We used mass-correlated rotational stretching spectroscopy (mass-CRASY) and obtained pure rotational Raman spectra for benzene over a wide spectral bandwidth of 500 GHz. With a combined optomechanical and electronic delay and random sparse sampling, we achieved single MHz resolution for the ground state frequency domain spectra of benzene. The rotational constants were obtained in the uncalibrated frequency domain rotational spectra in continuous 16 ns measurements.
The rotational constants were obtained in frequency domain rotational spectra in 100 ns random sparse sampling measurement with GPS clock calibration.
Explanation of terms and abbreviations
Introduction
The rotational constants for benzene in the electronically excited states have been determined from rotationally resolved spectra. In the spectrometer region, a linearly polarized strong 800 nm IR tuning pulse crossed the molecular beam and generated a spin wave packet by spin Raman excitation. The time delay between alignment and ionization laser pulse was controlled by a combination of opto-mechanical and electronic time delays.
The stretch pulse was routed through a folded optomechanical delay line (Physik Instrumente MD-531), adding from 0 to 4.8 m path length, equivalent to an adjustable time delay of 16 ns. It would consume impractical measurement time if CRASY measured and stored data for all stretch-ionization time delay points. Fig.2 presents a comparison between a random sparse sampling measurement with 2% sampling points for a time delay of 1 μs in Fig.2.(A) and a full continuous sampling measurement over 2 ns in Fig.2. 2. (B).
One advantage of random sparse sampling is the lower experimental cost for better resolution than is available with continuous measurements. The measurement time of random sparse sampling is much shorter than continuous measurement because it measures fewer points than the time of continuous measurement.
Result and Discussion
4-(c) shows the rotating Raman spectrum of ground state benzene obtained. 9 shows partially resolved K-splitting subbands of 𝐷𝐽 and 𝐷𝐽𝐾 in the two highest frequency sidebands of the spectrum at single MHz resolution. The fit gave the result of the ground state rotation constant and the centrifugal strain constants.
The rotational constant and the two centrifugal distortions 𝐷𝐽 and 𝐷𝐽𝐾 were obtained in the pure rotational spectrum measured in 1𝜇𝑠. Mass-CRASY acquired a one MHz resolution pure rotational Raman spectrum of benzene in 1 μs random sparse sampling measurements and 𝐵0, 𝐷𝐽 and 𝐷𝐽𝐾 in the ground state. Neglected values of 𝐷𝐽𝐾 and the absence of K-splitting in the spectra would cause errors in determining the values of the rotational constant and the centrifugal distortion constant 43.
The estimate of the temperature of the molecular bundle in the experiment also adds uncertainty to fit the rotational constant. The estimation of molecular bundle temperature therefore still has a limitation and adds uncertainty in the determination of the rotational constant and centrifugal strain constants.
Conclusion
To achieve individual K splitting and to explore even finer and more accurate molecular structures, the following improvements should be included: (1) Better resolution with longer delay time span, better data processing to deal with the burdensome mass-related data set. 2) better S/N ratio, (3) better temperature estimate for the molecular beam. They are asked to perform the upcoming high-resolution spectra with subMHz to subkHz resolution to explore spectral details that you and I have never seen before. -dependent signal modulation was observed in a Wiley-McLauren TOF (Time of Flight) mass spectrometer28 The angle between the alignment beam and the ionization beam increased along with the opto-mechanical delay, even though the beams started randomly at the beginning.
The calculated rotational constants of the zero vibration level in the ground state obtained by ab initio calculation.
Appendix
Position of bands in different resolution spectra
Above: the 1 MHz resolution spectrum in a range from 22740 MHz to 22775 MHz. There is only 1 transition Middle: the approximately 1.6 MHz resolution spectrum in the range. Above: the 1 MHz resolution spectrum in a range from 34115 MHz to 34155 MHz. There is only 1 transition Middle: the approximately 1.6 MHz resolution spectrum in the range.
Different centers and shapes of bands in different temperatures
The band shapes differ from each other due to Boltzmann scattering on S and R branch as well as individual transitions with different J and K values. A band shape of 1 K, 2 K, 3 K, 4 K and 5 K are similar to each other, but a center of the bands differs from each other due to different intensities of each transition in the different rotational temperature spectra. A band of 298 K is wider than other bands as an intensity of lines in R-branch is high enough and the lines are merged into one band in 10 MHz resolution.
Rotational constants and centrifugal distortion constants on oblate top molecules
- Relationship between the three rotational constants in oblate top molecules
- Selection rules on pure rotational Raman spectrum of symmetric molecules
- Relationship between/among three centrifugal distortion constants 𝑫 𝑱 , 𝑫 𝑱𝑲 , and 𝑫 𝑲
- Quadratic centrifugal distortion constants in planar molecules with
- Unresolved K structures of oblate top molecules and additional assumptions to determine the rotational constants and centrifugal
The rotational constants A and C can be calculated from the value of B and 𝐷𝐾 cannot be obtained in a pure rotational Raman spectrum of benzene in the ground state. However, the bands do not overlap, but there is a distance between two bands due to centrifugal strain constants. Relationship between/among three centrifugal strain constants 𝑫𝑱, 𝑫𝑱𝑲 and 𝑫𝑲 𝑫𝑱, 𝑫𝑱𝑲 and 𝑫𝑲. Ideally, planar molecules with 𝐷3ℎ and 𝐷6ℎ symmetry have solid relationships between the three centrifugal strain constants.
