Ab initio SCF and møller-plesset calculations on the hydrogen bond in hydrogen maleate

Journal of Molecular Structure (Theo&m), 209 (1990) 411-419 Elsevier Science Publishers B.V., Amsterdam

AB INITIO SCF AND MBLLER-PLESSET THE HYDROGEN BOND IN HYDROGEN

CALCULATIONS MALEATE

411

ON

M. HODOSCEK and D. HAD&* Boris KidriE Institute of Chemistry, 61115 Ljubljana, P.O. Box 30 (Yugoslavia) (Received 20 February 1996)

ABSTRACT Energies of the hydrogen maleate anion were calculated for the proton located centrally (C,, symmetry) and off centre of the hydrogen bond (C, symmetry) using the STO-3G, 4-31G, 6-311G, 6-31+ + G and 6-31G** basis sets with the Msller-Plesset (second order) (MP2) correlation correction on the 4-31G and 6-311G optimized geometries. The adiabatic proton potential barrier at the Hartree-Fock level is highest with the 6-311G calculation (2.12 kcal mol-I), but MP2 correction reduces it to 0.1 kcal mol-‘. Non-adiabatic barriers are substantially higher. The solvation effect, calculated with a model reported previously, raises the barrier slightly. Geometrical parameters are discussed with respect to the possible strain imposed by the hydrogen bond.

INTRODUCTION

Interest in the structure of dicarboxylate monoanions with possible intramolecular hydrogen bonding was kindled primarily by the anomalous ratio of the first and second ionization constants of the acids [l]. This ratio is outstanding with maleic acid and the existence of the potentially symmetric intramolecular hydrogen bond in its monoanion (HME) has been confirmed by X-ray diffraction [ 21 and neutron diffraction [ 3,4] in solid salts. Hydrogen bonding in HME has been investigated in more detail by various spectroscopic methods in both solids and solutions [ 561. For all practical purposes the hydrogen bond in HME indeed appears to be of the symmetrical single-minimum type unless influenced by asymmetric surroundings [ 71. CNDO/B and ab initio calculations with a minimal basis set [8,9] resulted in a single-minimum potential, but with the 4-31G basis set gave a non-negligible potential barrier of 1.37 kcal mol-’ [lo]. A recent analysis of the isotope effects occurring in the titration of maleic acid, as followed by NMR techniques, indicated the existence of an equilibrium between the protomeric forms *Also at iek-Pharmaceutical and Chemical Works, Ljubljana. Address for correspondence: P.O. Box 30,61115, Ljubljana, Yugoslavia.

412

of HME [ 111. This further increases the interest in the proton potential of HME and, particularly, in its sensitivity to medium effects. The anomalous ratio of the dissociation constant of malonic acid, though less pronounced, has also been connected [l] with the existence of an intramolecular hydrogen bond in hydrogen malonate (HMO). Although HMO indeed appears in some of its salts in this form (see Ref. 12 and references therein), the existence of the intramolecular hydrogen bond in aqueous solution of potassium HMO was disputed because of vibrational spectroscopic data [ 131. However, more recent NMR results on 13C shifts as a function of the degree of dissociation were interpreted in terms of intramolecular hydrogen bonding [ 141. Theoretical calculations, though at low level, favour symmetrical hydrogen bonding in HMO [ 15 1. Results of theoretical calculations on proton potentials are notoriously sensitive to basis set and effects of electron correlation (see Ref. 16 and references therein). The existing calculations on HME and HMO cannot be considered as satisfactory by present standards and, therefore, need to be improved in order to find out whether in these two anions the tendency towards formation of a centred, single-minimum type of hydrogen bond is inherent or not. However, more challenging than the question of a minor potential barrier in the isolated anions is the response of the potential to medium effects, particularly of the aqueous medium. The latter requires investigation by molecular dynamics or Monte-Carlo methods. However, as a preamble to the former type of theoretical approach to the solution behaviour of HMO, in which the very existence of intramolecular hydrogen bonding in aqueous solution is questionable, we wanted to re-examine by quantum chemical calculations the hydrogen bonds in isolated HME and HMO and to extend the calculations to the effect of hydration by using the method of Miertug et al. [ 171. There is, unfortunately, no possibility of checking the results of theoretical calculations of the proton potential in isolated HME and HMO anions against experiment, as is the case with hydroxyacrolein [ 181. The principle of trusting only the highest-level calculations is elusive in the case of HME and HMO, not only because of the size of the molecules, but also because of the need to extend the calculations to medium effects. This situation prompted us to examine several basis sets in order to find a compromise between reliability and economy in computer time and to lend more credence to the computational results. In this paper we report the results obtained with HME and in a companion paper the analogous work on HMO will be described [ 191. The parallel examination of the two anions with similar, intramolecular hydrogen bonding should contribute to a better understanding of this bonding. Moreover, the application of various basis sets to the same type of molecules should be useful in making proper selection for future work.

