap population increases. in agreement with the lower ionic character of the S-H bond when compared with the O-H bond. The above changes do not depend very much on the type of atom X= (0 or S), and are generally much more pronounced than those due to the 0= + S= substitution, in agreement with both the energetic and structural data (see Table 1) that point to a higher degree of similarity between properties of the pairs of molecules having equal -Yand different X= atoms, when compared to the pairs of molecules having equal =X and different -Yatoms. 3.3. What are the relevant electronic features which are responsible for the d@erent relative energies qf the s-cis and s-trans conformers of the HC(=X) YH (X, Y = 0 or S) molecules.T energy difThe AE((s-trauP(sPcis) conformational ferences in the studied molecules follow the order TNFA > FA > DTFA > TLFA (see Table 1). As noted previously, there is a marked decrease in AEc,_,,,,,)_(,_,-i,) upon the -0+ -Ssubstitution, while the 0= -+ S= substitution leads to only a slight increase in AEc,_,r,,,)._(s_,is). This indicates that the nature of the atom -Yis essential
and changes
u,(X=
in the rO(C-Y)
H(Y)) x lo3
16.5 8.6 28.3 10.9
in units of e (e = 1.6021892 x lo-l9 C); X, Y = 0 or S.
overlap
populations
associated
R. FaustolJournal
qf Molecular Structure (Theochem) 315 (1994) 123-136
in determining the relative order AEc,P,,,,,)P(,P,is) in the studied systems. As an overall result, the (s-cis) -+ (s-trans) isomerization leads an electron charge migration towards the positively charged hydrogen atoms (Tables 5 and 6). However, important changes are also observed in the electron distributions of the -C(=X)Yfragment. For all molecules studied, the 7r and total C-Y overlap populations are larger and the 7r and total C=X overlap populations are smaller in the most stable s-cis form. Thus, it can be concluded that the mesomerism within the -C(=X)Ygroup is more important in the s-cis form than in the s-trans conformer, contributing to its observed higher stability. Indeed, the results shown in Table 7 show that An,(C-Y) -- the calculated changes in the 7r overlap populations of the central C-Y bonds associated with the (s-cis) + (s-trans) isomerization - correlate with AEc,_,,,,,)P(,P,i,) in the whole set of molecules studied. In contrast, in the case of (Toverlap populations, the pattern of variation is more complex. For example, a,(C=S) is smaller in the s-cis than in the s-trans form in TNFA, while for the remaining molecules the opposite trend is observed. However, the relative values of the c overlap populations between the X= and H(Y) atoms in the s-cis conformer in the various molecules studied (in the s-trans form, these overlap populations are nearly zero) also correlate well with AEcsPtrans)P(s_,-is)(Table 7). Since gO(X= . H(Y)) can be considered to be a good measure of the relative strength of the X= . H(Y) intramolecular hydrogen bonding in the studied molecules, it can be concluded that such an interaction also contributes to the observed relative AEc,- irans)_(s_cis)values. In summary, the analysis of the differences exhibited by the electron populations of the s-cis and s-trans conformers in the studied molecules shows that both the relative degree of mesomerism within the -C(=X)Yfragment and the strength of the X= H(Y) intramolecular hydrogen bonding in the s-cis form are important in determining the relative values of AEc,_r,,,,)_(,P,is) in these compounds. Taking these results into account, the observed trend can be easily understood by considering (i) the larger electronegativity of the oxygen
133
atom (leading to stronger X= . H(0) intramolecular hydrogen bonds), (ii) the better conjugating properties of the -0-2~ orbitals when compared with the -S- 3p orbitals (leading to an increased importance of the mesomerism within the -C(=X)Ofragment), and (iii) the greater ability of the S= atom to accept electronic charge by mesomerism than the 0= atom. This latter feature leads to the observed slight increase of the important of the mesomerism upon 0= + S = substitution and is a direct consequence of the different degrees of polarization of the C=O and C=S bonds: in the C=O bond, the intrinsic electronic charge polarization towards the 0= atom is much larger than in the C=S bond (see Tables 4-6) and this makes this bond much less sensitive to any electron charge redistribution due, for instance, to conformational changes and, in particular, makes the 0= atom considerably less able to accept additional electronic charge. It is interesting to note that the electronic factors found to be the main factors in determining the relative values of A&, rans)_(s_,-is)in the molecules studied confirm our previous predictions based on geometric data [2]. The above conclusions from Mulliken’s population analysis are entirely in consonance with those which can be obtained from Bader’s analysis. However, this latter method provides an additional way of examining the origin of the relative energies of the s-cis and s-trans conformers. In fact, it provides us with the energies of the various atoms in a given molecule [9- 111. The results are summarized in Table 8, where T’ represents the kinetic energy of an atom obtained by Bader’s method, after being corrected for the virial defect found in the MO calculations (note that by the virial theorem T’ = -E, where E represents the total energy of an atom). Owing to the increased electron population on the H atoms in the s-trans form, the kinetic energies of these atoms in this conformer are larger (i.e. the changes in the energies of the H atoms due to the (s-cis) -+ (s-trans) isomerization tend to favour energetically the s-trans conformer relative to the s-cis form). However, this effect is exceeded by the changes observed in the energies of the atoms belonging to the -C(=X)Yfragment. In
134 Table 8 Atomic properties Molecule
calculated Atom C
HIC=O
0 H H sum
HCOOH
s-cis
C o= POH H(O) sum
HC(=O)SH
s-cis
C o= -SH H(S) sum
HC(=S)OH
s-cis
C s= -OH H(O) sum
HCSSH
s-cis
C s= -SH H(S) sum
from Bader electron
population
analysis”
-Eh
Molecule
Atom
4.142 9.296 0.981 0.981 16.000
37.0221 75.6100 0.6169 0.6169 113.8659 (-113.86633)’
H?C=S
C S H H sum
6.673 15.477 0.925 0.925 24.000
38.1286 397.1947 0.5913 0.5913 436.5059 (-436.506460)’
4.010 9.387 9.301 0.926 0.371 23.995
36.5291 75.7005 75.6049 0.5299 0.3289 188.7625 (-188.762309)’
HCOOH
C o= -OH
4.010 9.364 9.281 0.962 0.386 24.003
36.5162 75.7009 75.5811 0.6188 0.3422 188.7522 (-188.752466)’
4.811 9.333 15.965 0.938 0.957 32.004
36.9512 75.5458 391.7293 0.5999 0.5652 511.3914 (-511.3911416)’
HC(=O)SH
4.795 9.325 15.932 0.943 1.003 3 I.998
36.9455 75.5470 397.7103 0.6019 0.5848 5 11.3895 (-511.388747)’
5.762 15.689 9.295 0.890 0.364 32.000
37.5765 397.4078 75.4932 0.5858 0.3225 511.3858 (-511.386259)’
HC(=S)OH
5.799 15.617 9.278 0.927 0.379 32.000
37.5917 397.3765 75.4698 0.6002 0.3373 511.3755 (-511.375824)’
6.760 15.580 15.814 0.895 0.955 40.004
38.1318 397.2015 397.5455 0.5808 0.5663 834.0259 (-834.027102)”
HCSSH
6.758 15.555 15.792 0.901 0.997 40.003
38.1286 397.1949 397.5304 0.5847 0.5844 834.0230 (-834.024243)’
is
s-tram
H(O) sum
s-tram
C o= -SH H(S) sum
s-tram
C s= -OH H(O) sum
s-tram
C s= -SH H(S) sum
a Electron populations in units of e (e = 1.6021892 x 10mi9 C); Energies in hartrees (1 hartree = 2625.5001 kJmol_‘). b Energies are corrected for the virial defect found in the SCF calculations as described in [lO,l 11. The -V/T values are as follows: HIC=O, 2.00202693; H>C=S, 2.00047103; HCOOH s-cis, 2.00224821, s-tram, 2.00219840; HC(=O)SH s-c& 2.00060935, .s-truns, 2.00062243; HC(=S)OH s-c& 2.00076137, s-truns, 2.00075836; HCSSH s-c&, 2.00038503, s-tram, 2.00039341. ’ SCF calculated energies, ESCF. If the numerical integration of the kinetic energy were perfect, the sum of-E would equal -&-t:.
