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Chirantan Pramanik*, Ruby Saha', Swastika Chatterjee^ and Prosenjit Ghosh*
*IISc Bangalore, Bangalore 560012, India
'IIT Madras, Chennai 600036, India
^IISER-Kolkata, Nadia-741246, India
PRESENTED AT:
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Using first-principles density functional theory (DFT) and ab initio calculations, we study the nature of isotopic bonds in gaseous molecules
and find the distribution of most abundant, singly and multiply substituted isotopologues at varying temperatures.
In most cases, multiply substituted isotopologues are 1 to 2% enriched at Earth-surface temperature. This anomaly, defined as for
isotopologue i, varies with the temperature at which the gaseous molecules equilibrate, and their abundances in natural molecules can be
used as a Geothermometers.
We apply external electric field (EEF) on gas molecules to observe the shift in equilibrium constants of individual isotopic exchange
reactions. The shift in equilibrium constants alters the thermodynamic abundances of those isotopologues.
Starting from the work by Wang et al., 2004 on isotopic distribution of CO molecular gases in equilibrium as a function of temperature, we
study the change in equilibrium constants of those reactions in presence of an EEF.
Figure 1. Taken from Calvaresi et al., 2010
According to Calvaresi et al., 2010, CO molecule can be dissociated in presence of ~40 V/nm EEF along
its major axis. We studied CO molecule under EEF and found the shift in vibrational frequencies. We
calculated the equilibrium constants with and without the EEF.
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Twelve isotopologues of CO can be obtained from the linear combinations of the carbon and oxygen stable isotopes as
This matrix equation is expressed as E.M=C.A; Using Gauss-Jordan
reduction method, the matrix C is decomposed as
Since the rank of U is four, the rank of
transformation matrix C is also four.
That implies that we need four
isotopologues from matrix M to describe
all isotopologues of the CO molecule
(Wang et al., 2004).
Using ab initio Density Function Theory
(DFT) (Hohenberg et al., 1964 and Kohn et al., 1965) Structures of various isotopologues of CO
with and without the EEF are obtained in Gaussian09 computational chemistry package (Frisch et al., 2009).
Vibrational frequencies of each CO isotopologues are used in the expressions of the partition function ratios to find the
equilibrium constants (urey, 1947 and Bigeleisen & Mayer, 1947) of eight CO isotope exchange reactions.
For exchange reaction of type: aA + bB = aA +bB , equilibrium constant can be expressed as
Partition functions, Q can be expressed in terms of vibrational frequencies
where u =hc /kT, Q is partition functions, are vibrational frequencies in terms of wavenumber and are the symmetry
numbers. c is the speed of light, h is Planck’s constant, k is Boltzmann constant, and T is the exchange reaction temperature in K.
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We have carried out ab initio DFT calculations to determine the vibration frequencies for the CO isotopologues in the presence
of EEF of ~60 V/nm and in the absence of any EEF. All quantum chemical calculations were carried out using
Gaussian09(Frisch et al., 2009) suites of programs with DFT-B3LYP level of theory and 6-311G(d) basis sets. The input files
were generated in GaussView.
EEF was applied along the major axis of the CO molecule. We checked with EEF along other perpendicular axes and observed
very little polarization along the EEF direction. We applied EEF along the major axis because the maximum charge separation
leads to the alignment of the CO molecules along the EEF.
All the quantum chemical calculations were performed in the Dell cluster at the Supercomputer Education and Research Centre,
Indian Institute of Science, Bangalore.
With the application of the EEF, the charge center of the molecule shifts towards the field direction. In below figure we can see
the charge distribution of the CO molecule with and without EEF (numbers are in Mulliken).
Figure 2. Charge separation in CO molecule in presence of an external DC electric field
This charge separation introduces change in dipole moment of the symmetric stretching vibrational mode of the CO and the
symmetric stretching mode of CO becomes IR-active. In below table right column is for applied EEF and shaded row is
symmetric stretching mode of CO
In addition to the IR-activation of the symmetric stretching mode, the changes of vibrational frequencies due to EEF affect the
kinetics of the isotope exchange reactions among various CO isotopologues. The equilibrium constants of the eight isotope
exchange reactions discussed above change that alter the thermodynamic abundances of CO isotopologues.
These eight isotope exchange reactions at scrambling temperatures were shown by Wang et al., 2004. The re-equilibration
process in S.T.P. does not happen in weeks in the atmosphere. We determine the change in equilibrium constants of these re-
equilibration processes in the presence of an EEF, as shown below, which affects the thermodynamics of isotopologues.
Equilibrium constants K and K decreases and all other increases. This justifies that C- O and C- O bonds are stronger
than C- O, C- O and C- O bonds in presence of an EEF as well. Higher electric field strength acts analogously as the
lower temperature in isotope exchange; instead, the higher electric field breaks the molecule, whereas low temperature makes the
molecule more stable.
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Equilibrium constants without EEF
Equilibrium constants with EEF
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Figure 3. Equilibrium constants without and with EEF
Scrambling of CO at high temperature dissociates the molecule, and isotope exchange reactions occur. The amount of
equilibrium isotope fractionation was determined previously. We used an external electric field to excite the CO molecule and
observed the equilibrium isotope fractionation in exchange reactions.
EEF switch the symmetric stretching mode of CO vibration from IR-inactive to IR-active. All the vibrational frequencies shit.
The equilibrium isotope fractionation in the presence of EEF behaves similarly to the decrease in temperature without the field.
The clumping increases, and isotopic fractionation becomes more prominent with the increase of the EEF.
