Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

Multiscale electrostatic embedding simulations for modeling structure and dynamics of molecules in solution: A tutorial review

The main concepts and important technical details of electrostatic embedding quantum mechanics/molecular mechanics (QM/MM) simulations are explained and illustrated with the intent of assisting newcomers in performing and gauging the accuracy of such simulations, focused on smaller molecules in solution. Beginners are advised on how to increase the reliability and accuracy of the simulations through benchmarking. Central considerations on methodologies for QM/MM Molecular Dynamics (MD) simulations are presented, alongside technical fundamentals regarding the construction and manipulation of simulation systems using the python-based Atomic Simulation Environment (ASE). A worked example of QM/MM Born–Oppenheimer MD is included, and a flowchart summarizing the most salient decisions and tasks within the methodology is presented.     

Quantum embedding for material chemistry based on domain separation and open subsystems

This perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain-separated density functional theory (DS-DFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS-DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment-based embedding, which offers computational advantages to study intermolecular behavior such as electron hopping, spin-environment interaction, and charge-transfer excitations. However, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We explore paths to determine the charge-transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wave function-based embedding.     

Multipole moments for embedding potentials: Exploring different atomic allocation algorithms

Polarizable quantum mechanical (QM)/molecular mechanics (MM)‐embedding methods are currently among the most promising methods for computationally feasible, yet reliable, production calculations of localized excitations and molecular response properties of large molecular complexes, such as proteins and RNA/DNA, and of molecules in solution. Our aim is to develop a computational methodology for distributed multipole moments and their associated multipole polarizabilities which is accurate, computationally efficient, and with smooth convergence with respect to multipole order. As the first step toward this goal, we herein investigate different ways of obtaining distributed atom‐centered multipole moments that are used in the construction of the electrostatic part of the embedding potential. Our objective is methods that not only are accurate and computationally efficient, but which can be consistently extended with site polarizabilities including internal charge transfer terms. We present a new way of dealing with well‐known problems in relation to the use of basis sets with diffuse functions in conventional atomic allocation algorithms, avoiding numerical integration schemes. Using this approach, we show that the classical embedding potential can be systematically improved, also when using basis sets with diffuse functions, and that very accurate embedding potentials suitable for QM/MM embedding calculations can be acquired. © 2016 Wiley Periodicals, Inc.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

Modeling of phytochrome absorption spectra

Phytochromes constitute one of the six well‐characterized families of photosensory proteins in Nature. From the viewpoint of computational modeling, however, phytochromes have been the subject of much fewer studies than most other families of photosensory proteins, which is likely a consequence of relevant high‐resolution structural data becoming available only in recent years. In this work, hybrid quantum mechanics/molecular mechanics (QM/MM) methods are used to calculate UV‐vis absorption spectra of Deinococcus radiodurans bacteriophytochrome. We investigate how the choice of QM/MM methodology affects the resulting spectra and demonstrate that QM/MM methods can reproduce the experimental absorption maxima of both the Q and Soret bands with an accuracy of about 0.15 eV. Furthermore, we assess how the protein environment influences the intrinsic absorption of the bilin chromophore, with particular focus on the Q band underlying the primary photochemistry of phytochromes. © 2013 Wiley Periodicals, Inc.     

Coupled‐cluster frozen‐density embedding using resolution of the identity methods

Frozen‐density embedding (FDE) is combined with resolution of the identity (RI) Hartree–Fock and a RI‐variant of a second‐order approximate coupled‐cluster singles and doubles (RI‐CC2) to determine solvatochromic shifts for the lowest excitation energy of acetone and pyridazine, respectively, each solvated in different environments with total system sizes of about 2.5 nm diameter. The combination of FDE and RI‐CC2 increases efficiency and enables the calculation of numerous snapshots with 100 to 300 molecules, also allowing for larger basis sets as well as diffuse functions needed for an accurate treatment of properties. The maximum errors in the solvatochromic shifts amount up to 0.2 eV, which are similar to other approximated studies in the literature. © 2014 Wiley Periodicals, Inc.     

