A density functional tight binding model with an extended basis set and three-body repulsion for hydrogen under extreme thermodynamic conditions.

We present a new DFTB-p3b density functional tight binding model for hydrogen at extremely high pressures and temperatures, which includes a polarizable basis set (p) and a three-body environmentally dependent repulsive potential (3b). We find that use of an extended basis set is necessary under dissociated liquid conditions to account for the substantial p-orbital character of the electronic states around the Fermi energy. The repulsive energy is determined through comparison to cold curve pressures computed from density functional theory (DFT) for the hexagonal close-packed solid, as well as pressures from thermally equilibrated DFT-MD simulations of the liquid phase. In particular, we observe improved agreement in our DFTB-p3b model with previous theoretical and experimental results for the shock Hugoniot of hydrogen up to 100 GPa and 25000 K, compared to a standard DFTB model using pairwise interactions and an s-orbital basis set, only. The DFTB-p3b approach discussed here provides a general method to extend the DFTB method for a wide variety of materials over a significantly larger range of thermodynamic conditions than previously possible.

QM/MM simulations of vibrational spectra of bacteriorhodopsin and channelrhodopsin-2.

Channelrhodopsin-2 is a light-gated ion channel, which has been studied intensively over the last decade. Vibrational spectroscopic experiments started to shed light on the structural changes, that occur during the photocycle, especially in the hydrogen-bonded network surrounding the protonated D156 and C128 - the DC gate. However, the interpretation of these experiments was only based on homology models. Since then, an X-ray structure and better computational models became available. In this article, we show that in combination with a recent reparametrization, the approximate DFT method, DFTB, is able to describe the effects of hydrogen bonding on the C=O stretch vibration in carboxylic acids reliably and agrees well with full DFT results. We apply DFTB in a QM/MM framework to perform vibrational analysis of buried aspartic acids in bacteriorhodopsin and channelrhodopsin-2. Using this approach, we can simulate the FTIR spectral difference between D115 in the dark-adapted and K states of bacteriorhodopsin. The FTIR experiments on the DC gate in channelrhodopsin-2 are well described using an indirect model, where D156 and C128 are bridged via a water molecule.

Improved electronic properties from third-order SCC-DFTB with cost efficient post-SCF extensions.

The present work outlines the implementation and performance of two cost efficient post-SCF extensions into the third-order SCC-DFTB code. The first one, the charge model 3 (CM3), corrects for errors in bond dipoles for an improved description of molecular charge distribution as compared to the standard Mulliken partitioning scheme. The second one focuses on the response of the charge density, that is, the electronic molecular polarizability, described inaccurately from SCC-DFTB due to the usage of a minimal atomic orbital basis. Here, a variational approach, based on scaled dipole integrals, was implemented, which clearly outperforms standard finite electric field approaches for polarizability calculations by approximately 1 order of magnitude. Both extensions in the present work rely on a set of empirical parameters, which were fitted against 112 organic molecules to match a reference data set from full density functional calculations with a large basis. As an achievement, notably improved electronic properties, that is, molecular dipole moments and polarizabilities, result from SCC-DFTB calculations at negligible additional computational cost. Furthermore, the accuracy of infrared and Raman intensities was tested as first-order derivatives of the new dipoles and polarizabilities as a function of normal mode vibrations. As a result, the current implementations cannot contribute to an improved prediction of relative intensity pattern from SCC-DFTB as compared to ab initio reference data.

Extended polarization in third-order SCC-DFTB from chemical-potential equalization.

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response properties and has been applied to SCC-DFTB recently. CPE allows this inherent limitation of minimal basis methods to be overcome by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis (i.e., without increasing the overall computational cost significantly). The dependency of polarizability as a function of the molecular charge state, especially, was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional theory methods using large basis sets. However, the first-order derivatives of molecular polarizabilities (e.g., required to compute Raman activities) are not improved by the current CPE implementation (i.e., Raman spectra are not improved).

Proton storage site in bacteriorhodopsin: new insights from quantum mechanics/molecular mechanics simulations of microscopic pK(a) and infrared spectra.