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I am completing my Ph.D. from Indian Institute of Science, Bangalore, India this year and searching for postdoctoral
opportunities in the field of ab initio calculations in Geochemistry and Mineralogy. I worked on quantum chemical
calculations in stable isotope geochemistry and isotope fractionation. I used 'Gaussian09' and 'GAMESS quantum chemical
packages and skilled in python and Matlab. I am broadly interested in statistical physics, quantum chemistry, condensed
matter physics, chemical kinetics and molecular level calculations in Earth and Space sciences.
I did M.Sc. in Physics and post graduate in Material Science before joining Ph.D. My list of publications are given below:
email id: chirantanp88@gmail.com
https://www.researchgate.net/profile/Chirantan_Pramanik (https://www.researchgate.net/profile/Chirantan_Pramanik)
https://scholar.google.com/citations?hl=en&user=McDo9kUAAAAJ (https://scholar.google.com/citations?hl=en&
user=McDo9kUAAAAJ)
Pramanik C, Chatterjee S, Fosu BR, Ghosh P. Isotopic fractionation during acid digestion of
calcite: A combined ab initio quantum chemical simulation and experimental study. Rapid
Communications in Mass Spectrometry. 2020;34(13):e8790.
https://doi.org/10.1002/rcm.8790.
Pramanik C, Ghosh P, Banerjee S, Liang M-C. Ab initio quantum chemical studies of
isotopic fractionation during acid digestion reaction of dolomite for clumped isotope
application. Rapid Communications in Mass Spectrometry. 2020;34(23):e8926.
https://doi.org/10.1002/rcm.8926.
Banerjee S, Ghosh P, Pramanik C, Reddy B S. Fractionation of stable oxygen and clumped
isotopes during acid digestion of calcite in the presence of an external direct current electric
eld. Rapid Communications in Mass Spectrometry. 2020;34(22):e8921.
https://doi.org/10.1002/rcm.8921.
Thank you.
Chirantan Pramanik
Chirantan Pramanik
Centre for Atmospheric and Oceanic Sciences,
Indian Institute of Science, Bangalore - 560012, India
Ruby Saha
Department of Physics,
Indian Institute of Technology, Madras, Chennai - 600036, India
Swastika Chatterjee
Department of Earth Sciences,
Indian Institutes of Science Education and Research-Kolkata, Nadia - 741246, India
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Prosenjit Ghosh
Centre for Earth Sciences,
Indian Institute of Science, Bangalore - 560012, India
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Urey [1] and Bigeleisen & Mayer [2] used molecular partition function ratios to calculate the equilibrium constant of a
chemical reaction to study the isotope exchange process in equilibrium. At that time, it was not possible to measure the
energies of isotopic molecules relative to the completely dissociated energy states of the molecule, and precise determination
of zero-point energies were impossible [1]. Using harmonic potential approximation, the vibrational frequencies of the
molecules were calculated for ascertaining the partition functions at various temperatures. Vibrational frequencies of a large
number of molecules are available from spectroscopic data. In recent times, computational chemistry packages can provide
frequencies as well as energies of a molecule very accurately.
We use Gaussian09 [3] as the tool to study the abundances of multiply substituted isotopologues as a function of temperature
in the presence of an external electric field (EEF) by calculating the partition function ratios and equilibrium constants using
the vibrational frequencies of the CO molecules with different isotopologues. The vibrational frequencies of CO
isotopologues are obtained from Gaussian frequency calculation after optimizing the molecule in the EEF. We obtain
vibrational frequencies with and without the EEF from Gaussian09 [3] and evaluated the equilibrium constants of the various
isotope exchange reactions in comparison to Wang et al.,[4].
We observe that the vibrational modes of CO , which are IR-inactive due to the absence of change in dipole moment, can be
IR-active in the presence of the EEF[5]. We observed an increase in equilibrium constants for the isotope exchange reactions
in the presence of the EEF that leads to C- O and C- O bonds in the product CO , which is analogous to the
clumping[4] at low temperature without the EEF.
[1] Urey, H.C., Journal of the Chemical Society, 1947(0):p.562-581. [2] Bigeleisen, J., Mayer, M.G., The Journal of Chemical
Physics, 1947. 15(5): p. 261-267. [3] Frisch, M.J., et al., Gaussian 09 Rev. A.02.: 2009, Wallingford, CT. [4] Wang, Z.,
Schauble, E.A. and Eiler, J.M., Geochimica et Cosmochimica Acta, 2004. 68(23): p. 4779-4797. [5] Calvaresi, M. et al., The
Journal of Physical Chemistry Letters, 2010. 1: 3256-60.
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Bigeleisen, J. and Mayer. M. G. (1947). "Calculation of Equilibrium Constants for Isotopic Exchange Reactions." The
Journal of Chemical Physics 15(5): 261-267.
Calvaresi, M. et al., (2010) "Splitting CO with Electric Fields: A Computational Investigation." The Journal of Physical
Chemistry Letters 1: 3256-60.
Frisch, M. J. et al., (2009). "Gaussian 09, Revision D.01." Gaussian, Inc., Wallingford CT.
Hohenberg, P. and W. Kohn (1964). "Inhomogeneous Electron Gas." Physical Review 136(3B): B864-B871.
Kohn, W. and L. J. Sham (1965). "Self-Consistent Equations Including Exchange and Correlation Effects." Physical Review
140(4A): A1133-A1138.
Urey, H. C. (1947). "The thermodynamic properties of isotopic substances." Journal of the Chemical Society (Resumed)(0):
562-581.
Wang, Z. et al., (2004) "Equilibrium thermodynamics of multiply substituted isotopologues of molecular gases." Geochimica
et Cosmochimica Acta 68(23):4779-4797
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