agreement with the above conclusions from the the calculated electron population analysis, changes in the atom energies clearly indicate that the main changes occur in the C and -Y - atoms as well as in the S= atom, whereas the energy of the 0= atom is only very slightly changed on rotation.
3.4. What is the relative importance of the main steric efects which are operating in the studied molecules? Once the purely electronic effects that are operating in these molecules have been understood, it
R. Fausto/Journal qf‘blolecular Structure (Theochem)
s
II
122 so c
(070)
/\
H
12170
/'C
11439
H
H
H
II659
(s-crs)
(-177)
0 //
12143 (-347)
H-_C
9925
;;;-i
0
12897
(487)
// '1
12262
H-C\
(0.62)
10840
y;,"
\
(-5 50) 101.77
/O
(-9.84)
H
12788
0
12785
12349
(;1&2257 to 17)
128.23
s
12768
12109
;31&~~,56')
s
(6.07)
A22.42
H --c_ ;;i~;;
yz
H
(-1.88)
109.90 (-4.10,
\
101.81 (-9.99)
P /
H
12567
s
I2333
;7)ic//p8,J;1.38)
12602 (J'92)
//",2,.53
H -c ;;;
13.5
depend essentially on the steric effects, thus constituting a very convenient way of looking at these effects separately. The results are summarized in Fig. 4 and lead to the following conclusions:
(1 19)
(-1 4,)
12907
315 11994) 123-136
'f9;,H
(-3.18)
112.45 (-I 75)
\
99.0‘3 (159)
H Fig. 4. Bond path angles and deviations parentheses).
from bond angles (in
becomes both easier and more important to analyse the most important steric effects. Bader’s theory provides a very powerful and simple way of doing this, since the differences in the calculated bond path angles and geometric bond angles
(i) The A(u values associated with the X=C-Y angles are more negative when X= is a sulphur atom and can be easily correlated with more important steric repulsions involving the bigger S= atom and either the H(Y) atom in the s-cis forms or the -Y- lone electron pairs in the s-tram forms. Note that in agreement with this interpretation, in s-cis conformers, for a given X= atom Ad values associated with the X=C-Y angles are more negative when Y is an oxygen than when Y is a sulphur atom due to the shorter C-O and O-H bond lengths compared to the C-S and S-H bond lengths. In addition, in s-trans conformers, for a given X= atom Ao values are more negative when Y is a sulphur atom due to the “bigger” lone electron pairs of this atom. (ii) The Ao values associated with the C-Y-H angles are noticeably negative when Y is an oxygen and slightly positive when Y is a sulphur atom. This is also essentially determined by the different lengths of the C-Y and Y-H bonds, which tend to increase markedly the steric interactions for the oxygen molecules. In the s-cis conformers, for a given Y atom, AQ values associated with the C-Y-H angles become slightly more negative (or less positive) for thiocarbonyl molecules as can be easily anticipated considering the different sizes of the 0= and S= atoms. (iii) The A(r values associated with the H-C-Y angles are markedly more negative in s-trans than in s-cis conformers, due to the close distance between the two hydrogen atoms in the s-trans forms. In addition, for a given type of conformer, the Acu values associated with the H-C-Y angles are more negative when X= is an oxygen. This result can be explained considering that the effective volume of the H(C) atom increases in the carbonyl molecules due to the back-donation charge transfer from the carbonyl oxygen lone electron pairs to the hydrogen atom, as discussed in detail previously.
(iv) Finally, the relative Acu values associated with the H-C=X angles do not exhibit any systematic trend, being probably determined by the changes observed in the H-C-Y and X=C-Y angles discussed above. This is easily explained considering that there are no relevant steric interactions which might directly influence the H-C=X angles.
Acknowledgements The author would like to thank to Professor Hugh D. Burrows, Departamento de Quimica, Universidade de Coimbra, for his helpful comments and suggestions. This investigation was financially supported by Junta National de Investigacao Cientifica e Tecnologica, J.N.I.C.T., Lisboa.
References [1] R. Faust0 and J.J.C. Teixeira-Dias, J. Mol. Struct. (Theochem), 150 (1987) 381. [2] R. Fausto, L.A.E. Batista de Carvalho, J.J.C. TeixeiraDias and M.N. Ramos, J. Chem. Sot., Faraday Trans. 2, 85 (1989) 1945. [3] R. Fausto, L.A.E. Batista de Carvalho and J.J.C. TeixeiraDias, J. Mol. Struct. (Theochem), 207 (1990) 67. [4] L.A.E. Batista de Carvalho, J.J.C. Teixeira-Dias and R. Fausto, J. Mol. Struct. (Theochem), 208 (1990) 109. [5] J.J.C. Teixeira-Dias, L.A.E. Batista de Carvalho and R. Fausto, J. Comput. Chem., 12 (1991) 1047. [6] R. Fausto, L.A.E. Batista de Carvalho and J.J.C. TeixeiraDias, J. Comput. Chem., 13 (1992) 799. [7] J.J.C. Teixeira-Dias, R. Faust0 and L.A.E. Batista de Carvalho, J. Mol. Struct., (Theochem), 262 (1992) 87. [8] R.S. Mulliken, J. Chem. Phys., 23 (1955) 1833. [9] S. Srebrenik and R.F.W. Bader, J. Chem. Phys.. 63 (1975) 3945.
