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Resonance assisted hydrogen bonds in open-chain and cyclic structures of malonaldehyde enol: A theoretical study
Journal of Molecular Structure 1048 (2013) 138–151
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Resonance assisted hydrogen bonds in open-chain and cyclic structures of malonaldehyde enol: A theoretical study Cristina Trujillo a, Goar Sánchez-Sanz a, Ibon Alkorta a,⇑, José Elguero a, Otilia Mó b, Manuel Yáñez b a b
Instituto de Química Médica, CSIC, Juan de la Cierva 3, E-28006 Madrid, Spain Departamento de Química, C-9 Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Open-chain and cyclic structures of
malonaldehyde enol were compared. Catemers up to 9 monomers have
been calculated. Bader QTAIM analysis was used to
understand the structures. 1
NMR properties, H chemical shifts
and 2hJOO coupling constants, were analyzed.
a r t i c l e
i n f o
Article history: Received 11 April 2013 Received in revised form 27 April 2013 Accepted 29 April 2013 Available online 15 May 2013 Keywords: RAHB Malonaldehyde Catemers AIM NMR
a b s t r a c t In 1989 Gilli, Bellucci, Ferretti and Bertolasi introduced the notion of Resonance Assisted Hydrogen Bonding (RAHB) one of the most fruitful concepts in structural chemistry. After reviewing our previous contributions to this topic, the present work analyzes theoretically this concept especially in non-cyclic structures. Geometries, electron densities and Laplacian at the bond critical points, cooperativity through many body interaction energies, deformation energies as well as NMR properties (chemical shifts and 2h JOO coupling constants) are used for the discussion. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Resonance Assisted Hydrogen Bond (RAHB) has been and still is one of the most successful structural concepts. Introduced in 1989 by Gilli, Bellucci, Ferretti and Bertolasi it has been cited near 650 times [1], and a series of subsequent papers on the same topic by this group were cited more than 100 times each [2–7]. Besides,
⇑ Corresponding author. E-mail address: [email protected] (I. Alkorta). 0022-2860/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2013.04.069
Gastone and Paola Gilli published a book where this topic is reviewed [8]. The standard definition of RAHB is ‘‘A class of strong or very strong hydrogen bonds which cannot be accounted for by electric charges or steric hindrance, but is due to the fact that the neutral donor and acceptor atoms are connected by a system of p-conjugated double bonds; such a bond has been referred to as RAHB (resonance-assisted hydrogen bonding)’’ [3]. To understand the subsequent discussion we will slightly adapt some sentences from the 1989 paper [1]: ‘‘In this paper such methods . . . are applied to the -diketone fragment in its enol form 1 . . . with the aim of understanding what happens to the fragment geometry when it is perturbed by intramolecular, 2, or intermolec-
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Scheme 1. The main structures of Gilli’s first paper.
N N
N N H
H N N
N N H
N H N
H N N
H
H N N
Scheme 2. The first model used in our approach. Scheme 4. Pyrazole cyclamers (a trimer as example) and catemers (a tetramer is represented).
ular, 3, hydrogen bonding.’’ Their graphical scheme of the RAHB model is depicted in Scheme 1. Some authors have particularly stressed the aromatic character of cyclic structures 2 [9]. We have devoted five papers to the subject of RAHBs using two approaches. The first one, based in our expertise in the calculation of spin–spin coupling constants (SSCCs) [10–15] was used to analyze the structure of molecules where the RAHB concept applies, such as the enol of malonaldehyde 4a (Scheme 2). We compared the conjugated a structures of the ring-closed malonaldehyde enol (4a) [16,17]. We calculated at the EOM-CCSD level [10–15] the SSCC of 4a and 4b finding that they depend on the OAO distance but not on the conjugation. The same outcome was reached using the 1H chemical shifts of the proton involved in the HB. The main problem with this approach is that EOM-CCSD calculations are limited to small molecules; besides the Fermi contact term (FC) was used as an approximation to the total SSCC [10– 15]. The second one was to extend the skeleton of b-diketones and related compounds to other molecules, such as those represented in Scheme 3, containing rings of different sizes (the saturated counterparts are not represented). In this second approach no SSCC were calculated.
H O
H
O
H
H N
H
H
11
14
H N
9
15
N H N H
H
12 H
O
O
H
N
H
H N H
H O
H N
8
O
10 H
H
O H
N H
H
H H
7
6 O
N
H
O H
O
O
O
H
H
In the case of the phenyl series 6–9 [18], the aromatic compounds have much strong IMHB that the saturated homologues, but if a constrained geometry was used for the saturated compounds, that is, a geometry having all the non-hydrogen atoms in the same position as in the conjugated molecule, then their HBs are similar or even stronger than those of the aromatic analogues. In the case of cyclobutenones 10–13 and their corresponding saturated cyclobutanones, due to the fact that the ring strain is less severe in the saturated compounds, the IMHB is weaker in the unsaturated series [19]. In both series we conclude that the decisive term was the r-skeleton. The last paper we published [20], reports the study of tropolone 14 and its nitrogenated derivatives 15–17. These compounds have the interesting property that, although conjugated, the single bond marked by an arrow in Scheme 3 does not play any role in the conjugation, being limited to bring the functional groups together. Another peculiarity is that both the saturated and unsaturated systems have a coplanar HB. The conjugation enhances the acidity of the OH (NH) and the basicity of the O@C (N@C) although there is no cyclic conjugation. Some small acyclic compounds (three carbon atoms) were studied but not the open-ring 7-hydroxyhepta-2,4,6-trienal (O@CHACH@CHACH@CHACH@CHAOH, two H atoms more than
N
13 H
16
Scheme 3. The second model used in our approach.
H H N
N H
17
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 1 Relative energies (Erel) of the compounds of Scheme 6.
Intermolecular
Intramolecular
H O
H H
H O Conjugated
O
H
O
H H
H H
4a
H O H 18
O
A
C
E
H H
O
O
6.6 10.7 0.0 7.7 13.2 25.4 12.5 25.4
H H
H
H
MP2 energies Erel with regard to 18, EEZ
H O
H H
Saturated
Monomer 18, EEE 5.9 18, ZEE 9.4 18, EEZ 0.0 18, ZEZ 6.8 18, EZE 13.6 18, ZZE 26.0 18, EZZ 11.9 18, ZZZ 28.0
H
B
RAHB
B3LYP energies Erel with regard to 18, EEZ
O D
H
H H
H H
H H
H 4b
H O
19
O
Scheme 5. The four situations.
Fig. 1. 2-Phenylmalonaldehyde (PROLON) [72,73].
14). The conclusion was that the ring effects also play a significant role in the enhancement of the basicity and acidity of the hydrogen-bond donor and acceptor of tropolone with respect to its saturated counterpart. A final comment concerning literature results: in 1999, Bertolasi et al. reported that the concept of RAHB fails for pyrazole cyclamers and catemers although formally they have conjugated circuits (Scheme 4) [21]. This shows that RAHB has to be used taking care of possible cases where it is not applicable. In the present work, we will examine an aspect that has been neglected in most publications although it was discussed in Gilli’s original paper [1]: the case of ring-open molecules, such as 3 (Scheme 1) or 18/19 (Scheme 5). As stated above, we have already reported the 4a and 4b cases. It remains to study the 18 and 19 cases, i.e., chains of trans enols (catemers) (see Scheme 5). There are eight isomers of monomer 18 (see Scheme 6), including 18, ZZZ which corresponds precisely to structure 4a of Scheme 2. In Scheme 5, the catemers correspond to (EEE)n (see below).
H O
H
H
H
H
O O
18, EEE
H
H
H
O
18, EZE
H
H
O
H O
18, ZZE
H
O
H O H
18, ZEZ
H
H O
H H
18, EEZ
H H
H O
O
18, ZEE
H O H
The geometry of the systems under investigation has been optimized at the B3LYP [22,23]/6-311++G(d,p) [24] and MP2 [25]/6-311++G(d,p) [24] computational levels. In order to evaluate the resonance assistance, Cs symmetry has been imposed in all the systems studied, although they are not true minima. All the calculations have been performed with the Gaussian-09 program [26]. Absolute chemical shieldings have been calculated within the GIAO approximation [27,28] on the B3LYP/6-311++G(d,p) geometries. The bonding characteristics were analyzed by means of the atoms in molecules (AIM) theory [29,30]. For this purpose we have located the intermolecular bond critical points (BCP), and evaluated the electron density properties at each of them with the AIMAll program [31]. In the Ramsey approximation [32], the total coupling constant (J) is a sum of four contributions: the paramagnetic spin–orbit (PSO), diamagnetic spin–orbit (DSO), Fermi-contact (FC) and spin-dipole
H
O H
2. Computational methods
H H
H O H 18, EZZ
Scheme 6. The eight isomers of the enol of malonaldehyde 18.
H
H O O H 4a, ZZZ
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 2 B3LYP and MP2 geometries (Å, °) of 18n and 19n catemers. Bond distances of the central monomer (conjugated 18) only for odd n. OAH O bonds (conjugated 18) Catemer, n
Method
OAH
O H
O O
OAH O
1 (monomer)
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP
0.962 0.961 0.963 0.962 0.983 0.978 0.963 0.962 0.989 0.983 0.989 0.983 0.964 0.962 0.993 0.985 1.001 0.992 1.001 0.992 0.992 0.985 0.964 0.993 1.003 1.007 1.007 1.003 0.993 0.964 0.993 1.004 1.008 1.009 1.009 1.008 1.004 0.993
– – – – 1.732 1.741 – – 1.680 1.699 1.682 1.699 – – 1.658 1.681 1.606 1.633 1.607 1.634 1.663 1.682 – 1.654 1.596 1.579 1.580 1.596 1.659 – 1.652 1.593 1.573 1.567 1.567 1.574 1.593 1.657
– – – – 2.715 2.719 – – 2.667 2.679 2.671 2.681 – – 2.648 2.662 2.604 2.620 2.605 2.621 2.653 2.665 – 2.644 2.595 2.582 2.583 2.596 2.650 – 2.643 2.593 2.577 2.572 2.572 2.578 2.594 2.648
– – – – 178.5° 179.7° – – 175.8° 174.6° 177.1° 176.9° – – 175.0° 173.6° 174.1° 173.1° 174.2° 173.2° 175.9° 175.4° – 174.8° 173.6° 173.6° 173.4° 174.1° 175.4° – 174.8° 173.7° 173.5° 173.4° 173.4° 173.5° 173.9° 175.6°
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2
0.962 0.961 0.962 0.961 0.971 0.968 0.962 0.961 0.971 0.969 0.971 0.968
– – – – 1.918 1.925 – – 1.903 1.906 1.904 1.908
– – – – 2.872 2.855 – – 2.868 2.851 2.870 2.855
– – – – 166.7° 160.3° – – 172.3° 164.3° 172.5° 165.1°
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP
0.962 0.961 0.972 0.969 0.972 0.969 0.972 0.969 0.972 0.969 0.962 0.971 0.972 0.972 0.972 0.972 0.972
– – 1.898 1.900 1.888 1.890 1.888 1.890 1.900 1.902 – 1.898 1.887 1.884 1.883 1.888 1.900
– – 2.863 2.850 2.859 2.851 2.859 2.852 2.866 2.855 – 2.866 2.859 2.856 2.855 2.860 2.869
– – 172.0° 166.2° 176.9° 171.0° 177.3° 171.4° 172.6° 167.4° – 173.7° 178.4° 178.2° 178.0° 179.0° 174.6°
2 (dimer)
3 (trimer)
5 (pentamer)
7 (heptamer)
9 (nonamer)
OAHO bonds (saturated 19) 1 (monomer) 2 (dimer)
3 (trimer)
5 (pentamer)
7 (heptamer)
Bond distances of the central monomer (conjugated 18) only for odd n (continued on next page)
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Table 2 (continued) OAH O bonds (conjugated 18) n
Method
OAH
OAC
C@C
CAC
C@O
1
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP
0.962 0.961 0.989 0.983 1.001 0.992 1.007 1.009
1.349 1.352 1.322 1.328 1.314 1.321 1.311 1.309
1.341 1.348 1.355 1.358 1.359 1.361 1.361 1.362
1.457 1.461 1.432 1.440 1.425 1.434 1.423 1.421
1.214 1.222 1.232 1.234 1.237 1.238 1.239 1.240
3 5 7 9
Bond distances of the central monomer (saturated 19) only for odd n n
Method
OAH
OAC
CAC
CAC
C@O
1
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP
0.962 0.961 0.971 0.969 0.972 0.969 0.972
1.425 1.423 1.416 1.416 1.414 1.414 1.414
1.522 1.518 1.523 1.520 1.524 1.520 1.524
1.513 1.514 1.505 1.507 1.504 1.506 1.504
1.206 1.215 1.213 1.221 1.213 1.221 1.213
3 5 7
1.02
O-H distance
1.01 n=1
1
n=2
0.99
n=3
0.98
n=5 n=7
0.97
n=9
0.96 0.95 0
2
4
6
8
10
OH position along the chain 1.75 1.73
O···H distance
1.71 1.69
n=2
1.67
n=3
1.65
n=5
1.63
n=7
1.61
n=9
1.59 1.57 1.55 0
1
2
3
4
5
6
7
8
9
HB position along the chain Fig. 2. OH and O H distances for conjugated catemers as a function of the HB position along the chain for the 18n series.
