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.

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.

The polarizable embedding (PE) model is a fragment-based quantum-classical approach aimed at accurate inclusion of environment effects in quantum-mechanical response property calculations. The aim of this tutorial review is to give insight into the practical use of the PE model.Starting from a set of molecular structures and until you arrive at the final property, there are many crucial details to consider in order to obtain trustworthy results in an efficient manner. To lower the threshold for new users wanting to explore the use of the PE model, we describe and discuss important aspects related to its practical use. This includes directions on how to generate input files and how to run a calculation. K E Y W O R D S computational spectroscopy, molecular properties, polarizable embedding, QM/MM, response properties 1 | INTRODUCTION Hybrid quantum-classical approaches for modeling of chemical or biological systems have in recent years gained considerable interest. The reasonfor such popularity of these models relies, to a large degree, on their efficiency and the fact that such models enable calculations on systems of sizes that are otherwise impossible using pure quantum-mechanical methods. The dielectric continuum models belong to the simplest of the quantum-classical approaches, [1,2] and models like the polarizable continuum model [3,4] are today implemented in many of the available electronic-structure programs. In addition, such models are very easy to use: based on a predefined set of atomic radii and the dielectric constant of the solvent, the user can include solvation effects based only on a single calculation. Only one calculation is needed because the dielectric continuum models implicitly include sampling of solvent configurations. On the other hand, it is well-known that the dielectric continuum models possess several drawbacks, such as the inability to model the directionality of specific intermolecular interactions like hydrogen bonding or π-π stacking. Because of this, modeling of environment anisotropies, as found in, for example, protein matrices is lost.Another class of quantum-classical approaches consists of discrete models where the atomistic detail of the environment is kept, that is, models based on the concept of combined quantum mechanics and molecular mechanics (QM/MM). [5][6][7][8] Discrete models, compared to the dielectric continuum models, realistically describe the environment, but at an increased level of both complexity and computational requirements.Regarding the latter point, the increase in computational time is not linked to the discrete nature of the environment as such but rather that

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%. Disciplines Chemistry CommentsReprinted (adapted) ABSTRACT: 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%. INTRODUCTIONModern computational chemistry methods strive to accurately model chemical systems using efficient computational algorithms. Unfortunately, it is difficult to reconcile both of these goals, since most methods that are widely viewed as the most accurate 1 also require the most computational effort. A very effective compromise is the application of fragmentation approaches to these computationally intensive methods. Many such fragmentation methods have been introduced in recent years, 2−8 with several showing the ability to accurately model large molecular systems. Methods such as the systematic molecular fragmentation (SMF) method, 9−11 molecular fractionation with conjugate caps (MFCC), 12 the molecular tailoring approach (MTA), 13 and the explicit polarization potential (X-Pol) 14,15 have all exhibited success in describing different chemical systems.One such method, the fragment molecular orbital (FMO) method, 16 has been extensively developed 17 since the original implementation by Kitaura et al. Based upon a many-body expansion of the energy, the FMO method takes the effects of the entire system into account during each step of a given calculation through the use of an electrostatic potential (ESP). The FMO method, as well as other fragmentation methods, 18 also benefit from the relative ease with which calculations can be parallelized on modern computer architectures. This inherent parallelizability aids in lowering the computational cost of the most accurate ab initio methods.While not a fragmentation method in the same vein as the FMO method, the effective fragment potential (EFP) method 19−21 wa...

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.

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

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.

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.