The ionization potential (IP) of the aromatic alpha hydroxy carboxylic acid, 9-hydroxy-9-fluorene carboxylic acid (9HFCA), is shifted by complexation with hydrogen bonding ligands such as water and formic acid. Generalized Kohn-Sham energy decomposition analysis decomposes the intermolecular binding energies into a frozen energy term, polarization, correlation, and/or dispersion energy terms, as well as terms of geometric relaxation and zero point energy. We observe that in each dimer the attractive polarization always increases upon ionization, enhancing binding in the cation and shifting the IP toward the red. For 9HFCA—H2O, a substantial decrease of the repulsive frozen energy in cation further shifts the IP toward red. For 9HFCA—HCOOH, the increase of the frozen energy actually occurs in the cation and shifts the IP toward blue. Consistent with the experimental measurements, our analysis provides new, non-intuitive perspectives on multiple hydrogen bonds interactions in carboxylic acids and water complexes.

Hydrogen (H) bonding is a subtle and thoroughly studied phenomenon,1 and examples of networks of H-bonds occur in many chemical and biological settings.2–4 Still all the subtleties of such interactions are not fully explored.5 One exemplary case is the family of the hydroxy carboxylic acids, which can interact with water and other carboxylic acids through two distinct modes of intermolecular H-bonding, either through its carbonyl acceptor or its carboxylic donor, or in many cases both. In a hydroxy acid, an intramolecular H-bond forms between its carboxylic acid group —COOH carbonyl and the alcoholic —OH; this intramolecular H-bond can serve as a reporter, describing the nature of the H-bonding in the complex, since it is influenced upon complexation with water or formic acid.6 

Glycolic acid HO—CH2 —COOH is the smallest alpha hydroxy carboxylic acid and serves as a conveniently small system for the computational study of H-bonding. Spectroscopy and photochemistry on glycolic acid and its H-bonded complexes with water have been extensively studied by Vaida’s group7,8 and others.9 The direct study of ionic glycolic acid and its complexes is difficult owing to its lack of strong electronic absorption bands, and its ionization potential (IP) lies in the vacuum ultraviolet region, ∼120 nm. Its aromatic analog, 9-hydroxy-9-fluorene carboxylic acid (9HFCA) in Figure 1, is ideal for H-bonding network studies for neutral and cation.10,11 The fluorene moiety in 9HFCA has strong ultraviolet (UV) absorption ∼300 nm and allows study by electronic and ionization spectroscopy.12 

We computed optimized geometries and harmonic frequencies (no scaling) for 9HFCA and its complexes with water and formic acid with three density functionals B3LYP, ωB97x-D, and M06-2X, all with the 6-311++G(d,p) basis set, using the Gaussian 09 program.13 For cation calculations, both unrestricted (U) functional and restricted open (RO) density functional calculations were conducted and show similar results. Geometry optimization calculations on neutral and cationic species with the B3LYP/6-311++G(d,p) model are shown in Figure 1. Ionization of 9HFCA, which removes an electron from the fluorene fragment, has an indirect but pronounced impact on the H-bonding geometry in 9HFCA—H2O and 9HFCA—HCOOH complexes. The geometries of the complexes are strikingly altered upon ionization. For the water complex, the 9HFCA carboxyl =O⋯HO distance increases from 2.09 Å (neutral) to 3.06 Å (cation); that is, the weaker H-bond is weakened further upon ionization. The 9HFCA carboxylic —COOH⋯O distance decreases from 1.76 Å (neutral) to 1.64 Å (cation), as the stronger H-bond in the neutral strengthens further upon ionization. Computed harmonic frequencies change as well. In the neutral complex, the stretching frequency for 9HFCA’s carboxylic OH is 3360 cm−1 and the symmetric OH stretch for water is 3705 cm−1; in the cation, the corresponding values are 3169 cm−1 and 3811 cm−1. The latter value is close to the frequency for unbound water’s OH symmetric stretching mode. The cation is essentially a single H-bonded complex, water binding predominantly with the —OH of 9HFCA’s carboxyl group. The inter-H-bond network is then broken, primarily due to the charge redistribution.