(SD). All terms have been computed for all molecules. SOPPA calculations were performed using the Dalton-2 program [33].
3. Results and discussion The corresponding energies of the eight conformers of 18 are gathered in Table 1.
To build up the catemers of Scheme 5 we have selected the two monomers of lower energy, namely EEE and EEZ. The EEE monomer is present in the few X-ray structures of malonaldehyde derivatives that form catemers, for instance, 2-phenylmalonaldehyde (Fig. 1). Concerning their saturated counterparts we have only studied the 19, the EEE monomer that corresponding to 18. A search in the CSD [34] reveals that the only structure related to (19, EEE)n is CUJCOA [34]. Even if the differences are notable, CUJCOA
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Since the catemers (18, EEZ)n do not correspond to any known present structure we have relegated the corresponding results of these catemers to the Supporting Information.
Table 3 BCP electron densities and Laplacian at the BCP (B3LYP calculations). (OAH)1
(OAH)2
(OAH)3
143
(OAH)4
2
q» q 182 183 185 187 189
3.1. The catemers of the 18 and 19 series
0.040 0.046 0.049 0.049 0.050
(0.131) (0.1405) (0.1435) (0.144) (0.145)
0.057 (0.151) 0.058 (0.152) 0.059 (0.153)
0.061 (0.154) 0.062 (0.154)
0.026 0.027 0.027 0.027
(0.094) (0.097) (0.098) (0.098)
0.028 (0.100) 0.028 (0.1005)
0.028 (0.101)
0.063 (0.155)
q»2q 192 193 195 197
Table 4 B3LYP interaction energies (kJ mol1) of 18n and 19n catemers (MP2 values in parentheses). Catemer, n
Ei (1)
Ei (2)
Ei (3)
2 3 5 7
(182) (183) (185) (187)
47.4 (46.2) 58.0 (54.9) 63.5 (59.5) 64.8
– – 78.0 (71.3) 81.7
– – – 87.3
2 3 5 7
(192) (193) (195) (197)
24.8 (27.6) 26.4 (28.4) 27.2 (29.0) 27.4
– – 29.4 (30.3) 30.0
– – – 30.8
3.1.1. Geometries We have calculated at two levels, B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p), the 18n and 19n catemers for n = 2, 3, 5, 7 and 9 (B3LYP) and for n = 2, 3 and 5 (MP2). We report in Table 2 the most relevant geometrical parameters associated with all the OAH O hydrogen bonds within each catemer, as well as the OAH bond length for each monomer. In all cases the first monomer corresponds always to the one which acts as HB acceptor (terminal OH) and the latter to the one which behaves as HB donor (Terminal CO). Table 2 includes also all the information about the central monomer in odd catemers (n = 3, 5, 7 and 9). A detailed analysis of the values reported in Table 2 shows that the HB distances obtained at the B3LYP and MP2 levels of theory are linearly correlated,
B3LYP ¼ ð0:014 0:006Þ þ ð0:988 0:004ÞMP2; n ¼ 36; R2 ¼ 0:999 ð1Þ although the B3LYP values are systematically shorter than the MP2 ones. To account for this difference we have added a term, resulting in Eq. (2).
B3LYP ¼ ð0:098 0:014Þ þ ð1:104 0:014ÞMP2 ð0:098 0:012ÞO H; n ¼ 36; R2 ¼ 1:000
ð2Þ
In any case, Eqs. (1) and (2) allow using the much less expensive DFT vs. MP2 calculations. There are also good correlations between the OAH and O H bond lengths for the conjugated and saturated catemers [see Eqs. (3) and (4), respectively], although the former is poorer because the range of variation of the OAH bond length is very small (0.046 Å).
B3LYPðOHconj: Þ ¼ ð2:4 0:3Þ þ ð3:5 0:3ÞB3LYPðOHsat :Þ; 1emn ¼ 18; R2 ¼ 0:89
ð3Þ
B3LYPðO Hconj :Þ ¼ ð7:2 0:3Þ þ ð4:64 0:17ÞB3LYP ðO Hsat: Þ;
Fig. 3. Plot of q BCP (au) vs. O H interatomic distances (Å). Exponential fitting, R2 = 0.9994.
crystallizes as a catemer with OAH O HBs. From now on, and for the sake of simplicity the (19, EEE)n catemer will be called 19.
H3C CH3 O H H
H
O
O H
H
O
H
19, EEZ
H
O
O
H
H H3C CH3 CUJCOA
n ¼ 13; R2 ¼ 0:985
ð4Þ
As it has been shown for dihydrogen bonds [35,36], these values, when plotted against the position of the monomers within the catemers, appear as curvilinear plots (see Fig. 2). For the OH bond distances this indicates that the lengthening of the OH bond goes through a maximum for the central monomer, whereas for the OH O distance it goes through a minimum. Although Fig. 2 shows these trends only for the 18n series of catemers, similar variations are observed for the 19n series (see Fig. S1 of the Supporting information). These findings reflect the significant cooperative effects of the hydrogen bonds that stabilize the catemers. Obviously cooperative effects should be maximum for the HBs in which the central monomer participates and minimum for the two external monomers because they only act as HB donors or as HB acceptors. Indeed, the electron densities at the HB critical points (See Table 3) increase as we moved towards the central monomer, in both series, although, also consistently with the variations of the bond lengths, the effect is larger for the conjugated catemers. A similar increase is also observed for the corresponding value of the Laplacian of the electron density. It is worth noting that, for the two external monomers, cooperativity is significant since the values of the OH and the OH O distances involving the external monomers for catemers with n P 3
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Table 5 Terms of the MBIE partition (all in kJ mol1). The numbers in parentheses of the Terms column correspond to monomers ordered from C@O to OAH. Terms Er (1) Er (2) Er (3) Er (4) Er (5) RE r REr/n D2E (1–2) D2E (1–3) D2E (1–4) D2E (1–5) D2E (2–3) D2E (2–4) D2E (2–5) D2E (3–4) D2E (3–5) D2E (4–5) D3E (1–2–3) D3E (1–2–4) D3E (1–2–5) D3E (1–3–4) D3E (1–3–5) D3E (1–4–5) D3E (2–3–4) D3E (2–3–5) D3E (2–4–5) D3E (3–4–5) D4E (1–2–3–4) D4E (1–2–3–5) D4E (1–2–4–5) D4E (1–3–4–5) D4E (2–3–4–5) D5E (1–2–3–4–5)
182
192
183
193
184
194
1.83 0.97
0.30 0.24
2.97 5.16 1.43
0.36 0.62 0.26
3.40 7.45 6.47 1.61
0.38 0.70 0.65 0.27
2.80 1.40 50.16
0.54 0.27 25.35
9.56 3.19 52.48 1.94
1.24 0.41 25.35 0.24
18.93 6.31 53.15 2.07 0.50
2.00 0.50 25.37 0.32 0.21
52.27
25.32
54.85 2.12
25.21 0.42
52.81
25.27
9.16 0.67
1.61 0.04
0.55
0.00
9.22
1.60
1.06
0.27
167.23
78.24
8.26
47.36
24.81
1.57
105.38
51.24
are systematically longer and shorter, respectively than the corresponding values for the dimer. Similar trends, are observed as far as the electron densities at the BCPs are concerned (See Table 4). A plot of qBCP (au) vs. O H interatomic distances (Å) is reported in Fig. 3. Similar exponential relationships have been found for other HBs [37–43]. Note however that in a recent report by Mo [44] it was pointed out that the estimate of HB strengths in intramolecular RAHB systems based on the QTAIM topological properties can be questionable, since the deactivation of the p resonance lead to small changes on the electron density at the HB critical point. The cooperative effects discussed above in terms of geometrical parameters as well as the topology of the electron density are also reflected in the energies of the HBs. For this purpose we have calculated the energies involved in the HBs as the differences between the catemers and the different fragments which can be formed by eliminating a monomer, a dimer, a trimer, etc., so that,
Ei ð1Þ ¼ En Eðn1Þ E1 ;Ei ð2Þ ¼ En Eðn2Þ E2 ;Ei ð3Þ ¼ En Eðn3Þ E3 ... This procedure does not differentiate one end (the one which contains the terminal OH group) from the other (the one which contains the terminal C@O one) but it allows to classify the HBs according to their relative position in the chain. Note, for instance, that for a pentamer, it is fulfilled that E5(1) = E5(4) and the E5(2) = E5(3). From the values in Table 4 it can be observed that the B3LYP and MP2 estimates are rather similar, but more importantly, as it was found above for the distances, they are linearly correlated,
EMP2 ¼ ð6:4 0:3Þ þ ð0:834 0:007ÞEB3LYP ; i i
n ¼ 8; R2 ¼ 1:000 ð5Þ
185
195
3.61 8.38 9.27 7.07 1.71 30.04 6.01 53.41 2.13 0.54 0.16 55.62 2.26 0.54 55.56 2.15 53.12 9.50 0.73 0.23 0.66 0.06 0.20 10.31 0.77 0.68 9.56 1.13 0.01 0.12 0.06 1.05 230.78
0.38 0.72 0.74 0.68 0.27 2.79 0.56 25.37 0.34 0.21 0.02 25.20 0.48 0.21 25.20 2.15 25.35 1.63 0.04 0.04 0.02 0.03 0.02 1.70 0.09 0.05 1.63 0.22 0.02 0.21 0.04 0.15 105.48
therefore we are legitimated to use the B3LYP values in the following discussion. The systematic increase of the Ei values with the length of the catemer is a clear evidence of the importance of cooperativity in the stabilization of the polymers, both for the saturated and the conjugated series. Very significantly there is an extremely good linear correlation between both sets of values,
Ei 19 series ¼ ð17:64 0:04Þ þ ð0:151 0:001ÞEi 18 series; n ¼ 7; R2 ¼ 1:000
ð6Þ
which indicates that although the increase of Ei is much larger for the conjugated than for saturated catemers, the tendencies are similar, increasing with n and increasing with the proximity to the central position. The cooperativity can be quantitatively traced through a many body interaction energy (MBIE) analysis. Although the partition of energies of supramolecular structures using the MBIE is known at least from 1970 [45], it has been used extensively by Saykaly and Xantheas from 1994 [46–48]. Kulkarni et al. developed an algorithm and applied it to large molecular clusters [49–51]. Other authors have also applied the MBIE analysis to other clusters [52–54]. We have designed a small program to generate automatically from the Gaussian log file all the inputs necessary to evaluate all the terms of MBIE, which for the catemers investigated in this work, have been collected in Table 4. In this method two-, threeand four-body terms are defined by Eqs. (7)–(9), respectively. The interaction energy Ei(n) of a system of n-molecules is defined as the difference between the energy of the complex at its equilibrium geometry and the sum of the n isolated molecules.
