Singularities in the Hamiltonian at electronic degeneracies

Varandas, A. J. C.; Xu, Z. R.

doi:10.1016/s0301-0104(00)00202-0

Cited by 7 publications

(5 citation statements)

References 67 publications

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“…The accuracy and the limits of the BO approximation have been extensively discussed in literature. − An encouraging result for the muon case in this context has been provided by Takahashi and Takatsuka who considered the accuracy of the BO approximation for the ppμ – molecule ( p stands for proton) and found a deviation smaller than 5% from the non-BO vibronic energies calculated with semiclassical methods …”

Section: Discussion and Conclusionmentioning

confidence: 94%

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Bonfà¹,

Sartori²,

Renzi³

2015

J. Phys. Chem. C

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We revise the simple and yet powerful approach of the Double Adiabatic Approximation (DAA) to study positive muon embedding sites in condensed matter. This method introduces a tractable and reasonably accurate description of the quantum nature of the muon in Density Functional Theory (DFT) simulations aiming at identifying muon sites. Moreover, this approach overcomes the limitations of the harmonic approximation in terms of both computational efforts and accuracy. Notably, it also improves treatment of muon diffusion. We use the DAA and Nudged Elastic Band calculations to determine the muon sites and the activation energies between equivalent sites in MnSi and copper. In metallic Cu, the proposed phonon-assisted mechanism for the low-temperature muon diffusion in the lattice is confirmed. ■ INTRODUCTIONMuon spin rotation and relaxation (μSR) spectroscopy is an experimental technique that provides the time evolution of the muon spin polarization by exploiting the anisotropic emission of the decay positron.The main field of application of μSR is material science, but it is also adopted in chemistry for studying molecular dynamics and radical kinetics. 1−3 Both μ − SR and μ + SR exist, but, since μ − undergoes nuclear capture and the surviving μ − fall into atomic orbitals extremely close to the nuclei, μ + SR is more commonly used to investigate condensed matter.μSR experiments provide a measure of the microscopic field distribution at the interstitial site(s) where the μ + stop inside the sample. A seemingly embarrassing point is that these sites are usually unknown to the experimenter and the additional lack of knowledge on the perturbation generated locally by the positive muon probably represent the most common criticisms of the experimental technique. Even though in a large variety of cases ignoring the muon position does not represent a limitation, having access to information on interstitial sites and on muon-induced perturbations might be crucial to evaluate electronic properties such as long-range magnetic orders or localized magnetic moments.Predicting the position of interstitial muon sites is not a trivial task. During the final stages of thermalization in the sample the scattering between the muon and the atoms of the compound leads to a kinetic energy degradation from hundreds to tenths of electronvolts. Nonetheless, the identification of diamagnetic muon sites with approaches based on the Density Functional Theory (DFT) is emerging as a new and valuable strategy to routinely assist μSR experiments interpretation. After the pioneering work of Van de Walle et al., in recent years, this method, which provides information on the electronic and crystalline perturbations introduced by the muon, has been validated in many experimental cases with great success. 4−13 There are two main difficulties in the DFT approach. One is inherited from the mean-field description which cannot always correctly describe some classes of materials, like strongly correlated electrons systems or even some semiconductors mist...

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Section: Discussion and Conclusionmentioning

confidence: 94%

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Bonfà¹,

Sartori²,

Renzi³

2015

J. Phys. Chem. C

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“…By employing a line‐integral technique 54, 56–66 to study the GP effect in two coupled‐state hydrogenic systems, we also showed 50 that the adiabatic–diabatic‐transformation angle 56–59, 61 is identical (up to a constant) to the geometry‐dependent mixing angle γ( R ) of the orthogonal transformation that diagonalizes the diabatic potential matrix 47, 67–71. Most recently, we discussed 72 the singularities that arise in the Hamiltonian at the crossing seam and we established the relationship between the magnetic vector, the electric scalar gauge potentials, and the mixing angle.…”

Section: Introductionmentioning

confidence: 81%

Nuclear dynamics in the vicinity of a crossing seam: Vibrational spectrum of HD₂ revisited

Varandas

2001

Int J of Quantum Chemistry

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So far, most studies of the geometric phase effect have presumed that the phase is path-independent; hence, one must supply another restriction concerning the boundary condition on the nuclear wave functions when dealing with nonsymmetric isotopomers of X 3 systems. We report calculations of the vibrational spectra of HD 2 using a recently proposed generalized Born-Oppenheimer (GBO) formalism. The calculations demonstrate that there are significant differences between the results calculated from the present GBO method and those based on the preceding presumption.

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“…A similar problem that singularity appears in the Hamiltonian based on the diabatic representation has also been discussed. [13][14][15] In this paper, we will present a simple approximate analytical solution which satisfies the correct boundary condition at the origin for the dynamical linear E e problem in the strong coupling limit. First-order perturbation is employed to obtain up to 1/g 4 contribution.…”

Section: Introductionmentioning

confidence: 99%

The E⊗e dynamic Jahn-Teller problem: A new insight from the strong coupling limit

Sato

Chibotaru

Ceulemans

2005

The Journal of Chemical Physics

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Correct boundary conditions for the E x e dynamic Jahn-Teller problem are considered explicitly for the first time to obtain approximate analytical solutions in the strong coupling limit. Numerical solutions for the decoupled equations using the finite difference method are also presented. The numerical solutions for the decoupled equations exhibit avoided crossings in the weak coupling region, which explains the oscillating behavior of the solutions obtained by Longuet-Higgins et al. for the coupled equations. The obtained analytical energy expressions show improved agreement with the numerical calculations as compared with the previous treatment in which the potentials were assumed to be harmonic. We demonstrate that the pseudorotational energy j(2)/(2g(2)), where g is the dimensionless vibronic coupling constant, and j total angular momentum: j=+/-1/2,+/-3/2,..., in the conventional strong coupling expression for the vibronic levels of the lower sheet is exact. Non-Hermitian first-order perturbation theory gives the energy which is correct up to 1/g(4). The asymptotic behavior of the wave function at the origin does not influence the corrected energy up to order of 1/g(4). At the same time the treatment of the upper sheet with correct boundary conditions gives solutions which are entirely different from the corresponding Slonczewski's solutions. Besides, the correct boundary conditions enable us to evaluate the nonadiabatic coupling between the lower and upper potential sheets. The energy correction due to the nonadiabatic coupling is estimated to be of order 1/g(6).

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Singularities in the Hamiltonian at electronic degeneracies

Cited by 7 publications

References 67 publications

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Nuclear dynamics in the vicinity of a crossing seam: Vibrational spectrum of HD₂ revisited

The E⊗e dynamic Jahn-Teller problem: A new insight from the strong coupling limit

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Singularities in the Hamiltonian at electronic degeneracies

Cited by 7 publications

References 67 publications

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Nuclear dynamics in the vicinity of a crossing seam: Vibrational spectrum of HD2 revisited

The E⊗e dynamic Jahn-Teller problem: A new insight from the strong coupling limit

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Product

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Nuclear dynamics in the vicinity of a crossing seam: Vibrational spectrum of HD₂ revisited