Matrix Isolation and Ab Initio Study of Trans-Trans and Trans-Cis Dimers of FormicAcid

Kseniya Marushkevich,† Leonid Khriachtchev,*,† Jan Lundell,‡ Alexandra Domanskaya,† andMarkku Rasanen†

Department of Chemistry, UniVersity of Helsinki, P.O. Box 55, FIN-00014 Helsinki, Finland, and Departmentof Chemistry, UniVersity of JyVaskyla, PL 35, FIN-40014 JyVaskyla, Finland

ReceiVed: December 4, 2009; ReVised Manuscript ReceiVed: January 27, 2010

Six trans-trans and five trans-cis dimeric structures of formic acid (HCOOH) are revealed by ab initiocalculations. Four trans-trans and two trans-cis dimers are identified in the IR absorption spectra in argonmatrices. The trans-cis dimers are obtained by narrow-band IR excitation of the vibrational transitions ofthe trans-trans dimers. Two trans-trans (tt3 and tt6) and one trans-cis (tc4) dimer are characterizedexperimentally for the first time. The tunneling decay rates of two trans-cis dimers (tc1 and tc4) are evaluatedat different temperatures. A greater lifetime of the trans-cis dimers at elevated temperatures compared to thecis-monomer suggests that the high-energy conformers can be stabilized upon hydrogen bonding.

Introduction

Understanding the conformational properties of molecules isimportant in chemistry.1,2 For example, many life processesdepend on light-induced conformational changes,3 and somereactions have definite stereochemical requirements, like in thecase of the E2 elimination.4 Recent studies have demonstrateda dependence of photodissociation products on the groundconformation state for several molecules.5–7

Formic acid (FA) is the simplest carboxylic acid and a suitablemodel to study conformational changes. It has two planarconformers that differ by orientation of a hydrogen atom withrespect to the C-O bond (Figure 1).8,9 The trans form is lowerin energy by ca. 1365 cm-1 (15.3 kJ mol-1).8 cis-FA can beprepared by vibrational excitation of the lower-energy trans formby narrow-band IR light.9 This method proved to be a powerfultool to study conformational changes in cryogenic matrices.10

cis-FA converts back to trans-FA via hydrogen tunneling, whichis confirmed by the characteristic isotope and temperaturedependencies.10–12 The cis-FA to trans-FA tunneling ratedepends strongly on the matrix material.10–14 The conformationalchange can also be induced by vibrational excitation of the hostas demonstrated for FA in solid hydrogen.14

Formic acid is also useful to study the effects of hydrogenbonding. FA dimer is a simple organic system, which can formseveral hydrogen-bonded structures.15–17 Figure 2a shows sixcomputationally stable trans-trans dimers. The lowest in energyis the trans-trans cyclic symmetrical dimer tt1. The FA gasconsists mainly of this dimer (95% at standard temperature andpressure).18 Other trans-trans dimers are higher in energy. Someof these structures have been identified in the gas phase,19 noble-gas matrices,20–22 and helium droplets.23

Two “mixed” trans-cis FA dimers were computationallypredicted by Roszak et al.17 We previously reported thevibrational spectrum of the most stable trans-cis FA dimerisolated in argon and neon matrices (FAD6 in ref 17, tc1 in

Figure 2b).13,24 The tc1 dimer was prepared by selectivevibrational excitation of the trans-trans dimer tt2. The stabilityof the tc1 dimer against hydrogen tunneling is substantiallyenhanced compared to the cis-FA monomer, and the stabilizationeffect was attributed to a complexation-induced increase of thecis-to-trans reaction barrier in the dimer as compared with themonomer. A strong stabilization effect was also found for cis-

* To whom correspondence should be addressed, leonid.khriachtchev@helsinki.fi.

† University of Helsinki.‡ University of Jyvaskyla.

Figure 1. trans- and cis-formic acid conformers.8,9

Figure 2. Calculated structures of (a) trans-trans and (b) trans-cisformic acid dimers. The interaction energies are given in parentheses(in kJ mol-1). Dotted lines show the hydrogen bonds.

J. Phys. Chem. A 2010, 114, 3495–3502 3495

10.1021/jp911515f 2010 American Chemical SocietyPublished on Web 02/18/2010

FA complexed with water; the tunneling decay of cis-FA ispractically stopped by this complexation.25

In the present work, we study FA dimers in solid argon. Inorder to prepare new dimers, we use resonant excitation ofvibrational transitions of lower-energy dimers, which changesthe conformational state. The identification of novel dimericstructures is done using quantum chemical calculations. Thehydrogen tunneling rate in the trans-cis dimers is measuredand discussed.

