1
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Zhao C, Ou Q, Lee J, Dou W. Stochastic Resolution of Identity to CC2 for Large Systems: Excited State Properties. J Chem Theory Comput 2024; 20:5188-5195. [PMID: 38842259 DOI: 10.1021/acs.jctc.4c00629] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We apply a stochastic resolution of identity approximation (sRI) to the CC2 method for the excitation energy calculations. A set of stochastic orbitals are employed to decouple the crucial 4-index electron repulsion integrals and optimize the contraction steps in CC2 response theory. The CC2 response for excitations builds upon sRI-CC2 ground-state calculations, which scales as O(N3), where N is a measure for the system size. Overall, the current algorithm for excited states also allows a sharp scaling reduction from original O(N5) to O(N3). We test the sRI-CC2 for different molecular systems and basis sets, and we show that our sRI-CC2 method can accurately reproduce the results of the deterministic CC2 approach. Our sRI-CC2 exhibits an experimental scaling of O(N2.59) for a series of olefin chains, allowing us to calculate systems with nearly thousands of electrons.
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Affiliation(s)
- Chongxiao Zhao
- Department of Chemistry, Zhejiang University, Hangzhou 310027, China
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Qi Ou
- AI for Science Institute, Beijing 100080, China
| | - Joonho Lee
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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2
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Vu JP, Chen M. Noise reduction of stochastic density functional theory for metals. J Chem Phys 2024; 160:214125. [PMID: 38842491 DOI: 10.1063/5.0207244] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 05/16/2024] [Indexed: 06/07/2024] Open
Abstract
Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.
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Affiliation(s)
- Jake P Vu
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
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3
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Nguyen M, Duong T, Neuhauser D. Time-dependent density functional theory with the orthogonal projector augmented wave method. J Chem Phys 2024; 160:144101. [PMID: 38587220 DOI: 10.1063/5.0193343] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2023] [Accepted: 03/21/2024] [Indexed: 04/09/2024] Open
Abstract
The projector augmented wave (PAW) method of Blöchl linearly maps smooth pseudo wavefunctions to the highly oscillatory all-electron DFT orbitals. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic energy cutoffs and larger grid spacing at the cost of having to solve for non-orthogonal wavefunctions. We earlier developed orthogonal PAW (OPAW) to allow the use of PAW when orthogonal wavefunctions are required. In OPAW, the pseudo wavefunctions are transformed through the efficient application of powers of the PAW overlap operator with essentially no extra cost compared to NCPP methods. Previously, we applied OPAW to DFT. Here, we take the first step to make OPAW viable for post-DFT methods by implementing it in real-time time-dependent (TD) DFT. Using fourth-order Runge-Kutta for the time-propagation, we compare calculations of absorption spectra for various organic and biological molecules and show that very large grid spacings are sufficient, 0.6-0.7 bohr in OPAW-TDDFT rather than the 0.4-0.5 bohr used in traditional NCPP-TDDFT calculations. This reduces the memory and propagation costs by around a factor of 3. Our method would be directly applicable to any post-DFT methods that require time-dependent propagations such as the GW approximation and the Bethe-Salpeter equation.
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Affiliation(s)
- Minh Nguyen
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Tim Duong
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
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4
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Altman AR, Kundu S, da Jornada FH. Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations. PHYSICAL REVIEW LETTERS 2024; 132:086401. [PMID: 38457735 DOI: 10.1103/physrevlett.132.086401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2023] [Revised: 08/24/2023] [Accepted: 12/05/2023] [Indexed: 03/10/2024]
Abstract
We present an approach for GW calculations of quasiparticle energies with quasiquadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS_{2} bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.
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Affiliation(s)
- Aaron R Altman
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
| | - Sudipta Kundu
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
| | - Felipe H da Jornada
- Department of Materials Science and Engineering, Stanford University, Stanford, California 94305, USA
- Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
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5
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Bradbury NC, Allen T, Nguyen M, Neuhauser D. Deterministic/Fragmented-Stochastic Exchange for Large-Scale Hybrid DFT Calculations. J Chem Theory Comput 2023; 19:9239-9247. [PMID: 38051791 DOI: 10.1021/acs.jctc.3c00987] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
We develop an efficient approach to evaluate range-separated exact exchange for grid- or plane-wave-based representations within the generalized Kohn-Sham-density functional theory (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long-wavelength (low-k) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-k part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of the long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1320 electrons.
