J. Phys. Chem. 1994,98, 64594461
6459
Ab Initio Calculations of Supramolecular Recognition Modes. Cyclic versus Noncyclic Hydrogen Bonding in the Formic Acid/Formamide System Thomas Neuheuser and B e d A. Ha’ Institut fir Physikalische und Theoretische Chemie der Universitiit Bonn, Wegelerstrasse 12, 0-53113 Bonn, Germany Christiane Reutel and Edwin Weber’ Institut fir Organische Chemie der Technischen Universitiit Bergakademie Freiberg, Leipziger Strasse 29, 0-09596 FreiberglSa., Germany Received: December 1, 1993: In Final Form: April 28, 1994’
We present a theoretical investigation of the bonding between formic acid and formamide in various geometrical arrangements as a model for a motif that occurs in supramolecular 1:2 complexes of dicarboxylic,acids with dimethylformamide. We calibrate our theoretical model using the known energetics of the formic acid dimer as a benchmark. In these calculations we study the influence of basis set, in particular the basis set superposition error, as well as the correlation contributions to the hydrogen bond, and thus arrive at a theoretical model that provides an estimated accuracy of around 5 kJ/mol for the binding energy of the hydrogen bonds in complexes similar to the formic acid dimer. We apply the model to our target system as well as to some geometrical arrangements of the formamide dimer, which to our knowledge have not been studied so far in the literature. The calculations show that the weakest form of hydrogen-bonding interaction, substantiated by the C-H-.O bond in a cyclic complex of formic acid with formamide, still contributed a significant amount of 10-1 5 kJ/mol to the complex interaction energy. Thus we find a clear indication that the formyl proton may indeed participate in hydrogen bonding, despite of a long bond length of up to 250 pm. We interpret this result in relation to the structure of supramolecular complexes of 1,l’-binaphthyl-2,2’-dicarboxylicacid and 9,9’-spirobifluorene-2,2’dicarboxylic acid.
Introduction In recent years, molecular recognition has become a challenge in chemical research from both a practical and theoretical point of view.’ This amounts to developing a complementary relationship between the recognizing molecules on the basis of the shape and chemical characteristics of a so-called host and guest species, which are aimed at binding together selectively! Within this frame, hydrogen bonds (H bonds) are the most important interactions.’ Knowledge of the optimum mode of H bonds between a particular guest and its complementary receptor molecule is thus an important design question.* Crystalline complexes that contain H bonds are the most promising objects for the study of host-guest interactions, since their structures can be scrutinized easily via X-ray diffracti~n.~ In this context, we have studied a number of such complexes, dubbed coordinato-clathrates.11each involving a particular guest species but differently designed host molecule^.^^ It was found that preferential H-bond interactionsdooccur. For the carboxylic acid host molecules such as l,l’-binaphthyl-2,2’-dicarboxylicacid (1) and 9,9’-spirobifluorene-2,2’-dicarboxylicacid (2)and dim-
1
2
ethylformamide (DMF) as guest, the basic motif is a sevenmembered cyclic H-bonded structure (3) comprising the carboxylic acid unit and the formyl group;lq.20that is, we find two bonds from DMF to thecarboxylicacid function where one contact is a weak C-H-0 type of interaction. Although this latter contact
* Abstract published in Aduunce ACS Abstracts, June 1, 1994.
is long as compared to the O-H--O bridge, it is in the range of usual C-H-0 hydrogen bonds.21 Similar observationsapply to the bond angle C-Ha-0, which adopts a value typical for this type of hydrogen bond.21 On the other hand, a noncyclic binding between the carboxylic group and DMF (4),where the C-Ha-0
3
4
contact is missing, has also been observed.19~22Likewise, dimethyl sulfoxide (DMSO) as guest molecule is H-bonded to a carboxylic host mostly in ring fashion,23 including a C-H-0 contact, but there are also examples of linear binding.ll This raises the question about the role of C-Ha-0 secondary contacts for the molecular recognition of typical proton acceptor guests based on common carboxylic hosts. How much do these particular contacts contribute to the stabilization of the supramolecular complexes formed in the crystalline state, or are they only the result of packing effects of the crystal lattice? We are going to show that ab initio calculations are helpful in answering this question. Sincethe host molecules involved in the experimental structures are too complex for ab initio calculations, a model system was chosen. It is composed of formic acid and formamide instead of the carboxylicacids 1or 2 and DMF. Here we report and discuss the results of these calculations. Usually there are no error bounds that may be given for an ab initio calculation. Therefore, we first embark on a suite of calibration calculations on the monomers and the well-known dimer of formic acid. This will enable us to assess the influence of the size of the basis set, the method (Le., self-consistent field (SCF) vs treatment including electron correlation effects), and the determination of the complex geometry on structural features (bond lengths and angles) as
0022-3654/94/2098-6459So4.50/~0 1994 American Chemical Society
6460 The Journal of Physical Chemistry, Vol. 98. No. 26, 1994
