1,721,003 research outputs found
Calculation of Franck Condon factors for metal-containing diatomic molecules of interest to laser cooling using coupled-cluster techniques
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Previous issue date: 2019-06-17Franck Condon factors (FCFs) among low-lying electronic states
of a molecule
are of paramount importance in the study of laser cooling based on optical cycles.
The accurate calculation of potential energy surfaces
for these electronic states
is key to obtaining accurate FCFs.
Multireference configuration interaction as a standard approach
for computing potential energy surfaces has been
the method of choice in many applications.
Since the laser cooling procedure focuses on the low-lying vibrational states,
only the local potential energy surfaces, for which the multi-reference character is
often not pronounced and it is the treatment of dynamic correlation that determines
the accuracy of the calculation, are relevant.
Therefore, we advocate the use of coupled-cluster (CC) techniques,
which provide systematic treatments of dynamic electron correlation,
to obtain accurate computational results for FCFs.
The yttrium oxide molecule that is subject to active experimental studies [1-3]
is adopted here as an example
to demonstrate the accuracy of the FCFs
using CC potential energy surfaces.
\begin{thebibliography}{comment}
\bibitem{YO1} M. T. Hummon, M. Yeo, B. K. Stuhl, A. L. Collopy, Y. Xia,
and J. Ye, Phys. Rev. Lett. \textbf{110}, 143001 (2013).
\bibitem{YO2} A. L. Collopy, M. T. Hummon, M. Yeo, B. Yan, J. Ye,
New J. Phys. \textbf{17}, 055008 (2015).
\bibitem{YO3} A. L. Collopy, S. Ding, Y. Wu, lan A. Finneran, L. Anderegg,
B. L. Augenbraun, J. M. Doyle, and J. Ye,
Phys. Rev. Lett. \textbf{121}, 213201 (2018).
\end{thebibliography
"Is watson's ""charge-modified"" reduced mass always best for diatomic ions ?"
Get PDFWatson's landmark reformulation of the Born-Oppenheimer separation problem
has been the basis of most combined-isotopologue analyses of diatomic
spectroscopic data since 1980.\footnote{J.K.G.\ Watson, {\it J.\ Mol.\
Spectrosc.} {\bf 80}, 411 (1980)} One noteworthy feature of this work was
his proposal that description of the dynamical behaviour of a diatomic ion
with () charge , formed from atoms with isotopic masses of
and , should use a ``charge-modified'' reduced mass: , in which is the
electron mass, and this proposal seems to have been benignly accepted
and adopted. The first quantitative test of this proposal was in the
pioneering combined-isotopologue direct-potential-fit (CI-DPF) study of
HeH by Coxon and Hajigeorgiou in 1999,\footnote{J.A. Coxon and P.
Hajigeorgiou, {\it J.\ Mol.\ Spectrosc.}\ {\bf 193}, 306 (1999).} where
they compared the quality of fit for analyses that used different choices
for the definition of the reduced masses of the various isotopologues,
and found that the best choice seemed to be to use conventional two-body
reduced masses for and . This question was re-examined recently in
the context of a CI-DPF study of CH, and a rather different conclusion
was reached.\footnote{Y.-S. Cho and R.J.\ Le~Roy, {\it J.\ Chem.\ Phys.}\
{\bf 144}, 024311 (2016).} The present paper combines new CI-DPF studies
of HeH and BeH with our recent CH work, and attempts to draw
some general conclusions on this matter.Made available in DSpace on 2017-01-26T21:37:26Z (GMT). No. of bitstreams: 3
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Previous issue date: 2016-06-2
AN EMPIRICAL DIPOLE POLARIZABILITY FOR He FROM A FIT TO SPECTROSCOPIC DATA YIELDING ANALYTIC EMPIRICAL POTENTIALS FOR ALL ISOTOPOLOGUES OF HeH+
Get PDFAll available spectroscopic data for all stable isotopologues of HeH are analyzed with a direct-potential-fit (DPF) procedure that uses least-squares fits to experimental data in order to optimize the parameters defining an analytic potential. Since the coefficient of the leading () inverse-power term is , when treated as a free parameter in the fit, it provides an independent empirical estimate of the polarizability of the He atom. The fact that the present model for the long-range behaviour includes accurate theoretical , and coefficients (which are held fixed in the fits) should make it possible to obtain a good estimate of this quantity.