Computational Results

The equilibrium geometries, reaction barriers, and harmonicvibrational frequencies of trans and cis monomers and trans-transand trans-cis dimers of formic acid are calculated using thesecond-order Møller-Plesset perturbation method [MP2)full/6-311++G(2d,2p)] in the harmonic approximation. This levelof theory reproduces well the experimental structural andvibrational properties of trans-FA.26 The calculations wereperformed using the Gaussian 03 package.27 Six planartrans-trans and five planar trans-cis structures are found onthe intermolecular potential energy surface (PES) (see Figure2). All trans-trans dimers of formic acid contain two hydrogenbonds. Three trans-cis dimers possess two hydrogen bonds (tc1,tc2, tc4), and the tc3 and tc5 structures have one hydrogen bond.Our results for the trans-trans dimers are in agreement withthe results obtained by Chocholousova et al.16 and Olbert-Majkutet al.22 An ab initio study of Qian and Krimm reports seventrans-trans dimers.15 The cyclic structure VII from ref 15, whichis absent in our calculations, is the weakest dimer, and itprobably corresponds to a very shallow PES minimum. Severaldimers of different FA conformers were calculated by Roszaket al.17 In their calculations, the most stable trans-trans dimer(FAD1) has the symmetric cyclic structure and corresponds tothe tt1 dimer in our notation. The other trans-trans structuresdiscussed in their article are close to our structures tt2 (FAD2),tt5 (FAD3), and tt4 (FAD7), and their trans-cis structures FAD6and FAD8 have a similar geometry to the tc1 and tc5 dimersof the present work. The other structures considered in thepresent work (tt3, tt6, tc2, tc3, and tc4) were not studied byRoszak et al.17 The characteristic vibrational frequencies for thetrans-cis dimer tc1 were reported previously by our group.24

The tc2 structure has been recently computed by Yavuz andTrindle.28 To the best of our knowledge, no previous compu-tational reports are available for the tc3 and tc4 dimers.

Interaction Energies. The interaction energy of a dimer iscomputed as the energy difference between the dimer and thecomplex subunits (with the same geometry as in the dimer) atan infinite distance with the same basis sets and corrected byzero-point energies. The counterpoise method was used toaccount for the basis set superposition error (BSSE).29 Thecomputed interaction energies and hydrogen bond lengths arelisted in Table 1.

Structure tt1 (cyclic dimer), which corresponds to the globalenergy minimum, has two symmetrical O · · ·H-O hydrogenbonds and an interaction energy of -57.5 kJ mol-1. The firstlocal minimum for the trans-trans dimers corresponds to thenonsymmetrical structure tt2 (-30.5 kJ mol-1) with oneO · · ·H-O hydrogen bond and one C-H · · ·O hydrogen bond.The most stable trans-cis dimer (tc1, -34.2 kJ mol-1) differsfrom the trans-trans dimer tt2 by orientation of the free O-Hbond. Another trans-cis dimer (tc2, -31.4 kJ mol-1) is slightlyhigher in energy than tc1.

No correlation occurs between the number of hydrogen bondsand the interaction energy: the strongest and the weakest dimers

are double-bonded tt1 (-57.5 kJ mol-1) and tt3 (-8.7 kJ mol-1).However, the correlation between the interaction energy andthe hydrogen-bond type and length takes place. The FA dimershave two types of hydrogen bonds: O · · ·H-O (shorter than 2Å) and C-H · · ·O (substantially longer than 2 Å). As a trend,the structures with shorter hydrogen bonds are more stable thanthe dimers with longer hydrogen bonds. The weakest tt3 dimer(-8.7 kJ mol-1) has the longest C-H · · ·O bonds (2.41 and 2.51Å). For the trans-cis dimers, the strongest interaction is obtainedfor the tc1 structure (-34.2 kJ mol-1) with the shortestO-H · · ·O bond (1.76 Å). The single-bonded dimers tc3 andtc5 have similar interaction energies (-24.7 and -18.5 kJmol-1) and O-H · · ·O hydrogen bond lengths (1.81 and 1.86Å).

Complexation-Induced Shifts. Complexation promotes newintermolecular vibrational modes and influences the vibrationfrequencies of the dimer subunits. The complexation-inducedfrequency shifts are calculated as a difference between thefrequencies of the dimers and the monomers (see Table 2), andthey reflect the changes in the corresponding bonds and thecharge redistribution in the complex. The computational fre-quencies for characteristic modes of the trans-trans andtrans-cis dimers are given in Table 3 and Table 4.

The calculations predict large red shifts for the OH stretchingvibrations involved in hydrogen bonding (from -107.1 cm-1

for tt4 to -462.8 cm-1 for tt1). The shortest hydrogen bond(1.68 Å) and the largest OH stretching shift (-462.8 cm-1) arefound for the most stable structure tt1 with two symmetricalO-H · · ·O bonds. For the trans-cis dimers, the red shifts ofthe bonded OH stretching modes vary from -128.7 cm-1 (tc2)to -363.5 cm-1 (tc1). The unbounded OH stretching vibrationsshow small red shifts (<10 cm-1) in all trans-trans andtrans-cis dimers.

