Grand challenges in quantum‐classical modeling of molecule–surface interactions

A detailed understanding of the adsorption of small molecules or macromolecules to a materials surface is of importance, for example, in the context of material and biomaterial research. Classical atomistic simulations in principle provide microscopic insight in the complex entropic and enthalpic interplay at the interface. However, an application of classical atomistic simulation techniques to such interface systems is a nontrivial problem, mostly because commonly used force fields cannot be straightforwardly applied, as they are usually developed to reproduce bulk properties of either solids or liquids but not the interfacial region between two phases. Therefore, a dual‐scale modeling approach has often been the method of choice in the past, in which the classical force field is parameterized such that quantum chemical information on near‐surface conformations and adsorption energies is reproduced by the classical force field. We will discuss in this review the current state‐of‐the‐art of quantum‐classical modeling of molecule–surface interactions and outline the major challenges in this field. In this context, we will, among other things, lay emphasis on discussing ways to obtain representable force fields and propose systematic and system‐independent strategies to optimize the quantum‐classical fitting procedure. © 2013 Wiley Periodicals, Inc.     

Uptake of phenol on aerosol particles

We present a study of the interaction between a phenol molecule and an aerosol particle. The aerosol particle is represented by a cluster of 128 water molecules. Using a classical approach, we present interaction energy surfaces for different relative distances and for three orientations of phenol relative to the particle. From the energy surfaces we find the reaction pathways with the largest interaction between the molecule and the particle. We use a quantum mechanics/molecular mechanics (QM/MM) method to calculate a potential energy curve for each reaction path. Coupled cluster methods are used for the part of the system described by quantum mechanics, while the part described by molecular mechanics is represented by a polarizable force field. We compare results obtained from the classical approach with the QM/MM results. Furthermore, we use the QM/MM results to calculate mass accommodation coefficients using a quantum-statistical (QM-ST) model and show how the mass accommodation coefficient depends on the relative orientation of phenol with respect to the aerosol particle.     

Calibration of force-field dependency in free energy landscapes of peptide conformations by quantum chemical calculations

The free energy landscapes of peptide conformations were calibrated by ab initio quantum chemical calculations, after the enhanced conformational diversity search using the multicanonical molecular dynamics simulations. Three different potentials of mean force for an isolated dipeptide were individually obtained by the multicanonical molecular dynamics simulations using the conventional force fields, AMBER parm94, AMBER parm96, and CHARMm22. Each potential of mean force was then calibrated based upon the umbrella sampling algorithm from the adiabatic energy map that was calculated separately by the ab initio molecular orbital method, and all of the calibrated potentials of mean force coincided well. The calibration method was also applied to the simulations of a peptide dimer in explicit water models, and it was shown that the calibrated free energy landscapes did not depend on the force field used in the classical simulations, as far as the conformational space was sampled well. The current calibration method fuses the classical free energy calculation with the quantum chemical calculation, and it should generally make simulations for biomolecular systems much more reliable when combining with enhanced conformational sampling.     

Role of short-range electrostatics in torsional potentials

A force field needs to decide if it should contain a torsional potential or not. A helpful guide to this decision should come from a quantum mechanical energy partitioning. Here we analyze the energy profiles of eight simple molecules (ethane, hydrogen peroxide, hydrazine, methanol, acetaldehyde, formamide, acetamide and N-methylacetamide) subject to rotation around a torsion angle. Coulomb interaction energies between all atom pairs in a molecule are monitored during the rotation. Atoms are defined as finite electron density fragments by quantum chemical topology, a method that enables well-defined short-range interactions (1-2, 1-3 and 1-4). Energy profiles of Coulomb interaction energies mostly counteract the ab initio energy profiles. This and future work strives to settle ambiguities in current force field design.     

An analysis of molecular packing and chemical association in liquid water using quasichemical theory

We calculate the hydration free energy of liquid TIP3P water at 298 K and 1 bar using a quasi-chemical theory framework in which interactions between a distinguished water molecule and the surrounding water molecules are partitioned into chemical associations with proximal (inner-shell) waters and classical electrostatic-dispersion interactions with the remaining (outer-shell) waters. The calculated free energy is found to be independent of this partitioning, as expected, and in excellent agreement with values derived from the literature. An analysis of the spatial distribution of inner-shell water molecules as a function of the inner-shell volume reveals that water molecules are preferentially excluded from the interior of large volumes as the occupancy number decreases. The driving force for water exclusion is formulated in terms of a free energy for rearranging inner-shell water molecules under the influence of the field exerted by outer-shell waters in order to accommodate one water molecule at the center. The results indicate a balance between chemical association and molecular packing in liquid water that becomes increasingly important as the inner-shell volume grows in size.     

Quantum mechanical computations on very large molecular systems: The local self-consistent field method

Quantum chemical computations on a subset of a large molecule can be performed, at the neglect of diatomic differential overlap (NDDO) level, without further approximation provided that the atomic orbitals of the frontier atoms are replaced by parametrized orthogonal hybrid orbitals. The electrostatic interaction with the rest of the molecule, treated classically by the usual molecular mechanical approximations, is included into the self-consistent field (SCF) equations. The first and second derivatives of energy are obtained analytically, allowing the search for energy minima and transition states as well as the resolution of Newton equations in molecular dynamics simulations. The local self-consistent field (LSCF) method based on these approximations is tested by studying the intramolecular proton transfer in a Gly-Arg-Glu-Gly model tetrapeptide, which reveals an excellent agreement between a computation performed on the whole molecule and the results obtained by the present method, especially if the quantum subsystem includes the side chains and the peptidic unit in between. The merits of the LSCF method are examplified by a study of proton transfer in the Asp⁶⁹—Arg⁷¹ salt bridge in dihydrofolate reductase. Simulations of large systems, involving local changes of electronic structure, are therefore possible at a good degree of approximation by introducing a quantum chemical part in molecular dynamics studies. This methodology is expected to be very useful for reactivity studies in biomolecules or at the surface of covalent solids. © 1994 by John Wiley & Sons, Inc.     

