Quantum supercharger library: Hyper‐parallel integral derivatives algorithms for ab initio QM/MM dynamics

This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two‐electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one‐ and two‐electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree–Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS‐UK, which uses the efficient Schlegel method for ‐ and ‐orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6‐31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.     

Rapid QM/MM approach for biomolecular systems under periodic boundary conditions: Combination of the density‐functional tight‐binding theory and particle mesh Ewald method

A quantum mechanical/molecular mechanical (QM/MM) approach based on the density‐functional tight‐binding (DFTB) theory is a useful tool for analyzing chemical reaction systems in detail. In this study, an efficient QM/MM method is developed by the combination of the DFTB/MM and particle mesh Ewald (PME) methods. Because the Fock matrix, which is required in the DFTB calculation, is analytically obtained by the PME method, the Coulomb energy is accurately and rapidly computed. For assessing the performance of this method, DFTB/MM calculations and molecular dynamics simulation are conducted for a system consisting of two amyloid‐β(1‐16) peptides and a zinc ion in explicit water under periodic boundary conditions. As compared with that of the conventional Ewald summation method, the computational cost of the Coulomb energy by utilizing the present approach is drastically reduced, i.e., 166.5 times faster. Furthermore, the deviation of the electronic energy is less than . © 2016 Wiley Periodicals, Inc.     

The CHARMM–TURBOMOLE interface for efficient and accurate QM/MM molecular dynamics,free energies,and excited state properties

The quantum mechanical (QM)/molecular mechanical (MM) interface between Chemistry at HARvard Molecular Mechanics (CHARMM) and TURBOMOLE is described. CHARMM provides an extensive set of simulation algorithms, like molecular dynamics (MD) and free energy perturbation, and support for mature nonpolarizable and Drude polarizable force fields. TURBOMOLE provides fast QM calculations using density functional theory or wave function methods and excited state properties. CHARMM–TURBOMOLE is well‐suited for extended QM/MM MD simulations using first principles methods with large (triple‐ζ) basis sets. We demonstrate these capabilities with a QM/MM simulation of Mg²⁺(aq), where the MM outer sphere water molecules are represented using the SWM4‐NDP Drude polarizable force field and the ion and inner coordination sphere are represented using QM PBE, PBE0, and MP2 methods. The relative solvation free energies of Mg²⁺ and Zn²⁺ were calculated using thermodynamic integration. We also demonstrate the features for excited state properties. We calculate the time‐averaged solution absorption spectrum of indole, the emission spectrum of the indole excited state, and the electronic circular dichroism spectrum of an oxacepham. © 2014 Wiley Periodicals, Inc.     

Quantum chemical study of the autoxidation of ascorbate

Reactions involved in the autoxidation of ascorbate have been investigated with quantum chemical first‐principles and ab initio methods. Reaction energies and Gibbs energies of the reactions were calculated at the density functional theory level applying the gradient‐corrected BP86 and the hybrid B3LYP functionals together with def2‐TZVP basis sets. Results of single‐point CC2, CCSD, and CCSD(T) calculations were used for calibration of the density functional theory data and show excellent agreement with the B3LYP values. Based on the Gibbs energy ascorbic acid AscH₂ is found to be the energetically lowest species in aqueous solution, whereas the monoanion ascorbate AscH is the most abundant one near pH = 7. Asc was found to be the preferred reducing agent for autoxidation and oxidation processes. The results also support a metal‐catalyzed synthesis of the reactive oxygen species H₂O₂ according to a redox cycling mechanism proposed in literature. © 2016 Wiley Periodicals, Inc.     

