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# Quantum-Assisted Metrology of Neutral Vitamins in the Gas Phase

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## Abstract and Figures

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. Here, we use this feature to measure three 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 dynamical electric dipole moment. The dependence of the fringe pattern on the intensity of the central standing light-wave diffraction grating is used to determine the molecular optical polarizability. The comparison of our experimental findings with molecular dynamics simulations and density functional theory provides a rich picture of the electronic structure and dynamics of these biomolecules in the gas-phase with β-carotene as a particularly interesting example.
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Angewandte
International Edition
A Journal of the Gesellschaft Deutscher Chemiker
www.angewandte.org
Chemie
Accepted Article
Title: Quantum-assisted metrology of neutral vitamins in the gas-phase
Authors: Lukas Mairhofer, Sandra Eibenberger, Joseph P. Cotter,
Marion Romirer, Armin Shayeghi, and Markus Arndt
This manuscript has been accepted after peer review and appears as an
Accepted Article online prior to editing, proofing, and formal publication
of the final Version of Record (VoR). This work is currently citable by
using the Digital Object Identifier (DOI) given below. The VoR will be
published online in Early View as soon as possible and may be different
to this Accepted Article as a result of editing. Readers should obtain
the VoR from the journal website shown below when it is published
to ensure accuracy of information. The authors are responsible for the
content of this Accepted Article.
To be cited as: Angew. Chem. Int. Ed. 10.1002/anie.201704916
Angew. Chem. 10.1002/ange.201704916
http://dx.doi.org/10.1002/ange.201704916
COMMUNICATION
Quantum-assisted metrology of neutral vitamins in the gas-phase
L. Mairhofer,[a] S. Eibenberger,[a,b] J. P. Cotter, [a,c] M. Romirer, [a] A. Shayeghi,[a] and M. Arndt*[a]
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.
Here, we use this feature to measure three 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
dynamical electric dipole moment. The dependence of the fringe
pattern on the intensity of the central standing light-wave diffraction
grating is used to determine the molecular optical polarizability. The
comparison of our experimental findings with molecular dynamics
simulations and density functional theory provides a rich picture of the
electronic structure and dynamics of these biomolecules in the gas-
phase with β-carotene as a particularly interesting example.
Experimental studies with neutral biomolecules in the gas-phase
are important because they allow their intrinsic electronic
properties to be assessed without perturbation by matrix effects.[1]
In particular, vitamins in the gas-phase have recently received
renewed theoretical interests[2] and analytical experiments using
these ubiquitous but thermally sensitive particles in the gas-phase
have been carried out using mass spectrometry[3] and microwave
spectroscopy.[4] Here, we utilize the benefits of near-field quantum
interference to measure optical polarizabilities and electric
susceptibilities of molecules in the same setup. We compare
experimental data with molecular dynamics (MD) simulations
combined with density functional theory (DFT) for -tocopherol
(vitamin E, C29H50O2), phylloquinone (vitamin K1, C31H46O2) and
β-carotene (provitamin A, C40H56). They are similar in complexity
and mass, but differ in their symmetry, polarity, and thermal
folding dynamics. This influences their static and optical
polarizability, as well as their permanent and vibration-induced
electric dipole moment.[5]
Following Louis de Broglie,[6] quantum mechanics assigns a
wave-nature to matter, for instance to the center-of-mass of entire
molecules as well as to the electrons inside.[7] While electron
delocalization is the basis of covalent chemical bonding,[8] the
quantum nature of the center-of-mass motion of molecules is less
commonly observed, since it requires the dedicated preparation
of delocalization on the micrometer scale. We do this in our
Kapitza-Dirac-Talbot-Lau interferometer (KDTLI),[9] illustrated in
Figure 1. All vitamins are evaporated from a ceramic oven at
temperatures between 400 K and 460 K to form a molecular beam
in high vacuum. They pass through the interferometer and are
detected using electron impact ionization quadrupole mass
spectrometry, about two meters downstream from the source.
Thermal fragments occur but are rejected by the quadrupole mass
filter. We select a velocity class of the molecular beam by defining
a free-flight parabola in the gravitational field of the Earth using
three slits. The transmitted velocity distribution is determined by
chopping the molecular beam in a pseudo-random sequence and
measuring the time-of-flight to the detector.[10] For all vitamins
described here the velocity distribution has a mean of v 200 m/s
Broglie wavelengths  =/v of 3-6 pm, where is Planck’s
constant and the mass of the individual molecules. The
wavelength  is almost three orders of magnitude smaller than
the size of each molecule. However, at the position of the second
grating the center-of-mass wave function is delocalized across
the molecular beam over one million times .
