Benchmarking the multipole shielding polarizability/reaction field approach to solvation against QM/MM: applications to the shielding constants of N-methylacetamide

We present a benchmark study of a combined multipole shielding polarizability/reaction field (MSP/RF) approach to the calculation of both specific and bulk solvation effects on nuclear magnetic shielding constants of solvated molecules. The MSP/RF scheme is defined by an expansion of the shielding constants of the solvated molecule in terms of electric field and field gradient property derivatives derived from single molecule ab initio calculations. The solvent electric field and electric field gradient are calculated based on data derived from molecular dynamics simulations, thereby accounting for solute-solvent dynamical effects. The MSP/RF method is benchmarked against polarizable quantum mechanics/molecular mechanics (QM/MM) calculations. The best agreement between the MSP/RF and QM/MM approaches is found by truncating the electric field expansion in the MSP/RF approach at the linear electric field level which is due to the cancelation of errors. In addition, we investigate the sensitivity of the results due to the choice of one-electron basis set in the ab initio calculations of the property derivatives and find that these derivatives are affected by the basis set in a way similar to the shielding constants themselves.     

NMR spin-spin coupling constants in polymethine dyes as polarity indicators

Herein, we explore the use of spin-spin coupling constants (SSCCs) in merocyanine (MCYNE) dyes as indicators of polarity. For this purpose, we use Car-Parrinello hybrid quantum mechanics/molecular mechanics (QM/MM) to determine the structures of MCYNE in solvents of different polarity, followed by computations of the SSCCs by using QM/MM linear-response theory. The molecular geometry of MCYNE switches between neutral, cyanine-like, and zwitterionic depending on the polarity of the solvent. This structural variation is clearly reflected in the proton SSCCs in the polymethine backbone, which are highly sensitive to the dielectric nature of the environment; this mechanism can be used as a "polarity indicator" for different microenvironments. This result is highlighted by computing the SSCCs of the MCYNE probe in the cavity of the beta-lactoglobulin protein. The computed SSCCs clearly indicate a non-polar hydrophobic dielectric nature of this cavity.     

NMR Spin–Spin Coupling Constants in Polymethine Dyes as Polarity Indicators

Herein, we explore the use of spin–spin coupling constants (SSCCs) in merocyanine (MCYNE) dyes as indicators of polarity. For this purpose, we use Car–Parrinello hybrid quantum mechanics/molecular mechanics (QM/MM) to determine the structures of MCYNE in solvents of different polarity, followed by computations of the SSCCs by using QM/MM linear‐response theory. The molecular geometry of MCYNE switches between neutral, cyanine‐like, and zwitterionic depending on the polarity of the solvent. This structural variation is clearly reflected in the proton SSCCs in the polymethine backbone, which are highly sensitive to the dielectric nature of the environment; this mechanism can be used as a “polarity indicator” for different microenvironments. This result is highlighted by computing the SSCCs of the MCYNE probe in the cavity of the beta‐lactoglobulin protein. The computed SSCCs clearly indicate a non‐polar hydrophobic dielectric nature of this cavity.     

Nuclear magnetic resonance J coupling constant polarizabilities of hydrogen peroxide: A basis set and correlation study

In this article, we present the so far most extended investigation of the calculation of the coupling constant polarizability of a molecule. The components of the coupling constant polarizability are derivatives of the nuclear magnetic resonance (NMR) indirect nuclear spin–spin coupling constant with respect to an external electric field and play an important role for both chiral discrimination and solvation effects on NMR coupling constants. In this study, we illustrate the effects of one‐electron basis sets and electron correlation both at the level of density functional theory as well as second‐order polarization propagator approximation for the small molecule hydrogen peroxide, which allowed us to perform calculations with the largest available basis sets optimized for the calculation of NMR coupling constants. We find a systematic but rather slow convergence with the one‐electron basis set and that augmentation functions are required. We observe also large and nonsystematic correlation effects with significant differences between the density functional and wave function theory methods. © 2012 Wiley Periodicals, Inc.     

Developing ab initio quality force fields from condensed phase quantum-mechanics/molecular-mechanics calculations through the adaptive force matching method

A new method called adaptive force matching (AFM) has been developed that is capable of producing high quality force fields for condensed phase simulations. This procedure involves the parametrization of force fields to reproduce ab initio forces obtained from condensed phase quantum-mechanics/molecular-mechanics (QM/MM) calculations. During the procedure, the MM part of the QM/MM is iteratively improved so as to approach ab initio quality. In this work, the AFM method has been tested to parametrize force fields for liquid water so that the resulting force fields reproduce forces calculated using the ab initio MP2 and the Kohn-Sham density functional theory with the Becke-Lee-Yang-Parr (BLYP) and Becke three-parameter LYP (B3LYP) exchange correlation functionals. The AFM force fields generated in this work are very simple to evaluate and are supported by most molecular dynamics (MD) codes. At the same time, the quality of the forces predicted by the AFM force fields rivals that of very expensive ab initio calculations and are found to successfully reproduce many experimental properties. The site-site radial distribution functions (RDFs) obtained from MD simulations using the force field generated from the BLYP functional through AFM compare favorably with the previously published RDFs from Car-Parrinello MD simulations with the same functional. Technical aspects of AFM such as the optimal QM cluster size, optimal basis set, and optimal QM method to be used with the AFM procedure are discussed in this paper.     

A regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical-molecular-mechanical calculations

We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

Flexible effective fragment QM/MM method: validation through the challenging tests

A new version of the QM/MM method, which is based on the effective fragment potential (EFP) methodology [Gordon, M. et al., J Phys Chem A 2001, 105, 293] but allows flexible fragments, is verified through calculations of model molecular systems suggested by different authors as challenging tests for QM/MM approaches. For each example, the results of QM/MM calculations for a partitioned system are compared to the results of an all-electron ab initio quantum chemical study of the entire system. In each case we were able to achieve approximately similar or better accuracy of the QM/MM results compared to those described in original publications. In all calculations we kept the same set of parameters of our QM/MM scheme. A new test example is considered when calculating the potential of internal rotation in the histidine dipeptide around the C(alpha)bond;C(beta) side chain bond.     

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.     

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.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

NMR spin–spin coupling constants in hydrogen‐bonded glycine clusters

The influence of the hydrogen bond formation on the NMR spin–spin coupling constants (SSCC), including the Fermi contact (FC), the diamagnetic spin‐orbit, the paramagnetic spin‐orbit, and the spin dipole term, has been investigated systematically for the homogeneous glycine cluster, in gas phase, containing up to three monomers. The one‐bond and two‐bond SSCCs for several intramolecular (through covalent bond) and intermolecular (across the hydrogen‐bond) atomic pairs are calculated employing the density functional theory with B3LYP and KT3 functionals and different types of extended basis sets. The ab initio SOPPA(CCSD) is used as benchmark for the SSCCs of the glycine monomer. The hydrogen bonding is found to cause significant variations in the one‐bond SSCCs, mostly due to contribution from electronic interactions. However, the nature of variation depends on the type of oxygen atom (proton‐acceptor or proton‐donor) present in the interaction. Two‐bond intermolecular coupling constants vary more than the corresponding one‐bond constants when the size of the cluster increases. Among the four Ramsey terms that constitute the total SSCC, the FC term is the most dominant contributor followed by the paramagnetic spin‐orbit term in all one‐bond interaction.     

Theoretical study of vitamin properties from combined QM-MM methods: Comparison of chemical shifts and energy

The combination of quantum mechanics (QM) and molecular mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM-MM method has been used for different types of problems, for example, structural biology, surface phenomena, and the liquid phase. In this paper, we have implemented these methods for vitamins, an important kind of biological molecule, and then compared results. The calculations were done by the full ab initio method (HF/3–21 g and HF/6–31 g) and QM-MM (ONIOM) method with HF(3–21 g)/AM1/UFF; then, we found that the geometry obtained by the QM-MM method is very accurate and this rapid method can be used in place of time consuming ab initio methods for large molecules. A comparison of energy values in the QM-MM and QM methods is given. We compare chemical shifts and conclude that the QM-MM method is a perturbed full QM method. The text was submitted by the authors in English.     

Ab initio quantum mechanics-based free energy perturbation method for calculating relative solvation free energies

A free energy perturbation (FEP) method was developed that uses ab initio quantum mechanics (QM) for treating the solute molecules and molecular mechanics (MM) for treating the surroundings. Like our earlier results using AM1 semi empirical QMs, the ab initio QM/MM-based FEP method was shown to accurately calculate relative solvation free energies for a diverse set of small molecules that differ significantly in structure, aromaticity, hydrogen bonding potential, and electron density. Accuracy was similar to or better than conventional FEP methods. The QM/MM-based methods eliminate the need for time-consuming development of MM force field parameters, which are frequently required for drug-like molecules containing structural motifs not adequately described by MM. Future automation of the method and parallelization of the code for Linux 128/256/512 clusters is expected to enhance the speed and increase its use for drug design and lead optimization.     

Molecular geometry and polarizability of small cadmium selenide clusters from all-electron ab initio and Density Functional Theory calculations

We have calculated molecular geometries and electric polarizabilities for small cadmium selenide clusters. Our calculations were performed with conventional ab initio and density functional theory methods and Gaussian-type basis sets especially designed for (CdSe)(n). We find that the dipole polarizability per atom converges rapidly to the bulk value.     

Ab initio quantum mechanical charge field (QMCF) molecular dynamics: a QM/MM – MD procedure for accurate simulations of ions and complexes

A new formalism for quantum mechanical / molecular mechanical (QM/MM) dynamics of chemical species in solution has been developed, which does not require the construction of any other potential functions except those for solvent–solvent interactions, maintains all the advantages of large simulation boxes and ensures the accuracy of ab initio quantum mechanics for all forces acting in the chemically most relevant region. Interactions between solute and more distant solvent molecules are incorporated by a dynamically adjusted force field corresponding to the actual molecular configuration of the simulated system and charges derived from the electron distribution in the solvate. The new formalism has been tested with some examples of hydrated ions, for which accurate conventional ab initio QM/MM simulations have been previously performed, and the comparison shows equivalence and in some aspects superiority of the new method. As this simulation procedure does not require any tedious construction of two-and three-body interaction potentials inherent to conventional QM/MM approaches, it opens the straightforward access to ab initio molecular dynamics simulations of any kind of solutes, such as metal complexes and other composite species in solution.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

Nonempirical calculations of NMR indirect spin-spin coupling constants. Part 15: pyrrolylpyridines

Conformational study of 2-(2-pyrrolyl)pyridine and 2,6-di(2-pyrrolyl)pyridine was performed on the basis of the experimental measurements and high-level ab initio calculations of the one-bond 13C-13C, 13C-1H and 15N-1H spin-spin coupling constants showing marked stereochemical behavior upon the internal rotation around the pyrrole-pyridine interheterocyclic bonds. Both compounds were established to adopt predominant s-cis conformations with no noticeable out-of-plane deviations.