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Title: Gaussian and plane-wave mixed density fitting for periodic systems

ORCiD logo [1]; ORCiD logo [2];  [1];  [1]
  1. Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
  2. Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
Publication Date:
Sponsoring Org.:
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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 147; Journal Issue: 16; Related Information: CHORUS Timestamp: 2018-02-15 01:34:51; Journal ID: ISSN 0021-9606
American Institute of Physics
Country of Publication:
United States

Citation Formats

Sun, Qiming, Berkelbach, Timothy C., McClain, James D., and Chan, Garnet Kin-Lic. Gaussian and plane-wave mixed density fitting for periodic systems. United States: N. p., 2017. Web. doi:10.1063/1.4998644.
Sun, Qiming, Berkelbach, Timothy C., McClain, James D., & Chan, Garnet Kin-Lic. Gaussian and plane-wave mixed density fitting for periodic systems. United States. doi:10.1063/1.4998644.
Sun, Qiming, Berkelbach, Timothy C., McClain, James D., and Chan, Garnet Kin-Lic. 2017. "Gaussian and plane-wave mixed density fitting for periodic systems". United States. doi:10.1063/1.4998644.
title = {Gaussian and plane-wave mixed density fitting for periodic systems},
author = {Sun, Qiming and Berkelbach, Timothy C. and McClain, James D. and Chan, Garnet Kin-Lic},
abstractNote = {},
doi = {10.1063/1.4998644},
journal = {Journal of Chemical Physics},
number = 16,
volume = 147,
place = {United States},
year = 2017,
month =

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 31, 2018
Publisher's Accepted Manuscript

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  • The quantum chemical characterization of solid state systems is conducted with many different approaches, among which the adoption of periodic boundary conditions to deal with three-dimensional infinite condensed systems. This method, coupled to the Density Functional Theory (DFT), has been proved successful in simulating a huge variety of solids. Only in relatively recent years this ab initio quantum-mechanic approach has been used for the investigation of layer silicate structures and minerals. In the present work, a systematic comparison of different DFT functionals (GGA-PBEsol and hybrid B3LYP) and basis sets (plane waves and all-electron Gaussian-type orbitals) on the geometry, energy, andmore » phonon properties of a model layer silicate, talc [Mg{sub 3}Si{sub 4}O{sub 10}(OH){sub 2}], is presented. Long range dispersion is taken into account by DFT+D method. Results are in agreement with experimental data reported in literature, with minimal deviation given by the GTO/B3LYP-D* method regarding both axial lattice parameters and interaction energy and by PW/PBE-D for the unit-cell volume and angular values. All the considered methods adequately describe the experimental talc infrared spectrum.« less
  • Plane-wave density functional theory (DFT-PW) calculations were performed on bulk SnO{sub 2} (cassiterite) and the (100), (110), (001), and (101) surfaces with and without H{sub 2}O present. A classical interatomic force field has been developed to describe bulk SnO{sub 2} and SnO{sub 2}-H{sub 2}O surface interactions. Periodic density functional theory calculations using the program VASP (Kresse et al., 1996) and molecular cluster calculations using Gaussian 03 (Frisch et al., 2003) were used to derive the parametrization of the force field. The program GULP (Gale, 1997) was used to optimize parameters to reproduce experimental and ab initio results. The experimental crystalmore » structure and elastic constants of SnO{sub 2} are reproduced reasonably well with the force field. Furthermore, surface atom relaxations and structures of adsorbed H{sub 2}O molecules agree well between the ab initio and force field predictions. H{sub 2}O addition above that required to form a monolayer results in consistent structures between the DFT-PW and classical force field results as well.« less
  • The moments method is used to calculate the density of states and optical-absorption spectra of large quantum systems. This method uses random wave functions to calculate 500 Chebyshev moments of the density of states (500[sup 2] for the optical-absorption spectra), and transforms these moments back to energy space. The results compare well with direct calculations on a large, 2048 Si-atom bulklike supercell system. To demonstrate its utility, the spectra of a realistic quantum dot with 1035 Si and 452 H atoms are calculated using an empirical pseudopotential Hamiltonian and a plane-wave basis of wave functions.
  • High-frequency quasi-periodic oscillations (QPOs) from weakly magnetized neutron stars display rapid frequency variability (second timescales) and high coherence with quality factors up to at least 200 at frequencies about 800-850 Hz. Their parameters have been estimated so far from standard min({chi}{sup 2}) fitting techniques, after combining a large number of power density spectra (PDS), to have the powers normally distributed (the so-called Gaussian regime). Before combining PDS, different methods to minimize the effects of the frequency drift to the estimates of the QPO parameters have been proposed, but none of them relied on fitting the individual PDS. Accounting for themore » statistical properties of PDS, we apply a maximum likelihood method to derive the QPO parameters in the non-Gaussian regime. The method presented is general, easy to implement, and can be applied to fitting individual PDS, several PDS simultaneously, or their average, and is obviously not specific to the analysis of kHz QPO data. It applies to the analysis of any PDS optimized in frequency resolution and for low-frequency variability or PDS containing features whose parameters vary on short timescales, as is the case for kHz QPOs. It is equivalent to the standard {chi}{sup 2} minimization fitting when the number of PDS fitted is large. The accuracy, reliability, and superiority of the method is demonstrated with simulations of synthetic PDS, containing Lorentzian QPOs of known parameters. Accounting for the broadening of the QPO profile, due to the leakage of power inherent to windowed Fourier transforms, the maximum likelihood estimates of the QPO parameters are asymptotically unbiased and have negligible bias when the QPO is reasonably well detected. By contrast, we show that the standard min({chi}{sup 2}) fitting method gives biased parameters with larger uncertainties. The maximum likelihood fitting method is applied to a subset of archival Rossi X-ray Timing Explorer data of the neutron star X-ray binary 4U1608-522, for which we show that the lower kHz QPO parameters can be measured on timescales as short as 8 s. To demonstrate the potential use of the results of the maximum likelihood method, we show that in the observation analyzed the time evolution of the frequency is consistent with a random walk. We then show that the broadening of the QPO due to the frequency drift scales as {radical}T, as expected from a random walk (T is the integration time of the PDS). This enables us to estimate the intrinsic quality factor of the QPO to be {approx}260, whereas previous analysis indicated a maximum value around 200.« less
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