well as complex binding energies. The calibration allows us to findametbod for thecalculationofthecomplex weareinterested in, for which no experimental energetics are known, and permits us to give a confidence interval of S kJ/mol for our calculated binding energies. On the basis of this, we studied the formic acid-formamide complex in various geometric arrangements and determined their relative stabilities, as well as the energetic difference between the H-bonded ring structure 3 and the opcn structure 4, giving an estimate for the energetic contribution of the supposed C-H-0 interaction. Results Calibration of the Model. Methods. We used the program suites TURBOMOLE24and GAUSSIAN 9OZ5for self-consistent field (SCF) and second-order perturbation calculations of the Moller-Plesset type (MP2). In the MP2 calculations the Iscore electrons were kept frozen. For the determination of the geometry we employed the gradient techniques implemented in the programs mentioned, calculating analytical gradients at either theSCFortheMP2level. Thestationarypointsthusfound were in turn employed in a calculation of the Hessian matrix, the eigenvalues of which were generally used to decide if a true minimum or a saddle point is present. The counterpoise methodz6was used to correct for the basis set superposition error (BSSE), taking the relaxation of the monomers on dimer formation into account. Corresponding entries in the tables are denoted by an index CP. This method to correct for the BSSE has been discussed in the literature at large; a recent contribution21 addresses the arguments against and in favor of the CP correction, providing an extensive compilationofthe pertinent literature. Adiscussionofthevarious approaches is beyond the scope of the present paper; suffice it to say that not all authors unequivocally recommend the use of the CPcorrection,theirobj&ions being mostly basedontheargument that the occupied orbitals of the ‘ghost” monomer should not be accessible by the electrons of the monomer being ‘corrected”. Thus, the CP correction is suspected to overestimate the BSSE. A further complication arises due to the “secondary BSSE”,’e which is brought about by the change of the electric moments caused by the basis set of the ‘ghost”. For this kind of basis set deficiency no remedy is known, and it may be of a substantial size ifalargefractionoftheinteractionenngyiscausedbyelectrostatic interactions. In the light of these remarks, application of the CP correction is to he considered as an approximate, yet-also judging from our own experience-very successful method for correcting basis set deficienciesin the calculation of the monomers. Although its application is usually believed to be the “higher level of theory” ascompared toa refrainfromitsuse, its reliability for thespecific case at hand should be carefully scrutinized in calibration calculations. Entbalpiesofassociation werecalculated fromab initioenergies by considering zero-point energies and other corrections in the form
AHT= -De
+ AZPVE + AVE - 4 R T
(1)
De denoting the calculated dissociation energy at equilibrium. The difference in vibrational energies of the dimer and the dissociatedcompoundsas calculated from thevibrational partition function has been taken into account using vibrational data obtained from the harmonic SCF field it is composed of the difference of zero-point energies AZPVE and the temperaturedependent term
h V” AVE =
exp(hv,/kT)
-1
(2)
Neuheuser et al. which is due to the Boltzmann distribution of the vibrational quanta. The sum extends over all normal modes of the molecule, and the temperature T was taken as 300 K throughout. Basis sets with double-( (DZ) or triple-f (TZ) quality are derived from (8s4p) and (9sSp) basis sets of Gaussian functions as given by Huzinaga.29 which were augmented with a varying number of polarization functions as detailed in Table 1. The 8s4p functions were contracted according to the scheme [511 I / 3111, and the 9s5p set according to [ S l l l l / 3 l l ] , using the coefficients obtained from an atomic SCF calculation in the uncontracted basis set. The hydrogen basissetsfowerecontracted accordingto [31] and [311]. Moreover,wemadeuseofextended basissetsgiven byvanDuijneveldt,”namelya basissetof(l3s8p) quality for carbon and oxygen, and an (8s) basis set for hydrogen. The ( I 3s) basiswas contracted accordingto the scheme [7,4,4,1,1], the third contracted function employing the same primitive exponentsasthesecondone. Thecontraction coefficients for the first two functions were taken from the 1s orbital of an atomic SCF calculation, whereas the third function was formed using the 2s atomic orbital. The hydrogen contractions were formed analogously, using a [5,1,1,1] scheme. We thus arrived at a basisset of [5s4p/4s] quality, hereafter dubbed as VQZ,denoting its valencequadruple-( quality. This was in turn augmented by polarization functions, which for the oxygen and hydrogen atoms were directly obtained from Walch,” whereas those for carbon were derived from those of oxygen by scaling according to the Z ratio of A summary of the basis sets and their acronyms is compiled in Table I . Individual Molecules. The monomers of formic acid (5) and formamide (6) have been calculated the resulting structural data are compiled in Tables 2 and 3.
5
6 We havecarriedout geomctryoptimizations withvarious basis sets. as detailed in the tables. At the SCF level. all resulting sets of geometric parameters are in good accordance, bond lengths differing by less than 0.8 pm and angles by less than O S o , which
indicated that at the level of our simplest basis set (DZP) the SCF results are essentially converged. A slightly larger basisset dependence is observed at the correlated IcvcI. the various MPZ structuresoftheformicaciddifferinglcsstban1.3 pmandangles less than 0.4‘. The influence of correlation is clearly visible, leadingingeneral tolonger bondlengths. Thisiseasily interpreted in a configuration interaction picture as an admixture of configurations with occupied antibonding orbitals. This bond stretch is most pronounced in case of the CO bonds, which are longer by about 2-4 pm ai the correlated level. The influence on the OH bond is slightly smaller. about 1.5-2 pm, and still smaller for the CH bond. Angles are affected by less than 3’. Thegeometric parametersdetermined from the MP2 calculations are i n good accordance with experiment; i.e.. they agree Hith
