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Frank Neese - One of the best experts on this subject based on the ideXlab platform.
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analytical Gradient for the domain based local pair natural orbital second order moller plesset perturbation theory method dlpno mp2
Journal of Chemical Physics, 2019Co-Authors: Peter Pinski, Frank NeeseAbstract:Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basis). The most demanding single-point Gradient Calculation was performed for the small protein crambin containing 644 atoms and over 12 000 basis functions.
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analytical Gradient for the domain based local pair natural orbital second order moller plesset perturbation theory method dlpno mp2
Journal of Chemical Physics, 2019Co-Authors: Peter Pinski, Frank NeeseAbstract:Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basis). The most demanding single-point Gradient Calculation was performed for the small protein crambin containing 644 atoms and over 12 000 basis functions.Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basi...
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efficient time dependent density functional theory approximations for hybrid density functionals analytical Gradients and parallelization
Journal of Chemical Physics, 2011Co-Authors: Taras Petrenko, Simone Kossmann, Frank NeeseAbstract:In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the Calculation of the TDDFT/TDA excitation energies and analytical Gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the Calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and Gradient Calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total Calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and Gradient Calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the Calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.
Peter Pinski - One of the best experts on this subject based on the ideXlab platform.
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analytical Gradient for the domain based local pair natural orbital second order moller plesset perturbation theory method dlpno mp2
Journal of Chemical Physics, 2019Co-Authors: Peter Pinski, Frank NeeseAbstract:Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basis). The most demanding single-point Gradient Calculation was performed for the small protein crambin containing 644 atoms and over 12 000 basis functions.
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analytical Gradient for the domain based local pair natural orbital second order moller plesset perturbation theory method dlpno mp2
Journal of Chemical Physics, 2019Co-Authors: Peter Pinski, Frank NeeseAbstract:Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basis). The most demanding single-point Gradient Calculation was performed for the small protein crambin containing 644 atoms and over 12 000 basis functions.Building upon our previously published work [P. Pinski and F. Neese, J. Chem. Phys. 148, 031101 (2018)], we derive the formally complete analytical Gradient for the domain-based local pair natural orbital second order Moller-Plesset (MP2) perturbation theory method. Extensive testing of geometry optimizations shows that the deviations from resolution of the identity-based MP2 structures are small. Covalent bond lengths are reproduced to within 0.1 pm, whereas errors in interatomic distances between noncovalently interacting system parts do not exceed 1% with default truncation thresholds and 0.3% with tight thresholds. Moreover, we introduce a procedure to circumvent instabilities of the Gradient caused by singular coupled-perturbed localization equations, as they occur for some symmetric systems with continuously degenerate localized orbitals. The largest system for which a geometry optimization was completed is a host-guest complex with over 200 atoms and more than 4000 basis functions (triple-zeta basi...
Rongzong Huang - One of the best experts on this subject based on the ideXlab platform.
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density Gradient Calculation in a class of multiphase lattice boltzmann models
Physical Review E, 2019Co-Authors: Rongzong Huang, N A AdamsAbstract:The multiphase lattice Boltzmann (LB) models based on pairwise interactions show great potential for simulating multiphase flows due to the conceptual and computational simplicity. Although the dynamics of multiphase flows are reproduced by the pairwise interaction force, the Gradient of density (or effective density, i.e., pseudopotential) is implicitly involved in these models via the specialized forcing scheme or the consistent scheme for ɛ^{3}-order term. This work focuses on the Calculation of density Gradient in this class of multiphase LB models. Theoretical analyses are first carried out to reveal the involvement and Calculation of density Gradient. On the basis of a low Mach number approximation, an improved scheme is then proposed to calculate the density Gradient for the recent LB model with self-tuning equation of state. Analytical and numerical Calculations show that the improved scheme is more accurate and can help to reduce the numerical error when the reduced temperature is relatively low.
Bradley E Treeby - One of the best experts on this subject based on the ideXlab platform.
