Casper Steinmann

Effective Fragment Molecular Orbital Method: A Merger of the Effective Fragment Potential and Fragment Molecular Orbital Methods†

We present a new method called the effective fragment molecular orbital (EFMO) method. The EFMO method is a hybrid between the fragment molecular orbital (FMO) electronic structure method ( Kitaura , K. ; Ikeo , E. ; Asada , T. ; Nakano , T. ; Uebayasi , M. Chem. Phys. Lett. 1999 , 313 , 701 - 706 ) and the effective fragment potential multipole-based polarizable force field ( Day , P. N. ; Jensen , J. H. ; Gordon , M. S. ; Webb , S. P. ; Stevens , W. J. ; Krauss , M. ; Garmer , D. ; Basch , H. ; Cohen , D. J. Chem. Phys. 1996 , 105 , 1968 - 1986 ). The EFMO method is based on the FMO molecular fragmentation scheme and the many-body energy expression but uses the EFP multipole-based energy expressions for long-range interactions and for evaluating the many-body polarization. The accuracy and performance of the EFMO method is compared to FMO and conventional electronic structure theory for water clusters. The difference in the EFMO energy compared to that of conventional Hartree-Fock theory is roughly 0.5 kcal/mol per hydrogen using the 6-31G(d) basis set but less than 0.1 kcal/mol using the 6-31+G(d) basis set. The EFMO method is roughly two times faster than the FMO2 method using Hartree-Fock and five times when computing Hartree-Fock energy and gradients; preliminary density functional theory results are also presented.

Fully Integrated Effective Fragment Molecular Orbital Method.

In this work, the effective fragment potential (EFP) method is fully integrated (FI) into the fragment molecular orbital (FMO) method to produce an effective fragment molecular orbital (EFMO) method that is able to account for all of the fundamental types of both bonded and intermolecular interactions, including many-body effects, in an accurate and efficient manner. The accuracy of the method is tested and compared to both the standard FMO method as well as to fully ab initio methods. It is shown that the FIEFMO method provides significant reductions in error while at the same time reducing the computational cost associated with standard FMO calculations by up to 96%.

FragIt: A Tool to Prepare Input Files for Fragment Based Quantum Chemical Calculations

Near linear scaling fragment based quantum chemical calculations are becoming increasingly popular for treating large systems with high accuracy and is an active field of research. However, it remains difficult to set up these calculations without expert knowledge. To facilitate the use of such methods, software tools need to be available to support these methods and help to set up reasonable input files which will lower the barrier of entry for usage by non-experts. Previous tools relies on specific annotations in structure files for automatic and successful fragmentation such as residues in PDB files. We present a general fragmentation methodology and accompanying tools called FragIt to help setup these calculations. FragIt uses the SMARTS language to locate chemically appropriate fragments in large structures and is applicable to fragmentation of any molecular system given suitable SMARTS patterns. We present SMARTS patterns of fragmentation for proteins, DNA and polysaccharides, specifically for D-galactopyranose for use in cyclodextrins. FragIt is used to prepare input files for the Fragment Molecular Orbital method in the GAMESS program package, but can be extended to other computational methods easily.

Polarizable Density Embedding: A New QM/QM/MM-Based Computational Strategy

We present a new QM/QM/MM-based model for calculating molecular properties and excited states of solute-solvent systems. We denote this new approach the polarizable density embedding (PDE) model, and it represents an extension of our previously developed polarizable embedding (PE) strategy. The PDE model is a focused computational approach in which a core region of the system studied is represented by a quantum-chemical method, whereas the environment is divided into two other regions: an inner and an outer region. Molecules belonging to the inner region are described by their exact densities, whereas molecules in the outer region are treated using a multipole expansion. In addition, all molecules in the environment are assigned distributed polarizabilities in order to account for induction effects. The joint effects of the inner and outer regions on the quantum-mechanical core part of the system is formulated using an embedding potential. The PDE model is illustrated for a set of dimers (interaction energy calculations) as well as for the calculation of electronic excitation energies, showing promising results.

Nuclear Magnetic Shielding Constants from Quantum Mechanical/Molecular Mechanical Calculations Using Polarizable Embedding: Role of the Embedding Potential.

We present NMR shielding constants obtained through quantum mechanical/molecular mechanical (QM/MM) embedding calculations. Contrary to previous reports, we show that a relatively small QM region is sufficient, provided that a high-quality embedding potential is used. The calculated averaged NMR shielding constants of both acrolein and acetone solvated in water are based on a number of snapshots extracted from classical molecular dynamics simulations. We focus on the carbonyl chromophore in both molecules, which shows large solvation effects, and we study the convergence of shielding constants with respect to total system size and size of the QM region. By using a high-quality embedding potential over standard point charge potentials, we show that the QM region can be made at least 2 Å smaller without any loss of quality, which makes calculations on ensembles tractable by conventional density functional theory calculations.