The Journal oJ Physical Chemistry, Vol. 98, No. 26, 1994 6461
Supramolecular Recognition Modes TABLE 1: Basis Sets Used in This Study contraction scheme and acronym additional polarization functions DZP C (8s4p) [4s2p] + d(0.8)
TABLE J: Calculated and Experimental Geometries (pm, deg) of the Formamide Monomer SCFI SCF/ SCF/ TZZP TZZP DZP exr
-- + -- + --- + ++ - ++ - ++
TZP TZZP
TZZPP TZ2PP+ VQZZP-a VQZZpb
N (8s4p) [4sZp] d(l.O) 0 (8s4p) [4s2p] d(1.2) H (4s) l2sl + ~(0.8) c (9s5p) 2 [js3pl’+ d(O.8) 0 (9sSp) [Ss3p] d(l.2) H (5s) [3s] p(O.8) C (9sSp) [5s3p] Zd(0.46, 1.39) N (9sSp) [5s3p] Zd(0.58. 1.73) 0 (9s5p) [5s3p] Zd(0.69, 2.08) H (5s) [3s] Zp(O.46, 1.39) C same as TZZP f(0.6) 0 same as TZZP + f(1.0) H same as TZ2P + d(0.8) C same as TZ2PP sp(0.0438) 0 same as TZZPP sp(0.0845) H same as TZZPP C ( 1 3 ~ 8 ~ ) [5s4p] Zd(0.46, 1.39) 0 ( 1 3 ~ 8 ~ ) [Sdp] + 2d(0.69,2.08) H (8s) [4s] + Zp(O.46, 1.39) C (13s8p3d) [5s4p2d]; d exponents: 2.35235; 0.73755.0.28710; coefficients: 0.16866.0.58480. 1.0 0 (13s8p3d) [5s4pZd]; d exponents: 4.2770, 1.3410,0.5220; coefficients: same as for C H (8s3p) [4s2p] p exponents: 1.7983,0.4663,0.1644 coefficients: 0.17705,0.88560, 1.0
---
VQZZPP
+ + +
-
CsameasVQZ2P-b+Zf-[Ifl f exponents: 0.9933,0.3399; coefficients: 0.47694.0.65874 OsameasVQZ2P-b+2f-[lfl; f exponents: 1.806,0.618; coefficients: same as for C H same as VQZ2P-b + Zd [Id]; d exponents: 1.827.0.548; mfficients: 0.46662.0.66447
-
r(C,=O’) 117.7 117.6 ~(CI-01) 131.8 132.1 r(CI--Hi) 109.3 108.5 r(Ot-Hd95.2 94.8 LOICIO~124.9 124.9 LH’CiO’ 124.7 124.7 LCiOiHi 108.9 109.4 a
118.2 134.2 109.2 99.1 98.8
118.6 134.9 109.1 99.1 98.9
lZ1.9*l.Z l35.2* 1.2 l09.8* 1.0 100.16iO.3 100.15 0.3
119.0 121.6 112.4 125.2 0 180 180 180
119.5 121.3 112.6
119.1 120.8 112.7 125.0
121.6f0.3 I20.0*0.5 112.7*2.0 124.7 *0.3
7.8 -173.0 167.4 10.8
0
125.1
0 180 180
0
*
180 180 0
Calculatedwith theconstraintofaplanarstructure. Fullyoptimiztd structure. Experimental structurd6 as referenced in ref 61. Out of plane angle: angle between the CZ-NI anis and the N I H4 H5 plane. TABLE 4 Calculated and Experimental Geometries (pm, deg) of the Formic Acid Dimer SCF$ SCF$ SCFI -MP21 MP2 MP2 DZ
~~
~~~
TZ
TZZ 6 31G
DZd TZ21
*a
exptC
~~
r(Cl=o2) r(Cl-01) r(CI-€fZ)
119.1 119.0 119.0 129.4 129.7 129.6 109.2 108.4 108.3 r(0l-HI) 96.7 96.2 96.1 LO1 CI 0 2 125.9 125.8 125.9 LH2CI 0 2 122.3 122.5 122.3 L C l O I H l 111.0 111.2 111.1 r(02-HI’) 180.6 183.4 182.3 r(02-01’) 276.7 278.9 278.1 L02H1’01’ 172.3 171.6 174.6
diffraction data.
theoretically.‘-
122.9 131.8 109.1 99.4 126.7 122.0 109.4 170.6
122.1 121.9 121.7t0.3
131.0 110.2 99.8 126.7 121.9 108.9 167.2 267.0 177.8
131.4 108.9 99.3 126.4 122.1 109.2 167.9 267.2 180.0
132.0*0.3 103.3 *0.017 126.2t0.5 108.5*0.4
>
178.9
269.6
* 0.7
(18OY
Again weoptimized thegeometry ofthedimer
........... exb
121.2
134.7 109.0 96.7
134.9 109.1 97.1
l20.2*1 134.3il 109.7t0.5 97.2*0.5
125.0 125.4 125.1 124.6 125.5 125.4 108.9 105.8 106.1
125.2 125.4 106.0
124.9* 1 124.1 * 2 106.3 1
120.3 134.2 110.3 97.3
118.7 134.7 110.0 99.9 99.5
*Reference43.6 Experimental structure6’ as referenced in ref 61. parameter assumed in the refinement of the electron
120.1
117.5 132.1 108.4 94.7
r(CZ-iv1) r(C2-If3) r(NI-H4) r(NI-HS) LH4 N I H5 LH4 N I CZ LNI c2 n 3 LNI CZ 0 3 r(H3 C2 N I HS) r ( 0 3 C Z N I HS) r ( C 2 N l H5H4) 6(CZH4HSNl)d
(Geometrical
TABLE 2: Calculated and Experimental Geometries (pm, dee) of the Formic Acid Monomer this work ref 61 SCF/ SCF/ SCF/ MPZ/ MPZ/ MPZ/ DZP TZP TZZP DZP TZZP 6-3lG**
r(CZ=m)
HZ’
..,.._............
7
Experimental structure6’ as referenced in ref 61.
experiment within 0.7 pm and Zo. The deviation of the SCF results from experiment of about 2 pm and 3O is, however, still considered acceptable. It is worth noting that at the SCF level the formamide monomer in a TZZP basis is found to display a nonplanar minimum, withanangleofabout 1lo between theCN axis and the HNH plane, and a CO bond length which is 3.7 pm too short. MP2 calculations using the SCF optimum geometry and the same basis set yield, however, an energy lower by 1.2 kJ/mol for the planar geometry, which is consistent with the experimental determination of a planar structure with a shallow minimum.’l-3’ Againour calculatedbond lengthsare inexcellent agreement (better than 1 pm for single bonds) with experiments. All results are comparable to similar calculations known in the literature.‘The Formic Acid Dimer. In order to calibrate our methods for calculating the intermolecular interactions mediated by one or more hydrogen bonds, we investigated the formic acid dimer 7, which is well-studied both experimentally’Y8 and
Of
H1
usingbasissetsofDZP,TZP,andTZZPqualityattheSCFlevel. The effect of electron correlation was estimated by means of a MPZ calculation at the optimal SCF geometry. Moreover, we determined optimal MPZ geometries for the DZP and TZZP basis sets, in order to investigate the effect of electron correlation on the current type of dimers. Our results are collected in Table 4.
The influence of the basis set on the calculated SCF intermolecular distance is moderate. The largest change is an increase of the 02-H1‘ distance by 2.8 pm from the DZP to the TZPleve1,aneffectthat is presumablyattributableto thesmaller BSSEoftheTZP hasisset. Themaximalchangesofangleamount to 3O, and we conclude that the results are already satisfactory at the DZP level, taking the small force constants into account. At the MP2 level, the change in going from DZP to the TZ2P basis set is even smaller (we find an increase of the 02-H 1’ bond distanceof0.7pm) thanat theSCFlevel(I,7pm),anobservation that is in line with results obtained for the water dimer.“
Neuheuser et al.
