J. Phys. Chem. 1993,97, 12731-12736
12731
Theoretical Study of Hydrogen-Bonded Formaldehyde-Water Complexes Yordanka DTmitrova'*f and Sigrid D. Peyerimboff Lehrstuhl f i r Theoretische Chemie. Uniuersitiit Bonn, Wegelerstrasse 12,0-53115 Bonn, Germany Received: February 8, 19930
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The system HzCO HzO has been investigated by means of a b initio SCF and CI calculations. The geometry was SCF-optimized for the complex HzCO + HzO and for one and two additional HzO molecules bound to the optimal HzCO--H20 nuclear arrangements. The binding energy was evaluated with basis set superposition errors and zero-point vibrations taken into account. The solvent shift for the singlet and triplet n r* transitions was determined in C I calculations for the entire system. The solvent shift is found to be strongest (around 1140 cm-l) for the optimally HzO-bonded formaldehyde complexed with one water molecule. The shift is roughly proportional to the number of HzO molecules, going from 0.17 eV (one HzO) to 0.35 eV (two H20) to 0.47 eV (three H20) in the singlet (n T * ) transition. The influence on the triplet (n T * ) transition is wholly parallel.
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I. Introduction CCL. By a combination of quantum and classical mechanical calculations, the simulation of the absorption spectra in the n Ab initio calculations for hydrogen-bonded systems between r* singlet transition of formaldehydecomplexed with a few water a neutral proton acceptor and a proton donor were first carried molecules ( n = 1-3) and in water solution has been performed.16 out for dimeric HzO.**HzOin order to study the nature of the The aim of the present work is to study the n r*singlet and intermolecular interaction, i.e., hydrogen bonding.1 In many triplet transitions for various formaldehydewater complexes in organic and biological systems the carbonyl group is the most order to evaluate the influence of the hydrogen bonding on common base forming a hydrogen bond with a proton donor such electronic transitions. We therefore chose formaldehyde suras the OH and N H group. In biological systems the carbonyl rounded by 1-3 water molecules in various geometrical arrangegroup is by far the most important proton acceptor. For this ments. The first step then is to optimize the structures of the reason a largenumber of theoretical studies, by both semiempirical formaldehyde-water complexes studied. The second is to examine and ab initio procedures, have been undertaken in recent years the n r* transition energies by purely ab initio methods for for the simplest carbonyl-hydroxyl interaction, HzCO plus H ~ 0 . 2 ~ both singlet 'A2 and triplet 3Azelectronicstates. And finally, the Most calculationsdeal with the bonding properties in the ground work should be able to estimate the solvent shift for the carbonyl electronic state, in particular to elucidate the functional depenn r* transitions as a functionof the number of water molecules dence of the hydrogen bond strength and the shift in the carbonyl in such hydrogen-bonded complexes. stretching frequency5 due to hydrogen bonding; corresponding infrared measurements have been known for some time.6 11. Hydrogen-Bonded HzCO Structures and Tbeir Stabilities Much less work has been devoted to the study of the change 1. SCF Calculations. Geometry optimization of the formalin electronictransition energies due to hydrogen bond formation. dehyde-water complexes was made with the GAUSSIAN 90 Experimentally,the carbonyl n r* transition is found to make seriesof programsl7and the 6-3 1G** basis set. Our first problem a large blue shift (1920 cm-l for acetone in H20) while the r was to optimize the structures for the complexesof formaldehyde r* transition makes a red shift upon hydrogen bonding.' with 1-3 water molecules. In Figure 1 and Table I we show the Haberfield et a1.8 observed that then r*blue shift of carbonyl optimumvalues of the total energy and the equilibrium geometries compounds depends on the solvent. One explanation for this for the complexes studied at the 6-31G** level, employing the blue shift was that the excited state shows little or no hydrogen SCF procedure. bonding.*ll Taylorlz suggested that the blue shift arises from The first complex has the optimumgeometry for H--O distance the geometry changes of the excited states on hydrogen bonding. 