摘要:

Ab initio study of the p*�n electronic transition in formic acid–(water)n (n = 1, 2) hydrogen bonded complexes Gustavo Velardez,a† Jean Louis Heully,b J. Alberto Beswicka and Jean Pierre Daudeyb a Laboratoire Collisions, Agrégats, Réactivité (LCAR). Unité Mixte 5589 du CNRS, IRSAMC, Université Paul Sabatier, 31062 Toulouse, France bLaboratoire de Physique Quantique, Unité Mixte 5626 du CNRS, IRSAMC, Université Paul Sabatier, 31062 Toulouse, France Received 21st May 1999, Accepted 7th June 1999, Published 14th June 1999 Hydrogen bonded complexes of formic acid with one or two molecules of water have been studied using multiconfigurational SCF and second-order perturbation theory (CASSCF/CASPT2). Equilibrium geometries in the ground electronic state, S0, and vertical S1�S0 transition energies have been calculated for the three 1 : 1 complexes, and four 1 : 2 conformers found.The most stable conformers are the six-membered ring structures for the 1 : 1 and 1 : 2 complexes in agreement with previous calculations. All vertical transitions are blue-shifted with respect to the corresponding monomer transition. The paper is organized as follows. Section 2 presents the methodology and the results of our calculations. Sections 3 and 4 are devoted to the discussion and the conclusions. 1 Introduction Hydrogen bonding and intra- and intermolecular proton transfer are of paramount importance to understand a great number of structural and dynamical processes in chemistry and biochemistry1,2 and thus have received considerable attention both from theoretical3 and experimental points of view.4 The structures of biomolecules such as peptides and proteins, carbohydrates and nucleic acids, are influenced by the presence of water molecules, in turn leading to changes in their biological activity.Proton-bound clusters are known to form hydrogen-bonded networks which may form solvation shells surrounding a central core ion5 or have chain-like structure. There is a considerable amount of theoretical information about structures, dynamic and spectroscopic data for different complexes with hydrogen bonds such as water clusters6 and water bound to polyatomic molecules.7 Mixed clusters of water and formic acid for instance have been studied by electron impact.8 Minyaev9 has studied the double proton transfer and also obtained the structures of ground and transition state for 1 : 1 complex of formic acid–water by ab initio calculations at the RHF/6-31G** and MP2(full)/6-31G** levels. Similarly, Andrés et al.have obtained the structure of the transition state for proton transfer in solution considering the 1 : 1 and 1 : 2 complexes of formic acid–water at the HF/6-31+G* level.10 Recently, the structures of the most stable 1 : 1 conformers of formic acid–water have been obtained7,11 and Ha et al.12 have used those results in order to interpret their microwave experiments with formic acid– (water)n (n = 1, 2).13 In this work we present a study of the p*�n electronic transition in formic acid(water)n (n = 1, 2), using the complete active space SCF method (CASSCF)14 and multiconfigurational second-order perturbation theory, (CASPT2).15 The CASSCF/CASPT2 method has been applied to a variety of chemical problems in the last years and has been shown to give accurate results for molecular structure, binding energies and other properties not only for molecules with normal chemical bonds, but also for molecules in excited states and for weakly bonded systems.16,17 PhysChemComm, 1999, 6 2 Methodology In order to find the different conformers of HCOOH– (H2O)n, (n = 1, 2), the ground potential energy surface landscapes of the complexes has been explored in a first approximation by performing HF/6-31G** calculations with GAUSSIAN-92.18 With these initial inputs, the geometries of different conformers were optimized at a complete active space (CASSCF) level of theory.The CASSCF formulation stresses the effects of non-dynamic correlation.19,20,21 The geometries of different conformers have been optimized without symmetry constraints to yield energy minima with Cl symmetry using an atomic natural orbitals (ANO) basis set22–25 provided by the MOLCAS 4.0 program.26 For the calculations, the number of active orbitals was 2 (the last occupied