Probing Instantaneous Single-Molecule Chirality in the Planar Ground State of Formic Acid
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We experimentally demonstrate that individual molecules of formic acid are chiral even when they are in the vibronic ground state, which has a planar equilibrium structure. We ionize the \( \text{C } 1s \) shell of the molecule and record the photoelectron in coincidence with positively charged fragments. This provides two consecutive measurements of the structure of one molecule, the first by photoelectron diffraction imaging and the second by Coulomb explosion imaging. We find that both measurements show the same handedness of the specific molecule. The phenomenon of being achiral on average but chiral at the level of individual molecules is general to prochiral molecules and is a consequence of the three-dimensional zero-point delocalization of the nuclei in the vibrational ground state.
Figure 1: Coulomb explosion imaging of formic acid (HCOOH) following \( \text{C } 1s \) photoionization at a photon energy of 305.5 eV. Four charged particles (\( \text{C}^+ \), \( \text{O}^+ \), \( \text{O}^+ \), and \( \text{H}^+ \)) are detected, and the linear momentum vector of the fifth particle (H) is obtained using linear momentum conservation. Panel (a) shows the distribution of momenta in the plane of the molecule; the carbon ion is emitted upward (as indicated by the arrow; see text for definition of coordinates). The magnitudes of the momenta of the particles \( i \) are scaled by \( 1/\sqrt{m_i} \), where \( m_i \) is the mass of each fragment. The color bar represents the normalized relative intensity of the data. Superimposed in this plot is the equilibrium structure of formic acid with C in gray, O in red, and H in white. (b) Polar representation of a side view onto the plane shown in panel (a). The plane is located at \( \cos \theta = 0 \), where \( \theta \) is the polar angle with respect to the normal of the plane in panel (a). \( \phi = 90^\circ \) is selected to be the direction of the carbon ion and is visible as a sharp, vertical line.
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