EiðnÞ ¼
n n1 X n n2 X n1 X n X X X EðiÞ nE þ D2 EðijÞ þ D3 EðijkÞ þ ::: i¼1
i¼1 j>i
þ Dn Eð1; 2; 3 . . . nÞ
i¼1 j>i k>j
ð7Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Er/n (18n)
9
6
3
0 0
2
4
6
8
10
n
Er/n (19n)
0.6
0.3
0.0
0
2
4
6
8
n Fig. 4. Exponential fitting of the deformation energy per monomer as a function of the number of monomers forming the catemer. For the conjugated 18n and the saturated 19n series the fittings obey the equations: REr/n = (13.0 ± 1.1) – (15.4 ± 0.9) (0.86 ± 0.02)n and REr/n = (0.64 ± 0.01) – (1.06 ± 0.03) (0.60 ± 0.02)n, with R2 = 0.996 and R2 = 0.998, respectively.
ErðiÞ ¼ EðiÞ E
ð8Þ
D2 EðijÞ ¼ EðijÞ ½EðiÞ þ EðjÞ
ð9Þ
D3 EðijkÞ ¼ EðijkÞ ½EðiÞ þ EðjÞ þ EðkÞ bD2 EðijÞ þ D2 EðikÞ þ D2 EðjkÞc
ð10Þ
where E(i), E(ij), E(ijk) are the energy of monomer i, dimer ij, trimer ijk with the geometry of the complex and E is the minimum energy of the isolated monomer. The first term of the equation is known as relaxation, the second is associated to the 2-body, the third to the 3body and so on. The three body term and higher body terms [D3E(A–B–C) (Eq. (10)), D4E(A–B–C–D), etc.] are associated to cooperativity. They correspond to the difference of the interaction energy and the sum of the one and two body terms. As illustrated in Table 5 for the trimer of the conjugated system cooperative effects amount to more than 8 kJ mol1, and this value becomes, as expected slightly larger for the tetramer and the pentamer. For the saturated derivative, cooperativity is significantly smaller (1.6 kJ mol1 for the trimer) but not negligible. These differences are actually a manifestation of the so called RAHB; but what is its real origin? The fundamental reason is associated with the changes in the intrinsic basicity and acidity properties of the conjugated monomers with respect to the saturated analogues. Indeed, the intrinsic
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basicity of 18 (861 kJ mol1) is significantly larger than that calculated for 19 (776 kJ mol1), clearly showing [55,56] that 18 should be a much better HB acceptor than 19. Similarly, the conjugated compound 18 is a much stronger acid (DacidH = 1358 kJ mol1) than its saturated counterpart 19 (DacidH = 1556 kJ mol1), which indicates that the former is a much better HB donor than the latter. These results are transferable to the pseudo six-membered rings 4a and 4b, explaining the much stronger intramolecular HB of the former. This is actually consistent with the analysis carried out by Mo [44], who showed, through the use of the block-localized wavefunction (BLW) method, that when conjugation is deactivated from 4a the intramolecular HB becomes much weaker, and the optimized geometry leads to much longer O O distances. Still the intramolecular HB when conjugation is deactivated in 4a is stronger than that in the saturated derivative 4b. When the conjugation is deactivated in 4a it has been reported that the O O distance increases from 2.586 Å to 2.884 Å, whereas in the saturated 4b derivative this distance is still longer (2.926 Å). The explanation is that besides the decrease in the HB donor and acceptor ability of the C@O and the OH groups of 4b respect to 4a, in 4a the conjugation forces both groups to be coplanar and closer to each other. Very importantly, when the structure of compound 4b is optimized by imposing the C@O and the COH groups to be coplanar (Cs symmetry) the intramolecular HB reinforces and the O O distance becomes significantly shorter (2.742 Å) although still longer than that of the conjugated 4a analogue. This result clearly shows that the r-skeleton has also a significant influence on the strength of these interactions. Hence, in summary, the conjugation on going from 4b to 4a results in a reinforcement of the OAH O intramolecular HB through the concurs of three concomitant factors, an increase of the proton acceptor capacity of the C@O group, an increase of the proton donor capacity of the OH group, and a rskeleton arrangement which favors these kinds of interactions. Cooperativity has also a significant influence on the deformation energy, i.e. the energy required to deform an isolated monomer from its minimum energy geometry to the geometry it adopts in the catemer. The deformation energy is easily calculated in the framework of the MBIE approach, Eq. (8). Then REr/n is the average deformation energy per monomer. As expected from our previous discussion, it is much larger in the conjugated 18 series than in the saturated 19 ones and also it increases much faster. Obviously for both monomers REr = 0 and REr/n = 0, it is expected that for very long chains REr/n will be constant, i.e. an asymptotic equation going through (1, 0) will be found, as shown in Fig. 4 for both series of catemers. Coherently with the larger cooperative effects for the conjugated catemers, the asymptote is much larger for the 18n series (15.1 vs. 0.64) and the c term closer to 1 (0.88 vs. 0.60). This corresponds to a lower attenuation of the number of monomers (for c = 1, REr/n will be constant). The value of the asymptote for the 18n series means that the real strength of the HBs formed by the central monomer of the catemer is sizably larger than predicted by the energies reported in Table 5, since the real dissociation energies of these HBs would be about 7.5 kJ mol1 larger than those reported in Table 4. This strength enhancement due to the deformation of the monomers is rather small for the 18n saturated series, since it would account for 0.3 kJ mol1 only. Let us now analyze in more detail the changes observed in the HBs for these systems when the environment changes from the intramolecular HBs in 4a and 4b to the intermolecular HB in the conjugated and saturated catemers of infinite length (B and D), or when the corresponding intra- and intermolecular HBs appear in conjugated or saturated systems (A and C). E compares the saturated catemer 19n (n = 1) with the unsaturated 4a derivative. For this purpose we have summarized the relevant parameters
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Scheme 7. Analysis of conjugated vs. saturated and intramolecular vs. intermolecular (for n = 1) on the geometries. E values = A D = B C. The fourth column corresponds to experimental data.
Scheme 8. Effect of the method of calculation on the NMR parameters of the IMHB present in 4a and 4b.
in Scheme 7, in which, for the sake of completeness we have added E, which compares the saturated catemer 19n (n = 1) with the unsaturated 4a derivative. To carry out such comparisons we need to know, besides the geometrical parameters which characterize the intramolecular HBs in 4a and 4b the values for the catemers in the limit of an infinitely long (n ? 1) chain. For this purpose we have adjusted the data of Table 2 (central motive) using exponential Eqs. (11)–(19) of the form y = a + b cn, so that for n = 1, y = a (bold). The values so obtained are as follows: Conjugated catemer 18n (four points)
O—H ¼ ð1:011 0:008Þ ð0:074 0:007Þ ð0:671 0:026Þn ; R2 ¼ 0:998
ð11Þ
O H ¼ ð1:560 0:002Þ þ ð0:502 0:024Þ ð0:618 0:011Þn ; R2 ¼ 0:9996
ð12Þ
O O ¼ ð2:567 0:002Þ þ ð0:438 0:028Þ ð0:610 0:015Þn ; R2 ¼ 0:9994
ð13Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 6 B3LYP calculated 1H chemical shifts (ppm) and central monomer. d1H
2h
JOO coupling constants (Hz) of the
2h
JOO
n
OH-terminal
C@O-terminal
Average
Conjugated series 18 3 11.37 5 13.02 7 13.66 9 13.95 1 14.12a
4.97 6.64 7.33 7.64
4.72 6.59 7.29 7.62
4.84 6.62 7.31 7.63 7.82a
1.06 1.18 1.20
0.99 1.16 1.22
1.02 1.17 1.21 1.22a
Saturated series 19 3 5 7 1 Saturated 3 5 7 1 a
4.26 4.57 4.66 4.70a
series 19 with the geometry of the OAH O HB of 18 (19/18) 6.84 3.14 2.97 3.06 8.31 4.39 4.34 4.36 8.90 4.88 4.87 4.88 a 9.30 5.20a
Estimated with Eqs. (24) and (25).
