QM/MM modeling of enantioselective pybox-ruthenium- and box-copper-catalyzed cyclopropanation reactions: scope, performance, and applications to ligand design

An extensive comparison of full-QM (B3LYP) and QM/MM (B3LYP:UFF) levels of theory has been made for two enantioselective catalytic systems, namely, Pybox-Ru and Box-Cu complexes, in the cyclopropanation of alkenes (ethylene and styrene) with methyl diazoacetate. The geometries of the key reaction intermediates and transition structures calculated at the QM/MM level are generally in satisfactory agreement with full-QM calculated geometries. More importantly, the relative energies calculated at the QM/MM level are in good agreement with those calculated at the full-QM level in all cases. Furthermore, the QM/MM energies are often in better agreement with the stereoselectivity experimentally observed, and this suggests that QM/MM calculations can be superior to full-QM calculations when subtle differences in inter- and intramolecular interactions are important in determining the selectivity, as is the case in enantioselective catalysis. The predictive value of the model presented is validated by the explanation of the unusual enantioselectivity behavior exhibited by a new bis-oxazoline ligand, the stereogenic centers of which are quaternary carbon atoms.     

Spectral tuning in visual pigments: an ONIOM(QM:MM) study on bovine rhodopsin and its mutants

We have investigated geometries and excitation energies of bovine rhodopsin and some of its mutants by hybrid quantum mechanical/molecular mechanical (QM/MM) calculations in ONIOM scheme, employing B3LYP and BLYP density functionals as well as DFTB method for the QM part and AMBER force field for the MM part. QM/MM geometries of the protonated Schiff-base 11- cis-retinal with B3LYP and DFTB are very similar to each other. TD-B3LYP/MM excitation energy calculations reproduce the experimental absorption maximum of 500 nm in the presence of native rhodopsin environment and predict spectral shifts due to mutations within 10 nm, whereas TD-BLYP/MM excitation energies have red-shift error of at least 50 nm. In the wild-type rhodopsin, Glu113 shifts the first excitation energy to blue and accounts for most of the shift found. Other amino acids individually contribute to the first excitation energy but their net effect is small. The electronic polarization effect is essential for reproducing experimental bond length alternation along the polyene chain in protonated Schiff-base retinal, which correlates with the computed first excitation energy. It also corrects the excitation energies and spectral shifts in mutants, more effectively for deprotonated Schiff-base retinal than for the protonated form. The protonation state and conformation of mutated residues affect electronic spectrum significantly. The present QM/MM calculations estimate not only the experimental excitation energies but also the source of spectral shifts in mutants.     

Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential

A combined DFT quantum mechanical and AMBER molecular mechanical potential (QM/MM) is presented for use in molecular modeling and molecular simulations of large biological systems. In our approach we evaluate Lennard-Jones parameters describing the interaction between the quantum mechanical (QM) part of a system, which is described at the B3LYP/6-31+G* level of theory, and the molecular mechanical (MM) part of the system, described by the AMBER force field. The Lennard-Jones parameters for this potential are obtained by calculating hydrogen bond energies and hydrogen bond geometries for a large set of bimolecular systems, in which one hydrogen bond monomer is described quantum mechanically and the other is treated molecular mechanically. We have investigated more than 100 different bimolecular systems, finding very good agreement between hydrogen bond energies and geometries obtained from the combined QM/MM calculations and results obtained at the QM level of theory, especially with respect to geometry. Therefore, based on the Lennard-Jones parameters obtained in our study, we anticipate that the B3LYP/6-31+G*/AMBER potential will be a precise tool to explore intermolecular interactions inside a protein environment.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Combined quantum mechanical/molecular mechanical study on the pentacoordinated ferric and ferrous cytochrome P450cam complexes

The pentacoordinated ferric and ferrous cytochrome P450(cam) complexes have been investigated by combined quantum mechanical/molecular mechanical (QM/MM) calculations in the presence of a protein/solvent environment and by QM calculations on the isolated QM regions with use of density functional theory. The B3LYP functional has been found more reliable than the BLYP and BHLYP functionals for estimating the relative state energies. The B3LYP/CHARMM calculations with an all-electron basis set for iron give high-spin ground states for the title complexes, in agreement with experiment. The comparison of the B3LYP/CHARMM results of the entire protein system with the B3LYP calculations on the naked QM regions shows that the amount of stabilization by the protein environment is largest for the intermediate-spin states, followed by the high-spin states of the complexes. The calculation of M?ssbauer parameters in the presence of the enzyme environment confirms the double occupation of the d(xz) orbital in the quintet spin state of the ferrous complex, consistent with the computed QM/MM energies in the enzyme environment, while the d(x)2(-)(y)2 orbital is doubly occupied in the gas-phase quintet state.     