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Affiliation(s)
- Nadine C Bradbury
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Tucker Allen
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Minh Nguyen
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
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6
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Finkelstein J, Negre CFA, Fattebert JL. A fast, dense Chebyshev solver for electronic structure on GPUs. J Chem Phys 2023; 159:101101. [PMID: 37694745 DOI: 10.1063/5.0164255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2023] [Accepted: 08/14/2023] [Indexed: 09/12/2023] Open
Abstract
Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [Liang et al., J. Chem. Phys. 119, 4117-4125 (2003)] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.
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Affiliation(s)
- Joshua Finkelstein
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Jean-Luc Fattebert
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
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7
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Mejía L, Yin J, Reichman DR, Baer R, Yang C, Rabani E. Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures. J Chem Theory Comput 2023; 19:5563-5571. [PMID: 37539990 DOI: 10.1021/acs.jctc.3c00296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(Ne3), where Ne is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.
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Affiliation(s)
- Leopoldo Mejía
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jia Yin
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Chao Yang
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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8
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Sharma V, Collins LA, White AJ. Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter. Phys Rev E 2023; 108:L023201. [PMID: 37723794 DOI: 10.1103/physreve.108.l023201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 05/08/2023] [Indexed: 09/20/2023]
Abstract
Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.
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Affiliation(s)
- Vidushi Sharma
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Alexander J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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9
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Weng G, Mallarapu R, Vlček V. Embedding vertex corrections in GW self-energy: Theory, implementation, and outlook. J Chem Phys 2023; 158:144105. [PMID: 37061461 DOI: 10.1063/5.0139117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
The vertex function (Γ) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot GW correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest;" the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing cycle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot GW approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.
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Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - Rushil Mallarapu
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, USA
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10
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White AF, Li C, Zhang X, Chan GKL. Quantum harmonic free energies for biomolecules and nanomaterials. NATURE COMPUTATIONAL SCIENCE 2023; 3:328-333. [PMID: 38177936 DOI: 10.1038/s43588-023-00432-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2021] [Accepted: 03/13/2023] [Indexed: 01/06/2024]
Abstract
Obtaining the free energy of large molecules from quantum mechanical energy functions is a long-standing challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of large size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.
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Affiliation(s)
- Alec F White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, USA
- Quantum Simulation Technologies, Inc., Cambridge, MA, USA
| | - Chenghan Li
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, USA
| | - Xing Zhang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, USA
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, USA.
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11
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Chen M, Baer R, Rabani E. Structure optimization with stochastic density functional theory. J Chem Phys 2023; 158:024111. [PMID: 36641385 DOI: 10.1063/5.0126169] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
Linear-scaling techniques for Kohn-Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden-Fletcher-Goldfarb-Shanno algorithm. We further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.
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Affiliation(s)
- Ming Chen
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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12
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Sharma S, White AF, Beylkin G. Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method. J Chem Theory Comput 2022; 18:7306-7320. [PMID: 36417710 DOI: 10.1021/acs.jctc.2c00720] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
In this article, we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when a Gaussian basis set with pseudopotentials is used. The usual algorithm for evaluating exchange matrix scales cubically with the system size because one has to perform O(N2) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matrix without the need to do FFT, albeit at the cost of additional memory requirement. Although the basic idea of using auxiliary functions is not new, our algorithm is cheaper due to a combination of three ingredients: (a) we use a robust pseudospectral method that allows us to use a relatively small number of auxiliary basis to obtain high accuracy; (b) we use occ-RI exchange, which eliminates the need to construct the full exchange matrix; and (c) we use the (interpolative separable density fitting) ISDF algorithm to construct these auxiliary basis sets that are used in the robust pseudospectral method. The resulting algorithm is accurate, and we note that the error in the final energy decreases exponentially rapidly with the number of auxiliary functions.