The setup is as follows: The three gratings G1, G2 and G3 have
equal period of d = 266 nm and are positioned at equal distances
along the molecular beam. G1 and G3 are machined into 190 nm
thick silicon nitride. The first grating acts as an array of point-like
Figure 1. Nea r-field matter-wave interferometer with the addition of a high
voltage deflection electrode. The effusive source emits a beam of vit amins,
which diffract at the gr atings G1, G2 and G3. G1 and G3 are nanomechani cal
gratings (black), G2 is an optical grating (green). The deflection electrode
(brown) displaces the observed interference fringes. The quadrupole mass
spectrometer (QMS) ionizes and mass selects the molecules.
[a] Dr. Lukas Mairhof er, Dr. Sandra Eibenberger, Dr. Joseph P. Cotter,
Marion Romirer, Dr. A rmin Shayeghi, Prof. Dr. Markus Arndt*
Faculty of Physics, VCQ, University of Vienna
Boltzmanngasse 5, A -1090 Vienna
E-mail: markus.arndt@univie.ac.at
[b] Dr. Sandra Eibe nberger
Lyman Laboratory
Harvard Universit y, Department of Ph ysics,
17 Oxford Street, Cambridge, MA 02138, USA
[c] Dr. Joseph P. Cotter
Centre for cold matter, Blackett Laborat ory, Imperial College, Prince
Consort Road, Lond on SW7 2BW, UK
document.
10.1002/anie.201704916
Angewandte Chemie International Edition
COMMUNICATION
sources of width s = 110 nm. It follows from Heisenberg’s
uncertainty relation, that each molecule passing through any of
the slits of G1 acquires a transverse momentum uncertainty of
Δ ≥ ℎ/Δx = h/s. This delocalization increases linearly with the
distance behind G1. When molecules arrive at the second grating
L=10.5 cm downstream from G1, the indeterminacy of the
molecular positiontheir transverse coherence[11]has grown
to 2/ ≃ 1 µ such that it covers several periods of G2. The
diffraction grating G2 is an optical standing wave with a period of
/2 that is obtained by retro-reflecting a laser beam with a
wavelength = 532 nm from a mirror. Each molecule, with
optical polarizability (), passing through the electric field
of G2 experiences an electric dipole potential
 =
−() 2()/4 which modulates the de Broglie phase of the
molecular center-of-mass wave function. Free evolution of the
matter wave behind G2 leads to the formation of a periodic
molecular density distribution. Close to multiples of the Talbot
length =2/ this pattern is an image of the grating of
period d.
This interferometer concept is common in optics,[12] and has been
demonstrated in atom optics[13] as well as medical x-ray
imaging[14]. Recently, it has allowed revealing the wave nature of
molecules as massive as 10000 amu.[15] Here, we use this method
to study electronic properties of neutral vitamins in the gas-phase.
The interference pattern is detected by scanning the
nanomechanical mask G3 over the molecular beam, another 10.5
cm behind G2. If the molecular fringes and the grating G3 are in
phase, the number of molecules arriving at the spectrometer ()
is maximized. The fringe visibility of the sine fit to the data is
defined as =( − )/( +). It depends on the
optical polarizability  () and absorption cross
section () of the molecules as well as the laser intensity in
the center of the Gaussian light beam = 2/ with the
horizontal and vertical waist and .
High visibillity interference patterns are observed for all three
vitamins. In Figure 2, we show a typical high-contrast
interferogram of β-carotene, which is a clear evidence for the
quantum nature of its motional state.[16] The dependence of the
fringe visibility on the laser power P allows us to determine their
optical polarizability[17]. We plot a typical V(P)-curve for the cases
of -tocopherol and phylloquinone in Figure 3. A molecule may
also absorb a photon in transit through the diffracting laser field.
This is an additional matter-wave beam splitting mechanism,
which also modulates the fringe visibility.[10] A correct
interpretation of the V(P) curve (Figure 3) thus hinges on good
knowledge of the laser intensity in G2 which we have calibrated
in situ using C60 molecules.11
The nanoscale period of the molecular density pattern enables
high-resolution molecule deflectometry: Any transverse force
acting on the molecular beam will displace the fringes by a
distance Δ . Using a tailored pair of electrodes we create a
homogeneous force close to the second grating that shifts the
interference fringes[18] by Δ = ⋅ (/)()/v2. It grows
with the electric susceptibility-to-mass ratio (/), the gradient of
the square of the deflection field and inversely with the square
of the molecular velocity v. The geometrical factor K contains
information about the electrode geometry and position, here
calibrated using C60 molecules. The deflection Δ follows the
same law found in classical deflectometry[19] but quantum
interference adds the nanometric fine structure which is valuable
for achieving a spatial resolution of the shift of the order of 10 nm.