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Contributions of pauli repulsions to the energetics and physical properties computed in QM/MM methods

Conventional combined quantum mechanical/molecular mechanical (QM/MM) methods lack explicit treatment of Pauli repulsions between the quantum‐mechanical and molecular‐mechanical subsystems. Instead, classical Lennard‐Jones (LJ) potentials between QM and MM nuclei are used to model electronic Pauli repulsion and long‐range London dispersion, despite the fact that the latter two are inherently of quantum nature. Use of the simple LJ potential in QM/MM methods can reproduce minimal geometries and energies of many molecular clusters reasonably well, as compared to full QM calculations. However, we show here that the LJ potential cannot correctly describe subtle details of the electron density of the QM subsystem because of the neglect of Pauli repulsions between the QM and MM subsystems. The inaccurate electron density subsequently affects the calculation of electronic and magnetic properties of the QM subsystem. To explicitly consider Pauli interactions with QM/MM methods, we propose a method to use empirical effective potentials on the MM atoms. The test case of the binding energy and magnetic properties of a water dimer shows promising results for the general application of effective potentials to mimic Pauli repulsions in QM/MM calculations. © 2013 Wiley Periodicals, Inc.     

YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model

A simple interface is proposed for combined quantum mechanical (QM) molecular mechanical (MM) calculations for the systems where the QM and MM regions are connected through covalent bonds. Within this model, the atom that connects the two regions, called YinYang atom here, serves as an ordinary MM atom to other MM atoms and as a hydrogen-like atom to other QM atoms. Only one new empirical parameter is introduced to adjust the length of the connecting bond and is calibrated with the molecule propanol. This model is tested with the computation of equilibrium geometries and protonation energies for dozens of molecules. Special attention is paid on the influence of MM point charges on optimized geometry and protonation energy, and it is found that it is important to maintain local charge-neutrality in the MM region in order for the accurate calculation of the protonation and deprotonation energies. Overall the simple YinYang atom model yields comparable results to some other QM/MM models.     

QM/MM modeling of benzene hydroxylation in human cytochrome P450 2C9

The mechanism of benzene hydroxylation was investigated in the realistic enzyme environment of the human CYP 2C9 by using quantum mechanical/molecular mechanical (QM/MM) calculations of the whole reaction profile using the B3LYP method to describe the QM region. The calculated QM/MM barriers for addition of the active species Compound I to benzene are consistent with experimental rate constants for benzene metabolism in CYP 2E1. In contrast to gas-phase model calculations, our results suggest that competing side-on and face-on geometries of arene addition may both occur in the case of aromatic ring oxidation in cytochrome P450s. QM/MM profiles for three different rearrangement pathways of the initially formed sigma-adduct, leading to formation of epoxide, ketone, and an N-protonated porphyrin species, were calculated. Our results suggest that epoxide and ketone products form with comparable ease in the face-on pathway, whereas epoxide formation is preferred in the side-on pathway. Additionally, rearrangement to the N-protonated porphyrin species was found to be competitive with side-on epoxide formation. This suggests that overall, the competition between formation of epoxide and phenol final products in P450 oxidation of aromatic substrates is quite finely balanced.     

Multireference ab initio quantum mechanics/molecular mechanics study on intermediates in the catalytic cycle of cytochrome P450(cam)

We have investigated the elusive reactive species of cytochrome P450(cam) (Compound I), the hydroxo complex formed during camphor hydroxylation, and the ferric hydroperoxo complex (Compound 0) by combined quantum mechanical/molecular mechanical (QM/MM) calculations, employing both density functional theory (DFT) and correlated ab initio methods. The first two intermediates appear multiconfigurational in character, especially in the doublet state and less so in the quartet state. DFT(B3LYP)/MM calculations reproduce the relative energies from correlated ab initio QM/MM treatments quite well, except for the splitting of the lowest A(1u)-A(2u) radical states. The inclusion of dynamic correlation is crucial for the proper ab initio treatment of these intermediates.     