In contrast, for 9HFCA—HCOOH, the intermolecular H-bonds are more closely analogous in neutral and cation. For the formic acid complex, the 9HFCA carboxyl =O⋯HO distance increases from 1.70 Å (neutral) to 1.83 Å (cation), while the 9HFCA carboxylic —COOH⋯O = distance decreases from 1.69 Å (neutral) to 1.56 Å (cation). Formic acid is a much more effective proton donor than water, in both the neutral and (especially) the cationic complexes. The computed harmonic frequencies show the decoupling attending ionization. In the neutral, the two carboxylic OH stretching modes are strongly coupled into in-phase and out-of-phase combinations, with frequencies 3168 and 3262 cm−1, respectively. In the cation, they are almost completely de-coupled, and 9HFCA acidic OH frequency is 2812 cm−1 while the formic acid OH is 3448 cm−1. But the inter-H-bond network is still retained in the cation, surviving the charge flow.

As in both of the complexes, the intra-H-bond geometry remains intact and locks the nearby carboxylic acid group into a plane perpendicular to the fluorene group. The 9HFCA—HCOOH complex has Cs symmetry in both neutral and cation, and 9HFCA—H2O is C1 in its neutral state and Cs in the cationic form. This constraint prevents more drastic geometric changes upon ionization.

Experimentally, vibrational spectroscopy is routinely employed to provide an unambiguous signature of the inter- and intramolecular H-bonding interactions.14–16 Unfortunately in the carboxylic acid dimers, due to the substantial mode couplings arising from the two similar intermolecular H-bonds, these OH stretches become very broad, spanning the wide range from 2600 to 3200 cm−1.17 This conceals valuable information. Double resonance photoionization laser spectroscopy, specifically mass analyzed threshold ionization spectroscopy (MATI),18 can resolve the messy infrared spectra of the inter-H-bonds in carboxylic acid dimers. Well-defined, vibration-resolved UV laser-based photoionization spectra were observed successfully for 9HFCA, and its complexes with formic acid, prepared in cold gas phase.10 Figure 2 displays vibration resolved MATI spectra of 9HFCA and 9HFCA—HCOOH, as well as a photoionization efficiency (PIE) spectrum of 9HFCA—H2O. The spectra are plotted with x axis offset by 185.62 kcal/mol (64 920 cm−1), the IP of 9HFCA monomer; an arrow indicates each species’ IP shift. For 9HFCA—HCOOH, the IP shift is red and quite small, measured to be −1.56 kcal/mol (−545 cm−1), from 9HFCA monomer to its formic acid complex. That is, the intermolecular binding energy (D0) in the cation is indeed 1.56 kcal/mol bigger than the binding energy in the neutral complex. For 9HFCA—H2O, the PIE spectrum shows that the ion signal at −4.0 kcal/mol region, enhanced by the probe laser, is already significant, so the true IP shift is expected to be still more negative (redder) than −4.0 kcal/mol.

The measured IP value in monomer and its shifts in clusters are fundamentally important parameters. It is well known that IP red-shifts in H-bonded clusters are often substantial. In phenol and indole complexes with water, the IP values are shifted to the red by −13.15 kcal/mol and −9.03 kcal/mol, respectively.19,20 Generalized Kohn-Sham energy decomposition analysis (GKS-EDA)21 promises an understanding of the physical origins leading to the contrasting IP shifts in mixed carboxylic acids and water dimers, specifically 9HFCA—HCOOH and 9HFCA—H2O. Applying GKS-EDA to 9HFCA—HCOOH dimer leads to surprising results, quite different from the more common concepts, as found for 9HFCA—H2O.