In Figure 4 we demonstrate the molecular fringe deflection for
α
-
tocopherol and phylloquinone in an electric field of varying
strength. For rigid non-polar molecules, the static polarizability
can be directly extracted from such deflection measurements. In
most vitamins, however, molecular vibrations induce fluctuations
of the squared electric dipole moment µ2 whose thermal average
〈µ2 contributes to the total electric susceptibility[20] through the
van Vleck relation = +µ2/3, where is
Boltzmann’s constant.
To extract the electronic properties from our experiments we
compare the data to theory. The center-of-mass motion is
described by a well-established quantum formalism in phase
space[16]. In the absence of radiation, collisions and other
interactions with the environment, the internal degrees of freedom
are decoupled from the molecular center-of-mass motion and are
described by a combined MD and DFT approach. A full quantum
treatment of the internal states is conceivable[21].
Figure 2:
Molecular interference pattern of
β
-
carotene. Data points (red
circles) show the number of detected molecules as a function of the transverse
position of grating G3. We observe a sinusoidal variation in the number of
counts, the high amplitude of which is a cl ear evidence of quantum
interfe
rence. The solid line is a sinusoidal fit to the data
, from which we extract
a fringe visibility o f
V = 32 ± 2 %. The grey area hig hlights the dark counts.
Figure 3. Experimental interference fringe visibilities of phylloquinone (blue
diamonds)
and α-tocopherol (green squares)
as a function of the diffracting
laser power in G2
. In the interaction region, the hori zontal waist
was 20
µm
and the vertical waist 920
µm
. The error bars sh ow the uncertainties of the
visibility resulting from an error propagation of the amplitude and offset of the
sine curve using
68% confidence intervals for the sine fit.
10.1002/anie.201704916
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Here, we sample the molecular configurational space by MD
simulation to account for the floppiness of the vitamins and
compute their static and optical polarizabilities (at 532 nm) using
the Coupled-Perturbed Kohn-Sham method, as well as the
electric dipole moments for subsequent time steps using DFT.
The conformational space was scanned by a MD simulation using
the LAMMPS package[22] with CHARMM[23] force field parameters
obtained from the multipurpose atom-typer for CHARMM[24].
During the MD simulation, a single molecule is propagated over
100 ns (after an equilibration run of 10 ns) in time steps of 1 fs at
the respective experimental oven temperatures of around 450 K
controlled by a No-Hoover thermostat[25] with a relaxation time
of 0.1 ps. Assuming that the MD time-evolution of a single
molecule in vacuum covers a sufficiently large conformational
phase space the single time sequence samples a statistically
representative ensemble of conformations in the hot molecular
beam. Short ab initio molecular dynamics (AIMD) simulations
using NWChem[26] at the PBE0/3-21G level of theory[27] over 50
ps indicate that the CHARMM force field is a reasonable
approximation for our high temperature simulations.
The molecular structure was extracted from the MD simulation
every 2 ns and fed into DFT calculations at the CAM-
B3LYP/Def2TZVP level of theory[28] using the Gaussian program
package.[29] The range-separated hybrid exchange-correlation
functional CAM-B3LYP has been shown to perform well for
calculations of electronic (hyper)polarizabilities of organic
compounds.[30]
Figure 5 displays the electronic parameters for α-tocopherol.
Simulation data for the other two vitamins are compiled in the
Supplementary Information. Conformational changes occur on
the picosecond scale. Even under vigorous fluctuations the
optical and the static polarizability stay constant within a few
percent, while the dipole moment fluctuates by up to 400% peak-
to-peak when sampled at the nanosecond scale. Such
calculations allow us to determine the van Vleck susceptibility
χ
which we compare with our measurements in Table 1. We show
the DFT values for the electric dipole moment, extracted from a
thermal average over the MD time steps. Molecular dynamics
suggests that all-trans β-carotene is more rigid than the other two
vitamins, non-polar in its ground state. However, modelling shows
that β carotene can develop a non-zero average dipole moment
and may undergo thermally induced cis-trans isomerization in the
gas phase. In solution[31], this transition has been observed at a
temperature as low as 350 K. Cis-geometries are therefore
expected to contribute to the experimental results. Furthermore,
spectra in solution indicate that β-carotene exhibits strong
wavelength shifts even in moderate electric fields[32] , and its
optical polarizability should therefore depend on the field.
It surprises that the MD averaged optical polarizability of all-trans
β-carotene exhibits a negative sign, even though the diffraction
laser is red-detuned to the nearest expected dipole allowed
transition around 440 nm. Although the experiment is insensitive
to the sign of opt (532 ) we have cross-checked its value
using the global hybrid PBE0 functional. While for phylloquinone
and α-tocopherol PBE0 yields very similar predictions for all
electronic properties, β-carotene is again a special case as the
optical polarizability maintains the negative sign but its value
changes from 152 Å3 (CAM-B3LYP) to 107 Å3 (PBE0). This
is not surprising as the polarizability spectra are sensitive to the
percentage of Hartree-Fock exchange[33]. This lower value is also
closer to the experimental result (83 ±10 Å3).