[lo] F.W. Biegler-Konig, R.F.W. Bader and T.-H. Tang. J. Comput. Chem.. 3 (1982) 317. [l I] R.F.W. Bader. T.-H. Tang, Y Tal and F.W. BieglerKonig, J. Am. Chem. Sot., 104 (1982) 946. [12] A.C. Storer, W.F. Murphy and P.R. Carey, J. Biol. (‘hem.. 254 (1979) 3163. [13] G. Lowe and A. Williams, J. Biochem.. 96 (1965) 1X9. [14] R. Fausto. CiCnc. Biol., 13 (1988) 959. [I 51 W.H. Hehre, R. Ditchfield and A.J. Pople, J. Chem. Phys., 56 (1972) 2257. [ 161 M.J. Frisch. G.W. Trucks, M. Head-Gordon, P.M.W. Gill, M.W. Wong, J.B. Foresman, B.J. Johnson, H.B. Schlegel, M.A. Robb. E.S. Replogle, R. Gomperts, J.L. Andres, K. Raghavachari, J.S. Binkley. C. Gonzalez, R.L. Martin, D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A. Pople, Program GAUSSIAN 92 (Revision C), Gaussian Inc., Pittsburgh PA. 1992. [17] H.B. Schlegel, Ph.D. Thesis, Queen’s University, Kingston, Ontario. Canada, 1975. [IS] R.F.W. Bader, S.G. Anderson and A.J. Duke, J. Am. Chem. Sot., 101 (1979) 1389. [19] R.F.W. Bader, T.T. Nguyen-Dang and Y. Tal, J. Chem. Phys., 70 (1979) 4316. [20] R.F.W. Bader, J. Chem. Phys., 73 (1980) 2871. [21] Y. Tal, R.F.W. Bader. T.T. Nguyen-Dang, M. Ojha and S.G. Anderson, J. Chem. Phys., 74 (1981) 5162. [22] R.F.W. Bader and P.M. Beddall, J. Chem. Phys.. 56 (1972) 3320. [23] R.F.W. Bader and P.M. Beddall, J. Am. Chem. Sot.. 95 (1973) 305. [24] R.F.W. Bader, A. Larouche, C. Gatti, M.T. Carroll. P.J. MacDougall and K.B. Wiberg, J. Chem. Phys., 87 (1987) 1142. [25] R.F.W. Bader, Atoms in Molecules ~ A Quantum Theory, Oxford University Press, Oxford, UK, 1990. [26] R.F.W. Bader, in R. Faust0 (Ed.), Recent Experimental and Computational Advances in Molecular Spectroscopy, NATO-AS1 Series C, Vol. 406, Kluwer, Amsterdam, 1993. p. 313. [27] CA. Coulson, Valence, 2nd Edn, Oxford University Press, Oxford, 1961, p. 218. [28] K.B. Wiberg and K.E. Laidig, J. Am. Chem. Sot.. 109 (1987) 5935. [29] D.C. McKean, Chem. Sot. Rev., 7 (1978) 399. [30] C. Castiglioni, M. Gussoni and G. Zerbi, J. Chem. Phys., 82 (1985) 3534.
__---___-__
Bonding in carbonyl and thiocarbonyl compounds: an ab initio charge density study of H2C=X and HC(=X)YH (X, Y = 0 or S) Rui Faust0 Departamento de Quimica, Universidade de Coimhra, P-3049 Coimbra, Portugal
Received 25 March 1994; accepted 14 April 1994
Abstract Ab initio 6-31G* SCF-MO calculations have been carried out for formaldehyde, thioformaldehyde, and for both the scis and s-trans conformers of formic acid and their sulphur-containing analogues (thiol-, thiono- and dithioformic acids). The calculated wavefunctions were used to perform a detailed charge density analysis based on both the Mulliken and Bader partitioning schemes. Particular emphasis was given to the study of the effects of substitutions of oxygen-bysulphur on the electronic distributions of the whole set of molecules and to the conformational effects due to the s-cis --+ s-trans rotamerization in the acids and thiolacids studied. The calculated electronic properties are successfully correlated with several geometric features exhibited by the molecules and used to explain the relative differences in energy between the s-cis and s-trans forms in formic acid and its sulphur derivatives.
1. Introduction Equilibrium geometries and relative energies of a series of molecules containing the -C(=X)Y(X, Y = 0 or S) fragment, determined by ab initio SCF-MO methods, have been reported in previous publications from this laboratory [l-7]. Besides the series of molecules considered here, those previously studied include acetic and propionic acids, their methyl and ethyl esters, and the corresponding sulphur analogues [l-7]. Though a number of important questions were answered by those studies where the emphasis was given either to the analysis of the conformational dependence of relevant geometrical features or to the effects of oxygen-by-sulphur substitution on geometries - some important questions still remain open. Indeed, to further our understanding of these families of molecules, it is fundamental to carry out a detailed analysis of the
electronic structure of a series of representative molecules. Thus, in this article, we report the results of ab initio 6-3 lG* SCF-MO charge density analyses carried out by both Mulliken [8] and Bader [9-l l] methods on formaldehyde (F), formic acid (FA), and their sulphur-containing analogues, thioformaldehyde (TF), thiolformic acid (TLFA), thionoformic acid (TNFA) and dithioformic acid (DTFA). In particular, the following problems are analysed in detail: (i) How is the structural chemistry of the carbonyl and thiocarbonyl groups affected by the electronic properties of substituents like -H, -OH and -SH? (ii) How does the oxygen-by-sulphur substitution affect the electronic distribution in the molecules studied and, in particular, how does it affect their bonding?
0166-1280/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0166-1280(94)03787-L
(
(s-h)
Fig. 1. The s-cis and s-trans (X. Y = 0 or S) molecule.
conformers
.r-l,
at2.s)
of an HC(=X)YH
(iii) What are the relevant electronic features which are responsible for the different relative energies of the s-cis and s-trans conformers (Fig. 1) of the HC(=X)YH (X, Y = 0 or S) molecules? Besides its fundamental importance, the precise characterization, in electronic terms, of the differences between carbonyl and thiocarbonyl compounds achieved in the present study may also provide an important contribution to the understanding, at a molecular level, of a series of complex processes involving such groups in enzyme catalysis, such as catalytic hydrolysis of proteins by serine or cysteine proteases (e.g. chymotrypsin, papain), which have been studied by resonance Raman (RR) spectroscopy using a technique that involves an in situ generation of a thiocarbonyl RR chromophore differing from the natural substrate by a single atom substitution (=0 + =S) [12-141.
2. Computational
methods
The ab initio SCF-MO calculations were carried out with the 6-31G* basis set [ 151 using the GAUSSIAN 92 program system [16] running on a Molecular geometries VAX9000 computer. were fully optimized by the force gradient method using Berny’s algorithm [17]. The largest residual internal coordinate forces were always less than 3 x 10m4 hartree bohr-’ (1 hartree = 1 bohr = 5.29177 x lo-” m) 2625.5001 kJmol-‘; or hartree rad-’ , for bond stretches and angle bends, respectively. The analysis of the wavefunctions in terms of the charge distribution was carried out both by Mulliken’s method [8], using
the standard GAUSSIAN 9: built-in procedures, and Bader’s topological method, using the PROAIMS program package [9- 111. The principles and fundamentals of Bader’s topological method, as well as a series of practical applications to different chemical problems, can be found in the original articles of the author [9- 11,1&24] or in a series of more recent reviews [25,26]. Essentially, in this electron density partitioning scheme, an atom in a molecule is defined as a quantum mechanical subspace, obeying the generalized variational principle [23], which is uniquely defined in real space by a surface of zero-flux in the gradient vector of the charge density [9-l 1,231. Indeed, because of the principal topological property of a charge distribution for a many-electron system -~~ that it exhibits local maxima only at the positions of the nuclei ~ the quantum boundary condition above yields a partitioning of the real space of a molecule into a disjointed set of mononuclear regions, or atoms. As a result of this quantum description of an atom, any property of a molecule may be partitioned into a sum of atomic contributions, i.e. all the properties of an atom in a molecule, including energy, are uniquely defined and their average values may be calculated from the corresponding one-electron density distribution defined in real space by integration over the associated atomic volume defined by the zero-flux surface. Another important result derived from Bader’s theory of atoms in molecules is the unique definition of a bond between a pair of atoms as the path of maximum electron density joining the two nuclei (bond path) [lo]. The angles formed by bond paths are called bond path angles and, in general, as a result of steric interactions between substituents around a given atom, are different from the geometrical bond angles. A negative value of AU (Aa = a(bond path)- (lY(geometrlc) ) suggests a repulsive interaction between the outer atoms of those forming the angle. A positive value could indicate an attractive interaction, but it is more likely that it reflects a smaller repulsion than at other angles. Negative Acvs are generally found with small bond path angles that would tend to bring the end atoms close together, and positive Aas are generally found with large angles where the repulsion between the end atoms would be small.
