Quantum Modeling of Complex Molecular Systems

We review two essential features of the intermolecular interaction energies (ΔE) computed in the context of quantum chemistry (QC): non-isotropy and non-additivity. Energy-decomposition analyses show the extent to which each comes into play in the separate ΔE contributions, namely electrostatic, short-range repulsion, polarization, charge-transfer and dispersion. Such contributions have their counterparts in anisotropic, polarizable molecular mechanics (APMM), and each of these should display the same features as in QC. We review examples to evaluate the performances of APMM in this respect. They bear on the complexes of one or several ligands with metal cations, and on multiply H-bonded complexes. We also comment on the involvement of polarization, a key contributor to non-additivity, in the issues of multipole transferability and conjugation. In the last section we provide recent examples of APMM validations by QC, which relate to interactions taking place in the recognition sites of kinases and metalloproteins. We conclude by mentioning prospects of extensive applications of APMM.

In this chapter, we review the current state-of-the-art in quantum mechanical/molecular mechanical (QM/MM) simulations of reactions in aqueous solutions, and we discuss how proton transfer poses new challenges for its successful application. In the QM/MM description of an aqueous reaction, solvent molecules in the QM region are diffusive and need to be either constrained within the region, or their description (QM versus MM) needs to be updated as they diffuse away. The latter approach is known as adaptive QM/MM. We review several constrained and adaptive QM/MM methods, and classify them in a consistent manner. Most of the adaptive methods employ a transition region, where every solvent molecule can continuously change character (from QM to MM, and vice versa), temporarily becoming partially QM and partially MM. Where a conventional QM/MM scheme partitions a system into a set of QM and a set of MM atoms, an adaptive method employs multiple QM/MM partitions, to describe the fractional QM character. We distinguish two classes of adaptive methods: Discontinuous and continuous. The former methods use at most two QM/MM partitions, and cannot completely avoid discontinuities in the energy and the forces. The more recent continuous adaptive methods employ a larger number of QM/MM partitions for a given configuration. Comparing the performance of the methods for the description of solution chemistry, we find that in certain cases the low-cost constrained methods are sufficiently accurate. For more demanding purposes, the continuous adaptive schemes provide a good balance between dynamical and structural accuracy. Finally, we challenge the adaptive approach by applying it to the difficult topic of proton transfer and diffusion. We present new results, using a well-behaved continuous adaptive method (DAS) to describe an alkaline aqueous solution of methanol. Comparison with fully QM and fully MM simulations shows that the main discrepancies are rooted in the presence of a QM/MM boundary, and not in the adaptive scheme. An anomalous confinement of the hydroxide ion to the QM part of the system stems from the mismatch between QM and MM potentials, which affects the free diffusion of the ion. We also observe an increased water density inside the QM region, which originates from the different chemical potentials of the QM and MM water molecules. The high density results in locally enhanced proton transfer rates.

Molecular dynamics simulations based on adaptive QM/MM methods feature on-the-fly reclassifications of atoms and molecular groups as either QM or MM without causing abrupt changes in the trajectory propagations, thus allowing QM subsystems to automatically change over time. Such treatments are not possible in the framework of conventional QM/MM, where the QM and MM partitions are predetermined and immutable throughout the simulation. The present contribution reviews the recent progress in the adaptive QM/MM algorithms developed by ourselves and our collaborators, namely the family of adaptive-partitioning (AP) schemes. Initially developed for the studies of solvated ions and molecules, AP methods have been extended to model large molecules, such as biopolymers, to monitor the exchange of solvent molecules between a protein active site and the bulk solvent, and to describe proton hopping in water via the Grotthuss mechanism.