To further elucidate the origin of the sign of ⟨opt at the
wavelength of the grating laser (532 nm), we have calculated
optical polarizabilities and spectra from time-dependent DFT both
for the vibrational ground state with inversion symmetry and
distorted carotene geometries. While opt (532 ) is positive for
the inversion symmetric geometry it exhibits a negative value for
distorted structures. This correlates with the calculated optical
response: We find an intense dipole transition in the range 600-
650 nm for a distorted carotene but not for its ground state. W ith
respect to this transition, the grating laser is blue-detuned,
explaining the negative sign of ⟨opt (532 ). Our
computation is consistent with recent experiments, showing that
this transition is accessible in two-photon processes[34] and near-
edge x-ray absorption combined with UV photoelectron
spectroscopy[35].
Figure 4: Molecular fringe displ acement of phylloquinone (blue diamonds, left
scale)
and α-tocopherol (g reen squares, right scale)
as a function of the
deflection
voltage. As expected it
depends quadratically on the voltage. The
axes of the
two curves are offset vertically for clarity.
The velocities were 180
m/s for
-tocopherol and 195 m/s for phylloquinone.
The inset sketches the
molecular fringe position for two deflection voltages (r ed
= 6 kV, black = 1 kV ).
The error bars
are 68% confidence intervals for
the relative phase of the two
sinusoidal interfere nce curves
. At high voltage the uncertainty increases
,
because the fring e shift and visibility are sensitive to the finite v elocity spread o f
the molecular beam
. A shift of corresponds to a beam
displacement of half a
grating period.
Figure 5: Calculated electronic properties of
α
-tocopherol. Evoluti on of the
static (

,
red squares) and optic al (

(532 )) , blue diamonds)
polarizability as well as its electric dipole moment ( µ, black circles) d uring the
MD simulation displayed in 2 ns steps. Th e DFT calculations p erformed along
the MD trajectory ar e o
btained at the CAM-B3LYP/ Def2TZVP level of the ory.
10.1002/anie.201704916
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COMMUNICATION
Table 1: Molecula r electronic properties from experiments and theory. The
theoretical values represent a thermal average at the temperature of the
experiment. The co mputational result is the mean over all consid ered MD steps.
We estimated the experimental errors by testi ng the robustness of th e result
against the combined standard deviations of the contributi ng factors (see Suppl.
Info).
a) 1st row: CAM-B3LYP/Def2T ZVP; 2nd row: PBE0/Def2TZVP; 3rd row:
Experiment
b) Convert to SI units by multiplying wit h 40
In summary, we have shown that quantum-interference assisted
metrology opens a window to measuring electrical, optical and
dynamical information of biomolecules in a single comprehensive
setting. We have shown this here for the three pro/vitamins α-
tocopherol, phylloquinone and β-carotene. We find good
agreement with computational chemistry and also see that the
fully conjugated electronic structure of β-carotene opens a
number of interesting questions. Future studies in molecule
interference shall address them also using highly sensitive single-
photon recoil spectroscopy around 640 nm[36]. Sources of
internally cold molecules[37] will allow to further elucidate the role
of conformations, which can be supported by more elaborate
AIMD simulations. Matter-wave assisted metrology thus proves to
be an interesting link between quantum optics and chemistry. It
can be readily extended to magnetic, optical and collisional
properties, and thus help benchmarking computational models of
complex biomolecules.
Acknowledgements
We acknowledge financial support through the European Research
Council ERC AdvG 320694, as well as through the FWF within
W1210-25. JC acknowledges a VCQ fellowship. The computational
results presented have been achieved using the Vienna Scientific
Cluster (VSC). We are thankful to M.C. Böhm, E. Voyiatzisis and G.
G. Rondina for useful discussions.
Keywords: Vitamins • Matter-waves • Interferometry • Electronic
structure • Deflectometry • DFT • MD
The authors declare no financial interest in this work
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Vitamin E
α
-Tocopherol
K1
Phylloquinone
Pro-A
β
-Carotene
Sum formula C29H50O2 C31H46O2 C40H56
T / K 400 ± 5 450 ± 5 460 ± 5
Mass / amu 430.7 450.7 536.9
µ
/ D 1.8 ± 0.1
1.8 ± 0.1
1.1 ± 0.1
1.1 ± 0.1
1.3 ± 0.1
1.3 ± 0.1
αstat
/
54 ± 1
54 ± 1
58 ± 1
59 ± 1
211 ± 4
229 ± 3
αopt
a,b /
3
56 ± 1
56 ± 1
58 ± 5
62 ± 1
61 ± 1
52 ± 7
- 152 ± 11
- 107 ± 4
(-) 83 ± 10
χa,b /
3
78 ± 3
78 ± 3
80 ± 8
65 ± 1
66 ± 1
80 ± 10
229 ± 4
240 ± 3
n.a.