R. Fuusto/Journal of Molecular Structure (Theochem)
315 11994) 123-136
Table 1 Calculated equilibrium geometries and conformational relative energies for H$=X Parameter
c=x C-Y C-H Y-H H-C=X X-C-Y H-C-Y C-Y-H
H&=0
H,C=S
118.4
159.7
109.2
107.8
122.1
122.3
AEb
125
and HC(=X)YH (X, Y = 0
or S)” HCSSH
s-cis
s-trans
HC(=O)SH ______ s-cis s-trans
118.2 132.3 108.4 95.3
117.6 132.8 109.9 94.8
118.0 177.4 108.9 95.4
117.9 177.1 109.0 94.9
161.9 130.7 107.6 132.5
160.0 131.6 108.1 132.6
161.0 173.6 107.9 132.5
160.8 174.2 107.8 132.6
124.7 124.9 110.4 108.7
124.1 122.0 113.9 III.6
123.4 125.1 111.5 95.9
123.2 122.4 114.4 96.7
123.0 126.7 110.3
121.6 124.3 114.1 111.8
120.9 128.8 110.3 97.6
121.1 124.7 114.2 97.5
HCOOH
25.84
HC(=S)OH s-cis
s-trans
s-cis
s-trans
110.0
6.29
27.40
7.50
a Bond lengths in pm; angles in degrees. b Relative energies (kJ mol-’ ) to the most stable conformer (s-cis)I_
3. Results and discussion
3.1. How are the C=O and C=S groups qflected by the -H,
Table 1 shows the 6-31G* energies and optimized geometries for the molecules studied. For all the HC(=X)YH (X, Y = 0 or S) molecules, the s-cis conformer is more stable than the s-trans form, the energy difference reaching a minimum for X = 0 and Y = S, and a maximum for X = S and Y = 0. It is clear that while the =0 -+ =S substitution only slightly affects the relative energies of the conformers (a slight increase in is observed), the -0+ -SAE(,-rr,,,)-(,-,i,) substitution produces a large decrease in this energy difference. Indeed, the higher degree of similarity between properties of the pairs of molecules having equal -Y- and different X= atoms, when compared with the pairs of molecules having equal =X and different -Y - atoms, has also been found for other series of molecules containing the -C(=X)Yfragment [1,5-71, which seems to indicate that the nature of the -Y- atom determines to a large extent the properties exhibited by this kind of molecule. As noted for the energies, structural changes associated with the rotational isomerism reveal well-defined trends. For instance, the changes in the C=X bond length upon (s-cis) --+ (s-trans) isomerization increase along the series TLFA < DTFA << FA < TNFA calculated values are 0.08, (AC=X/C=Xc,_,is) 0.12, 0.51 and 0.62%, respectively).
-OH
and -SH
suhstituents?
Before looking in detail at the electronic factors which are the origin of both the energetic and structural differences mentioned above, it would appear desirable to examine the nature of the interactions between the carbonyl and thiocarbonyl groups and their substituents (-H, -OH and -SH). A very useful and convenient way of doing this is by considering the relative degrees of p character in the different bonds formed by the carbonyl (or thiocarbonyl) carbon atom [27]. In turn, an estimate of the fractional p character may be obtained either by a direct analysis of the electron populations at each atom on an MO by MO basis or, indirectly, from the calculated bond path angles around the carbonyl (thiocarbonyl) carbon atom (Table 2) considering that these angles correspond to the undeformed bond angles [lo]. In order to convert the angles to fractional p character, the following procedure, outlined in detail elsewhere [28], is adopted: the carbon orbitals involved in the molecular a-system are written as +c=x = (3 +
~PI)IJNl
&A
= (s + hP2JlJN2
4C-B
=
(s +
fP3)/@3
126 Table 2 Bond path angles and hybridization Molecule
A
H2C=0 H2C=S HCOOH s-cis HCOOH s-/rans HC(=O)SH s-cis HC(=O)SH s-tram HC(=S)OH s-ck HC(=S)OH .s-trans HCSSH s-cis HCSSH s-trans
H H OH OH SH SH OH OH SH SH
H H H H H H H H H H
in carbonyl
114.39 116.59 109.49 108.40 108.62 109.58 110.67 109.90 110.90 112.45
and thiocarbonyl
-1.41 1.19 -0.90 -5.50 -2.88 -4.83 0.37 -4.10 0.59 - 1.?S
a Angles in degrees; AN = (bond path angle - geometric C-B bond, respectively; X = 0= or S=.
AF= -l/
(a])
cos (CQ)
& = -l/cos
122.80 121.70 129.07 128.97 127.88 127.85 128.23 127.68 125.67 126.02
AU,
(xi
A%
Px
PA
Pa
0.70 -0.60 4.37 4.87 4.48 4.65 5.23 6.07 4.77 4.92
122.80 121.70 121.43 122.62 123.49 122.57 121.09 122.42 123.43 121.53
0.70 -0.60 -3.47 0.62 -1.61 0.17 -5.61 -1.88 -5.38 -3.18
0.57 0.61 0.58 0.45 0.46 0.48 0.50 0.48 0.50 0.53
0.71 0.70 0.81 0.82 0.80 0.80 0.80 0.79 0.76 0.77
0.71 0.70 0.71 0.73 0.74 0.72 0.70 0.72 0.73 0.70
angle); px. PA, pa, are the percentage
where the p orbials are aligned with the bond directions. Hence, the orthogonality requirement leads to AS = -l/cos
derivatives”
(cuj)
with the cys being the three bond path angles at the carbonyl carbon. The equations are then solved for A, S and c, and the carbon orbitals obtained by normalizing the $s (i.e. by obtaining the values of Ni, NZ and Nj). Finally, the fractions of p character shown in Table 2 (px, PA and ~a) are obtained by squaring the normalized p coefficients. From the calculated fractional p characters, the following conclusions can be drawn: (i) Both for the carbonyl and thiocarbonyl groups, the p fractional character of the 0 C=X bond is fairly small, when compared with those of the C-H or C-Y single bonds. (ii) The p fractional character of the g thiocarbonyl bond is slightly larger than that of the 0 carbonyl bond (for instance, in TF pZs is 0.61, while in F pZo is 0.57). (iii) The relative values of the p fractional characters of the C-S and C-O bonds are similar (very slightly higher values were found for the C-O bonds), while the p fractional character of the C-H bond is considerably lower than that associated with both the C-S and C-O bonds.
