High-Resolution Infrared Spectroscopy of the Formic Acid Dimer ¨ Ozg ¨ ur Birer 1 and Martina Havenith 2 1 Present address: Department of Chemistry, Koc ¸ University, Rumelifeneri Yolu, 34450 Sariyer Istanbul, Turkey 2 Department of Physical Chemistry II, Ruhr-University Bochum, Universit¨ atsstraße 150, D-44780 Bochum, Germany; email: [email protected]Annu. Rev. Phys. Chem. 2009. 60:263–75 First published online as a Review in Advance on November 14, 2008 The Annual Review of Physical Chemistry is online at physchem.annualreviews.org This article’s doi: 10.1146/annurev.physchem.040808.090431 Copyright c 2009 by Annual Reviews. All rights reserved 0066-426X/09/0505-0263$20.00 Key Words FAD, proton transfer Abstract The formic acid dimer (HCOOH) 2 (FAD), an eight-membered ring with double hydrogen bonds, has been a model complex for physical chemists. The acidic protons of the complex interchange between the oxygens of dif- ferent units in a concerted tunneling motion. This proton tunneling can be described by a symmetric double-well potential. The double well results in a splitting of each rovibrational level. The magnitude of the splitting de- pends sensitively on the shape of the potential and the reduced mass along the tunneling path. Experimentally, one can determine the proton transfer tunneling splittings in the ground and vibrationally excited states separately. It is possible to work out the splitting of the energy levels, assign the correct symmetry, and obtain the sum and the difference of the tunneling splitting in the ground and vibrationally excited states independently using isotopically labeled molecules. Conversely, an accurate prediction of tunneling splitting even for this small prototype system still remains a challenge for theoretical chemistry because of the splitting’s great sensitivity to the shape and bar- rier height of the potential surface. The FAD therefore has evolved into a prototype system to study theoretical methods for a description of proton transfer. 263 Annu. Rev. Phys. Chem. 2009.60:263-275. Downloaded from www.annualreviews.org by Laurentian University on 09/24/13. For personal use only.
Transcript
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High-Resolution InfraredSpectroscopy of the FormicAcid DimerOzgur Birer1 and Martina Havenith2
1Present address: Department of Chemistry, Koc University, Rumelifeneri Yolu,34450 Sariyer Istanbul, Turkey2Department of Physical Chemistry II, Ruhr-University Bochum, Universitatsstraße 150,D-44780 Bochum, Germany; email: [email protected]
Annu. Rev. Phys. Chem. 2009. 60:263–75
First published online as a Review in Advance onNovember 14, 2008
The Annual Review of Physical Chemistry is online atphyschem.annualreviews.org
This article’s doi:10.1146/annurev.physchem.040808.090431
AbstractThe formic acid dimer (HCOOH)2 (FAD), an eight-membered ring withdouble hydrogen bonds, has been a model complex for physical chemists.The acidic protons of the complex interchange between the oxygens of dif-ferent units in a concerted tunneling motion. This proton tunneling can bedescribed by a symmetric double-well potential. The double well results ina splitting of each rovibrational level. The magnitude of the splitting de-pends sensitively on the shape of the potential and the reduced mass alongthe tunneling path. Experimentally, one can determine the proton transfertunneling splittings in the ground and vibrationally excited states separately.It is possible to work out the splitting of the energy levels, assign the correctsymmetry, and obtain the sum and the difference of the tunneling splitting inthe ground and vibrationally excited states independently using isotopicallylabeled molecules. Conversely, an accurate prediction of tunneling splittingeven for this small prototype system still remains a challenge for theoreticalchemistry because of the splitting’s great sensitivity to the shape and bar-rier height of the potential surface. The FAD therefore has evolved into aprototype system to study theoretical methods for a description of protontransfer.
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DNA:deoxyribonucleic acid
FAD: formic aciddimer
1. INTRODUCTION
One important topic in physical chemistry is the accurate description of noncovalent interac-tions. The origin and manifestation of physical interactions between neutral bodies both withand without permanent dipole moments have been studied for a long time both theoretically andexperimentally. A special case of the noncovalent interaction, the hydrogen bond, is particularlyimportant because it is ubiquitous and participates in several chemical and biological systems (i.e.,the structure of water, the shape and function of certain proteins, and the binding of double-stranded DNA).