OHO ¼ ð173:3 0:03Þ þ ð14:0 1:0Þ ð0:560 0:015Þn ; R2 ¼ 0:9994
ð14Þ
C—O ¼ ð1:308 0:008Þ þ ð0:047 0:006Þ ð0:667 0:038Þn ; R2 ¼ 0:996
ð15Þ
C@O ¼ ð1:241 0:002Þ ð0:031 0:002Þ ð0:652 0:014Þn ; R2 ¼ 0:9994
ð16Þ
Saturated catemer 19n (three points, R2 = 1.0000)
O—H ¼ 0:972 ðalmost constantÞ O H ¼ ð1:883 0:001Þ þ ð0:150 0:006Þ ð0:516 0:007Þn ð17Þ O O ¼ ð2:854 0:002Þ þ ð0:071 0:003Þ ð0:576 0:011Þn ð18Þ OHO ¼ ð178:7 0:02Þ ð42:6 0:5Þ ð0:532 0:002Þn
ð19Þ
C—O ¼ 1:414 ðalmost constantÞ C@O ¼ 1:203 ðalmost constantÞ Note that the c coefficient is in average 0.63 and 0.54 for 18 and 19, respectively. That means that the sensitivity to the number of monomers is slightly larger in the conjugated series. The first conspicuous fact is that intermolecular calculated values for a chain of infinite length (second column) are in good agreement with the X-ray structures (last column) excepting the OAH and H O distances; this exception is due to the well known effect concerning the position of hydrogen atoms in X-ray crystallography (aspherically displaced towards the atom to which it is bonded, here the oxygen) [57–59]. The agreement is better for the less perturbed structure (PROLON). The third column of scheme 7 summarizes the ratio of the parameters of the intermolecular HB for catemers 18n and 19n (n = 1) with respect to those of the corresponding intramolecular HBs in 4a and 4b, respectively (B and D). The last file contains
147
similar ratios when the saturated systems 4b and 19n (n = 1) are compared with the conjugated analogues 4a and 18n (n = 1), respectively (A and C). The intersection of the third column and the last file presents the values obtained when the saturated catemer 19n (n = 1) is compared with the conjugated 4a derivative (E). A HB becomes stronger when the OAH bond lengthen, the O H bond shorten, the O O distance shorten, the C@O bond lengthen, and the CAO bond shorten. The contrary should happen if the HB becomes weaker. To better guide the reader, in Scheme 7 we have written in red the ratios which are consistent with a reinforcement of the HB and in blue those which are consistent with a weakening. Furthermore, the more different from 1 the ratios of Scheme 7, the larger the effect. It results that A and C correspond to weakening (in C more pronounced than in A), B corresponds to strengthening although these effects are quantitatively smaller than the weakening observed in A (for this comparison, we have used the inverse values), D shows three weakening and two strengthening values but all of them are very close to unity indicating very small effects and, finally, E which is a combination of structural effects (ratio of ratios A/C or B/D) corresponds to a weakening of the HB. Concerning E, the weakening effect results from C being larger than A and from B being larger than D. One important conclusion of this study of the geometrical changes is that the effect of conjugation is more important in a catemer (C values) than in a strained pseudo six-membered ring (A values). As we have discussed above this is mainly a consequence of larger cooperativity effects in the conjugated that in the saturated catemers. Similarly, on going from intra- to intermolecular HBs the geometrical changes are larger for conjugated (B values) than for saturated (D) compounds. The rationalization of these trends is not trivial. Firstly, in the strained pseudo six-membered rings, 4a and 4b, the HB donor and the HB acceptor belong to the same molecule, whereas in the catemers the HB donor donates to a different molecule and also accepts from a different one. Secondly, in the catemers there is a significant participation of cooperativity through three-body interactions which are not possible in the monomeric pseudo six-membered rings. Indeed, the formation of the catemers is accompanied by a significant change in the intrinsic acidity of the terminal OH groups and also by a significant enhancement of the basicity of the terminal C@O groups. Both effects are well reflected on the fact that on going from the monomer 18 to the trimer 183 the acidity of the terminal OH group increases by 107 kJ mol1, due to the significant delocalization of the negative charge through the conjugated p-system, and at the same time the basicity of the terminal carbonyl group also increases by 138 kJ mol1. This means that the trimer is both a better HB donor and a better HB acceptor than the monomer. Similar enhancements, but quantitatively much smaller because of the lack of conjugation are observed for the saturated catemers, and for instance the intrinsic basicity of the terminal C@O group of the trimer 193 is only 75 kJ mol1 larger than that of the monomer. 3.1.2. NMR properties, central 1H chemical shifts and 2hJOO coupling constants As we have stated in the Introduction, to avoid the limitations of EOM-CCSD calculations (only the FC term was calculated), chemical shifts and coupling constants of 4a and 4b have been calculated at the B3LYP/6-311++G(d,p) level (Scheme 8) [16,17]. To check the validity of the SSCC, they were calculated with the SOPPA (SecondOrder Polarization Propagator Approximation) [60–62] approximation that yields values similar to the EOM-CCSD [63]. It appears from Scheme 8 data, that B3LYP/6-311++G(d,p) SSCC are a reasonable approximation to SOPPA ones (for these
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Scheme 9. Analysis of conjugated vs. saturated and intramolecular vs. intermolecular (for n = 1) on the NMR properties of the OAH O HB. Ratios <1.000 (blue), >1.000 (red). Between parentheses, the conclusions from Scheme 7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
calculations, the Ahlrichs qzp basis set was placed on the heavy atoms, and the qz2p on the hydrogen atoms) [64]. Note that the small differences in dO O cannot explain the differences in 2hJOO. Unfortunately, these couplings have never been measured (17O, spin I = 5/2). Since our intention is to study the variation of these properties with increasing values of n, these small discrepancies can be put aside. In the catemers we are studying, the central monomer is bonded to the rest of the polymer through two different HBs that, however, will become identical in the n = 1 limit. Indeed the differences calculated for the 2hJOO coupling constants for n = 9 (see Table 6) are already rather small. Hence, in our analysis the corresponding average values will be used. It is well known that when an OH O HB becomes stronger, both d1H and 2hJOO increase [65–68]. Not surprisingly then good linear correlations between the proton chemical shifts and SSCC are found for both series of catemers.
18 : d1 H ¼ ð6:90 0:02Þ þ ð0:924 0:002Þ2h J OO ;
n ¼ 5; R2
¼ 1:000 19 : d1 H ¼ ð2:09 0:02Þ þ ð2:12 0:04Þ2h J OO ;
ð20Þ n ¼ 4; R2
¼ 0:999
ð21Þ
The slope of (21) is larger than the slope of (20) indicating that in the saturated series 19 a similar increase in 2hJOO produces a great effect on d1H than in the conjugated series 18. The extrapolated values for these magnetic properties in the limit of infinitely long catemers (bold in Eqs. (22)–(25), can be estimated through exponential fittings similar to the ones used above to extrapolate geometrical parameters: Conjugated catemer 18n (four points)
d1 H ¼ ð14:12 0:03Þ ð10:73 0:40Þ ð0:635 0:009Þn ; R2 ¼ 0:9997
ð22Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 2h
J OO ¼ ð7:82 0:04Þ ð11:51 0:49Þ ð0:637 0:011Þn ;
R2 ¼ 0:9997
d1 H ¼ ð83:5 1:2Þ ð27:1 0:5ÞdOO ;
d1 H ¼ ð100:6 2:5Þ ð33:6 0:9ÞdOO ; n
d H ¼ ð4:697 0:001Þ ð2:78 0:05Þ ð0:539 0:003Þ ; R2 ¼ 1:0000 2h
R2 ¼ 0:999 ð19Þn series ð27Þ
ð24Þ
J OO ¼ ð1:225 0:007Þ ð1:47 0:05Þ ð0:517 0:007Þn ;
R2 ¼ 1:0000
R2 ¼ 0:999 ð18Þn series ð26Þ
ð23Þ
Saturated catemer 19n (three points) 1
149
ð25Þ
With these values it is possible to build a diagram (see Scheme 9), similar to the one already used for the discussion of the geometrical parameters, to visualize the changes undergone by the NMR properties when the nature of the HBs changes from intra- to inter-molecular (n = 1) or from conjugated to saturated systems. The first conspicuous fact is that in all cases in which, according to the geometrical and electron density topological analysis, a HB weakening should be expected (A, C and E) a clear decrease in the proton chemical shift is observed, whereas HB reinforcements (B and D) are accompanied by an increase of this magnitude. This seems to be consistent with the fact that rather good linear correlations are found between the calculated proton chemical shifts and the OO distance for both series of catemers (Eqs. (26) and (27)).
Surprisingly however, and in spite of the good correlations quoted above between chemical shits and SSCC, a similar clear picture on HB strengths cannot be obtained by looking at the coupling constants. The problem with the SSCC is not only originated from the very small and negative value of 4b that leads to strange values for A, D and E, but by case B where 2hJOO decreases very significantly while according to the correlation with the chemical shifts a significant increase should be expected, since the HB becomes clearly reinforced. The case of C is the only one fully coherent. A possible explanation to this unexpected trend can be related with the dissimilarities of the OH O bond angle when 4a is compared with (18)1. The dependence of 2hJOO on the O O distance is well known; we have found very good linear correlations between these two magnitudes for both conjugated and saturated series of catemers (Eqs. (28) and (29)), 2h
J OO ¼ ð82:8 1:4Þ ð29:2 0:5ÞdOO ;
R2 ¼ 0:999ð18Þn series ð28Þ
2h
J OO ¼ ð47:0 1:9Þ ð16:0 0:7ÞdOO ;
R2 ¼ 0:998 ð19Þn series ð29Þ
Scheme 10. Conclusions from this work and the two preceding ones [16,17].
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but it appears to depend also on the OAH O angle. Note that for the pseudo-six membered rings / = 146.1° (4a) and 147.4° (4b), while the central monomer of the catemers is linearly arranged (/ 180.0°) with regard to the monomers to which it is bonded. Actually, in 4a with a slightly longer O O distance (2.583 Å) than in (18)1 (2.567 Å), the SSCC amounts to 11.5 Hz compared to 7.8 Hz. To test the angle dependence, we calculated (18)2 (dOO = 2.715 Å, OHO = 178.5°, 2hJOO = 3.8 Hz); when the distance was constrained to be 2.583 Å (like in 4a) without changing the OAH O angle, 2hJOO = 6.3 Hz (+2.5 Hz). This is the expected increase when the O O length decreases. Then, we modified the angle to 146.5° resulting in a further increase of 0.9 Hz (2hJOO = 7.2 Hz). Thus, the increase from 7.8 to 11.5 (+3.7 Hz) is in part due to the bending of the OAH O angle but other effects should play a role. In summary:
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruc.2013. 04.069. References [1] [2] [3] [4] [5] [6] [7] [8]
1
2h
4a, d H = 13.7 ppm, JOO = 11.5 Hz 4b, d1H = 4.2 ppm, 2hJOO = –0.1 Hz 4b with the OHO geometry of 4a, d1H = 7.5 ppm, 2hJOO = 1.2 Hz 18n (n = 1), d1H = 14.1 ppm, 2hJOO = 7.8 Hz 19n (n = 1), d1H = 4.7 ppm, 2hJOO = 1.2 Hz 19n with the OHO geometry of 18n, d1H = 9.3 ppm, 2hJOO = 5.2 Hz To the cyclic structures, the r/p skeleton dichotomy seems to apply [69–71].
4. Concluding remarks We have summarized in Scheme 10 the main conclusions of the present work. The main factor behind the different strength of the intramolecular HB in the pseudo-six membered rings 4a and 4b and the intermolecular HB in the catemers (18)n and (19)n is cooperativity. Another factor is the fact that in the pseudo-six membered rings the HB donor and the HB acceptor belong to the same molecule, whereas in the catemers the HB donor donates to a different molecule and also accepts from a different one. Furthermore the main effect of conjugation is the simultaneous increase of the proton donor and the proton acceptor capacity of the conjugated system with respect to the saturated analogue. On top of that, the arrangement of the r-frame favoring the coplanarity and the proximity of the HB donor and the HB acceptor in 4a is a second factor contributing to reinforce the intramolecular HB in this conjugated species with regard to its saturated counterpart 4b. The RAHB is not limited to cyclic structures; the reason why most examples concern these structures is the fact that RAHB is present in monomers that exist in the gas-phase and in solution. On the other hand, RAHB is also present in catemers but this situation occurs almost exclusively in the solid state. The Resonance Assisted Hydrogen Bond (RAHB) concept that is undoubtedly useful in crystallography appears to apply to NMR and to energetic properties although some care must be taken when using it [72,73] because it depends not only on the atoms involved but also on the molecular structure.
Acknowledgments This work has been partially supported by the Ministerio de Economía y Competitividad Project No. CTQ2012-35513-C02 and by the Project MADRISOLAR2, ref S2009PPQ/1533 of the Comunidad Auto´noma de Madrid, by Consolider on Molecular Nanoscience CSC2007-00010, and by the COST Action CM0702. A generous allocation of computing time from the CESGA, from the CTI (C.S.I.C.) and from the CCC of the U.A.M. were greatly appreciated.