413 COMPUTATIONAL DETAILS

GAUSSIAN 86 suite of programs was used throughout with standard basis sets [20]. The initial geometry of HME was taken from ref. 3. Geometry optimizations (the atom numbering is shown in Fig. 1) by the standard-gradient method were carried out under C, and CZVsymmetry, respectively. The optimization criterion was a maximum force less than 45 x 10m5a.u. Geometry optimization without any constraint was also carried out using the 4-31G basis set. The MP2 corrections for correlation were applied to SCF optimized geometries keeping the core frozen. The method of MiertuL et al. [ 171 was used to simulate medium effects. The solvent cavity used in this method was formed from spheres centred on atoms with radii derived from Mulliken population charges according to ref. 21. RESULTS AND DISCUSSION

The total energies and energy differences (hE) of HME calculated with the constraint to CzVsymmetry, i.e. with a centrally located proton, and under optimization to the planar structure (C, symmetry) are given in Table 1. The classical potential barrier (AE) is highest in the 6-311G basis calculation followed by the 6-31G basis augmented by diffuse or polarization functions and the lowest value is yielded by the 4-31G basis. The latter value is in complete agreement with a previous calculation [lo] using the same basis set. It is useful to compare at this point the results [ 221 obtained using the 4-31G and 6-31G** basis sets, on the intramolecularly hydrogen-bonded anion, ( H302 ) -, in which there were no constraints on the hydrogen-bond geometry. For the asymmetric $xucture which has the lower energy at the SCF level the 0. *00 distance (2.501 A) calculated with the 6-31G** basis set is larger than one calculated with the smaller base (2.45 A) whereas the inverse is true of AE (0.21 and 0.77 kcal mol-‘, respectively). The 0. 0 distances are larger in ( H302) - and yet AE are smaller than with HME (by 1.16 and 0.83 kcal mol-*). The shorter O* *-0 distance in HME is, however, not imposed by the skeletal constraint, reflected in the large C-C=C angles [ 71, since quite similar distances result from call

07

l

06

Fig. 1.Atom numbering of hydrogen maleate.

414 TABLE 1 Energies (in a.u. ) of hydrogen maleats SCF computed by various basis sets and with second-order Msller-Plesset corrections Basis set

STO-3G 4-31G 4-31G/MP2 6-311G 6-311++G 6-311G/MP2 6-31G**

Symmetry

AE (kcal mol- ’ )

C,

C2V

- 446.568860 -452.057146 -452.904012 - 452.640196 -452.546017 - 453.551393 - 452.738355

- 446.568860 - 452.054960 - 452.903941 -452.636812 -452.542999 -453.551390 - 452.735727

0.0 1.37 0.04 2.12 1.89 0.1 1.65

culations on hydrogen diformate [ 231 in which the 0 *- -0 distance is also free of skeletal constraints. However, the higher barriers in the proton potential of HME relative to ones calculated with the same basis sets for ( H302) - appear genuinely to reflect the differences in the electronic character of both anions. Calculations on HMO and hydrogen formate [ 231 support this conclusion. By constraining the geometry to C,, symmetry the 0. -0 distance in HME shrinks similarly as in the case of ( H302) - and the O-H-O angle opens up but does not reach 180”, except with the minimal base. Inclusion of correlation effects by using the Msller-Plesset perturbation theory to second order (MP2) on the SCF geometries lowers AE but the C, structure still remains more stable. Unfortunately, the size of the molecule precluded a geometry optimization under MP2. The reduction in AE by correcting for electron correlation is a wellknown effect which has been rationalized by Rohlfing et al. [ 221, particularly for the case of potentially symmetric hydrogen bonds. In addition to the calculation of the barrier height under geometry optimization that corresponds to the proton transfer with adjustment of the heavy atoms (adiabatic case ) we explored the potential for fast proton motion. This calculation was limited to three points (besides the one corresponding to the energy minimum) on the 01-05 line. The skeletal atoms were frozen in the C, structure, but the angular parameters of the proton were relaxed. The resulting non-adiabatic barriers are considerably higher (4.0 and 5.3 kcal mol-’ with the 4-31G and 6-31G** basis sets, respectively) than the adiabatic ones. The curve obtained by cubic spline interpolation is shown in Fig. 2. Although the present calculations do not provide the final answer concerning the barrier in the proton potential in HME, they indicate that the adiabatic barriers, vanishingly small and likely to be lower than the lowest OH0 stretching frequency that was found in potassium HME to be 372 cm-’ [5]. Such a low barrier should not cause any splitting of vibrational levels and indeed no l

