<i>Ab initio</i>calculation of optical second harmonic generation at the rutile<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Ti</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>110</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>surface

Sano, Hikaru; Mizutani, Goro; Wolf, W.; Podloucky, R.

doi:10.1103/physrevb.70.125411

Cited by 19 publications

(30 citation statements)

References 41 publications

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“…Comparison of these data to various published firstprinciples theoretical investigations of this system [2][3][4][5][6][7][8] reveals that, while some predicted atomic positions are in good agreement with the new experiment, othersmost noticeably those of the surface oxygen atomsare not. Indeed, the vertical relaxation of the bridging oxygen atoms was consistently predicted to be negative (i.e., inward relaxation relative to bulk termination), but was measured to be positive in Ref.…”

Section: A Recent Leed-iv Experimentssupporting

confidence: 58%

“…1 In particular, our computed vertical relaxations of the two surface oxygen atoms, O(1) and O(2), are very close to the experimental values. Recall that the largest discrepancies, by far, between the recent experiment 1 and earlier first-principles calculations [2][3][4][5][6][7][8] were for these two degrees of freedom. These observations raise two questions that will shape the remainder of this paper: First, why do the present calculations differ from earlier ones, resulting in better overall agreement with the experiment in Ref.…”

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confidence: 99%

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Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Thompson

Lewis

2006

Phys. Rev. B

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A detailed reexamination of the (110) surface structure of rutile TiO 2 has been carried out using first-principles total-energy methods. This investigation is in response to a recent high-precision LEED-IV measurement revealing certain significant quantitative discrepancies between experiment and previous theoretical calculations. We have been able to resolve these discrepancies and achieve excellent quantitative agreement with experiment by judicious attention to reducing computational approximation errors. Our analysis also reveals that bond lengths converge much faster with slab thickness than do relaxed absolute atomic positions, which are the structural parameters typically reported in the literature for this and related systems. The effect this observation has on both the choice of slab models and the way in which surfaces structures should be reported for covalently bonded solids is discussed. Finally, the efficacy of freezing the lowest several atomic layers of TiO 2 slab models in their bulk-like positions is examined. A recent LEED-IV experiment1 has produced what is arguably the highest precision measurement to date of the structure of the (110) surface of rutile TiO 2 .Comparison of these data to various published firstprinciples theoretical investigations of this system [2][3][4][5][6][7][8] reveals that, while some predicted atomic positions are in good agreement with the new experiment, othersmost noticeably those of the surface oxygen atomsare not. Indeed, the vertical relaxation of the bridging oxygen atoms was consistently predicted to be negative (i.e., inward relaxation relative to bulk termination), but was measured to be positive in Ref.[1]. An earlier surface x-ray diffraction study 9 had reported a significant inward relaxation for the bridging oxygen. Thus, the relaxed structure of the surface oxygen atoms has been a source of confusion both experimentally and theoretically.Given the prominence of TiO 2 (110) in applications and basic research, 10 as well as the extensive number of first-principles investigations on systems that build on TiO 2 (110) as a starting point, we felt this confusion was significant and merited further inquiry. As a result, we have undertaken an extensive first-principles analysis of the structure of TiO 2 (110), focusing on convergence and characterization issues. Our calculations resolve the discrepancy between theory and experiment on the relaxations of the surface oxygen atoms, while maintaining agreement in the other atomic relaxations. Furthermore, we find that much thicker slabs than have been typically used are necessary to achieve convergence not only in surface energy, as found previously, 11 but also in absolute atomic positions. However, if bond lengths are chosen as the "figures of merit" for assessing convergence, then our results show that the thinner slabs used to date in theoretical studies of this system are acceptable. We argue below in favor of switching to reporting bond lengths (and perhaps bond angles) as a more physically relevant descri...

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Section: A Recent Leed-iv Experimentssupporting

confidence: 58%

mentioning

confidence: 99%

Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Thompson

Lewis

2006

Phys. Rev. B

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“…Such an approach was recently proposed in ref. 18 to investigate the charge degree of freedom of the 1D EHM, which reproduced the ground-state phase diagram with high accuracy. Here we extend their method in order to calculate the finite-T properties by solving the RG equations in § 2.1 and stopping the scaling at l T as mentioned above.…”

Section: Methodsmentioning

confidence: 99%

“…The numerical ED data are implemented into the analytical bosonization + RG scheme, as initial conditions of the RG equations. 18) As for the properties below T CO , the T dependence of the CO order parameter is calculated by the QMC method, 15) and then adopted to the scheme above. This combined method enables us to compute the T dependences of physical properties such as the spin susceptibility and the electrical resistivity across T CO .…”

Section: Introductionmentioning

confidence: 99%

Finite-Temperature Properties across the Charge Ordering Transition –Combined Bosonization, Renormalization Group, and Numerical Methods–

et al. 2010

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We theoretically describe the charge ordering (CO) metal-insulator transition based on a quasi-onedimensional extended Hubbard model, and investigate the finite temperature (T ) properties across the transition temperature, TCO. In order to calculate T dependence of physical quantities such as the spin susceptibility and the electrical resistivity, both above and below TCO, a theoretical scheme is developed which combines analytical methods with numerical calculations. We take advantage of the renormalization group equations derived from the effective bosonized Hamiltonian, where Lanczos exact diagonalization data are chosen as initial parameters, while the CO order parameter at finite-T is determined by quantum Monte Carlo simulations. The results show that the spin susceptibility does not show a steep singularity at TCO, and it slightly increases compared to the case without CO because of the suppression of the spin velocity. In contrast, the resistivity exhibits a sudden increase at TCO, below which a characteristic T dependence is observed. We also compare our results with experiments on molecular conductors as well as transition metal oxides showing CO.

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“…It can give multiple information on the structural [22,27,58,59,70,92,174,175] and electronic properties of materials by detecting the modifications induced by the presence of adsorbates [14], stress [13] or external perturbing electromagnetic fields [176] and also permitting an in situ monitoring of dynamical processes [14,15].…”

Section: The Si/caf 2 Interfacementioning

confidence: 99%

Second-Harmonic Generation

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Field Guide to Nonlinear Optics

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Ab initiocalculation of optical second harmonic generation at the rutileTiO2(110)surface

Cited by 19 publications

References 41 publications

Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Finite-Temperature Properties across the Charge Ordering Transition –Combined Bosonization, Renormalization Group, and Numerical Methods–

Second-Harmonic Generation

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