The CdO stretching mode is less sensitive to the complex-ation than the OH stretching mode, and the corresponding shifts

TABLE 1: Calculated Hydrogen Bond Lengths (Å) andInteraction Energies (in kJ mol-1) of the Trans-Trans andTrans-Cis Formic Acid Dimers (see Figure 2)

interaction energy

dimerhydrogen

bond length this work ref 16a ref 17b ref 22c

tt1 1.68 (O · · ·H-O) -57.5 -58.7 -63.3 -61.11.68 (O · · ·H-O)

tt2 2.34 (C-H · · ·O) -30.5 -35.8 -35.9 -34.51.77 (O · · ·H-O)

tt3 2.41 (C-H · · ·O) -8.7 -12.4 -7.82.51 (C-H · · ·O)

tt4 1.93 (O · · ·H-O) -22.7 -22.8 -27.1 -24.71.97 (O · · ·H-O)

tt5 2.41 (C-H · · ·O) -18.5 -27.6 -22.9 -18.31.89 (O · · ·H-O)

tt6 2.41 (C-H · · ·O) -11.9 -15.9 -12.22.41 (C-H · · ·O)

tc1 1.76 (O · · ·H-O) -34.2 -38.22.29 (C-H · · ·O)

tc2d 1.95 (O · · ·H-O) -31.41.85 (O · · ·H-O)

tc3 1.81 (O · · ·H-O) -24.7tc4 2.39 (C-H · · ·O) -9.6

2.50 (C-H · · ·O)tc5 1.86 (O · · ·H-O) -18.5 -22.5

a Calculations at the MP2/aug-cc-pVDZ level, BSSE-corrected.b Obtained from the dissociation energy of the complex, the MP2/aug-cc-pVDZ level, dimer-centered basis set. c B3LYP/6-311++G(2d,2p),BSSE-corrected. d This structure was calculated in ref 28, yieldingan interaction energy of -27.2 kJ mol-1.

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are typically below 40 cm-1. If a dimer has no center ofsymmetry, the two CdO stretching vibrations absorb at twodifferent frequencies. The calculated frequencies of the trans-transdimers tt1, tt2, tt3, and tt6 are red-shifted. The tt2 structureshows the largest shift of -50.1 cm-1 (-15.0 cm-1 for thesecond subunit). The tt3 structure exhibits the smallest shiftsof -12.8 and -4.1 cm-1 and the weakest interaction. The tt4and tt5 dimers have rather large red shifts (-27.8 and -16.1cm-1, respectively) for one subunit and small blue shifts (+3.3and +6.3 cm-1, respectively) for the second subunit. The shiftsobtained for the trans-cis dimers are of the same order ofmagnitude, varying from -3.8 and -12.9 cm-1 for tc4 (the leaststable trans-cis dimer) to -37.4 and -32.8 cm-1 for tc1 (themost stable trans-cis dimer).

The deformation mode (CO-COH) is very sensitive to thecomplexation. For the strongly bound trans-trans dimers (tt1and tt2) and all trans-cis dimes (except for tc4), the deformationfrequency undergoes a blue shift (up to +133.8 cm-1, i.e., ca.12% in tt1). The other trans-trans dimers demonstrate both redand blue shifts (up to -44.5 and +68.7 cm-1 in tt5).

For the tt3 and tt5 dimers, the torsional frequencies are blue-shifted (up to +159.6 cm-1 in tt5) for one molecule and red-shifted for the other molecule (up to -40.4 cm-1 in tt3). Forthe tt1, tt2, tt4, and tt6 dimers, both torsional vibrations areblue-shifted (up to +338.9 cm-1 in tt1). In all trans-cis dimers,the torsional frequencies are blue-shifted (up to +281.4 cm-1,i.e., ca. 52% in tc3).

Experimental Results and Discussion

The gaseous samples were prepared by mixing formic acid(HCOOH, KEBO LAB, 99%) with argon (AGA, 99.9999%)typically in the proportion 1:500. The samples were depositedonto a CsI substrate at about 25 K in a closed-cycle heliumcryostat (APD, DE 202A). Typically 100 µm thick matriceswere deposited during ca. 30 min. The IR absorption spectra inthe 4000-400 cm-1 spectral region were measured with aNicolet SX-60 FTIR spectrometer with resolution from 0.25 to1.0 cm-1 by coadding 100 or 200 interferograms. The matriceswere usually kept at 8.5 K during measurements.

Tunable pulsed IR radiation of an optical parametric oscillator(OPO Sunlite, Continuum with an IR extension) was used forvibrational excitation with the pulse duration of 5 ns, spectralline width of 0.1 cm-1, and a repetition rate of 10 Hz. A BurleighWA-4500 wavemeter measured the OPO signal frequencyproviding an absolute accuracy better than 1 cm-1 for the IR

difference frequency. During the kinetic measurements, a long-pass filter transmitting below 1800 cm-1 was installed betweenthe Globar source and the matrix to eliminate light-inducedconformational conversion.

Trans-Trans Dimers. Two trans-trans FA dimers (tt1 andtt2) have been previously identified in rare-gas matrices.20–22,24

We also observed the spectral features of these structures after

TABLE 2: Characteristic Calculated and ExperimentalFrequencies (in cm-1) and Intensities (in km mol-1 inparentheses) of the trans- and cis-FA Monomers

vibrational frequency

monomer assignment calculated experimenta

trans-FA ν(OH) 3783.9 (82.6) 3550ν(CdO) 1788.7 (335.2) 1767CO-COH def. 1316.8 (9.3) 1306b

1216b

1123.3 (284.1) 1104τ(COH) 676.6 (144.0) 635

cis-FA ν(OH) 3851.2 (82.6) 3616ν(CdO) 1829.0 (269.2) 1808CO-COH def. 1287.1 (297.0) 1249

1113.0 (79.5) 1105τ(COH) 536.6 (88.7) 505

a The strongest bands are shown. b Fermi resonance, 2τCOH/CO-COH def.

