Excited-State Geometry Optimization of Small Molecules with Many-Body Green’s Functions Theory

<div>We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green’s functions theory in the GW approximation with the Bethe–Salpeter Equation (BSE). This work provides a summary of the underlying theory and discusses details of its implementation based on Gaussian orbitals, including, i.a., resolution-of-identity techniques, different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using GPUs in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW -BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron-hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW -BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrene-fullerene mixtures. These showcases demonstrate that our implementation currently allows to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron-hole excited states of various character on an equal footing.</div>

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Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory

10.26434/chemrxiv.13106813.v1 ◽

2020 ◽

Author(s):

Onur Çaylak ◽

Björn Baumeier

Keyword(s):

Density Functional ◽

Green's Functions ◽

Green’S Functions ◽

Structural Parameters ◽

Geometry Optimization ◽

Many Body ◽

Excitation Energies ◽

Functional Theory ◽

Self Energy ◽

Relative Errors

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE). We scrutinize the influence of several typical approximations in the GW-BSE framework: using of one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully-analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm--Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC), second-order approximate coupled cluster (CC2), and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield reliable excitation energies but also geometries.

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Excited-State Geometry Optimization of Small Molecules with Many-Body Green's Functions Theory

10.26434/chemrxiv.13106813 ◽

2020 ◽

Author(s):

Onur Çaylak ◽

Björn Baumeier

Keyword(s):

Density Functional ◽

Green's Functions ◽

Green’S Functions ◽

Structural Parameters ◽

Geometry Optimization ◽

Many Body ◽

Excitation Energies ◽

Functional Theory ◽

Self Energy ◽

Relative Errors

We present a benchmark study of gas phase geometry optimizations in the excited states of carbon monoxide, acetone, acrolein, and methylenecyclopropene using many-body Green's functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE). We scrutinize the influence of several typical approximations in the GW-BSE framework: using of one-shot G0W0 or eigenvalue self-consistent evGW, employing a fully-analytic approach or plasmon-pole model for the frequency dependence of the electron self-energy, or performing the BSE step within the Tamm--Dancoff approximation. The obtained geometries are compared to reference results from multireference perturbation theory (CASPT2), variational Monte Carlo (VMC), second-order approximate coupled cluster (CC2), and time-dependent density-functional theory (TDDFT). We find overall a good agreement of the structural parameters optimized with the GW-BSE calculations with CASPT2, with an average relative error of around 1% for the G0W0 and 1.5% for the evGW variants, respectively, while the other approximations have negligible influence. The relative errors are also smaller than those for CC2 and TDDFT with different functionals and only larger than VMC, indicating that the GW-BSE method does not only yield reliable excitation energies but also geometries.

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Excited-State Electronic Structure of Molecules Using Many-Body Green's Functions: Quasiparticles and Electron-Hole Excitations with VOTCA-XTP

10.26434/chemrxiv.11477895.v1 ◽

2019 ◽

Author(s):

Gianluca Tirimbò ◽

Vivek Sundaram ◽

Onur Çaylak ◽

Wouter Scharpach ◽

Javier Sijen ◽

...

Keyword(s):

Electronic Structure ◽

Excited State ◽

Excited States ◽

Green's Functions ◽

Green’S Functions ◽

Molecular Architecture ◽

Many Body ◽

Electron Hole ◽

Structure Of Molecules ◽

Dynamics Simulations

<div>We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green’s functions theory in the GW approximation with the Bethe–Salpeter Equation (BSE). This work provides a summary of the underlying theory and discusses details of its implementation based on Gaussian orbitals, including, i.a., resolution-of-identity techniques, different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using GPUs in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on atomistic level in a coupled quantum- and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW -BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron-hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW -BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrene-fullerene mixtures. These showcases demonstrate that our implementation currently allows to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron-hole excited states of various character on an equal footing.</div>

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AN INTRODUCTORY GUIDE TO GREEN’S FUNCTION METHODS IN NUCLEAR MANY-BODY PROBLEMS

International Journal of Modern Physics E ◽

10.1142/s0218301394000140 ◽

1994 ◽

Vol 03 (02) ◽

pp. 523-589 ◽

Cited By ~ 6

Author(s):

T.T.S. KUO ◽

YIHARN TZENG

Keyword(s):

Green’S Function ◽

Green's Function ◽

Green's Functions ◽

Green’S Functions ◽

Model Space ◽

Many Body ◽

Diagram Expansion ◽

Nucleus Scattering ◽

Many Body Systems ◽

General Method

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

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