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[27] [28] [29]
[30] [31] [32] [33]
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Resonance assisted hydrogen bonds in open-chain and cyclic structures of malonaldehyde enol: A theoretical study Cristina Trujillo a, Goar Sánchez-Sanz a, Ibon Alkorta a,⇑, José Elguero a, Otilia Mó b, Manuel Yáñez b a b
Instituto de Química Médica, CSIC, Juan de la Cierva 3, E-28006 Madrid, Spain Departamento de Química, C-9 Universidad Autónoma de Madrid, Cantoblanco, E-28049 Madrid, Spain
h i g h l i g h t s
g r a p h i c a l a b s t r a c t
Open-chain and cyclic structures of
malonaldehyde enol were compared. Catemers up to 9 monomers have
been calculated. Bader QTAIM analysis was used to
understand the structures. 1
NMR properties, H chemical shifts
and 2hJOO coupling constants, were analyzed.
a r t i c l e
i n f o
Article history: Received 11 April 2013 Received in revised form 27 April 2013 Accepted 29 April 2013 Available online 15 May 2013 Keywords: RAHB Malonaldehyde Catemers AIM NMR
a b s t r a c t In 1989 Gilli, Bellucci, Ferretti and Bertolasi introduced the notion of Resonance Assisted Hydrogen Bonding (RAHB) one of the most fruitful concepts in structural chemistry. After reviewing our previous contributions to this topic, the present work analyzes theoretically this concept especially in non-cyclic structures. Geometries, electron densities and Laplacian at the bond critical points, cooperativity through many body interaction energies, deformation energies as well as NMR properties (chemical shifts and 2h JOO coupling constants) are used for the discussion. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Resonance Assisted Hydrogen Bond (RAHB) has been and still is one of the most successful structural concepts. Introduced in 1989 by Gilli, Bellucci, Ferretti and Bertolasi it has been cited near 650 times [1], and a series of subsequent papers on the same topic by this group were cited more than 100 times each [2–7]. Besides,
⇑ Corresponding author. E-mail address: [email protected] (I. Alkorta). 0022-2860/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molstruc.2013.04.069
Gastone and Paola Gilli published a book where this topic is reviewed [8]. The standard definition of RAHB is ‘‘A class of strong or very strong hydrogen bonds which cannot be accounted for by electric charges or steric hindrance, but is due to the fact that the neutral donor and acceptor atoms are connected by a system of p-conjugated double bonds; such a bond has been referred to as RAHB (resonance-assisted hydrogen bonding)’’ [3]. To understand the subsequent discussion we will slightly adapt some sentences from the 1989 paper [1]: ‘‘In this paper such methods . . . are applied to the -diketone fragment in its enol form 1 . . . with the aim of understanding what happens to the fragment geometry when it is perturbed by intramolecular, 2, or intermolec-
139
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Scheme 1. The main structures of Gilli’s first paper.
N N
N N H
H N N
N N H
N H N
H N N
H
H N N
Scheme 2. The first model used in our approach. Scheme 4. Pyrazole cyclamers (a trimer as example) and catemers (a tetramer is represented).
ular, 3, hydrogen bonding.’’ Their graphical scheme of the RAHB model is depicted in Scheme 1. Some authors have particularly stressed the aromatic character of cyclic structures 2 [9]. We have devoted five papers to the subject of RAHBs using two approaches. The first one, based in our expertise in the calculation of spin–spin coupling constants (SSCCs) [10–15] was used to analyze the structure of molecules where the RAHB concept applies, such as the enol of malonaldehyde 4a (Scheme 2). We compared the conjugated a structures of the ring-closed malonaldehyde enol (4a) [16,17]. We calculated at the EOM-CCSD level [10–15] the SSCC of 4a and 4b finding that they depend on the OAO distance but not on the conjugation. The same outcome was reached using the 1H chemical shifts of the proton involved in the HB. The main problem with this approach is that EOM-CCSD calculations are limited to small molecules; besides the Fermi contact term (FC) was used as an approximation to the total SSCC [10– 15]. The second one was to extend the skeleton of b-diketones and related compounds to other molecules, such as those represented in Scheme 3, containing rings of different sizes (the saturated counterparts are not represented). In this second approach no SSCC were calculated.
H O
H
O
H
H N
H
H
11
14
H N
9
15
N H N H
H
12 H
O
O
H
N
H
H N H
H O
H N
8
O
10 H
H
O H
N H
H
H H
7
6 O
N
H
O H
O
O
O
H
H
In the case of the phenyl series 6–9 [18], the aromatic compounds have much strong IMHB that the saturated homologues, but if a constrained geometry was used for the saturated compounds, that is, a geometry having all the non-hydrogen atoms in the same position as in the conjugated molecule, then their HBs are similar or even stronger than those of the aromatic analogues. In the case of cyclobutenones 10–13 and their corresponding saturated cyclobutanones, due to the fact that the ring strain is less severe in the saturated compounds, the IMHB is weaker in the unsaturated series [19]. In both series we conclude that the decisive term was the r-skeleton. The last paper we published [20], reports the study of tropolone 14 and its nitrogenated derivatives 15–17. These compounds have the interesting property that, although conjugated, the single bond marked by an arrow in Scheme 3 does not play any role in the conjugation, being limited to bring the functional groups together. Another peculiarity is that both the saturated and unsaturated systems have a coplanar HB. The conjugation enhances the acidity of the OH (NH) and the basicity of the O@C (N@C) although there is no cyclic conjugation. Some small acyclic compounds (three carbon atoms) were studied but not the open-ring 7-hydroxyhepta-2,4,6-trienal (O@CHACH@CHACH@CHACH@CHAOH, two H atoms more than
N
13 H
16
Scheme 3. The second model used in our approach.
H H N
N H
17
140
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 1 Relative energies (Erel) of the compounds of Scheme 6.
Intermolecular
Intramolecular
H O
H H
H O Conjugated
O
H
O
H H
H H
4a
H O H 18
O
A
C
E
H H
O
O
6.6 10.7 0.0 7.7 13.2 25.4 12.5 25.4
H H
H
H
MP2 energies Erel with regard to 18, EEZ
H O
H H
Saturated
Monomer 18, EEE 5.9 18, ZEE 9.4 18, EEZ 0.0 18, ZEZ 6.8 18, EZE 13.6 18, ZZE 26.0 18, EZZ 11.9 18, ZZZ 28.0
H
B
RAHB
B3LYP energies Erel with regard to 18, EEZ
O D
H
H H
H H
H H
H 4b
H O
19
O
Scheme 5. The four situations.
Fig. 1. 2-Phenylmalonaldehyde (PROLON) [72,73].
14). The conclusion was that the ring effects also play a significant role in the enhancement of the basicity and acidity of the hydrogen-bond donor and acceptor of tropolone with respect to its saturated counterpart. A final comment concerning literature results: in 1999, Bertolasi et al. reported that the concept of RAHB fails for pyrazole cyclamers and catemers although formally they have conjugated circuits (Scheme 4) [21]. This shows that RAHB has to be used taking care of possible cases where it is not applicable. In the present work, we will examine an aspect that has been neglected in most publications although it was discussed in Gilli’s original paper [1]: the case of ring-open molecules, such as 3 (Scheme 1) or 18/19 (Scheme 5). As stated above, we have already reported the 4a and 4b cases. It remains to study the 18 and 19 cases, i.e., chains of trans enols (catemers) (see Scheme 5). There are eight isomers of monomer 18 (see Scheme 6), including 18, ZZZ which corresponds precisely to structure 4a of Scheme 2. In Scheme 5, the catemers correspond to (EEE)n (see below).
H O
H
H
H
H
O O
18, EEE
H
H
H
O
18, EZE
H
H
O
H O
18, ZZE
H
O
H O H
18, ZEZ
H
H O
H H
18, EEZ
H H
H O
O
18, ZEE
H O H
The geometry of the systems under investigation has been optimized at the B3LYP [22,23]/6-311++G(d,p) [24] and MP2 [25]/6-311++G(d,p) [24] computational levels. In order to evaluate the resonance assistance, Cs symmetry has been imposed in all the systems studied, although they are not true minima. All the calculations have been performed with the Gaussian-09 program [26]. Absolute chemical shieldings have been calculated within the GIAO approximation [27,28] on the B3LYP/6-311++G(d,p) geometries. The bonding characteristics were analyzed by means of the atoms in molecules (AIM) theory [29,30]. For this purpose we have located the intermolecular bond critical points (BCP), and evaluated the electron density properties at each of them with the AIMAll program [31]. In the Ramsey approximation [32], the total coupling constant (J) is a sum of four contributions: the paramagnetic spin–orbit (PSO), diamagnetic spin–orbit (DSO), Fermi-contact (FC) and spin-dipole
H
O H
2. Computational methods
H H
H O H 18, EZZ
Scheme 6. The eight isomers of the enol of malonaldehyde 18.
H
H O O H 4a, ZZZ
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 2 B3LYP and MP2 geometries (Å, °) of 18n and 19n catemers. Bond distances of the central monomer (conjugated 18) only for odd n. OAH O bonds (conjugated 18) Catemer, n
Method
OAH
O H
O O
OAH O
1 (monomer)
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP
0.962 0.961 0.963 0.962 0.983 0.978 0.963 0.962 0.989 0.983 0.989 0.983 0.964 0.962 0.993 0.985 1.001 0.992 1.001 0.992 0.992 0.985 0.964 0.993 1.003 1.007 1.007 1.003 0.993 0.964 0.993 1.004 1.008 1.009 1.009 1.008 1.004 0.993
– – – – 1.732 1.741 – – 1.680 1.699 1.682 1.699 – – 1.658 1.681 1.606 1.633 1.607 1.634 1.663 1.682 – 1.654 1.596 1.579 1.580 1.596 1.659 – 1.652 1.593 1.573 1.567 1.567 1.574 1.593 1.657
– – – – 2.715 2.719 – – 2.667 2.679 2.671 2.681 – – 2.648 2.662 2.604 2.620 2.605 2.621 2.653 2.665 – 2.644 2.595 2.582 2.583 2.596 2.650 – 2.643 2.593 2.577 2.572 2.572 2.578 2.594 2.648
– – – – 178.5° 179.7° – – 175.8° 174.6° 177.1° 176.9° – – 175.0° 173.6° 174.1° 173.1° 174.2° 173.2° 175.9° 175.4° – 174.8° 173.6° 173.6° 173.4° 174.1° 175.4° – 174.8° 173.7° 173.5° 173.4° 173.4° 173.5° 173.9° 175.6°
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2
0.962 0.961 0.962 0.961 0.971 0.968 0.962 0.961 0.971 0.969 0.971 0.968
– – – – 1.918 1.925 – – 1.903 1.906 1.904 1.908
– – – – 2.872 2.855 – – 2.868 2.851 2.870 2.855
– – – – 166.7° 160.3° – – 172.3° 164.3° 172.5° 165.1°
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP B3LYP
0.962 0.961 0.972 0.969 0.972 0.969 0.972 0.969 0.972 0.969 0.962 0.971 0.972 0.972 0.972 0.972 0.972
– – 1.898 1.900 1.888 1.890 1.888 1.890 1.900 1.902 – 1.898 1.887 1.884 1.883 1.888 1.900
– – 2.863 2.850 2.859 2.851 2.859 2.852 2.866 2.855 – 2.866 2.859 2.856 2.855 2.860 2.869
– – 172.0° 166.2° 176.9° 171.0° 177.3° 171.4° 172.6° 167.4° – 173.7° 178.4° 178.2° 178.0° 179.0° 174.6°
2 (dimer)
3 (trimer)
5 (pentamer)
7 (heptamer)
9 (nonamer)
OAHO bonds (saturated 19) 1 (monomer) 2 (dimer)
3 (trimer)
5 (pentamer)
7 (heptamer)
Bond distances of the central monomer (conjugated 18) only for odd n (continued on next page)
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C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Table 2 (continued) OAH O bonds (conjugated 18) n
Method
OAH
OAC
C@C
CAC
C@O
1
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP B3LYP
0.962 0.961 0.989 0.983 1.001 0.992 1.007 1.009
1.349 1.352 1.322 1.328 1.314 1.321 1.311 1.309
1.341 1.348 1.355 1.358 1.359 1.361 1.361 1.362
1.457 1.461 1.432 1.440 1.425 1.434 1.423 1.421
1.214 1.222 1.232 1.234 1.237 1.238 1.239 1.240
3 5 7 9
Bond distances of the central monomer (saturated 19) only for odd n n
Method
OAH
OAC
CAC
CAC
C@O
1
B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP
0.962 0.961 0.971 0.969 0.972 0.969 0.972
1.425 1.423 1.416 1.416 1.414 1.414 1.414
1.522 1.518 1.523 1.520 1.524 1.520 1.524
1.513 1.514 1.505 1.507 1.504 1.506 1.504
1.206 1.215 1.213 1.221 1.213 1.221 1.213
3 5 7
1.02
O-H distance
1.01 n=1
1
n=2
0.99
n=3
0.98
n=5 n=7
0.97
n=9
0.96 0.95 0
2
4
6
8
10
OH position along the chain 1.75 1.73
O···H distance
1.71 1.69
n=2
1.67
n=3
1.65
n=5
1.63
n=7
1.61
n=9
1.59 1.57 1.55 0
1
2
3
4
5
6
7
8
9
HB position along the chain Fig. 2. OH and O H distances for conjugated catemers as a function of the HB position along the chain for the 18n series.
