Interactive tool for visualization of adiabatic adjustment in APH coordinates for computational studies of vibrational motion and chemical reactions

Teplukhin, Alexander; Babikov, Dmitri

doi:10.1016/j.cplett.2014.09.015

Cited by 14 publications

(20 citation statements)

References 29 publications

(12 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Qualitatively, the hyper-radius describes a "breathing" vibration mode, also known as symmetric stretch, whereas the hyper-angles and correspond to bending and asymmetric-stretching modes of a triatomic. 39,40,41 In these coordinates the exact rotational-vibrational Hamiltonian operator is expressed in the following form: 13 ̂=̂v ib +̂r ot +̂c or (1) The vibrational part of the Hamiltonian is separable in , and and includes, besides the potential energy surface pes , what we call the "extra-potential" term ext :…”

Section: Theorymentioning

confidence: 99%

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

et al. 2020

Self Cite

View full text Add to dashboard Cite

Several alternative methods for description of interaction between rotation and vibration are compared and contrasted using hyper-spherical coordinates for a triatomic molecule. These methods differ by the choice of z-axis and by the assumption of a prolate or oblate rotor shape of the molecule. For each case, block-structure of the rotational-vibrational Hamiltonian matrix is derived and analyzed, and the advantages and disadvantages of each method are made explicit.This theory is then employed to compute ro-vibrational spectra of singly substituted ozone; roughly, 600 vibrational states of 16 O 18 O 16 O and 16 O 16 O 18 O isomers combined, with rotational excitations up to = 5 and both inversion parities (21600 coupled ro-vibrational states total). Splittings between the states of different parities, so called K-doublings, are calculated and analyzed. The roles of the asymmetric-top rotor term and the Coriolis coupling term are determined individually, and it is found that they both affect these splittings, but in the opposite directions. Thus, the two effects partially cancel out, and the residual splittings are relatively small. Energies of the ro-vibrational states reported in this work for 16 O 18 O 16 O and 16 O 16 O 18 O are in excellent agreement with literature (available for low vibrational excitation). New data obtained here for the highly excited vibrational states enable the first systematic study of the Coriolis effect in symmetric and asymmetric isotopomers of ozone.

show abstract

Section: Theorymentioning

confidence: 99%

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the three-dimensional ozone system, we plot the probability density (the wave function squared) as a function of the symmetric-stretch coordinate ρ in Fig. 1b (36,37). The SDT basis functions span the other two internal degrees of freedom (not plotted) at each value of ρ and are computed classically (32).…”

Section: Application To O 2 and Omentioning

confidence: 99%

Calculation of Molecular Vibrational Spectra on a Quantum Annealer

Teplukhin

Kendrick

Babikov

2019

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing hardware have been limited to quantum simulators. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer.The method is applied to two chemically important molecules: O 2 (oxygen) and O 3 (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer. * Correspondence should be addressed to BKK (bkendric@lanl.gov).

show abstract

“…More details can be found in our recent papers. (43,44) Three vibrational degrees of freedom of a triatomic molecule, like ozone, can be described by the APH hyperspherical coordinates. (45) Although not as intuitive as Jacobi coordinates, hyper-spherical coordinates lead to the simplest form of the ro-vibrational Hamiltonian operator, but also, they permit to take into account molecular symmetry in a rigorous way, and to treat all reaction pathways on equal footing, which is essential for the ozone formation reaction.…”

Section: Iia Coordinates Pes and Reaction Pathwaysmentioning

confidence: 99%

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect

Teplukhin

Babikov

2018

J. Phys. Chem. A

Self Cite

View full text Add to dashboard Cite

The essential components of theory for the description of isotope effects in recombination reaction that forms ozone are presented, including the introduction of three reaction pathways for symmetric and asymmetric isotopomers, a brief review of relevant experimental data for singly-and doubly substituted isotopologues, the definitions of ζ-effect and η-effect, and the introduction of isotopic enrichment δ. Two levels of theory are developed to elucidate the role of molecular symmetry, atomic masses, vibrational zero-point energies, and rotational excitations in the recombination process. The issue of symmetry is not trivial, since the important factors, such as 1/2 and 2, appear in seven different places in the formalism. It is demonstrated that if all these effects are taken into account properly, then no anomalous isotope effects emerge. At the next level of theory, a model is considered in which one scattering resonance (sitting right at the top of centrifugal barrier) is introduced per ro-vibrational channel. It is found that this approach is equivalent to statistical treatment with partition functions at the transition state. Accurate calculations using hyper-spherical coordinates show that no isotope effects come from difference in the number of states. In contrast, differences in vibrational and rotational energies lead to significant isotope effects. However, those effects appear to be local, found for the rather extreme values of rotational quantum numbers. They largely cancel when rate coefficients are computed for the thermal distribution of rotational excitations. Although large isotope effects (observed in experiments) are not reproduced here, this level of theory can be used as a foundation for more detailed computational treatment, with accurate information about resonance energies and lifetimes computed and included.

show abstract

Interactive tool for visualization of adiabatic adjustment in APH coordinates for computational studies of vibrational motion and chemical reactions

Cited by 14 publications

References 29 publications

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

Theoretical Treatment of the Coriolis Effect Using Hyperspherical Coordinates, with Application to the Ro-Vibrational Spectrum of Ozone

Calculation of Molecular Vibrational Spectra on a Quantum Annealer

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect

Contact Info

Product

Resources

About