Wave‐function frozen‐density embedding: Approximate analytical nuclear ground‐state gradients

We report the derivation of approximate analytical nuclear ground‐state uncoupled frozen density embedding (FDEu) gradients for the resolution of identity (RI) variant of the second‐order approximate coupled cluster singles and doubles (RICC2) as well as density functional theory (DFT), and an efficient implementation thereof in the KOALA program. In order to guarantee a computationally efficient treatment, those gradient terms are neglected which would require the exchange of orbital information. This approach allows for geometry optimizations of single molecules surrounded by numerous molecules with fixed nuclei at RICC2‐in‐RICC2, RICC2‐in‐DFT, and DFT‐in‐DFT FDE level of theory using a dispersion correction, required due to the DFT‐based treatment of the interaction in FDE theory. Accuracy and applicability are assessed by the example of two case studies: (a) the Watson‐Crick pair adenine‐thymine, for which the optimized structures exhibit a maximum error of about 0.08 Å for our best scheme compared to supermolecular reference calculations, (b) carbon monoxide on a magnesium oxide surface model, for which the error amount up to 0.1 Å for our best scheme. Efficiency is demonstrated by successively including environment molecules and comparing to an optimized conventional supermolecular implementation, showing that the method is able to outperform conventional RICC2 schemes already with a rather small number of environment molecules, gaining significant speed up in computation time. © 2016 Wiley Periodicals, Inc.     

Influence of the protein and DFT method on the broken‐symmetry and spin states in nitrogenase

The enzyme nitrogenase contains a complicated MoFe₇CS₉ cofactor with 35 possible broken‐symmetry (BS) states. We have studied how the energies of these states depend on the geometry, the surrounding protein, the DFT functional and the basis set, studying the resting state, a one‐electron reduced state and a protonated state. We find that the effect of the basis set is small, up to 11 kJ/mol. Likewise, the effect of the surrounding protein is restricted, up to 10 and 7 kJ/mol for the electrostatic and van der Waals energy terms. Single‐point energies calculated on a single geometry give a good correlation (R² = 0.92‐0.98) to energies calculated after geometry optimization, but some BS states may be disfavored by up to 37 kJ/mol. A change from the pure TPSS functional to the hybrid B3LYP functional may change the relative energies by up to 58 kJ/mol and the correlation between the two results is only 0.57‐0.72. Both functionals agree that BS7 is the most stable BS state and that the ground spin state is the quartet for the resting state and the quintet for the reduced state. With the TPSS functional, the BS6 state is the second most stable state, always at least 21 kJ/mol less stable than the BS7 state. However, with the B3LYP functional, BS10 is the second most stable state and for the protonated state it comes close in energy. Based on these results, we suggest a procedure how to consider the 35 BS states in future investigations of the nitrogenase reaction mechanism.     

Virial relations in density embedding

The accuracy of charge-transfer excitation energies, solvatochromic shifts, and other environmental effects calculated via various density-embedding techniques depend critically on the approximations employed for the nonadditive noninteracting kinetic energy functional, . Approximating this functional remains an important challenge in electronic-structure theory. To assist in the development and testing of approximations for , we derive two virial relations for fragments in molecules. These establish separate connections between the nonadditive kinetic energies of the noninteracting and interacting systems of electrons, and quantities such as the electron-nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn-Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules.     

Response properties of embedded molecules through the polarizable embedding model

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.     

Efficient determination of accurate atomic polarizabilities for polarizeable embedding calculations

We evaluate embedding potentials, obtained via various methods, used for polarizable embedding computations of excitation energies of para‐nitroaniline in water and organic solvents as well as of the green fluorescent protein. We found that isotropic polarizabilities derived from DFTD3 dispersion coefficients correlate well with those obtained via the LoProp method. We show that these polarizabilities in conjunction with appropriately derived point charges are in good agreement with calculations employing static multipole moments up to quadrupoles and anisotropic polarizabilities for both computed systems. The (partial) use of these easily‐accessible parameters drastically reduces the computational effort to obtain accurate embedding potentials especially for proteins. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

QM/MM vibrational mode tracking

Vibrational spectroscopy is a powerful tool to investigate the structure and dynamics of biomolecules. When small subsystems of large molecules such as active centers of enzymes are studied, quantum chemical calculations based on quantum mechanics/molecular mechanics (QM/MM) coupling schemes are a valuable means to interpret the spectra. The goal of this work is a methodological pilot study on how to selectively and thus efficiently extract certain vibrational information for extended molecular systems described by QM/MM methods. This is achieved by an extension of the mode tracking algorithm and a comparison with the partial Hessian diagonalization approach. After validating the methodology for the CO stretching vibration of 2-butanone and a delocalized CO stretch in acetylacetone, the stretching and bending modes of the CO ligand in CO myoglobin are tracked. Such systems represent an ideal application for mode tracking, because only a few strongly localized vibrations are sought for, while the large remainder of the molecule is of interest only as far as it affects these local vibrations. This influence is treated exactly by mode tracking.     

