Implementation and Testing of a Frozen Density Matrix−Divide and Conquer Algorithm

Ermolaeva, Maria D.; Vaart, and Arjan van der; Merz, Kenneth M.

doi:10.1021/jp984312o

Cited by 26 publications

(24 citation statements)

References 35 publications

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“…Such a method divides the density matrix into fragments that are treated by conventional quantum chemistry techniques to ultimately obtain the properties of the whole system. Later, Merz and coworkers developed a semiempirical version of divide-and-conquer (Dixon & Merz, 1996, 1997; Ermolaeva, van der Vaart, & Merz, 1999), Exner and Mezey proposed the adjustable density-matrix assembler approach (Exner & Mezey, 2002, 2003, 2004), Zhang and coworkers developed the molecular fractionation with conjugated caps approach (Gao, Zhang, Zhang, & Zhang, 2004; Kurisu, Zhang, Smith, & Cramer, 2003; Mei, Zhang, & Zhang, 2005; Zhang, Xiang, & Zhang, 2003; Zhang & Zhang, 2003), Gadre and coworkers developed the molecular tailoring approach (Babu & Gadre, 2003; Babu, Ganesh, Gadre, & Ghermani, 2004; Gadre, Shirsat, & Limaye, 1994), Kitaura and coworkers proposed the fragment molecular-orbital FMO method (Fedorov & Kitaura, 2004a, 2004b; Kitaura, Ikeo, Asada, Nakano, & Uebayasi, 1999; Kitaura, Sugiki, Nakano, Komeiji, & Uebayasi, 2001), Li and coworkers proposed the localized molecular-orbital assembler approach (Li & Li, 2005; Li, Li, & Fang, 2005), Mayhall and Raghavachari proposed the multilayer molecules-in-molecules method that is similar in spirit to the ONIOM approach (Mayhall & Raghavachari, 2011) (vide infra), while Collins and Bettens introduced the combined and systematic fragmentation approach (Collins, Cvitkovic, & Bettens, 2014). …”

Section: Introductionmentioning

confidence: 99%

The MOD-QM/MM Method

Askerka

Batista

et al. 2016

Methods in Enzymology

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Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and catalytic sites embedded in macrobiomolecules (eg, proteins and nucleic acids). QM/MM methodologies are highly efficient since they implement quantum chemistry methods for modeling only the portion of the system involving bond-breaking/forming processes (QM layer), as influenced by the surrounding molecular environment described in terms of molecular mechanics force fields (MM layer). Some of the limitations of QM/MM methods when polarization effects are not explicitly considered include the approximate treatment of electrostatic interactions between QM and MM layers. Here, we review recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in biomacromolecules and structural refinement, beyond the common limitations of QM/MM hybrid methods. We focus on photosystem II (PSII) with emphasis on the description of the oxygen-evolving complex (OEC) and its high-resolution extended X-ray absorption fine structure spectra (EXAFS) in conjunction with Monte Carlo structural refinement. Furthermore, we review QM/MM structural refinement studies of DNA G4 quadruplexes with embedded monovalent cations and direct comparisons to NMR data.

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Section: Introductionmentioning

confidence: 99%

The MOD-QM/MM Method

Askerka

Batista

et al. 2016

Methods in Enzymology

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“…Other authors have developed this work adding more sophisticated buffer regions and extending applicability to other ab initio and quantum chemistry methods [15]. Recent large scale efforts have shown promising results [16,17,18,19,20,21,22]. One of the principle challenges when using divide and conquer methods is the selection of subsystems.…”

Section: Introductionmentioning

confidence: 99%

The potential, limitations, and challenges of divide and conquer quantum electronic structure calculations on energetic materials.

Tucker¹,

Magyar²

2012

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High explosives are an important class of energetic materials used in many weapons applications. Even with modern computers, the simulation of the dynamic chemical reactions and energy release is exceedingly challenging. While the scale of the detonation process may be macroscopic, the dynamic bond breaking responsible for the explosive release of energy is fundamentally quantum mechanical. Thus, any method that does not adequately describe bonding is destined to lack predictive capability on some level. Performing quantum mechanics calculations on systems with more than dozens of atoms is a gargantuan task, and severe approximation schemes must be employed in practical calculations. We have developed and tested a divide and conquer (DnC) scheme to obtain total energies, forces, and harmonic frequencies within semi-empirical quantum mechanics. The method is intended as an approximate but faster solution to the full problem and is possible due to the sparsity of the density matrix in many applications. The resulting total energy calculation scales linearly as the number of subsystems, and the method provides a path-forward to quantum mechanical simulations of millions of atoms. 3This page intentionally left blank.4

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“…The DC method has been used for many chemical applications by the Yang laboratory [29][30][31][32][33] and elsewhere. [34][35][36][37][38][39][40][41][42][43][44][45] There are also several approximate fragment approaches. 6,8,12,[46][47][48][49][50][51][52][53] In this paper, we propose a density-fragment interaction ͑DFI͒ approach for large-scale calculations based on a meanfield treatment of the electronic interaction between the fragments.…”

Section: Introductionmentioning

confidence: 99%

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg2+-sensitive dye

Fujimoto

Yang

2008

The Journal of Chemical Physics

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A density-fragment interaction ͑DFI͒ approach for large-scale calculations is proposed. The DFI scheme describes electron density interaction between many quantum-mechanical ͑QM͒ fragments, which overcomes errors in electrostatic interactions with the fixed point-charge description in the conventional quantum-mechanical/molecular-mechanical ͑QM/MM͒ method. A self-consistent method, which is a mean-field treatment of the QM fragment interactions, was adopted to include equally the electron density interactions between the QM fragments. As a result, this method enables the evaluation of the polarization effects of the solvent and the protein surroundings. This method was combined with not only density functional theory ͑DFT͒ but also time-dependent DFT. In order to evaluate the solvent polarization effects in the DFI-QM/MM method, we have applied it to the excited states of the magnesium-sensitive dye, KMG-20. The DFI-QM/MM method succeeds in including solvent polarization effects and predicting accurately the spectral shift caused by Mg 2+ binding.

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Implementation and Testing of a Frozen Density Matrix−Divide and Conquer Algorithm

Cited by 26 publications

References 35 publications

The MOD-QM/MM Method

The MOD-QM/MM Method

The potential, limitations, and challenges of divide and conquer quantum electronic structure calculations on energetic materials.

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg2+-sensitive dye

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