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Affiliation(s)
- Sandeep Sharma
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
| | - Alec F White
- Quantum Simulation Technologies, Inc., Boston, Massachusetts02135, United States
| | - Gregory Beylkin
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado80309, United States
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13
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Shafir U, Kosloff R. Wave Function Realization of a Thermal Collision Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1808. [PMID: 36554213 PMCID: PMC9777790 DOI: 10.3390/e24121808] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/05/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on the quantum collision model. Modeling systems dynamics with wave functions and modeling the interaction with the environment with a collision sequence reduces the scale of the complexity significantly. The algorithm developed can be implemented on quantum computers. We introduce stochastic methods that exploit statistical characteristics of the model such as Markovianity, Brownian motion, and binary distribution. The central limit theorem is employed to study the convergence of distributions of stochastic dynamics of pure quantum states represented by wave vectors. By averaging a sample of functions in the distribution we prove and demonstrate the convergence of the dynamics to the mixed quantum state described by a density operator.
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14
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Nguyen M, Neuhauser D. Gapped-filtering for efficient Chebyshev expansion of the density projection operator. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.140036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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15
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Dou W, Lee J, Zhu J, Mejía L, Reichman DR, Baer R, Rabani E. Time-Dependent Second-Order Green's Function Theory for Neutral Excitations. J Chem Theory Comput 2022; 18:5221-5232. [PMID: 36040050 DOI: 10.1021/acs.jctc.2c00057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We develop a time-dependent second-order Green's function theory (GF2) for calculating neutral excited states in molecules. The equation of motion for the lesser Green's function (GF) is derived within the adiabatic approximation to the Kadanoff-Baym (KB) equation, using the second-order Born approximation for the self-energy. In the linear response regime, we recast the time-dependent KB equation into a Bethe-Salpeter-like equation (GF2-BSE), with a kernel approximated by the second-order Coulomb self-energy. We then apply our GF2-BSE to a set of molecules and atoms and find that GF2-BSE is superior to configuration interaction with singles (CIS) and/or time-dependent Hartree-Fock (TDHF), particularly for charge-transfer excitations, and is comparable to CIS with perturbative doubles (CIS(D)) in most cases.
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Affiliation(s)
- Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Department of Physics, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Jian Zhu
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China.,Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Leopoldo Mejía
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.,The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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16
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Weng G, Romanova M, Apelian A, Song H, Vlček V. Reduced Scaling of Optimal Regional Orbital Localization via Sequential Exhaustion of the Single-Particle Space. J Chem Theory Comput 2022; 18:4960-4972. [PMID: 35817013 PMCID: PMC9367006 DOI: 10.1021/acs.jctc.2c00315] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Wannier functions have become a powerful tool in the
electronic
structure calculations of extended systems. The generalized Pipek-Mezey
Wannier functions exhibit appealing characteristics (e.g., reaching
an optimal localization and the separation of the σ–π
orbitals) compared with other schemes. However, when applied to giant
nanoscale systems, the orbital localization suffers from a large computational
cost overhead if one is interested in localized states in a small
fragment of the system. Herein, we present a swift, efficient, and
robust approach for obtaining regionally localized orbitals of a subsystem
within the generalized Pipek-Mezey scheme. The proposed algorithm
introduces a reduced work space and sequentially exhausts the entire
orbital space until the convergence of the localization functional.
It tackles systems with ∼10000 electrons within 0.5 h with
no loss in localization quality compared to the traditional approach.
Regionally localized orbitals with a higher extent of localization
are obtained via judiciously extending the subsystem’s size.
Exemplifying on large bulk and a 4 nm wide slab of diamond with an
NV– center, we demonstrate the methodology and discuss
how the choice of the localization region affects the excitation energy
of the defect. Furthermore, we show how the sequential algorithm is
easily extended to stochastic methodologies that do not provide individual
single-particle eigenstates. It is thus a promising tool to obtain
regionally localized states for solving the electronic structure problems
of a subsystem embedded in giant condensed systems.