415

08

09

10

11

1.2

1.3

'O-H

Fig. 2. Energy of hydrogen maleate as a function of proton position (05-HlO). (0 ) 6-31G** calculations (energy minima set to zero).

(X

)

4-31G and

indication of splitting has been observed [ 51. Since the isotope effect in NMR shielding is also based on differences in vibrational parameters it is not surprising that the observed value [ 61 did not reflect the existence of a barrier. In contrast to the hydrogen bond in hydroxyacrolein [ 181 the barrier in HME may be considered to be vanishingly low and this confirms the general contention that in anionic systems the barrier is much lower than in neutral ones. Recent NMR investigation on the perturbation by ‘*O substitution of the dissociation equilibrium of maleic acid has led to the conclusion that in the aqueous solution HME exists in two protomeric structures [ 111. It is quite possible that water molecules perturb the proton potential by specific interactions with HME and even charges induced by a solvent cavity might be effective in doing so. We have explored the latter possibility by applying the method of Miertug et al. [ 171 at the 4-31G basis-set level. However, the solvation energies of the C, and CpVstructures are only slightly different so that AE increases to 1.99 kcal mol-l. The relative stabilization of the C, structure by the solvent reaction field is understandable by considering the more asymmetric charge disposition in this structure. The resulting barrier is hardly sufficient to explain the observed isotope effect, but it is quite possible that the overall geometry is influenced by the effect of the aqueous medium which is not covered by the present calculation in which the initial geometry is preserved. Moreover, the dynamic properties of water [ 241 may be quite important in influencing the effective proton potential. The most interesting skeletal features are the angles subtended by the C-C and C=C bonds. The experimental value of these angles of ca. 130’) closely met by calculation, is considered to be so wide because it takes up the strain imposed by the hydrogen bond if the other bond angles and bond lengths are taken at their normal values [2,7]. Calculated parameters are collected in

416

Table 2 and experimental values representative of both the symmetric [ 2 ] and asymmetric [ 71 structures are listed for comparison. Although experimental values obtained for crystals are not strictly comparable with ones calculated for HME in vacua, the overall agreement is satisfactory if the known tendencies of the basis sets [ 2.51 are taken into account. Thus we briefly examine here the trends in geometrical parameters computed with the various basis sets. The addition of the polarizing functions tends to shorten the double bonds and lengthen the C-C single bonds. With this exception, increasing complexity of the basis sets, including the addition of diffuse functions, tends to elongate all bonds except for the C=C bond in the CBVstructure, which is too short relative to the experimental data with any base, and the C2-06 bond in the C, structure. The trends in the C-C bonds in the C, structure (longer on the protondonating side and shorter on the proton-accepting side) were reproduced correctly by all basis sets. The sum of the two C-O bond lengths is an appropriate quantity for evaluating basis-set performance. The statistical average over many experimental values (2.522 A [26] ) is slightly exceeded [2,7] with HME in the C, (2.526 A) but not in the CaVstructure (2.519 A). The average values for the C, structure are well approached in the callations using the simple basis sets (43-lG, 2.518 A; 6-311G, 2.52 A), exaggerated by 6-31+ +G (2.539 A) and underestimated by the 6-31G** (2.469 A) basis sets. The same trend is observed with the average calculated for the C,, structure (2.521,2.526,2.530 and 2.482 A, respectively). The bond lengths are unlikely to be influenced by the strain, but the O-CC angles might be affected by it. However, the experimental values are close to 120’ and the computed ones tend to be rather smaller. Thus no clear indication of the strain shows up in either bond lengths or angles except for those at the double bond. However, not all the excess over the usual angle of 120’ seems to be due to strain relief. The C-C=C angle in the acrylic anion, which represents a fragment of HME, was calculated [ 271, with the 4-31G basis set, to be 123.7”, a value close to the experimental one [ 281. Furthermore, using the same base we calculated [ 281 the optimized geometry of the maleate dianion. One of the carboxylate groups is rotated by 10” out of the plane of the remaining skeleton thus relieving the repulsion between the oxygen atoms, but the C-C=C angles are 131.7” and 135.5’. Apparently bonding conditions in the conjugated carboxylic anions are somewhat peculiar and we plan to investigate these in more detail. Concerning the performance of the various basis sets, we conclude that the differences between the smallest split-valence basis set used and the more flexible ones are not dramatic with regard to the height of the potential barrier and the geometrical parameters. Major differences are expected to appear in the calculations of, for example, anharmonic force constants. However, such calculations and employment of even higher levels of theory would be justified only if appropriate experimental data were available for comparison. In conclusion, the difference in energy (AE) between the structure with the