2.077 A. The hydrogen bonds for complexes 2 and 3 are weaker A recent theoretical study13combiningab initio molecular orbital and longer than the hydrogen bond for complex 1. As can be and molecular mechanics type methods was able to reproduce seen from the data in Table I, the most stable structure is the the transition energy measured in water relative to that in the gas first-with the deepest minimum in the total energy and the phase by modeling the formaldehyde-water system, including strongest hydrogen bond. Structures 1,2,and 3 are very similar one and two water molecules. The solvation of formaldehydeby to structures la, Id, and li, found earlier by Kumpf and water in its ground ('AI) and singlet excited ('Az) states has been Damewood! Furthermore, the ab initio calculations show that studied by a combination of ab initio and molecular dynamics for complexes 1,2,and 3 the planar structures are more stable techniques.'' In this study the calculated shift is in the 600than the nonplanar structures. 19OO-cm-' range: the lower limit for one and the higher for 209 For the complexes of formaldehyde with two and three water water molecules taken into consideration. molecules, we optimized at the 6-31G** level only the intramoDeBolt and Kollman15 with calculations using a statistical lecular coordinates and used the optimum geometries of the mechanical free energy perturbation method (FEP) have satiscomplexes of formaldehyde with one water molecule. We selected factorily reproduced the spectroscopically observed solvent shifts structures 4, L,and 5 for the complexes with two and three for the n r*electronictransitions for the carbonyl-containing water molecules, because in our study complex 1 is the most chromophoresformaldehydeand acetone. The calculationshave stable complex of formaldehyde with a single water molecule. been carried out for the carbonyl solutes in water, methanol, and 2. Counterpoise C a l ~ u l a t i ~For ~ . the complexes of formaldehyde with 1-3 water molecules, the binding energy at different t Permanentaddreas: Instituteof Organic Chemistry,Bulgarian Academy levels of ab initio MO theory has been calculated. The results of Sciences, Acad. G. Bonchev Str., BI. 9, 1040 Sofia, Bulgaria. are shown in Table 11. *Abstract published in Aduancc ACS Absrracrs, November 1. 1993.
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0022-3654/93/2097- 12731$04.00/0
Q 1993 American Chemical Society
Dimitrova and Peyerimhoff
12132 The Journal of Physical Chemistry, Vol. 97, No. 49, 1993 equation
cs
(1) - “‘0-H
czv
(2)
AE=EAB-(EA+EB) (2) where EA and EBare the energies of A and B in their own basis sets, we calculated the AE (uncorrected binding energy).
,O-H
BSSE = AE’- AE = ( E A
‘0-H
c*,
c,
(4)
(46)
/O-H
H\O-
H
Figure 1. Optimized structures of the complexes of formaldehyde with 1-3 water molecules.
TABLE I: Equilibrium Geome (Distances in A, Angles in deg) and Total Energies E (in a ! for the Hydrogen-Bonded Formaldehyde-Water Complexes Shown in Figure 1, Obtained from SCF Calculations Employing the 6-316** Basis Set system geometry E -189.900 83 CO (1.185), CH (1.095), 1 OH (0.941), 0.-H (2.077) -189.898 64 CO (1.186), CH (1.092), 2 OH (0.943), 0.-H (2.567) -189.897 63 CO (1.186), CH (1.091), 3 OH (0.943), O-*H (2.805) -265.930 65 4 CO (1.188), CH (1.095), OH (0.941), O*-H (2.084) -265.929 77 CO1(1.190), CH (1.091), 4a 02H (0.943), O’-.H (2.056), 02-H (2.757,2.748) -341.960 48 CO’ (1.192), CH (1.088), 5 02H (0.942), O’-.-H (2.083), 02-H (2.800) -1 13.869 74 CO (1.184), CH (1.093), HCH (1 15.7) CH2O -76.023 61 OH (0.943), HOH (106.0) HzO The exact determination of the interaction energies between two or more hydrogen-bonded partners is a very difficult problem. Electron correlation must generally be taken into account, corrections have to be made for the basis set superposition error (BSSE) in the calculations, and zero-point vibrations cannot be neglected. Counterpoise calculations are used to estimate the magnitude of basis set superpositionerror (BSSE). The original counterpoise method of Boys and Bernardil*is the procedure most frequently used for computing the BSSE. In this method the energies of the monomer constituents A and B are calculated separately within the basis set of the whole complex A-B. If B is designated a “ghost” molecule, the calculated monomer energy is EA’. In a similar calculation, in which A is the “ghost” molecule, the calculated monomer energy is EB’. From the equation
AE’= EA, - (EA’ + E;)
(1)
we calculated the AE’(corrected binding energy), and from the
+ E,) - (EA’ + E