The formic acid dimer (FAD) (HCOOH)2 has drawn considerable attention over the yearsand is an important model complex for studying the hydrogen bond. The dimer forms aneight-membered ring in which the carboxylic oxygen of each unit is bound via a hydrogen bondto the acidic proton of the other unit, thus forming double hydrogen bonds. In addition, theacidic protons interchange between the oxygens of different units in a concerted tunneling. Asymmetric double-well potential (Figure 1) determines the parameters of this proton tunneling(i.e., each rovibrational level splits into two levels). The magnitude of the splitting stronglydepends on the potential’s shape and the reduced mass along the tunneling path. The FAD hasbeen one of the most studied carboxylic acid dimers both experimentally and theoretically, notonly because of the double-hydrogen-bonded structure, but also because of the relevance of theproton exchange for the biological systems (i.e., enzymatic catalysis) (1).
C2h C2hD2h
Figure 1Formic acid dimer structure through proton tunneling along with the corresponding potential energy curve.
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TDL: tunable diodelaser
2. EXPERIMENTAL METHODS
Experimentally, one has to fulfill several requirements to perform high-resolution spectroscopyof molecular complexes. First, cold weakly bound complexes must be prepared and preserved ina collision-free environment until they interact with the radiation. Second, a radiation sourcewith sufficiently narrow line width to resolve the substructure should be employed. Finally, thespectroscopic probing technique should not contribute to line broadening.
Seeded supersonic expansion of the molecules of interest with a carrier gas and probing of themolecules (or complexes) with a continuous-wave narrow-line-width laser satisfy all these require-ments. During supersonic expansion, the molecules cool by collisions. Optimized conditions leadto the formation of molecular complexes, which are held by only up to a few hundreds of cm−1
binding energy. Crossing the expansion perpendicular to its centerline velocity vector with a laserminimizes the Doppler broadening.
Two different approaches for high-resolution infrared spectroscopy of complexes meet therequirements above. The first approach involves optothermal spectroscopy, introduced by Goughet al. (2), in which a skimmed molecular beam of complexes is perpendicularly crossed with anarrow-line-width laser. The absorption path length is increased using a multipass cell. The laser-induced dissociation of the complex is registered with an on-axis bolometer, measuring the kineticenergy flux of the molecular beam. In the second approach, one uses a slit expansion to form thecomplexes, couples a tunable diode laser (TDL) along the long axis of the expansion, and measuresthe relative absorption of the radiation. Typically a Herriot-type multipass cell is used to increasethe effective path length of interaction.
The supersonic expansion converts the thermalized random motion of the molecules in thenozzle into directional mass flow due to the collisions during the expansion at the narrow channelof the nozzle (3). The internal energy of the molecules decreases to compensate for the increase inthe directional kinetic energy of the molecules because expansion into vacuum creates zero work.The rotational energy levels can cool to as low as 3 K. However, the vibrational temperatures aretypically higher (10–50 K). This nonequilibrium energy distribution arises because vibrationalcooling requires collisions with specific orientations and adequate energies, which are statisticallyfar less than the ordinary collisions required to cool the rotational levels. In a free jet expansion,molecular complexes can also be formed, provided there are enough three-body collisions. Thesecomplexes are only formed at the early stages of the expansion because the number of three-bodycollisions diminishes approximately 5 nozzle diameters away from the nozzle.
In a slit or planar expansion, the density of the molecules decreases with the distance to thenozzle as R−1 instead of R−2, which is the case for axially symmetric supersonic expansions (4).Therefore, slit nozzles are particularly efficient for complex formation because the number ofthree-body collisions required for cluster formation is much higher compared with that forpoint nozzles. Combined with the increased effective optical path length along the long axis(∼10 cm), slit nozzles are ideal for absorption studies of molecular complexes. Although con-tinuous and pulsed nozzles can be used, the pumping requirements to reduce the backgroundgas pressure are less demanding for the pulsed case. Typically, experiments can be carried outwith several high-throughput mechanical pumps working in tandem rather than high vacuumpumps.
