Quantum entanglement between electronic and vibrational degrees of freedom in molecules

McKemmish, Laura K.; McKenzie, Ross H.; Hush, Noel S.; Reimers, Jeffrey R.

doi:10.1063/1.3671386

Cited by 65 publications

(94 citation statements)

References 100 publications

(113 reference statements)

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“…Previous studies [98,99] of the Hamiltonian (23) suggest that the most significant deviations from the BornOppenheimer approximation will occur when the bare vibrational frequency ω ∼ ∆(R) and also the barrier height. This will occur when R ∼ 2.5Å.…”

Section: B Hamiltonian For Non-adiabatic Effectsmentioning

confidence: 99%

Effect of quantum nuclear motion on hydrogen bonding

McKenzie

Bekker

Athokpam

et al. 2014

The Journal of Chemical Physics

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160

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This work considers how the properties of hydrogen bonded complexes, X-H· · · Y, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (X) and acceptor (Y) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H· · · O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4 − 3.0Å, i.e., from strong to weak hydrogen bonds. The position of the proton (which determines the X-H bond length) and its longitudinal vibrational frequency, along with the isotope effects in both are described quantitatively. An analysis of the secondary geometric isotope effect, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of bending modes is also considered: their quantum effects compete with those of the stretching mode for weak to moderate Hbond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several trends.

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Section: B Hamiltonian For Non-adiabatic Effectsmentioning

confidence: 99%

Effect of quantum nuclear motion on hydrogen bonding

McKenzie

Bekker

Athokpam

et al. 2014

The Journal of Chemical Physics

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160

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“…This entropy ranges from zero for a classical system to unity for a completely entangled qubit. Evaluated across the parameter space of the single-mode two-state chemical model [46], the developed entanglement is shown in figure 7. Different plots show the entanglement as a function of 2/ J  and The simplest way to model the effects of environment on coherence and hence entanglement is to treat the environment as simply generating random fluctuations in the energy asymmetry 0 E .…”

Section: Choice Of Chemical Reaction For Use As a Chemical Quantum Qubitmentioning

confidence: 99%

“…Of the molecular systems considered, the dipyridyl polyene 1 and the Alq3 2 sit in the region of greatest entanglement and greatest environmental immunity, whilst BNB 4 and the Creutz-Taube ion 5 sit in a region where the entanglement never gets much more than one half but it is quite stable to environmental perturbation. Whether or not the ground-state vibrational density is bimodal (i.e., zero-point vibration is supported in each well) is a critical indicator of qubit performance [46].…”

Section: Choice Of Chemical Reaction For Use As a Chemical Quantum Qubitmentioning

confidence: 99%

“…It also forms the basis for understanding of primary charge separation in natural and artificial solar-energy harvesting systems used in plants, bacteria, organic photovoltaics and artificial photosynthesis, as well as the reverse process, light emission in organic light-emitting diodes. A critical feature of the approach is that it leads to very many analytical or numerically exactly-solvable relationships linking system properties, as recently summarized in a number of contexts [28,[43][44][45][46]. Exemplary in Hush's description of intervalence compounds is that he showed how from measurement of the visible absorption spectrum of the dye Prussian blue, it was possible to deduce kinetics parameters critical to the understanding of the charge conductivity of the material [5].…”

Section: Related Contentmentioning

confidence: 99%

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Diabatic models with transferrable parameters for generalized chemical reactions