TABLE 3: Characteristic Calculated and ExperimentalFrequencies and Complexation-Induced Shifts (from theTrans Monomer, in cm-1) and Calculated AbsoluteIntensities (in km mol-1 in parentheses) of the Trans-TransDimers (see Figure 2a)

calculateda experimentb

dimer assignment frequency shift frequency shift

tt1 ν(OH) 3321.1 (2206.2) -462.8 3072 -478ν(CdO) 1767.0 (758.2) -21.7 1728 -39CO-COH def. 1421.4 (29.2) +104.6 1224 +120

1257.1 (364.1) +133.8 1225 +121τ(COH) 1015.5 (121.1) +338.9 939 +304

tt2 ν(OH) 3776.2 (91.1) -7.7 3540 -103451.0 (935.6) -332.9 3184 -366

3168 -3823154 -3963142 -4083101 -449

ν(CdO) 1773.7 (594.0) -15.0 1748 -191738.6 (130.0) -50.1

CO-COH def. 1402.0 (5.7) +85.21340.1 (30.1) +23.31205.3 (241.6) +82.0 1180 +761156.0 (298.0) +32.7 1131 +27

τ(COH) 936.1 (94.2) +259.5 868 +233699.0 (141.3) +22.4 658 +23

tt3 ν(OH) 3781.5 (77.2) -2.4 3537 -133779.4 (91.5) -4.5

ν(CdO) 1784.6 (342.6) -4.1 1765 -21775.9 (336.1) -12.8

CO-COH def. 1323.0 (15.9) +6.2 1114.6 +111131.6 (307.9) +8.31103.7 (299.6) -19.6

τ(COH) 684.6 (236.9) +8.0 661 +26636.2 (61.2) -40.4 667 +32

tt4 ν(OH) 3676.8 (514.9) -107.13566.2 (283.1) -217.7

ν(CdO) 1792.0 (227.7) +3.31760.9 (514.1) -27.8

CO-COH def. 1314.3 (36.7) -2.51179.9 (275.6) +56.61134.6 (510.9) +11.3

τ(COH) 864.4 (200.6) +187.8681.1 (59.6) +4.5

tt5 ν(OH) 3779.5 (86.8) -4.43634.8 (554.0) -149.1

ν(CdO) 1795.0 (392.7) +6.31772.6 (275.0) -16.1

CO-COH def. 1385.5 (9.0) +68.71181.3 (302.2) +58.01078.8 (234.8) -44.5

τ(COH) 836.2 (107.9) +159.6650.4 (141.8) -26.2

tt6 ν(OH) 3781.3 (168.7) -2.6ν(CdO) 1778.6 (629.1) -10.1 1756 -11CO-COH def. 1320.2 (26.7) +3.4 1092 -12

1119.4 (684.8) -3.9τ(COH) 685.5 (279.5) +8.9 642 +7

a Calculated bands with intensity >5 km mol-1 are presented.b The strongest experimental bands are presented.

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matrix deposition (see Table 3). According to Gantenberg etal., the tt2 dimer reorganizes to tt1 in argon matrices at 40 K,which suggests that the tt2 to tt1 conversion has a smallactivation energy.20 This model has been recently confirmed byRaman scattering measurements upon annealing of a FA/Armatrix from 4 to 35 K.22 Our annealing experiments are inagreement with the previous observations. This annealing-induced conversion can be useful for the identification of thecorresponding bands in various spectral regions.

The absorption bands in the bonded OH stretching region(3000-3200 cm-1) are broad and not well-defined as seen inFigure 3a, and the interpretation is not straightforward. Theassignments have been suggested several times.19,21,30 In themolecular jet experiments, the OH stretching band of the tt1dimer is observed at 3084 cm-1 accompanied by a number ofweaker bands at 3103, 3139, 3158, and 3180 cm-1.19 In an argonmatrix, the band at 3076 cm-1 was assigned to the OH stretchingmode of the tt1 dimer.21 In the present experiments, weconsistently observed the OH stretching band of tt1 at 3072cm-1, and the other tt1 absorptions are also in reasonableagreement with literature.20,21

The absorptions at 3101, 3142, 3154, 3168, and 3184 cm-1

observed in the present work are assigned to the tt2 dimer. The3101 and 3142 cm-1 bands were assigned to the tt2 dimerpreviously based on the tunneling recovery of tt2 from tc1.24

