Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis
Abstract
We present, within KohnSham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then introduce a simple and efficient formalism (which can be written as generalization of other wellknown population analyses) to extract, from first principles, electrostatic multipoles for these fragments. The corresponding fragment multipoles can in this way be seen as reliable (pseudo) observables. By applying our formalism within the code BigDFT, we show that the usage of a minimal set of insitu optimized basis functions is of utmost importance for having at the same time a proper fragment definition and an accurate description of the electronic structure. With this approach it becomes possible to simplify the modeling of environmental fragments by a set of multipoles, without notable loss of precision in the description of the active quantum mechanical region. Furthermore, this leads to a considerable reduction of the degrees of freedom by an effective coarsegraining approach, eventually also paving the way towards efficient QM/QM and QM/MM methods coupling together different levels of accuracy.
 Authors:
 Barcelona Supercomputing Center (BSC), Barcelona (Spain)
 Institut de Biologie et de Technologie de Saclay, GifsurYvette Cedex (France)
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Univ. Grenoble Alpes, Grenoble (France); CEA, Grenoble (France)
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 European Commission, Community Research and Development Information Service (CORDIS), EXTended Model of Organic Semiconductors (ExtMOS); Energy Oriented Centre of Excellence (EoCoE); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); Argonne National Laboratory, Argonne Leadership Computing Facility; MaX Centre of Excellence
 OSTI Identifier:
 1400406
 Grant/Contract Number:
 AC0206CH11357
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Chemical Theory and Computation
 Additional Journal Information:
 Journal Volume: 13; Journal Issue: 9; Journal ID: ISSN 15499618
 Publisher:
 American Chemical Society
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Mohr, Stephan, Masella, Michel, Ratcliff, Laura E., and Genovese, Luigi. Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis. United States: N. p., 2017.
Web. doi:10.1021/acs.jctc.7b00291.
Mohr, Stephan, Masella, Michel, Ratcliff, Laura E., & Genovese, Luigi. Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis. United States. doi:10.1021/acs.jctc.7b00291.
Mohr, Stephan, Masella, Michel, Ratcliff, Laura E., and Genovese, Luigi. 2017.
"Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis". United States.
doi:10.1021/acs.jctc.7b00291.
@article{osti_1400406,
title = {Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis},
author = {Mohr, Stephan and Masella, Michel and Ratcliff, Laura E. and Genovese, Luigi},
abstractNote = {We present, within KohnSham Density Functional Theory calculations, a quantitative method to identify and assess the partitioning of a large quantum mechanical system into fragments. We then introduce a simple and efficient formalism (which can be written as generalization of other wellknown population analyses) to extract, from first principles, electrostatic multipoles for these fragments. The corresponding fragment multipoles can in this way be seen as reliable (pseudo) observables. By applying our formalism within the code BigDFT, we show that the usage of a minimal set of insitu optimized basis functions is of utmost importance for having at the same time a proper fragment definition and an accurate description of the electronic structure. With this approach it becomes possible to simplify the modeling of environmental fragments by a set of multipoles, without notable loss of precision in the description of the active quantum mechanical region. Furthermore, this leads to a considerable reduction of the degrees of freedom by an effective coarsegraining approach, eventually also paving the way towards efficient QM/QM and QM/MM methods coupling together different levels of accuracy.},
doi = {10.1021/acs.jctc.7b00291},
journal = {Journal of Chemical Theory and Computation},
number = 9,
volume = 13,
place = {United States},
year = 2017,
month = 7
}
Web of Science

Chemical bonding analysis for solidstate systems using intrinsic oriented quasiatomic minimalbasisset orbitals
A chemical bonding scheme is presented for the analysis of solidstate systems. The scheme is based on the intrinsic oriented quasiatomic minimalbasisset orbitals (IOQUAMBOs) previously developed by Ivanic and Ruedenberg for molecular systems. In the solidstate scheme, IOQUAMBOs are generated by a unitary transformation of the quasiatomic orbitals located at each site of the system with the criteria of maximizing the sum of the fourth power of interatomic orbital bond order. Possible bonding and antibonding characters are indicated by the single particle matrix elements, and can be further examined by the projected density of states. We demonstrate the method bymore » 
Charge transfer interaction using quasiatomic minimalbasis orbitals in the effective fragment potential method
The charge transfer (CT) interaction, the most timeconsuming term in the general effective fragment potential method, is made much more computationally efficient. This is accomplished by the projection of the quasiatomic minimalbasisset orbitals (QUAMBOs) as the atomic basis onto the selfconsistent field virtual molecular orbital (MO) space to select a subspace of the full virtual space called the valence virtual space. The diagonalization of the Fock matrix in terms of QUAMBOs recovers the canonical occupied orbitals and, more importantly, gives rise to the valence virtual orbitals (VVOs). The CT energies obtained using VVOs are generally as accurate as those obtainedmore » 
Nanoplasmonics simulations at the basis set limit through completenessoptimized, local numerical basis sets
We present an approach for generating local numerical basis sets of improving accuracy for firstprinciples nanoplasmonics simulations within timedependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semicore delectrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussiantype orbitals generated by the completenessoptimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate thatmore » 
Intrinsic Local Constituents of Molecular Electronic Wave Functions.I. Exact Representation of the Density Matrix in Terms of Chemically Deformed and Oriented Atomic Minimal Basis Set Orbitals
A coherent, intrinsic, basissetindependent analysis is developed for the invariants of the firstorder density matrix of an accurate molecular electronic wavefunction. From the hierarchical ordering of the natural orbitals, the zerothorder orbital space is deduced, which generates the zerothorder wavefunction, typically an MCSCF function in the full valence space. It is shown that intrinsically embedded in such wavefunctions are elements that are local in bond regions and elements that are local in atomic regions. Basissetindependent methods are given that extract and exhibit the intrinsic bond orbitals and the intrinsic minimalbasis quasiatomic orbitals in terms of which the wavefunction can bemore »