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Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Mariya Romanova
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Arsineh Apelian
- Department of Materials, University of California, Santa Barbara, California 93106-9510, United States
| | - Hanbin Song
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
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17
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Fabian MD, Shpiro B, Baer R. Linear Weak Scalability of Density Functional Theory Calculations without Imposing Electron Localization. J Chem Theory Comput 2022; 18:2162-2170. [PMID: 35343234 PMCID: PMC9009081 DOI: 10.1021/acs.jctc.1c00829] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Marcel D. Fabian
- Fritz Haber Research Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Ben Shpiro
- Fritz Haber Research Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Roi Baer
- Fritz Haber Research Center for Molecular Dynamics and the Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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18
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White AJ, Collins LA, Nichols K, Hu SX. Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:174001. [PMID: 35081511 DOI: 10.1088/1361-648x/ac4f1a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.
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Affiliation(s)
- Alexander J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 NM, United States of America
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 NM, United States of America
| | - Katarina Nichols
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 NM, United States of America
- Laboratory of Laser Energetics, University of Rochester, Rochester 14623 NY, United States of America
| | - S X Hu
- Laboratory of Laser Energetics, University of Rochester, Rochester 14623 NY, United States of America
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19
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Xu Q, Jing X, Zhang B, Pask J, Suryanarayana P. Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature. J Chem Phys 2022; 156:094105. [DOI: 10.1063/5.0082523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Qimen Xu
- Georgia Institute of Technology, United States of America
| | - Xin Jing
- School of Computational Science and Engineering, Georgia Institute of Technology, United States of America
| | - Boqin Zhang
- Georgia Institute of Technology, United States of America
| | - John Pask
- Physics, LLNL, United States of America
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20
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Shpiro B, Fabian MD, Rabani E, Baer R. Forces from Stochastic Density Functional Theory under Nonorthogonal Atom-Centered Basis Sets. J Chem Theory Comput 2022; 18:1458-1466. [PMID: 35099187 PMCID: PMC8908760 DOI: 10.1021/acs.jctc.1c00794] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We
develop a formalism for calculating forces on the nuclei within
the linear-scaling stochastic density functional theory (sDFT) in
a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.:
Comput. Mol. Sci.2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide
solvated in water. We use an embedded-fragment approach to reduce
the statistical errors (fluctuation and systematic bias), where the
entire peptide is the main fragment and the remaining 425 water molecules
are grouped into small fragments. We analyze the magnitude of the
statistical errors in the forces and find that the systematic bias
is of the order of 0.065 eV/Å (∼1.2 × 10–3Eh/a0) when 120 stochastic orbitals are used, independently
of system size. This magnitude of bias is sufficiently small to ensure
that the bond lengths estimated by stochastic DFT (within a Langevin
molecular dynamics simulation) will deviate by less than 1% from those
predicted by a deterministic calculation.
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Affiliation(s)
- Ben Shpiro
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Marcel David Fabian
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States.,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States.,The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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21
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Baer R, Neuhauser D, Rabani E. Stochastic Vector Techniques in Ground-State Electronic Structure. Annu Rev Phys Chem 2022; 73:255-272. [PMID: 35081326 DOI: 10.1146/annurev-physchem-090519-045916] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss highly effective techniques to reduce statistical errors. Finally, we review the use of stochastic vector techniques for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel;
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California, USA;
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California, USA; .,Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA.,The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel
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22
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Nguyen M, Li W, Li Y, Rabani E, Baer R, Neuhauser D. Tempering stochastic density functional theory. J Chem Phys 2021; 155:204105. [PMID: 34852484 DOI: 10.1063/5.0063266] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the warm component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction in the statistical fluctuations and systematic deviation compared to sDFT for the same computational effort. We demonstrate the method's performance on large hydrogen-passivated silicon nanocrystals, finding a reduction in the systematic deviation in the energy by more than an order of magnitude, while the systematic deviation in the forces is also quenched. Similarly, the statistical fluctuations are reduced by factors of ≈4-5 for the total energy and ≈1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.