(SD). All terms have been computed for all molecules. SOPPA calculations were performed using the Dalton-2 program [33].
3. Results and discussion The corresponding energies of the eight conformers of 18 are gathered in Table 1.
To build up the catemers of Scheme 5 we have selected the two monomers of lower energy, namely EEE and EEZ. The EEE monomer is present in the few X-ray structures of malonaldehyde derivatives that form catemers, for instance, 2-phenylmalonaldehyde (Fig. 1). Concerning their saturated counterparts we have only studied the 19, the EEE monomer that corresponding to 18. A search in the CSD [34] reveals that the only structure related to (19, EEE)n is CUJCOA [34]. Even if the differences are notable, CUJCOA
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Since the catemers (18, EEZ)n do not correspond to any known present structure we have relegated the corresponding results of these catemers to the Supporting Information.
Table 3 BCP electron densities and Laplacian at the BCP (B3LYP calculations). (OAH)1
(OAH)2
(OAH)3
143
(OAH)4
2
q» q 182 183 185 187 189
3.1. The catemers of the 18 and 19 series
0.040 0.046 0.049 0.049 0.050
(0.131) (0.1405) (0.1435) (0.144) (0.145)
0.057 (0.151) 0.058 (0.152) 0.059 (0.153)
0.061 (0.154) 0.062 (0.154)
0.026 0.027 0.027 0.027
(0.094) (0.097) (0.098) (0.098)
0.028 (0.100) 0.028 (0.1005)
0.028 (0.101)
0.063 (0.155)
q»2q 192 193 195 197
Table 4 B3LYP interaction energies (kJ mol1) of 18n and 19n catemers (MP2 values in parentheses). Catemer, n
Ei (1)
Ei (2)
Ei (3)
2 3 5 7
(182) (183) (185) (187)
47.4 (46.2) 58.0 (54.9) 63.5 (59.5) 64.8
– – 78.0 (71.3) 81.7
– – – 87.3
2 3 5 7
(192) (193) (195) (197)
24.8 (27.6) 26.4 (28.4) 27.2 (29.0) 27.4
– – 29.4 (30.3) 30.0
– – – 30.8
3.1.1. Geometries We have calculated at two levels, B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p), the 18n and 19n catemers for n = 2, 3, 5, 7 and 9 (B3LYP) and for n = 2, 3 and 5 (MP2). We report in Table 2 the most relevant geometrical parameters associated with all the OAH O hydrogen bonds within each catemer, as well as the OAH bond length for each monomer. In all cases the first monomer corresponds always to the one which acts as HB acceptor (terminal OH) and the latter to the one which behaves as HB donor (Terminal CO). Table 2 includes also all the information about the central monomer in odd catemers (n = 3, 5, 7 and 9). A detailed analysis of the values reported in Table 2 shows that the HB distances obtained at the B3LYP and MP2 levels of theory are linearly correlated,
B3LYP ¼ ð0:014 0:006Þ þ ð0:988 0:004ÞMP2; n ¼ 36; R2 ¼ 0:999 ð1Þ although the B3LYP values are systematically shorter than the MP2 ones. To account for this difference we have added a term, resulting in Eq. (2).
B3LYP ¼ ð0:098 0:014Þ þ ð1:104 0:014ÞMP2 ð0:098 0:012ÞO H; n ¼ 36; R2 ¼ 1:000
ð2Þ
In any case, Eqs. (1) and (2) allow using the much less expensive DFT vs. MP2 calculations. There are also good correlations between the OAH and O H bond lengths for the conjugated and saturated catemers [see Eqs. (3) and (4), respectively], although the former is poorer because the range of variation of the OAH bond length is very small (0.046 Å).
B3LYPðOHconj: Þ ¼ ð2:4 0:3Þ þ ð3:5 0:3ÞB3LYPðOHsat :Þ; 1emn ¼ 18; R2 ¼ 0:89
ð3Þ
B3LYPðO Hconj :Þ ¼ ð7:2 0:3Þ þ ð4:64 0:17ÞB3LYP ðO Hsat: Þ;
Fig. 3. Plot of q BCP (au) vs. O H interatomic distances (Å). Exponential fitting, R2 = 0.9994.
crystallizes as a catemer with OAH O HBs. From now on, and for the sake of simplicity the (19, EEE)n catemer will be called 19.
H3C CH3 O H H
H
O
O H
H
O
H
19, EEZ
H
O
O
H
H H3C CH3 CUJCOA
n ¼ 13; R2 ¼ 0:985
ð4Þ
As it has been shown for dihydrogen bonds [35,36], these values, when plotted against the position of the monomers within the catemers, appear as curvilinear plots (see Fig. 2). For the OH bond distances this indicates that the lengthening of the OH bond goes through a maximum for the central monomer, whereas for the OH O distance it goes through a minimum. Although Fig. 2 shows these trends only for the 18n series of catemers, similar variations are observed for the 19n series (see Fig. S1 of the Supporting information). These findings reflect the significant cooperative effects of the hydrogen bonds that stabilize the catemers. Obviously cooperative effects should be maximum for the HBs in which the central monomer participates and minimum for the two external monomers because they only act as HB donors or as HB acceptors. Indeed, the electron densities at the HB critical points (See Table 3) increase as we moved towards the central monomer, in both series, although, also consistently with the variations of the bond lengths, the effect is larger for the conjugated catemers. A similar increase is also observed for the corresponding value of the Laplacian of the electron density. It is worth noting that, for the two external monomers, cooperativity is significant since the values of the OH and the OH O distances involving the external monomers for catemers with n P 3
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Table 5 Terms of the MBIE partition (all in kJ mol1). The numbers in parentheses of the Terms column correspond to monomers ordered from C@O to OAH. Terms Er (1) Er (2) Er (3) Er (4) Er (5) RE r REr/n D2E (1–2) D2E (1–3) D2E (1–4) D2E (1–5) D2E (2–3) D2E (2–4) D2E (2–5) D2E (3–4) D2E (3–5) D2E (4–5) D3E (1–2–3) D3E (1–2–4) D3E (1–2–5) D3E (1–3–4) D3E (1–3–5) D3E (1–4–5) D3E (2–3–4) D3E (2–3–5) D3E (2–4–5) D3E (3–4–5) D4E (1–2–3–4) D4E (1–2–3–5) D4E (1–2–4–5) D4E (1–3–4–5) D4E (2–3–4–5) D5E (1–2–3–4–5)
182
192
183
193
184
194
1.83 0.97
0.30 0.24
2.97 5.16 1.43
0.36 0.62 0.26
3.40 7.45 6.47 1.61
0.38 0.70 0.65 0.27
2.80 1.40 50.16
0.54 0.27 25.35
9.56 3.19 52.48 1.94
1.24 0.41 25.35 0.24
18.93 6.31 53.15 2.07 0.50
2.00 0.50 25.37 0.32 0.21
52.27
25.32
54.85 2.12
25.21 0.42
52.81
25.27
9.16 0.67
1.61 0.04
0.55
0.00
9.22
1.60
1.06
0.27
167.23
78.24
8.26
47.36
24.81
1.57
105.38
51.24
are systematically longer and shorter, respectively than the corresponding values for the dimer. Similar trends, are observed as far as the electron densities at the BCPs are concerned (See Table 4). A plot of qBCP (au) vs. O H interatomic distances (Å) is reported in Fig. 3. Similar exponential relationships have been found for other HBs [37–43]. Note however that in a recent report by Mo [44] it was pointed out that the estimate of HB strengths in intramolecular RAHB systems based on the QTAIM topological properties can be questionable, since the deactivation of the p resonance lead to small changes on the electron density at the HB critical point. The cooperative effects discussed above in terms of geometrical parameters as well as the topology of the electron density are also reflected in the energies of the HBs. For this purpose we have calculated the energies involved in the HBs as the differences between the catemers and the different fragments which can be formed by eliminating a monomer, a dimer, a trimer, etc., so that,
Ei ð1Þ ¼ En Eðn1Þ E1 ;Ei ð2Þ ¼ En Eðn2Þ E2 ;Ei ð3Þ ¼ En Eðn3Þ E3 ... This procedure does not differentiate one end (the one which contains the terminal OH group) from the other (the one which contains the terminal C@O one) but it allows to classify the HBs according to their relative position in the chain. Note, for instance, that for a pentamer, it is fulfilled that E5(1) = E5(4) and the E5(2) = E5(3). From the values in Table 4 it can be observed that the B3LYP and MP2 estimates are rather similar, but more importantly, as it was found above for the distances, they are linearly correlated,
EMP2 ¼ ð6:4 0:3Þ þ ð0:834 0:007ÞEB3LYP ; i i
n ¼ 8; R2 ¼ 1:000 ð5Þ
185
195
3.61 8.38 9.27 7.07 1.71 30.04 6.01 53.41 2.13 0.54 0.16 55.62 2.26 0.54 55.56 2.15 53.12 9.50 0.73 0.23 0.66 0.06 0.20 10.31 0.77 0.68 9.56 1.13 0.01 0.12 0.06 1.05 230.78
0.38 0.72 0.74 0.68 0.27 2.79 0.56 25.37 0.34 0.21 0.02 25.20 0.48 0.21 25.20 2.15 25.35 1.63 0.04 0.04 0.02 0.03 0.02 1.70 0.09 0.05 1.63 0.22 0.02 0.21 0.04 0.15 105.48
therefore we are legitimated to use the B3LYP values in the following discussion. The systematic increase of the Ei values with the length of the catemer is a clear evidence of the importance of cooperativity in the stabilization of the polymers, both for the saturated and the conjugated series. Very significantly there is an extremely good linear correlation between both sets of values,
Ei 19 series ¼ ð17:64 0:04Þ þ ð0:151 0:001ÞEi 18 series; n ¼ 7; R2 ¼ 1:000
ð6Þ
which indicates that although the increase of Ei is much larger for the conjugated than for saturated catemers, the tendencies are similar, increasing with n and increasing with the proximity to the central position. The cooperativity can be quantitatively traced through a many body interaction energy (MBIE) analysis. Although the partition of energies of supramolecular structures using the MBIE is known at least from 1970 [45], it has been used extensively by Saykaly and Xantheas from 1994 [46–48]. Kulkarni et al. developed an algorithm and applied it to large molecular clusters [49–51]. Other authors have also applied the MBIE analysis to other clusters [52–54]. We have designed a small program to generate automatically from the Gaussian log file all the inputs necessary to evaluate all the terms of MBIE, which for the catemers investigated in this work, have been collected in Table 4. In this method two-, threeand four-body terms are defined by Eqs. (7)–(9), respectively. The interaction energy Ei(n) of a system of n-molecules is defined as the difference between the energy of the complex at its equilibrium geometry and the sum of the n isolated molecules.
