1
|
Schreder L, Luber S. Propagated (fragment) Pipek-Mezey Wannier functions in real-time time-dependent density functional theory. J Chem Phys 2024; 160:214117. [PMID: 38832736 DOI: 10.1063/5.0203442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2024] [Accepted: 05/14/2024] [Indexed: 06/05/2024] Open
Abstract
Localization procedures are an important tool for analysis of complex systems in quantum chemistry, since canonical molecular orbitals are delocalized and can, therefore, be difficult to align with chemical intuition and obscure information at the local level of the system. This especially applies to calculations obeying periodic boundary conditions. The most commonly used approach to localization is Foster-Boys Wannier functions, which use a unitary transformation to jointly minimize the second moment of the orbitals. This procedure has proven to be robust and fast but has a side effect of often mixing σ- and π-type orbitals. σ/π-separation is achieved by the Pipek-Mezey Wannier function (PMWF) approach [Lehtola and Jónsson, J. Chem. Theory Comput. 10, 642 (2014) and Jónsson et al., J. Chem. Theory Comput. 13, 460 (2017)], which defines the spread functional in terms of partial charges instead. We have implemented a PMWF algorithm in the CP2K software package using the Cardoso-Souloumiac algorithm to enable their application to real-time time-dependent density functional theory. The method is demonstrated on stacked CO2 molecules, linear acetylenic carbon, boron and nitrogen co-doped graphene, and nitrogen-vacancy doped diamond. Finally, we discuss its computational scaling and recent efforts to improve it with fragment approaches.
Collapse
Affiliation(s)
- Lukas Schreder
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| |
Collapse
|
2
|
Canestraight A, Lei X, Ibrahim KZ, Vlček V. Efficient Quasiparticle Determination beyond the Diagonal Approximation via Random Compression. J Chem Theory Comput 2024; 20:551-557. [PMID: 38175913 DOI: 10.1021/acs.jctc.3c01069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Abstract
Calculations of excited states in the Green's function formalism often invokes the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. In this paper, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO2 on an extended gold surface with nearly 3000 electrons. We find that in the extended system the size of the problem can be compressed up to 95% using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determination of Dyson orbitals in large systems.
Collapse
Affiliation(s)
- Annabelle Canestraight
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-9510, United States
| | - Xiaohe Lei
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Khaled Z Ibrahim
- Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
- Department of Materials, University of California, Santa Barbara, California 93106-9510, United States
| |
Collapse
|
3
|
Amblard D, Blase X, Duchemin I. Many-body GW calculations with very large scale polarizable environments made affordable: A fully ab initio QM/QM approach. J Chem Phys 2023; 159:164107. [PMID: 37873961 DOI: 10.1063/5.0168755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Accepted: 10/05/2023] [Indexed: 10/25/2023] Open
Abstract
We present a many-body GW formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is based on a fragment approximation in the construction of the Green's function and independent-electron susceptibilities. Further, the environing fragments susceptibility matrices are reduced to a minimal but accurate representation preserving low order polarizability tensors through a constrained minimization scheme. This approach dramatically reduces the cost associated with inverting the Dyson equation for the screened Coulomb potential W, while preserving the description of short to long-range screening effects. The efficiency and accuracy of the present scheme is exemplified in the paradigmatic cases of fullerene bulk, surface, subsurface, and slabs with varying number of layers.
Collapse
Affiliation(s)
- David Amblard
- Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Xavier Blase
- Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France
| | - Ivan Duchemin
- Univ. Grenoble Alpes, CEA, IRIG-MEM-L_Sim, 38054 Grenoble, France
| |
Collapse
|
4
|
Lei X, Canestraight A, Vlcek V. Exceptional Spatial Variation of Charge Injection Energies on Plasmonic Surfaces. J Phys Chem Lett 2023; 14:8470-8476. [PMID: 37721434 DOI: 10.1021/acs.jpclett.3c02223] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/19/2023]
Abstract
Charge injection into a molecule on a metallic interface is a key step in many photoactivated reactions. We employ the many-body perturbation theory and compute the hole and electron injection energies for CO2 molecule on an Au nanoparticle with ∼3,000 electrons and compare it to results for idealized infinite surfaces. We demonstrate a surprisingly large variation of the injection energy barrier depending on the precise molecular position on the surface. Multiple "hot spots," characterized by low energy barriers, arise due to the competition between the plasmonic coupling and the degree of hybridization between the molecule and the substrate. The charge injection barrier to the adsorbate on the nanoparticle surface decreases from the facet edge to the facet center. This finding contrasts with the typical picture in which the electric field enhancement on the nanoparticle edges is considered the most critical factor.
Collapse
Affiliation(s)
- Xiaohe Lei
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Annabelle Canestraight
- Department of Chemical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States
| | - Vojtech Vlcek
- Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106, United States
- Department of Materials, University of California Santa Barbara, Santa Barbara, California 93106, United States
| |
Collapse
|
5
|
Förster A, van Lenthe E, Spadetto E, Visscher L. Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants. J Chem Theory Comput 2023; 19:5958-5976. [PMID: 37594901 PMCID: PMC10501001 DOI: 10.1021/acs.jctc.3c00512] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Indexed: 08/20/2023]
Abstract
We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.