Solvatochromic shifts of Br2 and I2 in water cages of type 512, 51262, 51263, and 51264

Despite the relatively small size of molecular bromine and iodine, the physicochemical behavior in different solvents is not yet fully understood, in particular when excited‐state properties are sought. In this work, we investigate isolated halogen molecules trapped in clathrate hydrate cages. Relativistic supermolecular calculations reveal that the environment shift to the excitation energies of the (nondegenerate) states and lie within a spread of 0.05 eV, respectively, suggesting that environment shifts can be estimated with scalar‐relativistic treatments. As even scalar‐relativistic calculations are problematic for excited‐state calculations for clathrates with growing size and basis sets, we have applied the subsystem‐based scheme frozen‐density embedding, which avoids a supermolecular treatment. This allows for the calculation of excited states for extended clusters with coupled‐cluster methods and basis sets of triple‐zeta quality with additional diffuse functions mandatory for excited‐state properties, as well as a facile treatment at scalar‐relativistic exact two‐component level of theory for the heavy atoms bromine and iodine. This simple approach yields scalar‐relativistic estimates for solvatochromic shifts introduced by the clathrate cages. © 2015 Wiley Periodicals, Inc.     

Revealing the physical nature and the strength of charge‐inverted hydrogen bonds by SAPT(DFT), MP2, SCS‐MP2, MP2C,and CCSD(T) methods

The physical nature of charge‐inverted hydrogen bonds in H₃XH YH₃ (X = Si, Ge; Y = Al, Ga) dimer systems is studied by means of the SAPT(DFT)‐based decomposition of interaction energies and supermolecular interaction energies based on MP2, SCS‐MP2, MP2C, and CCSD(T) methods utilizing dimer‐centered aug‐cc‐pCVnZ (n = D, T, Q) basis sets as well as an extrapolation to the complete basis set limit. It is revealed that charge‐inverted hydrogen bonds are inductive in nature, although dispersion is also important. Computed interaction energies form the following relation: . It is confirmed that the aug‐cc‐pCVDZ basis set performs poorly and that very accurate values of interaction and dispersion energies require basis sets of at least quadrupole‐ζ quality. Considerably large binding energies suggest potential usefulness of charge‐inverted hydrogen bonds as an important structural motif in molecular binding. Terminology applying to σ‐ and π‐hole interactions as well as to triel and tetrel bonds is discussed. According to this new terminology the charge‐inverted hydrogen bond would become the first described case of a hydride‐triel bond. © 2017 Wiley Periodicals, Inc.     

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band‐gap energies of the , Pc, and structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path‐integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero‐point energy and temperature‐induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band‐gaps substantially, leading to metallization of the and Pc phases via band overlap; the effect on the band‐gap of the structure is less pronounced. Our combined DMC‐PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band‐gap energy and vibron modes. This strong coupling induces a band‐gap reduction of more than 2.46 eV in high‐pressure solid molecular hydrogen. Comparing our DMC‐PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.     

Comparison of the periodic slab approach with the finite cluster description of metal–organic interfaces at the example of PTCDA on Ag(110)

We present a comparative study of metal–organic interface properties obtained from dispersion corrected density functional theory calculations based on two different approaches: the periodic slab‐supercell technique and cluster models with 32–290 Ag atoms. Fermi smearing and fixing of cluster borders are required to make the cluster calculation feasible and realistic. The considered adsorption structure and energy of a PTCDA molecule on the Ag(110) surface is not well reproduced with clusters containing only two metallic layers. However, all clusters with four layers of silver atoms and sufficient lateral extension reproduce the adsorbate structure within 0.04 Å with respect to the slab‐supercell structure and provide adsorption energies of ( 0.08 eV) consistent with the slab result of −4.47 eV. Thus, metal–organic adsorbate systems can be realistically represented by properly defined cluster models. © 2018 Wiley Periodicals, Inc.     