10.1002/anie.201704916
Angewandte Chemie International Edition
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10.1002/anie.201704916
Angewandte Chemie International Edition
COMMUNICATION
COMMUNICATION
Molecule interferometry exploits the
quantum wave-nature of molecules
to prepare a nanoscale density
pattern in high vacuum. Here this is
used to determine various electric
properties of vitamins isolated in the
gas-phase, including β-Carotene
(Provitamin A),
α
-Tocopherol
(Vitamin E), and
Phylloquinone (Vitamin K1).
Lukas Mairhofer, Sandra Eibenberger,
Joseph Cotter, Marion Romirer, Armin
Shayeghi and Markus Arndt*
Page 1
Quantum-assisted metrology of
neutral vitamins in the gas-phase
10.1002/anie.201704916
Angewandte Chemie International Edition

## Supplementary resources (2)

Data
August 2017
... This molecule has several structural isomers -it can form a straight line, called a trans-state, or one of the bonds can bend, which is called a cis-state. Here an isomerisation of the molecule from the trans-into one of its cis-states prevents the transfer of the delocalized pi-electrons across the whole molecule and therefore significantly reduces its response to the standing light-wave ( [51]). ...
... Both semiclassical and quantum mechanical approaches depend on the assumption of localized atomic cores whose positions as well as dynamics determine the elec-tronic band structure. Only when all of the six possible isomeric states of the molecule are taken into account, the simulation agrees with the experimental results ( [51]). The dynamics of the localized structure of the molecule thus becomes visible in the interference pattern of its delocalized center-of-mass. ...
Preprint
Full-text available
Interference of more and more massive objects provides a spectacular confirmation of quantum theory. It is usually regarded as support for "wave-particle duality" and in an extension of this duality even as support for "complementarity". We first give an outline of the historical development of these notions. Already here it becomes evident that they are hard to define rigorously, i.e. have mainly a heuristic function. Then we discuss recent interference experiments of large and complex molecules which seem to support this heuristic function of "duality". However, we show that in these experiments the diffraction of a {\em delocalized} center-of-mass wave function depends on the interaction of the {\em localized} structure of the molecule with the diffraction element. Thus, the molecules display "dual features" at the same time, which contradicts the usual understanding of wave-particle duality. We conclude that the notion of "wave-particle duality" deserves no place in modern quantum physics.
... This molecule has several structural isomers-it can form a straight line, called a trans-state, or one of the bonds can bend, which is called a cisstate. Here an isomerisation of the molecule from the trans-into one of its cis-states prevents the transfer of the delocalized pi-electrons across the whole molecule and therefore significantly reduces its response to the standing light-wave [55]. ...
... Both semi-classical and quantum mechanical approaches depend on the assumption of localized atomic cores whose positions as well as dynamics determine the electronic band structure. Only when all of the six possible isomeric states of the molecule are taken into account, the simulation agrees with the experimental results [55]. The dynamics of the localized structure of the molecule thus becomes visible in the interference pattern of its delocalized center-of-mass. ...
Article
Full-text available
Interference of more and more massive objects provides a spectacular confirmation of quantum theory. It is usually regarded as support for “wave–particle duality” and in an extension of this duality even as support for “complementarity”. We first give an outline of the historical development of these notions. Already here it becomes evident that they are hard to define rigorously, i.e. have mainly a heuristic function. Then we discuss recent interference experiments of large and complex molecules which seem to support this heuristic function of “duality”. However, we show that in these experiments the diffraction of a delocalized center-of-mass wave function depends on the interaction of the localized structure of the molecule with the diffraction element. Thus, the molecules display “dual features” at the same time, which contradicts the usual understanding of wave–particle duality. We conclude that the notion of “wave–particle duality” deserves no place in modern quantum physics.
... Matter-wave interference is a versatile tool for testing the quantum superposition principle with large molecules [22,36] and for measuring molecular properties in the gas phase [37][38][39]. In addition, far-field matter-wave interferometry combined with spatial filtering has been proposed for sorting conformers [40] and enantiomers [41,42] from a racemic mixture. ...
Article
Full-text available
Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunneling dynamics can be observed. We determine the impact of rovibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund’s paradox. Using ab initio tunneling calculations, we identify [4]-helicene derivatives as promising candidates to implement the proposal with state-of-the-art techniques. This work opens the door for quantum sensing with chiral molecules.
... where the second term is due to the thermally averaged value of the dipole moment [116]. In the electric deflectometry experiments described here the total susceptibility is measured, and with the aid of ab initio molecular dynamics simulations the relative contributions of the static polarizability and the averaged thermally induced dipole moments can be extracted [88,103]. It is interesting that de Broglie interferometry, which is primarily concerned with center-of-mass motion, can still reveal the influence of fast conformational changes through their influence on the molecules' response in an electric field. ...