and the first unoccupied) and the number of active electrons was 2 (valence electrons). The rest of the orbitals are inactive. The calculated bond-lengths and angles are given in Tables 1 and 2 for the 1 : 1 and 1 : 2 complexes, respectively.The dynamic correlation effects are treated by second order perturbation theory with the CASSCF wavefunction as the zeroth-order component (CASPT2).27,28 The zeroth-order Hamiltonian is defined as a sum of Fock-type one-electron operators such as in Møller–Plesset (MP) perturbation theory is obtained in the limiting case of the zeroth-order reference being the closed-shell single-determinantal wavefunction. Using the CASSCF wavefunction as a reference function, the CASPT2 method was used to compute the first-order wavefunctions and the second-order energies in the full CI space without any other approximation. The basis-set, symmetry and orbitals were the same as those in CASSCF calculations. The binding energies for the different conformers were computed as: BE = E(complex) - E(HCOOH) - nE(H2O) (1)Table 1 Geometrical parameters of formic acid, alone and in 1 : 1 complexes.The distances are in Å and angles in degrees H1C2 C2O5 C2O3 O3H4 <H1C2O3 <H1C2O5 <O5C2O3 <C2O3H4 O5H6 H4O7 H1O7 O3H6 Table 2 Geometrical parameters of 1 : 2 complexes. The distances are in Å and angles in degrees H1C2 C2O5 C2O3 O3H4 <H1C2O3 <H1C2O5 <O5C2O3 <C2O3H4 O5H6 O7H4 O10H4 O7H4 H8O10 H1O10 O3H9 O5H9 where E(complex), E(HCOOH) and E(H2O) have been calculated at the optimized ground state geometry at the same level of theory. E(complex), E(HCOOH) and E(H2O) in eqn. (1) include the corresponding zero point energy (ZPE) which was estimated by its simplest approximation: ) 2 / 1 ( ZPE åh ni (2) i = where ni is the frequency for mode i obtained at the optimized geometry and corrected by a scale factor of 0.9.29 The binding energies defined in this way are affected by the basis set superposition error (BSSE), which has been estimated using the counterpoise procedure.30–33 The counterpoise correction, CP, is the sum of differences in the energies of the constituent monomers in the geometry of the supermolecule with and without the full basis of the whole aggregate. For 1 : 1 conformers, the CP correction was applied to the HCOOH + H2O pair.For the C1:2#1 and #2 the CP correction was applied to the HCOOH + 2H2O pair while for the C1:2#3 and #4, C1:1#1 + H2O was considered.This method has been discussed in the literature at large and there are arguments in favour and against the counterpoise correction. A discussion of these different C1:1#2 C1:1#1 1.082 1.190 1.341 0.954 111.3 124.2 124.4 110.2 2.085 1.108 1.110 1.310 0.960 110.4 123.4 126.2 110.8 2.141 1.916 2.975 C1:2#2 C1:2#1 1.087 1.185 1.305 0.961 110.4 123.3 125.7 110.4 2.512 1.108 1.194 1.301 0.967 110.6 122.5 126.9 113.0 1.939 1.877 1.781 1.822 2.002 HCOOH C1:1#3 1.083 1.193 1.332 0.955 110.6 124.6 124.8 109.8 1.082 1.197 1.326 0.953 110.4 125.4 124.1 110.1 2.948 2.135 C1:2#4 C1:2#3 1.083 1.197 1.310 0.955 112.1 122.9 125.0 110.9 2.458 1.082 1.191 1.323 0.955 111.5 123.9 124.6 110.7 2.401 1.902 1.900 3.259 3.023 2.153 2.085 approaches is beyond the scope of this article.The counterpoise correction is an approximate but successful method for correcting basis set deficiencies in the calculation of the monomers.34 The calculated bond-lengths and angles are given in Tables 1 and 2 for the 1 : 1 and 1 : 2 complexes, respectively. The calculated total, relative, and binding energies, for the 1 : 1 and 1 : 2 complexes are presented in Tables 3 and 4 respectively. The values of the total energies for the monomers, HCOOH and H2O, are also given in Table 3. For the optimized geometries of the conformers, the first vertical trans, S1�S0 were calculated at CASSCF and CASPT2 level of theory.In the calculation of the S1 energy with S0 geometry, the number of active orbitals was 5 and the number of active electrons was 6 (valence electrons): two orbitals with 2 electrons, two orbitals with 1 electron and the last orbital remained unoccupied. The rest of the orbitals were inactive with 2 electrons in each one. Similar calculations were done for free HCOOH and the corresponding spectroscopic shifts induced by the complexation were determined for all the