The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Todd J Martinez - One of the best experts on this subject based on the ideXlab platform.
-
Atomic Orbital based sos mp2 with tensor hypercontraction i gpu based tensor construction and exploiting sparsity
Journal of Chemical Physics, 2016Co-Authors: Chenchen Song, Todd J MartinezAbstract:We present a tensor hypercontracted (THC) scaled opposite spin second order Moller-Plesset perturbation theory (SOS-MP2) method. By using THC, we reduce the formal scaling of SOS-MP2 with respect to molecular size from quartic to cubic. We achieve further efficiency by exploiting sparsity in the Atomic Orbitals and using graphical processing units (GPUs) to accelerate integral construction and matrix multiplication. The practical scaling of GPU-accelerated Atomic Orbital-based THC-SOS-MP2 calculations is found to be N2.6 for reference data sets of water clusters and alanine polypeptides containing up to 1600 basis functions. The errors in correlation energy with respect to density-fitting-SOS-MP2 are less than 0.5 kcal/mol for all systems tested (up to 162 atoms).
-
an Atomic Orbital based formulation of analytical gradients and nonadiabatic coupling vector elements for the state averaged complete active space self consistent field method on graphical processing units
Journal of Chemical Physics, 2015Co-Authors: James W Snyder, Edward G Hohenstein, Nathan Luehr, Todd J MartinezAbstract:We recently presented an algorithm for state-averaged complete active space self-consistent field (SA-CASSCF) Orbital optimization that capitalizes on sparsity in the Atomic Orbital basis set to reduce the scaling of computational effort with respect to molecular size. Here, we extend those algorithms to calculate the analytic gradient and nonadiabatic coupling vectors for SA-CASSCF. Combining the low computational scaling with acceleration from graphical processing units allows us to perform SA-CASSCF geometry optimizations for molecules with more than 1000 atoms. The new approach will make minimal energy conical intersection searches and nonadiabatic dynamics routine for molecular systems with O(102) atoms.
-
an Atomic Orbital based formulation of the complete active space self consistent field method on graphical processing units
Journal of Chemical Physics, 2015Co-Authors: Edward G Hohenstein, Nathan Luehr, Todd J Martinez, Ivan S UfimtsevAbstract:Despite its importance, state-of-the-art algorithms for performing complete active space self-consistent field (CASSCF) computations have lagged far behind those for single reference methods. We develop an algorithm for the CASSCF Orbital optimization that uses sparsity in the Atomic Orbital (AO) basis set to increase the applicability of CASSCF. Our implementation of this algorithm uses graphical processing units (GPUs) and has allowed us to perform CASSCF computations on molecular systems containing more than one thousand atoms. Additionally, we have implemented analytic gradients of the CASSCF energy; the gradients also benefit from GPU acceleration as well as sparsity in the AO basis.
Stefan Grimme - One of the best experts on this subject based on the ideXlab platform.
-
small Atomic Orbital basis set first principles quantum chemical methods for large molecular and periodic systems a critical analysis of error sources
ChemistryOpen, 2016Co-Authors: Rebecca Sure, Jan Gerit Brandenburg, Stefan GrimmeAbstract:In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small Atomic Orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.
-
consistent structures and interactions by density functional theory with small Atomic Orbital basis sets
Journal of Chemical Physics, 2015Co-Authors: Stefan Grimme, Jan Gerit Brandenburg, Christoph Bannwarth, Andreas HansenAbstract:A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The Orbitals are expanded in Ahlrichs-type valence-double zeta Atomic Orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, ...
-
consistent structures and interactions by density functional theory with small Atomic Orbital basis sets
Journal of Chemical Physics, 2015Co-Authors: Stefan Grimme, Jan Gerit Brandenburg, Christoph Bannwarth, Andreas HansenAbstract:A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The Orbitals are expanded in Ahlrichs-type valence-double zeta Atomic Orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust “high-speed” computational tool in theoretical chemistry and physics.
Christian Ochsenfeld - One of the best experts on this subject based on the ideXlab platform.