By the GKS-EDA analysis, the dissociation energy D0 is represented as the sum of a geometrical deformation or relaxation energy term, ΔE(geo), a difference in harmonic vibrational zero point energy between the complex and separate monomers, ΔE(ZPE), and the interaction energy, ΔEint. ΔEint is negative and attractive, stabilizing the heterodimer and enhancing D0, while ΔE(geo) and ΔE(ZPE) are positive in general, diminishing D0. The IP shifts from monomer to complex are exactly defined by the differences in dissociation energies between the neutral and the cation complexes, so we will focus on differences in each of these terms between cation and neutral.

Implemented in the local version of GAMESS,22 GKS-EDA divides the total interaction energy, corrected for basis set superposition error (BSSE), into electrostatic, exchange, repulsion, polarization, correlation, and dispersion terms,

ΔEint=ΔEele+ΔEex+ΔErep+ΔEpol+ΔEdisp+ΔEcorr.

ΔEele is the electrostatic interaction energy between fragments. ΔEex and ΔErep are exchange and repulsion term, respectively. The sum of ΔEele, ΔEex, and ΔErep can be regarded as the frozen energy ΔEfro, indicating the monomers’ interaction arising from frozen electronic density.23–25 ΔEpol derives from the orbital relaxation, calculated by a self-consistent-field step in which the Kohn-Sham orbitals relax to their optimal forms. ΔEdisp is a dispersion interaction computed from the density functionals methods such as ωB97x-D which includes a dispersion correction.26 ΔEcorr is the correlation term, derived from Kohn-Sham correlation energy.

D0 can be decomposed into the following terms:

D0=|ΔEfro+ΔEpol+ΔEdisp+ΔEcorr+ΔE(geo)+ΔE(ZPE)|.

Such calculations do not promise highly accurate values, either of D0 or its energy components, for either the neutral or cationic complex. This is illustrated by the scatter in computed values discussed below. We expect that the differences of energy components between cation and neutral should be more reliable, owing to error cancelation.

D0 energy components computed with B3LYP (B3LYP1 in GAMESS), M06-2X, and ωB97X-D in a 6-311++G(d,p) basis are listed in Table I for 9HFCA—H2O in neutral and cationic forms. The energy terms with negative sign increase the D0 while terms with positive sign decrease the D0. For example, in the B3LYP calculation, the D0 for the neutral complex is 7.14 kcal/mol, which increases to 12.09 kcal/mol for the cation. The dominant contribution to D0 for both the neutral and cationic complexes is the polarization energy (8.87 and 10.58 kcal/mol respectively), while correlation energy and zero point energy terms make more modest contributions. The difference between cation and neutral binding energies arises largely from the ΔEfro term, with a significant contribution from the change in polarization energy and a smaller contribution from the change in zero point energy. A semi-quantitatively similar picture emerges from M06-2X and ωB97x-D calculations. In estimation of the differences for each term, all three methods are consistent. B3LYP and ωB97x-D results are very similar while M06-2X results depart slightly.

TABLE I.

GKS-EDA on D0 of 9HFCA—H2O in neutral and cation with a basis set of 6-311++G(d,p). The difference (Diff) is the cation minus the neutral. The unit is kcal/mol.