417 TABLE 2 Selected geometrical parameters of hydrogen maleate calculated with various basis sets under full optimization and with constraint to CzVgeometry STO-3G Bond lengths (A) 05-H10 lb 2

4-31G

6-311G

6-31+ +G

6-31G**

Exp.

1.160 1.160

1.017 1.187

1.000 1.183

1.011 1.188

1.004 1.178

1.079 (1.218)

2.319 2.319

2.464 2.363

2.481 2.358

2.484 2.365

2.474 2.355

2.445 2.437

01-05

1 2

05-HlO-01

1 2

c4-05

1 2

1.323 1.323

1.314 1.292

1.318 1.295

1.317 1.295

1.296 1.272

1.304 1.284

c4-07

1 2

1.240 1.240

1.221 1.229

1.223 1.231

1.227 1.235

1.202 1.210

1.228 1.235

c2-01

1

1.323

1.272

1.275

1.275

1.251

1.268

C2-06

1

1.240

1.229

1.231

1.295

1.218

1.251

C2-C3

1 2

1.551 1.551

1.515 1.502

1.512 1.501

1.516 1.504

1.531 1.515

1.503 1.498

c3-Cl1

1 2

1.318 1.318

1.326 1.325

1.330 1.329

1.333 1.333

1.328 1.327

1.343 1.348

c4-Cl1

1

1.551

1.489

1.489

1.493

1.502

1.493

180.0 180.0

166.1 169.3

165.7 170.0

165.3 169.3

173.2 176.0

176.1 (180)

Bond angles (“) C2-C3-Cl1 1 2

129.7 129.7

131.5 130.7

131.5 130.7

131.4 130.6

131.6 130.4

130.6 130.4

c3-Cll-c4

1

129.7

131.9

132.1

132.0

131.6

130.4

C3-C2-01

1 2

118.7 118.7

117.9 118.3

117.8 118.3

118.1 118.5

117.6 118.0

120.2 120.3

06-C2-01

1 2

124.4 124.4

127.3 125.0

127.3 124.8

127.1 124.7

128.2 125.6

123.0 122.7

Cll-c4-05

1

118.7

119.9

120.2

120.3

119.4

120.5

07-c4-05

1

124.4

121.9

121.5

121.6

122.4

120.9

“C,, symmetry: Ref. 2. C, symmetry (approximate): Ref. 7. bl and 2 refer to C, and Cpysymmetry, respectively. Under C, geometry C2-01 equals C4-05, C2-06 equals C4-07, C2-C3 equals C4-Cll, and C2-C3-Cl1 equals C3-Cll-C4.

418

proton centred between the oxygen atoms (C,, symmetry) and the fully optimized structure (C, symmetry) is very small when calculated at the HF level with any of the basis sets used and is decreased further if the energies are corrected for correlation at the MP2 level. However, the energy of the C, structure remains slightly lower. The proton potential is, at any rate, very flat which is in agreement with the low OH0 stretching frequencies observed in the vibrational spectra of potassium hydrogen malonate [ 51 and the absence of isotope effect on NMR chemical shifts [ 61. The potential barrier is raised slightly by the medium effect. Consideration of bond lengths and angles in HME and the comparison with hydrogen-bond dimensions [ 22 ] in ( H302) - suggest that the hydrogen bond in HME is not influenced to any major extent by the molecular skeleton but that it is the angle subtended by the C-C=C bonds that yields to the hydrogen-bond extension. ACKNOWLEDGEMENT

This work was supported by the Research Community of Slovenia. Thanks are due to Professor J. Tomasi for the program calculating the solvent effect.

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