of p character
of the g(C=X),
C-A
or
(iv) In the studied acids and thiolacids, the conformational isomerization does not produce important changes in the relative p fractional characters of the bonds formed by the carbonyl (or thiocarbonyl) carbon atom. It is a general rule for single bonds that the larger the electronegativity of a substituent, the larger the fractional p character of the bond formed with this substituent. Indeed, this rule is obeyed in the systems studied for C-H, C-S and C-O single bonds (conclusion (iii) above), although it could be expected that the p characters of the C-O bonds would be significantly larger than those of the C-S bonds. However, considering the relative values found for either pEo or pZs and those associated with the C-H bonds, it must be concluded that the above rule does not seem to be valid in the case of a double bond. Indeed, this conclusion is supported by the direct analysis of the electron populations at each atom on an individual MO basis, as presented in Table 3 for F and TF. For both molecules, this analysis reveals that the p fractional character of the CTcomponent of the double bond is fairly small. In F, the percentage of p character of the (TC=O bond can be estimated from the carbon atom contributions to the electron populations of MO 3 and MO 6, which are formed using the carbon 2s and 2p, orbitals, respectively. The carbon contributions to each orbital are about the same, and the value obtained from Table 3, 0.460/(0.460 + 0.417) = 0.52, is similar to that derived from the bond path angles (0.57,
H. FaustolJournal Table 3 MO electron
populations
for H2C=0
of MolecularStructure
and H2C=Sa
MO
0
C
H
H2C=0 1 @I) 2 (AI)
2.000 0.000
0.000 2.000
0.000 0.000
0 1s c 1s
0.417 1.122 0.863 0.460 0.582
0.003 0.146 0.205 0.041 0.000
g(C-0);
7 @I)
1.576 0.586 0.726 1.459 1.417
8
1.334
0.137
0.264
01,
3 (AI) 4 (AI) 5 U32) 6 (AI)
(B2)
S
Type
01,
4CH2) 74CH2)
fl(C-0); K(C-0)
01,
H2C=S
16%)
0.000
0.000
2 (AI) 3 (AI)
2.000 0.000
0.000 0.000
4 5 6 7 8 9
(AI) 0%)
0.000 0.000
0.000 0.000
U-32)
0.000
0.000
(AI) (AI)
116%)
0.792 0.680 1.189 0.524 0.654
12
0.033
(B2)
10 (A,)
032)
2.000 0.000 2.000
s 1s c 1s s 2s
0.030 0.110 0.326 0.033 0.000
2.000 2.000 2.000 1.148 1.099 0.158 1.409 1.346
S 2P S 2P S 2P dC-Sk
0.099
1.769
SI,
S,,
dCH2) 74’332)
g(C-S); x(C-S)
S,,
a Units of e (e = 1.6021892 x lo-l9 C).
Table 2). On the contrary, in TF, the p fractional character of the 0 component of the double bond, as derived from the carbon electron populations of MO 7 and MO 10 (Table 3), amounts to only 0.40. Table 4 Results of Mulliken
H2C=0 C 0 H c=o C-H H2C=S C S H
5.866 8.415 0.859
6.382 16.056 0.781
electron
population
0.670 1.297
0.796 3 177
partitioning
for H2C=0
5.196 7.118 0.859
5.586 12.879 0.781
4.571 7.981 0.612
5.194 15.720 0.510
(Theochem)
Thus, this result also supports the conclusions derived from the above analysis based on the bond path angles with regard to the general small p character exhibited by the o component of double bonds (conclusion (i) above). It is. however, important to note that the relative values of the fractional p characters of the CTC=O and C-S bonds obtained from direct inspection of the MO electron populations on the atoms and based on the bond path angles give results in opposite directions, with the first method predicting a larger p character for the IT C=O bond and the second a larger p character for the 0 C=S bond (conclusion (ii) above). This apparent discrepancy can be easily overcome if we take into consideration the corresponding 0 C=X overlap opulations, o0 (C==X) (Table 4), as well as the carbon electron population in the MOs involved in the g C=X bonds in F and TF (respectively MOs 3 and 6, and MOs 7 and 10). The absolute values of the total carbon p electron populations in the relevant orbitals (MO 6 in F; 0.460e, and MO 10 in TF; 0.524e, see Table 3) follow the order predicted by the bond path angle analysis. However, the total carbon s electron population in MO 3 of F (0.417e) is much smaller than the corresponding population in the MO 7 of TF (0.792e) which leads both to a larger value for the sum of the carbon atom electron populations in the two relevant MOs in TF than in F (1.316e vs. 0.877e) and to a relative p and H2C=S”
0.449 1.073
0.571 2.952
c=s C-H a Units of e (e = 1.6021892 x lo-l9 C); Total populations,
121
315 11994) 123-136
X, = xf + ui, where
4.122 6.098 0.612 1.086 0.752
0.441
0.646 0.752
0.890 0.742
0.450
0.440 0.742
4.624 12.768 0.510
i is gross (g). net (n) or overlap (0) electron populations.
R. FausfoiJournal of Molecular Structure (Throchem
128
Table 5 Results of Mulliken
HCOOH C =o -oH H(O)
5.475 8.511 8.662 0.819 0.534
electron
population
0.643 1.445 1.853
partitioning
for the s-cis conformers
4.832 7.065 6.808 0.819 0.534
4.196 8.039 8.293 0.530 0.283
0.405 1.258 1.813
J315 i 1994) 123~ 136
of HC(=X)YH
3.791 6.781 6.480 0.530 0.283
c=o c-o C-H O-H
HC(=O)SH C =o -sH H(S)
5.838 8.444 16.033 0.815 0.869
0.692 1.369 3.894
5.146 7.075 12.139 0.815 0.869
4.684 8.039 15.608 0.557 0.609
0.450 1.174 3.871
5.899 16.208 8.624 0.756 0.513
0.712 3.420 1.820
5.186 12.788 6.803 0.756 0.513
4.828 15.858 8.245 0.476 0.263
0.477 3.246 1.793
6.356 16.102 15.924 0.748 0.870
0.817 3.303 3.842
5.539 12.799 12.081 0.748 0.870
c=s c-s C-H S-H a Units of e (e = 1.6021892 x lo-l9 C); Total populations,
5.339 15.824 15.540 0.487 0.608
0.574 3.129 3.837
0.388 0.088
0.807 0.472 0.818 0.489
1.034 0.582 0.737 0.553
0.41 I 0.073
0.623 0.509 0.737 0.553
0.934 0.511 0.746 0.511
0.252 0.078
0.682 0.433 0.746 0.511
0.835 0.522 0.732 0.561
0.415 0.070
0.420 0.452 0.732 0.561
4.351 12.611 6.453 0.476 0.263
c=s c-o C-H O-H
HCSSH C =s -SH H(S)
1.195 0.560 0.818 0.489
4.234 6.865 11.736 0.557 0.609
c=o c-s C-H S-H
HC(=.S)OH C =s -OH H(O)
(X, Y = 0 or S)”
4.76 12.695 11.703 0.487 0.608
xi = xI + ci, where i is gross (g), net (n), or overlap
(0) electron
populations.