Chapter
Full-text available
Otto Stern became famous for molecular beam physics, matter-wave research and the discovery of the electron spin, with his work guiding several generations of physicists and chemists. Here we discuss how his legacy has inspired the realization of universal interferometers, which prepare matter waves from atomic, molecular, cluster or eventually nanoparticle beams. Such universal interferometers have proven to be sensitive tools for quantum-assisted force measurements, building on Stern’s pioneering work on electric and magnetic deflectometry. The controlled shift and dephasing of interference fringes by external electric, magnetic or optical fields have been used to determine internal properties of a vast class of particles in a unified experimental framework.
... Matter-wave interference is a versatile tool for testing the quantum superposition principle with large molecules [22,36] and for measuring molecular properties in the gas phase [37][38][39]. In addition, far-field matterwave interferometry combined with spatial filtering has been proposed for sorting conformers [40] and enantiomers [41,42] from a racemic mixture. ...
Preprint
Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunnelling dynamics can be observed. We determine the impact of ro-vibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund's paradox. Using ab-initio tunnelling calculations, we identify [4]-helicene derivatives as promising candidates to implement the proposal with state-of-the-art techniques. This work opens the door for quantum sensing and metrology with chiral molecules.
... Electron and neutron diffraction are key techniques in condensed-matter physics and materials science [1,2], while atom interferometers are utilized in tests of fundamental physics, as well as for measuring physical constants and inertial forces [3,4]. Extending matter-wave interference experiments to large molecules enabled quantumassisted studies of molecular properties [5,6] as well as the interference of biomolecules [7,8] and particles with masses beyond 25000 u [9]. ...
Article
Full-text available
We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of 14ℏk (photon momenta) and maximum momentum transfer of 18ℏk. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.
... Electron and neutron diffraction are key techniques in condensedmatter physics and materials science [1,2], while atom interferometers are utilized in tests of fundamental physics, as well as for measuring physical constants and inertial forces [3,4]. Extending matter-wave interference experiments to large molecules enabled quantum-assisted studies of molecular properties [5,6] as well as the interference of biomolecules [7,8] and particles with masses beyond 25000 u [9]. ...
Preprint
Full-text available
We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of $14 \hbar k$ (photon momenta) and maximum momentum transfer of $18 \hbar k$. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.
Chapter
Complex molecules are intriguing objects at the interface between quantum and classical phenomena. Compared to the electrons, neutrons, or atoms studied in earlier matter-wave experiments, they feature a much more complicated internal structure, but can still behave as quantum objects in their center-of-mass motion. Molecules may involve a large number of vibrational modes and highly excited rotational states, they can emit thermal photons, electrons, or even atoms, and they exhibit large cross sections for collisional interactions with residual background gases. This makes them ideal candidates for decoherence experiments which we review in this contribution.KeywordsMatter-wave decoherenceMolecule interferometryQuantum-to-classical transition
Article
Full-text available
We measure the diamagnetic deflection of anthracene and adamantane in a long-baseline matter-wave interferometer. From the nanometer-level deflection we extract the magnetic susceptibilities of the molecules which we compare with calculations and previous results. Adamantane yields an isotropic average mass susceptibility of −8.0 ± 1.1 m³ kg⁻¹, consistent with expectations, while anthracene yields a higher-than-anticipated value of −13.6 ± 1.3 m³ kg⁻¹. We attribute the high anthracene value to the planar aromatic molecule's magnetic anisotropy and partial alignment in the molecular beam, and estimate the magnitude of the effect on the observed deflection.
Article
Full-text available
We study the effect of rotational state–dependent alignment in the scattering of molecules by optical fields. CS 2 molecules in their lowest few rotational states are adiabatically aligned and transversely accelerated by a nonresonant optical standing wave. The width of the measured transverse velocity distribution increases to 160 m/s with the field intensity, while its central peak position moves from 10 to −10 m/s. These changes are well reproduced by numerical simulations based on the rotational state–dependent alignment but cannot be modeled when ignoring these effects. Moreover, the molecular scattering by an off-resonant optical field amounts to manipulating the translational motion of molecules in a rotational state–specific way. Conversely, our results demonstrate that scattering from a nonresonant optical standing wave is a viable method for rotational state selection of nonpolar molecules.
Article
Full-text available
Nose has modified Newtonian dynamics so as to reproduce both the canonical and the isothermal-isobaric probability densities in the phase space of an N-body system. He did this by scaling time (with s) and distance (with VÂ¹D/ in D dimensions) through Lagrangian equations of motion. The dynamical equations describe the evolution of these two scaling variables and their two conjugate momenta p/sub s/ and p/sub v/. Here we develop a slightly different set of equations, free of time scaling. We find the dynamical steady-state probability density in an extended phase space with variables x, p/sub x/, V, epsilon-dot, and zeta, where the x are reduced distances and the two variables epsilon-dot and zeta act as thermodynamic friction coefficients. We find that these friction coefficients have Gaussian distributions. From the distributions the extent of small-system non-Newtonian behavior can be estimated. We illustrate the dynamical equations by considering their application to the simplest possible case, a one-dimensional classical harmonic oscillator.
