Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

Leopoldo Mejía; Jia Yin; David R. Reichman; Roi Baer; Chao Yang; Eran Rabani

doi:10.1021/acs.jctc.3c00296

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

Leopoldo Mejía^*, Jia Yin^*, David R. Reichman^*, Roi Baer^*, Chao Yang^*, Eran Rabani^*

^*Corresponding author for this work

Institute of Chemistry

Research output: Contribution to journal › Article › peer-review

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(N_e³), where N_e 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.

Original language	American English
Journal	Journal of Chemical Theory and Computation
DOIs	https://doi.org/10.1021/acs.jctc.3c00296
State	Accepted/In press - 2023

Bibliographical note

Funding Information:
C.Y., D.R.R., and E.R. are grateful for support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) program, under award no. DE-SC0022088. Some of the methods used in this work were provided by the “Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM)”, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division, via contract no. DE-AC02-05CH11231 as part of the Computational Materials Sciences program. Resources of the National Energy Research Scientific Computing Center (NERSC) and a U.S. Department of Energy Office of Science User Facility operated under contract no. DE-AC02-05CH11231 are also acknowledged. R.B. and E.R. acknowledge support from the US-Israel Binational Science Foundation BSF-201836.

Publisher Copyright:
© 2023 American Chemical Society.

Access to Document

10.1021/acs.jctc.3c00296

Cite this

@article{710f4c1be0fc432ab29cb8fe2c37d26e,

title = "Stochastic Real-Time Second-Order Green{\textquoteright}s Function Theory for Neutral Excitations in Molecules and Nanostructures",

abstract = "We present a real-time second-order Green{\textquoteright}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.",

author = "Leopoldo Mej{\'i}a and Jia Yin and Reichman, {David R.} and Roi Baer and Chao Yang and Eran Rabani",

note = "Funding Information: C.Y., D.R.R., and E.R. are grateful for support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) program, under award no. DE-SC0022088. Some of the methods used in this work were provided by the “Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM)”, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division, via contract no. DE-AC02-05CH11231 as part of the Computational Materials Sciences program. Resources of the National Energy Research Scientific Computing Center (NERSC) and a U.S. Department of Energy Office of Science User Facility operated under contract no. DE-AC02-05CH11231 are also acknowledged. R.B. and E.R. acknowledge support from the US-Israel Binational Science Foundation BSF-201836. Publisher Copyright: {\textcopyright} 2023 American Chemical Society.",

year = "2023",

doi = "10.1021/acs.jctc.3c00296",

language = "American English",

journal = "Journal of Chemical Theory and Computation",

issn = "1549-9618",

publisher = "American Chemical Society",

}

TY - JOUR

T1 - Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

AU - Mejía, Leopoldo

AU - Yin, Jia

AU - Reichman, David R.

AU - Baer, Roi

AU - Yang, Chao

AU - Rabani, Eran

N1 - Funding Information: C.Y., D.R.R., and E.R. are grateful for support from the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of Basic Energy Sciences, Scientific Discovery through Advanced Computing (SciDAC) program, under award no. DE-SC0022088. Some of the methods used in this work were provided by the “Center for Computational Study of Excited State Phenomena in Energy Materials (C2SEPEM)”, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division, via contract no. DE-AC02-05CH11231 as part of the Computational Materials Sciences program. Resources of the National Energy Research Scientific Computing Center (NERSC) and a U.S. Department of Energy Office of Science User Facility operated under contract no. DE-AC02-05CH11231 are also acknowledged. R.B. and E.R. acknowledge support from the US-Israel Binational Science Foundation BSF-201836. Publisher Copyright: © 2023 American Chemical Society.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85168428153&partnerID=8YFLogxK

U2 - 10.1021/acs.jctc.3c00296

DO - 10.1021/acs.jctc.3c00296

M3 - Article

C2 - 37539990

AN - SCOPUS:85168428153

SN - 1549-9618

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

ER -

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this