complexes. These values are given in Tables 5 and 6.Table 3 Total energies (E/hartrees), zero point energies (ZPE/hartrees), total energies corrected by ZPE (Ezpe/hartrees), relative energies (DE/kJ mol–1), binding energies (BE/kJ mol–1) and binding energies corrected by the counterpoise method (BEcp/kJ mol–1) for 1 : 1 complexes HCOOH H2O C1:1#3 C1:1#2 C1:1#1 EEE HF CASSCF CASPT2 –76.01075 –76.10417 –76.26170 0.02298 –76.24102 –188.76231 –188.85157 –189.34568 0.03705 –189.31233 ZPE BE EDEzpe –264.78182 –264.91991 –265.63143 0.06305 –265.57468 40.3 40.6 13.6 –264.77875 –264.92171 –265.63357 0.06231 –265.57749 32.9 46.3 27.0 –264.79027 –264.91751 –265.64788 0.06429 –265.59002 083.8 54.8 BEcp Table 4 Total energies (E/hartrees), zero point energies (ZPE/hartrees), total energies corrected by ZPE (Ezpe/hartrees), relative energies (DE/kJ mol–1), binding energies (BE/kJ mol–1) and binding energies corrected by the counterpoise method (BEcp/kJ mol–1) for 1 : 2 complexes C1:2#4 C1:2#3 C1:2#2 C1:2#1 HF CASSCF CASPT2 EEEDEzpe EE Dzpe –340.80966 –340.96794 –341.91630 0.08789 –341.83720 59.5 14.0 0.5 –340.80702 –340.98693 –341.91869 0.08969 –341.83797 57.5 19.3 1.2 –340.81154 –340.98944 –341.92117 0.08992 –341.84024 51.5 109.6 72.1 –340.81939 –340.98895 –341.94219 0.09147 –341.85987 0164.8 123.7 BE BEcp Table 5 DE n for transitions S1�S0 and blue-shifts with respect to HCOOH alone (eV) for 1 : 1 complexes HCOOH C1:1#3 C1:1#2 C1:1#1 CASSCF 4.842 5.125 0.283 5.281 0.438 5.172 0.329 DE n dblue CASPT2 5.824 5.899 0.075 5.965 0.142 6.258 0.435 DE n dblue Experiment39 5.83 C1:2#4 C1:2#3 C1:2#2 C1:2#1 DE n Table 6 DE n for transitions S1�S0 and blue-shifts with respect to isolated HCOOH (eV) for 1 : 2 complexes CASSCF 4.859 0.017 5.423 0.581 5.409 0.566 5.195 0.352 DE n dblue CASPT2 DE n dblue 5.861 0.037 5.864 0.040 6.047 0.223 6.157 0.333 3 Results and discussion Fig.1 Calculated optimized geometries of HCOOH–H2O complexes. 3.1 Ground state 1 : 1 conformers For complexes of carboxylic acids with water, the potential energy surfaces generally have multiple minima with quite different binding energies. In the ground electronic state (S0) three conformers are found for the 1 : 1 complex.They are represented in Fig. 1.Table 7 Comparison between experimental and calculated band origin for the S1�S0 transitions in isolated HCOOH and the C1:1#1 complex. The values of DEo are in eV Ioannoni et al.40 4.64 HCOOH C1:1#1 As can be seen in Table 3, the most stable is the C1:1#1 which has a six-membered ring structure with two hydrogen bonds: O5···H6 = 2.145 Å and H4···O7 1.916 Å. Comparing the geometry of HCOOH in the complex with respect to isolated HCOOH, it can be noted that the distances C2=O5 and C2–O3 are shorter and the angle O5–C2–O3 is 2º wider in the complex while the other bonds remain essentially unchanged. The binding energy, BE = 54.8 kJ mol–1 with BSSE correction included. The geometry of this conformer is comparable to the one obtained by Minyaev using RHF/6-31G** and MP2(full)/6- 31G** methods9 and those obtained by Rablen et al.using a hybrid density functional procedure (Becke3LYP) and MP2 theory.11 The value of the binding energy obtained by Kumaresan et al. for open complexes at the HF/3-21G level of theory is comparable to our results (BE = 67.5 kJ mol–1 without BSSE correction).35 We have found three minima in the potential energy surface, but the deeper minimum corresponds to C1:1#1, as it has been observed by other authors and the values of the binding energies are in good agreement with theirs.7,11 In the C1:1#2 conformer, the water molecule interacts with H1–C2 and O5 of the carbonyl group, leaving the hydroxy group, O3–H4, free.The distances are H1···O7 = 2.975 Å and H6···O5 = 2.085 Å. With respect to free HCOOH, the change in geometry is not so important except that C2–O3 is shorter and C2–O5 is stretched. The BE is 27.0 kJ mol–1 and is almost half of the BE C interaction is between H 1:1#1. In this case, the main 6 and O5. For the C1:1#3 complex, the water molecule interacts with H1 and O3 leaving the carbonyl group free. The distances are longer: H1···O7 = 2.948 Å and H6···O3 = 2.135 Å. With respect to the free HCOOH, the C2–O3 bond is stretched to 1.341 Å. The binding energy is 13.6 kJ mol–1. 