-
low scaling analytical gradients for the direct random phase approximation using an Atomic Orbital formalism
Journal of Chemical Physics, 2018Co-Authors: Matthias Beuerle, Christian OchsenfeldAbstract:We present an Atomic Orbital formalism to obtain analytical gradients within the random phase approximation for calculating first-order properties. Our approach allows exploiting sparsity in the electronic structure in order to reduce the computational complexity. Furthermore, we introduce Cholesky decomposed densities to remove the redundancies present in Atomic Orbital basis sets, making our method a competitive alternative to canonical theories also for small molecules. The approach is presented in a general framework that allows extending the methodology to other correlation methods. Beyond showing the validity and accuracy of our approach and the approximations used in this work, we demonstrate the efficiency of our method by computing nuclear gradients for systems with up to 600 atoms and 5000 basis functions.
-
communication an effective linear scaling Atomic Orbital reformulation of the random phase approximation using a contracted double laplace transformation
Journal of Chemical Physics, 2016Co-Authors: Henry F Schurkus, Christian OchsenfeldAbstract:An Atomic-Orbital (AO) reformulation of the random-phase approximation (RPA) correlation energy is presented allowing to reduce the steep computational scaling to linear, so that large systems can be studied on simple desktop computers with fully numerically controlled accuracy. Our AO-RPA formulation introduces a contracted double-Laplace transform and employs the overlap-metric resolution-of-the-identity. First timings of our pilot code illustrate the reduced scaling with systems comprising up to 1262 atoms and 10 090 basis functions.
-
a linear and sublinear scaling method for calculating nmr shieldings in Atomic Orbital based second order moller plesset perturbation theory
Journal of Chemical Physics, 2013Co-Authors: Marina Maurer, Christian OchsenfeldAbstract:An Atomic-Orbital (AO) based formulation for calculating nuclear magnetic resonance chemical shieldings at the second-order Moller-Plesset perturbation theory level is introduced, which provides a basis for reducing the scaling of the computational effort with the molecular size from the fifth power to linear and for a specific nucleus to sublinear. The latter sublinear scaling in the rate-determining steps becomes possible by avoiding global perturbations with respect to the magnetic field and by solving for quantities that involve the local nuclear magnetic spin perturbation instead. For avoiding the calculation of the second-order perturbed density matrix, we extend our AO-based reformulation of the Z-vector method within a density matrix-based scheme. Our pilot implementation illustrates the fast convergence with respect to the required number of Laplace points and the asymptotic scaling behavior in the rate-determining steps.
-
linear scaling Atomic Orbital based second order moller plesset perturbation theory by rigorous integral screening criteria
Journal of Chemical Physics, 2009Co-Authors: Bernd Doser, Daniel S Lambrecht, Jorg Kussmann, Christian OchsenfeldAbstract:A Laplace-transformed second-order Moller–Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the Atomic Orbital (AO)-MP2 energy are preselected using the so-called multipole-based integral estimates (MBIE) introduced earlier by us [J. Chem. Phys. 123, 184102 (2005)]. Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AO-MP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the c...
-
an Atomic Orbital based reformulation of energy gradients in second order moller plesset perturbation theory
Journal of Chemical Physics, 2008Co-Authors: Sabine Schweizer, Bernd Doser, Christian OchsenfeldAbstract:A fully Atomic Orbital (AO)-based reformulation of second-order Moller–Plesset perturbation theory (MP2) energy gradients is introduced, which provides the basis for reducing the computational scaling with the molecular size from the fifth power to linear. Our formulation avoids any transformation between the AO and the molecular Orbital (MO) basis and employs pseudodensity matrices similar to the AO-MP2 energy expressions within the Laplace scheme for energies. The explicit computation of perturbed one-particle density matrices emerging in the new AO-based gradient expression is avoided by reformulating the Z-vector method of Handy and Schaefer [J. Chem. Phys. 81, 5031 (1984)] within a density matrix-based scheme.
Xinguo Ren - One of the best experts on this subject based on the ideXlab platform.
-
accurate stress calculations based on numerical Atomic Orbital bases implementation and benchmarks
Computer Physics Communications, 2021Co-Authors: Daye Zheng, Xinguo RenAbstract:Abstract We present the detailed formalism for stress calculations within the framework of numerical Atomic Orbital (NAO) bases, as implemented in the first-principles electronic code package ABACUS. The validity and numerical precision of our implementation are benchmarked against reference results obtained using the finite difference method as well as those calculated using plane wave (PW) bases. The equation of state for α -quartz calculated using our NAO-based implementation is in excellent agreement with the experimental data. We further show that the stresses calculated in terms of NAO bases converge much faster with respect to the energy cutoff than those calculated using PW bases. This enables accurate stress calculations at relatively low cost. An analysis is provided to elucidate the origin of this behavior.