To increase the optical path length along which the molecules interact with the laser light,one usually places a multipass cell several millimeters below the slit expansion. A commonly usedcell type is the Herriot multipass cell arrangement, which consists of two identical gold-platedspherical mirrors separated by a distance equal to the radius of curvature. The laser beam is coupledthrough a hole on one of the mirrors. The laser beam makes multiple passes (∼30) between the
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Tunablediode laser
Monochromator HgCdTedetector
HgCdTedetector
EtalonSlit nozzle
Vacuum chamber
Computer
Stepper motor
Temperature
Current
Lock-in amplifier
Lock-in amplifier
Figure 2Experimental setup of a lead salt diode laser spectrometer coupled to a supersonic slit expansion.
Lead salt TDL:device with a lasermedium of epitaxiallygrown lead salts suchas Pb1-xSnxTe orPbS1-xSex; also knownas an IV-VI laser
HgCdTe detector:mercury(II)cadmium(II) telluridedetector; ahigh–quantumefficiency infrareddetector that works atliquid nitrogentemperature
mirrors, creating a dense optical field between the center of the mirrors. The laser exits the cellthrough the same hole it is coupled.
Lead salt TDLs with typical power in the 0.1–1-mW range are used for direct absorptionstudies. Closed-cycle helium refrigerators maintain the cryogenic temperature conditions requiredfor the operation of the TDLs. The emission frequency depends on the temperature and the biascurrent of the diode; therefore, the TDL’s temperature must be controlled with an active feedbackloop. They have multimode emission, and each mode can be continuously tuned in 0.5–2 cm−1
intervals with a typical line width of 30–100 MHz. The absolute frequency is determined byan external monochromator and a reference gas. A jitter is added to the frequency by currentmodulation, and phase-sensitive detection is used at the second harmonic (2f ) frequency. Theschematics of the setup are presented in Figure 2.
In the slit nozzle setup, the vacuum chamber is evacuated by a series of mechanical pumps: a2600 m3 h−1 roots blower, backed by a 500 m3 h−1 second roots blower, backed by a 65 m3 h−1
mechanical pump. The typical operating pressure is 0.3 mbar. A 25:75% helium-neon carrier gasmixture at 1000 mbar passes through a bubbler that contains liquid HCOOH (or isotopomers)before expanding at the slit nozzle (50 μm × 10 cm). Under pulsed operation, the nozzle is openfor 2 ms and closed for 23 ms. The effective absorption length is increased to 190 cm using aHerriot multipass cell. An HgCdTe detector records the absorption signal, which is identifiedusing phase-sensitive detection with a lock-in detector at twice the frequency of the laser’s currentmodulation. Absolute frequency calibration is achieved by an etalon with a 300-MHz free spectralrange and by comparison with the spectrum of a reference gas (N2O). Figure 3 displays a typicalexperimental spectrum of FAD.
3. STRUCTURE OF THE FORMIC ACID DIMER
It is not possible to perform microwave spectroscopy of FAD because it has a zero permanentdipole moment. Almenningen and coworkers (5, 6) reported the first experimentally determinedstructure of FAD using electron diffraction. The Fourier transform infrared spectrum of FAD inthe gas phase in the 500–4000 cm−1 region was reported in the late 1980s (7). Madeja & Havenith
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1221.0–0.8
–0.6
–0.4
–0.2
0
0.2
0.4
0.6
0.8
1221.4 1221.8
Wave number (cm–1)
Inte
nsi
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.u.)
1222.2 1221.6 1225.60 1225.65 1225.70
Wave number (cm–1)1225.75 1225.851225.80 1225.90
Figure 3Measured infrared spectrum of formic acid dimer. In the detailed view (right panel ), the upper and lower traces show the experimentalspectrum and the simulation, respectively. The transition marked with an asterisk is attributed to the formic acid monomer.