The Boltzmann constant , a fundamental constant that can define temperature, is directly related to the dipole polarizability of a gas by the expression
,
%%
in which is the permitivity of free space, and is the relative dielectric permitivity at pressure and temperature . If can be determined with greater precision, it can be used to define temperature based on a fundamental constant, rather than based on the rather arbitrary triple point of water, which is only known to 5 digits of precision. for He is known theoretically to 8 digits of precision, but an empirical value lags behind. This work, examines the question of how precisely can be determined from a DPF to spectroscopic HeH data, where the limiting long-range tail of the analytic potential has the correct form implied by Rydberg theory: . Although the highest observed vibrational level is bound by over 1000 cm, our current fits determine an empirical with an uncertainty of only 0.6%. It has been shown that with more precise spectroscopic data near the dissociation, can be determined with high enough precision to determine a more precise and hence redefine temperature more accuratelyfootnote{Dattani N S. & Puchalski M. (2015) textit{Physical Review Letters} (in press)}.Made available in DSpace on 2016-01-05T20:07:12Z (GMT). No. of bitstreams: 3
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Previous issue date: 2
HOW TO CALCULATE SPIN-SPIN COUPLING AND SPIN-ROTATION COUPLING STRENGTHS AND THEIR UNCERTAINTIES FROM SPECTROSCOPIC DATA: APPLICATION TO THE STATE OF DIATOMIC LITHIUM
No full textAuthor Institution: Department of Chemistry, Oxford University, Oxford, OX1 3QZ, UK; Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, 94720-8176, USARecent high-resolution ( cm) photo-association spectroscopy (PAS) data of seven previously unexplored vibrational levels of the state of Li have allowed for the first ever experimental determination of the spin-spin and spin-rotation coupling constants in a diatomic lithium system, XX (2013)}. For triplet states of diatomic molecules such as the state of Li, the three spin-spin/spin-rotation resolved energies associated with a ro-vibrational state were expressed explicity in terms of and in 1929 by Kramer's first-order formulas, 422 (1929)} and then in 1937 by Schlapp's more refined formulas, 342 (1937)}. Given spectroscopic data, while it has never been difficult to extract and from Schlapp's formulas, it has been a challenge to reliably predict how accurate these extracted values are. This is for two reasons: (1) the lack of a rigorous method to estimate the uncertainty in , (2) the non-linearity of Schlapp's coupled equations has meant that traditionally they have had to be solved numerically by Newton iterations which makes error propagation difficult. The former challenge has been this year solved by Le Roy with a modification of Hutson's perturbation theory of, 851 (1981)}, and the latter problem has now been solved by symbolic computing software that solves Schlapp's coupled non-linear equations analytically for the first time since their introduction in 1937
PolyMLR: AN ANALYTIC MODEL FOR POLYATOMIC POTENTIALS WITH FEWER UNPHYSICAL PARAMETERS. APPLICATION TO CO2.
No full textOne has to calculate thousands or millions of \textit{ab initio} points for potential energy surfaces even for molecules with only a few atoms. For diatomics, the MLR (Morse/long-range)\footnote{Dattani N. S., LeRoy R. J., Ross A., Linton C. (2008) Proceedings of the 63rd Annual International Symposium on Molecular Spectroscopy. {\textbf{p301}}}\footnote{LeRoy R. J., Dattani N. S., Coxon J. A., Ross A. J., Crozet P., Linton C. (2009) \textit{J. Chem Phys.} \textbf{131}, 204309} model has been very successful, making it possible to represent the entire curve accurately with just a few \textit{ab initio} points, or a few spectral lines. With the MLR model it is also possible to extrapolate and interpolate in a way that allows successful predictions of energy level locations several thousand cm away from the data region\footnote{Dattani N. S., LeRoy R. J. (2011) \textit{J. Mol. Spec.}. \textbf{268}, 199-210.; Semczuk M., \textit{et al.} (2013) \textit{Phys. Rev. A} \textbf{87}, 052505}.
However no analogous model has existed yet for the intramolecular potentials of polyatomic molecules. A simple model is presented which accurately describes some small molecules with far fewer parameters than previous models, and can be extended to larger molecules too. The benefit of having a good model function is orders of magnitude greater for polyatomics than for diatomics since the amount of data needed for an accurate potential is reduced in each dimension. For example if the calculation of 100 \textit{ab initio} points is reduced to 10 in a diatomic molecule, we may estimate that this factor of 10 reduction in cost becomes at least 10 for a molecule whose potential depends on 10 radial coordinates.
As an example, an analytic potential for CO is built, which requires fewer parameters than the previous state-of-the-art analytic potential, and obeys the theoretical long-range behavior more closely than all previous potentials, including inclusion of the Axelrod-Teller three-body interaction. The model is based on accurate diatomic potentials representing all atom-atom pairwise interactions, and for CO, a three-body correction representing the rest of the energy. This emphasizes the value of accurate molecular spectroscopy for simple diatomics, which is sometimes considered to be less interesting than research involving large molecules. Diatomic potentials are valuable as building blocks for large-molecule potentials.