-
strategy for constructing compact numerical Atomic Orbital basis sets by incorporating the gradients of reference wavefunctions
Physical Review B, 2021Co-Authors: Peize Lin, Xinguo RenAbstract:We develop an algorithm to construct high-quality numerical Atomic Orbital (NAO) basis sets suitable for large-scale, efficient density-functional calculations. The key idea behind this algorithm is that, in addition to fitting the reference wavefunctions themselves generated by plane-wave based calculations of chosen target systems, the first derivatives of the reference wavefunctions are also taken into account as the fitting target. By doing so, the quality of the generated NAO basis sets is significantly improved in the sense that the same level of numerical precision can be achieved with smaller basis set sizes or with reduced cutoff radii of the NAOs.
-
all electron periodic g 0 w 0 implementation with numerical Atomic Orbital basis functions algorithm and benchmarks
Physical Review Materials, 2021Co-Authors: Xinguo Ren, Volker Blum, Yi Yao, Florian Merz, Hong Jiang, Markus Rampp, Hermann Lederer, Matthias SchefflerAbstract:We present an all-electron, periodic ${G}_{\text{0}}{W}_{\text{0}}$ implementation within the numerical Atomic Orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent ${G}_{\text{0}}{W}_{\text{0}}$ implementation based on linearized augmented plane waves (LAPWs) plus high-energy localized Orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims tier 2) NAO basis set, our ${G}_{\text{0}}{W}_{\text{0}}$ calculations produce band gaps that typically lie in between the standard LAPW and the $\mathrm{LAPW}+\mathrm{HLO}$ results. Complementing tier 2 with highly localized Slater-type Orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the $\mathrm{LAPW}+\mathrm{HLO}$ results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.
-
all electron periodic g_0w_0 implementation with numerical Atomic Orbital basis functions algorithm and benchmarks
arXiv: Materials Science, 2020Co-Authors: Xinguo Ren, Volker Blum, Yi Yao, Florian Merz, Hong Jiang, Markus Rampp, Hermann Lederer, Matthias SchefflerAbstract:We present an all-electron, periodic {\GnWn} implementation within the numerical Atomic Orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent $G_0W_0$ implementation based on linearized augmented plane waves (LAPW) plus high-energy localized Orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims \textit{tier} 2) NAO basis set, our $G_0W_0$ calculations produce band gaps that typically lie in between the standard LAPW and the LAPW+HLO results. Complementing \textit{tier} 2 with highly localized Slater-type Orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the LAPW+HLO results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.
-
all electron periodic g0w0 implementation with numerical Atomic Orbital basis functions algorithm and benchmarks
arXiv: Materials Science, 2020Co-Authors: Xinguo Ren, Volker Blum, Yi Yao, Florian Merz, Hong Jiang, Markus Rampp, Hermann Lederer, Matthias SchefflerAbstract:We present an all-electron, periodic {\GnWn} implementation within the numerical Atomic Orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent $G_0W_0$ implementation based on linearized augmented plane waves (LAPW) plus high-energy localized Orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims \textit{tier} 2) NAO basis set, our $G_0W_0$ calculations produce band gaps that typically lie in between the standard LAPW and the LAPW+HLO results. Complementing \textit{tier} 2 with highly localized Slater-type Orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the LAPW+HLO results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.
Andreas Hansen - One of the best experts on this subject based on the ideXlab platform.
-
consistent structures and interactions by density functional theory with small Atomic Orbital basis sets
Journal of Chemical Physics, 2015Co-Authors: Stefan Grimme, Jan Gerit Brandenburg, Christoph Bannwarth, Andreas HansenAbstract:A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The Orbitals are expanded in Ahlrichs-type valence-double zeta Atomic Orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, ...
-
consistent structures and interactions by density functional theory with small Atomic Orbital basis sets
Journal of Chemical Physics, 2015Co-Authors: Stefan Grimme, Jan Gerit Brandenburg, Christoph Bannwarth, Andreas HansenAbstract:A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The Orbitals are expanded in Ahlrichs-type valence-double zeta Atomic Orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust “high-speed” computational tool in theoretical chemistry and physics.