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arXiv:1902.10520

Interaction of the hydrogen molecule with the environment: stability of the system

Izabela A. Wrona, M.W. Jarosik, Radosław Szczȩśniak, Kamila A. Szewczyk, M. K. Stala, W. Leoński

Published Jan 13, 2019• 0 citations
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Abstract

We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ($γ$) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time ($T_{D}$) decreases, if the $γ$ parameter increases (for $γ\rightarrow 0$, we get $T_{D}\rightarrow +\infty$). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant $γ$ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule ($γ_{MS}=0.659374$~Ry). The hydrogen molecule is statically unstable for $γ>γ_{D}=1.024638$~Ry. One can also observed the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian ($γ_{\mathcal {PT}}=0.520873$~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.

DOI
10.48550/arxiv.1902.10520

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Abstract The stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme was studied. We determined the properties of the molecule taking into account all electronic interactions, the parameters of the Hamiltonian being computed by the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ( γ ) by means of the non-Hermitian, $${\mathscr{PT}}$$ P T -symmetric Hamiltonian. We showed that the hydrogen molecule is dynamically unstable. Its dissociation time ( T D ) decreases if the γ parameter increases (for γ → 0 we got T D → + ∞). The dynamic instability of the hydrogen molecule is superimposed on the decrease in its static stability as γ increases. Then we can observe the decrease in the dissociation energy value and the existence of the metastable state of the molecule as γ MS reaches 0.659374 Ry. The hydrogen molecule is statically unstable when γ > γ D = 1.024638 Ry. Moreover, we can also observe the $${\mathscr{PT}}$$ P T symmetry breaking effect for the electronic Hamiltonian when $${\gamma }_{{\mathscr{PT}}}$$ γ P T = 0.520873 Ry. This effect does not affect such properties of the hydrogen molecule as: the electronic Hamiltonian parameters, the phonon and the rotational energies, and the values of the electron-phonon coupling constants neither it disturbs the dynamics of the electronic subsystem. However, the number of available quantum states goes down to four.

