Formic acid tetramers: structure isomers in the gas phase

14 March 1997

CHEMICAL PHYSICS LETTERS Chemical

Physics Letters 267 ( 1997) 11 I-1 15

Formic acid tetramers: structure isomers in the gas phase Matthias Stein, Joachim Sauer Mwc-Planck-Gesellschaft, Arbeitsgruppe Quantenchemie an der Humboldt-Universitiit, Jiigerstrape 10-I 1, D-101 17 Berlin, Germany Received 17 December

1996; in final form 8 January

1997

Abstract HF. DFT and MP2 calculations are employed to predict the structures and stabilities of formic acid tetramers. Three nearly equally stable structures were identified: a stack of two dimers (“sandwich”, CI symmetry), a cyclic structure (S4 symmetry) and a “butterlly” structure obtained from the nearly planar cycle by folding. The latter was the global minimum when electron correlation was taken into account. DFT and MP2 yield the same energetic ordering but DFT overestimates hydrogen bonding. The stability is discussed in terms of two- and three-body contributions. @ 1997 Elsevier Science B.V.

1. Introduction It is well known that clusters of hydrogen-bonded molecules minimize their energies by assuming intermolecular structures in which the number of hydrogen bonds is maximised. For example, tetramers of water [ 1,2] and methanol [ 3,4] form rings stabilized by one hydrogen bond per monomer. Each OH group acts at the same time as proton donor and acceptor. The dimers of these molecules prefer an open linear structure with a single hydrogen bond rather than a cyclic structure with two highly strained hydrogen bonds. The situation is different with formic acid molecules which have two sites available for hydrogen bond formation. The OH group is the proton donor while another site, the CO group, acts as proton acceptor. It has been known for decades [ 51 that cyclic dimers, 1, with C2h symmetry are formed, wherein each formic acid molecule simultaneously acts as a hydrogen bond donor and acceptor (Fig. 1, top). To our knowledge, structures of formic acid tetramers have not been reported so far, neither in theoretical nor in experimental studies. We used 0009-2614/97/$17.00 @ 1997 Elsevier Science B.V. All rights reserved. PII SOOO9-2614(97)00060-2

quantum chemical ab initio calculations for structure predictions. Besides the Hat-tree-Fock (HF) method, density functional theory (DFT) and second-order Moller-Plesset perturbation theory (MP2) were employed to account for electron correlation effects.

2. Computational

details

In all the calculations the TURBOMOLE program of Ahlrichs et al. [6-83 was used. The HF calculations used the recently optimised split-valence polarisation basis set (SVP) including p-functions on H atoms [ 91. The density functional calculations (DFT) were performed using Becke’s three-parameter functional (B3LYP) [ 10,111. The DFT and MP2 calculations used a double-5 polarisation basis set (DZP) on the H atoms and a valence triple-[ contraction (TZP) on 0 and C [ 91. The exponents of the polarisation functions are 1.2 and 0.8 for d on 0 and C, respectively, and 0.8 for p on H. The contraction scheme is [511111/411] for 0 and C, and [31] for H. This choice of basis set guarantees that the BSSE is within

112

M. Stein, J. SauerlChemical Physics Letters 267 (1997) I II-I 15

tolerable limits, Corrections for the basis set superposition error (BSSE) were made by the usual function counterpoise method. The HF and DFT structures were characterised by diagonalisation of the harmonic force constant matrix as minima on the potential energy surface. HF force constants were obtained by analytical differentiation, DFT force constants by numerical differentiation. MP2 force constants have not been obtained.

1

3. Results and discussion The principle of maximising the number of hydrogen bonds suggests a cyclic structure of the formic acid tetramer in which all the monomer units are equivalent. A second possibility of forming a cluster with four hydrogen bonds is a stack of two dimer units. Indeed, both a stack of two dimer units twisted by 135 degrees, 2 (Cl point group, Fig. 1, bottom) and a puckered ring structure 3 (Sq symmetry, Fig. 2, top) proved to be minima on the potential energy surface. Table 1 shows the interaction energies which are corrected for the basis set superposition error (BSSE). The stacked tetramer is stabilised by 112.6 kJ mol-’ and the ring is less stable than the stack structure by 3.8 kJ mol-t (MP2 results). To our surprise the calculations revealed a third stable structure: the cyclic structure can “fold” to yield a “butterfly” type structure, 4, retaining its Sq symmetry (Fig. 2, bottom). Two formic acid molecules opposite in the ring are folded up and the other two are folded down. The symmetry axis is perpendicular to the planes spanned by C and 0 atoms of opposite monomers. The mirror plane is orthogonal to the C axis and bisects all four hydrogen bonds. It turns out to be the most stable formic acid tetramer structure when electron correlation is taken into account (2 kJ mol-’ more stable than the stack of dimers). The close contact of monomer units that are opposite in the cyclic structure leads to an energy gain. In addition, this structure profits from an uninterrupted chain of hydrogen bonds which is also present in the cyclic tetramer. The different contributions to the stabilisation of different isomers become obvious when an analysis is made in terms of n-body contributions. The BSSEcorrected interaction energy, AE, defined as

