Chapter 1 Introduction 1 General Introduction
Adaptation of the QM/MM Coupling Scheme of Maseras and Morokuma
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| 2.3 Adaptation of the QM/MM Coupling Scheme of Maseras and Morokuma
In this section we describe a modification of the IMOMM methodology of Maseras and Morokuma where no coordinate transformation is required, thereby avoiding the potential difficulties associated with utilizing internal coordinates. The modification allows for practical IMOMM simulations of macroscopic systems, explicitly solvated systems, it allows for energy conserving molecular dynamics simulations and frequency calculations to be performed. The combined QM/MM coupling scheme described here is based on the original IMOMM scheme of Maseras and Morokuma.15 All of the rules for determining which MM potentials to accept and discard are the same as in the original IMOMM scheme. We will deal exclusively with defining the relationship between the atoms associated with a QM/MM link bond and how the QM and MM based gradients are combined. We start by defining the relationship between the link atoms and the capping atoms that are involved in a covalent bond that crosses the QM/MM boundary. In the IMOMM scheme, the position of the MM-link atom is not an independent variable. Instead, the MM-link atom is always placed along the bond vector of the QM-link atom and the capping atom bond. Expressed in Cartesian coordinates, this relationship can be defined by equation 2-11 (and rearranged in equation 2-12).  (2-11)
 (2-12)
If is defined in the following way,  (2-13)
then the original implementation of Maseras and Morokuma is recovered in Cartesian coordinates where equation 2-2 is satisfied. In our implementation we define as a constant parameter. In this way the bond distance, RMM, between the QM and MM-link atoms is defined as a constant factor of the QM-link - capping atom bond distance, Rcapping, such that equation 2-14 is satisfied.  (2-14)
The relationship defined in equation 2-14 is analogous to equation 2-2 of the original scheme, and the 's for each link bond is chosen in a similar fashion as ∆R as described by Maseras and Morokuma.15 Comparison of the relationships (Eqns 2-2 and 2-14) reveals that they are similar in that both allow changes in Rcapping to be reflected in the bond distance RMM-link. There is no clear advantage in using either relationship in terms of the physical model of the QM/MM link bond. However, by defining as a constant, combining the MM and QM forces in Cartesian coordinates is simplified. By applying the relationship defined in equation 2-12 where is a constant and applying the chain rule, the combined QM/MM gradients on the QM-link atom and the capping atom are expressed by equations 2-15 and 2-16, respectively.  (2-15)
 (2-16)
Equations 2-15 and 2-16 are valid the Cartesian coordinate system and there is no need to add the QM and MM forces in an internal coordinate system.◊ Directory: wp-content -> uploads uploads -> 587 Return function, r i(X) r i(0) r i(1) r i(2) r i(3) 1 0 2 4 6 Thermal Station, I 2 0 1 5 6 3 0 3 5 6 10 uploads -> The Case Against the nypd’s Quota-Driven ‘Broken Windows’ Policing What Is It? uploads -> For want of a nail uploads -> Police Militarization uploads -> Stop Militarizing Law Enforcement Act of 2014 uploads -> 2017 afoCo Landmark Scholarship Program uploads -> Instructions for the Preparation of Camera-Ready Contributions to the Conference Proceedings uploads -> Medical Radiography Program uploads -> Ihbb asian Championships 2014 middle school bowl Round 4 First Quarter uploads -> Ihbb european Championships 2014 Bowl Round 4 First Quarter Download 4.36 Mb. Share with your friends:
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