Article
Full-text available
Matter-wave interferometry can be used to probe the foundations of physics and to enable precise measurements of particle properties and fundamental constants. It relies on beam splitters that coherently divide the wave function. In atom interferometers, such elements are often realised using lasers by exploiting the dipole interaction or through photon absorption. It is intriguing to extend these ideas to complex molecules where the energy of an absorbed photon can rapidly be redistributed across many internal degrees of freedom. Here, we provide evidence that center-of-mass coherence can be maintained even when the internal energy and entropy of the interfering particle are substantially increased by absorption of photons from a standing light wave. Each photon correlates the molecular center-of-mass wave function with its internal temperature and splits it into a superposition with opposite momenta in addition to the beam-splitting action of the optical dipole potential.
Article
Full-text available
The electronic structures and photoelectron spectra of several fat-soluble vitamins including A (all-trans-retinol and its two derivatives (13-cis-retinoic acid and all-trans-retinoic acid), D2, D3, E (consisted of α-Tocopherol, β-Tocopherol, γ-Tocopherol, δ-Tocopherol) and K were studied, theoretically in this work. For this purpose, the vertical ionization energies of these compounds, considering the electron correlations, were calculated in the gas phase for the first time. The direct symmetry adapted cluster/configuration interaction method which employs the single and double excitation operators (Direct-SAC-CI SD-R) and D95(df,pd) basis set was used for the calculations. It was found that more than one conformer contribute in the photoelectron spectrum of vitamin A, all-trans-retinoic acid, D2 and D3 which shows that there is more than one biological active form for these vitamins. The photoelectron spectrum of each vitamin was simulated, assigned and the previous assignments, reported in literature, were revisited. It was found that the ionization of vitamin D from HOMO-2 and the lone electron pairs of oxygen atom do not take place below 10 eV. Also, the first ionization band of vitamin E was assigned to the ionization from πC=C and π*C=C of its aromatic ring unlike the previous assignment that this ionization band is related to the lone electron pair of oxygen atom. In addition, it was found that the ionization of vitamin A and its derivatives from the lone electron pairs of oxygen atoms does not occur below 11 eV in the gas phase.
Book
This book gives physical chemists a broader view of potential biological applications of their techniques for the study of nucleic acids in the gas phase. It provides organic chemists, biophysicists, and pharmacologists with an introduction to new techniques they can use to find the answers to yet unsolved questions. Laboratory sciences have bloomed with a variety of techniques to decipher the properties of the molecules of life. This volume introduces techniques used to investigate the properties of nucleic acids in the absence of solvent. It highlights the specificities pertaining to the studies of nucleic acids, although some of the techniques can similarly be applied to the study of other biomolecules, like proteins. The first part of the book introduces the techniques, from the transfer of nucleic acids to the gas-phase, to their detailed physico-chemical investigation. Each chapter is devoted to a specific molecular property, and illustrates how various approaches (experimental and theoretical) can be combined for the interpretation. The second part of the book is devoted to applying the gas-phase approaches to solve specific questions related to the biophysics, biochemistry or pharmacology of nucleic acids.
Article
We have linked an ab initio approach of the Hartree-Fock (HF) type to the Feynman path integral quantum Monte Carlo (PIMC) formalism in order to study C6H6 and C6D6 under consideration of the quantum character of the nuclei and electrons. The combination of the statistical Monte Carlo approach with an electronic Hamiltonian offers the possibility to study the influence of the quantum and classical (=thermal) nuclear degrees of freedom on electronic expectation values. The PIMC technique has been used to derive the finite-temperature properties of the nuclei of both π rings. We discuss the temperature (T) dependence of the energy of the C6H6 and C6D6 nuclei, their spatial delocalization properties as well as the radial and angular distribution functions. The nuclear configurations generated by the PIMC formalism have been used as input for ab initio HF calculations. Electronic expectation values have been derived as ensemble averages over 6000 different nuclear configurations which are populated in thermal equilibrium. As a result of the large quantum effects of the C6H6 and C6D6 nuclei, we derive ensemble averaged electronic expectation values which differ sizeable from the corresponding single-configuration quantities at the energy minimum. This difference is mainly caused by nuclear quantum effects; thermal degrees of freedom are of minor importance only. The electronic origin of the potential energy part of the total vibrational energy is emphasized. It is largely determined by the raise in the electron-core attraction under the influence of the spatial uncertainty of the nuclei. The all-quantum approach yields a temperature and isotope dependence of bare electronic quantities already in the framework of the Born-Oppenheimer approximation (BOA). The principal findings of the all-quantum study have been used to reconsider certain solid state problems. We mention theoretical difficulties to reproduce Compton profiles and consider metal-insulator transitions of the Mott type as well as superconductivity. On the basis of the present all-quantum results we have to emphasize, that there is no unambiguous justification to adopt an observed isotope shift in the superconducting transition temperature Tc as an indicator of an electron-phonon-coupled superconducting pairing mechanism.