The classical modeling of proton transfer reactions in chemical simulations requires the application of reactive force field formulations. A common feature of these dissociative potential models of aqueous systems is the possibility to transfer protons between water, oxonium and hydroxide ions. Since molecules undergo a change of their composition as the simulation progresses, the respective topology defining which atoms form a molecular unit at a given configuration becomes time-dependent. Knowledge of this variable topology is a key prerequisite to apply dissociative models in the framework of hybrid quantum mechanical/molecular mechanical (QM/MM) simulation studies. In order to effectively execute QM/MM simulations, the simulation software has to be able to independently monitor all occurring bond formation and cleavage events and automatically adjust the respective topology information, thereby discriminating between short-time fluctuations and sustained proton transfer events. The properties of a simple yet effective automated topology update criterion developed for excess protons are presented and its performance for hydroxide containing solutions and systems containing excess protons is compared. Furthermore, the influence of deuteration of the different systems is discussed. The data clearly demonstrates that it is possible to apply a global setting for the automated topology update of both proton and proton-hole migration.

It is well known that solvents can modify the frequency and intensity of the solute spectral bands, the thermodynamics and kinetics of chemical reactions, the strength of molecular interactions or the fate of solute excited states. The theoretical study of solvent effects is quite complicated since the presence of the solvent introduces additional difficulties with respect to the study of analogous problems in gas phase. The mean field approximation (MFA) is used for many of the most employed solvent effect theories as it permits to reduce the computational cost associated to the study of processes in solution. In this chapter we revise the performance of ASEP/MD, a quantum mechanics/molecular mechanics method developed in our laboratory that makes use of this approximation. It permits to combine state of the art calculations of the solute electron distribution with a detailed, microscopic, description of the solvent. As examples of application of the method we study solvent effects on the absorption spectra of some molecules involved in photoisomerization processes of biological systems.

In this contributed article we review our method, referred to as QM/MM-ER, which combines the hybrid QM/MM simulation with the theory of energy representation. Our recent developments and applications related to the method are also introduced. First, we describe the parallel implementation of the Kohn-Sham DFT for the QM region that utilizes the real-space grids to represent the one-electron wave functions. Then, the efficiency of our code on a modern parallel machine is demonstrated for a large water cluster with an ice structure. Secondly, the theory of energy representation (ER) is formulated within the framework of the density functional theory of solutions and its application to the free energy analyses of the protein hydration is provided. Thirdly, we discuss the coupling of the QM/MM approach with the method of energy representation, where the formulation for free energy δμ due to the electron density fluctuation of a QM solute plays a key role. As a recent progress in QM/MM-ER we developed a rigorous free energy functional to compute free energy contribution δμ. The outline of the method as well as its extension to the QM/MM simulation coupled with a second-order perturbation approach are described.

A discussion on the structure, dynamics and electronic properties of liquids and complex molecular systems in solution is presented. Special emphasis is placed on the sequential coupling of electronic structure calculations to Monte Carlo and Molecular dynamics sampling procedures. A promising approach to investigate the electronic absorption spectra of liquids and molecular solutions relying on a many-body energy decomposition scheme is presented and some applications to hydrogen bonding liquids are discussed. The possibility to parametrize classical force fields by using information generated by first principles molecular dynamics is investigated and preliminary results for the structure of chlorophyll-c₂ in liquid methanol relying on this approach are reported.

To obtain stable states (SS) and transition states (TS) of chemical reaction system in condensed state at a finite temperature, the free energy gradient (FEG) method was proposed in 1998 as an optimization method on a multidimensional free energy surface (FES). This is analogous to the method for the Born Oppenheimer potential energy surface (PES) considered by ab initio molecular orbital (MO) calculation, and utilizes the force and Hessian on the FES with respect to the coordinates of a solute molecule, which can be adiabatically calculated by molecular dynamics (MD) method. In this chapter, we reviewed the FEG methodology that is the method for estimating molecular properties based on the free energy (FE) landscape in condensed state and also discussed a future perspective for the improvement and the extension of the theoretical methods. We believe that a family of the FEG methodologies should become more efficient as one promising strategic setting and will play important roles to survey condensed state chemistry on the basis of recent supercomputing technology.

The overwhelming progress and constant evolution of computational and theoretical methods in chemistry have provided us a more detailed molecular description of some complex molecular properties. Our group has intended to do so for an old problem: the solvatochromic properties of halogens in aqueous systems. There are beautiful experiments that show how sensitive Br₂ and Cl₂ are to the structure of the environment around them. In this chapter, we present the tests and calculations performed with different theoretical methods to identify their reliability as pieces of a multi-scale study aimed to address open questions related with this phenomenon. We used different approaches to explicitly take into account the solvent effect and tested several theoretical methods on the solvatochromic effect of small clusters. The combination of a semiempirical Born-Oppenheimer molecular dynamics study (SEBOMD) of Br₂ in liquid water solution using PM3-PIF and then, the evaluation of the effect the closest water molecules have on the shifts are presented. This is a first step towards a robust multi-scale protocol ad hoc designed for these systems.

