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

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• Tunnelling (i.e. Proton Transfer) motion in formic acid dimer:

Formic acid dimer

H1 H1

H2 H2

= 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, 7162.

(2) Ortlieb, M.; Havenith, M. J. Phys. Chem. A 2007, 111, 7355.

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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;

CH3COOH – HCOOH dimer

0 60 120

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Wave-functions

C

O1

O2 H6

C

O4

O3H5

HH3C C

O2

O1 H5

C

O3

O4H6

HH3C

a a b b

a a b b

1( )21( )2

aa bb

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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)

(12)(34)(56)

Ra/2

C

O1

O2 H6

C

O4

O3H5

HH3C C

O2

O1 H5

C

O3

O4H6

HH3C

C

O2

O1 H5

C

O3

O4H6

HH3C

Weight + Ka=even 4 12

Ka=odd 12 4

a a b b

a a b b

1( )21( )2

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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).

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Real spectra for J = 4 3 (Ka = 3)

Weight A+ A E+ E

Ka=even 1 3 1 3

Ka=odd 3 1 3 1

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.

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Without tunnelling motions, we always choose a principal axis system to simplify the rotation Hamiltonian as

H = A Ja2 + B Jb

2 + C Jc2

However, the proton transfer tunnelling motion tilts the principal axis system between a1 to a2.

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 FabJaJb comes out.

Why FabJaJb comes out?

a1

a2

aaverage

+ Fab(JaJb+JbJa)

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Rotational Motion

H = A (Ja - ja)2 + B (Ja - ja)2 + C (Jc - jc)2

+ Fab [(Ja - ja) (Jb - jb)+ (Jb - jb) (Ja - ja)]

+ centrifugal distortion

= A Ja2 + B Jb

2 + C Jc2 + Fab (JaJb+JbJa)

-2AJa ja -2BJb jb -2CJc jc -2Fab (Ja jb+Jb ja) (Coriolis)

+A ja2 + B jb2 + C jc2 + Fab (jajb+jaja) (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 DaJa in the Hamiltonian (with Da = -2Aja and ja =λa 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 5880.017 5879.833 5794.836 5794.986

B/MHz 1360.291 1360.282 1360.039 1360.043

C/MHz 1106.936 1106.930 1106.910 1106.922

Da/MHz - - 1418.976 1427.350

Fab/MHz 170.66 167.11

Gb/MHz 34.51

V-+/MHz 250.444 -136.167

Δa/MHz -1.577

Centrifugal constants - DJ, DJK, DK, d1 and d2 - all determined

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Dynamics

H = Hinternal + Hrotational

where

Hinternal = F j2 + (V3 / 2) (1 – cos3 ) z

– (ħ2/2) ∂ 2/∂ z2 +V2 (1 – z2)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 V2 = 8000 ±100 cm-1 and V3 = 107.0 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 250.444 MHz to 252.476 MHz. However as the reduced mass for the motion must increase slightly, this implies a slight reduction in the V2 barrier, possibly from zero-point motion effects

• Similarly the internal angular momentum increases from 0.1178 to 0.1185, with a reduction in the barrier V3 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

HH HD DH DD

A/MHz 5892.791 5798.368 5802.834 5707.374

B/MHz 1347.425 1351.286 1347.506 1353.843

C/MHz 1100.489 1102.069 1099.777 1095.051

Fab/MHz 170.66

νtun/MHz 250.444 - - 3.322

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

HH HD DH DD

A/MHz 5784.920 5707.555 5723.248 5637.157

B/MHz 1350.032 1351.167 1345.388 1345.065

C/MHz 1103.213 1099.784 1099.777 1095.053

νtun/MHz -136.167 - - -1.577

Da/MHz 1423.163 1403.962 1360.081 1351.927

Db/MHz 34.511 19.513 19.431 19.239

j 0.11776 0.11817 0.11417 0.11528

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

13C Isotopic Substitution

• The dimers formed by 13C 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 13C 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• 13C 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