A third-generation dispersion and third-generation hydrogen bonding corrected PM6 method: PM6-D3H+.

We present new dispersion and hydrogen bond corrections to the PM6 method, PM6-D3H+, and its implementation in the GAMESS program. The method combines the DFT-D3 dispersion correction by Grimme et al. with a modified version of the H+ hydrogen bond correction by Korth. Overall, the interaction energy of PM6-D3H+ is very similar to PM6-DH2 and PM6-DH+, with RMSD and MAD values within 0.02 kcal/mol of one another. The main difference is that the geometry optimizations of 88 complexes result in 82, 6, 0, and 0 geometries with 0, 1, 2, and 3 or more imaginary frequencies using PM6-D3H+ implemented in GAMESS, while the corresponding numbers for PM6-DH+ implemented in MOPAC are 54, 17, 15, and 2. The PM6-D3H+ method as implemented in GAMESS offers an attractive alternative to PM6-DH+ in MOPAC in cases where the LBFGS optimizer must be used and a vibrational analysis is needed, e.g., when computing vibrational free energies. While the GAMESS implementation is up to 10 times slower for geometry optimizations of proteins in bulk solvent, compared to MOPAC, it is sufficiently fast to make geometry optimizations of small proteins practically feasible.

Mapping Enzymatic Catalysis Using the Effective Fragment Molecular Orbital Method: Towards all ab initio Biochemistry

We extend the Effective Fragment Molecular Orbital (EFMO) method to the frozen domain approach where only the geometry of an active part is optimized, while the many-body polarization effects are considered for the whole system. The new approach efficiently mapped out the entire reaction path of chorismate mutase in less than four days using 80 cores on 20 nodes, where the whole system containing 2398 atoms is treated in the ab initio fashion without using any force fields. The reaction path is constructed automatically with the only assumption of defining the reaction coordinate a priori. We determine the reaction barrier of chorismate mutase to be kcal mol−1 for MP2/cc-pVDZ and for MP2/cc-pVTZ in an ONIOM approach using EFMO-RHF/6-31G(d) for the high and low layers, respectively.

The Effective Fragment Molecular Orbital Method for Fragments Connected by Covalent Bonds

We extend the effective fragment molecular orbital method (EFMO) into treating fragments connected by covalent bonds. The accuracy of EFMO is compared to FMO and conventional ab initio electronic structure methods for polypeptides including proteins. Errors in energy for RHF and MP2 are within 2 kcal/mol for neutral polypeptides and 6 kcal/mol for charged polypeptides similar to FMO but obtained two to five times faster. For proteins, the errors are also within a few kcal/mol of the FMO results. We developed both the RHF and MP2 gradient for EFMO. Compared to ab initio, the EFMO optimized structures had an RMSD of 0.40 and 0.44 Å for RHF and MP2, respectively.

Electronic Energy Transfer in Polarizable Heterogeneous Environments: A Systematic Investigation of Different Quantum Chemical Approaches.

Theoretical prediction of transport and optical properties of protein-pigment complexes is of significant importance when aiming at understanding the structure-function relationship in such systems. Electronic energy transfer (EET) couplings represent a key property in this respect since such couplings provide important insight into the strength of interaction between photoactive pigments in protein-pigment complexes. Recently, attention has been payed to how the environment modifies or even controls the electronic couplings. To enable such theoretical predictions, a fully polarizable embedding model has been suggested (Curutchet, C., et al. J. Chem. Theory Comput., 2009, 5, 1838-1848). In this work, we further develop this computational model by extending it with an ab initio derived polarizable force field including higher-order multipole moments. We use this extended model to systematically examine three different ways of obtaining EET couplings in a heterogeneous medium ranging from use of the exact transition density to a point-dipole approximation. Several interesting observations are made, for example, the explicit use of transition densities in the calculation of the electronic couplings, and also when including the explicit environment contribution, can be replaced by a much simpler transition point charge description without comprising the quality of the model predictions.

Inhibitor ranking through QM based chelation calculations for virtual screening of HIV-1 RNase H inhibition.

Quantum mechanical (QM) calculations have been used to predict the binding affinity of a set of ligands towards HIV-1 RT associated RNase H (RNH). The QM based chelation calculations show improved binding affinity prediction for the inhibitors compared to using an empirical scoring function. Furthermore, full protein fragment molecular orbital (FMO) calculations were conducted and subsequently analysed for individual residue stabilization/destabilization energy contributions to the overall binding affinity in order to better understand the true and false predictions. After a successful assessment of the methods based on the use of a training set of molecules, QM based chelation calculations were used as filter in virtual screening of compounds in the ZINC database. By this, we find, compared to regular docking, QM based chelation calculations to significantly reduce the large number of false positives. Thus, the computational models tested in this study could be useful as high throughput filters for searching HIV-1 RNase H active-site molecules in the virtual screening process.