Serenity: A subsystem quantum chemistry program

We present the new quantum chemistry program Serenity . It implements a wide variety of functionalities with a focus on subsystem methodology. The modular code structure in combination with publicly available external tools and particular design concepts ensures extensibility and robustness with a focus on the needs of a subsystem program. Several important features of the program are exemplified with sample calculations with subsystem density‐functional theory, potential reconstruction techniques, a projection‐based embedding approach and combinations thereof with geometry optimization, semi‐numerical frequency calculations and linear‐response time‐dependent density‐functional theory. © 2018 Wiley Periodicals, Inc.     

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER–HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single‐point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo‐bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.     

Conformational preference and mechanism of decarboxylation of levodopa. A quantum dynamics/quantum mechanics study

The present study addresses the conformational preferences and the mechanism of decarboxylation of levodopa (LD). LD is used to increase dopamine concentrations in the treatment of Parkinson's disease. LD crosses the protective blood–brain barrier, where it is converted into dopamine by the process of decarboxylation. Molecular dynamics simulation has been carried out at the DFT/6‐31++G level of theory to identify the global minimum structure of LD. Conformational preferences of the amino acid side chain of LD has been investigated at the B3LYP/6‐311++G** level of theory. Fourier transform analysis has been performed to identify the origin of the rotational barriers. Electrostatic dipole moment and bond interactions underlie the observed potential energy barriers for rotation of the amino acid side chain of LD. The vital biological process of decarboxylation of LD has been examined in the gas phase and in aqueous solution. Without the presence of water, there is only one possible route for the decarboxylation of LD. In this concerted mechanism, a proton transfer and breakage of the C₁₀—C₁₈ bond, take place simultaneously (ΔE^# = 73.2 kcal/mol). In solution, however, two possible decarboxylation routes are available for LD. The first involve the formation of a zwitterionic intermediate (ΔE^# = 72.4 kcal/mol). The zwitterionic form of LD have been localized using explicitly bound water molecules to model short‐range solvent effects and self‐consistent reaction field polarized continuum model to estimate long‐range solvent interactions. The second route involve the formation of a cyclic structure in which a water molecule acts as a bridge linking the anticarboxylic hydrogen and α‐position carbon atom (ΔE^# = 59.8 kcal/mol). Natural bond orbital (NBO) analysis reveals that the conformational and overall stability of the amino acid side chain is facilitated by the antiperiplanar interactions between the phenyl moiety C—H and C—C bonds and C—X bonds of the amino acid side chain. However, much of the major donor–acceptor interactions is of the lone pair type and is localized within the amino acid side chain itself. Results of the present work reveal that NBO data reflect nicely and identify clearly reaction coordinates at the transition species. © 2013 Wiley Periodicals, Inc.     

Computational mutation analysis of hydrogen abstraction and radical rearrangement steps in the catalysis of coenzyme B12-dependent diol dehydratase

A mutation analysis of the catalytic functions of active-site residues of coenzyme B(12)-dependent diol dehydratase in the conversion of 1,2-propanediol to 1,1-propanediol has been carried out by using QM/MM computations. Mutants His143Ala, Glu170Gln, Glu170Ala, and Glu170Ala/Glu221Ala were considered to estimate the impact of the mutations of His143 and Glu170. In the His143Ala mutant the activation energy for OH migration increased to 16.4 from 11.5 kcal mol(-1) in the wild-type enzyme. The highest activation energy, 19.6 kcal mol(-1), was measured for hydrogen back-abstraction in this reaction. The transition state for OH migration is not sufficiently stabilized by the hydrogen-bonding interaction formed between the spectator OH group and Gln170 in the Glu170Gln mutant, which demonstrates that a strong proton acceptor is required to promote OH migration. In the Glu170Ala mutant, a new strong hydrogen bond is formed between the spectator OH group and Glu221. A computed activation energy of 13.6 kcal mol(-1) for OH migration in the Glu170Ala mutant is only 2.1 kcal mol(-1) higher than the corresponding barrier in the wild-type enzyme. Despite the low activation barrier, the Glu170Ala mutant is inactive because the subsequent hydrogen back-abstraction is energetically demanding in this mutant. OH migration is not feasible in the Glu170Ala/Glu221Ala mutant because the activation barrier for OH migration is greatly increased by the loss of COO(-) groups near the spectator OH group. This result indicates that the effect of partial deprotonation of the spectator OH group is the most important factor in reducing the activation barrier for OH migration in the conversion of 1,2-propanediol to 1,1-propanediol catalyzed by diol dehydratase.