Reimers

McKemmish

McKenzie

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. Diabatic models applied to adiabatic electron-transfer theory yield many equations involving just a few parameters that connect ground-state geometries and vibration frequencies to excited-state transition energies and vibration frequencies to the rate constants for electrontransfer reactions, utilizing properties of the conical-intersection seam linking the ground and excited states through the Pseudo Jahn-Teller effect. We review how such simplicity in basic understanding can also be obtained for general chemical reactions. The key feature that must be recognized is that electron-transfer (or hole transfer) processes typically involve one electron (hole) moving between two orbitals, whereas general reactions typically involve two electrons or even four electrons for processes in aromatic molecules. Each additional moving electron leads to new high-energy but interrelated conical-intersection seams that distort the shape of the critical lowest-energy seam. Recognizing this feature shows how conicalintersection descriptors can be transferred between systems, and how general chemical reactions can be compared using the same set of simple parameters. Mathematical relationships are presented depicting how different conical-intersection seams relate to each other, showing that complex problems can be reduced into an effective interaction between the ground-state and a critical excited state to provide the first semi-quantitative implementation of Shaik's "twin state" concept. Applications are made (i) demonstrating why the chemistry of the firstrow elements is qualitatively so different to that of the second and later rows, (ii) deducing the bond-length alternation in hypothetical cyclohexatriene from the observed UV spectroscopy of benzene, (iii) demonstrating that commonly used procedures for modelling surface hopping based on inclusion of only the first-derivative correction to the Born-Oppenheimer approximation are valid in no region of the chemical parameter space, and (iv), demonstrating the types of chemical reactions that may be suitable for exploitation as a chemical qubit in some quantum information processor. IntroductionThough chemical reactions involve complicated restructuring of the electronic and nuclear configuration and dynamics, it can be useful to use the simplification of envisaging reactions as occurring along a single reaction coordinate. This basic concept forms the conceptual framework of Transition-State Theory and much of modern chemistry. Modern electronic-structure calculation methods can predict wide ranges of properties to within the accuracy of experimental measurements, capturing all chemical and spectroscopic features of the system, but such approaches rarely provide insight into why processes occur and have to be repeated for each small system variation. Diabatic models can be used to interpret these calculations, however, revealing the chemical features controlling the process. Basically, simple forms, called diabatic surfaces, are used to describe the reactants and pro...

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“…Few studies have treated this subject and these works consider Hilbert spaces with low dimensionality. Special attention is attached to double-welled chemical systems, as embodying electronic-vibrational entanglement through the role played by the wavefunction delocalization [17,18], and to entanglement in relation with quantum chaos induced by non-adiabatic interaction due to the breakdown of the Born-Oppenheimer approximation [19].…”

Section: Introductionmentioning

confidence: 99%

Entanglement between electronic and vibrational degrees of freedom in a laser-driven molecular system

Vatasescu

2013

Phys. Rev. A

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We investigate the entanglement between electronic and vibrational degrees of freedom produced by a vibronic coupling in a molecular system described in the Born-Oppenheimer approximation.Entanglement in a pure state of the Hilbert space H=H el H vib is quantified using the von Neumann entropy of the reduced density matrix and the reduced linear entropy. Expressions for these entanglement measures are derived for the 2 × N v and 3 × N v cases of the bipartite entanglement, where 2 and 3 are the dimensions of the electronic Hilbert space H el , and N v is the dimension of H vib . We study the entanglement dynamics for two electronic states coupled by a laser pulse (a 2 × N v case), taking as an example a coupling between the a 3 Σ + u (6s, 6s) and 1 g (6s, 6p 3/2 ) states of the Cs 2 molecule. The reduced linear entropy expression obtained for the 3 × N v case is used to follow the entanglement evolution in a scheme proposed for the control of the vibronic dynamics in a Cs 2 cold molecule, implying the a 3 Σ + u (6s, 6s), 0 − g (6s, 6p 3/2 ), and 0 − g (6s, 5d) electronic states, which are coupled by a non-adiabatic radial coupling and a sequence of chirped laser pulses.

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Quantum entanglement between electronic and vibrational degrees of freedom in molecules

Cited by 65 publications

References 100 publications

Effect of quantum nuclear motion on hydrogen bonding

Effect of quantum nuclear motion on hydrogen bonding

Diabatic models with transferrable parameters for generalized chemical reactions

Entanglement between electronic and vibrational degrees of freedom in a laser-driven molecular system

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