Fig. 1. The cyclic dimer (Czh) symmetry, top) and the sandwich tetramer (Cl symmetry, bottom) of formic acid. Al? = EABcD -

c

Ei(jk[)//ABCD i

+ CCEi//ABCD i is decomposed AG,,,,

= EABCD

(1)

- Ei)

into the intermolecular - c

Ei(jkl)/jABCD9

energy,

(2)

i and the deformation

energy,

( Ei//Anco - Ei) .

A&form = C

(3)

i ABCD denotes the tetramer, i(jkZ)//ABCD is the monomer i in the presence of the basis set of the other monomers and in the structure of the complex, i//ABCD is the monomer i in the presence of the basis set of this monomer only, but in the equilibrium structures of the tetramer and i is an isolated monomer

M. Stein, J. Sauer/Chemicul

Physics Letters 267 (1997) I I I-1 15

113

Table I Interaction energies for the dimer and different tetramer structures of formic acid and the decomposition into n-body contributions (kJ mol-‘) 1

2

3

4

Dimer

Stack

Cycle

Butterfly

AE (HF/SVP) AE (B3LYP/T(O,C)DZP) AE (MK!/T(O,C)DZP)

-55.0 -64.3 -52.5

deformation intermolecular

+11.0 -63.5

4-body 3-body 2-body

-114.2 -116.8 -129.0 -127.2 ’ -I 12.6 -108.8

-63.5

H-bonded through space

-63.5

AE(MP2)

-45.0

+ AZPE(B3LYP)

’

-115.8 -130.2 -114.6

+22.8 -135.4

+16.1 -124.8

+20.1 -134.7

$0.1

-2.6

+I.5

-1 .O -21.2 -134.4 -95.0

-26.7 -109.5

-127.8 -6.6

-87.1 -7.9

-89.1 -20.4

-97.5

-93.8

-99.8

a Ref. [ 121, -52.8 and -43.6 kJ/mol for AE and AE + AZPE, respectively.

4 Fig. 2. The cyclic tetramer (S4 symmetry, top) and the “butterfly” structure (S4 symmetry, bottom) of the formic acid tetramer.

in its equilibrium structure. The intermolecular energy can be decomposed into two-body (six terms), threebody (four terms) and four-body (one term) contributions, e.g. the BSSE-corrected two-body interaction between monomers A and B is defined as AE:B

= EAB(CD)//AB~D

-EB(ACD)//ABCD'

-EAWXJ~IIABCD

(4)

The three-body and four-body contributions are defined similarly. Table 1 shows the results for the MP2 interaction energies. The deformation energy is largest for the largest intermolecular energy. The four-body term is negligible for all isomers, but there is a significant three-body term for the cycle and the butterfly, while this term is nearly zero for the stack. In the cy-

cle and the butterfly the three-body contribution is an expression of the cooperativity in a closed chain of Hbonds. A particular monomer donates its OH proton to its one neighbour, but accepts the OH proton from the other neighbour. In the stack, both donor and acceptor interactions occur with the same partner. The stabilisation of the stack which results from a twobody interaction between two monomers in different pairs (“through space”) makes a tiny contribution to the total pair interaction, much smaller than one might have thought. The decomposition also nicely illustrates the “driving force” for the conversion of the cycle into the butterfly structure. While the cooperativity effects (three-body) and the two-body interactions between direct neighbours are about the same in both isomers (27 and 88-89 kJ mol-' , respectively), the “through space” two-body interactions between opposite monomers are significantly more stabilising (by 12.5 kJ mol-‘) for the butterfly structure than for the nearly planar cycle. The net difference in stability is smaller (5.8 kJ mol-‘) since the close proximity of the monomers in opposite positions raises the destabilising deformation energy and makes the four-body contribution repulsive. All the tetramer clusters exhibit an extra stabilisation compared to the two separate dimers. The energetic ordering of the tetrameric clusters is maintained

