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      On the Difference Between Additive and Subtractive QM/MM Calculations

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          Abstract

          The combined quantum mechanical (QM) and molecular mechanical (MM) approach (QM/MM) is a popular method to study reactions in biochemical macromolecules. Even if the general procedure of using QM for a small, but interesting part of the system and MM for the rest is common to all approaches, the details of the implementations vary extensively, especially the treatment of the interface between the two systems. For example, QM/MM can use either additive or subtractive schemes, of which the former is often said to be preferable, although the two schemes are often mixed up with mechanical and electrostatic embedding. In this article, we clarify the similarities and differences of the two approaches. We show that inherently, the two approaches should be identical and in practice require the same sets of parameters. However, the subtractive scheme provides an opportunity to correct errors introduced by the truncation of the QM system, i.e., the link atoms, but such corrections require additional MM parameters for the QM system. We describe and test three types of link-atom correction, viz. for van der Waals, electrostatic, and bonded interactions. The calculations show that electrostatic and bonded link-atom corrections often give rise to problems in the geometries and energies. The van der Waals link-atom corrections are quite small and give results similar to a pure additive QM/MM scheme. Therefore, both approaches can be recommended.

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          Most cited references51

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          Fully optimized contracted Gaussian basis sets for atoms Li to Kr

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            QM/MM methods for biomolecular systems.

            Combined quantum-mechanics/molecular-mechanics (QM/MM) approaches have become the method of choice for modeling reactions in biomolecular systems. Quantum-mechanical (QM) methods are required for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. However, QM methods are restricted to systems of up to a few hundred atoms. However, the size and conformational complexity of biopolymers calls for methods capable of treating up to several 100,000 atoms and allowing for simulations over time scales of tens of nanoseconds. This is achieved by highly efficient, force-field-based molecular mechanics (MM) methods. Thus to model large biomolecules the logical approach is to combine the two techniques and to use a QM method for the chemically active region (e.g., substrates and co-factors in an enzymatic reaction) and an MM treatment for the surroundings (e.g., protein and solvent). The resulting schemes are commonly referred to as combined or hybrid QM/MM methods. They enable the modeling of reactive biomolecular systems at a reasonable computational effort while providing the necessary accuracy.
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              Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids

              The electron density, its gradient, and the Kohn-Sham orbital kinetic energy density are the local ingredients of a meta-generalized gradient approximation (meta-GGA). We construct a meta-GGA density functional for the exchange-correlation energy that satisfies exact constraints without empirical parameters. The exchange and correlation terms respect {\it two} paradigms: one- or two-electron densities and slowly-varying densities, and so describe both molecules and solids with high accuracy, as shown by extensive numerical tests. This functional completes the third rung of ``Jacob's ladder'' of approximations, above the local spin density and GGA rungs.
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                Author and article information

                Contributors
                Journal
                Front Chem
                Front Chem
                Front. Chem.
                Frontiers in Chemistry
                Frontiers Media S.A.
                2296-2646
                03 April 2018
                2018
                : 6
                : 89
                Affiliations
                Department of Theoretical Chemistry, Chemical Centre, Lund University , Lund, Sweden
                Author notes

                Edited by: Sam P. De Visser, University of Manchester, United Kingdom

                Reviewed by: Albert Poater, University of Girona, Spain; Jiayun Pang, University of Greenwich, United Kingdom

                *Correspondence: Ulf Ryde Ulf.Ryde@ 123456teokem.lu.se

                This article was submitted to Theoretical and Computational Chemistry, a section of the journal Frontiers in Chemistry

                Article
                10.3389/fchem.2018.00089
                5891596
                29666794
                1ed47e16-0495-4ccf-97ec-d1d1af711364
                Copyright © 2018 Cao and Ryde.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 31 January 2018
                : 14 March 2018
                Page count
                Figures: 5, Tables: 5, Equations: 8, References: 65, Pages: 15, Words: 12141
                Funding
                Funded by: Vetenskapsrådet 10.13039/501100004359
                Award ID: 2014-5540
                Funded by: Knut och Alice Wallenbergs Stiftelse 10.13039/501100004063
                Award ID: 2013.0022
                Funded by: European Cooperation in Science and Technology 10.13039/501100000921
                Categories
                Chemistry
                Original Research

                qm/mm,haem oxygenase,sulfite oxidase,mechanical embedding,electrostatic embedding,additive qm/mm,subtractive qm/mm

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