Quantum‐Assisted Metrology of Neutral Vitamins in the Gas Phase

Abstract It has recently been shown that matter‐wave interferometry can be used to imprint a periodic nanostructure onto a molecular beam, which provides a highly sensitive tool for beam displacement measurements. Herein, we used this feature to measure electronic properties of provitamin A, vitamin E, and vitamin K1 in the gas phase for the first time. The shift of the matter‐wave fringes in a static electric field encodes the molecular susceptibility and the time‐averaged dynamic electric dipole moment. The dependence of the fringe pattern on the intensity of the central light‐wave diffraction grating was used to determine the molecular optical polarizability. Comparison of our experimental findings with molecular dynamics simulations and density functional theory provides a rich picture of the electronic structures and dynamics of these biomolecules in the gas phase with β‐carotene as a particularly interesting example.

Laser power and beam diameter were calibrated with 5% accuracy outside the vacuum chamber before the beam was focused by an f = 100 mm cylindrical lens onto the interferometer mirror in vacuo. Changes in the optical polarizability and laser power calibration shift the ( ) curve horizontally. Additional optical absorption reduces the effective interference contrast. This may be mimicked by imperfect alignment of the interferometer as well as by dephasing noise 1 , thermal 2 or collisional decoherence 3 . We have used the well-known C60 molecules to calibrate any possible experimental visibility reduction as well as the optical beam parameters by comparing the observed C60 interference contrast with the theoretical model 4 . The vertical waist of the light grating is calculated from the horizontal position of the maximum of the V(P) curve. Using the C60 polarizability = 4 0 × 87(10) Å 3 and optical absorption cross section (532 ) = 2.9×10 −18 2 we confirm a waist of 440 µm for the polarizability-measurement and interference of β-carotene and 920 µm for all other measurements.

c) Electric susceptibilities Measurement of the fringe shift
In our setup an interference pattern is obtained by scanning the third grating transversely over the molecular beam. To determine the field-dependent fringe shift and from this the molecular susceptibility, we record two interference patterns at the same time, one for the reference voltage of 1 kV and one for the deflection voltage. At each position of the third grating G3 we switch between the two voltages and record the respective number of molecules arriving in the detector. We have measured in a rising and falling voltage sequence to exclude potential residual systematics.

Calibration of the electric deflection field
The proportionality factor K in our electric deflection experiments depends on the electrode and the molecular beam geometry and can be calibrated with an atom or molecule of known polarizability. Here we used the known static polarizability of C60 to determine K=1924(78) for identical conditions as used for the vitamins K and E (see Figure S1). We plot the shift in units of the fringe phase Δ = 2 ⋅ Δ / . A shift of corresponds to half a period of an interference pattern. Figure S2. Determination of the geometric scaling factor K using a quadratic fit to the C60 matter-wave deflection curve. From a series of such measurements we determine the calibration for K.

d) Computation of the electronic molecular properties
In our MD simulations, the molecules were set into a computational box of 100 × 100 × 100 Å 3 size using periodic boundary conditions. The DFT calculations were then performed using Gaussian09 using the functionals described in the main text and the default settings with respect to convergence criteria and field strength.
To obtain an ensemble average over an equilibrium thermodynamic quantity in the MD simulation one can, in principle, average over many particles in a single time step, over one particle over all time steps or even over many particles and many time steps. For simplicity, we here assume that ergodicity applies and that these different approaches converge within the limit of experimental accuracy. Improved precision could be obtained by additional simulations with parallel tempering (replica exchange) and the quality of the statistics can be controlled with additional Monte Carlo simulation. One may further ask whether molecules in high vacuum -as in our experiment -can be rightfully described by CHARMM force fields which have been originally optimized for collective ensembles with non-bonding interactions, i.e. in solvents. The agreement between theory and experiment suggests that this is no issue for phylloquinone or α-tocopherol. The observations for β-carotene are expected to be dominated by the dynamics rather than by the force field. Additional ab initio molecular dynamics (AIMD) simulations support the statement that at high experimental temperatures the classical MD simulations employing the CHARMM force field describe the trajectories in conformational space reasonably well. In the AIMD simulations the nuclear motion is integrated using the velocity-Verlet algorithm, and the electronic potential is provided by DFT at the PBE0/3-21G level of theory. Since AIMD simulations are computationally expensive, we have here only calculated the first 50 ps using a small basis set for a preliminary comparison. In contrast to our classical MD simulations, the stochastic velocity rescaling thermostat 5 has been used with the same relaxation time of 0.1 ps. The small basis set can be justified since the binding and torsion angles are the relevant geometric parameters in our simulations. They are generally less sensitive to changes in the basis set than bond lengths. Following the theoretical approaches described in the main text we have simulated the electronic properties of all three (pro)vitamins. Complementary to the data of the main text, here we show the time evolution of the static polarizability and dipole moment of -carotene and phylloquinone.

e) Molecular configurations with extreme electronic properties
While the polarizability stays rather constant throughout all thermal evolution, the electric dipole moment can vary by several hundred percent. This is due to the exposure of charge imbalances in the bending process. Figure   S3 shows highest and lowest dipole moment configurations together with the dipole moments for β-carotene and phylloquinone. While structural changes are dramatic in case of α-tocopherol and phylloquinone, β-carotene is more rigid. However, due to its inversion symmetry and the corresponding dipole moment of zero in the thermal ground state, the influence of the vibrations is much stronger than in α-tocopherol and phylloquinone. Table 1 For the polarizability, a systematic contribution results from the necessary scaling of the experimental visibility to the theoretically expected visibility. We consider that the measured susceptibilities depend not only on the deflecting field but also on the assumed interaction of the molecular beam with the light grating, as in our deflection experiments we imprint a shift on an interference pattern that is evolving in free flight. Furthermore, we consider the cross correlation of the uncertainty in the molecules' velocity and the light grating intensity with the calibration factor K.