Effects of zero point vibration on the reaction dynamics of water dimer cations following ionization

Reactions of water dimer cation following ionization have been investigated by means of a direct ab initio molecular dynamics method. In particular, the effects of zero point vibration and zero point energy (ZPE) on the reaction mechanism were considered in this work. Trajectories were run on two electronic potential energy surfaces (PESs) of : ground state (²A″‐like state) and the first excited state (²A′ ‐ like state). All trajectories on the ground‐state PES lead to the proton‐transferred product: H₂O⁺(Wd)‐H₂O(Wa) → OH(Wd)‐H₃O⁺(Wa), where Wd and Wa refer to the proton donor and acceptor water molecules, respectively. Time of proton transfer (PT) varied widely from 15 to 40 fs (average time of PT = 30.9 fs). The trajectories on the excited‐state PES gave two products: an intermediate complex with a face‐to‐face structure (H₂O‐OH₂)⁺ and a PT product. However, the proton was transferred to the opposite direction, and the reverse PT was found on the excited‐state PES: H₂O(Wd)‐H₂O⁺ (Wa) → H₃O⁺(Wd)‐OH(Wa). This difference occurred because the ionizing water molecule in the dimer switched between the ground and excited states. The reaction mechanism of and the effects of ZPE are discussed on the basis of the results. © 2017 Wiley Periodicals, Inc.     

Structure and electrochemical properties for complexes of nitrocompounds with inorganic ions: A theoretical approach

Reduction and oxidation (redox) reactions are widely used for removal of nitrocompounds from contaminated soil and water. Structures and redox properties for complexes of nitrocompounds, such as 2,4,6‐trinitrotoluene (TNT), 2,4‐dinitrotoluene (DNT), 2,4‐dinitroanisole (DNAN), and 5‐nitro‐2,4‐dihydro‐3H?1,2,4‐triazol‐3‐one (NTO), with common inorganic ions (Na⁺, Cl^?, ) were investigated at the SMD(Pauling)/PCM(Pauling)/MPWB1K/TZVP level of theory. Atoms in molecules (AIM) theory was applied to analyze the topological properties of the bond critical points involved in the interactions between the nitrocompounds and the ions. Topological analyses show that intermolecular interactions of the types O(N)…Na⁺, C‐H…Cl^?( ), and C…Cl^?( ) may be discussed as noncovalent closed‐shell interactions, while N‐H···Cl^?( ) hydrogen bonds are partially covalent in nature. Complexation causes significant decrease of redox activity of the nitrocompounds. Analysis of the reduction potentials of the complexes obtained through application of the Pourbaix diagram of an iron/water system revealed that sodium complexes of NTO might be reduced by metallic iron. © 2016 Wiley Periodicals, Inc.     

Aqueous acidities of primary benzenesulfonamides: Quantum chemical predictions based on density functional theory and SMD

Aqueous of selected primary benzenesulfonamides are predicted in a systematic manner using density functional theory methods and the SMD solvent model together with direct and proton exchange thermodynamic cycles. Some test calculations were also performed using high‐level composite CBS‐QB3 approach. The direct scheme generally does not yield a satisfactory agreement between calculated and measured acidities due to a severe overestimation of the Gibbs free energy changes of the gas‐phase deprotonation reaction by the used exchange‐correlation functionals. The relative values calculated using proton exchange method compare to experimental data very well in both qualitative and quantitative terms, with a mean absolute error of about 0.4 units. To achieve this accuracy, we find it mandatory to perform geometry optimization of the neutral and anionic species in the gas and solution phases separately, because different conformations are stabilized in these two cases. We have attempted to evaluate the effect of the conformer‐averaged free energies in the predictions, and the general conclusion is that this procedure is highly too costly as compared with the very small improvement we have gained. © 2015 Wiley Periodicals, Inc.     

The solvent effect on two competing reaction mechanisms involving hypervalent iodine reagents (λ3‐iodanes): Facing the limit of the stationary quantum chemical approach

Trifluoromethylation of acetonitrile with 3,3‐dimethyl‐1‐(trifluoromethyl)?1λ³,2‐ benziodoxol is assumed to occur via reductive elimination (RE) of the electrophilic CF₃‐ligand and MeCN bound to the hypervalent iodine. Computations in gas phase showed that the reaction might also occur via an S_N2 mechanism. There is a substantial solvent effect present for both reaction mechanisms, and their energies of activation are very sensitive toward the solvent model used (implicit, microsolvation, and cluster‐continuum). With polarizable continuum model‐based methods, the S_N2 mechanism becomes less favorable. Applying the cluster‐continuum model, using a shell of solvent molecules derived from ab initio molecular dynamics (AIMD) simulations, the gap between the two activation barriers ( ) is lowered to a few kcal mol^?1 and also shows that the activation entropies ( ) and volumes ( ) for the two mechanisms differ substantially. A quantitative assessment of will therefore only be possible using AIMD. A natural bond orbital‐analysis gives further insight into the activation of the CF₃‐reagent by protonation. © 2014 Wiley Periodicals, Inc.     