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Affiliation(s)
- Minh Nguyen
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Wenfei Li
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Yangtao Li
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA and The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, and California Nanoscience Institute, Los Angeles, California 90095, USA
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23
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Marzari N, Ferretti A, Wolverton C. Electronic-structure methods for materials design. NATURE MATERIALS 2021; 20:736-749. [PMID: 34045704 DOI: 10.1038/s41563-021-01013-3] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 04/19/2021] [Indexed: 05/24/2023]
Abstract
The accuracy and efficiency of electronic-structure methods to understand, predict and design the properties of materials has driven a new paradigm in research. Simulations can greatly accelerate the identification, characterization and optimization of materials, with this acceleration driven by continuous progress in theory, algorithms and hardware, and by adaptation of concepts and tools from computer science. Nevertheless, the capability to identify and characterize materials relies on the predictive accuracy of the underlying physical descriptions, and on the ability to capture the complexity of realistic systems. We provide here an overview of electronic-structure methods, of their application to the prediction of materials properties, and of the different strategies employed towards the broader goals of materials design and discovery.
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Affiliation(s)
- Nicola Marzari
- Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
| | | | - Chris Wolverton
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA
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24
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Chen M, Baer R, Neuhauser D, Rabani E. Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction. J Chem Phys 2021; 154:204108. [PMID: 34241170 DOI: 10.1063/5.0044163] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1/Nχ according to the central limit theorem, where Nχ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon.
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Affiliation(s)
- Ming Chen
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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25
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Fay TP, Lindoy LP, Manolopoulos DE. Spin relaxation in radical pairs from the stochastic Schrödinger equation. J Chem Phys 2021; 154:084121. [PMID: 33639770 DOI: 10.1063/5.0040519] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
We show that the stochastic Schrödinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. We also analyze the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.
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Affiliation(s)
- Thomas P Fay
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Lachlan P Lindoy
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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26
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Bradbury NC, Chuang C, Deshmukh AP, Rabani E, Baer R, Caram JR, Neuhauser D. Stochastically Realized Observables for Excitonic Molecular Aggregates. J Phys Chem A 2020; 124:10111-10120. [PMID: 33251807 DOI: 10.1021/acs.jpca.0c07953] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.
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Affiliation(s)
- Nadine C Bradbury
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Chern Chuang
- Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
| | - Arundhati P Deshmukh
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Eran Rabani
- Department of Chemistry, University of California and Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
| | - Justin R Caram
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
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27
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White AJ, Collins LA. Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma. PHYSICAL REVIEW LETTERS 2020; 125:055002. [PMID: 32794867 DOI: 10.1103/physrevlett.125.055002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Revised: 06/09/2020] [Accepted: 07/15/2020] [Indexed: 06/11/2023]
Abstract
Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.
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Affiliation(s)
- A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - L A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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28
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Lee J, Reichman DR. Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead. J Chem Phys 2020; 153:044131. [DOI: 10.1063/5.0015077] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joonho Lee
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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29
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Philbin JP, Rabani E. Auger Recombination Lifetime Scaling for Type I and Quasi-Type II Core/Shell Quantum Dots. J Phys Chem Lett 2020; 11:5132-5138. [PMID: 32513003 DOI: 10.1021/acs.jpclett.0c01460] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Having already achieved near-unity quantum yields, with promising properties for light-emitting diode, lasing, and charge separation applications, colloidal core/shell quantum dots have great technological potential. The shell thickness and band alignment of the shell and core materials are known to influence the efficiency of these devices. In many such applications, improving the efficiency requires a deep understanding of multiexcitonic states. Herein, we elucidate the shell thickness and band alignment dependencies of the biexciton Auger recombination lifetime for quasi-type II CdSe/CdS and type I CdSe/ZnS core/shell quantum dots. We find that the biexciton Auger recombination lifetime increases with the total nanocrystal volume for quasi-type II CdSe/CdS core/shell quantum dots and is independent of the shell thickness for type I CdSe/ZnS core/shell quantum dots. To perform these calculations and compute Auger recombination lifetimes, we developed a low-scaling approach based on the stochastic resolution of identity. The numerical approach provided a framework for studying the scaling of the biexciton Auger recombination lifetimes in terms of the shell thickness dependencies of the exciton radii, Coulomb couplings, and density of final states in quasi-type II CdSe/CdS and type I CdSe/ZnS core/shell quantum dots.
