Implementation of the SCC-DFTB method for hybrid QM/MM simulations within the amber molecular dynamics package

Self-consistent charge density functional tight-binding (SCC-DFTB) is a semiempirical method based on density functional theory and has in many cases been shown to provide relative energies and geometries comparable in accuracy to full DFT or ab initio MP2 calculations using large basis sets. This article shows an implementation of the SCC-DFTB method as part of the new QM/MM support in the AMBER 9 molecular dynamics program suite. Details of the implementation and examples of applications are shown.     

Self-interaction and strong correlation in DFTB

The density functional based tight-binding (DFTB) method can benefit substantially from a number of developments in density functional theory (DFT) while also providing a simple analytical proving ground for new extensions. This contribution begins by demonstrating the variational nature of charge-self-consistent DFTB (SCC-DFTB), proving the presence of a defined ground-state in this class of methods. Because the ground state of the SCC-DFTB method itself can be qualitatively incorrect for some systems, suitable forms of the recent LDA+U functionals for SCC-DFTB are also presented. This leads to both a new semilocal self-interaction correction scheme and a new physical argument for the choice of parameters in the LDA+U method. The locality of these corrections can only partly repair the HOMO-LUMO gap and chemical potential discontinuity, hence a novel method for introducing this further physics into the method is also presented, leading to exact derivative discontinuities in this theory at low computational cost. The prototypical system NiO is used as an illustration for these developments.     

Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra

An extension of the self-consistent charge density-functional tight-binding (SCC-DFTB) method is presented that allows for calculating intensities of peaks in vibrational Raman spectra for very large molecules. The extension is based on a simple ansatz: an extra term, which describes interaction of an external electric field with induced atomic charges, is added to the SCC-DFTB energy expression. We apply the modified SCC-DFTB formalism for reproducing vibrational Raman spectra of 17 organic molecules. The calculated spectra are compared with experiment and with spectra obtained from density functional theory (DFT) calculations. We find that the SCC-DFTB method is capable of reproducing most of the features of experimental Raman spectra. Limitations and advantages of this approach are analyzed and suggestions for interpreting calculated SCC-DFTB Raman spectra are given.     

An efficient LDA+U based tight binding approach

The functionals usually applied in DFT calculations have deficiencies in describing systems with strongly localized electrons such as transition metals or rare earth (RE) compounds. In this work, we present the self-consistent charge density based functional tight binding (SCC-DFTB) calculation scheme including LDA+U like potentials and apply it for the simulation of RE-doped GaN. DFTB parameters for the simulation of GaN and a selection of rare earth ions, where the f electrons were explicitly included in the valence, have been created. The results of the simulations were tested against experimental data (where present) and against various more sophisticated but computationally more costly DFT calculations. Our approach is found to correctly reproduce the geometry and the energetic of the studied systems.     

Modeling zinc in biomolecules with the self consistent charge-density functional tight binding (SCC-DFTB) method: applications to structural and energetic analysis

Parameters for the zinc ion have been developed in the self-consistent charge density functional tight-binding (SCC-DFTB) framework. The approach was tested against B3LYP calculations for a range of systems, including small molecules that contain the typical coordination environment of zinc in biological systems (cysteine, histidine, glutamic/aspartic acids, and water) and active site models for a number of enzymes such as alcohol dehydrogenase, carbonic anhydrase, and aminopeptidase. The SCC-DFTB approach reproduces structural and energetic properties rather reliably (e.g., total and relative ligand binding energies and deprotonation energies of ligands and barriers for zinc-assisted proton transfers), as compared with B3LYP/6-311+G** or MP2/6-311+G** calculations.     

Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70)

The self-consistent charge density-functional tight-binding (SCC-DFTB) method is employed for studying various molecular properties of small fullerenes: C(28), C(60), and C(70). The computed bond distances, vibrational infrared and Raman spectra, vibrational densities of states, and electronic densities of states are compared with experiment (where available) and density-functional theory (DFT) calculations using various basis sets. The presented DFT benchmark calculations using the correlation-consistent polarized valence triple zeta basis set are at present the most extensive calculations on harmonic frequencies of these species. Possible limitations of the SCC-DFTB method for the prediction of molecular vibrational and optical properties are discussed. The presented results suggest that SCC-DFTB is a computationally feasible and reliable method for predicting vibrational and electronic properties of such carbon nanostructures comparable in accuracy with small to medium size basis set DFT calculations at the computational cost of standard semiempirical methods.     

Systematic study of vibrational frequencies calculated with the self-consistent charge density functional tight-binding method

We present a detailed study of harmonic vibrational frequencies obtained with the self-consistent charge density functional tight-binding (SCC-DFTB) method. Our testing set comprises 66 molecules and 1304 distinct vibrational modes. Harmonic vibrational frequencies are computed using an efficient analytical algorithm developed and coded by the authors. The obtained results are compared to experiment and to other theoretical findings. Scaling factor for the SCC-DFTB method, determined by minimization of mean absolute deviation of scaled frequencies, is found to be 0.9933. The accuracy of the scaled SCC-DFTB frequencies is noticeably better than for other semiempirical methods (including standard DFTB method) and approximately twice worse than for other well established scaled ab initio quantum chemistry methods (e.g., HF, BLYP, B3LYP). Mean absolute deviation for the scaled SCC-DFTB frequencies is 56 cm(-1), while standard deviation is 82 cm(-1), and maximal absolute deviation is as large as 529 cm(-1). Using SCC-DFTB allows for substantial time savings; computational time is reduced from hours to seconds when compared to standard ab initio techniques.     