Accurate,robust, and reliable calculations of Poisson–Boltzmann binding energies

Poisson–Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, , and binding free energy, , is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with solvent excluded surfaces for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of obtained at the grid spacing of 1.0 Å compared to at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.     

Efficient optimization of van der Waals parameters from bulk properties

Due to the computational cost involved, when developing a force field for new compounds, one often avoids fitting van der Waals (vdW) terms, instead relying on a general force field based on the atom type. Here, we provide a novel approach to efficiently optimize vdW terms, based on both ab initio dimer energies and condensed phase properties. The approach avoids the computational challenges of searching the parameter space by using an extrapolation method to obtain a reliable difference quotient for the parameter derivatives based on the central difference. The derivatives are then used in an active‐space optimization method which convergences quadratically. This method is applicable to polarizable and nonpolarizable force fields, although we focus on the parameterization of the AMBER force field. The scaling of the electrostatic potential (ESP) of the compounds is also studied. The algorithm is tested on 12 compounds, reducing the root mean squared error (RMSE) of the density from 0.061 g/cm³ with GAFF parameters to 0.004 g/cm³, and the heat of vaporization from 1.13 to 0.05 kcal/mol. This is done with only four iterations of molecular dynamic runs. Using the optimized vdW parameters, the RMSE of the self‐diffusion was reduced from 1.22 × 10^?9 to 0.78 × 10^?9 m² s^?1 and the RMSE of the hydration free energies was reduced from 0.30 to 0.26 kcal/mol. Scaling the ESP to improve dimer energies resulted in the RMSE improving to 0.77× 10^?9 m² s^?1, but the worsened to 0.33 kcal/mol. © 2013 Wiley Periodicals, Inc.     

Development of spin‐orbit coupling for stochastic configuration interaction techniques

To perform spin‐orbit coupling calculations on atoms and molecules, good zeroth‐order wavefunctions are necessary. Here, we present the software development of the Monte Carlo Configuration Interaction (MCCI) method, to enable calculation of such properties, where MCCI iteratively constructs a multireference wavefunction using a stochastic procedure. In this initial work, we aim to establish the efficacy of this technique in predicting the splitting of otherwise degenerate energy levels on a range of atoms and small diatomic molecules. It is hoped that this work will subsequently act as a gateway toward using this method to investigate singlet‐triplet interactions in larger multireference molecules. We show that MCCI can generate very good results using highly compact wavefunctions compared to other techniques, with no prior knowledge of important orbitals. Higher‐order relativistic effects are neglected and spin‐orbit coupling effects are incorporated using first‐order degenerate perturbation theory with the Breit‐Pauli Hamiltonian and effective nuclear charges in the one‐electron operator. Results are obtained and presented for B, C, O, F, Si, S, and Cl atoms and OH, CN, NO, and C₂ diatomic radicals including spin‐orbit coupling constants and the relative splitting of the lowest energy degenerate state for each species. Convergence of MCCI to the full configuration interaction result is demonstrated on the multireference problem of stretched OH. We also present results from the singlet‐triplet interaction between the and both the and states of the O₂ molecule. © 2017 Wiley Periodicals, Inc.     