MP2: Møller-Plessetperturbation theory ofthe second order
carried out the first high-resolution infrared (ν0 = 1244.8461 cm−1) spectroscopic study (8) andobtained the rotational constants in the ground and the vibrationally excited state of (DCOOH)2
following an early lower-resolution work in the C==O stretching region (9). Rotational constants for(HCOOH)2 were obtained using femtosecond degenerate four-wave mixing (10) and by perform-ing high-resolution infrared (ν0 = 1225.3350 cm−1) spectroscopy (11). More recently, Gutberletet al. (12) carried out a high-resolution infrared (ν0 = 1717.5177 cm−1) spectroscopic analysis of(DCOOD)2. The early works indicated that a resonance exists between the C==O asymmetricstretch and combination bands owing to the anomalous isotope effects on the intensities (7, 13).Ito and coworkers studied the FAD in the gas phase using cavity ring-down spectroscopy in theC–H and O–H stretching regions (14, 15). They reported Fourier transform infrared spectra inrare-gas matrices (16). In the time domain, femtosecond pump-probe methods were employed re-cently to study vibrational coupling both in solution and in the gas phase (17). Zielke & Suhm (18)reported the first Raman spectrum and the first direct observation of the intermonomer stretchingmode of the jet-cooled FAD. Yoon and coworkers (19) recorded the vibrational action spectrumof FAD, revealing strong Fermi coupling in (DCOOH)2 and its absence in (HCOOD)2 in theC–D and C–H stretching regions, respectively.
Early theoretical work obtained the approximate FAD equilibrium geometry and its elec-tronic structure. Ab initio predictions on the structure of FAD agreed well with the experimentalstructures as determined by electron diffraction. Specifically, Neuheuser and coworkers’ (20) abinitio structure predictions at the MP2 level of theory with counterpoise correction for basis setsuperposition error still provide the best agreement with the high-resolution data. These cal-culations predicted an O–O distance of 2.672 A. Density functional theory calculations yield aslightly smaller distance (2.645 A), estimating a slightly larger B value. In contrast, Kim’s (21)MP2 calculations and Yokoyama and coworkers’ (22) extended molecular mechanics calculationsslightly overestimated the O–O distance (2.707 A), thereby yielding a too small B value. Thesame argument holds for the results of the electron diffraction measurements, which obtained adistance of 2.696 A. There is also a reasonable agreement with the rotational constants as pre-dicted by the potential of Yokoyama and coworkers (22). However, their semiempirical modelpotential was directly set up to reproduce the experimental vibrational frequencies and the bondlengths in the monomers. Table 1 compares the rotational constants of FAD isotopes at theground vibrational level obtained from theoretical predictions with the experimental results todate.
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Table 1 Experimental and theoretical rotational constants
Matrix isolation:spectroscopytechnique in which afew percent of theanalyte is codepositedon a transparentcryogenic (T < 100 K)surface together withan inert matrix such asrare-gas, N2, orglass-forminghydrocarbons
4. AGGREGATION OF THE FORMIC ACID DIMERAT ULTRACOLD TEMPERATURES
The aggregation in supersonic nozzles is known to yield an efficient population of the thermody-namically most stable structure. The monomers are at room temperature before they cool downby collision. A distinct aggregation process is found in argon and neon matrices and in heliumnanodroplets. For both cases, the monomers are cooled prior to aggregation, which can leadto aggregation in structures that correspond to local rather than global minima in the potentialsurface. Gantenberg et al. (23) reported an infrared matrix isolation study of FAD in argon ma-trices, indicating the presence of an additional isomeric structure that could be attributed to anacyclic dimer. This structure rearranged into the well-known double-hydrogen-bonded structureat higher temperatures. The special dimerization process of FAD in ultracold matrices has been
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found to be a more general phenomenon: In 2004, the observation of the same polar acyclicsingle-hydrogen-bonded structure was reported in superfluid liquid helium droplets, establishingthe unique cluster growth process at ultracold temperatures (24). Based on these experimentalresults, researchers investigated theoretically a new alternative dimerization mechanism by whichtwo formic acid monomers proceed through an acyclic dimer to the cyclic dimer in a stepwiseprocess and predicted the corresponding barrier and dissociation energy. When the monomers areprecooled, dimerization leads preferentially to the formation of an acyclic polar dimer with oneO–H· · ·O and one C–H· · ·O contact. The accompanying calculation shows that this structure,which corresponds to a local minimum on the potential surface, is formed because the dominatingdipole-dipole interaction at long range favors a preorientation and alignment of the two monomersand thus the formation of a polar structure rather than the double-hydrogen-bonded nonpolarstructure. Although the binding energy of the double-hydrogen-bonded structure exceeds thatof the acyclic structure by 4.4 kcal mol−1, the formation of the cyclic structure would involve atransition state that exceeds the internal energy of the precooled monomers and the helium envi-ronment by far. The FAD is thus trapped in the local minimum. In general, it is interesting thatthe unique growth of dimers in helium nanodroplets leads to a kinetically rather than thermody-namically controlled aggregation process and can give access to parts of the potential surface thatcannot be explored in gas-phase studies.