1:1#2 and #3 with C1:1#1, it is clear that the 1–C2 distance is longer in the latter (for C1:1#2 and #3, 1–C2 is 1.081 Å and 1.082 Å respectively while it is 1.108 Comparing C HHÅ for C1:1#1).This trend was also observed in formic acid dimers36 and acetic acid dimers37 in which the H–C is not attacked by water. On C1:1#1 formation, the C2–O5 and C2–O3 bonds become shorter than in the isolated formic acid and this trend in turn leads to weaker C2–H1 and O3–H4 bonds, adjacent to the two bonds mentioned before. For angles, small changes of 1–2º are observed on complex formation which may be correlated with the shortening of the C2–O3 bond. For C1:1#2 and C1:1#3, the changes on lengths and angles with respect to isolated HCOOH are less important than in the C1:1#1 complex. In the three different conformers of formic acid–water, the hydrogen of water which does not interact with HCOOH is out of plane.However, the potential energy surface as a function of the out of plane motion of that hydrogen atom is This work Ng et al.41 4.78 4.61 4.81 very flat. This can be seen in Fig. 2 where the energy (at CASPT2 level) of the C1:1#1 conformer has been represented as a function of the angle between the H8–O7 bond and the normal to the plane of the rest of the molecule. It is seen that there is a barrier of only 280 cm–l at the planar configuration. Since the zero-point energy associated with this coordinate is much higher than the barrier, there will be a large amplitude vibration associated with the out-of-plane mode. The effect of that floppiness will be that in the spectra the complex will appear to be effectively planar.13 Fig.3 Calculated optimized geometries of HCOOH–(H2O)2 complexes. 3.2 Ground state 1 : 2 conformers Four conformers have been found for the 1 : 2 complex. they are represented in Fig. 3. As can be seen in Table 4, the most stable one, the C1:2#1, has three hydrogen bonds in a closed 8-membered ring structure: O5···H6 = 1.939 Å, O7···H9 = 1.874 Å and O10···H4 = 1.781 Å. In this cyclic structure the oxygen atoms are in the plane of the carboxy group, similar to those of phenylpropionic acid–(H2O)2.4 This conformer was observed in recent microwave experiments.13 Similarly to C1:1#1, the length C2–H1 is longer than in HCOOH, C2–O3 is shorter while C2–O5 is unchanged. We have obtained BE = 123.7 kJ mol–1 with BSSE correction included.Table 7 Comparison between experimental and calculated band origin for the S1�S0 transitions in isolated HCOOH and the C1:1#1 complex.The values of DEo are in eV Ioannoni et al.40 This work 4.64 HCOOH C1:1#1 The second more stable complex (C1:2#2) is composed of a six-membered ringone in C1:1#1, plus the other water molecule forming a dimer with one in the ring. This complex is similar to one studied by Nagaoka et al.38 There are three hydrogen bonds: O5···H6 = 2.512 Å, H8···O10 = 2.008 Å and O7···H4 = 1.822 Å. With respect to isolated HCOOH, C2–O5 (1.185 Å) and C2–O3 (1.305 Å) are shortened. The effect on the geometry is the same as that observed in C1:1#1 except for the H1–C2 bond. The energy difference is 51.5 kJ mol–1 with respect to C1:2#1.Thus, the formation of a ring is more energetic than the interaction between the two water molecules. The C1:2#3 complex can be considered to be similar to C1:2#2 with a six-membered ring, but the second water molecule interacts with H1 and O3. The distances of hydrogen bonds are: O5···H6 = 2.401 Å, H4···O7 = 1.900 Å, H1···O10 = 3.023 Å and O3···H9 = 2.153 Å. The geometry of HCOOH in the complex is not influenced by the molecules of water and there is only a little difference in the angles, about 1–2º. In this case. the BE is small: 1.2 kJ mol–1. Fig. 4 Coulombic interaction in the ground S0 state (black), and the excited S1 state (white) for (a) 1 : 1 complexes; (b) 1 : 2 complexes. Ng et al.41 4.78 4.61 4.81 The C1:2#4 complex has also a six-membered portion but O5 interacts with two H atoms from the two molecules of water.The distances between formic acid and water are longer than in the other cases: O5···H6 = 2.458 Å, H4···O7 = 1.902 Å. H1···O10 = 3.259 Å and O5···H9 = 2.085 Å. In this case, the BE is the smallest for all the conformers: 0.5 kJ mol–1. The geometry of HCOOH in the conformer is not affected by the presence of water molecules, similar to the C1:2#3 complex. 