R. Fausto/Journal of Molecular Structure (Theochem)
character associated with such MOs that is smaller for TF than for F (0.40 vs. 0.52), as mentioned above. Thus, it is the s component that varies to a greater extent. On the contrary, o0 (C=O) in F is larger than go (C=S) in TF (0.646e vs. 0.440e, see Table 4), indicating that the g electrons are more localized in the C=O bond in F than in the C=S bond in TF, while they are more localized in the carbon atom in TF than in F. This conclusion is in consonance with the expected greater electronegativity of oxygen when compared with sulphur, which makes this atom more efficient in attracting electrons by the inductive effect. Indeed, in F, the large inductive effect of the oxygen substituent requires a more extensive participation of the carbon s electrons in the bonding than in TF. Such a conclusion receives support from the observation given above, that it is the carbon s electrons that are mainly affected by the 0 ---f S substitution, with these migrating from the u C=X bond towards the carbon atom. Therefore, the fractional p character associated with the P C=S bond must be considerably larger than that directly obtained from the MOs as made above (without considering the effective contribution of the electrons to the bonding, i.e. without distinguishing between the net and overlap populations), thus being in consonance with the results derived from the bond path angles. From the results presented in Table 3, some other interesting conclusions can be obtained: (i) Im F, MO 3 and MO 6 have nearly identical contributions from the 0 atom, indicating that this atom distributes equally its s and p electrons by the lone pair and by the u C=O bond. On the contrary, in TF, MO 10 has a much larger contribution from the S atom than MO 7, clearly showing that MO 10 relates to a greater extent to the sulphur lone pair than MO 7, which participates more in the c C=S bonding. As MO 10 has a larger p character, it can be concluded that the sulphur atom lone electron pair has a fairly large p character, being certainly larger than that of the carbony1 lone electron pair in F. (ii) The large fraction of the hydrogen electron population derived from MO 8 in F (0.264e)
315 11994) 123-136
129
shows the importance of back-donation from the oxygen lone pairs into the hydrogens. This effect have been considered to explain both the observed values of the stretching frequencies of isolated CH groups in similar molecules [29] and the charges on hydrogen atoms, as evaluated from infrared intensities in F and ethene [30]. However, the fraction of the electron population derived from MO 12 in TF due to the hydrogen atoms is small (O.O99e), indicating that back-donation is not important in this molecule. (iii) Finally, the carbon and X= electron populations derived from MO 7 in F and MO 11 in TF (7r C=X MOs) clearly show that, as in the case of the 0 electrons, the 7r electrons associated with the C=X moiety are also more localized on the 0 atom in F than on the S atom in TF. 3.2. What is the relative importance of the effects of the 0 + S substitutions on the CTand the YTsystems in the studied molecules?
This is another fundamental question which has not yet been clearly answered and which has important structural and chemical implications. To answer it requires a detailed electronic analysis carried out by using a suitable o/r electron distribution partitioning scheme. Since the results obtained by both the Bader and Mulliken partitioning schemes were found to exhibit a general qualitative agreement, we have decided to discuss in detail here those obtained by the more widely used Mulliken method (Tables 4-6). For the HC(=X)YH molecules, the following analysis is based on the results obtained for the most stable s-cis conformers, though identical conclusions can also be derived from the s-trans data. In the case of the O= + S= substitution, the general pattern of changes observed in the electron populations may be summarized as follows. The total, CJ,and n electron populations on the carbon atom (x,(C), g,(C) and n,(C), respectively) increase, while the corresponding electron populations of the X= atom decrease (see also Fig. 2). These results can be easily correlated with the different electronegativities of the 0 and S atoms.
130
R. Fuusto/Journul
Table 6 Results of Mulliken
HCOOH C =o -OH H(O)
5.476 8.479 8.652 0.855 0.538
electron
population
0.667 1.417 1.858
qf .Moleculrrr Structure
partitioning
for the s-tram
4.809 7.062 6.794 0.855 0.538
4.209 7.992 8.301 0.593 0.290
i Theo&m
conformers
0.427 1.225 1.823
I 315 ( 1994) 123 136
of HC(=X)YH
3.783 6.766 6.478 0.593 0.290
c=o c-o C-H O-H
HC(=O)SH C =o -SH H(S)
5.839 8.439 15.989 0.818 0.914
0.698 1.360 3.896
5.141 7.079 12.093 0.818 0.914
4.677 8.022 15.588 0.576 0.677
0.456 1.165 3.876
5.919 16.156 8.606 0.790 0.529
0.746 3.384 1.823
5.173 12.772 6.783 0.790 0.529
4.854 15.791 8.254 0.532 0.290
0.511 3.205 1.800
6.366 16.085 15.891 0.751 0.907
0.829 3.284 3.847
5.536 12.801 12.044 0.751 0.907
c=s c-s C-H S-H a Units of e (e = 1.6021892 x IO-l9 C); Total populations,
5.350 15.792 15.539 0.503 0.672
0.587 3.111 3.848
0.399 0.080
0.834 0.432 0.808 0.507
1.054 0.579 0.723 0.498
0.414 0.071
0.641 0.509 0.723 0.498
0.963 0.446 0.750 0.508
0.403 0.068
0.559 0.378 0.750 0.508
0.861 0.487 0.720 0.508
0.420 0.064
0.441 0.422 0.720 0.508
4.343 12.586 6.454 0.532 0.290
c=s c-o C-H O-H
HCSSH C =s -SH H(S)
1.233 0.513 0.808 0.507
4.221 6.857 11.713 0.576 0.677
c=o c-s C-H S-H
HC(=S)OH C =s -OH H(O)
(X, Y = 0 or S)”
4.763 12.681 11.691 0.503 0.672
xi = ri + ui, where i is gross (g), net (n) or overlap
(0) electron
populations.
R. FaustolJournal of Molecular Structure (Theochem)
315 (1994) 123-136
131
b
Fig. 2. Contour maps of the molecular charge density (p) in the molecular plane of (a) F and (b) TF, and the trajectories of the corresponding gradients. The points marked with the symbol l correspond to saddle points in p and are named bond critical points,as the presence of a bond between two atoms in a molecule leads to the appearance of such a critical point in p [lO,ll]. The two unique gradient paths which originate at infinity and terminate at a bond critical point define the boundary between a pair of bonded atoms, in the considered plane. Note that the position of the bond critical point associated with the C=X bond deviates markedly towards the C atom on going from TF to F, in agreement both with a decrease in the electron population of this atom and an increase in the electron population of the X= atom. Contour values(u) in this figure are 2 x lo”, 4 x 10” and 8 x 10”. where n starts at -3 and increases in steps of unity.