I14

M. Stein, J. Sauer/Chemical

and the preference for the “butterfly” structure even slightly more pronounced when zero point energies (ZPE) are taken into account (Table 1 gives MP2 stabilization energies to which ‘harmonic’ zero point energies at the DFT level were added). At the HF level the stability of the cyclic tetramer is overestimated. It is calculated to be the most stable tetramer at this level. If, however, electron correlation is included (MP2), the stacked tetramer gains stabilisation energy and the “folded” tetramer becomes the global minimum structure. Density functional calculations reproduce the MP2 stability sequence, but yield systematically larger stabilisation energies than the MP2 method. Table 2 gives H-O bond lengths as well as 0. . .O distances. Upon dimerisation the H-O bond is stretched from 97.8 pm in the monomer to 100.5 pm in the dimer (MP2). MP2/D95++(d,p) calculations [ 121 yield 97.4 and 99.7 pm, respectively. The experimental values [ 131 yield 97.2 pm for the monomer and 103.3 pm for the dimer. The H-O bond lengths are all similar for different tetrameric clusters, ranging from the shortest bond length of 99.9 pm in the cycle to the longest ( 100.4 pm) in the stack. HF consistently gives shorter H-O bond lengths whereas DFT overestimates these. The 0. . .O distance in the planar dimer is 267.7 pm at MP2 which is in agreement with Ref. [ 121 (269.8 pm). The experimental value is 269.6 pm [ 131. The 0. . .O distance is shortest in the butterfly (267.7 pm at MP2) and longest for the cycle (268.8 pm). The 0. . .O distance slightly extends when two dimers are stacked to form the sandwich structure (267.7 pm in the dimer, 268.0 in the stack at MP2). Still, the stack is lower in energy than the two separate dimers. HF gives 0. . .O distances which are about 7-8 pm longer compared to MP2 while those of DFT are shorter than MP2. The smallest deviation of DFT from MP2 (about 0.6 pm) is observed for those structures almost exclusively described by twobody interactions (dimer and stack), the largest (1.7 to 1.9 pm) corresponds to those tetramers with large three-body contributions (cycle and butterfly). As expected, the OH bond in the tetramers is significantly stretched by H-bond formation compared to the monomer. In the stack, the OH distance is about the same as in the dimer. In the butterfly structure, the OH bonds are not as long as in the stack although the total stabilisation is larger. However, from the decomposition analysis we learnt that about 20 kJ mol-’ of the stabilisation energy of the butterfly structure is

Physics Lptters 267 (I 997) 111-I 15

Fig. 3. Hypothetical models for self-assembling complexes adapted from Ref. [ 141.

supramolecular

due to “through space” pair interactions which do not contribute to stretching of the OH bonds. This means that the OH vibrational bands of the stack may be expected at about the same position as that of the dimer, while the OH bands of the butterfly structure may be less red-shifted and close to the bands of the cycle. Hence, these structure predictions of the three nearly equally stable isomers could provide a clue for understanding the numerous IR bands observed by Huisken et al. for formic acid tetramers in the gas phase [ 151. In a review article discussing self-assembling of supramolecular complexes, Lawrence et al. recently put forward a general hypothetical model system for the self-assembly of sub-units by a head-to-tail interaction [ 141. They mentioned the possible existence of several spectroscopically indistinguishable structure “isomers” (Fig. 3). These are exactly the structure types we found for a system as small as the formic acid tetramer. The most stable “butterfly” structure shows the same head-to-tail interaction pattern as the cubeshaped structure (bottom right of Fig. 3). The structure forming principles discussed in this Letter do not seem to be limited to tetramers. There are indications that also for hexamers a stack consisting of three dimers and a “W’‘-shaped B-membered ring belong to the stable structures.

M. Stein, J. Sauer/Chemical Table 2 Characteristic Bond

H-O

0.

distances

Method

Monomer

95.10 97.83 97.82 p

HFISVP B3LYP/T(O,C)DZP MPZ/T(O,C)DZP

1

2

3

4

Dimer

Stack c

Cycle

Buttertly

96.65 101.16 100.50 L

96.59 101.08 100.42

96.5 I 100.50 99.93

96.60 100.7 1 100.08

276.7 267. I 267.7 h

276.9 267.4 268.0

275.8 266.8 268.8

275.2 266.0 267.7

a The values from Ref. [ 121 are 97.4 and 99.7 pm, respectively. h Ref. [ 121 gives 269.8 pm. C Due to the Ct point group there are four slightly different values. The differences

Acknowledgements This project was supported by the “Fonds der chemischen Industrie”. We are grateful to Mr. S. Hoffmann who first identified the “butterfly” structure by force field methods during the course of his final year project.

References ] I ] J.D. Cruzan, L.B. and R.J. Saykally, 12 ] S.S. Xantheas and 8774. [ 3 1 F. Huisken and M. 391. [4] A. Bleiber and J. preparation.

115

in clusters of formic acid in pm

HFISVP B3LYP/T(O,C)DZP MP2/T(O,C)DZP

.o

Physics Letters 267 (1997) 1 I I-l 15

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