Microwave Spectroscopy and Proton Transfer Dynamics in the Formic Acid-Acetic Acid Dimer Brian Howard, Edward Steer, Michael Tayler, Bin Ouyang (Oxford University); Helen Leung, Mark Marshall (Amherst College) and John Muenter (University of Rochester )

Carboxylic Acid Dimers Some of the most strongly bound hydrogen bonded complexes; Present in large concentrations in the gas phase; Microwave spectra of complexes including trifluoroacetic acid well studied; Would appear to have very simple spectra. However!!!! – can be many complications

3 Tunnelling (i.e. Proton Transfer) motion in formic acid dimer: Formic acid dimer H1H1 H1H1 H2H2 H2H2 = 474 MHz for (HCOOH) 2,  = 1.0 ns; 369 MHz for (DCOOH) 2 (1, 2),  = 1.3 ns. (1)Madeja, F.; Havenith, M. J. Chem. Phys. 2002, 117, (2)Ortlieb, M.; Havenith, M. J. Phys. Chem. A 2007, 111, 7355.

4 For acetic acid – formic acid dimer, we have two different tunnelling motions: (1) internal rotation of the methyl group; (2) proton transfer in carboxylic groups; CH 3 COOH – HCOOH dimer 00 60  120 

5 Wave-functions aaaa bbbb

6 For proton transfer to occur, we need not only permute identical atoms (12), (34) and (56) but also rotate about the a-axis by  2, therefore the spin statistics of the “+” and “-” states depend on symmetry the rotational wavefunctions. Spin statistics of motion (2) Weight+  K a =even412 K a =odd124

7 Resultant states Internal rotation gives A and E states, each with weight of 4; Proton transfer motion gives “+” and “  ” states, each with weight of either 3 or 1. Four resultant states: A +, A , E + and E  with nuclear spin statistics either being 12 or 4 (ratio 3:1).

8 Real spectra for J = 4  3 (K a = 3) WeightA+A+ AA E+E+ EE K a =even1313 K a =odd3131

Further complications As well as the effects of proton transfer tunnelling and the methyl group internal rotation, the proton transfer itself creates “vibrational” angular momentum. To overcome this one can move to an axis system in which this vibrational angular momentum is zero (a so-called Eckart frame). This corresponds to a non-principal axis system as the directions of the a- and b- principal axes change their directions on tunnelling.

10 Without tunnelling motions, we always choose a principal axis system to simplify the rotation Hamiltonian as H = A J a 2 + B J b 2 + C J c 2 However, the proton transfer tunnelling motion tilts the principal axis system between a 1 to a 2. There is no unique principal axis system for both conformations, and we have to instead use the average axis system from which the cross-term F ab J a J b comes out. Why F ab J a J b comes out? a1a1 a2a2 a average + F ab (J a J b +J b J a )

11 Rotational Motion H = A (J a - j a ) 2 + B (J a - j a ) 2 + C (J c - j c ) 2 + F ab [(J a - j a ) (J b - j b )+ (J b - j b ) (J a - j a )] + centrifugal distortion = A J a 2 + B J b 2 + C J c 2 + F ab (J a J b +J b J a ) -2AJ a j a -2BJ b j b -2CJ c j c -2F ab (J a j b +J b j a ) (Coriolis) +A j a 2 + B j b 2 + C j c 2 + F ab (j a j b +j a j a ) (Internal rotation) Hamiltonian describing the rotation:

Effects of Coriolis term In A state no Coriolis interaction (behaves normally) In E states, the Coriolis interactions can have first order effects on the spectrum (because of non-zero internal angular momentum) This is modelled by including terms like D a J a in the Hamiltonian (with D a = -2Aj a and j a =λ a j) The Coriolis terms can also have second order effects in both A and E states, yielding corrections to the rotational constants, which are different for the A and E states

Spectroscopic Constants A+A-E+E- A/MHz B/MHz C/MHz D a /MHz F ab /MHz G b /MHz34.51 V-+/MHz Δ a /MHz Centrifugal constants - D J, D JK, D K, d 1 and d 2 - all determined

14 Dynamics H = H internal + H rotational where H internal = F j 2 + (V 3 / 2) (1 – cos3  ) z – (ħ 2 /2  ) ∂ 2 /∂ z 2 +V 2 (1 – z 2 ) 2 Hamiltonian describing the dynamics: The underlined potential term couples the two tunnelling motions. (z is the tunnelling coordinate, like the NORMAL coordinate, describing how far motion (2) has gone)

Analysis of potential constants The internal rotation and the H-transfer tunnelling frequency enable the modelling of the potential Least squares fitting of the data provide V 2 = 8000 ±100 cm -1 and V 3 = cm -1 Although these numbers are slightly dependent upon the precise functional form of the potential surface, they do provide a reliable estimate of the barriers to the two tunnelling motions.

Effects of deuteration (1) Deuteration of the formic acid at the C atom provides similar spectra These can be analysed in the same way Rotational constants respond as expected on deuteration The proton tunnelling frequency increases on deuteration from MHz to MHz. However as the reduced mass for the motion must increase slightly, this implies a slight reduction in the V 2 barrier, possibly from zero-point motion effects Similarly the internal angular momentum increases from to , with a reduction in the barrier V 3 barrier

Effects of deuteration (2) Partial deuteration of the carboxylic acid protons permits the formation of several species: D-formic + H-acetic (abbreviated DH) H-formic + D-acetic (abbreviated HD) D-formic + D-acetic (abbreviated DD) For the asymmetric dimers (DH and HD) proton/deuteron transfer is suppressed; they can still have methyl rotation. The DD form can still possess hydrogen (or deuteron) transfer + internal rotation All three forms have been analysed. They also show deuterium quadrupole structure which further complicates the spectroscopy.

A State Constants HHHDDHDD A/MHz B/MHz C/MHz F ab /MHz ν tun/ MHz Χaa/kHz 167.3(11)168.9(15)167.8(6) Note strange behaviour of B rotational constants Increase on acetic acid deuteration Example of the Ubbelohde effect H-bond length shortens on deuteration Large decrease in tunnelling frequency on deuteration

E State Constants HHHDDHDD A/MHz B/MHz C/MHz ν tun/ MHz D a /MHz D b /MHz j Χaa/kHz 176(10)166(10)162(4) Internal angular momentum increases on acetic deuteration, but reduces on formic deuteration Reflects change in barrier height

13 C Isotopic Substitution The dimers formed by 13 C substitution at each of the three carbon atoms have been observed in natural abundance. All tunnelling components (A +,A -,E + and E - ) for each of the three species have been observed, although the analysis is incomplete. Because of the low concentration of species and the very small b-type dipole moment, it has not been possible to directly observe the proton tunnelling frequency.

Conclusions for 13 C species In all cases, none of the tunnelling frequencies were measured directly, but the data are compatible with no change The shift in rotational constants is exactly what is expected from the change in isotope mass No detectable change in the internal angular momentum 13 C substitution has little effect on the barrier to internal rotation Very little zero-point motion to the internal potential energy surface

Acknowledgements We thank the EPSRC(UK) for financial support MT thanks Corpus Christi College, Cambridge for a Summer Studentship