ΔEfroΔEpolΔEcorrΔEdispΔE(geo)ΔE(ZPE)D0
B3LYPa 1.54 −8.87 −2.70 … 0.73 2.16 7.14 
RO-B3LYPb −1.49 −10.58 −2.28 … 0.88 1.38 12.09 
Diffc −3.03 −1.71 0.42 … 0.15 −0.78 4.95 
M06-2Xa 0.77 −8.37 −4.32 … 0.60 2.21 9.11 
RO-M06-2Xb −1.25 −10.74 −4.16 … 0.87 1.64 13.64 
Diffc −2.02 −2.37 0.16 … 0.27 −0.57 4.53 
ωB97x-Da 1.41 −8.57 −3.27 −1.01 0.66 2.22 8.56 
RO-ωB97x-Db −1.52 −10.47 −2.62 −0.98 0.84 1.75 13.00 
Diffc −2.93 −1.90 0.65 0.03 0.18 −0.47 4.44 
Measured diff       ≥4.00 
ΔEfroΔEpolΔEcorrΔEdispΔE(geo)ΔE(ZPE)D0
B3LYPa 1.54 −8.87 −2.70 … 0.73 2.16 7.14 
RO-B3LYPb −1.49 −10.58 −2.28 … 0.88 1.38 12.09 
Diffc −3.03 −1.71 0.42 … 0.15 −0.78 4.95 
M06-2Xa 0.77 −8.37 −4.32 … 0.60 2.21 9.11 
RO-M06-2Xb −1.25 −10.74 −4.16 … 0.87 1.64 13.64 
Diffc −2.02 −2.37 0.16 … 0.27 −0.57 4.53 
ωB97x-Da 1.41 −8.57 −3.27 −1.01 0.66 2.22 8.56 
RO-ωB97x-Db −1.52 −10.47 −2.62 −0.98 0.84 1.75 13.00 
Diffc −2.93 −1.90 0.65 0.03 0.18 −0.47 4.44 
Measured diff       ≥4.00 
a

Neutral.

b

Cation.

c

Cation–Neutral.

TABLE II.

GKS-EDA on D0 of 9HFCA—HCOOH in neutral and cation with a basis set of 6-311++G(d,p). The difference (Diff) is the cation minus the neutral. The unit is kcal/mol.

ΔEfroΔEpolΔEcorrΔEdispΔE(geo)ΔE(ZPE)D0
B3LYPa 6.48 −19.85 −3.08 … 2.52 1.37 12.56 
RO-B3LYPb 8.02 −23.57 −2.72 … 3.06 1.32 13.89 
Diffc 1.54 −3.72 0.36 … 0.54 −0.05 1.33 
M06-2Xa 4.76 −18.12 −4.39 … 2.11 1.31 14.33 
RO-M06-2Xb 7.92 −23.47 −4.63 … 3.19 1.03 15.96 
Diffc 3.16 −5.35 −0.24 … 1.08 −0.28 1.63 
ωB97x-Da 5.88 −19.02 −3.83 −1.68 2.47 1.40 14.78 
RO-ωB97x-Db 7.44 −22.62 −3.57 −1.67 3.04 1.26 16.12 
Diffc 1.56 −3.60 0.26 0.01 0.57 −0.14 1.34 
Measured diff       1.56 
ΔEfroΔEpolΔEcorrΔEdispΔE(geo)ΔE(ZPE)D0
B3LYPa 6.48 −19.85 −3.08 … 2.52 1.37 12.56 
RO-B3LYPb 8.02 −23.57 −2.72 … 3.06 1.32 13.89 
Diffc 1.54 −3.72 0.36 … 0.54 −0.05 1.33 
M06-2Xa 4.76 −18.12 −4.39 … 2.11 1.31 14.33 
RO-M06-2Xb 7.92 −23.47 −4.63 … 3.19 1.03 15.96 
Diffc 3.16 −5.35 −0.24 … 1.08 −0.28 1.63 
ωB97x-Da 5.88 −19.02 −3.83 −1.68 2.47 1.40 14.78 
RO-ωB97x-Db 7.44 −22.62 −3.57 −1.67 3.04 1.26 16.12 
Diffc 1.56 −3.60 0.26 0.01 0.57 −0.14 1.34 
Measured diff       1.56 
a

Neutral.

b

Cation.

c

Cation–Neutral.

FIG. 1.

9HFCA and their complexes with water and formic acid in neutral and cation. Geometries and harmonic frequency calculations were done with B3LYP/6-311++G(d,p).

FIG. 1.

9HFCA and their complexes with water and formic acid in neutral and cation. Geometries and harmonic frequency calculations were done with B3LYP/6-311++G(d,p).