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Affiliation(s)
- John P Philbin
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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30
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Brooks J, Weng G, Taylor S, Vlcek V. Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:234001. [PMID: 31958775 DOI: 10.1088/1361-648x/ab6d8c] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We implement stochastic many-body perturbation theory for systems with 2D periodic boundary conditions. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. Excitation energies are studied using stochastic [Formula: see text] and partially self-consistent [Formula: see text] approaches. The approach is inexpensive; it is used to study twisted systems with unit cells containing >2700 atoms (>13 500 valence electrons), which corresponds to a minimum twisting angle of [Formula: see text] [Formula: see text]. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moiré impurity states, as documented by band-structure unfolding. Structural changes in twisted structures lift band degeneracies. Energies of the impurity states vary with the twisting angle due to an interplay between non-local exchange and polarization effects. The mechanisms of quasiparticle energy (de)stabilization due to twisting are likely applicable to a wide range of low-dimensional Moiré superstructures.
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Affiliation(s)
- Jacob Brooks
- Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-9510, United States of America
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31
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Arnon E, Rabani E, Neuhauser D, Baer R. Efficient Langevin dynamics for “noisy” forces. J Chem Phys 2020; 152:161103. [DOI: 10.1063/5.0004954] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eitam Arnon
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA and The Raymond and Beverly Sackler Center for Computational Molecular and Materials Sciences, Tel Aviv University, Tel Aviv 69978, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Roi Baer
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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32
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Zhang X, Lu G, Baer R, Rabani E, Neuhauser D. Linear-Response Time-Dependent Density Functional Theory with Stochastic Range-Separated Hybrids. J Chem Theory Comput 2020; 16:1064-1072. [DOI: 10.1021/acs.jctc.9b01121] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xu Zhang
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Gang Lu
- Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330, United States
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
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33
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Li W, Chen M, Rabani E, Baer R, Neuhauser D. Stochastic embedding DFT: Theory and application to p-nitroaniline in water. J Chem Phys 2019; 151:174115. [PMID: 31703523 DOI: 10.1063/1.5110226] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.
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Affiliation(s)
- Wenfei Li
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Ming Chen
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
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34
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Dou W, Takeshita TY, Chen M, Baer R, Neuhauser D, Rabani E. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. J Chem Theory Comput 2019; 15:6703-6711. [DOI: 10.1021/acs.jctc.9b00918] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wenjie Dou
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
| | - Tyler Y. Takeshita
- Mercedes-Benz Research and Development North America, Sunnyvale, California 94085, United States
| | - Ming Chen
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Roi Baer
- Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California Los Angeles, Los Angeles, California 90095, United States
| | - Eran Rabani
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials Sciences Devision, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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35
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Vlček V. Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies. J Chem Theory Comput 2019; 15:6254-6266. [DOI: 10.1021/acs.jctc.9b00317] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, Santa Barbara, California 93106, United States
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36
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Chen M, Baer R, Neuhauser D, Rabani E. Energy window stochastic density functional theory. J Chem Phys 2019; 151:114116. [PMID: 31542024 DOI: 10.1063/1.5114984] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for Nχ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as Nχ -1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.