However, we now see that the excitation of the tt2 dimer at3540 cm-1 (unbounded OH stretching mode)24 efficientlybleaches all five absorptions (see Figure 3a). The calculationsshow that these bands are suitable to the bonded OH stretchingmode of the tt2 dimer (Table 3), and the splitting appearsprobably due to matrix site effect. When the matrix is annealedat 35 K, these five bands decrease together with other bands oftt2 whereas the bands of the tt1 dimer rise. The CdO stretchingand deformation bands of tt2 observed in the present work arein reasonable agreement with the literature data.20 The free OHstretching band of tt2 at 3540 cm-1 was assigned in our previouswork.24

One set of IR bands including the OH stretching band at 3537cm-1, CdO stretching band at 1765 cm-1, and CO-COHdeformation band at 1114.6 cm-1 is bleached by excitation at3537 cm-1. The calculations suggest that these absorption bandsbelong to the tt3 dimer (see Figure 2 and Table 3). Theexperimental OH and CdO stretching bands are red-shifted by-13 and -2 cm-1, and the computational shifts of the tt3 dimer

TABLE 4: Characteristic Calculated and ExperimentalFrequencies and Complexation-Induced Shifts (in cm-1),Calculated Absolute Intensities (in km mol-1 in Parentheses)of the Trans-Cis Dimers (see Figure 2b)

calculateda,b experimenta

dimer assignment frequency shift frequency shift

tc1 ν(OH) 3846.6 (108.1) -4.6 3604 -123420.4 (965.1) -363.5 3115 -435

3081 -4693074 -476

ν(CdO) 1796.2 (506.8) -32.8 1767 -411751.3 (122.0) -37.4

CO-COH def. 1300.8 (416.5) +13.7 1259 +101212.6 (221.0) +89.3 1186 +821153.1 (68.9) +40.1 1143 +39

τ(COH) 945.6 (91.7) +269.0 875 +240572.7 (85.5) +36.1 550 +45

tc2 ν(OH) 3655.2 (693.7) -128.73572.1 (287.6) -279.1

ν(CdO) 1819.7 (285.6) -9.31756.8 (334.6) -31.9

CO-COH def. 1392.6 (33.5) +75.81305.5 (686.4) +18.41186.9 (242.3) +63.61130.5 (77.7) +17.5

τ(COH) 847.6 (193.7) +171.0680.3 (20.6) +143.7

tc3 ν(OH) 3774.5 (95.2) -9.43615.2 (980.0) -236.0

ν(CdO) 1818.0 (242.2) -11.01765.4 (544.4) -23.3

CO-COH def. 1396.4 (305.7) +109.31339.5 (64.6) +22.71164.2 (182.2) +51.21159.6 (284.0) +36.3

τ(COH) 818.0 (78.9) +281.4694.5 (144.3) +17.9

tc4 ν(OH) 3850.4 (90.6) -0.8 3603 -133778.4 (77.0) -5.5

ν(CdO) 1816.1 (274.9) -12.9 1807 -11785.1 (324.4) -3.8

CO-COH def. 1302.3 (7.6) -14.51289.1 (345.6) +2.0 1268 +191122.3 (84.6) +9.3 1119 +141099.3 (295.9) -24.0 1060 -44

τ(COH) 678.3 (142.6) +1.7 686 +51547.0 (84.2) +10.4 534 +29

tc5 ν(OH) 3846.6 (106.0) -4.63586.3 (803.1) -197.6

ν(CdO) 1814.8 (246.8) -14.21776.3 (465.2) -12.4

CO-COH def. 1290.3 (319.5) +3.21173.7 (342.5) +50.41141.0 (28.3) +28.0

τ(COH) 884.5 (103.6) +207.9551.1 (93.8) +14.5

a The shifts are given from the frequencies of the correspondingmonomers. The data for the cis molecule in a dimer are shown initalics. b Calculated bands with intensity >5 km mol-1 are presented.

Figure 3. (a) IR spectra in the bonded OH stretching fundamentalregion (HCOOH:Ar ) 1:1000, deposited at 25 K). The upper traceshows the spectrum after deposition with the tt1 and tt2 absorptions.The lower trace is a difference spectrum demonstrating the appearanceof the tc1 dimer by vibrational excitation of the tt2 dimer. (b) Action(RVE) spectrum of the IR-induced tt2 to tc1 conversion efficiency inthe bound OH stretching overtone region. Symbols (0) and (b) showthe data of two different series of experiments.

3498 J. Phys. Chem. A, Vol. 114, No. 10, 2010 Marushkevich et al.

are -4.5 and -2.4 cm-1 for the OH stretching modes and -12.8and -4.1 cm-1 for the CdO stretching modes. For theCO-COH deformation mode, the calculations predict a blueshift for one component +8.3 cm-1 and red shift for another(-19.6 cm-1), but only the blue-shifted band (+11 cm-1) isobserved experimentally.