EiðnÞ ¼
n n1 X n n2 X n1 X n X X X EðiÞ nE þ D2 EðijÞ þ D3 EðijkÞ þ ::: i¼1
i¼1 j>i
þ Dn Eð1; 2; 3 . . . nÞ
i¼1 j>i k>j
ð7Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151
Er/n (18n)
9
6
3
0 0
2
4
6
8
10
n
Er/n (19n)
0.6
0.3
0.0
0
2
4
6
8
n Fig. 4. Exponential fitting of the deformation energy per monomer as a function of the number of monomers forming the catemer. For the conjugated 18n and the saturated 19n series the fittings obey the equations: REr/n = (13.0 ± 1.1) – (15.4 ± 0.9) (0.86 ± 0.02)n and REr/n = (0.64 ± 0.01) – (1.06 ± 0.03) (0.60 ± 0.02)n, with R2 = 0.996 and R2 = 0.998, respectively.
ErðiÞ ¼ EðiÞ E
ð8Þ
D2 EðijÞ ¼ EðijÞ ½EðiÞ þ EðjÞ
ð9Þ
D3 EðijkÞ ¼ EðijkÞ ½EðiÞ þ EðjÞ þ EðkÞ bD2 EðijÞ þ D2 EðikÞ þ D2 EðjkÞc
ð10Þ
where E(i), E(ij), E(ijk) are the energy of monomer i, dimer ij, trimer ijk with the geometry of the complex and E is the minimum energy of the isolated monomer. The first term of the equation is known as relaxation, the second is associated to the 2-body, the third to the 3body and so on. The three body term and higher body terms [D3E(A–B–C) (Eq. (10)), D4E(A–B–C–D), etc.] are associated to cooperativity. They correspond to the difference of the interaction energy and the sum of the one and two body terms. As illustrated in Table 5 for the trimer of the conjugated system cooperative effects amount to more than 8 kJ mol1, and this value becomes, as expected slightly larger for the tetramer and the pentamer. For the saturated derivative, cooperativity is significantly smaller (1.6 kJ mol1 for the trimer) but not negligible. These differences are actually a manifestation of the so called RAHB; but what is its real origin? The fundamental reason is associated with the changes in the intrinsic basicity and acidity properties of the conjugated monomers with respect to the saturated analogues. Indeed, the intrinsic
145
basicity of 18 (861 kJ mol1) is significantly larger than that calculated for 19 (776 kJ mol1), clearly showing [55,56] that 18 should be a much better HB acceptor than 19. Similarly, the conjugated compound 18 is a much stronger acid (DacidH = 1358 kJ mol1) than its saturated counterpart 19 (DacidH = 1556 kJ mol1), which indicates that the former is a much better HB donor than the latter. These results are transferable to the pseudo six-membered rings 4a and 4b, explaining the much stronger intramolecular HB of the former. This is actually consistent with the analysis carried out by Mo [44], who showed, through the use of the block-localized wavefunction (BLW) method, that when conjugation is deactivated from 4a the intramolecular HB becomes much weaker, and the optimized geometry leads to much longer O O distances. Still the intramolecular HB when conjugation is deactivated in 4a is stronger than that in the saturated derivative 4b. When the conjugation is deactivated in 4a it has been reported that the O O distance increases from 2.586 Å to 2.884 Å, whereas in the saturated 4b derivative this distance is still longer (2.926 Å). The explanation is that besides the decrease in the HB donor and acceptor ability of the C@O and the OH groups of 4b respect to 4a, in 4a the conjugation forces both groups to be coplanar and closer to each other. Very importantly, when the structure of compound 4b is optimized by imposing the C@O and the COH groups to be coplanar (Cs symmetry) the intramolecular HB reinforces and the O O distance becomes significantly shorter (2.742 Å) although still longer than that of the conjugated 4a analogue. This result clearly shows that the r-skeleton has also a significant influence on the strength of these interactions. Hence, in summary, the conjugation on going from 4b to 4a results in a reinforcement of the OAH O intramolecular HB through the concurs of three concomitant factors, an increase of the proton acceptor capacity of the C@O group, an increase of the proton donor capacity of the OH group, and a rskeleton arrangement which favors these kinds of interactions. Cooperativity has also a significant influence on the deformation energy, i.e. the energy required to deform an isolated monomer from its minimum energy geometry to the geometry it adopts in the catemer. The deformation energy is easily calculated in the framework of the MBIE approach, Eq. (8). Then REr/n is the average deformation energy per monomer. As expected from our previous discussion, it is much larger in the conjugated 18 series than in the saturated 19 ones and also it increases much faster. Obviously for both monomers REr = 0 and REr/n = 0, it is expected that for very long chains REr/n will be constant, i.e. an asymptotic equation going through (1, 0) will be found, as shown in Fig. 4 for both series of catemers. Coherently with the larger cooperative effects for the conjugated catemers, the asymptote is much larger for the 18n series (15.1 vs. 0.64) and the c term closer to 1 (0.88 vs. 0.60). This corresponds to a lower attenuation of the number of monomers (for c = 1, REr/n will be constant). The value of the asymptote for the 18n series means that the real strength of the HBs formed by the central monomer of the catemer is sizably larger than predicted by the energies reported in Table 5, since the real dissociation energies of these HBs would be about 7.5 kJ mol1 larger than those reported in Table 4. This strength enhancement due to the deformation of the monomers is rather small for the 18n saturated series, since it would account for 0.3 kJ mol1 only. Let us now analyze in more detail the changes observed in the HBs for these systems when the environment changes from the intramolecular HBs in 4a and 4b to the intermolecular HB in the conjugated and saturated catemers of infinite length (B and D), or when the corresponding intra- and intermolecular HBs appear in conjugated or saturated systems (A and C). E compares the saturated catemer 19n (n = 1) with the unsaturated 4a derivative. For this purpose we have summarized the relevant parameters
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Scheme 7. Analysis of conjugated vs. saturated and intramolecular vs. intermolecular (for n = 1) on the geometries. E values = A D = B C. The fourth column corresponds to experimental data.
Scheme 8. Effect of the method of calculation on the NMR parameters of the IMHB present in 4a and 4b.
in Scheme 7, in which, for the sake of completeness we have added E, which compares the saturated catemer 19n (n = 1) with the unsaturated 4a derivative. To carry out such comparisons we need to know, besides the geometrical parameters which characterize the intramolecular HBs in 4a and 4b the values for the catemers in the limit of an infinitely long (n ? 1) chain. For this purpose we have adjusted the data of Table 2 (central motive) using exponential Eqs. (11)–(19) of the form y = a + b cn, so that for n = 1, y = a (bold). The values so obtained are as follows: Conjugated catemer 18n (four points)
O—H ¼ ð1:011 0:008Þ ð0:074 0:007Þ ð0:671 0:026Þn ; R2 ¼ 0:998
ð11Þ
O H ¼ ð1:560 0:002Þ þ ð0:502 0:024Þ ð0:618 0:011Þn ; R2 ¼ 0:9996
ð12Þ
O O ¼ ð2:567 0:002Þ þ ð0:438 0:028Þ ð0:610 0:015Þn ; R2 ¼ 0:9994
ð13Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 Table 6 B3LYP calculated 1H chemical shifts (ppm) and central monomer. d1H
2h
JOO coupling constants (Hz) of the
2h
JOO
n
OH-terminal
C@O-terminal
Average
Conjugated series 18 3 11.37 5 13.02 7 13.66 9 13.95 1 14.12a
4.97 6.64 7.33 7.64
4.72 6.59 7.29 7.62
4.84 6.62 7.31 7.63 7.82a
1.06 1.18 1.20
0.99 1.16 1.22
1.02 1.17 1.21 1.22a
Saturated series 19 3 5 7 1 Saturated 3 5 7 1 a
4.26 4.57 4.66 4.70a
series 19 with the geometry of the OAH O HB of 18 (19/18) 6.84 3.14 2.97 3.06 8.31 4.39 4.34 4.36 8.90 4.88 4.87 4.88 a 9.30 5.20a
Estimated with Eqs. (24) and (25).