We present the main results of a comprehensive research program related to the identification of the solvation patterns of abundant toxic Hg-containing species in aqueous media. Two different solvation models have been used. A systematic study of stepwise hydration using cluster models at the Density Functional Theory level with the B3PW91 exchange-correlation functional. We address solvation free energies, optimized geometries, vibrational frequencies and Hg-coordination patterns for the Hg(II)XY–(H₂O)_n (X,Y = Cl,OH; n ≤ 24) complexes. One to three direct Hg-water interactions appear along the hydration process. A stable pentacoordinated Hg trigonal bipyramid structures arises from n = 15. The first solvation shell is fully formed with 22 and 24 water molecules for HgClOH and Hg(OH)₂ species respectively. The thermal stability and the persistence of the trigonal bipyramid coordination around Hg of fully solvated structures Hg(II)XY-(H₂O)_n (X,Y = Cl,OH; n = 24) has been verified using Born-Oppenheimer molecular dynamics simulations at the B3PW91/6-311G** level.

We review recent studies carried out in our group on the modeling of aqueous interfaces using Molecular Dynamics simulations with a combined Quantum Mechanics and Molecular Mechanics force-field (QM/MM). We first present the methodology and we comment on some ongoing developments. Since in the QM/MM approach the adsorbed molecule is described quantum mechanically, this computational scheme has allowed us to get insights on interface solvation effects on molecular properties. In particular, we have shown that polarization phenomena at the air–water interface may produce larger effects than polarization in bulk water. This finding contrasts with the usual assumption that polarity at liquid interfaces is close to the arithmetic average of the polarity of the two bulk phases, and that solvation effects at the air–water interface should be similar to the effects in a low polar solvent such as butyl ether. A summary of previous results is presented with some selected examples that are briefly discussed, and which include systems of atmospheric interest at the air–water interface, as well as systems of biological relevance at a water-organic interface. Then, we report some new results for a series of small volatile organic compounds at the air–water interface, namely methyl chloride, acetonitrile and methanol. These molecules share a similar structure but display quite different behaviors at the interface; the discussion focuses on the orientational dynamics and the solvation effects on reactivity indices. Finally, some conclusions and future directions in this exciting field are presented.

Multiscale QM/MM approaches are nowadays a well-established computational tool to study properties and processes of supramolecular systems. In this chapter, an overview of the extension of these methods to photoinduced processes in biological systems will be presented and discussed. The attention will be focused on the strategies which can be used to properly describe the static and dynamic effects that the environment exerts on the electronic states involved in the processes. Specific problems related to the modeling of stationary properties and correlations, as well as reactive events will be analyzed and the computational tools developed so far within the QM/MM framework to solve them will be described.

The present chapter starts with an analysis of the problems encountered when applying a mixed Quantum Mechanics/Molecular Mechanics to a large molecular system, which cannot be approached at a full quantum level of computation and a review of the possible solutions. A Non Empirical Local Self Consistent Field methodology, allowing computing at any quantum chemical level a part of a very large molecule interacting with the rest of this molecule is described in some detail. This approach is illustrated by various applications to the spectroscopic properties of various bio-macromolecules. Finally, and as a test case we will focus on the QM/MM modelling of spectroscopic and photophysical properties of exogenous chromophores interacting with DNA. Hence, we will show how the combination of high-level QM/MM methods with Molecular Dynamics simulations allows us to gain unprecedented insights in the process of DNA Photosensitization that is of paramount importance to understand the induction of DNA photolesions and to unravel novel anticancer therapeutic strategies.