6462 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994
The difference between the 02-H1’ bond length at the SCF level and the same quantity at the MP2 level is, however, substantial: The minimum for the correlated calculations occurs at a bond length that is shorter by 14 pm. An analogous enhancement of hydrogen bonding due to correlation was found for the water dimefl9 and the C O y H F and N2O-HF complexes.sO Likewise, the angle 02-H1’-01’ increases by 5.4’ to the ideal hydrogen-bond angle of 180’. The deviations of the calculated bond distances for C 1 4 2 and C 1 - 0 1 from the experimental results are comparable to those of the monomer. By contrast, the 01-H1 distance is calculated to be 6-7 pm shorter (4 pm for MP2). It is hard to see why the theoretical method should result in a deviation of this size in the case of an unproblematic 0-H distance (which is calculated very satisfactorily in the monomer). On the other hand, the reliable experimental determination of such a distance is known to be difficult. We therefore are tempted to attribute the discrepancy rather to an experimental uncertainty than to a shortcoming of the calculation. The distance of the monomers in the dimer-strictly speaking, the 02-01’distance, for which the experimental error is specified as 0.7 pm-is calculated to be 2.5 pm longer at the MP2 level, a much better result than that obtained at the SCF level, where the distance is underestimated by 7-9 pm. The rather large discrepancyis attributable to the shallow potential well connected with the small force constant. For the same reason we expect, however, that the bond energy is comparatively insensitive to the exact intermolecular bond distance. This conjecture is corroborated by the calculations; see the discussion of the binding energies below. The largest deviation of angles between SCF and experiment is less than 3’, a satisfactory agreement that is improved substantially at the MP2 level, where the deviation is less than 1’. We observed a systematic change in intramolecular bond lengths and angles on dimer formation, which is small (1-2 pm in absolute value for heavy-atom distances, largest for C1-01 with -2.4 pm) but clearly visible for all basis sets and experiment as well. On dimer formation, the bonds adjacent to the intermolecular hydrogen bonds ( C 1 4 2 and 01-H1) become longer than in the monomers; i.e., they are weakened, and this weakening in turn leads to a stronger C1-01 bond adjacent to the two bonds mentioned before. Also, for the angles small changes of 1-2’ are observed on dimer formation, which may be correlated with the shortening of the C1-01 bond. We now turn to the discussion of the dissociation enthalpy of the formic acid dimer. Our goal is the convincing choice of a method feasible from the point of view of computational expense, yet capable of giving a reliable figure for the complex dissociation energy (De) to within a few kJ/mol. We are going to address separately the influence of the method of geometry optimization, carried out with or without correlation treatment in various basis sets, and the influence of the basis set and correlation energy at a given SCF minimum (a “single-point calculation”) for the dimer dissociation energy. We denote the calculations by specifying the method used for geometry optimization after a double slash and the method used at this single point for determination of the complex dissociation energy before the double slash; e.g., MPZ/TZZPP//SCF/DZP denotes a correlated calculation with extended basis set (see Table 1) at a geometry obtained from an SCF calculation with DZP basis set. The results are summarized in Tables 5 and 6. Acomparison of //SCFcalculations with /IMP2 calculations, using a fixed basis set, shows that the SCF dissociation energies uncorrected for BSSE are lower by about 1-2 kJ/mol at the geometry obtained from a correlated calculation. The corresponding MP2 dissociation energies are higher by the same amount for the MP2 geometry. After a counterpoise correction (CP), which is distinctly larger at the correlated level (partially
TABLE 5: Dissociation Energy of the Formic Acid Dimer (kJ/mol) Obtained with Various Methods’ geometry basisset SCF MP2 SCFCP MP2CP CPxp CPyn MPZIDZP
DZP DZP SCF/DZP TZP SCFIDZP TZ2P SCF/TZP TZP MP21TZ2P TZ2P SCFITZZP TZ2P SCFITZZP TZ2PP SCFITZZP TZ2PP+ SCFITZZP VQZ2P-a SCFITZZP VQZ2P-b SCF/TZ2P VQZZPP
SCFIDZP
67.5 81.3 68.7 80.2 59.0 67.1. 55.4 68.2 59.0 66.5 53.8 70.0 55.7 68.4 56.3 70.6 53.0 66.0 51.6 63.3 51.9 65.3 52.0 66.5
51.2 53.9 52.7 50.4 52.9 48.4 50.7 51.7 51.3 50.9 50.9 51.3
50.3 53.4 53.0 56.3 52.9 55.8 56.7 60.3 60.0 57.6 59.2 61.7
16.3 14.8 6.3 5.0 6.2 5.5 5.0 4.6 1.7 0.7 1.0
0.6
31.0 26.8 14.2 11.9 13.6 14.2 11.7 10.3 5.9 5.8 6.1 4.7
CP den()tes a value including a counterpoise correction. TABLE 6 Dissociation Energy (kJ/mol) of the Formic Acid Dimer: Comparison with Experiment’ basis set method opt SP De AZPVE AVE-4RT AHT 68.7 7.3 -0.4 -61.7 SCF DZP DZP 7.3 53.4 -0.4 -46.4 MP2CP DZP DZP 7.1 52.9 MP2CP TZP TZP -0.2 -46.0 56.7 7.0 MP2CP TZ2P TZ2P -0.1 -49.8 7.0 MP2CP TZ2P TZ2PP 60.3 -0.1 -53.4 7.0 -0.1 -53.2 MP2CP TZ2P TZ2PP+ 60.0 7.0 MP2CP TZ2P VQZ2P-a 57.6 -0.1 -50.7 MP2CP TZ2P VQZ2P-b 59.2 7.0 -0.1 -52.3 7.0 MP2CP TZ2P VQZ2PP 61.7 -0.1 -54.8 exp45
exp46 exp47 exp48
-61.9 -59.0 -49.0 -61.8
i 2.1 i 6.3 i 0.4 i 0.5
a Enthalpies are given for T = 300 K, SP denotes a “single-point calculation”,ZPVE the zerctpoint vibrationalenergy, VE the temperaturedependent part of the vibrational partition function,and CPcounterpoisecorrected results.