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full wave nonlinear ultrasound simulation on distributed clusters with applications in high intensity focused ultrasound
IEEE International Conference on High Performance Computing Data and Analytics, 2016Co-Authors: Jiri Jaros, Alistair P Rendell, Bradley E TreebyAbstract:Model-based treatment planning and exposimetry for high-intensity focused ultrasound requires the numerical simulation of nonlinear ultrasound propagation through heterogeneous and absorbing media. This is a computationally demanding problem due to the large distances travelled by the ultrasound waves relative to the wavelength of the highest frequency harmonic. Here, the k-space pseudospectral method is used to solve a set of coupled partial differential equations equivalent to a generalised Westervelt equation. The model is implemented in C++ and parallelised using the message passing interface MPI for solving large-scale problems on distributed clusters. The domain is partitioned using a 1D slab decomposition, and global communication is performed using a sparse communication pattern. Operations in the spatial frequency domain are performed in transposed space to reduce the communication burden imposed by the 3D fast Fourier transform. The performance of the model is evaluated using grid sizes up to 4096×2048×2048 grid points, distributed over a cluster using up to 1024 compute cores. Given the global nature of the Gradient Calculation, the model shows good strong scaling behaviour, with a speed-up of 1.7x whenever the number of cores is doubled. This means large-scale simulations can be distributed across high numbers of cores on a cluster to minimise execution times with a relatively small overhead. The efficacy of the model is demonstrated by simulating the ultrasound beam pattern for a high-intensity focused ultrasound sonication of the kidney.
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full wave nonlinear ultrasound simulation on distributed clusters with applications in high intensity focused ultrasound
arXiv: Medical Physics, 2014Co-Authors: Jiri Jaros, Alistair P Rendell, Bradley E TreebyAbstract:Model-based treatment planning and exposimetry for high-intensity focused ultrasound (HIFU) requires the numerical simulation of nonlinear ultrasound propagation through heterogeneous and absorbing media. This is a computationally demanding problem due to the large distances travelled by the ultrasound waves relative to the wavelength of the highest frequency harmonic. Here, the k-space pseudospectral method is used to solve a set of coupled partial differential equations equivalent to a generalised Westervelt equation. The model is implemented in C++ and parallelised using the message passing interface (MPI) for solving large-scale problems on distributed clusters. The domain is partitioned using a 1D slab decomposition, and global communication is performed using a sparse communication pattern. Operations in the spatial frequency domain are performed in transposed space to reduce the communication burden imposed by the 3D fast Fourier transform. The performance of the model is evaluated using grid sizes up to 4096 x 2048 x 2048 grid points distributed over a cluster using up to 1024 compute cores. Given the global nature of the Gradient Calculation, the model shows good strong scaling behaviour, with a speed-up of 1.7x whenever the number of cores is doubled. This means large-scale simulations can be distributed across high numbers of cores on a cluster to minimise execution times with a relatively small computational overhead. The efficacy of the model is demonstrated by simulating the ultrasound beam pattern for a HIFU sonication of the kidney.
Danilo P Mandic - One of the best experts on this subject based on the ideXlab platform.
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the hc calculus quaternion derivatives and caylay hamilton form of quaternion adaptive filters and learning systems
International Joint Conference on Neural Network, 2014Co-Authors: Yili Xia, Cyrus Jahanchahi, Danilo P MandicAbstract:We introduce a novel and unifying framework for the Calculation of Gradients of both quaternion holomorphic functions and nonholomorphic real functions of quaternion variables. This is achieved by considering the isomorphism between the quaternion domain H and the bivariate complex domain C×C, and by exploiting complex calculus to simplify the quaternion Gradient Calculation. The validation of the proposed HC calculus is performed against the existing HR calculus, and its convenience is illustrated in the context of Gradient-based quaternion optimisation as well as in adaptive learning systems. Quaternion adaptive filtering algorithms and a dynamical perceptron update are next derived based on the bivariate complex representation of quaternions and the HC calculus. Simulations on both synthetic and real-world multidimensional signals support the analysis.
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on Gradient Calculation in quaternion adaptive filtering
International Conference on Acoustics Speech and Signal Processing, 2012Co-Authors: Cyrus Jahanchahi, Clive Cheong Took, Danilo P MandicAbstract:A novel way to calculate the Gradient of real functions of quaternion variables, typical cost functions in quaternion signal processing, is proposed. This is achieved by revisiting quaternion involutions and by simplifying the existing ℍℝ derivatives. This has allowed us to express the class of quaternion least mean square (QLMS) algorithms in a more compact form while keeping the same generic form of LMS. Simulations in the prediction setting support the approach.