An open-source computer program for building PolyMLR potentials for polyatomic molecules is introduced
Analytic empirical potentials for BeH+, BeD+, and BeT+ including up to 4th order QED in the long-range, and predictions for the halo nucleonic molecules 11BeH+ and 14BeH+.
Get PDFThe 13.81(8)s half-life of the halo nucleonic atom Be is orders of magnitude longer than those for any other halo nucleonic atom known, and makes Be-based diatomics the most promising candidates for the formation of the first halo nucleonic molecules. However, the 4 species LiH and BeH are some of the first molecules for which the highest accuracy textit{ab initio} methods {it are not}, accessible, so empirical potential energy functions will be important for making predictions and for benchmarking how textit{ab initio} calculations break down at this transition from 3 to 4. BeH is also very light, and has one of the most extensive data sets involving a tritium isotopologue, making it a very useful benchmark for studying Born-Oppenheimer breakdown. We therefore seek to determine an empirical analytic potential energy function for BeH that has as much precision as possible. To this end, all available spectroscopic data for all stable isotopologues of BeH are analyzed in a standard direct-potential-fit procedure that uses least-squares fits to optimize the parameters defining an analytic potential. The ``Morse/Long-range'' (MLR) model used for the potential energy function incorporates the inverse-power long-range tail required by theory, and the calculation of the leading long-range coefficients , , , and include non-adiabatic terms, and up to 4th order QED corrections. As a by-product, we have calculated some fundamental properties of 1 systems with unprecedented precision, such as the dipole, quadrupole, octupole, non-adiabatic, and mixed higher order polarizabilities of hydrogen, deuterium, and tritium. We provide good first estimates for the transition energies for the halo nucleonic species BeH and BeH.Made available in DSpace on 2016-01-05T20:05:42Z (GMT). No. of bitstreams: 3
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Previous issue date: 2
Full CI benchmark potentials for the 6e− system LI2 with a cbs extrapolation from AUG-CC-PCV5Z and AUG-CC-PCV6Z basis sets using FCIQMC and DMRG
Get PDF"Being the simplest uncharged homonuclear dimer after H that has a stable ground state, Li is one of the most important benchmark systems for theory and experiment. In 1930, Delbr{\""u}ck used Li to test his theory of homopolar binding, and it was used again and again as a prototype to test what have now become some of the most ubiquitous concepts in molecular physics (LCAO, SCF, MO, just to name a few). Experimentally, Roscoe and Schuster studied alkali dimers back in 1874. At the dawn of quantum mechanics, the emerging types of spectroscopic analyses we now use today, were tested on Li in the labs of Wurm (1928), Harvey (1929), Lewis (1931), and many others, independently. Li was at the centre of the development of PFOODR in the 80s, and PAS in the 90s"and Lithium Bose-Einstein condensates were announced only 1 month after the Nobel Prize winning BEC announcement in 1995. Even now in the 2010s, numerous experimental and theoretical studies on Li have tested QED up to the 7th power of the fine structure constant. Li has also been of interest to sub-atomic physicists, as it was spectroscopic measurements on Li that determined the spin of Li to be 3/2 in 1931"and Li has been proposed in 2014 as a candidate for the first ``halo nucleonic molecule"".
The lowest triplet state is an excellent benchmark system for all newly emerging \textit{ab initio} techniques because it has only 6, its potential is only 334\,cm deep, it avoids harsh complications from spin-orbit coupling, and it is the deepest potential for which \textit{all} predicted vibrational energy levels have been observed with 0.0001\,cm precision. However the current best \textit{ab initio} potentials do not even yield all vibrational energy spacings correct to within 1\,cm. This could be because the calculation was only done on a cc-pV5Z basis set, or because the QCISD(T,full) method that the authors used, only considered triple excitations while a full CI calculation should include up to hexuple excitations. CCSDTQPH calculations have never yet been reported for anything larger than a DZ basis set, and deterministic FCI calculations for 6 have not exceeded the level of TZ basis sets. With FCIQMC and DMRG we are able to calculate the potential with all levels of excitation included, and the hardware requirements for an aug-cc-pCV6Z basis set are modest. Energies for aug-cc-pCVQZ have already converged to the full CI limit within 0.3\,cm, and 6Z potentials are underway."Made available in DSpace on 2017-01-26T21:38:54Z (GMT). No. of bitstreams: 3
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Previous issue date: 2016-06-2
0.06 cm−1 DISCREPANCY FOR Li2→ 2Li AND 0.994 cm−1 FOR C → C+ BETWEEN LABORATORY AND COMPUTER SPECTROMETERS.