due to a shorter bond length), we obtain a De that is slightly smaller at the MP2 geometry. The difference between De(MP2CP//SCF) and De(MP2CP//MP2) amounts to 3 kJ/mol for the DZP basis set but less than 1 kJ/mol for TZZP, an effect brought about by the smaller BSSE in the larger basis set. We conclude from these findings that the SCF geometries are appropriate for determining the dissociation energies to within a few kJ/mol, if a single-point calculation is carried out using a high-quality basis set associated with a small BSSE. From the small difference of TZP//SCF/DZP to TZP//SCF/TZP and TZ2P//SCF/DZP to TZ2P//SCF/TZ2P (maximum 0.6 kJ/ mol), we conclude that a DZP basis set is appropriate for the determinationof the geometry. Therefore,weconsider henceforth only geometries obtained at the SCF level and understand an SCF calculation if not specified otherwise in the acronym for the method of geometry optimization. The calculated value of the dissociation energy is dependent on the basis set, and at the SCF level this dependency is largely due to the different BSSE in different basis sets. A comparison of DZP//DZP with TZP//DZP results shows that the BSSE is smaller by about 10 kJ/mol in the larger basis set, an error that is corrected by a counterpoise procedure to within 1 kJ/mol, assuming that all of the difference at the SCF level is attributable to the BSSE if valence basis sets of different sizes are employed but the number of polarization functions is kept fixed. The BSSE convergesveryslowly to zero, as shown by a comparison of TZ2P/ /TZ2P with VQZ2P-a//TZ2P, displaying a BSSE smaller by 4 kJ/mol. Even diffuse functions (compare TZ2PP//T2ZP with TZZPP+//TZZP) contribute to the BSSE (3.3 kJ/mol), but again the CP correction is able to recover the error up to a few tens of kJ/mol. In general, the effect of enlarging the basis set may be estimated to high accuracy (say within 1 kJ/mol) at the SCF level.
Supramolecular Recognition Modes
A second kind of basis set dependency may be traced to the number of polarization functions. Now keeping the quality of thevalence basis set fixed and varying thenumber of polarization functions, we compareTZP//DZPwith TZZP/DZP. Whilethe counterpoise correction is different by only 1.3 kJ/mol, the difference in dissociation energies after correction is still 2.3 kJ/ mol, identifyinga contribution attributable to polarizationeffects. On the other hand, comparing TZ2P//TZ2P with TZZPP// TZ2Por VQZZP-h//TZ2P with VQZ2P-a//TZ2PorVQZ2PP/ /TZZPshows thatatthelevelofat leasttwopolarization functions the SCF dissociation energies are converged to within 1 kJ/mol at the counterpoise-corrected level. We now turn to the discussion of basis set effects at the correlated level. An analysis similar to that carried out for the SCF results above reveals that again the effect of enlarging the valence basis set is stabilized to within 1 kJ/mol by using the CP method. However, addition of diffuse and semidiffuse d and f functions will now lead, apart from polarization of the charge distribution, toa different descriptionofcorrelation. Indeed, we find that more flexible hasis sets lead to a dissociation energy larger by 3.3 kJ/mol after CP correction (TZP//DZP vs TZ2P/ /DZP), indicating the effect of the larger correlation energy recovered in the larger hasis set. A further increase is observed in going to TZ2PP//TZZP, and even for the largest basis set studied we cannot claim convergence with respect to the differentialcorrelation effects. While the BSSEmaybecorrected by the CP procedure to within at most 1 kJ/mol, the absolute error in the determination of the differential correlation is still at least 5 kJ/mol for the TZ2P hasis, and much larger hasis sets approaching convergenceof this contribution to the dissociation energy are still prohibitively expensive. The differential correlation effects tend to increase the dissociationenergy,andwith our best MP2counterpoise-corrected value (61.7 kJ/mol for VQZ2PP) we have a clear tendency hack to the SCFJDZP value without CP correction (68.7 kJ/mol). Weroughlyestimatethat theMP2limit forthedissociationenergy is still a few kJ/mol larger than the VQZ2PP value of 61.7 kJ/ mol, since MP2 recovers only a fraction of the order of say 70% of the correlation energy. We therefore propose to study our target system (the formic acidlformamide complex) using the SCF/DZP without CP correction, since in this scheme a compensation of the BSSE and the correlation contribution to the binding energy may be expected from the results of the calibration calculations. This choice is clearly a compromise motivated by the limited computational power to be expended, but the above analysis indicates that this approach will give us avaluereliabletowithin5 kJ/molfor hydrogen-bondedcomplexes of a type similar to the formic acid dimer. Acomparison withexperiment shows that theSCF/DZPvalue without CP correction for the enthalpy of association (AH = 4 1 . 7 kJ/mol) is in almost perfect agreement with most recent measurement^,^^ yielding AH = 4 1 . 8 f 0.5 kJ/mol, which in turn corroborates earlier experimental ~ o r k ~which S . ~ had been questioned in the meantime.47 The latter experiment gives a value smaller by about 10 kJ/mol, but our calculations clearly favor a value for AH around 4 0 kJ/mol, our best calculation (AH = -54.8 kJ/mol) still underestimating the "true" value according to the discussion above. The Formic Aci&Fonnamide Complexes. With reference to the preceding section, we shall investigate OUT target system, the formic acid-formamide complex, using an SCF geometry optimization at the DZP level. We expect that the dissociation energies obtained from SCF differences without counterpoise correction are reliable to within 5 kJ/mol due to cancellation of nonrecoveredcorrelationcontributions and BSSE. Although this model was carefully calibrated using the formic acid dimer as a benchmark system, we wanted to check our assumptions for variousgeometries of the formic acid-formamidecomplex again,
The Journal of Physical Chemistry. Vol. 98, No. 26. 1994 6463 provided such a check is feasible in regard to computational expense. Calculations at the TZ2P level for the structures 8. and 8d corroborate the premises of our model.
',oa
"P
01
!......
A
..........