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Affiliation(s)
- Ming Chen
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center of Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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37
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Zandkarimi B, Alexandrova AN. Surface‐supported cluster catalysis: Ensembles of metastable states run the show. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1420] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Borna Zandkarimi
- Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles California
| | - Anastassia N. Alexandrova
- Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles California
- California NanoSystems Institute University of California, Los Angeles Los Angeles California
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38
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Abstract
A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
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Affiliation(s)
- Ronnie Kosloff
- The Institute of Chemistry and The Fritz Haber Centre for Theoretical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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39
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Vlček V, Baer R, Neuhauser D. Stochastic time-dependent DFT with optimally tuned range-separated hybrids: Application to excitonic effects in large phosphorene sheets. J Chem Phys 2019; 150:184118. [DOI: 10.1063/1.5093707] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
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40
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Stochastic density functional theory. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1412] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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41
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Chen M, Baer R, Neuhauser D, Rabani E. Overlapped embedded fragment stochastic density functional theory for covalently-bonded materials. J Chem Phys 2019; 150:034106. [DOI: 10.1063/1.5064472] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ming Chen
- Department of Chemistry, University of California, and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, USA
| | - Eran Rabani
- Department of Chemistry, University of California, and Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
- The Raymond and Beverly Sackler Center of Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
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42
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Tsuchimochi T, Ten-No SL. Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique. J Comput Chem 2018; 40:265-278. [PMID: 30520115 DOI: 10.1002/jcc.25587] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Revised: 07/31/2018] [Accepted: 08/01/2018] [Indexed: 11/06/2022]
Abstract
Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F2 and transition metal complexes such as NiO, Mn2 , and [Cu2 O2 ]2+ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Takashi Tsuchimochi
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo, 657-0025, Japan
| | - Seiichiro L Ten-No
- Graduate School of Science, Technology, and Innovation, Kobe University, Kobe, Hyogo, 657-0025, Japan
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43
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Spencer JS, Neufeld VA, Vigor WA, Franklin RST, Thom AJW. Large scale parallelization in stochastic coupled cluster. J Chem Phys 2018; 149:204103. [DOI: 10.1063/1.5047420] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- J. S. Spencer
- Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - V. A. Neufeld
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - W. A. Vigor
- Department of Chemistry, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - R. S. T. Franklin
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - A. J. W. Thom
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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44
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Hernandez S, Xia Y, Vlček V, Boutelle R, Baer R, Rabani E, Neuhauser D. First-principles spectra of Au nanoparticles: from quantum to classical absorption. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1471235] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Samuel Hernandez
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA
| | - Yantao Xia
- Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, USA
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA
| | - Robert Boutelle
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel
| | - Eran Rabani
- Department of Chemistry, University of California, Berkeley, CA, USA
- The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, Israel
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA
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45
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Affiliation(s)
- Zhu Ruan
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
| | - Roi Baer
- Fritz Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem, Israel
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46
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Rossi M, Kapil V, Ceriotti M. Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation. J Chem Phys 2018; 148:102301. [DOI: 10.1063/1.4990536] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mariana Rossi
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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47
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Wang Z, Chern GW, Batista CD, Barros K. Gradient-based stochastic estimation of the density matrix. J Chem Phys 2018. [DOI: 10.1063/1.5017741] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zhentao Wang
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
| | - Gia-Wei Chern
- Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
| | - Cristian D. Batista
- Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
- Quantum Condensed Matter Division and Shull-Wollan Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Kipton Barros
- Theoretical Division and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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48
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Neuhauser D, Baer R, Zgid D. Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems. J Chem Theory Comput 2017; 13:5396-5403. [DOI: 10.1021/acs.jctc.7b00792] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel Neuhauser
- Department
of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
| | - Roi Baer
- Fritz
Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Dominika Zgid
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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49
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Vlček V, Rabani E, Neuhauser D, Baer R. Stochastic GW Calculations for Molecules. J Chem Theory Comput 2017; 13:4997-5003. [DOI: 10.1021/acs.jctc.7b00770] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Vojtěch Vlček
- Department
of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
- Fritz
Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department
of Chemistry, University of California and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The
Raymond and Beverly Sackler Center for Computational Molecular and
Materials Science, Tel Aviv University, Tel Aviv, Israel 69978
| | - Daniel Neuhauser
- Department
of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Roi Baer
- Fritz
Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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50
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Takeshita TY, de Jong WA, Neuhauser D, Baer R, Rabani E. Stochastic Formulation of the Resolution of Identity: Application to Second Order Møller–Plesset Perturbation Theory. J Chem Theory Comput 2017; 13:4605-4610. [DOI: 10.1021/acs.jctc.7b00343] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Tyler Y. Takeshita
- Department
of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Wibe A. de Jong
- Computational
Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Daniel Neuhauser
- Department
of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Roi Baer
- Fritz
Harber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Eran Rabani
- Department
of Chemistry, University of California Berkeley, Berkeley, California 94720, United States
- Materials
Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- The Sackler
Center for Computational Molecular Science, Tel Aviv University, Tel Aviv 69978, Israel
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