No full textThe energy at the empirical bond length of Li of 4.1700\AA\,\footnote{Dattani N. S., LeRoy R. J. (2011) \textit{J. Mol. Spec.}. \textbf{268}, 199-210.; Semczuk M., \textit{et al.} (2013) \textit{Phys. Rev. A} \textbf{87}, 052505} was obtained at all-electron FCI level with an aug-cc-pCV5Z-NR basis set, all-electron CCSDT(Q) with aug-cc-pCV7Z-NR, and all-electron CCSD(T) with aug-cc-pCV8Z-NR; along with corrections due to special relativity converged with respect to electron correlation and basis set size using the spin-free Dirac-Coulomb Hamiltonian, and further such corrections at the Hartree-Fock level using the Breit and Gaunt Hamiltonians. Corrections to the point-size nucleus approximation were calculated but found to be negligible. The result was compared to the lowest energy of the best empirical potentials with the empirical Born-Oppenheimer breakdown corrections removed, making it essentially an infinite-mass to infinite-mass comparison. The discrepancy between the energy obtained from laboratory spectroscopy and the energy obtained completely by the computer was only 0.06\,cm, which is of the same order of magnitude as the uncertainty on the empirical value, which is 0.007\,cm before including the added uncertainty coming from the Born-Oppenheimer breakdown parameter which itself has an uncertainty of 0.01\,cm. It is discussed what is necessary for the computer spectrometer to outperform the laboratory spectrometer.
The ionization energy of the carbon atom was calculated at all-electron FCI level with aug-cc-pCV8Z-NR and aug-cc-pCV7Z-NR basis sets (the latter only for basis set extrapolation); along with corrections due to special relativity converged with respect to electron correlation and basis set size using the 1 X2C Hamiltonian, further corrections using state-averaged Dirac-Fock for the contribution from the Breit Hamiltonian and some QED contributions; along with DBOC corrections to the clamped nucleus approximation converged with respect to electron correlation and basis set size. Again, corrections to the point-size nucleus approximation were calcualted but found to be negligible. The final energy was compared to the very recent experimental value published by NIST\footnote{Haris K., Krimada A. E., (2017) arXiv:1704.07474.} with the experimental spin-orbit lowering of 12.672508\,cm removed. The discrepancy was 0.994\,cm compared to the 0.009\,cm uncertainty in the laboratory value
Halo Nucleic Molecules: Molecules Formed From At Least One Atom With A Halo Nucleus. Emphasis On 11,11li2 Along With Other Exotic Isotopologues.
Get PDFAtoms whose nuclei have an exotic number of nucleons can have a `core nucleus' surrounded by a `halo' formed by a nucleon orbiting the core nucleus. For example, due to the two halo neutrons orbiting the core nucleus of Li, its nucleus has a cross section that is roughly the same size as that of Pb. Halo nucleic atoms have been studied extensively both in theory and in experiments, however halo nucleic molecules have not been studied in either. We first show, using HeH, BeH, and MgH as examples, that with measurements of any two isotopologues of a molecule, we can determine crucial properties of a third isotopologue well within spectroscopic accuracy. We then use the extremely precise empirical information available\footnote{R. J. LeRoy, N. S. Dattani, J. A. Coxon, A. J. Ross, P. Crozet, C. Linton, \textit{J. Chem. Phys.} \textbf{131}, 204309 (2009).}\footnote{N. S. Dattani, R. J. LeRoy, \textit{J. Mol. Spec.} \textbf{268}, 199-210 (2011).}\footnote{M. Semczuk, X. Li, W. Gunton, M. Haw, N. S. Dattani, J. Witz, A. Mills, D. J. Jones, K. W. Madison, \textit{Phys. Rev. A} \textbf{87}, 052505 (2013)}\footnote{W. Gunton, M. Semczuk, N. S. Dattani, K. W. Madison, \textit{Phys. Rev. A} \textbf{88}, 062510 (2013)} for the low-lying states of Li, Li and Li to predict potentials and various properties of the halo nucleic molecule Li, along with isotopologues containing Li, Li, Li, Li, Li, Li, and Li. We believe that our predictions of the ro-vibrational energies are reliable for experiments for the first detection of a halo nucleic molecule.Made available in DSpace on 2014-09-17T16:56:24Z (GMT). No. of bitstreams: 3
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Previous issue date: 2014-06-1
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