5. PROTON TUNNELING DYNAMICS
The exchange of the acidic protons can be described by a multidimensional potential with equiva-lent double-well minima. Because the dimers are bound by two cooperatively strengthened hydro-gen bonds, the barriers are high compared to the zero point energy. The proton transfer gives riseto a splitting of each rotational-vibrational state into two states (El and Eu) that are separated by�E = hνtunneling, where νtunneling is the tunneling frequency of double-proton transfer. An accurateprediction of tunneling splitting even for this small prototype system still remains as a challengefor theoretical chemistry because of the great sensitivity of the splitting to the shape and barrier ofthe potential surface. The FAD has therefore evolved into a prototype system to study theoreticalmethods for a description of proton transfer.
The exact mechanism of proton transfer has been a matter of debate for a long time. We candescribe the coherent proton transfer either as a synchronous concerted double-proton transferor as an asynchronous step-by-step movement (at least in the beginning phase). It was initiallysuggested that it is synchronous using a direct dynamics calculation, in which two monomers firstapproach each other and decrease the barrier for tunneling before proton transfer takes place(21). At the transition state, the structure of FAD changes from C2h to D2h symmetry. Shida andcoworkers (25) predicted that a synchronous concerted double-proton transfer is the major modeof the reaction, which was confirmed in a molecular dynamics calculation (26). However, thereare also studies that describe the reaction as a successive step-by-step reaction (27). More recently,Car-Parrinello molecular dynamics was employed to study the nature of the double-proton trans-fer, and a concerted proton transfer reaction was predicted (28). One group proposed a differentmechanism for the interconversion of the hydrogen-bonded FAD (quantum entanglement) (29).More recently, it has become possible to use a diabatic approach to the problem using a reac-tion surface Hamiltonian (30). Barnes and coworkers (30) were able to predict the vibrationalmode-specific enhancement of the splitting, which requires the development of high-precisiontheoretical methods. Matanovic and coworkers (31) derived a set of mass-weighted internal coor-dinates to study the proton transfer reaction and calculated four doublets with splittings of 2.76,0.07, 0.60, and 4.03 cm−1 in the symmetric OH-stretch vibration region.
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Table 2 Experimental and predicted tunneling splitting values in cm−1 of theground and vibrationally excited state
Reference Ground state Excited statePredictedChang et al. (32) 0.3Shida et al. (25) 0.004Ushiyama et al. (27) 111Vener et al. (33) 0.3Tautermann et al. (34) 0.0022Smedarchina et al. (35) 0.012509Mil’nikov et al. (36) 0.0038Luckhaus (37) 0.0013Barnes et al. (30) 0.006ExperimentalMadeja & Havenith (8)a 0.00286(25) 0.00999(21)Ortlieb & Havenith (11)b 0.0158(4) 0.0100(3)Gutberlet et al. (12)c ≤0.002
a(DCOOH)2.b(HCOOH)2.c(DCOOD)2.
In the literature, the values for the tunneling splitting for proton transfer in the vibrationalground state cover a broad range. The initial predictions place the value at 0.3 cm−1 (32). Shidaand coworkers (25) estimated the splitting as 0.004 cm−1 using a reaction surface Hamiltonian andmodified couple pair functionals. However, using a similar approach, Vener and coworkers (33)estimated a tunneling splitting of 0.3 cm−1. Conversely, Ushiyama & Takatsuka (27) predicted
Table 3 Correlation between C2h and G8 symmetry groups
C2h G8
(HCOOH)2
Ag (10)a A′1 (1) ⊕ A′′
1 (9)Au (10) A′
2 (1) ⊕ A′′2 (9)
Bg (6) B ′1 (3) ⊕ B ′′
1 (3)Bu (6) B ′
2 (3) ⊕ B ′′2 (3)
(DCOOH)2
Ag (5) A′1 (2) ⊕ A′′
1 (3)Au (5) A′
2 (2) ⊕ A′′2 (3)
Bg (7) B ′1 (6) ⊕ B ′′
1 (1)Bu (7) B ′
2 (6) ⊕ B ′′2 (1)
(DCOOD)2
Ag (5) A′1 (4) ⊕ A′′
1 (1)Au (5) A′
2 (4) ⊕ A′′2 (1)
Bg (4) B ′1 (2) ⊕ B ′′
1 (2)Bu (4) B ′
2 (2) ⊕ B ′′2 (2)
aThe spin statistical weights are shown in parentheses in case of proton transfer.