OHO ¼ ð173:3 0:03Þ þ ð14:0 1:0Þ ð0:560 0:015Þn ; R2 ¼ 0:9994
ð14Þ
C—O ¼ ð1:308 0:008Þ þ ð0:047 0:006Þ ð0:667 0:038Þn ; R2 ¼ 0:996
ð15Þ
C@O ¼ ð1:241 0:002Þ ð0:031 0:002Þ ð0:652 0:014Þn ; R2 ¼ 0:9994
ð16Þ
Saturated catemer 19n (three points, R2 = 1.0000)
O—H ¼ 0:972 ðalmost constantÞ O H ¼ ð1:883 0:001Þ þ ð0:150 0:006Þ ð0:516 0:007Þn ð17Þ O O ¼ ð2:854 0:002Þ þ ð0:071 0:003Þ ð0:576 0:011Þn ð18Þ OHO ¼ ð178:7 0:02Þ ð42:6 0:5Þ ð0:532 0:002Þn
ð19Þ
C—O ¼ 1:414 ðalmost constantÞ C@O ¼ 1:203 ðalmost constantÞ Note that the c coefficient is in average 0.63 and 0.54 for 18 and 19, respectively. That means that the sensitivity to the number of monomers is slightly larger in the conjugated series. The first conspicuous fact is that intermolecular calculated values for a chain of infinite length (second column) are in good agreement with the X-ray structures (last column) excepting the OAH and H O distances; this exception is due to the well known effect concerning the position of hydrogen atoms in X-ray crystallography (aspherically displaced towards the atom to which it is bonded, here the oxygen) [57–59]. The agreement is better for the less perturbed structure (PROLON). The third column of scheme 7 summarizes the ratio of the parameters of the intermolecular HB for catemers 18n and 19n (n = 1) with respect to those of the corresponding intramolecular HBs in 4a and 4b, respectively (B and D). The last file contains
147
similar ratios when the saturated systems 4b and 19n (n = 1) are compared with the conjugated analogues 4a and 18n (n = 1), respectively (A and C). The intersection of the third column and the last file presents the values obtained when the saturated catemer 19n (n = 1) is compared with the conjugated 4a derivative (E). A HB becomes stronger when the OAH bond lengthen, the O H bond shorten, the O O distance shorten, the C@O bond lengthen, and the CAO bond shorten. The contrary should happen if the HB becomes weaker. To better guide the reader, in Scheme 7 we have written in red the ratios which are consistent with a reinforcement of the HB and in blue those which are consistent with a weakening. Furthermore, the more different from 1 the ratios of Scheme 7, the larger the effect. It results that A and C correspond to weakening (in C more pronounced than in A), B corresponds to strengthening although these effects are quantitatively smaller than the weakening observed in A (for this comparison, we have used the inverse values), D shows three weakening and two strengthening values but all of them are very close to unity indicating very small effects and, finally, E which is a combination of structural effects (ratio of ratios A/C or B/D) corresponds to a weakening of the HB. Concerning E, the weakening effect results from C being larger than A and from B being larger than D. One important conclusion of this study of the geometrical changes is that the effect of conjugation is more important in a catemer (C values) than in a strained pseudo six-membered ring (A values). As we have discussed above this is mainly a consequence of larger cooperativity effects in the conjugated that in the saturated catemers. Similarly, on going from intra- to intermolecular HBs the geometrical changes are larger for conjugated (B values) than for saturated (D) compounds. The rationalization of these trends is not trivial. Firstly, in the strained pseudo six-membered rings, 4a and 4b, the HB donor and the HB acceptor belong to the same molecule, whereas in the catemers the HB donor donates to a different molecule and also accepts from a different one. Secondly, in the catemers there is a significant participation of cooperativity through three-body interactions which are not possible in the monomeric pseudo six-membered rings. Indeed, the formation of the catemers is accompanied by a significant change in the intrinsic acidity of the terminal OH groups and also by a significant enhancement of the basicity of the terminal C@O groups. Both effects are well reflected on the fact that on going from the monomer 18 to the trimer 183 the acidity of the terminal OH group increases by 107 kJ mol1, due to the significant delocalization of the negative charge through the conjugated p-system, and at the same time the basicity of the terminal carbonyl group also increases by 138 kJ mol1. This means that the trimer is both a better HB donor and a better HB acceptor than the monomer. Similar enhancements, but quantitatively much smaller because of the lack of conjugation are observed for the saturated catemers, and for instance the intrinsic basicity of the terminal C@O group of the trimer 193 is only 75 kJ mol1 larger than that of the monomer. 3.1.2. NMR properties, central 1H chemical shifts and 2hJOO coupling constants As we have stated in the Introduction, to avoid the limitations of EOM-CCSD calculations (only the FC term was calculated), chemical shifts and coupling constants of 4a and 4b have been calculated at the B3LYP/6-311++G(d,p) level (Scheme 8) [16,17]. To check the validity of the SSCC, they were calculated with the SOPPA (SecondOrder Polarization Propagator Approximation) [60–62] approximation that yields values similar to the EOM-CCSD [63]. It appears from Scheme 8 data, that B3LYP/6-311++G(d,p) SSCC are a reasonable approximation to SOPPA ones (for these
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Scheme 9. Analysis of conjugated vs. saturated and intramolecular vs. intermolecular (for n = 1) on the NMR properties of the OAH O HB. Ratios <1.000 (blue), >1.000 (red). Between parentheses, the conclusions from Scheme 7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
calculations, the Ahlrichs qzp basis set was placed on the heavy atoms, and the qz2p on the hydrogen atoms) [64]. Note that the small differences in dO O cannot explain the differences in 2hJOO. Unfortunately, these couplings have never been measured (17O, spin I = 5/2). Since our intention is to study the variation of these properties with increasing values of n, these small discrepancies can be put aside. In the catemers we are studying, the central monomer is bonded to the rest of the polymer through two different HBs that, however, will become identical in the n = 1 limit. Indeed the differences calculated for the 2hJOO coupling constants for n = 9 (see Table 6) are already rather small. Hence, in our analysis the corresponding average values will be used. It is well known that when an OH O HB becomes stronger, both d1H and 2hJOO increase [65–68]. Not surprisingly then good linear correlations between the proton chemical shifts and SSCC are found for both series of catemers.
18 : d1 H ¼ ð6:90 0:02Þ þ ð0:924 0:002Þ2h J OO ;
n ¼ 5; R2
¼ 1:000 19 : d1 H ¼ ð2:09 0:02Þ þ ð2:12 0:04Þ2h J OO ;
ð20Þ n ¼ 4; R2
¼ 0:999
ð21Þ
The slope of (21) is larger than the slope of (20) indicating that in the saturated series 19 a similar increase in 2hJOO produces a great effect on d1H than in the conjugated series 18. The extrapolated values for these magnetic properties in the limit of infinitely long catemers (bold in Eqs. (22)–(25), can be estimated through exponential fittings similar to the ones used above to extrapolate geometrical parameters: Conjugated catemer 18n (four points)
d1 H ¼ ð14:12 0:03Þ ð10:73 0:40Þ ð0:635 0:009Þn ; R2 ¼ 0:9997
ð22Þ
C. Trujillo et al. / Journal of Molecular Structure 1048 (2013) 138–151 2h
J OO ¼ ð7:82 0:04Þ ð11:51 0:49Þ ð0:637 0:011Þn ;
R2 ¼ 0:9997
d1 H ¼ ð83:5 1:2Þ ð27:1 0:5ÞdOO ;
d1 H ¼ ð100:6 2:5Þ ð33:6 0:9ÞdOO ; n
d H ¼ ð4:697 0:001Þ ð2:78 0:05Þ ð0:539 0:003Þ ; R2 ¼ 1:0000 2h
R2 ¼ 0:999 ð19Þn series ð27Þ
ð24Þ
J OO ¼ ð1:225 0:007Þ ð1:47 0:05Þ ð0:517 0:007Þn ;
R2 ¼ 1:0000
R2 ¼ 0:999 ð18Þn series ð26Þ
ð23Þ
Saturated catemer 19n (three points) 1
149
ð25Þ
With these values it is possible to build a diagram (see Scheme 9), similar to the one already used for the discussion of the geometrical parameters, to visualize the changes undergone by the NMR properties when the nature of the HBs changes from intra- to inter-molecular (n = 1) or from conjugated to saturated systems. The first conspicuous fact is that in all cases in which, according to the geometrical and electron density topological analysis, a HB weakening should be expected (A, C and E) a clear decrease in the proton chemical shift is observed, whereas HB reinforcements (B and D) are accompanied by an increase of this magnitude. This seems to be consistent with the fact that rather good linear correlations are found between the calculated proton chemical shifts and the OO distance for both series of catemers (Eqs. (26) and (27)).
Surprisingly however, and in spite of the good correlations quoted above between chemical shits and SSCC, a similar clear picture on HB strengths cannot be obtained by looking at the coupling constants. The problem with the SSCC is not only originated from the very small and negative value of 4b that leads to strange values for A, D and E, but by case B where 2hJOO decreases very significantly while according to the correlation with the chemical shifts a significant increase should be expected, since the HB becomes clearly reinforced. The case of C is the only one fully coherent. A possible explanation to this unexpected trend can be related with the dissimilarities of the OH O bond angle when 4a is compared with (18)1. The dependence of 2hJOO on the O O distance is well known; we have found very good linear correlations between these two magnitudes for both conjugated and saturated series of catemers (Eqs. (28) and (29)), 2h
J OO ¼ ð82:8 1:4Þ ð29:2 0:5ÞdOO ;
R2 ¼ 0:999ð18Þn series ð28Þ
2h
J OO ¼ ð47:0 1:9Þ ð16:0 0:7ÞdOO ;
R2 ¼ 0:998 ð19Þn series ð29Þ
Scheme 10. Conclusions from this work and the two preceding ones [16,17].
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but it appears to depend also on the OAH O angle. Note that for the pseudo-six membered rings / = 146.1° (4a) and 147.4° (4b), while the central monomer of the catemers is linearly arranged (/ 180.0°) with regard to the monomers to which it is bonded. Actually, in 4a with a slightly longer O O distance (2.583 Å) than in (18)1 (2.567 Å), the SSCC amounts to 11.5 Hz compared to 7.8 Hz. To test the angle dependence, we calculated (18)2 (dOO = 2.715 Å, OHO = 178.5°, 2hJOO = 3.8 Hz); when the distance was constrained to be 2.583 Å (like in 4a) without changing the OAH O angle, 2hJOO = 6.3 Hz (+2.5 Hz). This is the expected increase when the O O length decreases. Then, we modified the angle to 146.5° resulting in a further increase of 0.9 Hz (2hJOO = 7.2 Hz). Thus, the increase from 7.8 to 11.5 (+3.7 Hz) is in part due to the bending of the OAH O angle but other effects should play a role. In summary:
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.molstruc.2013. 04.069. References [1] [2] [3] [4] [5] [6] [7] [8]
1
2h
4a, d H = 13.7 ppm, JOO = 11.5 Hz 4b, d1H = 4.2 ppm, 2hJOO = –0.1 Hz 4b with the OHO geometry of 4a, d1H = 7.5 ppm, 2hJOO = 1.2 Hz 18n (n = 1), d1H = 14.1 ppm, 2hJOO = 7.8 Hz 19n (n = 1), d1H = 4.7 ppm, 2hJOO = 1.2 Hz 19n with the OHO geometry of 18n, d1H = 9.3 ppm, 2hJOO = 5.2 Hz To the cyclic structures, the r/p skeleton dichotomy seems to apply [69–71].
4. Concluding remarks We have summarized in Scheme 10 the main conclusions of the present work. The main factor behind the different strength of the intramolecular HB in the pseudo-six membered rings 4a and 4b and the intermolecular HB in the catemers (18)n and (19)n is cooperativity. Another factor is the fact that in the pseudo-six membered rings the HB donor and the HB acceptor belong to the same molecule, whereas in the catemers the HB donor donates to a different molecule and also accepts from a different one. Furthermore the main effect of conjugation is the simultaneous increase of the proton donor and the proton acceptor capacity of the conjugated system with respect to the saturated analogue. On top of that, the arrangement of the r-frame favoring the coplanarity and the proximity of the HB donor and the HB acceptor in 4a is a second factor contributing to reinforce the intramolecular HB in this conjugated species with regard to its saturated counterpart 4b. The RAHB is not limited to cyclic structures; the reason why most examples concern these structures is the fact that RAHB is present in monomers that exist in the gas-phase and in solution. On the other hand, RAHB is also present in catemers but this situation occurs almost exclusively in the solid state. The Resonance Assisted Hydrogen Bond (RAHB) concept that is undoubtedly useful in crystallography appears to apply to NMR and to energetic properties although some care must be taken when using it [72,73] because it depends not only on the atoms involved but also on the molecular structure.
Acknowledgments This work has been partially supported by the Ministerio de Economía y Competitividad Project No. CTQ2012-35513-C02 and by the Project MADRISOLAR2, ref S2009PPQ/1533 of the Comunidad Auto´noma de Madrid, by Consolider on Molecular Nanoscience CSC2007-00010, and by the COST Action CM0702. A generous allocation of computing time from the CESGA, from the CTI (C.S.I.C.) and from the CCC of the U.A.M. were greatly appreciated.
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