DFTB method

This chapter reviewed some of our group s contributions to the development and application of QM/MM methods specifically as applied to enzymatic reactions, including the use of sequential MD/QM methods, the use of effective fragment potentials for reaction mechanisms, the development of the new QM/MM interface in Amber, as well as the implementation and optimization of the SCC-DFTB method in the Amber program. This last implementation allows the application of advanced MD and sampling techniques available in Amber to QM/MM problems, as exemplified by the potential and free energy surface surfaces for the reaction catalyzed by the Tripanosoma cruzi enzyme /ram-sialidasc shown here. 

Abstract Recent QM/MM developments based on the SCC-DFTB method as the QM level are dis-... 

In the following, we first briefly review the SCC-DFTB method and comment on a few issues related to the implementation of SCC-DFTB/MM, such as the multi-scale SCC-DFTB/MM-GSBP protocol. Next, a few specific examples of SCC-DFTB/MM simulations are given. The basic motivation is to highlight a number of issues that might impact either the quantitative or even qualitative nature of the result. We hope that the chapter is particularly instructive to researchers who are relatively new to the field and able to help them carry out meaningful QM/MM simulations. 

In DFT the total energy is expressed as a functional of the electron density p of the molecular system of interest. The derivation of the SCC-DFTB method starts by choosing a reference density po as a superposition of densities p of the neutral atoms a constituting the molecular system,... 

As a consequence of the size limitations of the ab initio schemes, a large number of more-approximate methods can be found in the literature. Here, we mention only the density functional-based tight binding (DFTB) method, which is a two-center approach to DFT. The method has been successfully applied to the study of proton transport in perov-skites and imidazole (see Section 3.1.1.3). The fundamental constraints of DFT are (i) treatment of excited states and (ii) the ambiguous choice of the exchange correlation function. In many cases, the latter contains several parameters fitted to observable properties, which makes such calculations, in fact, semiempirical. 

Cui Q, M Elstner, E Kaxiras, T Frauenheim, M Karplus (2001) A QM/MM implementation of the self-consistent charge density functional tight binding (SCC-DFTB) method. J. Phys. Chem. B 105 (2) 569-585... 

Since the brilliant conceptual proposal by Warshel and Levitt [1], the hybrid method of QM/MM has been extensively applied to simulate some very large systems, such as enzymes, nano-scale materials etc. The purpose of this chapter is not to give a complete review of the QM/MM methods, because the developments and applications of QM/MM methods have been well documented and reviewed in many previous articles, for example. Refs. [2-5]. We try to in this manuscript introduce one of recent developed semi-empirical methods, self consistent charge density tight binding (SCC-DFTB) method [6], and its applications to enzymatic processes when integrated with CHARMM force field. 

In this work, a recently developed semi-empirical method, SCC-DFTB method, is employed to account for the electronic structure of QM part. The details of this method and its implementation to CHARMM have been summarized elsewhere [6, 22-24]. Here we just give a short description. This method is derived by a second order expansion of the DFT total energy functional with respect to the charge density fluctuation around a given reference density. The total energy can be expressed as following [22] ... 

In addition, a workshop on the theory, code and application of DFTB+ method was held on April 21, 2011. 

Cui, Q., Flstnee, M., Kaxieas, E., Feauenheim, T., Karplus, M., A QM/ MM Implementation of the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) Method,... 

The resulting density functional-based tight binding (DFTB) method works well for homo-nuclear systems, where the charge transfer between the atoms in the system does not occur or is... 

Because of the crystal anisotropy, on the other hand, the sequence and the frequency of phase transformations depend on the character of compression. For example, the compression in z forces the molecules to develop more rapidly electrostatic interactions, which in turn affect the electronic charge of the nitro group and therefore result in a steeper decrease of the band gap with applied pressure. Since charge transfer is important in the description of atomic forces, we expect that its realistic description within the SCC-DFTB method captures the general features of the molecular response to external stress. 

To directly simulate the condensed-phase chemical reactivity of HMX, we use the SCC-DFTB method to determine the interatomic forces and simulate the decomposition at constant-volume and temperature conditions. The initial condition of the simulation included six HMX molecules in a cell, corresponding to the unit cell of the S phase of HMX (Fig. 10) with a total of 168 atoms. It is well known [76] that HMX undergoes a phase transition at 436 K from the P phase (two molecules per unit cell with a chair molecular conformation, density = 1.89 g/cm ) to the 6 phase (with boat molecular conformation, density=1.50 g/cm ). We thus chose the 8 phase as the initial starting structure so as to include all the relevant physical attributes of the system prior to chemical decomposition. The calculation started with the experimental unit cell parameters and atomic positions of 8 HMX. The atomic positions were then relaxed in an energy minimization procedure. The resulting atomic positions were verified to be close to the experimental positions. 

A self-consistent charge density functional based tight binding (SCC-DFTB) method was used for the calculations of the geometries, electronic... 

Analyzing the electronic properties of the investigated systems, the flat silicide and the SiH sheets, as well as all nanotubes considered here, were found to be semiconducting. Within our DFTB method, we obtain band gaps of 2.49 eV and 2.50 eV for Sf and SiH layers, respectively, agreeing quite nicely with that obtained by other calculations (2.48 eV) and experimental results... 

Figure 17.5. Structure (side and top views) of a siloxene layer as predicted by our DFTB method. The OH-groups above and the hydrogens below the silicon "backbone" layer can be seen clearly, as can the puckered structure. (Taken from ref 1).

Within our DFTB method stable, puckered layers are predicted with respective bond lengths of 2.34, 1.51, and 1.63 A. The Si-O-H bond angle exactly matches the experimental value. 

Table 2.2 Structural parameters for GOTHS and THVS selected structural parameters calculated using the different DFT functionals and the DFTB method for the two silane coupling agents studied in this work.

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