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pK(a) of a hydronium by almost 11 pK(a) units, which is difficult considering known cases of pK(a) shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative "intermolecular proton bond" model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pK(a) values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the "intermolecular proton bond" model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the "intermolecular proton bond" model is likely applicable to the PRG in biomolecular proton pumps in general.

Effect of nitrogen adsorption on the mid-infrared spectrum of water clusters.

Experimental Fourier-transform infrared spectra and DFT calculated infrared spectra are compared to investigate the effect of adsorbed nitrogen on the OH-stretch band complex of water clusters. Using a collisional cooling experiment, pure as well as partially and completely N(2)-covered water clusters consisting of 20-200 water molecules have been generated in thermal equilibrium in the aerosol phase within the temperature range of 5-80 K. Computational IR-spectra simulations have been performed for discrete pure and N(2)-covered water clusters including 10, 15, 20, and 30 water molecules. The adsorbed N(2) molecules especially affect the three-coordinated water molecules at the cluster surface which could be observed as a blue shift of the companion O-H band at 2900 cm(-1) and a red shift of the dangling O-H band at 3700 cm(-1) by about 20 cm(-1) in both cases. The most striking effect of the N(2) adsorbate is an intensity increase of the dangling O-H band by a factor of 3-5. Furthermore, the onset temperature of nitrogen adsorption at the water cluster surface was experimentally found to be roughly 30 K for cluster sizes of about 100 water molecules. Experimental and computational results are in good agreement. The presented results are based on and support the work of V. Buch, J. P. Devlin, and co-workers (e.g., J. Phys. Chem. B, 1997; J. Phys. Chem. A, 2003; Int. Rev. Phys. Chem., 2004).

Automatized parametrization of SCC-DFTB repulsive potentials: application to hydrocarbons.

In this work, we derive and test a new automatized strategy to construct repulsive potentials for the self-consistent charge density functional tight-binding (SCC-DFTB) method. This approach allows one to explore the parameter space in a systematic fashion in order to find optimal solutions. We find that due to the limited flexibility of the SCC-DFTB electronic part, not all properties can be optimized simultaneously. For example, the optimization of heats of formation is in conflict with the optimization of vibrational frequencies. Therefore, a special parametrization for vibrational frequencies is derived. It is shown that the performance of SCC-DFTB can be significantly improved using a more elaborate fitting strategy. A new fit for C and H is presented, which results in an average error of 2.6 kcal/mol for heats of formations for a large set of hydrocarbons, indicating that the performance of SCC-DFTB can be systematically improved also for other elements.

Copper Oxidation/Reduction in Water and Protein: Studies with DFTB3/MM and VALBOND Molecular Dynamics Simulations.

We apply two recently developed computational methods, DFTB3 and VALBOND, to study copper oxidation/reduction processes in solution and protein. The properties of interest include the coordination structure of copper in different oxidation states in water or in a protein (plastocyanin) active site, the reduction potential of the copper ion in different environments, and the environmental response to copper oxidation. The DFTB3/MM and VALBOND simulation results are compared to DFT/MM simulations and experimental results whenever possible. For a copper ion in aqueous solution, DFTB3/MM results are generally close to B3LYP/MM with a medium basis, including both solvation structure and reduction potential for Cu(II); for Cu(I), however, DFTB3/MM finds a two-water coordination, similar to previous Born-Oppenheimer molecular dynamics simulations using BLYP and HSE, whereas B3LYP/MM leads to a tetrahedron coordination. For a tetraammonia copper complex in aqueous solution, VALBOND and DFTB3/MM are consistent in terms of both structural and dynamical properties of solvent near copper for both oxidation states. For copper reduction in plastocyanin, DFTB3/MM simulations capture the key properties of the active site, and the computed reduction potential and reorganization energy are in fair agreement with experiment, especially when the periodic boundary condition is used. Overall, the study supports the value of VALBOND and DFTB3(/MM) for the analysis of fundamental copper redox chemistry in water and protein, and the results also help highlight areas where further improvements in these methods are desirable.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications.