I
H
-
b
03
b
4
02
8a
HS
8b Thegoalofthecalculationsin the present section is todetermine the bond energiesof various geometricarrangements ofthe formic acid-formamide complex with the hope that we can contribute to the study of the properties of the C-H-0 hydrogen bond in particular. The geometries studied include the noncyclic Hbonded structures Sa and 8b as well as various types of ring structures, namely the eight-membered H-bonded ring 8c and two seven-membered ring structures 8d and 8e. Two of them (8b
8c .....,............ O
-$
I
\~
P
03
J
.... H3
02
"e
n4
8d
8e and Sc), as a matter of fact, do not meet the experimental circumstance,since theN-H-.Ohydrogenbondcannot beformed
6464 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994
TABLE 7: Calculated Geometries of Various Geometric Amngements of the Formic Acid-Fonnrmide Complex. 8b
81 r(02...C2) r(02-Nl) r(01.-03) r ( 01-N 1) r(02-**H3) r(02--H5) r(02--H4) r(03*-Hl) r(N 1 -H1)
308.6 278.9 (+3.2)
8c 298.1 273.9
8d
8e
318.3 (+5.9)
330.8
274.5 (+1.7) 242.9 (+5.2)
291.5 243.6
201.8 213.9 183.9 (+4.0)
176.9
177.9 (+2.1) 194.9 124.9 (+1.3)
LO2 H3 C2 LO2 H5 N1 LO2 H4 N 2 LO1 H 1 0 1 LO1 H1 N1
135.8
159.2 158.8
168.3 ( 4 . 7 )
179.3
174.2 (+2.5) 177.2
Bond lengths are given in pm, bond angles in deg. Values are given for the DZP basis set; the difference to TZ2P is given in parentheses. a
TABLE 8: Dissociation Energies (kJ/mol) of Formamide-Formic Acid Complexes in Various Geometric Arrangements' basis set
structure
opt
SP
88 8a 8a 8b 8e 8d
DZP DZP TZ2P DZP DZP DZP DZP TZZP DZP
DZP TZ2P TZ2P DZP DZP DZP TZ2P TZ2P DZP
8d 8d
ae
SCF MP2 SCFP MP2CP CPSCF CPMFZ 29.4 6.2 35.0 41.2 28.8 11.8 28.8 35.9 26.4 30.1 2.3 5.7 29.1 37.0 26.8 31.6 2.3 5.5 20.7 23.7 16.6 16.1 4.1 7.6 65.7 78.0 51.7 52.9 14.0 25.1 53.1 62.0 40.8 40.0 12.3 22.1 43.8 53.8 39.5 44.0 4.3 9.8 44.4 55.4 40.2 45.9 4.2 9.5 -25.1 -12.4 -36.6 -33.1 11.6 20.8
denotes a single-point calculation, opt the mode of geometry optimization, and CP a counterpoise-corrected value. a SP
ingoing from the model toreality, Le., when we replace formamide by DMF. These latter structures were included to obtain insight into the energetics of the N-H-0 bond as well as the C-H-0 and 0-H-0 bonds feasible also for the acid-DMF complex. Structural results for the intermolecular coordinates and calculated dissociation energies are collected in Tables 7 and 8. For the complex 8a, 0-Ha-0 bond lengths of 184 pm at DZP and of 188 pm at the TZ2P level were obtained. These findings are in line with the calibration calculations, indicating that the potential curve corresponding to the studied degree of freedom is very shallow and the minimum is at a shorter bond distance for the DZP basis set due to larger BSSE. A quantity which is probably more appropriate for comparison with experiment is the distance of the two heavy atoms partaking in the hydrogen bonding, which is 279 pm at the DZP level (282 pm for TZ2P). This length may beconsidered typical for a 0-Ha-0 bond length, which is generally expected in the range of 275-285 pm. Note that the calculated angle of the 0-H-0 bond is 13' smaller than the ideal value of 180O. Apart from changes of about 1 pm, which are smaller than our expected accuracy, though in line with the expectationsderived from our experienceswith the formic acid dimer, the geometries of the moieties in the dimer are the same as those of the monomers. The bond energy is calculated as-35.0 kJ/mol, a number that we may take as a bond increment for the interaction of the 0-He-0 type in a rough estimate. The reported structure was found to be unstable with respect to rotation of the monomers around the 0-H-0 bond. The small imaginary frequency of the corresponding mode of 24i cm-l indicates a very small rotational barrier, similar to the case of the formamide dimer 9d to be discussed below. For the other noncyclic structure, 8b, with its characteristic N-H-0 hydrogen bond, we find a H-0 bond distance of 214 pm, much larger than in the previous case. This reflects the weaker H-bond interaction owing to the nitrogen atom. The
Neuheuser et al. Ne-0 distance is 309 pm, which is distinctly outside the range characteristic for a strong H bond (275-285 pm). Likewise, the bond energy for 8b (-20.7 kJ/mol) is also significantly smaller than for 8a. The structure 8c displays two comparatively strong hydrogen bonds. This is reflected both in the bond distances (202 pm for N-H-0 and 177 pm for O-H.