Inverse Ubbelohde effect in the short hydrogen bond of photosystem II: Relation between H/D isotope effect and symmetry in potential energy profile

The short hydrogen bond between tyrosine Y_z and D1‐His190 of photosystem II (PSII) was investigated using multicomponent quantum mechanics, where the quantum fluctuation of a hydrogen nucleus was incorporated into electronic structure calculation. Our computation demonstrated that the deuteration for hydrogen in the short hydrogen bond of PSII led to the reduction of the O…N distance. It indicated an inverse Ubbelohde effect typically recognized in strong and symmetric hydrogen‐bonding clusters such as FHF^– and . We confirmed that the relation between the geometric isotope effect and the symmetry of the potential energy profile of FHF^– was reasonably agreed with that of PSII. According to this agreement, the short hydrogen bond in PSII can be regarded as a short strong hydrogen bond. © 2016 Wiley Periodicals, Inc.     

A multipolar approach to the interatomic covalent interaction energy

Interatomic exchange‐correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp ) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities and , we examine in this work the mp approach to approximate the interatomic exchange‐correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1–2 pairs) albeit it works reasonably well most times for 1– n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole‐monopole xc mp term and the inter‐atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.     

Free energies of solvation in the context of protein folding: Implications for implicit and explicit solvent models

Implicit solvent models for biomolecular simulations have been developed to use in place of more expensive explicit models; however, these models make many assumptions and approximations that are likely to affect accuracy. Here, the changes in free energies of solvation upon folding of several fast folding proteins are calculated from previously run μs–ms simulations with a number of implicit solvent models and compared to the values needed to be consistent with the explicit solvent model used in the simulations. In the majority of cases, there is a significant and substantial difference between the values calculated from the two approaches that is robust to the details of the calculations. These differences could only be remedied by selecting values for the model parameters—the internal dielectric constant for the polar term and the surface tension coefficient for the nonpolar term—that were system‐specific or physically unrealistic. We discuss the potential implications of our findings for both implicit and explicit solvent simulations. © 2015 Wiley Periodicals, Inc.     

Perturbative treatment of anharmonic vibrational effects on bond distances: An extended langevin dynamics method

In this work, we first review the perturbative treatment of an oscillator with cubic anharmonicity. It is shown that there is a quantum‐classical correspondence in terms of mean displacement, mean‐squared displacement, and the corresponding variance in the first‐order perturbation theory, provided that the amplitude of the classical oscillator is fixed at the zeroth‐order energy of quantum mechanics . This correspondence condition is realized by proposing the extended Langevin dynamics (XLD), where the key is to construct a proper driving force. It is assumed that the driving force adopts a simple harmonic form with its amplitude chosen according to , while the driving frequency chosen as the harmonic frequency. The latter can be improved by using the natural frequency of the system in response to the potential if its anharmonicity is strong. By comparing to the accurate numeric results from discrete variable representation calculations for a set of diatomic species, it is shown that the present method is able to capture the large part of anharmonicity, being competitive with the wave function‐based vibrational second‐order perturbation theory, for the whole frequency range from ～4400 cm^?1 (H₂) to ～160 cm^?1 (Na₂). XLD shows a substantial improvement over the classical molecular dynamics which ceases to work for hard mode when zero‐point energy effects are significant. © 2013 Wiley Periodicals, Inc.     

Bonding analysis of planar hypercoordinate atoms via the generalized BLW‐LOL

The multicenter bonding pattern of the intriguing hexa‐, hepta‐, and octacoordinate boron wheel series (e.g., , , , and SiB₈ as well as the experimentally detected isomer) is revised using the block‐localized wave function analyzed by the localized orbital locator (BLW‐LOL). The more general implementation of BLW combined with the LOL scalar field is not restricted to the analysis of the out‐of‐plane π‐system but can also provide an intuitive picture of the σ‐radial delocalization and of the role of the central atom. The results confirm the presence of a π‐ring current pattern similar to that of benzene. In addition, the LOL_π isosurfaces along with the maximum intensity in the  ΔLOL profiles located above and below the ring suggest that the central atom plays a minor role in the π‐delocalized bonding pattern. Finally, the analysis of the σ‐framework in these boron wheels is in line with a moderated inner cyclic rather than disk‐type delocalization. © 2013 Wiley Periodicals, Inc.