Article
Das Zusammenspiel von kinetischer und potentieller Energie über die Unschärfebeziehung wird zunächst anhand einer Variationsfunktion für den Grundzustand des H-Atoms erläutert. Zur Erklärung des physikalischen Mechanismus für das Zustandekommen der chemischen Bindung dient das H-Ion. Die Ausbildung der chemischen Bindung kann man in drei Teilschritte zerlegen: 1. die quasiklassische (elektrostatische) Wechselwirkung der unveränderten Elektronenladungen der getrennten Atome; 2. die Interferenz der Atomorbitale, die (im Falle positiver Interferenz) zu einer Ladungsverschiebung in die Bindungsregion und einer Erniedrigung der kinetischen Energie führt; 3. eine Deformation der Molekülorbitale zur Wiederherstellung der richtigen Bilanz von kinetischer und potentieller Energie. In einfachen Modellen kann man sich oft auf den zweiten Beitrag beschränken. Die Zweielektronenbindung ist von der Einelektronenbindung nicht grundsätzlich verschieden. In größeren Molekülen können interatomare Beiträge großer und kleiner Reichweite zur chemischen Bindung unterschieden werden. Wenn die erstgenannten klein sind, nämlich bei Molekülen mit unpolaren Bindungen, kann eine Einelektronen-MO-Theorie gerechtfertigt werden. Zum Abschluß wird die Möglichkeit der Beschreibung von Molekülen durch lokalisierte Bindungen diskutiert.
Article
The field frequency has recently been taken into account in the coupled-perturbed Hartree- Fock (CPHF) or Kohn-Sham (CPKS) method implemented in the CRYSTAL code for calculating the high-frequency dielectric constant of semi-conductors up to the first electronic transitions. In this work, we document how the code has been generalized and improved in order to compute the full UV-visible absorption spectrum (UV), the electron loss function (ELF) and the reflectivity (R) from the real and imaginary parts of the electric response property. We show how spectra are modified when the crystalline orbital relaxation due to the dynamic electric field is taken into account, and how this modification increases with the percentage of Hartree-Fock exchange in the unperturbed hybrid hamiltonian.
Article
A cold, continuous, high flux beam of benzonitrile has been created via buffer gas cooling. The beam has a typical forward velocity of 67 ± 5 m s(-1), a velocity spread of ±30 m s(-1) and a typical flux of 10(15) molecules s(-1), measured via microwave spectroscopy. This beam represents the slowest demonstrated forward velocity for any cold beam of medium sized (>5 atoms) polyatomic molecules produced to date, demonstrating a new source for high resolution spectroscopy. The expected resolution of a spectrometer based on such beams exceeds current instrument-limited resolution by almost an order of magnitude. This source also provides an attractive starting point for further spatial manipulation of such molecules, including eventual trapping.
Article
Gas-phase studies of biomolecules are often difficult to initiate because of the thermolability of these systems. Such studies are nevertheless important to determine fundamental intrinsic properties of the molecules. Here we present the valence shell photoionization of gas-phase vitamins A and B1 close to their ionization threshold. The study was performed by means of an aerosol thermodesorption source coupled to an electron/ion coincidence spectrometer and synchrotron radiation (SOLEIL facility, France). Ion yield curves were recorded for both molecules over a few eV energy range and the threshold photoelectron spectrum was also obtained for vitamin A. Some fundamental properties were extracted for both ions such as adiabatic and the three first vertical ionization energies of retinol (IEad. = 6.78 ± 0.16 eV and IEvert. = 7.4, 8.3 and 9.3 eV) and dissociation appearance energies for the main fragment ions of vitamin B1. Analysis of the data was supported by ab initio calculations which show a very good agreement with our experimental observations.
Book
A broad range of state-of-the-art molecular beam methods to determine dielectric of clusters are presented. The experimental setup and underlying physical concepts of these experiments are described. Furthermore, existing theoretical models to explain the experimental observations are introduced and the possibility to deduce structural information from measurements of dielectric properties is discussed. Additional case studies are presented in the book to emphasize the possibilities but also drawbacks of the methods. Furthermore, two newly developed experimental tools are described which allow to experimentally determine dynamic polarizabilities and to manipulate the motion of neutral species using their known dielectric properties.