-O) and in the bond energy (-65.7 kJ/mol), the latter being the largest one found among the complexes we have studied. The distances between the heavy atoms are 298 (N-0) and 274 pm (O-.O), showing clearly that the 0-H-0 bond is stronger than the N-H-.O bond. This in turn leads to an angle of 179O for 0-Ha-0, practically the ideal value, whereas N-H-0 shows a relatively large distortion from linearity (21O). Summing up the bond energies of 8a and 8b yields -55.7 kJ/mol. This value is by 10 kJ/mol lower than that for 8c. Hence, attributable to cooperativeeffects, the interaction energy of cyclic structure 8c is distinctly higher than the sum of the individual H bonds involved in 8a and 8b. To the best of our knowledge, structure 8c is the only one for which theoretical results areavailable in the literature." Although the 6-3 1G**basis set employed in this calculation differs slightly from ours, the bond lengths correspond to our data within 1 pm, except for the lengths of the hydrogen bonds which are reported with somewhat different distances (1 1 pm longer for O-H.-O and 7 pm shorter for N-H-.O). Part of this difference is attributable to a smaller BSSE for the 6-31G** basis set as compared to our DZP; in contrast to the literature," we find the N-H-0 bond length essentially the same as the corresponding one in the formamide dimer. On the other hand, the bond energy reported for 8c (-59.6 kJ/mol) is in reasonable agreement with our result, and our counterpoise-corrected result (-5 1.7 kJ/mol) agrees perfectly well with the literaturea (-51.2 kJ/mol), although theseauthors determine the BSSE correction using a procedure slightly different from ours, employing monomer calculations in monomer geometries. Unlike the geometry discussed before, the ring structures 8d and 8e can be adopted by the experimental DMF compound. Structure 8d is a seven-membered H-bonded ring involving an 0-H--0 and a C-H-.O interaction with H-.O distances of 178 pm (180 pm at TZ2P level) for O-H-.O and 243 pm (248 pm at TZ2P level) for C-H.-0. The heavy-atom distances are 275276 and 3 18-324 pm, respectively. Normally, the bond lengths found for C-Ha-0 interactions range between 300 and 400 pm,21 and the angles C-Ha-0 are usually in a wide range (90-180"). Indeed, for the case of 8d we calculate a C-Ha-0 angle of 125126O, whereas the O-H-.O angle was calculated as 174-177', near the ideal value. Although the C-H-.O interaction under consideration is much weaker than the strong hydrogen bonds discussed so far, we find a clear stabilization of the sevenmembered ring as compared to the open-chained structure. The calculated bond energy of 8d is -53.1 kJ/mol, suggesting a contribution of the C-H.0-0 interaction of about -15 to -20 kJ/ mol. This number is clearly several times outside our bona fide error bound of 5 kJ/mol, and therefore we stipulate that an interaction of the C-H-.O type is indeed present in structure 8d. As a result, structure 8d is the most stable among those that are feasible also for the formic acid-DMF complex. The same conclusion may be based on calculations carried out at a higher level of theory: The MP2 bond energy obtained from a TZ2P basis set is -18.4 kJ/mol, ignoring the CP correction, and -14.3 kJ/mol including it. The difference is brought about by the considerably larger CP correction in the 8d geometry. The last structure we have studied is the nonplanar sevenmembered ring 8e. In this structure the sp3-hybridizednitrogen atom acts as a H acceptor and not as a donor, as in the cases before. This structure turned out to be unbound with a bond energy of +25.1 kJ/mol, and indeed the stationary point was
The Journal of Physical Chemistry, Vol. 98. No. 26. 1994 6465
Supramolecular Recognition Modes TABLE 9 Calculated Gometries of Various Geometric Arrangements of the Fornmmide Dimer. r(03-HS') r(03-H4') r(03-NI') r(03'-H3) r103'-C2) Lc2 ~3 03, LNI'H5'03 LNI' H4'03 LC2 0 3 H4'
90
9b
198.6 (+3.3)
200.9
298.5 (+2.4)
299.2 238.0 328.2 138.7 164.3
169.7 (+0.3)
9d
9c
205.1 304.8 246.2 (+4.7) 331.7 1+6.3) 134.0 {+2.4j 113.7 151.7
contribution of a N-H-0 bond (520-25 W/mol) and an increment of 10-15 kJ/mol for the weak interaction, the figures now at the upper end of the range since the interactions mutually reinforce each other. Previous authors" obtained the same bond length within 2 pm. The estimate for the contribution of the C-H-0 bond may also be derived from the bond energy of the noncyclic structure 9c, the energy of which (-28.2 kJ/mol) is again less bonding by about 13kJ/molcomparedtothatoftheringstructure9hbecause of the missing C-H-0 bond. This structure is found to be a saddle point with respect to rotation about the N-H-0 axis.
a Bond lengths are given in pm, bond angles in deg. Values are given for the DZP basis set; the difference to TZ2P is given in parenthex.
TABLE 1 0 Dissociation Energies (kJ/mol) of FormamideDimer Complexes in Various Geometric Arrangements* basis set structure
opt
SP
9.
DZP DZP DZP DZP DZP TZ2P
DZP DZP DZP DZP TZZP TZ2P
9b 9c 9d 9d
9d
SCF MP2 S C P MP2ff CP,, 57.7 40.7 28.2 23.5 19.3 20.0
71.0 49.1 32.4 26.5 23.4 26.8
44.4 29.7 23.3 14.9 16.0 16.8
47.7 29.9 23.4 11.9 16.8 20.4
13.3 11.0 4.9 8.5 3.3 3.2
CPm 23.4 19.2 9.0 14.5 6.6 6.3
9a
a SP denotes a single-pint calculation, opt the mode of geometry optimization, and CP a counterpoise-correctedvalue.