These ratios were used to validate the value of obtained centrifugal distortion constants in the planar molecules whose K substructures have not been solved yet. These ground state constants are zero under the assumption of rotational moment of inertia for planar molecules (𝐼𝐶 = 𝐼𝐵 + 𝐼𝐴, and A=B=1/2 C). They were not calculated to obtain rotational constants for B and two centrifugal distortion constants for 𝐷𝐽 and 𝐷𝐽𝐾 in the benzene.
Since the two centrifugal strain constants are small and opposite in sign to each other. Therefore, a low-resolution spectrum barely observes split lines due to 𝐷𝐽 and 𝐷𝐽𝐾. Therefore, previous studies on rotational constants and centrifugal strain constants of benzene needed additional assumptions to calculate centrifugal strains in the low-resolution spectra. If the K components are not resolved in the rotational spectra, intensity analyzes may be useful for prolate apex molecules but not for oblate apex molecules.
Even if K splitting is not observed in a low-resolution spectrum, the position of the maximum intensity corresponds to K=0 in the given J value. Some researchers set the centrifugal distortions to zero in the pass, since a resolution of spectra could not resolve them. They tried to calculate both 𝐷𝐽𝐾 and 𝐷𝐾 in the oblate top molecules, but they got different sets of rotational constants and centrifugal strain constants in individual S and R branch.
51 However, according to Aliev 38 and Dowling 39 the term of 𝐷𝐽𝐾 cannot be ignored in the pure rotational Raman spectra for planar molecules with 𝐷3ℎ and 𝐷6ℎ molecules. These theoretical relationships were used to check certain constants in the experimental spectra and compare them with distortion constants from literature. Due to unresolved K structures in the oblate top, many assumptions and calculation methods have been applied.
A.5 . Cold pure rotational Raman spectra
Unresolved K structures annoy researchers when they investigate molecular structures with a planar structure and their harmonics with low-resolution rotational spectra or rotationally resolved rovibronic spectra. Even though there were reasonable assumptions in the assignment of bands and lines of rotational spectra or rotationally resolved spectra for benzene, these different assumptions merely showed numerical differences of the rotational constant and centrifugal strain constants.
Rotational constants of fragments and parental molecules in uncalibrated mass-correlated frequency domain spectrum
Values from the literature were used to determine the rotational constant and the centrifugal distortion constant. 13 were used to fit the rotational constant of benzene, and the literature values of the rotational constants of carbon disulfide isotopologues were also used. The rotational constant of the benzene fragment is MHz, which is similar to its parent molecule.
MHz, which is obtained in the uncalibrated rotation spectrum since the measurement was performed without any external calibration during the experiment. The rotational constant of 76 u is far from other literature values and the rotational constants obtained in CRASY spectra with the external GPS calibration.
Rotational constant of benzene, CS2 and fragments of benzene in 8 MHz resolution spectrum
Rotational constant of benzene, CS2 and fragments of benzene of the single MHz resolution spectrum
The rotation constant of a fragment at 44 h is one of the fragments derived from the major isotope of carbon disulfide. The rotation constant of the fragment is MHz and the centrifugal strain constant of 359.72 Hz was used to determine the rotation constant for the fragment. Top is the rotation spectrum of 34 S. Middle is the rotation spectrum of 34S12C. At the bottom is the rotational spectrum of the parent molecule of 34S12C32S. Figure B.1.13: Rotation spectrum of the main isotope of benzene and the fragment in the frequency domain.
Rotational constants were obtained in uncalibrated frequency-domain rotational spectra in a 16 ns continuous measurement. a) : One sigma uncertainty (b) : Anhonen et al. Rotational constants were obtained in uncalibrated frequency-domain rotational spectra in a 16 ns continuous measurement. a) : One sigma uncertainty (b) Winther et al. Spectra with one MHz resolution were obtained by random sparse sampling measurement in 1 μs random sparse sampling measurement with GPS calibration (a): pure rotational spectrum of 76 u of 12C32S, carbon disulfide fragment (32S12C) and benzene (12C6H6) in the frequency range between 0 and 300 GHz.
Sieghard Albert, Hans Hollenstein, Carine Manca Tanner, Martin Quack, in Handbook of High-Resolution Spectroscopy, edited by a. First of all, I would like to thank Jong Chan Lee, who collaborated on the high-resolution benzene spectra in the ground state study, for his expert experimental assistance and fruitful discussions in this research. Thomas Schultz, He taught me how to start a scientific investigation and how to complete it properly.