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Asymmetric rotor:rigid rotor withdifferent moment ofinertia around allthree-principle axes
Tunnelingmotion/protontunneling: describesthe transfer of onehydrogen atom fromone oxygen to another;although the energybarrier is too high toovercome in a classicalpath, the hydrogentunnels through thebarrier instead
a transfer time of less than 150 fs, which places the estimated splitting (∼111 cm−1) orders ofmagnitude larger than any other prediction before. The first experimental determination ofproton transfer was reported by Madeja & Havenith (8). Owing to an ambiguity, they deduced thesplitting to be in the region between 0.00286 cm−1 and 0.0125 cm−1. More recently, this ambiguitywas removed when the tunneling splitting of the vibrational ground state of (HCOOH)2 wasdetermined to be 0.0158(4) cm−1 (11). In comparison, the theoretical studies following this initialestimate obtained the following results: Tautermann and coworkers (34) estimated the value as0.0022 cm−1; Smedarchina and coworkers (35) predicted the splitting closer to the experimentalvalue, 0.012509 cm−1; and other predictions place the splitting at 0.0038 cm−1 (36) and 0.0013 cm−1
(37). Table 2 presents a comparison of the experimental and predicted tunneling splittings.
6. ANALYSIS
The vibrational symmetry of the ground state and the vibrationally excited (antisymmetric C==Ostretch) state of FAD is Ag and Bu, respectively. The FAD ring assumes the C2h symmetry aroundthe double-well minima. The rotational levels are described by their quantum number J, Ka, and Kc
because the FAD is an asymmetric rotor. When a tunneling motion is feasible, molecular symmetrybecomes G8 (isomorphic to D2h; see Table 3). Each rovibrational level is split into two states due to
Au/Bu
B2'' /A2
'
B1u /Au
C2h G8 D2h C2h
B2u /B3u
B2u /B3u
B1u /Au
B2u
B1u
B2'' /A2
'
B2' /A2
''
T2
T2
b-typea-type
T2
B2' /A2
''
Ka = 1
Ka = 1
Ka = 0
Ka = 1
Ka = 0
Au/BuBu Bu
Ka = 0
Ag/Bg
A1' /B1
''
A1'' /B1
'
A1'' /B1
'
A1' /B1
''
Ag/B1g
Ag/B1g
B3g/B2g
B3g/B2g
B3g
Ag
T1
T1 T1
Ka = 1Ka = 1
Ka = 0
Ka = 1
Ka = 0
Ag/BgAg Ag
Ka = 0
Figure 4Energy-level scheme of formic acid dimer. The vibrational symmetry for v = 0 and v = 1 is Ag and Bu,respectively. The rovibrational symmetries in C2h are Ag and Bg for v = 0 and Au and Bu for v = 1. Eachrovibrational level is then split into two tunneling states. On the left side, the energy-level scheme displaysthe case when the rotational splittings exceed the tunneling splitting; on the right side, the scheme displaysthe case when the tunneling splitting exceeds the rotational splitting.