On going from F to TF, both the total and c C=X overlap populations (x,(C=X) and CJ~(C=X), respectively) decrease, while r,(C=X) increases. This reflects a weakening of the g C=X bond upon the 0= -+ S= substitution which is partially compensated by a slight strengthening of the 7r bond, which receives electronic charge from the less electronegative S= atom. However, both a,(H) and G,(C-H) decrease, mainly due to the absence in TF of the back-donation charge transfer from the X= atom to the hydrogens, which in turn is observed in F, as shown in the previous section. In the HC(=X)SH molecules (i.e. in TLFA and DTFA) the patterns of variation with the 0= + S= substitution followed by the C=X and C-H overlap populations and by a,(H) are the same as on going from F to TF, and have the same origin. However, the observed increase in
rr,(C=X) is very small, and in the HC(=X)OH molecules (i.e. in FA and TNFA) r,(C=X) decreases. These results may be correlated with the well-known greater ability of the S= atom to accept electronic charge by mesomerism when compared with the 0= atom [l-7]. Note that in F and TF the mesomeric interaction involving the -C(=X)Yfragment (Fig. 3) cannot take place, and that this effect is considerably more important in the HC(=X)OH than in the HC(=X)SH molecules, as it will be shown in detail below.
/i H-C ‘YH
Fig. 3. Canonical with the -C(=X)Y-
forms showing the mesomerism group (X, Y = 0 or S).
associated
Both the total, 0 and rr net electron populations on the Y atom and the total, c and 7r overlap populations of the C-Y bond decrease. Thus. the C-Y bond becomes weaker and the Y atom becomes less negative. The reduction of the considered 7r populations is also in consonance with the above-mentioned greater ability of the S= atom to accept electronic charge by mesomerism. In turn, the changes found in the case of the (T populations are more difficult to interpret, but it seems that the electronic charge is transferred from both -Yand C-Y to either the Y-H overlap or a,(C). Considering now the changes observed in the electron populations due to the -0+ -S- substitution, the following conclusions can be drawn. The total and r C-Y overlap populations increase, while the rr C-Y overlap population decreases. However, the overlap populations associated with the C=X bond change in the opposite direction, i.e. the total and 0 C=X overlap populations reduce, while the rr C=X overlap population increases. Such results indicate that the mesomerism within the -C(=X)Ygroup is more important when Y is an oxygen atom, thus reinforcing the conclusions of previous studies on related molecules [l-7]. In addition, they show that the overall electronic effect of the -04 -Ssubstitution, resulting from both rr and (T effects, leads to a weakening of the C-Y bond and to a strengthening of the C=X bond, as the changes in the P system (inductive effects) are opposite to and larger than those occurring in the rr system. Indeed, the most relevant electronic changes due to the -0+ -Ssubstitution occur in the ~7 system. In consonance with the results found for the C-Y and C=X overlap populations, the total Table 7 Conformer relative energies, s-cis u,(X= with the (s-cis) + (s-trans) isomerization”
H(Y)) overlap
Molecule
A%,ran+j\+c,i~
An,(C-Y)
HCOOH HC(=O)SH HC(=S)OH HCSSH
25.84 6.29 27.40 7.50
7.48 2.50 9.66 6.14
AEnergies in kJ mol
ml’, Electron populations
populations
x 103
and (T net electron populations of the Y atom reduce and those of the X atom increase, while the 7r net electron populations of these atoms vary inversely (i.e. r,(Y) increases and T,,(X) reduces). The total. ~7and 7r net electron populations of the carbon atom and the electron populations of the hydrogen atoms increase, due to the reduction of the electronegativity of the substituent. The Y-H overlap population increases. in agreement with the lower ionic character of the S-H bond when compared with the O-H bond. The above changes do not depend very much on the type of atom X= (0 or S), and are generally much more pronounced than those due to the 0= + S= substitution, in agreement with both the energetic and structural data (see Table 1) that point to a higher degree of similarity between properties of the pairs of molecules having equal -Yand different X= atoms, when compared to the pairs of molecules having equal =X and different -Yatoms. 3.3. What are the relevant electronic features which are responsible for the d@erent relative energies qf the s-cis and s-trans conformers of the HC(=X) YH (X, Y = 0 or S) molecules.T energy difThe AE((s-trauP(sPcis) conformational ferences in the studied molecules follow the order TNFA > FA > DTFA > TLFA (see Table 1). As noted previously, there is a marked decrease in AEc,_,,,,,)_(,_,-i,) upon the -0+ -Ssubstitution, while the 0= -+ S= substitution leads to only a slight increase in AEc,_,r,,,)._(s_,is). This indicates that the nature of the atom -Yis essential
and changes
u,(X=
in the rO(C-Y)
H(Y)) x lo3
16.5 8.6 28.3 10.9
in units of e (e = 1.6021892 x lo-l9 C); X, Y = 0 or S.
overlap
populations
associated
R. FaustolJournal
qf Molecular Structure (Theochem) 315 (1994) 123-136
in determining the relative order AEc,P,,,,,)P(,P,is) in the studied systems. As an overall result, the (s-cis) -+ (s-trans) isomerization leads an electron charge migration towards the positively charged hydrogen atoms (Tables 5 and 6). However, important changes are also observed in the electron distributions of the -C(=X)Yfragment. For all molecules studied, the 7r and total C-Y overlap populations are larger and the 7r and total C=X overlap populations are smaller in the most stable s-cis form. Thus, it can be concluded that the mesomerism within the -C(=X)Ygroup is more important in the s-cis form than in the s-trans conformer, contributing to its observed higher stability. Indeed, the results shown in Table 7 show that An,(C-Y) -- the calculated changes in the 7r overlap populations of the central C-Y bonds associated with the (s-cis) + (s-trans) isomerization - correlate with AEc,_,,,,,)P(,P,i,) in the whole set of molecules studied. In contrast, in the case of (Toverlap populations, the pattern of variation is more complex. For example, a,(C=S) is smaller in the s-cis than in the s-trans form in TNFA, while for the remaining molecules the opposite trend is observed. However, the relative values of the c overlap populations between the X= and H(Y) atoms in the s-cis conformer in the various molecules studied (in the s-trans form, these overlap populations are nearly zero) also correlate well with AEcsPtrans)P(s_,-is)(Table 7). Since gO(X= . H(Y)) can be considered to be a good measure of the relative strength of the X= . H(Y) intramolecular hydrogen bonding in the studied molecules, it can be concluded that such an interaction also contributes to the observed relative AEc,- irans)_(s_cis)values. In summary, the analysis of the differences exhibited by the electron populations of the s-cis and s-trans conformers in the studied molecules shows that both the relative degree of mesomerism within the -C(=X)Yfragment and the strength of the X= H(Y) intramolecular hydrogen bonding in the s-cis form are important in determining the relative values of AEc,_r,,,,)_(,P,is) in these compounds. Taking these results into account, the observed trend can be easily understood by considering (i) the larger electronegativity of the oxygen
133