Dehalopeoxidase A (DHP A) is a detoxifying enzyme found in the marine worm Amphitrite ornata. This enzyme converts halophenols found in the environment where the worm lives, into quinones by dehalogenation. The enzyme has globin structure and function, but works also as a peroxidase in the presence of H₂O₂ which binds to the iron present in the heme group. The initial step in the enzymatic reaction path is the transformation of the heme Fe(III) ion into a ferryl (Fe = O) moiety. A distal histidine, His55, is crucial for this process. His55 can occupy two positions, either in the distal pocket of the active center (“closed”), or exposed to the solvent (“open”). NMR experiments show that His55 moves between those positions in the resting state of the enzyme. For this process to occur it is necessary that a gate, composed of a triad Asn37-Lys36-Lys51 and two carboxylates on the heme group, suffer a conformational change before and after the passage of the histidine. We examined computationally this process at the B3LYP/6-31G(d,p) level, within a PCM simulated aqueous environment. This analysis leads us to propose a correction of the experimental structure of the enzyme determined by X-ray crystallography and offers an explanation for different conformations of the twin carboxylates at the heme group observed in the crystals. This new proposal agrees with the experimentally determined electron density distributions and explains the role of the His55 as a functional hook for the peroxide in the aqueous media.

Enzymes are the catalysts used by living organisms to accelerate chemical processes under physiological conditions. In this chapter, we illustrate the current view about the origin of their extraordinary rate enhancement based on molecular simulations and, in particular, on methods based on the combination of Quantum Mechanics and Molecular Mechanics potentials which provide a solution to treat the chemical reactivity of these large and complex molecular systems. Computational studies on Dihydrofolate Reductase have been selected as a conductor wire to present the evolution and difficulties to model chemical reactivity in enzymes. The results discussed here show that experimental observations can be currently understood within the framework of Transition State Theory provided that the adequate simulations are carried out. Protein dynamics, quantum tunnelling effects and conformational diversity are essential ingredients to explain the complex behaviour of these amazing molecular machineries.

This chapter presents multi-scale models of the reactions that occur in the in situ oil sands upgrading process. Its focus is on the various modelling tools and their applications to the benzene hydrogenation reactions catalyzed by molybdenum carbide nanoparticles. As the reaction mechanism of benzene hydrogenation on molybdenum carbide is not clear, we start with density functional theory (DFT) studies to elucidate the reaction mechanism, using both periodic and cluster models. Benzene hydrogenation on molybdenum carbide follows the Langmuir-Hinshelwood mechanism, with the six-member ring tilting up gradually. A tight-binding quantum chemical molecular dynamics (TB-QCMD) method is used to track the physical motion of the atoms in the reaction processes of C₆H₆ on a Mo-terminated α-Mo₂C (0001) surface. The approximate DFT method, density functional tight-binding (DFTB), was parameterized to allow the quantum mechanical treatment of nanoscale systems. With the nudged elastic band method, the potential energy profiles of benzene hydrogenation on molybdenum carbide nanoparticles have been obtained. Finally a force field was brought in to describe the solvent environment in the system, leading to a multiscale quantum mechanical/molecular mechanical (QM/MM) model. This study suggests that entropy and the environment play important roles in heterogeneous reactions catalyzed by molybdenum carbide nanoparticles.

In this contribution, some issues related to the interpretation, simulation and modelling of solvent effects on the absorption and emission spectra of organic dyes are presented and discussed. First, a brief analysis of the physical basis of solvent effects on the electronic transitions is reported, in order to introduce the most important phenomena and quantities tuning the so-called solvatochromic shifts. This is followed by a general discussion of the most common models employed for the interpretation, simulation and prediction of such effects. A general and effective multilayer scheme is analyzed in some detail, which has been developed in the past years and is known to provide—in most cases—quantitative predictions of the spectral features of solvated molecules. Afterwards, starting from this general model, some approximations are introduced, leading to simplified and cost effective analytical schemes. In order to sketch a more complete perspective of the models still used by spectroscopists, phenomenological methods are critically discussed. Finally, broadening of spectral lines by both symmetric (solvent relaxation) and possibly asymmetric (vibronic) contributions is shortly analysed. In all cases, the theoretical bases of the methods, as well as practical applications and test cases are given, in order to clarify the most interesting aspects of all the discussed models.