New force field for calcium binding sites in annexin-membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.     

Development of glycyl radical parameters for the OPLS-AA/L force field

On the basis of quantum chemical calculations C(alpha)-glycyl radical parameters have been developed for the OPLS-AA/L force field. The molecular mechanics hypersurface was fitted to the calculated quantum chemical surface by minimizing their molecular mechanics parameter dependent sum-of-squares deviations. To do this, a computer program in which the molecular mechanics energy derivatives with respect to the parameters were calculated analytically was developed, implementing the general method of Lifson and Warshel (J Chem Phys 1968, 49, 5116) for force field parameter optimization. This program, in principle, can determine the optimal parameter set in one calculation if enough representative value points on the quantum chemical potential energy surface are available and there is no linear dependency between the parameters. Some of the parameters in quantum calculations, including several new torsion types around a bond as well as angle parameters at a new central atom type, are not completely separable. Consequently, some restrictions and/or presumptions were necessary during parameter optimization. The relative OPLS-AA energies reproduced those calculated quantum chemically almost perfectly.     

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well-defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (methanol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol^?1, and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.     

Quantum chemical investigation of the adsorption of methanol on a cluster model of faujasite

The adsorption of methanol in zeolites of the faujasite type with sodium and calcium counter ions is studied with quantum chemical methods. The zeolite is represented with a cluster model allowing calculations at the Møller-Plesset as well as the DFT level of theory. An adsorption energy of −62.4 kJ/mol is calculated at the MP2/TZVP//BP86/TZVP level of theory for one methanol molecule at one site II sodium cation. Insight into the adsorption process is obtained with a three-body decomposition which reveals a strong destabilisation of the adsorption strength by large, positive three-body terms, which is important for force field development.     

Hybrid quantum/classical path integral approach for simulation of hydrogen transfer reactions in enzymes

A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.     

Molecular recognition in cyclodextrin complexes of amino acid derivatives: the effects of kinetic energy on the molecular recognition of a pseudopeptide in a nonconstraining host environment as revealed by a temperature-dependent crystallographic study

The crystal structure of a triclinic 2:2 inclusion complex of beta-cyclodextrin with N-acetyl-L-phenylalanine methyl ester has been determined at several temperatures between 298 and 20 K to further study molecular recognition using solid-state supramolecular beta-cyclodextrin complexes. The study reveals kinetic energy dependent changes in guest molecule conformations, orientations, and positions in the binding pocket presented by the crystal lattice. Accompanying these changes are observable differences in guest-guest interactions and hydrogen-bonding interactions in the binding pocket that involve guest molecules, water of hydration molecules, and beta-cyclodextrin molecules. On the basis of the differences observed in the crystal structures, we present a solid-state example of a system that displays the properties of both classical and quantum chemical models. At higher temperatures, the structure conforms to a classical mechanical model with dynamic disorder. At lower temperatures, the observations conform to examples in which there is static disorder representative of models in which quantum states differing in conformation, position, and orientation of components in the crystal structure are occupied. Ab initio theoretical calculations on the different guest molecule conformations have been carried out. Superpositions of theoretical electrostatic surface potential diagrams on the observed molecular positions in the complexes provide confidence that the deconvolution of the guest molecule disorder is acceptable. Temperature-dependent solid-state magic angle spinning deuteron NMR measurements provide evidence for large-amplitude, diffusive motion on a microsecond time scale in the complex.     

氟磺酸氯分子振动光谱的从头算研究

采用从头算HF方法以6-31G^*基组研究了对ClOSO₂F分子的几何结构、振动谐性力场和红外光谱.理论力场由Pulay的标度量子力学方法进行标度,算得的振动频率与实验值比较,平均偏差为6.0cm^-1.根据振动频率的势能分布和从头算红外光谱强度值对此分子的振动基频进行了理论归属.     

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.     

硼烷缺电子多中心桥键的H-F力研究

Hellmann-Feynman静电力表现了分子中电荷分布及对各原子核的作用。H-F力的方向性可描述电子电荷的数量和位置,具有定量、形象和直观的特点,已在弯键的研究中显示出来。这一方法尚可用于多中心缺电子桥键的研究。 1 理论与方法 按LCAO-MO理论对H-F力进行分解,除有重叠力、极化力和屏蔽力外,还有一     

2-氟-5-溴吡啶分子振动光谱的密度泛涵理论研究

用密度泛函理论方法B3LYP以及6-311++G(2df,2pd)基组对2-氟-5-溴吡啶分子 的平衡几何构型进行了优化并计算了该分子的振动谐力场。使用Pulay的标度方法 对理论力场进行了标度。采用Wilson的GF矩阵方法,根据标度后的理论力场进行了 简正坐标分析,对2-氟-5-溴吡啶分子的振动基频进行了理论研究,得到了势能分 布和红外振动频率。与红外频率的实验值相比较,理论频率的均方差为24 cm~(-1) 。此外,根据振动模式的势能分布对此分子的振动基频进行了理论归属,并对前人 的指认进行了修正和补充。