The present assignment of the tt3 dimer requires specialattention because its bands appear close and sometimes evenoverlapped with the absorptions of the FA complex withnitrogen which may be always present in matrices as animpurity. FA forms two types of complexes with N2 in an Armatrix (structure 1 and structure 2 in ref 31) with differentthermal stability. In our experiments, the matrices were depositedat higher temperatures than those in ref 31 (25 K vs 15 K). Asa result, we observe the relatively abundant complex withstructure 1 (more stable) whereas structure 2 leaves only weaktraces. Figure 4a presents IR absorption spectra of the OHstretching region of an FA/Ar matrix after deposition. The bandat 3550 cm-1 belongs to the trans-FA monomer;9 the bands at3540 and 3537 cm-1 are assigned to tt2 (ref 24) and tt3 (thiswork). The band at 3531.7 cm-1 originates from HCOOH · · ·N2

in structure 1 (marked with asterisk),31 and this band remainsunchanged upon resonant IR irradiation and annealing at 35 K.The 3538.0 cm-1 absorption band of structure 2 (ref 31) cannotbe found in the present experimental spectra.

In the CdO stretching region, the tt3 absorption at 1765 cm-1

overlaps with the corresponding band of the nitrogen complex(structure 1). We suppose that the tt3 dimer absorbs at thisfrequency because the band intensity partly decreases underirradiation at 3537 cm-1 whereas the 3531.7 cm-1 band ofHCOOH · · ·N2 (structure 1) in the OH stretching region remainsunchanged. In Figure 4b, the bands at 1728, 1748, 1765, and1767 cm-1 belong to the tt1, tt2, tt3 (together with the nitrogencomplex) dimers and the trans-FA monomer, respectively.

A similar situation occurs in the CO-COH deformationregion. The band of the tt3 dimer at 1114.6 cm-1 is very closeto the band at 1114.3 cm-1 of the N2 complex (structure 1),although some asymmetry of the absorption profile can be seen

in the high-resolution spectra. The assignment of this band isbased on the IR-induced conformational change. In the sameregion, a weak absorption at 1108.7 cm-1 of HCOOH · · ·N2

(structure 2) is observed.31 It does not decrease upon IRirradiation but completely vanishes after annealing at 35 K.

The bands at 661 and 667 cm-1 (broad) are assigned to thetorsional mode of the tt3 dimer. In this region, the tt3 dimerdoes not interfere with the HCOOH · · ·N2 absorption. The bandsof the N2 complexes are shifted by +1.4 cm-1 for structure 1and -4.9 cm-1 for structure 2 from the trans-FA monomerwhereas the tt3 dimer demonstrates a larger blue shift (+26and +32 cm-1).

Three bands at 1756, 1092, and 642 cm-1 slowly rise uponexcitation at 3168 cm-1 of the bonded OH stretching mode ofthe tt2 dimer, and they are assigned to the tt6 dimer. In additionto tt6, this prolonged irradiation produces the tt1 dimer and thecomplex of trans-FA with water which is present in the matrixas an impurity (see Figure 5).25,32 For the tt6 dimer, thecomputational and experimental complexation-induced shifts ofthe CdO stretching mode are -10.1 and -11 cm-1, respec-tively, and the CO-COH deformation mode is also red-shiftedby -3.9 (calculation) and -12 cm-1 (experiment). Similar tothe tt3 dimer, the calculations predict two CO-COH deforma-tion absorptions with shifts of different sign (-3.9 and +3.4cm-1), but we observed only the red-shifted band (-12 cm-1).The blue-shifted band is computationally much weaker than thered-shifted band, which explains its absence in the experimentalspectra. The experimental shift of the torsional mode (+7 cm-1)agrees well with the computational value (+8.9 cm-1). Thecomputations give no alternative candidates for these experi-mental absorptions. The tt6 dimer presumably forms from thett2 dimer upon vibrational excitation, which is energeticallypossible and involves an extensive rearrangement of the heavyatoms. It should be noted that the tt1 dimer (the most stablestructure) is the second product of this irradiation process, andit is produced in relatively large amounts. To our knowledge,the tt3 and tt6 dimers are identified in the present work for thefirst time.

The concentration of different trans-trans dimers after matrixdeposition does not correlate with their relative energies. Thett1 dimer, which is the lowest in energy, is not dominating inas-deposited matrices in contrast to the gas phase data. On theother hand, the higher-energy tt3 dimer is relatively abundantafter deposition, suggesting a matrix stabilization effect. Thett1:tt2:tt3 ratio of the CdO stretching band intensities afterdeposition is ca. 1:1:1.5. This ratio depends on the depositionconditions in a complex way. The bands of the tt2 and tt3 dimersdecrease upon annealing at 35 K while the tt1 bands rise.

Figure 4. IR spectrum of formic acid in solid argon deposited at 25K. (a) OH stretching region. Asterisk marks the band of HCOOH · · ·N2

complex (structure 1).31 (b) CdO stretching region. Here theHCOOH · · ·N2 complex band overlaps with the tt3 band. The spectrumis recorded at 8.5 K.

Figure 5. Difference spectrum in the CdO stretching region showingthe result of prolonged excitation of the bonded OH stretching band ofthe tt2 dimer (3168 cm-1). The tt2 dimer (1748 cm-1) converts to thett1 and tt6 structures (1728 and 1756 cm-1) upon irradiation. Asteriskmarks the band of trans-FA complex with water,25,32 which is formedfrom matrix impurity water.

