GeneralIntroduction

QM Modeling of Soft Matter

Unlike mechanical engineering with its foremost example of entirely computer-based design of aircraft Boeing-777, simulation in Chemistry and Biology will unlikely be able to substitute experiments in near future. In the face of Chemistry and Biology, Nature found a more efficient device to produce new materials. Nevertheless, simulation in Chemistry and Biology is immensely important because it provides atomic-level details not available from experimental studies. Simulations help understanding experimental data, and through that assist in designing new experiments and materials.

The advent of Force Fields brought an immense progress in linking molecular theory with chemical and biological experiments. Central is the discovery that biological processes are driven by free energy changes and that the role of dispersion interactions increases with the size of the system. Increasing accuracy and reliability of binding free energy computations, ligand scoring, accounting for bond breaking and formation, simulating interaction of light with matter, among others require incorporating greater level of physics into the simulation theory which is naturally offered by quantum mechanical (QM) methods. However, the problem of high-level QM methods being extremely computationally expensive and lower-level QM methods being insufficiently accurate makes challenging simultaneously reaching high speed and accuracy.

Since in material simulation performance determines the utility of the computational method, the success of force fields suggests the path of carefully chosen approximations. This leads to the rediscovery of semiempirical quantum mechanical methods. Though, even at this level the computational performance is insufficient for simulation of soft matter. Gaining necessary performance requires introducing additional approximations. Variational Finite LMO (VFL) approximation extends the Roothaan-Hall method to very large systems by applying constrained expansion to molecular orbitals.

Additional performance gain is obtained by treating different parts of the system with different expansion criteria and correspondingly with the different accuracy as dictated by the need. Such multi-layer QM/QM approach naturally expands the idea of QM/MM. The problem of using too small QM region in QM/MM methods which distorts the electronic structure of the active site is resolved in semiempirical QM/QM where choosing large reactive center is computationally tractable. Treating all layers at the same level of theory also solves the boundary problem. Immediate advantage follows for high-throughput protein-ligand docking where large part of the protein bulk can be treated with frozen density matrix and only the linear coefficients of the active site need to be variationally determined.

Expanding the range of applications is treating transition metals in proteins, which has been a traditionally difficult problem. It is naturally solved via the multilayer approach where the reactive center is represented by a delocalized density matrix whereas the bulk is treated approximately using the VFL approximation thus significantly reducing the computational cost. This technique also makes feasible treatment of local electronic excitations in condensed phase. Further on, simulation of materials requires accounting for long-range dispersion forces and entropic factors. This requires the use of large unit cells and performing extensive sampling of configuration space.

Treating nuclear motion at classical mechanics level in semiempirical QM MD makes feasible the application of QM methods to condensed phase on comparable footing to MM methods. Treating electronic degrees of freedom by using extended Lagrangian formalism additionally improves computational performance. A nanosecond simulation of a water droplet treating water as a fully flexible molecule shows excellent stability and practical utility of QM MD. QM MD of protein in water reveals intermolecular charge transfer effects governing protein structure and dynamics which are not accounted at force field level.

Unlike intramolecular charge transfer the intermolecular charge redistribution is a quantum phenomenon which limits the applicability of mean field approximation representing a theoretical foundation of classical force fields. The intermolecular charge transfer is readily encountered in salt bridges and ion pairs. Due to the abundance of ionized species in Nature, charge transfer may be a predominant way of polarization of large and highly ionized biomolecular systems.

QM MD is a necessary approach to account for influence of media on thermal relaxation of the photo-excited electronic state and its transition to the ground state. Since excited and transition states are highly delocalized, traditional QM/MM treatment of these systems is insufficient due to severe truncation of the QM area. In addition to reactive center itself, the delocalization involves adjacent solvent molecules and nearby protein atoms which collectively define the electronic state of the reactive center and through that determine the thermal motion through which the system will relax.

The accuracy of semiempirical methods greatly improves upon adopting multiple atom type parameters. The parametrization technique targets reproducing physical properties of condensed phase. In conclusion, semiempirical QM methods represent a natural extension of classical force field methods to material simulation by offering a comparable computational performance and adding a greater level of physics into the system Hamiltonian, while still offering sufficient number of parameters that allow tuning the method to the same or better accuracy exhibited on a much wider range of applications.