atom (leading to stronger X= . H(0) intramolecular hydrogen bonds), (ii) the better conjugating properties of the -0-2~ orbitals when compared with the -S- 3p orbitals (leading to an increased importance of the mesomerism within the -C(=X)Ofragment), and (iii) the greater ability of the S= atom to accept electronic charge by mesomerism than the 0= atom. This latter feature leads to the observed slight increase of the important of the mesomerism upon 0= + S = substitution and is a direct consequence of the different degrees of polarization of the C=O and C=S bonds: in the C=O bond, the intrinsic electronic charge polarization towards the 0= atom is much larger than in the C=S bond (see Tables 4-6) and this makes this bond much less sensitive to any electron charge redistribution due, for instance, to conformational changes and, in particular, makes the 0= atom considerably less able to accept additional electronic charge. It is interesting to note that the electronic factors found to be the main factors in determining the relative values of A&, rans)_(s_,-is)in the molecules studied confirm our previous predictions based on geometric data [2]. The above conclusions from Mulliken’s population analysis are entirely in consonance with those which can be obtained from Bader’s analysis. However, this latter method provides an additional way of examining the origin of the relative energies of the s-cis and s-trans conformers. In fact, it provides us with the energies of the various atoms in a given molecule [9- 111. The results are summarized in Table 8, where T’ represents the kinetic energy of an atom obtained by Bader’s method, after being corrected for the virial defect found in the MO calculations (note that by the virial theorem T’ = -E, where E represents the total energy of an atom). Owing to the increased electron population on the H atoms in the s-trans form, the kinetic energies of these atoms in this conformer are larger (i.e. the changes in the energies of the H atoms due to the (s-cis) -+ (s-trans) isomerization tend to favour energetically the s-trans conformer relative to the s-cis form). However, this effect is exceeded by the changes observed in the energies of the atoms belonging to the -C(=X)Yfragment. In
134 Table 8 Atomic properties Molecule
calculated Atom C
HIC=O
0 H H sum
HCOOH
s-cis
C o= POH H(O) sum
HC(=O)SH
s-cis
C o= -SH H(S) sum
HC(=S)OH
s-cis
C s= -OH H(O) sum
HCSSH
s-cis
C s= -SH H(S) sum
from Bader electron
population
analysis”
-Eh
Molecule
Atom
4.142 9.296 0.981 0.981 16.000
37.0221 75.6100 0.6169 0.6169 113.8659 (-113.86633)’
H?C=S
C S H H sum
6.673 15.477 0.925 0.925 24.000
38.1286 397.1947 0.5913 0.5913 436.5059 (-436.506460)’
4.010 9.387 9.301 0.926 0.371 23.995
36.5291 75.7005 75.6049 0.5299 0.3289 188.7625 (-188.762309)’
HCOOH
C o= -OH
4.010 9.364 9.281 0.962 0.386 24.003
36.5162 75.7009 75.5811 0.6188 0.3422 188.7522 (-188.752466)’
4.811 9.333 15.965 0.938 0.957 32.004
36.9512 75.5458 391.7293 0.5999 0.5652 511.3914 (-511.3911416)’
HC(=O)SH
4.795 9.325 15.932 0.943 1.003 3 I.998
36.9455 75.5470 397.7103 0.6019 0.5848 5 11.3895 (-511.388747)’
5.762 15.689 9.295 0.890 0.364 32.000
37.5765 397.4078 75.4932 0.5858 0.3225 511.3858 (-511.386259)’
HC(=S)OH
5.799 15.617 9.278 0.927 0.379 32.000
37.5917 397.3765 75.4698 0.6002 0.3373 511.3755 (-511.375824)’
6.760 15.580 15.814 0.895 0.955 40.004
38.1318 397.2015 397.5455 0.5808 0.5663 834.0259 (-834.027102)”
HCSSH
6.758 15.555 15.792 0.901 0.997 40.003
38.1286 397.1949 397.5304 0.5847 0.5844 834.0230 (-834.024243)’
is
s-tram
H(O) sum
s-tram
C o= -SH H(S) sum
s-tram
C s= -OH H(O) sum
s-tram
C s= -SH H(S) sum
a Electron populations in units of e (e = 1.6021892 x 10mi9 C); Energies in hartrees (1 hartree = 2625.5001 kJmol_‘). b Energies are corrected for the virial defect found in the SCF calculations as described in [lO,l 11. The -V/T values are as follows: HIC=O, 2.00202693; H>C=S, 2.00047103; HCOOH s-cis, 2.00224821, s-tram, 2.00219840; HC(=O)SH s-c& 2.00060935, .s-truns, 2.00062243; HC(=S)OH s-c& 2.00076137, s-truns, 2.00075836; HCSSH s-c&, 2.00038503, s-tram, 2.00039341. ’ SCF calculated energies, ESCF. If the numerical integration of the kinetic energy were perfect, the sum of-E would equal -&-t:.
agreement with the above conclusions from the the calculated electron population analysis, changes in the atom energies clearly indicate that the main changes occur in the C and -Y - atoms as well as in the S= atom, whereas the energy of the 0= atom is only very slightly changed on rotation.
3.4. What is the relative importance of the main steric efects which are operating in the studied molecules? Once the purely electronic effects that are operating in these molecules have been understood, it
R. Fausto/Journal qf‘blolecular Structure (Theochem)
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s
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\
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depend essentially on the steric effects, thus constituting a very convenient way of looking at these effects separately. The results are summarized in Fig. 4 and lead to the following conclusions:
(1 19)
(-1 4,)
12907
315 11994) 123-136
'f9;,H
(-3.18)
112.45 (-I 75)
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99.0‘3 (159)
H Fig. 4. Bond path angles and deviations parentheses).
from bond angles (in
becomes both easier and more important to analyse the most important steric effects. Bader’s theory provides a very powerful and simple way of doing this, since the differences in the calculated bond path angles and geometric bond angles
(i) The A(u values associated with the X=C-Y angles are more negative when X= is a sulphur atom and can be easily correlated with more important steric repulsions involving the bigger S= atom and either the H(Y) atom in the s-cis forms or the -Y- lone electron pairs in the s-tram forms. Note that in agreement with this interpretation, in s-cis conformers, for a given X= atom Ad values associated with the X=C-Y angles are more negative when Y is an oxygen than when Y is a sulphur atom due to the shorter C-O and O-H bond lengths compared to the C-S and S-H bond lengths. In addition, in s-trans conformers, for a given X= atom Ao values are more negative when Y is a sulphur atom due to the “bigger” lone electron pairs of this atom. (ii) The Ao values associated with the C-Y-H angles are noticeably negative when Y is an oxygen and slightly positive when Y is a sulphur atom. This is also essentially determined by the different lengths of the C-Y and Y-H bonds, which tend to increase markedly the steric interactions for the oxygen molecules. In the s-cis conformers, for a given Y atom, AQ values associated with the C-Y-H angles become slightly more negative (or less positive) for thiocarbonyl molecules as can be easily anticipated considering the different sizes of the 0= and S= atoms. (iii) The A(r values associated with the H-C-Y angles are markedly more negative in s-trans than in s-cis conformers, due to the close distance between the two hydrogen atoms in the s-trans forms. In addition, for a given type of conformer, the Acu values associated with the H-C-Y angles are more negative when X= is an oxygen. This result can be explained considering that the effective volume of the H(C) atom increases in the carbonyl molecules due to the back-donation charge transfer from the carbonyl oxygen lone electron pairs to the hydrogen atom, as discussed in detail previously.
(iv) Finally, the relative Acu values associated with the H-C=X angles do not exhibit any systematic trend, being probably determined by the changes observed in the H-C-Y and X=C-Y angles discussed above. This is easily explained considering that there are no relevant steric interactions which might directly influence the H-C=X angles.
Acknowledgements The author would like to thank to Professor Hugh D. Burrows, Departamento de Quimica, Universidade de Coimbra, for his helpful comments and suggestions. This investigation was financially supported by Junta National de Investigacao Cientifica e Tecnologica, J.N.I.C.T., Lisboa.
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