Classical molecular mechanics force fields typically model interatomic electrostatic interactions with point charges or multipole expansions, which can fail for atoms in close contact due to the lack of a description of penetration effects between their electron clouds. These short-range penetration effects can be significant and are essential for accurate modeling of intermolecular interactions. In this work we report parametrization of an empirical charge–charge function previously reported (PiquemalJ.-P.26313624J. Phys. Chem. A200310353) to correct for the missing penetration term in standard molecular mechanics force fields. For this purpose, we have developed a database (S101×7) of 101 unique molecular dimers, each at 7 different intermolecular distances. Electrostatic, induction/polarization, repulsion, and dispersion energies, as well as the total interaction energy for each complex in the database are calculated using the SAPT2+ method (ParkerT. M.09410624606352J. Chem. Phys.2014140). This empirical penetration model significantly improves agreement between point multipole and quantum mechanical electrostatic energies across the set of dimers and distances, while using only a limited set of parameters for each chemical element. Given the simplicity and effectiveness of the model, we expect the electrostatic penetration correction will become a standard component of future molecular mechanics force fields.

The Non-Covalent Interaction (NCI) index is a new topological tool that has recently been added to the theoretical chemist's arsenal. NCI fills a gap that existed within topological methods for the visualization of non-covalent interactions. Based on the electron density and its derivatives, it is able to reveal both attractive and repulsive interactions in the shape of isosurfaces, whose color code reveals the nature of the interaction. It is interesting to note that NCI can even be calculated at the promolecular level, making it a suitable tool for big systems, such as proteins or DNA. Within this chapter we will review the main characteristics of NCI, its similarities with and differences from previous approaches. Special attention will be paid to the visualization of new interaction types. Being based on the electron density, NCI is not only very stable with respect to the calculation method, but it is also a suitable tool for detecting new bonding mechanisms, since all such mechanisms should have a detectable effect on the electron density. This type of approach overcomes the limitations of bond definition, revealing all interaction types, irrespective of whether they have a name or have previously been identified. Finally, we will show how this tool can be used to understand chemical change along a chemical reaction. We will show several examples of torquoselectivity and put forward an explanation of selectivity based on secondary interactions which is complementary to the historical orbital approach.A complete NCI perspective: from new bonds to reactivity 3

We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.

We propose a general coupling of the Smooth Particle Mesh Ewald (spme) approach for distributed multipoles to a short-range charge penetration correction modifying the charge-charge, charge-dipole and charge-quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry-Adapted Perturbation Theory (sapt) reference data. Various neutral molecular dimers have been tested as results on charged systems (metal cation complexes) are provided. Transferability of the correction is adressed in the context of the implementation of the amoeba and sibfa polarizable force fields in the Tinker-hp software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration-corrected polarizable force fields highlighting the mandatory need of non-spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally scalability and parallelism of the short-range corrected spme approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complexe bio- or bioinorganic systems in periodic boundary conditions.

Electron transfer in biological systems drives the processes of life. From cellular respiration to photosynthesis and enzymatic catalysis, electron transfers (ET) are chemical processes on which essential biological functions rely. Over the last 40 years, scientists have sought understanding of how these essential processes function in biology. One important breakthrough was the discovery that Marcus theory (MT) of electron transfer is applicable to biological systems. Chemists have experimentally collected both the reorganization energies (λ) and the driving forces (ΔG°), two parameters of Marcus theory, for a large variety of ET processes in proteins. At the same time, theoretical chemists have developed computational approaches that rely on molecular dynamics and quantum chemistry calculations to access numerical estimates of λ and ΔG°. Yet another crucial piece in determining the rate of an electron transfer is the electronic coupling between the initial and final electronic wave functions. This is an important prefactor in the nonadiabatic rate expression, since it reflects the probability that an electron tunnels from the electron donor to the acceptor through the intervening medium. The fact that a protein matrix supports electron tunneling much more efficiently than vacuum is now well documented, both experimentally and theoretically. Meanwhile, many chemists have provided examples of the rich physical chemistry that can be induced by protein dynamics. This Account describes our studies of the dynamical effects on electron tunneling. We present our analysis of two examples of natural biological systems through MD simulations and tunneling pathway analyses. Through these examples, we show that protein dynamics sustain efficient tunneling. Second, we introduce two time scales: τcoh and τFC. The former characterizes how fast the electronic coupling varies with nuclear vibrations (which cause dephasing). The latter reflects the time taken by the system to leave the crossing region. In the framework of open quantum systems, τFC is a short time approximation of the characteristic decoherence time of the electronic subsystem in interaction with its nuclear environment. The comparison of the respective values of τcoh and τFC allows us to probe the occurrence of non-Condon effects. We use ab initio MD simulations to analyze how decoherence appears in several biological cofactors. We conclude that we cannot account for its order of magnitude by considering only the atoms or bonds directly concerned with the transfer. Decoherence results from contributions from all atoms of the system appearing with a time delay that increases with the distance from the primarily concerned atoms or bonds. The delay and magnitude of the contributions depend on the chemical nature of the system. Finally, we present recent developments based on constrained DFT for efficient and accurate evaluations of the electronic coupling in ab initio MD simulations. These are promising methods to study the subtle fluctuations of the electronic coup...

We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT­(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT­(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.

Summary. 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.

Understanding solvation interactions is a key problem for many industrial fields: from pharmaceutical to material sciences. From a quantum mechanical viewpoint, two main difficulties arise: firstly, solvation takes place through weak interactions (hydrogen bonds, van der Waals interactions), which are inherently difficult to describe. Secondly, solvation properties are dynamic in nature, which means a proper statistical averaging is required to reproduce experimental properties. In this contribution, we dwell on the analysis of solutesolvent interactions by means of the averaged-NCI index, derived from an MD averaged picture of the electron density in the system. Firstly, we show how the approach enables to distinguish static vs labile and strong vs weak hydrogen bonds. Then, by means of this approach we are able to characterize the fact that the strength of hydrogen bonds with water solvent remains similar upon branching for aliphatic alcohols. On the contrary large differences have been observed between aliphatic alcohols and phenol derivatives. This statistical analysis of interactions is expected to be useful in the derivation of microscopic parameters for solute/solvent interactions.