Absorption and emission spectra of fluorescent silica nanoparticles from TD-DFT/MM/PCM calculations

A multi-scale computational protocol, which combines Quantum Mechanics and Molecular Mechanics (QM/MM) calculations with the polarisable continuum model (PCM), has been used to study the tetramethylrhodamine isothiocyanate (TRITC) fluorophore, embedded in three different environments, namely in water, on an amorphous silica surface and covalently encapsulated in a silica nanoparticle (C dot). Absorption and emission spectra have been simulated by using TD-B3LYP/PCM calculations, performed on the TRITC ground and excited state geometries, optimized at the QM/MM level. The results are in good agreement with experimental data confirming the caging effect played by the silica shell on the mobility of the TRITC molecule when covalently encapsulated in silica nanoparticles. This could result in a decrease of the nonradiative decay rate and thus an increase of the quantum yield of the molecule.     

Computational characterization of reaction intermediates in the photocycle of the sensory domain of the AppA blue light photoreceptor

The AppA protein with the BLUF (blue light using flavin adenine dinucleotide) domain is a blue light photoreceptor that cycle between dark-adapted and light-induced functional states. We characterized possible reaction intermediates in the photocycle of AppA BLUF. Molecular dynamics (MD), quantum chemical and quantum mechanical-molecular mechanical (QM/MM) calculations were carried out to describe several stable structures of a molecular system modeling the protein. The coordinates of heavy atoms from the crystal structure (PDB code 2IYG) of the protein in the dark state served as starting point for 10 ns MD simulations. Representative MD frames were used in QM(B3LYP/cc-pVDZ)/MM(AMBER) calculations to locate minimum energy configurations of the model system. Vertical electronic excitation energies were estimated for the molecular clusters comprising the quantum subsystems of the QM/MM optimized structures using the SOS-CIS(D) quantum chemistry method. Computational results support the occurrence of photoreaction intermediates that are characterized by spectral absorption bands between those of the dark and light states. They agree with crystal structures of reaction intermediates (PDB code 2IYI) observed in the AppA BLUF domain. Transformations of the Gln63 side chain stimulated by photo-excitation and performed with the assistance of the chromophore and the Met106 side chain are responsible for these intermediates.     

Characteristics of CO3(2-)-water hydrogen bonds in aqueous solution: insights from HF/MM and B3LYP/MM MD simulations

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, namely HF/MM and B3LYP/MM, have been performed to investigate the local hydration structure and dynamics of carbonate (CO(3)(2-)) in dilute aqueous solution. With respect to the QM/MM scheme, the QM region, which contains the CO(3)(2-) and its surrounding water molecules, was treated at HF and B3LYP levels of accuracy, respectively, using the DZV+ basis set, while the rest of the system is described by classical MM potentials. For both the HF/MM and B3LYP/MM simulations, it is observed that the hydrogen bonds between CO(3)(2-) oxygens and their nearest-neighbor waters are relatively strong, i.e., compared to water-water hydrogen bonds in the bulk, and that the first shell of each CO(3)(2-) oxygen atom somewhat overlaps with the others, which allows migration of water molecules among the coordinating sites to exist. In addition, it is observed that first-shell waters are either "loosely" or "tightly" bound to the respective CO(3)(2-) oxygen atoms, leading to large fluctuations in the number of first-shell waters, ranging from 1 to 6 (HF/MM) and 2 to 7 (B3LYP/MM), with the prevalent value of 3. Upon comparing the HF and B3LYP methods in describing this hydrated ion, the latter is found to overestimate the hydrogen-bond strength in the CO(3)(2-)-water complexes, resulting in a slightly more compact hydration structure at each of the CO(3)(2-) oxygens.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

Importance of selecting proper basis set in quantum mechanical studies of potential energy surfaces of carbohydrates

An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d -aldo- and d -ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6-31G** 5d), we found at the higher level calculation (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d -aldo- and d -ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999