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3-5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

Parameterization of the DFTB3 method for Br, Ca, Cl, F, I, K, and Na in organic and biological systems.

We present an extension to the recent 3OB parametrization of the Density Functional Tight Binding Model DFTB31,2 for biological and organic systems. Parameters for the halogens F, Cl, Br, and I have been developed for use in covalently bound systems and benchmarked on a test set of 106 molecules (the 'OrgX' set), using bonding distances, bonding angles, atomization energies, and vibrational frequencies to assess the performance of the parameters. Additional testing has been done with the X40 set of 40 supramolecular systems containing halogens,3 adding a simple correction for the halogen bonds that are strongly overbound in DFTB3. Furthermore, parameters for Ca, K, and Na as counterions in biological systems have been created. To benchmark geometries as well as ligand binding energies a test set 'BioMe' of 210 molecules has been created that cover coordination to various functional groups frequently occurring in biological systems. The new DFTB3/3OB parameter set outperforms DFT calculations with a double-ζ basis set in terms of energies and can reproduce DFT geometries, with some minor deviations in bond distances and angles due to the use of a minimal basis set.

DFTB3 Parametrization for Copper: The Importance of Orbital Angular Momentum Dependence of Hubbard Parameters.

We report the parametrization of a density functional tight binding method (DFTB3) for copper in a spin-polarized formulation. The parametrization is consistent with the framework of 3OB for main group elements (ONCHPS) and can be readily used for biological applications that involve copper proteins/peptides. The key to our parametrization is to introduce orbital angular momentum dependence of the Hubbard parameter and its charge derivative, thus allowing the 3d and 4s orbitals to adopt different sizes and responses to the change of charge state. The parametrization has been tested by applying to a fairly broad set of molecules of biological relevance, and the properties of interest include optimized geometries, ligand binding energies, and ligand proton affinities. Compared to the reference QM level (B3LYP/aug-cc-pVTZ, which is shown here to be similar to the B97-1 and CCSD(T) results, in terms of many properties of interest for a set of small copper containing molecules), our parametrization generally gives reliable structural properties for both Cu(I) and Cu(II) compounds, although several exceptions are also noted. For energetics, the results are more accurate for neutral ligands than for charged ligands, likely reflecting the minimal basis limitation of DFTB3; the results generally outperform NDDO based methods such as PM6 and even PBE with the 6-31+G(d,p) basis. For all ligand types, single-point B3LYP calculations at DFTB3 geometries give results very close (∼1-2 kcal/mol) to the reference B3LYP values, highlighting the consistency between DFTB3 and B3LYP structures. Possible further developments of the DFTB3 model for a better treatment of transition-metal ions are also discussed. In the current form, our first generation of DFTB3 copper model is expected to be particularly valuable as a method that drives sampling in systems that feature a dynamical copper binding site.

Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications.

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.

Parametrization and Benchmark of DFTB3 for Organic Molecules.

DFTB3 is a recent extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB) and derived from a third order expansion of the density functional theory (DFT) total energy around a given reference density. Being applied in combination with the parametrization of its predecessor (MIO), DFTB3 improves for hydrogen binding energies, proton affinities, and hydrogen transfer barriers. In the present study, parameters especially designed for DFTB3 are presented, and its performance is evaluated for small organic molecules focusing on thermochemistry, geometries, and vibrational frequencies from our own and several databases from literature. The new parameters remove significant overbinding errors, reduce errors for geometries of noncovalent interactions, and improve the overall performance.

Parametrization of the SCC-DFTB Method for Halogens.

Parametrization of the approximative DFT method SCC-DFTB for halogen elements is presented. The new parameter set is intended to describe halogenated organic as well as inorganic molecules, and it is compatible with the established parametrization of SCC-DFTB for carbon, hydrogen, oxygen, and nitrogen. The performance of the parameter set is tested on a representative set of molecules and discussed.

DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB).

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges, and second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.