Thomas Frauenheim

Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment

We extend an approximate density functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irrespective of the correlation function applied. An empirical formula, consisting of an R−6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coefficient, which is calculated from experimental atomic polarizabilities, can be consistently added to the total energy expression of the method. We apply this approximate DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.

Atomistic simulations of complex materials: ground-state and excited-state properties

The present status of development of the density-functional-based tightbinding (DFTB) method is reviewed. As a two-centre approach to densityfunctional theory (DFT), it combines computational efficiency with reliability and transferability. Utilizing a minimal-basis representation of Kohn–Sham eigenstates and a superposition of optimized neutral-atom potentials and related charge densities for constructing the effective many-atom potential, all integrals are calculated within DFT. Self-consistency is included at the level of Mulliken charges rather than by self-consistently iterating electronic spin densities and effective potentials. Excited-state properties are accessible within the linear response approach to time-dependent (TD) DFT. The coupling of electronic and ionic degrees of freedom further allows us to follow the non-adiabatic structure evolution via coupled electron–ion molecular dynamics in energetic particle collisions and in the presence of ultrashort intense laser pulses. We either briefly outline or give references describing examples of applications to ground-state and excited-state properties. Addressing the scaling problems in size and time generally and for biomolecular systems in particular, we describe the implementation of the parallel ‘divide-and-conquer’ order-N method with DFTB and the coupling of the DFTB approach as a quantum method with molecular mechanics force fields.

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.

An approximate DFT method for QM/MM simulations of biological structures and processes

In the last years, we have developed a computationally efficient approximation to density functional theory, the so called self-consistent charge density functional tight-binding scheme (SCC-DFTB). To extend its applicability to biomolecular structures, this method has been implemented into quantum mechanical/molecular mechanics (QM/MM) and linear scaling schemes and augmented with an empirical treatment of the dispersion forces. We review here applications of the SCC-DFTB QM/MM method to proton transfer (PT) reactions in enzymes like liver alcohol dehydrogenase and triosephosphate isomerase. The computational speed of SCC-DFTB allows not only to compute minimum energy pathways for the PT but also the potential of mean force. Further applications concern the dynamics of polypeptides in solution and of ligands in their biological environment. The developments reviewed allowed for the first time realistic QM simulations of polypeptides, a protein and a DNA dodecamer in the nanosecond time scale.

Quantum mechanics simulation of protein dynamics on long timescale.

Protein structure and dynamics are the keys to a wide range of problems in biology. In principle, both can be fully understood by using quantum mechanics as the ultimate tool to unveil the molecular interactions involved. Indeed, quantum mechanics of atoms and molecules have come to play a central role in chemistry and physics. In practice, however, direct application of quantum mechanics to protein systems has been prohibited by the large molecular size of proteins. As a consequence, there is no general quantum mechanical treatment that not only exceeds the accuracy of state‐of‐the‐art empirical models for proteins but also maintains the efficiency needed for extensive sampling in the conformational space, a requirement mandated by the complexity of protein systems. Here we show that, given recent developments in methods, a general quantum mechanical‐based treatment can be constructed. We report a molecular dynamics simulation of a protein, crambin, in solution for 350 ps in which we combine a semiempirical quantum‐mechanical description of the entire protein with a description of the surrounding solvent, and solvent‐protein interactions based on a molecular mechanics force field. Comparison with a recent very high‐resolution crystal structure of crambin (Jelsch et al., Proc Natl Acad Sci USA 2000;102:2246–2251 ) shows that geometrical detail is better reproduced in this simulation than when several alternate molecular mechanics force fields are used to describe the entire system of protein and solvent, even though the structure is no less flexible. Individual atomic charges deviate in both directions from “canonical” values, and some charge transfer is found between the N and C‐termini. The capability of simulating protein dynamics on and beyond the few hundred ps timescale with a demonstrably accurate quantum mechanical model will bring new opportunities to extend our understanding of a range of basic processes in biology such as molecular recognition and enzyme catalysis. Proteins 2001;44:484–489.

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.

Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB, AM1 and PM3 methods in comparison with DFT, HF and MP2 calculations

We calculate relative energies and geometries of important secondary structural elements for small glycine and alanine based polypeptides containing up to eight residues. We compare the performance of the approximate methods AM1, PM3 and self-consistent charge, density-functional tight-binding (SCC-DFTB) to density-functional theory (DFT), Hartree‐Fock (HF) and MP2. The SCC-DFTB is able to reproduce structures and relative energies of various peptide models reliably compared to DFT results. The AM1 and PM3 methods show deficiencies in describing important secondary structure elements like extended, helical or turn structures. The discrepancies between diAerent ab initio (HF, MP2) and DFT (B3LYP) methods for medium sized basis sets (6-31G*) also show the need for higher level calculations, since systematic errors found for small molecules may add up when investigating longer polypeptides. ” 2001 Elsevier Science B.V. All rights reserved.

Validation of the density-functional based tight-binding approximation method for the calculation of reaction energies and other data

We investigated the performance of the approximative density functional method DFTB versus BLYP and G2 with respect to zero-point corrected reaction energies, vibrational frequencies, and geometry parameters for a set of 28 reactions and 22 representative molecules containing C, H, N, and O (DFTB--density-functional based tight-binding approximation). The DFTB reaction energies show a mean absolute deviation versus the G2 reference of 4.3 kcalmol only. The corresponding value for the vibrational frequencies amounts to 75 cm(-1) versus BLYP/cc-pVTZ. With very few exceptions bond lengths and angles are in excellent agreement with the results of higher-level methods.

Understanding the inelastic electron-tunneling spectra of alkanedithiols on gold

We present results for a simulated inelastic electron-tunneling spectra (IETS) from calculations using the gDFTB code. The geometric and electronic structure is obtained from calculations using a local-basis density-functional scheme, and a nonequilibrium Greens function formalism is employed to deal with the transport aspects of the problem. The calculated spectrum of octanedithiol on gold(111) shows good agreement with experimental results and suggests further details in the assignment of such spectra. We show that some low-energy peaks, unassigned in the experimental spectrum, occur in a region where a number of molecular modes are predicted to be active, suggesting that these modes are the cause of the peaks rather than a matrix signal, as previously postulated. The simulations also reveal the qualitative nature of the processes dominating IETS. It is highly sensitive only to the vibrational motions that occur in the regions of the molecule where there is electron density in the low-voltage conduction channel. This result is illustrated with an examination of the predicted variation of IETS with binding site and alkane chain length.

Performance of the AM1, PM3, and SCC-DFTB methods in the study of conjugated Schiff base molecules

Abstract In this work, we study the performance of approximate quantum mechanical methods AM1, PM3 and SCC-DFTB in their description of conjugated Schiff base (SBn) models. The structure, isomerization barriers and proton affinities have been calculated in several different models of the retinal SBn, including different lengths of the polyene chain and different alkyl substitutions. Furthermore, the external effects originating from the protein environment of bacteriorhodopsin (bR) have also been investigated. Comparison of the results with those obtained from DFT calculations clearly indicates that the SCC-DFTB method can be considered as a promising method for the examination of these molecules and for explicitly including large parts of the protein environment in the calculations. While structures are well described by PM3, it largely underestimates rotational barriers.