Trans-Trans and Trans-Cis Dimers of Formic Acid J. Phys. Chem. A, Vol. 114, No. 10, 2010 3499

Trans-Cis Dimers. The trans-cis FA dimers were preparedby light-induced rotation of the free OH bond of the corre-sponding trans-trans dimers. In particular, excitation of the tt2dimer at the free OH stretching frequency promotes several newbands, for instance, a characteristic absorption at 1259 cm-1 inthe CO-COH deformation region. The bands rising uponexcitation at 3540 cm-1 were assigned in our previous work tothe trans-cis dimer tc1 (see Figure 2).13,24 The trans-to-cisconversion can occur even at excitation below the torsionalbarrier (computationally ca. 4500 cm-1, see Figure 6), due tothe strong delocalization of the torsional states just below thebarrier as observed previously for monomeric FA.33

Excitation of the bonded OH stretching overtone of tt2produces the tc1 dimer. The irradiation frequency was tuned inthe 5800 to 6200 cm-1 spectral region, and the amount of tc1was estimated from the intensity of the CO-COH deformationband (1259 cm-1). The resulting reactive vibrational excitationspectrum (RVE or “action spectrum”) is shown in Figure 3b.These experiments demonstrate that the excitation of the bondedOH stretching overtone of the tt2 dimer leads to the rotation ofthe free OH bond in the other subunit (see Figure 7a). It isevidence of intermolecular energy transfer through a hydrogen

bond from one interacting molecule to the other subunit. Incontrast, the irradiation at the fundamental frequency of thebonded OH stretching mode of the tt2 dimer does not provideenough energy for the trans-to-cis conformational changes;however, it reorganizes the tt2 dimer to tt1 and tt6 as discussedabove.

Five broad bands at 6037, 6070, 6115, 6160, and 6185 cm-1

seen in the RVE spectrum correspond to the maximum tt2 totc1 conversion efficiency in the bonded OH overtone region.The RVE profile in this overtone region (Figure 3b) ap-proximately follows the absorption pattern of the bonded OHstretching fundamental (Figure 3a), suggesting a direct matchbetween these regions. We estimated the anharmonicity con-stants of the observed transitions by the formula x11 ) (ν0f2 -2ν0f1)/2.34 The anharmonicity constants vary from ca. -82 cm-1

(for the 3101 and 6037 cm-1 bands) to ca. -107 cm-1 (for the3142 and 6070 cm-1 bands) whereas this value is ca. -83 cm-1

for the trans-FA monomer (ν0f2OH ) 6933 cm-1).35 These data

agree with the hypothesis by Sandorfy that the hydrogen bondingtends to increase the anharmonicity.36

The excitation at 3537 cm-1 (free OH stretching mode ofthe tt3 dimer) gives rise to several bands, in particular, one at1807 cm-1 in the CdO stretching region. These bands areassigned to the trans-cis dimer tc4 produced by light-inducedrotation of the free OH bond in the tt3 dimer (see Table 4 andFigure 7). A reasonable agreement between the tc4 characteristicbands and the theoretical spectrum is observed. The OHstretching band of the cis subunit of tc4 is red-shifted from thecis-FA monomer by -13 cm-1 experimentally and by -0.8cm-1 computationally. The CdO stretching band of the cissubunit also appears red-shifted by -1 cm-1 (experiment) and-12.9 cm-1 (theory). Three deformation bands are observedwith proper complexation-induced shifts. The torsional modeshows a blue shift of +29 cm-1 experimentally and +10.4 cm-1

theoretically for the cis subunit. When comparing the theoreticaland experimental data, one should keep in mind that the structureand IR spectra of complexes in matrices can differ from thosecalculated in vacuum.

Cis-to-Trans Tunneling Decay. The trans-cis dimers (tc1and tc4) convert back to the corresponding trans-trans forms(tt2 and tt3) via hydrogen tunneling. A similar process of thecis-to-trans conversion was previously studied for monomericformic acid.10–12,37 Figure 8a shows the result of excitation at3538.6 cm-1, which is between the free OH stretching absorp-tions of the trans-trans dimers tt2 and tt3. This excitationpromotes both observed trans-cis dimers (tc1, tc4) and cis-FAmonomer, which is due to overlap of their OH stretchingabsorptions. The upper trace in Figure 8a presents the spectrumafter the IR excitation, and the lower trace is the spectrummeasured 6 min later. It is seen that the bands of the threespecies decrease differently. We followed the tunneling decaykinetics by monitoring the intensities of the deformation modesof the cis-FA monomer (1249 cm-1), dimer tc1 (1259 cm-1),and dimer tc4 (1268 cm-1). The high-frequency part of theGlobar light, which could accelerate the cis-to-trans conversion,was suppressed by a long-pass optical filter (>1800 cm-1).

The decay of the cis-FA monomer and tc1 and tc4 dimers at8.5 K is presented in Figure 8b. The tc1 dimer is evidently morestable than the tc4 dimer and cis-FA monomer. The tc1 lifetimeat 8.5 K is ca. 24 min, which is about three times greater thanthe tc4 lifetime (8.0 min) and the cis-FA monomer lifetime (7.3min). We have evaluated the computational torsional barriersfor the conformational processes at the MP2/6-311++G(2d,2p)level of theory with zero point energy correction (see Figure

Figure 6. Torsional barriers for the cis-trans conversion of FAmonomer, tc1-tt2 dimers, and tc4-tt3 dimers at the MP2/6-311++G(2d,2p) level of theory.