3.3 Vertical transitions p*�n With the optimized geometries of HCOOH and HCOOH– (H2O)n (n = 1, 2) in their electronic ground state S0, we have calculated the CASSCF and CASPT2 excitation energies, DE n for the vertical transition p*�n in HCOOH. These results are collected in Table 5 for HCOOH and the 1 : 1 complexes and in Table 6 for the 1 : 2 complexes.We have also calculated the origin band for free HCOOH and the C1:1#1 conformer and the results are compared to the available experimental values in Table 7. For free HCOOH, we have obtained DE n = 5.82 eV (CASPT2) which is in agreement with the value obtained by Iwata and Morokuma using the electron-hole potential method.39 We have also calculated the CASPT2 energy difference between the optimized geometries of HCOOH in ground (S0) and excited states (S1), and we obtained the band origin DE0 = 4.61 eV in agreement with the experimental value determined by Ioannoni et al.40 and Ng and Bell (Table 7).41 The same calculation was performed for C1:1#1 and we have obtained DE0 = 4.81 eV.In the energy minimum of the excited state S1, the formic acid has a pyramidal geometry, in which C2 has sp3 hybridization and the distance C2–O5 is stretched to 1.3 Å. The same effect is observed in formic acid for C1:1#1. For the HCOOH–(H2O)n (n = 1, 2) complexes (see Tables 5 and 6), we have obtained an increase of DE0, with respect to the value obtained for HCOOH (blue-shifted transitions). By examining the change of the net charge of the atoms particularly in the carbonyl group, we observed that there is a transfer of negative charge from O5 to C2 when the system is excited to the S1 surface. The hydrogen bond is thus weakened destabilizing the excited state with respect to the ground state.This is similar to the behavior observed in other systems with a carbonyl group, such as CH2O– (H2O)n.42 In the first approximation, the destabilization of the excited state can be estimated in terms of the coulombic interaction between formic acid and water. We have: water HCOOH r (3) DE ij coulomb i j i j = å åq q where qi are the net atomic charges in H2O, qj are the net charges in HCOOH and rij is the distance between the atoms. The charge distributions per atom for each basis function have been obtained by Mulliken population analysis.26 The results are presented in Fig. 4. It is seen thatindeed the transfer of net charges in the excited state can account for a significant part of the blue-shift. 4 Conclusions We have calculated p*�n transitions for the most stable conformers of formic acid–(water)n (n = 1, 2) complexes.The most stable conformers, the 6-membered ring and 8- membered ring structures for the 1 : 1 and 1 : 2 complexes respectively, are in agreement with previous calculations.11,13 We have found that the vertical transitions are blue-shifted with respect to the free HCOOH. This blue-shift is due to the destabilization of the excited state with respect to the ground state mainly due to the charge transfer between O and C in the C=O group which weakens the hydrogen bonds. There is also a blue-shift in the band origin of C1:1#1. This is due to the change of geometry in formic acid upon excitation (passing from a planar to a pyramidal structure) producing a destabilization in the hydrogen bonds.This behavior is also observed in other systems with carbonyl groups, such as formaldehyde–(water)n.42 5 Acknowledgements We acknowledge the support of a French–British collaborative programme (Alliance) number 98107. Financial support by ECOS fellowship to one of the authors (G.V.) is gratefully acknowledged. We thank J. P. Simons for suggesting the study of these systems and A. Bauder for providing us with his results prior to publication. Footnote † Permanent address: INFIQC, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba, AP4. CC61. 5000, Córdoba, Argentina. References 1 Hydrogen bonding in biological structures, ed. G. A. Jeffrey and W. Saenger, Springer–Verlag, Berlin, 1991.2 R. Desiraju, Acc. Chem. Res., 1991, 24, 290. 3 O. Mó, M. Yáñez and J. Elguero, J. Chem. Phys., 1997, 107, 3592. 4 J. A. 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ISSN:1460-2733    

DOI:10.1039/a904105b

出版商:RSC    

年代:1999

数据来源: RSC