Close modal
FIG. 2.

Ionization spectra of 9HFCA, 9HFCA—H2O, and 9HFCA—HCOOH complexes; arrows indicate the IP thresholds determined from PIE or MATI experiments.

FIG. 2.

Ionization spectra of 9HFCA, 9HFCA—H2O, and 9HFCA—HCOOH complexes; arrows indicate the IP thresholds determined from PIE or MATI experiments.

Close modal

To explain the IP shifts, the re-arrangement of the inter H-bonds is the key. As Figure 1 shows, as the system passes from neutral to cation, charge redistribution occurs so that the stronger H-bond of the neutral (9HFCA carboxyl OH⋯OH2) is further strengthened in the cation, at the expense of the weaker; the two distinct intermolecular H-bonds of the neutral species are replaced by a single dominant intermolecular H-bond in the cation. 9HFCA becomes a much more powerful proton donor upon ionization, and the strengthening of the associated H-bond compensates for the loss of the proton donation from water. The changes in the H-bond network upon ionization result in the decrease of the frozen electron density interaction ΔEfro which turns from repulsion in neutral to attraction in cation. Meanwhile the newly strengthened single intermolecular H-bond in the cation has much higher polarization energy, consistent with its shorter intermolecular distance and a red-shifted carboxylic OH frequency. In the B3LYP calculation, the change in ΔEfro is −3.03 kcal/mol, and the change in ΔEpol is −1.71 kcal/mol. The total −4.74 kcal/mol constitutes the greater part of the red IP shifts, −4.94 kcal/mol. The change in ΔE(ZPE) is substantial and negative, −0.78 kcal/mol, and thus further favors a red-shifted IP. If anharmonic corrections were to be incorporated by a scaling factor for frequencies, the magnitude of ΔE(ZPE) would decrease, but the sign would not be altered. Overall, we see noticeable changes in the strength of intermolecular vibrational modes upon ionization. ΔE(geo) in neutral and cation are small and similar, less than 1 kcal/mol, so the change is even smaller. The difference in ΔEdisp is almost zero from ωB97x-D, suggesting minimal influence from the charge flow. The differences in D0 for 9HFCA—H2O, calculated by the three methods, are quite consistent: 4.95 kcal/mol by B3LYP, 4.52 kcal/mol by M06-2X, and 4.44 kcal/mol by ωB97x-D. The values are all in line with the experimental PIE estimate of the red shift, to be more than 4.00 kcal/mol.

Several isomers are possible for both neutral and cationic 9HFCA—HCOOH. The forms, shown in Figure 1, are the actual global minima. The two parallel intermolecular H-bonds maximize H-bonding. The structures are very similar in neutral and cationic complexes. Threshold photoionization on the neutral 9HFCA—HCOOH then directly accesses the Franck-Condon region, so the vertical IP is also the adiabatic IP. In Table II, the energy components are listed for neutral and cationic 9HFCA—HCOOH complexes, as computed in B3LYP, M06-2X, and ωB97x-D with the 6-311++G(d,p) basis set. The dominant contributions to the D0 values are the ΔEpol term along with a smaller term of ΔEfro. For the IP shifts, the changes in ΔEfro, ΔE(geo), and ΔEpol are most significant. They work in opposite directions, the first two favoring a blue shift and the latter a red shift in ionization potential, which defines the final sign of the IP shift. The changes of ΔEcorr and ΔE(ZPE) are not significant. The ΔEdisp is much larger than in 9HFCA—H2O, but its change is again almost zero. All methods are consistent, so we refer only to B3LYP results in the following discussion.