found to be unstable with respect to rotation of the NH2 group around the C-N bond, as indicated by an imaginary frequency as large as 380i cm-I. We note the marked change of 9 pm in the C-N bond, compared to the structures considered before, reflecting the transition from sp2 to sp' hybridization at the nitrogen. At that stage wemay already conclude that the ring structnres foundin theX-ray structuresofthe host-guestcomplexes are the most stablespecies and that theopenstructuresare brought about by packing effects, contributing the energy difference of 15-20 kJ/mol we have found for the gas-phase compounds. However, before we turn to a discussion including a comparison with experiments, we would also like to study the formamide dimer, which is another pattern competing among the various possible associationsof the molecules present in the host-guest complexes with the amide. TheFormamideDimer. Theformamidedimer hasbeenstudied in many cases in experimental35.5'-53 and theoretical respect^.'^^^^^^^^ We reinvestigated this system, since structure 9d, which can also be formed by DMF, has not been reported so far. Moreover, we wanted to supplement the energetics of the three types of H bonds studied in the last section by more data for the N-H-0 and C-H-0 interactions, enabling us to give rough estimates for bond increments and typical ranges of bond distances for the various types of hydrogen bridges. Again we checked our model by additional calculations of the complex 9d, using a TZ2P basis set. The results are reported in Tables 9 and
9b
9c
IO. For complex 9d, characterized by two interactions of the C-H-0 type, we calculated a H-0 bond length of 246 pm (251 at the TZ2P level). The C-0 distance was found as 332 pm (338 pm at the TZ2P level), well within the range of 300-400 pm that is considered typical for this weak interaction?! The same holds for the C-H-0 angle of 134" (136" at the TZ2P level), which is consistent with the observation2' that C-H-0 bonds occur in the whole range of 9&180°. More interesting is probably the interaction energy of structure 9d, calculated to be -23.5 kJ/mol. This suggests an increment of-IO to-15 kJ/mol for the C-H-0 interaction. The calculation of complex 9b corroborates this assumption. With a total binding energy of -40.7 kJ/mol we may identify a
9d The structure most of the theoretical studies deal with is the eight-membered ring 9. Two N-H-0 bonds are present here. Thebonddistances (H-O)and thedistancesN-Owith 199and 299 pm, respectively,arerelativelyshort,reflectingthemoderately strong natureoftheinteraction. The bond energy isconsequently the largestofthestudiedformamidedimers. It amounts to-57.7 kJ/mol, which is in good approximation twice the value of -25 to-30 kJ/mol attributable to a N-H-0 bond. The structural data obtained in our calculations are in agreement with the literature." On the other hand, the length of the H bridge has
6466 The Journal of Physical Chemistry, Vol. 98, No. 26, 1994 also been calculated to be longer by about 9 pm.60 Our optimization with a TZ2P basis reduces this figure by 2.4 pm. In the same paper@the dissociation energies for the complexes 9a-9c are calculated slightly differently, owing to the fact that the optimization was carried out for the C 4 distance only with a basis set of essentially TZ2P quality, whereas we determined the equilibriumby a full optimizationwith a DZP basis set. After counterpoise correction, however, they agree to within 3 kJ/moi and are essentially in accord with those reported in ref 58, which agree with ours to within 5 kJ/mol (for 9c) or better. Discussion Based on Experimental and Theoretical Data. The structure motifs substantiated by Sa and 8d can also be formed by DMF interacting with a carboxylic acid. Both motifs have indeed been found in the X-ray crystal structures of the supramolecular 1:2 complexes of dicarboxylic acids 1,l’-binaphthyL2,2’-dicarboxylic acid (1)11J9and 9,9’-spirobifluorene-2,2’dicarboxylicacid (2)’l3 with DMF. The spirocompound 2 forms two seven-membered ring structures with DMF, according to motif Sd, which are planar to good approximation. By contrast, the crystal structure of l.DMF( 1:2) reveals a seven-membered ring as well as a chain motif similar to Sa, both being distorted from planar geometry. From the ab initio calculations we conclude that the spiro compound 2 displays the energetically most favorable motifs in an essentially strain-free environment, while in the binaphthyl compound 1 packing effects may cause the observed distortion as well as the open-chain structure, which is less stable than the ring by about 20 kJ/mol. The calculations show clearly that the additional interaction present in structure 8d leads to an additional stabilization and thus represents a definitively important mode for molecular recognition. This is in line with reasonings based on the study of a large number of experimental results.*’ Fromour calculations it is possible to recover a characterization of the different X-He-Y interactions, the strongest being O-H-.O with a bond energy of -35 to 4 0 kJ/mol, leading to typical heavy-atom distances of 275-285 pm. The angle is usually near the ideal angle of 180O. The N-H-.O bond is perceivable weaker, leading to a binding energy of -20 to -25 kJ/mol and a longer X-Y distance of about 30&3 10 pm. Bond angles occasionally deviate to a larger extent from linearity. Values of 160-180O are known from the literature.*’ The C-H--O interaction is the weakest but still contributes -10 to -15 kJ/mol to the complex formation energy. The bond is rather long, and values up to 400 pm for the heavyatom distance are still indicative of a weak attraction.21 In our examples, the values range between 325 and 340 pm. If more than one interaction is present, the attraction tends to be slightly stronger than the sum of the individual interactions derived from linear motifs, leading to a somewhat smaller bond length in the ring structures.
Summary and Conclusions We have investigated the hydrogen-bond interactionsG H - 0 , N-H--O, and C-H-0, using the formic acid-formamide complex and the formamide dimer in various geometric arrangements as examples. These motifs are understood as paradigms for ring structures in supramolecular 1:2 complexes of dicarboxylicacids with DMF, for which X-ray data are available. We found that a careful calibration of the theoretical methods is necessary in order to achieve a reliable estimate of the complex binding energy, since correlation contributions to the binding energy are non-negligible and the basis set superposition error must be taken into account. This has been accomplished in benchmark calculations on the formic acid dimer, in the course of which various basis sets have been studied and the influence of basis set and correlation on complex structure and binding energy has been determined. The studies suggest that correlation contributions and BSSE compensate to a large extent. Hence,
Neuheuser et al.
we decided to describe our target system by an SCF model without BSSEcorrection. From our calibration we estimated theaccuracy of the calculated binding energies to be around 5 kJ/mol. The conclusions based on this model are corroborated by MP2/TZ2P calculationswith and without CP correction, which were carried out in the most prominent cases. The calculations show that the weakest form of interaction, substantiated by the C-H-.O bond, still contributes a significant amount of -10 to -1 5 kJ/mol to the complex interaction energy. This gives an indication of the degree of packing effects present in the DMF complex of l,l’-binaphthy1-2,2’-dicarboxylicacid 1, where the X-ray structurelg reveals the presence of H-bonded ring structures as well as a noncyclic motif, indicatingthat crystal forces have partly overcome the energy difference to the ring structure, thelatter beiig theonly one present in the DMFcomplex of 9,9’-spirobifluorene2,2’dicarboxylicacid (2).M The hydrogenbonded rings found in the crystal structures correspond to the motif calculated as the most stable out of those feasible for DMF. In summary, we conclude from our calculations that the C-H-0 interaction is a non-negligiblesupramolecularrecognition mode despite the comparatively large distances involved.
Acknowledgment. This work has been funded by the Deutsche Forschungsgemeinschaft (SFB 334) and in part by the Fonds der Chemischen Industrie. The calculations were carried out on the workstations at theInstituteofPhysicalandTheoretica1Chemistry and on the NEC SX3 computer at the computing center K61n.
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