Figure 7. Observed conversion processes in formic acid dimers.

3500 J. Phys. Chem. A, Vol. 114, No. 10, 2010 Marushkevich et al.

6). The lowest stabilization barrier is obtained for the cis-FAmonomer (2676 cm-1). For the tc1 to tt2 and tc4 to tt3 processes,the barriers are 3432 and 2903 cm-1, respectively. The higheststabilization barrier can explain the slowest tunneling decay ofthe tc1 dimer compared to that of the cis-FA monomer and tc4dimer at the lowest temperature. A similar correlation betweenthe experimental tunneling rates and the computational reactionbarriers is observed for a number of carboxylic acids.10

The tunneling decay rates of cis-FA and tc1 and tc4 weremeasured at temperatures from 8.5 to 35 K (see Figure 8c). Asreported earlier, the cis-to-trans conversion of FA monomer issubstantially enhanced at elevated temperatures due to theinteraction with the matrix.11 The tc4 decay accelerates withthe increasing temperature but remains slower than that of cis-FA monomer. The tc1 decay is practically independent oftemperature in the 8.5-35 K interval. At temperatures below15 K, the tunneling reaction rate reaches a plateau for all threespecies, and this low-temperature limit is a fingerprint ofquantum tunneling from the lowest vibrational level of the initialspecies.38 The mechanism of the temperature dependencies ofthe tunneling reaction is not fully understood. The observed

difference between the temperature dependencies can in prin-ciple originate from the different reorganization energies of themedium and different couplings with phonon bath of theembedded species. Extensive theoretical work is required tounderstand the related mechanisms, which exceeds the scopeof the present work.

Conclusions

Six stable trans-trans and five trans-cis structures have beencomputationally characterized (see Figure 2), and their geom-etries, interaction energies, and IR spectra are evaluated at theMP2)full/6-311++G(2d,2p) level of theory. To our knowledge,the tc3 and tc4 dimers are considered here for the first time.

Four trans-trans and two trans-cis dimers are experimentallyidentified in solid argon. The trans-cis dimers are obtained byvibrational excitation of the trans-trans dimers. Figure 7summarizes the observed conformational changes. Excitationof the first overtone of the bonded OH stretching mode in thetrans-trans dimer tt2 (5800-6200 cm-1) leads to a conforma-tional change of the free OH bond in the other dimer subunit,resulting in the tc1 dimer. This observation is evidence of theenergy flow through a hydrogen bond, which is a remarkableresult that requires additional attention in future research.

The experimental frequency shifts upon complexation are ina good agreement with the calculated values (see Tables 3 and4). The present data for the tt1, tt2, and tc1 dimers develop theprevious assignements.13,20–24 To the best of our knowledge, twotrans-trans (tt3 and tt6) structures and one trans-cis (tc4)structure are experimentally found in the present work for thefirst time. The computationally predicted tt4, tt5, tc2, tc3, andtc5 dimers have not been identified in our experiments.

The trans-cis dimers convert to the trans-trans dimers viaquantum tunneling of hydrogen through the torsional barrier.The tunneling rates are obtained for two trans-cis dimers tc1and tc4 at different temperatures. At the lowest temperature (8.5K), the tc4 dimer and cis-FA monomer demonstrate a similarstability whereas the tc1 dimer appears more stable. Both dimerstc1 and tc4 are more stable than cis-FA monomer at elevatedtemperatures (∼30 K). Thus, the hydrogen bonding can lead tothe stabilization of unstable conformers. This stabilization effectwas also found previously for complexes of cis-FA with water25

and with atomic oxygen.39

Acknowledgment. This work was supported by the Academyof Finland through the Finnish Centre of Excellence in Compu-tational Molecular Science and by the Magnus Ehrnrooth founda-tion. A.D. acknowledges a postdoctoral grant from the Faculty ofScience of the University of Helsinki (Project No. 7500101).

Note Added after ASAP Publication. This article waspublished ASAP on February 18, 2010. In the first sentence ofthe Interaction Energies section of the Computational Results,the word “taking” was removed. The correct version wasreposted on February 22, 2010.

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Figure 8. Quantum tunneling of hydrogen in FA monomer and twodimers. (a) Two spectra in the CO-COH deformation region recordedwith an interval of 6 min. The bands at 1249 and 1243 cm-1 belong tocis-FA monomer, the bands at 1259 and 1268 cm-1 belong to the tc1and tc4 dimers, respectively. (b) Relative concentration of cis-FAmonomer and the tc1 and tc4 dimers as a function of time at 8.5 K.The lines show single exponential fits. (c) Tunneling decay rateconstants of the cis-to-trans conversion of monomeric FA and tc4 andtc1 dimers at different temperatures. The lines guide the eye. Thetunneling rate constants were determined by fitting the integrated bandintensities with a single exponential function.

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