Collapse
Affiliation(s)
- Arno Förster
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Erik van Lenthe
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Edoardo Spadetto
- Software
for Chemistry and Materials NV, 1081 HV Amsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical
Chemistry, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Weng G, Pang A, Vlček V. Spatial Decay and Limits of Quantum Solute-Solvent Interactions. J Phys Chem Lett 2023; 14:2473-2480. [PMID: 36867592 DOI: 10.1021/acs.jpclett.3c00208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy decays with increasing intermolecular distance and vanishes at ∼9 Å, and this pattern is independent of the type of solvent environment. The 9 Å cutoff defines an effective interacting volume within which the ionization energy shift per solvent molecule is proportional to the macroscopic solvent polarizability. Finally, we propose a simple model for computing the ionization energies of molecules in an arbitrary solvent environment.
Collapse
Affiliation(s)
- Guorong Weng
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States
| | - Amanda Pang
- 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
- Materials Department, University of California, Santa Barbara, California 93106-5050, United States
| |
Collapse
|
8
|
Ceriotti M, Jensen L, Manolopoulos DE, Martinez T, Reichman DR, Sciortino F, Sherrill CD, Shi Q, Vega C, Wang LS, Weiss EA, Zhu X, Stein J, Lian T. 2021 JCP Emerging Investigator Special Collection. J Chem Phys 2023; 158:060401. [PMID: 36792492 DOI: 10.1063/5.0143234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023] Open
|
9
|
Förster A, Visscher L. Quasiparticle Self-Consistent GW-Bethe-Salpeter Equation Calculations for Large Chromophoric Systems. J Chem Theory Comput 2022; 18:6779-6793. [PMID: 36201788 PMCID: PMC9648197 DOI: 10.1021/acs.jctc.2c00531] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The GW-Bethe–Salpeter equation
(BSE) method
is promising for calculating the low-lying excitonic states of molecular
systems. However, so far it has only been applied to rather small
molecules and in the commonly implemented diagonal approximations
to the electronic self-energy, it depends on a mean-field starting
point. We describe here an implementation of the self-consistent and
starting-point-independent quasiparticle self-consistent (qsGW)-BSE approach, which is suitable for calculations on
large molecules. We herein show that eigenvalue-only self-consistency
can lead to an unfaithful description of some excitonic states for
chlorophyll dimers while the qsGW-BSE vertical excitation
energies (VEEs) are in excellent agreement with spectroscopic experiments
for chlorophyll monomers and dimers measured in the gas phase. Furthermore,
VEEs from time-dependent density functional theory calculations tend
to disagree with experimental values and using different range-separated
hybrid (RSH) kernels does change the VEEs by up to 0.5 eV. We use
the new qsGW-BSE implementation to calculate the
lowest excitation energies of the six chromophores of the photosystem
II (PSII) reaction center (RC) with nearly 2000 correlated electrons.
Using more than 11,000 (6000) basis functions, the calculation could
be completed in less than 5 (2) days on a single modern compute node.
In agreement with previous TD-DFT calculations using RSH kernels on
models that also do not include environmental effects, our qsGW-BSE calculations only yield states with local characters
in the low-energy spectrum of the hexameric complex. Earlier works
with RSH kernels have demonstrated that the protein environment facilitates
the experimentally observed interchromophoric charge transfer. Therefore,
future research will need to combine correlation effects beyond TD-DFT
with an explicit treatment of environmental electrostatics.
Collapse
Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| | - Lucas Visscher
- Theoretical Chemistry, Vrije Universiteit, De Boelelaan 1083, NL-1081 HVAmsterdam, The Netherlands
| |
Collapse
|
10
|
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.
Collapse
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
| |
Collapse
|
11
|
Förster A, Visscher L. Low-Order Scaling Quasiparticle Self-Consistent GW for Molecules. Front Chem 2021; 9:736591. [PMID: 34540804 PMCID: PMC8446457 DOI: 10.3389/fchem.2021.736591] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2021] [Accepted: 08/13/2021] [Indexed: 11/13/2022] Open
Abstract
Low-order scaling GW implementations for molecules are usually restricted to approximations with diagonal self-energy. Here, we present an all-electron implementation of quasiparticle self-consistent GW for molecular systems. We use an efficient algorithm for the evaluation of the self-energy in imaginary time, from which a static non-local exchange-correlation potential is calculated via analytical continuation. By using a direct inversion of iterative subspace method, fast and stable convergence is achieved for almost all molecules in the GW100 database. Exceptions are systems which are associated with a breakdown of the single quasiparticle picture in the valence region. The implementation is proven to be starting point independent and good agreement of QP energies with other codes is observed. We demonstrate the computational efficiency of the new implementation by calculating the quasiparticle spectrum of a DNA oligomer with 1,220 electrons using a basis of 6,300 atomic orbitals in less than 4 days on a single compute node with 16 cores. We use then our implementation to study the dependence of quasiparticle energies of DNA oligomers consisting of adenine-thymine pairs on the oligomer size. The first ionization potential in vacuum decreases by nearly 1 electron volt and the electron affinity increases by 0.4 eV going from the smallest to the largest considered oligomer. This shows that the DNA environment stabilizes the hole/electron resulting from photoexcitation/photoattachment. Upon inclusion of the aqueous environment via a polarizable continuum model, the differences between the ionization potentials reduce to 130 meV, demonstrating that the solvent effectively compensates for the stabilizing effect of the DNA environment. The electron affinities of the different oligomers are almost identical in the aqueous environment.
Collapse
Affiliation(s)
- Arno Förster
- Theoretical Chemistry, Vrije Universiteit, Amsterdam, Netherlands
| | | |
Collapse
|