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Table 4 Molecular constants for formic acid dimer isotopomers in cm−1
(HCOOH)2
State El νC = O = 0 Eu νC = O = 0 El νC = O = 1 Eu νC = O = 1A 0.20240(3) 0.20241(3) 0.20190(3) 0.20186(3)B 0.07623(2) 0.07645(2) 0.07575(2) 0.07552(2)C 0.05547(3) 0.05537(3) 0.05504(3) 0.05501(3)DJ/10−8 −3(8) 7.4(5) 10.6(7) 8(3)DJK /10−7 8.1(2) −5.5(2) 6.4(2) 9.8(2)ν0 0 0.0158(4) 1225.3480(4) 1225.3380(2)�I (amu A2) −0.5078 0.7036 0.2188 −0.3054(DCOOH)2
State El νC = O = 0 Eu νC = O = 0 El νC = O = 1 Eu νC = O = 1A 0.20205(1) 0.20205(1) 0.20162(1) 0.201606(9)B 0.070585(5) 0.070628(6) 0.070288(6) 0.070256(5)C 0.052373(4) 0.052309(4) 0.052210(4) 0.052103(4)DJ/10−8 6(3) 6(3) 8(3) 6(2)DJK /10−7 3(1) 4(1) 2.4(9) 1.8(9)ν0 0 0.00286(25) 1244.83963(24) 1244.85248(9)�I (amu A2) −0.38(3) 0.16(3) −0.57(3) −0.02(3)(DCOOD)2
State νC = O = 0 νC = O = 1A 0.19636(2) 0.19597(2)B 0.06998(4) 0.06936(5)C 0.05159(7) 0.05132(8)DJK /10−7 −5.8(8) −8(7)ν0 0 1717.5177(4)�I (amu A2) 0.0(3) −0.6(3)
Watson S-reducedHamiltonian:commonly usedHamiltonianintroduced by J.K.G.Watson to model therotational levels of thevibrational groundstate of polyatomicmolecules
tunneling, designated as the upper and lower state (Figure 4). The overall symmetry of each statein the molecular symmetry group G8 is the product of the vibrational, rotational, and tunnelingsymmetries. Experimentally, one can determine the proton transfer tunneling splittings in theground and vibrationally excited states separately when measuring both a- and b-type transitions.The a-type (�Ka = 0) and the b-type (�Ka = 1) transitions describe a distinct reorientation ofthe angular momentum with respect to the axes of inertia of the molecule upon rovibrationalexcitation. It is possible to work out the splitting of the energy levels, assign the correct symmetry,and obtain the sum and the difference of the tunneling splitting in the ground and vibrationallyexcited states independently using isotopically labeled molecules. The intensity ratio arising fromthe spin statistics allows one to assign the observed transitions. Table 3 presents an overview ofthe statistical weights of the symmetry species in the relevant point groups.
For instance, in the (HCOOH)2 [(DCOOH)2] case, the electric dipole moment has A′1 (A′
2)symmetry, which implies that the transitions A′
1 ↔ A′2, A′′
1 ↔ A′′2, B′
1 ↔ B ′2, and B ′′
1 ↔ B ′′2
are allowed. For the b-type transitions, the selection rules require a change of tunneling state as(u) ↔ (l), where u represents the upper state and l the lower state. Conversely, for the a-typetransitions, the rules dictate (u) ↔ (u) or (l) ↔ (l).
The experimental data can be analyzed using a standard rigid rotor Watson S-reduced Hamil-tonian. Following the simultaneous fitting procedure, molecular constants reported in Table 4are obtained.
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For planar molecules, the inertial defect �I, �I = IA − IB − IC , where IX is the moment ofinertia around the x axis, should be zero. Slightly positive values for Eu and negative values forEl states of the ground state of (DCOOH)2 were reported (8). For the excited state, the El stateshad similar negative values (see Table 4). Ortlieb & Havenith (11) also observed positive andnegative values for the inertial defects of the Eu and El states of the ground state of (HCOOH)2,respectively. However, for the vibrationally excited state, although the order of magnitude remainsthe same, the sign of the inertial defect changes. In the case of (DCOOD)2, a zero inertial defect(within experimental uncertainty) for the ground state and slightly negative inertial defect for thevibrationally excited state were reported (12). A semiempirical fit of the structure eliminated theinitial assumption of an out-of-plane motion, which was initially anticipated. However, the fit alsohints that the hydrogen-to-deuterium substitution slightly affects the hydrogen bonds, changingboth the intermolecular distance and the tunneling probability, especially in the ground state ofthe complex.
7. CONCLUSIONS
The double-proton tunneling phenomena of the FAD has been studied with high-resolution in-frared spectroscopy. These experiments reached high-enough resolution to observe the tunnelingsplitting and to deduce the amount of the splitting in the ground and in the vibrationally excitedstate of the dimer. This information is essential to use this system as a benchmark to test theoreticalapproaches to double-proton tunneling before tackling more complicated systems.
DISCLOSURE STATEMENT
The authors are not aware of any biases that might be perceived as affecting the objectivity of thisreview.
ACKNOWLEDGMENTS
We would like to acknowledge financial support from the DFG within and FOR 618(HA2394/13-1).
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