The most surprising feature for 9HFCA—HCOOH is the change in ΔEfro, starkly different from that seen for 9HFCA—H2O. How can this be? Frozen and polarization interaction energies are derived predominantly from the two intermolecular H-bonds. Upon ionization, an electron is removed from the fluorene moiety, but charge redistribution also takes place evidently along intermolecular H-bonds in 9HFCA—HCOOH (also seen in electron density difference map between cation and neutral). The changes of intermolecular H-bonds distances shown in Figure 1 indicate that 9HFCA is more acidic (a better proton donor) in the cationic state. The two intermolecular H-bonds differ in strength; upon ionization, proton donation from 9HFCA tends to increase while proton donation from the binding partner HCOOH tends to decrease. However, the H-bonding network is preserved after ionization, thanks to the competitive intermolecular H-bond donation from HCOOH. B3LYP calculations indicate that the frozen interaction is repulsive in the neutral complex by 6.48 kcal/mol and is even more repulsive in the cation, increasing by 1.54 kcal/mol to 8.02 kcal/mol. It is dramatically different from 9HFCA—H2O. The attractive polarization energy, on the other hand, is still more negative, by −3.72 kcal/mol.

The change in geometric relaxation energy is of interest. Since the binding strength in 9HFCA—HCOOH is considerably stronger than that for 9HFCA—H2O both for neutral and cationic complexes, the 9HFCA geometry is more seriously distorted in the formic acid complex than in water complex. This is reflected by the much bigger geometric relaxation energy for the formic acid complex, with the larger portion from the 9HFCA moiety. ΔE(geo) is 2.52 kcal/mol in the neutral complex vs 3.06 kcal/mol in the cation according to our B3LYP calculations. In 9HFCA—H2O, the corresponding values are only 0.73 kcal/mol and 0.88 kcal/mol. The change of ΔE(geo) upon ionization in 9HFCA—HCOOH is more positive, by 0.54 kcal/mol, than the value (0.15 kcal/mol) found for 9HFCA—H2O. This reduces the red-shift of the IP in 9HFCA—HCOOH. Since the H-bonding network in 9HFCA—HCOOH remains intact in the cation, the change of its zero point energy is much smaller than that for 9HFCA—H2O in which the H-bond network is disrupted. The total calculated IP shifts for 9HFCA—HCOOH are −1.33 kcal/mol by B3LYP, −1.63 by M06-2X, and −1.35 kcal/mol by ωB97x-D; these values agree very well with the experimental measurement, −1.56 kcal/mol.

In summary, shifts of the ionization potentials of 9HFCA complexes with partners HCOOH and H2O have been studied quantitatively using the generalized Kohn-Sham energy decomposition analysis. The computed shifts agree well with the experimental measurements. It reveals the physical effects leading to the large red shift in IP in 9HFCA—H2O and the small red shift IP in 9HFCA—HCOOH. In each complex, the polarization term always increases upon ionization, showing that the orbital relaxation energy between molecules is the major contributor to IP’s red shift upon complexation. Upon ionization, for 9HFCA—H2O the H-bonding network breaks down, and the decrease of the repulsive frozen interaction in the cation substantially enhances binding in the cation, and contributes further to the red-shift of the IP. However, for 9HFCA—HCOOH the H-bonding network preserves, and the increase in the cation of both the repulsive frozen interaction energy and the geometric relaxation energy decreases the D0 of the cation. These effects both tend to shift the IP toward blue. The partial cancelation then results in an IP still shifted to the red, but by a much smaller amount than seen for 9HFCA—H2O. Some of the non-intuitive interactions of multiple H-bonds are then extracted to quantitatively explain the IP shifts in the mixed carboxylic acids and water clusters. This approach is generally applicable and provides new perspectives associated with charge redistribution and subtle interactions of multiple H-bonds in clusters of carboxylic acids and water.

Q.G. would like to dedicate this work to the Barbara A. Body Foundation fellowship for generous support. P.S. acknowledges the grants from the Natural Science Foundation of China (Grant Nos. 21373165, 21120102035, 21273176, 21290190, and 21573176) and the Fundamental Research Funds for the Central Universities, China (Grant No. 20720150037). Computation time at Wesleyan University is supported by the NSF of USA under Grant No. CNS-0619508.

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