Structure, spectroscopy, and reactivity properties of porphyrin pincers: a conceptual density functional theory and time-dependent density functional theory study

Porphyrin and pincer complexes are both important categories of compounds in biological and catalytic systems. The idea to combine them is computationally investigated in this work. By employment of density functional theory (DFT), conceptual DFT, and time-dependent DFT approaches, structure, spectroscopy, and reactivity properties of porphyrin pincers are systematically studied for a selection of divalent metal ions. We found that the porphyrin pincers are structurally and spectroscopically different from their precursors and are more reactive in electrophilic and nucleophilic reactions. A few quantitative linear/exponential relationships have been discovered between bonding interactions, charge distributions, and DFT chemical reactivity indices. These results are implicative in chemical modification of hemoproteins and understanding chemical reactivity in heme-containing and other biologically important complexes and cofactors.     

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.     

Antibiotic binding to dizinc beta-lactamase L1 from Stenotrophomonas maltophilia: SCC-DFTB/CHARMM and DFT studies

A dizinc beta-lactamase (L1 from Stenotrophomonas maltophilia) complexed with an antibiotic compound (moxalactam) has been studied using a hybrid quantum mechanical/molecular mechanical (QM/MM) approach. The QM region is described by the self-consistent charge-density functional tight binding (SCC-DFTB) model while the MM by CHARMM. The Michaelis complex, which is constructed from a recent X-ray structure of the L1 enzyme with the hydrolyzed moxalactam, is simulated by molecular dynamics. The simulation yields valuable insights into substrate-enzyme interaction, whose implications in the enzyme catalysis are discussed. Finally, the QM/MM results are compared with a high-level density functional theory study of a truncated active-site model and the agreement provides strong support for the SCC-DFTB treatment of the QM region.     

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.     

DFT ×TB − a unified quantum-mechanical hybrid method

A unified quantum mechanical hybrid method on the basis of density functional theory (DFT) is presented. The method is based on an LCAO-Kohn-Sham ansatz. While a part is treated with standard DFT, for the remaining system non-orthogonal tight-binding (TB) approximations are made for potential and basis functions. This means that it is possible to have covalent bonds in between the DFT and TB parts. The charge fluctuation within the system is controlled by the self-consistent charge technique. Theory, implementation, and first example molecules are presented in this article, and further development is discussed. Dedicated to Professor Karl Jug on the occasion of his 65th birthday.     

Looking at self-consistent-charge density functional tight binding from a semiempirical perspective

The self-consistent-charge density functional tight binding (SCC-DFTB) method is compared with other semiempirical methods (MNDO, AM1, PM3, OM1, OM2, OM3). Despite the differences in the underlying philosophy and derivation, these methods share many common features. Systematic evaluations of their performance are reported for standard test sets that are in common use. The overall accuracy of SCC-DFTB and the other methods is in the same range, with the overall tendency AM1相似文献   

DFT study of “all-metal” aromatic compounds

An overview of recent quantum chemical studies on all-metal aromatic compounds is presented. Novel classes of inorganic molecules containing bonds that are characterized by a common ring-shaped electron density are reviewed. The mechanistic insight gained for the aromatic character of all-metal aromatic molecules is discussed and the predictive nature of the electronic structure calculation methods particularly those based on density functional theory (DFT) is highlighted. The indicators of aromaticity (aromaticity criteria) - structural, magnetic, energetic and reactivity-based measures - many of which are accessible through quantum chemical calculations are also outlined herein.     

Cluster Amplitudes and Their Interplay with Self-Consistency in Density Functional Methods

Density functional theory (DFT) provides convenient electronic structure methods for the study of molecular systems and materials. Regular Kohn-Sham DFT calculations rely on unitary transformations to determine the ground-state electronic density, ground state energy, and related properties. However, for dissociation of molecular systems into open-shell fragments, due to the self-interaction error present in a large number of density functional approximations, the self-consistent procedure based on the this type of transformation gives rise to the well-known charge delocalization problem. To avoid this issue, we showed previously that the cluster operator of coupled-cluster theory can be utilized within the context of DFT to solve in an alternative and approximate fashion the ground-state self-consistent problem. This work further examines the application of the singles cluster operator to molecular ground state calculations. Two approximations are derived and explored: i) A linearized scheme of the quadratic equation used to determine the cluster amplitudes. ii) The effect of carrying the calculations in a non-self-consistent field fashion. These approaches are found to be capable of improving the energy and density of the system and are quite stable in either case. The theoretical framework discussed in this work could be used to describe, with an added flexibility, quantum systems that display challenging features and require expanded theoretical methods.