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We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically (γγγ) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time (TDT_{D}TD​) decreases, if the γγγ parameter increases (for γ→0γ\rightarrow 0γ→0, we get TD→+∞T_{D}\rightarrow +\inftyTD​→+∞). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant γγγ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule (γMS=0.659374γ_{MS}=0.659374γMS​=0.659374~Ry). The hydrogen molecule is statically unstable for γ>γD=1.024638γ>γ_{D}=1.024638γ>γD​=1.024638~Ry. One can also observed the PT\mathcal{PT}PT symmetry breaking effect for the electronic Hamiltonian (γPT=0.520873γ_{\mathcal {PT}}=0.520873γPT​=0.520873~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.
Interaction of the hydrogen molecule with the environment: stability of the system and the PT{\mathscr{PT}}PT symmetry breaking
Abstract The stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme was studied. We determined the properties of the molecule taking into account all electronic interactions, the parameters of the Hamiltonian being computed by the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ( γ ) by means of the non-Hermitian, PT{\mathscr{PT}}PT P T -symmetric Hamiltonian. We showed that the hydrogen molecule is dynamically unstable. Its dissociation time ( T D ) decreases if the γ parameter increases (for γ → 0 we got T D → + ∞). The dynamic instability of the hydrogen molecule is superimposed on the decrease in its static stability as γ increases. Then we can observe the decrease in the dissociation energy value and the existence of the metastable state of the molecule as γ MS reaches 0.659374 Ry. The hydrogen molecule is statically unstable when γ > γ D = 1.024638 Ry. Moreover, we can also observe the PT{\mathscr{PT}}PT P T symmetry breaking effect for the electronic Hamiltonian when γPT{\gamma }_{{\mathscr{PT}}}γPT​ γ P T = 0.520873 Ry. This effect does not affect such properties of the hydrogen molecule as: the electronic Hamiltonian parameters, the phonon and the rotational energies, and the values of the electron-phonon coupling constants neither it disturbs the dynamics of the electronic subsystem. However, the number of available quantum states goes down to four.
A theoretical study is conducted on the stability of exotic antiproton-hydrogen molecular anions (p‾H\overline{p}\mathrm{H}p​H), which in the separated atom limit correlate with p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) (nnn being the principal quantum number). The p‾H\overline{p}\mathrm{H}p​H molecule in the electronic ground state is highly unstable due to pair annihilation and autodetachment ($\ensuremath{\rightarrow}\overline{p}p+e$). However, if the p‾H\overline{p}\mathrm{H}p​H molecule is electronically excited, the molecular stability can be drastically improved. Since the excited states of the H\mathrm{H}H atom have accidental degeneracy, the asymptotic form of the Born-Oppenheimer potential curve of p‾+H(n=2)\overline{p}+\mathrm{H}(n=2)p​+H(n=2) behaves as 1/R21/{R}^{2}1/R2 (RRR being the relative distance), which can play a critical role in the bonding and stability of the molecule. It is found that the p‾H\overline{p}\mathrm{H}p​H molecule in the first electronic excited state and in a high rotational state is sufficiently stable and has a lifetime dominated by spontaneous radiative emission ($\ensuremath{\rightarrow}\overline{p}+\mathrm{H}+h\ensuremath{\nu}$). The p‾H\overline{p}\mathrm{H}p​H system is dynamically similar to ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$, which had been commonly considered to be unstable due to autodetachment. However, recent measurements of ion-beam sputtering unambiguously verified the existence of long-lived ${\mathrm{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{-}}$ molecules in high rotational states. This suggests that the p‾H\overline{p}\mathrm{H}p​H molecules may actually be created if one employs experimental means such as the chemical sputtering of hydrogen-rich targets with p‾\overline{p}p​ beams.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
We report a theoretical study of antihydrogen-hydrogen molecular resonance states consisting of a positron, an antiproton, an electron and a proton. The four particles strongly correlate and show different character from the hydrogen molecule. Because of the non-separability of the positron and electron motions from the antiproton and proton motions, the adiabatic approximation breaks down at the short antiproton-proton distance. Based on a non-adiabatic method, we directly solve the four-body problem and obtain the resonance energies and widths. In order to examine the roles of positron–antiproton and electron–proton correlations as well as positron–electron and antiproton–proton correlations, we introduce two different types of coordinate systems. One is suited for describing an antihydrogen–hydrogen configuration, and the other is a positronium–protonium configuration. The antihydrogen–hydrogen configuration contributes to the existence of the molecular resonance states, and the positronium–protonium configuration makes the resonance states unstable. Mixing of the two configurations results in an antihydrogen-hydrogen molecular resonance state, and the resonance state has an energy of −0.077 9(3) a.u. from the antihydrogen–hydrogen dissociation threshold with its lifetime 16 (2) fs.
An attempt is made to derive the parameters of the Hubbard Hamiltonian for the hydrogen molecule from state-of-the-art quantum chemistry calculations of the ground and excited states of the neutral and singly ionized molecules (eight states altogether). Calculations are carried out for interatomic distances in the range 0.6−−4.3A˚0.6--4.3\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}0.6−−4.3A˚. The results clearly indicate that the on-site repulsion UUU is not enough to fit the ab initio energies and that it is necessary to incorporate the intersite repulsion (usually referred to as JJJ). If JJJ is ignored, the fitted on-site repulsion approaches the atomic value very slowly as the interatomic distance is increased, a clearly unphysical behavior. For finite JJJ and at the equilibrium interatomic distance, the energies of the eight states mentioned above are reasonably fitted with an atomic orbital energy ${ϵ}_{0}\ensuremath{\approx}\ensuremath{-}24.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, Coulomb interaction parameters $U\ensuremath{\approx}11.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $J\ensuremath{\approx}8.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and a hopping integral $t\ensuremath{\approx}7.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.
We investigate the dynamical properties of one-dimensional dissipative Fermi-Hubbard models, which are described by the Lindblad master equations with site-dependent jump operators. The corresponding non-Hermitian effective Hamiltonians with pure loss terms possess parity-time (PT\mathcal{PT}PT) symmetry if we compensate the system additionally with an overall gain term. By solving exactly the two-site Lindblad equation with fixed dissipation, we find that the dynamics of the rescaled density matrix shows an instability as the interaction increases over a threshold, which can be equivalently described in the scheme of non-Hermitian effective Hamiltonians. This instability is also observed in multisite systems and closely related to the PT\mathcal{PT}PT-symmetry breaking accompanied by appearance of complex eigenvalues of the effective Hamiltonian. Moreover, we unveil that the dynamical instability of the antiferromagnetic Mott phase comes from the PT\mathcal{PT}PT-symmetry breaking in highly excited bands, although the low-energy effective model of the non-Hermitian Hubbard model in the strongly interacting regime is always Hermitian. We also provide a quantitative estimation of the time for the observation of dynamical PT\mathcal{PT}PT-symmetry breaking which could be probed in experiments.